TSTP Solution File: ITP234^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP234^1 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n028.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 03:23:09 EDT 2023
% Result : Theorem 99.06s 99.38s
% Output : Proof 99.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 1.85/1.88 % Problem : ITP234^1 : TPTP v8.1.2. Released v8.1.0.
% 1.85/1.89 % Command : do_cvc5 %s %d
% 1.88/2.10 % Computer : n028.cluster.edu
% 1.88/2.10 % Model : x86_64 x86_64
% 1.88/2.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 1.88/2.10 % Memory : 8042.1875MB
% 1.88/2.10 % OS : Linux 3.10.0-693.el7.x86_64
% 1.88/2.10 % CPULimit : 300
% 1.88/2.10 % WCLimit : 300
% 1.88/2.10 % DateTime : Sun Aug 27 10:49:55 EDT 2023
% 1.88/2.10 % CPUTime :
% 3.82/3.99 %----Proving TH0
% 3.82/4.00 %------------------------------------------------------------------------------
% 3.82/4.00 % File : ITP234^1 : TPTP v8.1.2. Released v8.1.0.
% 3.82/4.00 % Domain : Interactive Theorem Proving
% 3.82/4.00 % Problem : Sledgehammer problem VEBT_InsertCorrectness 00806_052000
% 3.82/4.00 % Version : [Des22] axioms.
% 3.82/4.00 % English :
% 3.82/4.00
% 3.82/4.00 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 3.82/4.00 % : [Des22] Desharnais (2022), Email to Geoff Sutcliffe
% 3.82/4.00 % Source : [Des22]
% 3.82/4.00 % Names : 0067_VEBT_InsertCorrectness_00806_052000 [Des22]
% 3.82/4.00
% 3.82/4.00 % Status : Theorem
% 3.82/4.00 % Rating : 0.23 v8.1.0
% 3.82/4.00 % Syntax : Number of formulae : 9032 (4087 unt; 882 typ; 0 def)
% 3.82/4.00 % Number of atoms : 24172 (9833 equ; 0 cnn)
% 3.82/4.00 % Maximal formula atoms : 71 ( 2 avg)
% 3.82/4.00 % Number of connectives : 92254 (2519 ~; 426 |;1757 &;77540 @)
% 3.82/4.00 % ( 0 <=>;10012 =>; 0 <=; 0 <~>)
% 3.82/4.00 % Maximal formula depth : 39 ( 6 avg)
% 3.82/4.00 % Number of types : 81 ( 80 usr)
% 3.82/4.00 % Number of type conns : 4235 (4235 >; 0 *; 0 +; 0 <<)
% 3.82/4.00 % Number of symbols : 805 ( 802 usr; 66 con; 0-5 aty)
% 3.82/4.00 % Number of variables : 22301 (2208 ^;19443 !; 650 ?;22301 :)
% 3.82/4.00 % SPC : TH0_THM_EQU_NAR
% 3.82/4.00
% 3.82/4.00 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 3.82/4.00 % from the van Emde Boas Trees session in the Archive of Formal
% 3.82/4.00 % proofs -
% 3.82/4.00 % www.isa-afp.org/browser_info/current/AFP/Van_Emde_Boas_Trees
% 3.82/4.00 % 2022-02-17 21:34:31.088
% 3.82/4.00 %------------------------------------------------------------------------------
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% 3.82/4.00 listre4828114922151135584at_nat: set_Pr8693737435421807431at_nat > set_Pr1542805901266377927at_nat ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_List_Olistrel1_001t__VEBT____Definitions__OVEBT,type,
% 3.82/4.00 listrel1_VEBT_VEBT: set_Pr6192946355708809607T_VEBT > set_Pr1916528119006554503T_VEBT ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_List_Olistrel1p_001t__Int__Oint,type,
% 3.82/4.00 listrel1p_int: ( int > int > $o ) > list_int > list_int > $o ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_List_Olistrel1p_001t__Nat__Onat,type,
% 3.82/4.00 listrel1p_nat: ( nat > nat > $o ) > list_nat > list_nat > $o ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_List_Onth_001t__Extended____Nat__Oenat,type,
% 3.82/4.00 nth_Extended_enat: list_Extended_enat > nat > extended_enat ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_List_Onth_001t__Int__Oint,type,
% 3.82/4.00 nth_int: list_int > nat > int ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_List_Onth_001t__Nat__Onat,type,
% 3.82/4.00 nth_nat: list_nat > nat > nat ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_List_Onth_001t__Num__Onum,type,
% 3.82/4.00 nth_num: list_num > nat > num ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 3.82/4.00 nth_Pr4439495888332055232nt_int: list_P5707943133018811711nt_int > nat > product_prod_int_int ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J,type,
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% 3.82/4.00
% 3.82/4.00 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Int__Oint_Mt__VEBT____Definitions__OVEBT_J,type,
% 3.82/4.00 nth_Pr3474266648193625910T_VEBT: list_P7524865323317820941T_VEBT > nat > produc1531783533982839933T_VEBT ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J,type,
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% 3.82/4.00
% 3.82/4.00 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
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% 3.82/4.00
% 3.82/4.00 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__VEBT____Definitions__OVEBT_J,type,
% 3.82/4.00 nth_Pr744662078594809490T_VEBT: list_P5647936690300460905T_VEBT > nat > produc8025551001238799321T_VEBT ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 3.82/4.00 nth_Pr6744343527793145070at_nat: list_P8469869581646625389at_nat > nat > produc859450856879609959at_nat ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J,type,
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% 3.82/4.00
% 3.82/4.00 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
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% 3.82/4.00
% 3.82/4.00 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J,type,
% 3.82/4.00 nth_Pr4953567300277697838T_VEBT: list_P7413028617227757229T_VEBT > nat > produc8243902056947475879T_VEBT ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_List_Onth_001t__Real__Oreal,type,
% 3.82/4.00 nth_real: list_real > nat > real ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_List_Onth_001t__Set__Oset_It__Nat__Onat_J,type,
% 3.82/4.00 nth_set_nat: list_set_nat > nat > set_nat ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_List_Onth_001t__VEBT____Definitions__OVEBT,type,
% 3.82/4.00 nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_List_Oproduct_001t__Int__Oint_001t__Int__Oint,type,
% 3.82/4.00 product_int_int: list_int > list_int > list_P5707943133018811711nt_int ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_List_Oproduct_001t__Int__Oint_001t__Nat__Onat,type,
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% 3.82/4.00
% 3.82/4.00 thf(sy_c_List_Oproduct_001t__Int__Oint_001t__VEBT____Definitions__OVEBT,type,
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% 3.82/4.00
% 3.82/4.00 thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__Int__Oint,type,
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% 3.82/4.00
% 3.82/4.00 thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__Nat__Onat,type,
% 3.82/4.00 product_nat_nat: list_nat > list_nat > list_P6011104703257516679at_nat ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
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% 3.82/4.00
% 3.82/4.00 thf(sy_c_List_Oproduct_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 3.82/4.00 produc3544356994491977349at_nat: list_P6011104703257516679at_nat > list_P6011104703257516679at_nat > list_P8469869581646625389at_nat ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 3.82/4.00 produc7292646706713671643BT_int: list_VEBT_VEBT > list_int > list_P4547456442757143711BT_int ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 3.82/4.00 produc7295137177222721919BT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
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% 3.82/4.00
% 3.82/4.00 thf(sy_c_List_Oremdups_001t__Nat__Onat,type,
% 3.82/4.00 remdups_nat: list_nat > list_nat ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_List_Oreplicate_001t__Extended____Nat__Oenat,type,
% 3.82/4.00 replic7216382294607269926d_enat: nat > extended_enat > list_Extended_enat ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_List_Oreplicate_001t__Int__Oint,type,
% 3.82/4.00 replicate_int: nat > int > list_int ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_List_Oreplicate_001t__Nat__Onat,type,
% 3.82/4.00 replicate_nat: nat > nat > list_nat ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_List_Oreplicate_001t__Real__Oreal,type,
% 3.82/4.00 replicate_real: nat > real > list_real ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_List_Oreplicate_001t__Set__Oset_It__Nat__Onat_J,type,
% 3.82/4.00 replicate_set_nat: nat > set_nat > list_set_nat ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_List_Oreplicate_001t__VEBT____Definitions__OVEBT,type,
% 3.82/4.00 replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_List_Osorted__wrt_001t__Int__Oint,type,
% 3.82/4.00 sorted_wrt_int: ( int > int > $o ) > list_int > $o ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_List_Osorted__wrt_001t__Nat__Onat,type,
% 3.82/4.00 sorted_wrt_nat: ( nat > nat > $o ) > list_nat > $o ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_List_Otake_001t__Nat__Onat,type,
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% 3.82/4.00
% 3.82/4.00 thf(sy_c_List_Oupt,type,
% 3.82/4.00 upt: nat > nat > list_nat ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_List_Oupto,type,
% 3.82/4.00 upto: int > int > list_int ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_List_Oupto__aux,type,
% 3.82/4.00 upto_aux: int > int > list_int > list_int ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_List_Oupto__rel,type,
% 3.82/4.00 upto_rel: product_prod_int_int > product_prod_int_int > $o ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_Nat_OSuc,type,
% 3.82/4.00 suc: nat > nat ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_Nat_Ocompow_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 3.82/4.00 compow_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_Nat_Onat_Ocase__nat_001_Eo,type,
% 3.82/4.00 case_nat_o: $o > ( nat > $o ) > nat > $o ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_Nat_Onat_Ocase__nat_001t__Nat__Onat,type,
% 3.82/4.00 case_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_Nat_Onat_Opred,type,
% 3.82/4.00 pred: nat > nat ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_Nat_Osemiring__1__class_ONats_001t__Int__Oint,type,
% 3.82/4.00 semiring_1_Nats_int: set_int ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Complex__Ocomplex,type,
% 3.82/4.00 semiri8010041392384452111omplex: nat > complex ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Extended____Nat__Oenat,type,
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% 3.82/4.00
% 3.82/4.00 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
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% 3.82/4.00
% 3.82/4.00 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
% 3.82/4.00 semiri1316708129612266289at_nat: nat > nat ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Real__Oreal,type,
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% 3.82/4.00
% 3.82/4.00 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Complex__Ocomplex,type,
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% 3.82/4.00
% 3.82/4.00 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Extended____Nat__Oenat,type,
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% 3.82/4.00
% 3.82/4.00 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Int__Oint,type,
% 3.82/4.00 semiri8420488043553186161ux_int: ( int > int ) > nat > int > int ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Nat__Onat,type,
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% 3.82/4.00
% 3.82/4.00 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Real__Oreal,type,
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% 3.82/4.00
% 3.82/4.00 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Complex__Ocomplex_J,type,
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% 3.82/4.00
% 3.82/4.00 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Extended____Nat__Oenat_J,type,
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% 3.82/4.00
% 3.82/4.00 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Int__Oint_J,type,
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% 3.82/4.00
% 3.82/4.00 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Nat__Onat_J,type,
% 3.82/4.00 size_size_list_nat: list_nat > nat ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Num__Onum_J,type,
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% 3.82/4.00
% 3.82/4.00 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
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% 3.82/4.00
% 3.82/4.00 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J_J,type,
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% 3.82/4.00 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Int__Oint_Mt__VEBT____Definitions__OVEBT_J_J,type,
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% 3.82/4.00 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
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% 3.82/4.00
% 3.82/4.00 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__VEBT____Definitions__OVEBT_J_J,type,
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% 3.82/4.00 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Real__Oreal_J,type,
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% 3.82/4.00
% 3.82/4.00 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Set__Oset_It__Nat__Onat_J_J,type,
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% 3.82/4.00 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
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% 3.82/4.00 thf(sy_c_Nat_Osize__class_Osize_001t__Num__Onum,type,
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% 3.82/4.00
% 3.82/4.00 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Num__Onum_J,type,
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% 3.82/4.00 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
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% 3.82/4.00 thf(sy_c_Nat__Bijection_Olist__decode,type,
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% 3.82/4.00
% 3.82/4.00 thf(sy_c_Nat__Bijection_Olist__decode__rel,type,
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% 3.82/4.00 thf(sy_c_Nat__Bijection_Olist__encode,type,
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% 3.82/4.00
% 3.82/4.00 thf(sy_c_Nat__Bijection_Olist__encode__rel,type,
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% 3.82/4.00
% 3.82/4.00 thf(sy_c_Nat__Bijection_Oprod__decode,type,
% 3.82/4.00 nat_prod_decode: nat > product_prod_nat_nat ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_Nat__Bijection_Oprod__decode__aux,type,
% 3.82/4.00 nat_prod_decode_aux: nat > nat > product_prod_nat_nat ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_Nat__Bijection_Oprod__decode__aux__rel,type,
% 3.82/4.00 nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_Nat__Bijection_Oprod__encode,type,
% 3.82/4.00 nat_prod_encode: product_prod_nat_nat > nat ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_Nat__Bijection_Oset__decode,type,
% 3.82/4.00 nat_set_decode: nat > set_nat ).
% 3.82/4.00
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% 3.82/4.00 sin_coeff: nat > real ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_Transcendental_Otan_001t__Complex__Ocomplex,type,
% 3.82/4.00 tan_complex: complex > complex ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_Transcendental_Otan_001t__Real__Oreal,type,
% 3.82/4.00 tan_real: real > real ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_Transfer_Obi__total_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 3.82/4.00 bi_tot896582865486249351at_int: ( product_prod_nat_nat > int > $o ) > $o ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_Transitive__Closure_Ortrancl_001t__Nat__Onat,type,
% 3.82/4.00 transi2905341329935302413cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_Transitive__Closure_Otrancl_001t__Nat__Onat,type,
% 3.82/4.00 transi6264000038957366511cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_VEBT__Definitions_OVEBT_OLeaf,type,
% 3.82/4.00 vEBT_Leaf: $o > $o > vEBT_VEBT ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_VEBT__Definitions_OVEBT_ONode,type,
% 3.82/4.00 vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_VEBT__Definitions_OVEBT_Osize__VEBT,type,
% 3.82/4.00 vEBT_size_VEBT: vEBT_VEBT > nat ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oboth__member__options,type,
% 3.82/4.00 vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oelim__dead,type,
% 3.82/4.00 vEBT_VEBT_elim_dead: vEBT_VEBT > extended_enat > vEBT_VEBT ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ohigh,type,
% 3.82/4.00 vEBT_VEBT_high: nat > nat > nat ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oin__children,type,
% 3.82/4.00 vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > nat > $o ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_VEBT__Definitions_OVEBT__internal_Olow,type,
% 3.82/4.00 vEBT_VEBT_low: nat > nat > nat ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima,type,
% 3.82/4.00 vEBT_VEBT_membermima: vEBT_VEBT > nat > $o ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima__rel,type,
% 3.82/4.00 vEBT_V4351362008482014158ma_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member,type,
% 3.82/4.00 vEBT_V5719532721284313246member: vEBT_VEBT > nat > $o ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member__rel,type,
% 3.82/4.00 vEBT_V5765760719290551771er_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H,type,
% 3.82/4.00 vEBT_VEBT_valid: vEBT_VEBT > nat > $o ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H__rel,type,
% 3.82/4.00 vEBT_VEBT_valid_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_VEBT__Definitions_Oinvar__vebt,type,
% 3.82/4.00 vEBT_invar_vebt: vEBT_VEBT > nat > $o ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_VEBT__Definitions_Oset__vebt,type,
% 3.82/4.00 vEBT_set_vebt: vEBT_VEBT > set_nat ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_VEBT__Definitions_Ovebt__buildup,type,
% 3.82/4.00 vEBT_vebt_buildup: nat > vEBT_VEBT ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_VEBT__Definitions_Ovebt__buildup__rel,type,
% 3.82/4.00 vEBT_v4011308405150292612up_rel: nat > nat > $o ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_VEBT__Insert_Ovebt__insert,type,
% 3.82/4.00 vEBT_vebt_insert: vEBT_VEBT > nat > vEBT_VEBT ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_VEBT__Insert_Ovebt__insert__rel,type,
% 3.82/4.00 vEBT_vebt_insert_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_VEBT__Member_OVEBT__internal_Obit__concat,type,
% 3.82/4.00 vEBT_VEBT_bit_concat: nat > nat > nat > nat ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_VEBT__Member_OVEBT__internal_OminNull,type,
% 3.82/4.00 vEBT_VEBT_minNull: vEBT_VEBT > $o ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_VEBT__Member_OVEBT__internal_Oset__vebt_H,type,
% 3.82/4.00 vEBT_VEBT_set_vebt: vEBT_VEBT > set_nat ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_VEBT__Member_Ovebt__member,type,
% 3.82/4.00 vEBT_vebt_member: vEBT_VEBT > nat > $o ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_VEBT__Member_Ovebt__member__rel,type,
% 3.82/4.00 vEBT_vebt_member_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_Wellfounded_Oaccp_001t__List__Olist_It__Nat__Onat_J,type,
% 3.82/4.00 accp_list_nat: ( list_nat > list_nat > $o ) > list_nat > $o ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_Wellfounded_Oaccp_001t__Nat__Onat,type,
% 3.82/4.00 accp_nat: ( nat > nat > $o ) > nat > $o ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 3.82/4.00 accp_P1096762738010456898nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > product_prod_int_int > $o ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 3.82/4.00 accp_P4275260045618599050at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 3.82/4.00 accp_P2887432264394892906BT_nat: ( produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ) > produc9072475918466114483BT_nat > $o ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_Wellfounded_Oless__than,type,
% 3.82/4.00 less_than: set_Pr1261947904930325089at_nat ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_Wellfounded_Opred__nat,type,
% 3.82/4.00 pred_nat: set_Pr1261947904930325089at_nat ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_Wellfounded_Owf_001t__Int__Oint,type,
% 3.82/4.00 wf_int: set_Pr958786334691620121nt_int > $o ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_Wellfounded_Owf_001t__Nat__Onat,type,
% 3.82/4.00 wf_nat: set_Pr1261947904930325089at_nat > $o ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_member_001t__Complex__Ocomplex,type,
% 3.82/4.00 member_complex: complex > set_complex > $o ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_member_001t__Extended____Nat__Oenat,type,
% 3.82/4.00 member_Extended_enat: extended_enat > set_Extended_enat > $o ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_member_001t__Int__Oint,type,
% 3.82/4.00 member_int: int > set_int > $o ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_member_001t__List__Olist_It__Int__Oint_J,type,
% 3.82/4.00 member_list_int: list_int > set_list_int > $o ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_member_001t__List__Olist_It__Nat__Onat_J,type,
% 3.82/4.00 member_list_nat: list_nat > set_list_nat > $o ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_member_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 3.82/4.00 member2936631157270082147T_VEBT: list_VEBT_VEBT > set_list_VEBT_VEBT > $o ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_member_001t__Nat__Onat,type,
% 3.82/4.00 member_nat: nat > set_nat > $o ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_member_001t__Num__Onum,type,
% 3.82/4.00 member_num: num > set_num > $o ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_member_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 3.82/4.00 member5262025264175285858nt_int: product_prod_int_int > set_Pr958786334691620121nt_int > $o ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Int__Oint_J_Mt__List__Olist_It__Int__Oint_J_J,type,
% 3.82/4.00 member6698963635872716290st_int: produc1186641810826059865st_int > set_Pr765067013931698361st_int > $o ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__List__Olist_It__Nat__Onat_J_J,type,
% 3.82/4.00 member7340969449405702474st_nat: produc1828647624359046049st_nat > set_Pr3451248702717554689st_nat > $o ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 3.82/4.00 member6693912407220327184at_nat: produc6392793444374437607at_nat > set_Pr1542805901266377927at_nat > $o ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__VEBT____Definitions__OVEBT_J_Mt__List__Olist_It__VEBT____Definitions__OVEBT_J_J,type,
% 3.82/4.00 member4439316823752958928T_VEBT: produc9211091688327510695T_VEBT > set_Pr1916528119006554503T_VEBT > $o ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 3.82/4.00 member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 3.82/4.00 member8206827879206165904at_nat: produc859450856879609959at_nat > set_Pr8693737435421807431at_nat > $o ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_member_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 3.82/4.00 member373505688050248522BT_nat: produc9072475918466114483BT_nat > set_Pr7556676689462069481BT_nat > $o ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_member_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J,type,
% 3.82/4.00 member568628332442017744T_VEBT: produc8243902056947475879T_VEBT > set_Pr6192946355708809607T_VEBT > $o ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_member_001t__Real__Oreal,type,
% 3.82/4.00 member_real: real > set_real > $o ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_member_001t__Set__Oset_It__Int__Oint_J,type,
% 3.82/4.00 member_set_int: set_int > set_set_int > $o ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_member_001t__Set__Oset_It__Nat__Onat_J,type,
% 3.82/4.00 member_set_nat: set_nat > set_set_nat > $o ).
% 3.82/4.00
% 3.82/4.00 thf(sy_c_member_001t__VEBT____Definitions__OVEBT,type,
% 3.82/4.00 member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).
% 3.82/4.00
% 3.82/4.00 thf(sy_v_deg____,type,
% 3.82/4.00 deg: nat ).
% 3.82/4.00
% 3.82/4.00 thf(sy_v_i____,type,
% 3.82/4.00 i: nat ).
% 3.82/4.00
% 3.82/4.00 thf(sy_v_m____,type,
% 3.82/4.00 m: nat ).
% 3.82/4.00
% 3.82/4.00 thf(sy_v_ma____,type,
% 3.82/4.00 ma: nat ).
% 3.82/4.00
% 3.82/4.00 thf(sy_v_mi____,type,
% 3.82/4.00 mi: nat ).
% 3.82/4.00
% 3.82/4.00 thf(sy_v_na____,type,
% 3.82/4.00 na: nat ).
% 3.82/4.00
% 3.82/4.00 thf(sy_v_summary____,type,
% 3.82/4.00 summary: vEBT_VEBT ).
% 3.82/4.00
% 3.82/4.00 thf(sy_v_treeList____,type,
% 3.82/4.00 treeList: list_VEBT_VEBT ).
% 3.82/4.00
% 3.82/4.00 thf(sy_v_xa____,type,
% 3.82/4.00 xa: nat ).
% 3.82/4.00
% 3.82/4.00 % Relevant facts (8120)
% 3.82/4.00 thf(fact_0_True,axiom,
% 3.82/4.00 ( i
% 3.82/4.00 = ( vEBT_VEBT_high @ mi @ na ) ) ).
% 3.82/4.00
% 3.82/4.00 % True
% 3.82/4.00 thf(fact_1_insprop,axiom,
% 3.82/4.00 ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) @ ( vEBT_VEBT_low @ mi @ na ) ) ) @ ( vEBT_VEBT_high @ mi @ na ) )
% 3.82/4.00 = ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) @ ( vEBT_VEBT_low @ mi @ na ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % insprop
% 3.82/4.00 thf(fact_2_bit__split__inv,axiom,
% 3.82/4.00 ! [X: nat,D: nat] :
% 3.82/4.00 ( ( vEBT_VEBT_bit_concat @ ( vEBT_VEBT_high @ X @ D ) @ ( vEBT_VEBT_low @ X @ D ) @ D )
% 3.82/4.00 = X ) ).
% 3.82/4.00
% 3.82/4.00 % bit_split_inv
% 3.82/4.00 thf(fact_3_tc,axiom,
% 3.82/4.00 vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) ).
% 3.82/4.00
% 3.82/4.00 % tc
% 3.82/4.00 thf(fact_4__C161_C,axiom,
% 3.82/4.00 ~ ? [X_1: nat] : ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) @ X_1 ) ).
% 3.82/4.00
% 3.82/4.00 % "161"
% 3.82/4.00 thf(fact_5_list__update__id,axiom,
% 3.82/4.00 ! [Xs: list_nat,I: nat] :
% 3.82/4.00 ( ( list_update_nat @ Xs @ I @ ( nth_nat @ Xs @ I ) )
% 3.82/4.00 = Xs ) ).
% 3.82/4.00
% 3.82/4.00 % list_update_id
% 3.82/4.00 thf(fact_6_list__update__id,axiom,
% 3.82/4.00 ! [Xs: list_int,I: nat] :
% 3.82/4.00 ( ( list_update_int @ Xs @ I @ ( nth_int @ Xs @ I ) )
% 3.82/4.00 = Xs ) ).
% 3.82/4.00
% 3.82/4.00 % list_update_id
% 3.82/4.00 thf(fact_7_list__update__id,axiom,
% 3.82/4.00 ! [Xs: list_VEBT_VEBT,I: nat] :
% 3.82/4.00 ( ( list_u1324408373059187874T_VEBT @ Xs @ I @ ( nth_VEBT_VEBT @ Xs @ I ) )
% 3.82/4.00 = Xs ) ).
% 3.82/4.00
% 3.82/4.00 % list_update_id
% 3.82/4.00 thf(fact_8_nth__list__update__neq,axiom,
% 3.82/4.00 ! [I: nat,J: nat,Xs: list_nat,X: nat] :
% 3.82/4.00 ( ( I != J )
% 3.82/4.00 => ( ( nth_nat @ ( list_update_nat @ Xs @ I @ X ) @ J )
% 3.82/4.00 = ( nth_nat @ Xs @ J ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % nth_list_update_neq
% 3.82/4.00 thf(fact_9_nth__list__update__neq,axiom,
% 3.82/4.00 ! [I: nat,J: nat,Xs: list_int,X: int] :
% 3.82/4.00 ( ( I != J )
% 3.82/4.00 => ( ( nth_int @ ( list_update_int @ Xs @ I @ X ) @ J )
% 3.82/4.00 = ( nth_int @ Xs @ J ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % nth_list_update_neq
% 3.82/4.00 thf(fact_10_nth__list__update__neq,axiom,
% 3.82/4.00 ! [I: nat,J: nat,Xs: list_VEBT_VEBT,X: vEBT_VEBT] :
% 3.82/4.00 ( ( I != J )
% 3.82/4.00 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ J )
% 3.82/4.00 = ( nth_VEBT_VEBT @ Xs @ J ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % nth_list_update_neq
% 3.82/4.00 thf(fact_11__C162_C,axiom,
% 3.82/4.00 ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) @ X_1 ) ).
% 3.82/4.00
% 3.82/4.00 % "162"
% 3.82/4.00 thf(fact_12_list__update__overwrite,axiom,
% 3.82/4.00 ! [Xs: list_int,I: nat,X: int,Y: int] :
% 3.82/4.00 ( ( list_update_int @ ( list_update_int @ Xs @ I @ X ) @ I @ Y )
% 3.82/4.00 = ( list_update_int @ Xs @ I @ Y ) ) ).
% 3.82/4.00
% 3.82/4.00 % list_update_overwrite
% 3.82/4.00 thf(fact_13_list__update__overwrite,axiom,
% 3.82/4.00 ! [Xs: list_nat,I: nat,X: nat,Y: nat] :
% 3.82/4.00 ( ( list_update_nat @ ( list_update_nat @ Xs @ I @ X ) @ I @ Y )
% 3.82/4.00 = ( list_update_nat @ Xs @ I @ Y ) ) ).
% 3.82/4.00
% 3.82/4.00 % list_update_overwrite
% 3.82/4.00 thf(fact_14_list__update__overwrite,axiom,
% 3.82/4.00 ! [Xs: list_VEBT_VEBT,I: nat,X: vEBT_VEBT,Y: vEBT_VEBT] :
% 3.82/4.00 ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ I @ Y )
% 3.82/4.00 = ( list_u1324408373059187874T_VEBT @ Xs @ I @ Y ) ) ).
% 3.82/4.00
% 3.82/4.00 % list_update_overwrite
% 3.82/4.00 thf(fact_15_nsprop,axiom,
% 3.82/4.00 ( ~ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) )
% 3.82/4.00 => ( summary
% 3.82/4.00 = ( vEBT_vebt_insert @ summary @ ( vEBT_VEBT_high @ mi @ na ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % nsprop
% 3.82/4.00 thf(fact_16__C11_C,axiom,
% 3.82/4.00 ! [X2: vEBT_VEBT] :
% 3.82/4.00 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) @ ( vEBT_VEBT_low @ mi @ na ) ) ) ) )
% 3.82/4.00 => ( vEBT_invar_vebt @ X2 @ na ) ) ).
% 3.82/4.00
% 3.82/4.00 % "11"
% 3.82/4.00 thf(fact_17_False,axiom,
% 3.82/4.00 ~ ( ord_less_nat @ mi @ xa ) ).
% 3.82/4.00
% 3.82/4.00 % False
% 3.82/4.00 thf(fact_18_list__update__swap,axiom,
% 3.82/4.00 ! [I: nat,I2: nat,Xs: list_VEBT_VEBT,X: vEBT_VEBT,X3: vEBT_VEBT] :
% 3.82/4.00 ( ( I != I2 )
% 3.82/4.00 => ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ I2 @ X3 )
% 3.82/4.00 = ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I2 @ X3 ) @ I @ X ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % list_update_swap
% 3.82/4.00 thf(fact_19_list__update__swap,axiom,
% 3.82/4.00 ! [I: nat,I2: nat,Xs: list_int,X: int,X3: int] :
% 3.82/4.00 ( ( I != I2 )
% 3.82/4.00 => ( ( list_update_int @ ( list_update_int @ Xs @ I @ X ) @ I2 @ X3 )
% 3.82/4.00 = ( list_update_int @ ( list_update_int @ Xs @ I2 @ X3 ) @ I @ X ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % list_update_swap
% 3.82/4.00 thf(fact_20_list__update__swap,axiom,
% 3.82/4.00 ! [I: nat,I2: nat,Xs: list_nat,X: nat,X3: nat] :
% 3.82/4.00 ( ( I != I2 )
% 3.82/4.00 => ( ( list_update_nat @ ( list_update_nat @ Xs @ I @ X ) @ I2 @ X3 )
% 3.82/4.00 = ( list_update_nat @ ( list_update_nat @ Xs @ I2 @ X3 ) @ I @ X ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % list_update_swap
% 3.82/4.00 thf(fact_21_in__children__def,axiom,
% 3.82/4.00 ( vEBT_V5917875025757280293ildren
% 3.82/4.00 = ( ^ [N: nat,TreeList: list_VEBT_VEBT,X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X4 @ N ) ) @ ( vEBT_VEBT_low @ X4 @ N ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % in_children_def
% 3.82/4.00 thf(fact_22__C5_Ohyps_C_I7_J,axiom,
% 3.82/4.00 ord_less_eq_nat @ mi @ ma ).
% 3.82/4.00
% 3.82/4.00 % "5.hyps"(7)
% 3.82/4.00 thf(fact_23__C12_C,axiom,
% 3.82/4.00 vEBT_invar_vebt @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) ) @ ( vEBT_vebt_insert @ summary @ ( vEBT_VEBT_high @ mi @ na ) ) @ summary ) @ m ).
% 3.82/4.00
% 3.82/4.00 % "12"
% 3.82/4.00 thf(fact_24_not__min__Null__member,axiom,
% 3.82/4.00 ! [T: vEBT_VEBT] :
% 3.82/4.00 ( ~ ( vEBT_VEBT_minNull @ T )
% 3.82/4.00 => ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_12 ) ) ).
% 3.82/4.00
% 3.82/4.00 % not_min_Null_member
% 3.82/4.00 thf(fact_25_min__Null__member,axiom,
% 3.82/4.00 ! [T: vEBT_VEBT,X: nat] :
% 3.82/4.00 ( ( vEBT_VEBT_minNull @ T )
% 3.82/4.00 => ~ ( vEBT_vebt_member @ T @ X ) ) ).
% 3.82/4.00
% 3.82/4.00 % min_Null_member
% 3.82/4.00 thf(fact_26__C1_C,axiom,
% 3.82/4.00 vEBT_invar_vebt @ summary @ m ).
% 3.82/4.00
% 3.82/4.00 % "1"
% 3.82/4.00 thf(fact_27_both__member__options__equiv__member,axiom,
% 3.82/4.00 ! [T: vEBT_VEBT,N2: nat,X: nat] :
% 3.82/4.00 ( ( vEBT_invar_vebt @ T @ N2 )
% 3.82/4.00 => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 3.82/4.00 = ( vEBT_vebt_member @ T @ X ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % both_member_options_equiv_member
% 3.82/4.00 thf(fact_28_valid__member__both__member__options,axiom,
% 3.82/4.00 ! [T: vEBT_VEBT,N2: nat,X: nat] :
% 3.82/4.00 ( ( vEBT_invar_vebt @ T @ N2 )
% 3.82/4.00 => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 3.82/4.00 => ( vEBT_vebt_member @ T @ X ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % valid_member_both_member_options
% 3.82/4.00 thf(fact_29__C5_C,axiom,
% 3.82/4.00 ( ( mi = ma )
% 3.82/4.00 => ! [X2: vEBT_VEBT] :
% 3.82/4.00 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ treeList ) )
% 3.82/4.00 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X_1 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % "5"
% 3.82/4.00 thf(fact_30_abcdef,axiom,
% 3.82/4.00 ord_less_nat @ xa @ mi ).
% 3.82/4.00
% 3.82/4.00 % abcdef
% 3.82/4.00 thf(fact_31_member__correct,axiom,
% 3.82/4.00 ! [T: vEBT_VEBT,N2: nat,X: nat] :
% 3.82/4.00 ( ( vEBT_invar_vebt @ T @ N2 )
% 3.82/4.00 => ( ( vEBT_vebt_member @ T @ X )
% 3.82/4.00 = ( member_nat @ X @ ( vEBT_set_vebt @ T ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % member_correct
% 3.82/4.00 thf(fact_32__C0_C,axiom,
% 3.82/4.00 ! [X2: vEBT_VEBT] :
% 3.82/4.00 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ treeList ) )
% 3.82/4.00 => ( vEBT_invar_vebt @ X2 @ na ) ) ).
% 3.82/4.00
% 3.82/4.00 % "0"
% 3.82/4.00 thf(fact_33__C163_C,axiom,
% 3.82/4.00 ~ ( vEBT_V8194947554948674370ptions @ summary @ i ) ).
% 3.82/4.00
% 3.82/4.00 % "163"
% 3.82/4.00 thf(fact_34_mimaxrel,axiom,
% 3.82/4.00 ( ( xa != mi )
% 3.82/4.00 & ( xa != ma ) ) ).
% 3.82/4.00
% 3.82/4.00 % mimaxrel
% 3.82/4.00 thf(fact_35__C8_C,axiom,
% 3.82/4.00 ( ( suc @ na )
% 3.82/4.00 = m ) ).
% 3.82/4.00
% 3.82/4.00 % "8"
% 3.82/4.00 thf(fact_36_set__vebt__set__vebt_H__valid,axiom,
% 3.82/4.00 ! [T: vEBT_VEBT,N2: nat] :
% 3.82/4.00 ( ( vEBT_invar_vebt @ T @ N2 )
% 3.82/4.00 => ( ( vEBT_set_vebt @ T )
% 3.82/4.00 = ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % set_vebt_set_vebt'_valid
% 3.82/4.00 thf(fact_37_valid__eq,axiom,
% 3.82/4.00 vEBT_VEBT_valid = vEBT_invar_vebt ).
% 3.82/4.00
% 3.82/4.00 % valid_eq
% 3.82/4.00 thf(fact_38_valid__eq1,axiom,
% 3.82/4.00 ! [T: vEBT_VEBT,D: nat] :
% 3.82/4.00 ( ( vEBT_invar_vebt @ T @ D )
% 3.82/4.00 => ( vEBT_VEBT_valid @ T @ D ) ) ).
% 3.82/4.00
% 3.82/4.00 % valid_eq1
% 3.82/4.00 thf(fact_39_valid__eq2,axiom,
% 3.82/4.00 ! [T: vEBT_VEBT,D: nat] :
% 3.82/4.00 ( ( vEBT_VEBT_valid @ T @ D )
% 3.82/4.00 => ( vEBT_invar_vebt @ T @ D ) ) ).
% 3.82/4.00
% 3.82/4.00 % valid_eq2
% 3.82/4.00 thf(fact_40_order__refl,axiom,
% 3.82/4.00 ! [X: real] : ( ord_less_eq_real @ X @ X ) ).
% 3.82/4.00
% 3.82/4.00 % order_refl
% 3.82/4.00 thf(fact_41_order__refl,axiom,
% 3.82/4.00 ! [X: set_nat] : ( ord_less_eq_set_nat @ X @ X ) ).
% 3.82/4.00
% 3.82/4.00 % order_refl
% 3.82/4.00 thf(fact_42_order__refl,axiom,
% 3.82/4.00 ! [X: set_int] : ( ord_less_eq_set_int @ X @ X ) ).
% 3.82/4.00
% 3.82/4.00 % order_refl
% 3.82/4.00 thf(fact_43_order__refl,axiom,
% 3.82/4.00 ! [X: nat] : ( ord_less_eq_nat @ X @ X ) ).
% 3.82/4.00
% 3.82/4.00 % order_refl
% 3.82/4.00 thf(fact_44_order__refl,axiom,
% 3.82/4.00 ! [X: int] : ( ord_less_eq_int @ X @ X ) ).
% 3.82/4.00
% 3.82/4.00 % order_refl
% 3.82/4.00 thf(fact_45_dual__order_Orefl,axiom,
% 3.82/4.00 ! [A: real] : ( ord_less_eq_real @ A @ A ) ).
% 3.82/4.00
% 3.82/4.00 % dual_order.refl
% 3.82/4.00 thf(fact_46_dual__order_Orefl,axiom,
% 3.82/4.00 ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ) ).
% 3.82/4.00
% 3.82/4.00 % dual_order.refl
% 3.82/4.00 thf(fact_47_dual__order_Orefl,axiom,
% 3.82/4.00 ! [A: set_int] : ( ord_less_eq_set_int @ A @ A ) ).
% 3.82/4.00
% 3.82/4.00 % dual_order.refl
% 3.82/4.00 thf(fact_48_dual__order_Orefl,axiom,
% 3.82/4.00 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 3.82/4.00
% 3.82/4.00 % dual_order.refl
% 3.82/4.00 thf(fact_49_dual__order_Orefl,axiom,
% 3.82/4.00 ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 3.82/4.00
% 3.82/4.00 % dual_order.refl
% 3.82/4.00 thf(fact_50_inthall,axiom,
% 3.82/4.00 ! [Xs: list_Extended_enat,P: extended_enat > $o,N2: nat] :
% 3.82/4.00 ( ! [X5: extended_enat] :
% 3.82/4.00 ( ( member_Extended_enat @ X5 @ ( set_Extended_enat2 @ Xs ) )
% 3.82/4.00 => ( P @ X5 ) )
% 3.82/4.00 => ( ( ord_less_nat @ N2 @ ( size_s3941691890525107288d_enat @ Xs ) )
% 3.82/4.00 => ( P @ ( nth_Extended_enat @ Xs @ N2 ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % inthall
% 3.82/4.00 thf(fact_51_inthall,axiom,
% 3.82/4.00 ! [Xs: list_real,P: real > $o,N2: nat] :
% 3.82/4.00 ( ! [X5: real] :
% 3.82/4.00 ( ( member_real @ X5 @ ( set_real2 @ Xs ) )
% 3.82/4.00 => ( P @ X5 ) )
% 3.82/4.00 => ( ( ord_less_nat @ N2 @ ( size_size_list_real @ Xs ) )
% 3.82/4.00 => ( P @ ( nth_real @ Xs @ N2 ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % inthall
% 3.82/4.00 thf(fact_52_inthall,axiom,
% 3.82/4.00 ! [Xs: list_set_nat,P: set_nat > $o,N2: nat] :
% 3.82/4.00 ( ! [X5: set_nat] :
% 3.82/4.00 ( ( member_set_nat @ X5 @ ( set_set_nat2 @ Xs ) )
% 3.82/4.00 => ( P @ X5 ) )
% 3.82/4.00 => ( ( ord_less_nat @ N2 @ ( size_s3254054031482475050et_nat @ Xs ) )
% 3.82/4.00 => ( P @ ( nth_set_nat @ Xs @ N2 ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % inthall
% 3.82/4.00 thf(fact_53_inthall,axiom,
% 3.82/4.00 ! [Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o,N2: nat] :
% 3.82/4.00 ( ! [X5: vEBT_VEBT] :
% 3.82/4.00 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ Xs ) )
% 3.82/4.00 => ( P @ X5 ) )
% 3.82/4.00 => ( ( ord_less_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 3.82/4.00 => ( P @ ( nth_VEBT_VEBT @ Xs @ N2 ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % inthall
% 3.82/4.00 thf(fact_54_inthall,axiom,
% 3.82/4.00 ! [Xs: list_int,P: int > $o,N2: nat] :
% 3.82/4.00 ( ! [X5: int] :
% 3.82/4.00 ( ( member_int @ X5 @ ( set_int2 @ Xs ) )
% 3.82/4.00 => ( P @ X5 ) )
% 3.82/4.00 => ( ( ord_less_nat @ N2 @ ( size_size_list_int @ Xs ) )
% 3.82/4.00 => ( P @ ( nth_int @ Xs @ N2 ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % inthall
% 3.82/4.00 thf(fact_55_inthall,axiom,
% 3.82/4.00 ! [Xs: list_nat,P: nat > $o,N2: nat] :
% 3.82/4.00 ( ! [X5: nat] :
% 3.82/4.00 ( ( member_nat @ X5 @ ( set_nat2 @ Xs ) )
% 3.82/4.00 => ( P @ X5 ) )
% 3.82/4.00 => ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs ) )
% 3.82/4.00 => ( P @ ( nth_nat @ Xs @ N2 ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % inthall
% 3.82/4.00 thf(fact_56_deg__not__0,axiom,
% 3.82/4.00 ! [T: vEBT_VEBT,N2: nat] :
% 3.82/4.00 ( ( vEBT_invar_vebt @ T @ N2 )
% 3.82/4.00 => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 3.82/4.00
% 3.82/4.00 % deg_not_0
% 3.82/4.00 thf(fact_57__C3_C,axiom,
% 3.82/4.00 ( deg
% 3.82/4.00 = ( plus_plus_nat @ na @ m ) ) ).
% 3.82/4.00
% 3.82/4.00 % "3"
% 3.82/4.00 thf(fact_58_nat__less__le,axiom,
% 3.82/4.00 ( ord_less_nat
% 3.82/4.00 = ( ^ [M: nat,N: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ M @ N )
% 3.82/4.00 & ( M != N ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % nat_less_le
% 3.82/4.00 thf(fact_59_less__imp__le__nat,axiom,
% 3.82/4.00 ! [M2: nat,N2: nat] :
% 3.82/4.00 ( ( ord_less_nat @ M2 @ N2 )
% 3.82/4.00 => ( ord_less_eq_nat @ M2 @ N2 ) ) ).
% 3.82/4.00
% 3.82/4.00 % less_imp_le_nat
% 3.82/4.00 thf(fact_60_even__odd__cases,axiom,
% 3.82/4.00 ! [X: nat] :
% 3.82/4.00 ( ! [N3: nat] :
% 3.82/4.00 ( X
% 3.82/4.00 != ( plus_plus_nat @ N3 @ N3 ) )
% 3.82/4.00 => ~ ! [N3: nat] :
% 3.82/4.00 ( X
% 3.82/4.00 != ( plus_plus_nat @ N3 @ ( suc @ N3 ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % even_odd_cases
% 3.82/4.00 thf(fact_61_valid__tree__deg__neq__0,axiom,
% 3.82/4.00 ! [T: vEBT_VEBT] :
% 3.82/4.00 ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 3.82/4.00
% 3.82/4.00 % valid_tree_deg_neq_0
% 3.82/4.00 thf(fact_62_valid__0__not,axiom,
% 3.82/4.00 ! [T: vEBT_VEBT] :
% 3.82/4.00 ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 3.82/4.00
% 3.82/4.00 % valid_0_not
% 3.82/4.00 thf(fact_63_old_Onat_Oinject,axiom,
% 3.82/4.00 ! [Nat: nat,Nat2: nat] :
% 3.82/4.00 ( ( ( suc @ Nat )
% 3.82/4.00 = ( suc @ Nat2 ) )
% 3.82/4.00 = ( Nat = Nat2 ) ) ).
% 3.82/4.00
% 3.82/4.00 % old.nat.inject
% 3.82/4.00 thf(fact_64_nat_Oinject,axiom,
% 3.82/4.00 ! [X22: nat,Y2: nat] :
% 3.82/4.00 ( ( ( suc @ X22 )
% 3.82/4.00 = ( suc @ Y2 ) )
% 3.82/4.00 = ( X22 = Y2 ) ) ).
% 3.82/4.00
% 3.82/4.00 % nat.inject
% 3.82/4.00 thf(fact_65_mem__Collect__eq,axiom,
% 3.82/4.00 ! [A: extended_enat,P: extended_enat > $o] :
% 3.82/4.00 ( ( member_Extended_enat @ A @ ( collec4429806609662206161d_enat @ P ) )
% 3.82/4.00 = ( P @ A ) ) ).
% 3.82/4.00
% 3.82/4.00 % mem_Collect_eq
% 3.82/4.00 thf(fact_66_mem__Collect__eq,axiom,
% 3.82/4.00 ! [A: real,P: real > $o] :
% 3.82/4.00 ( ( member_real @ A @ ( collect_real @ P ) )
% 3.82/4.00 = ( P @ A ) ) ).
% 3.82/4.00
% 3.82/4.00 % mem_Collect_eq
% 3.82/4.00 thf(fact_67_mem__Collect__eq,axiom,
% 3.82/4.00 ! [A: list_nat,P: list_nat > $o] :
% 3.82/4.00 ( ( member_list_nat @ A @ ( collect_list_nat @ P ) )
% 3.82/4.00 = ( P @ A ) ) ).
% 3.82/4.00
% 3.82/4.00 % mem_Collect_eq
% 3.82/4.00 thf(fact_68_mem__Collect__eq,axiom,
% 3.82/4.00 ! [A: set_nat,P: set_nat > $o] :
% 3.82/4.00 ( ( member_set_nat @ A @ ( collect_set_nat @ P ) )
% 3.82/4.00 = ( P @ A ) ) ).
% 3.82/4.00
% 3.82/4.00 % mem_Collect_eq
% 3.82/4.00 thf(fact_69_mem__Collect__eq,axiom,
% 3.82/4.00 ! [A: nat,P: nat > $o] :
% 3.82/4.00 ( ( member_nat @ A @ ( collect_nat @ P ) )
% 3.82/4.00 = ( P @ A ) ) ).
% 3.82/4.00
% 3.82/4.00 % mem_Collect_eq
% 3.82/4.00 thf(fact_70_mem__Collect__eq,axiom,
% 3.82/4.00 ! [A: int,P: int > $o] :
% 3.82/4.00 ( ( member_int @ A @ ( collect_int @ P ) )
% 3.82/4.00 = ( P @ A ) ) ).
% 3.82/4.00
% 3.82/4.00 % mem_Collect_eq
% 3.82/4.00 thf(fact_71_Collect__mem__eq,axiom,
% 3.82/4.00 ! [A2: set_Extended_enat] :
% 3.82/4.00 ( ( collec4429806609662206161d_enat
% 3.82/4.00 @ ^ [X4: extended_enat] : ( member_Extended_enat @ X4 @ A2 ) )
% 3.82/4.00 = A2 ) ).
% 3.82/4.00
% 3.82/4.00 % Collect_mem_eq
% 3.82/4.00 thf(fact_72_Collect__mem__eq,axiom,
% 3.82/4.00 ! [A2: set_real] :
% 3.82/4.00 ( ( collect_real
% 3.82/4.00 @ ^ [X4: real] : ( member_real @ X4 @ A2 ) )
% 3.82/4.00 = A2 ) ).
% 3.82/4.00
% 3.82/4.00 % Collect_mem_eq
% 3.82/4.00 thf(fact_73_Collect__mem__eq,axiom,
% 3.82/4.00 ! [A2: set_list_nat] :
% 3.82/4.00 ( ( collect_list_nat
% 3.82/4.00 @ ^ [X4: list_nat] : ( member_list_nat @ X4 @ A2 ) )
% 3.82/4.00 = A2 ) ).
% 3.82/4.00
% 3.82/4.00 % Collect_mem_eq
% 3.82/4.00 thf(fact_74_Collect__mem__eq,axiom,
% 3.82/4.00 ! [A2: set_set_nat] :
% 3.82/4.00 ( ( collect_set_nat
% 3.82/4.00 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ A2 ) )
% 3.82/4.00 = A2 ) ).
% 3.82/4.00
% 3.82/4.00 % Collect_mem_eq
% 3.82/4.00 thf(fact_75_Collect__mem__eq,axiom,
% 3.82/4.00 ! [A2: set_nat] :
% 3.82/4.00 ( ( collect_nat
% 3.82/4.00 @ ^ [X4: nat] : ( member_nat @ X4 @ A2 ) )
% 3.82/4.00 = A2 ) ).
% 3.82/4.00
% 3.82/4.00 % Collect_mem_eq
% 3.82/4.00 thf(fact_76_Collect__mem__eq,axiom,
% 3.82/4.00 ! [A2: set_int] :
% 3.82/4.00 ( ( collect_int
% 3.82/4.00 @ ^ [X4: int] : ( member_int @ X4 @ A2 ) )
% 3.82/4.00 = A2 ) ).
% 3.82/4.00
% 3.82/4.00 % Collect_mem_eq
% 3.82/4.00 thf(fact_77_Collect__cong,axiom,
% 3.82/4.00 ! [P: real > $o,Q: real > $o] :
% 3.82/4.00 ( ! [X5: real] :
% 3.82/4.00 ( ( P @ X5 )
% 3.82/4.00 = ( Q @ X5 ) )
% 3.82/4.00 => ( ( collect_real @ P )
% 3.82/4.00 = ( collect_real @ Q ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % Collect_cong
% 3.82/4.00 thf(fact_78_Collect__cong,axiom,
% 3.82/4.00 ! [P: list_nat > $o,Q: list_nat > $o] :
% 3.82/4.00 ( ! [X5: list_nat] :
% 3.82/4.00 ( ( P @ X5 )
% 3.82/4.00 = ( Q @ X5 ) )
% 3.82/4.00 => ( ( collect_list_nat @ P )
% 3.82/4.00 = ( collect_list_nat @ Q ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % Collect_cong
% 3.82/4.00 thf(fact_79_Collect__cong,axiom,
% 3.82/4.00 ! [P: set_nat > $o,Q: set_nat > $o] :
% 3.82/4.00 ( ! [X5: set_nat] :
% 3.82/4.00 ( ( P @ X5 )
% 3.82/4.00 = ( Q @ X5 ) )
% 3.82/4.00 => ( ( collect_set_nat @ P )
% 3.82/4.00 = ( collect_set_nat @ Q ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % Collect_cong
% 3.82/4.00 thf(fact_80_Collect__cong,axiom,
% 3.82/4.00 ! [P: nat > $o,Q: nat > $o] :
% 3.82/4.00 ( ! [X5: nat] :
% 3.82/4.00 ( ( P @ X5 )
% 3.82/4.00 = ( Q @ X5 ) )
% 3.82/4.00 => ( ( collect_nat @ P )
% 3.82/4.00 = ( collect_nat @ Q ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % Collect_cong
% 3.82/4.00 thf(fact_81_Collect__cong,axiom,
% 3.82/4.00 ! [P: int > $o,Q: int > $o] :
% 3.82/4.00 ( ! [X5: int] :
% 3.82/4.00 ( ( P @ X5 )
% 3.82/4.00 = ( Q @ X5 ) )
% 3.82/4.00 => ( ( collect_int @ P )
% 3.82/4.00 = ( collect_int @ Q ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % Collect_cong
% 3.82/4.00 thf(fact_82_Suc__less__eq,axiom,
% 3.82/4.00 ! [M2: nat,N2: nat] :
% 3.82/4.00 ( ( ord_less_nat @ ( suc @ M2 ) @ ( suc @ N2 ) )
% 3.82/4.00 = ( ord_less_nat @ M2 @ N2 ) ) ).
% 3.82/4.00
% 3.82/4.00 % Suc_less_eq
% 3.82/4.00 thf(fact_83_Suc__mono,axiom,
% 3.82/4.00 ! [M2: nat,N2: nat] :
% 3.82/4.00 ( ( ord_less_nat @ M2 @ N2 )
% 3.82/4.00 => ( ord_less_nat @ ( suc @ M2 ) @ ( suc @ N2 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % Suc_mono
% 3.82/4.00 thf(fact_84_lessI,axiom,
% 3.82/4.00 ! [N2: nat] : ( ord_less_nat @ N2 @ ( suc @ N2 ) ) ).
% 3.82/4.00
% 3.82/4.00 % lessI
% 3.82/4.00 thf(fact_85_less__nat__zero__code,axiom,
% 3.82/4.00 ! [N2: nat] :
% 3.82/4.00 ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 3.82/4.00
% 3.82/4.00 % less_nat_zero_code
% 3.82/4.00 thf(fact_86_neq0__conv,axiom,
% 3.82/4.00 ! [N2: nat] :
% 3.82/4.00 ( ( N2 != zero_zero_nat )
% 3.82/4.00 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 3.82/4.00
% 3.82/4.00 % neq0_conv
% 3.82/4.00 thf(fact_87_bot__nat__0_Onot__eq__extremum,axiom,
% 3.82/4.00 ! [A: nat] :
% 3.82/4.00 ( ( A != zero_zero_nat )
% 3.82/4.00 = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 3.82/4.00
% 3.82/4.00 % bot_nat_0.not_eq_extremum
% 3.82/4.00 thf(fact_88_Suc__le__mono,axiom,
% 3.82/4.00 ! [N2: nat,M2: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ ( suc @ N2 ) @ ( suc @ M2 ) )
% 3.82/4.00 = ( ord_less_eq_nat @ N2 @ M2 ) ) ).
% 3.82/4.00
% 3.82/4.00 % Suc_le_mono
% 3.82/4.00 thf(fact_89_le0,axiom,
% 3.82/4.00 ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N2 ) ).
% 3.82/4.00
% 3.82/4.00 % le0
% 3.82/4.00 thf(fact_90_bot__nat__0_Oextremum,axiom,
% 3.82/4.00 ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 3.82/4.00
% 3.82/4.00 % bot_nat_0.extremum
% 3.82/4.00 thf(fact_91_add__Suc__right,axiom,
% 3.82/4.00 ! [M2: nat,N2: nat] :
% 3.82/4.00 ( ( plus_plus_nat @ M2 @ ( suc @ N2 ) )
% 3.82/4.00 = ( suc @ ( plus_plus_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % add_Suc_right
% 3.82/4.00 thf(fact_92_Nat_Oadd__0__right,axiom,
% 3.82/4.00 ! [M2: nat] :
% 3.82/4.00 ( ( plus_plus_nat @ M2 @ zero_zero_nat )
% 3.82/4.00 = M2 ) ).
% 3.82/4.00
% 3.82/4.00 % Nat.add_0_right
% 3.82/4.00 thf(fact_93_add__is__0,axiom,
% 3.82/4.00 ! [M2: nat,N2: nat] :
% 3.82/4.00 ( ( ( plus_plus_nat @ M2 @ N2 )
% 3.82/4.00 = zero_zero_nat )
% 3.82/4.00 = ( ( M2 = zero_zero_nat )
% 3.82/4.00 & ( N2 = zero_zero_nat ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % add_is_0
% 3.82/4.00 thf(fact_94_nat__add__left__cancel__less,axiom,
% 3.82/4.00 ! [K: nat,M2: nat,N2: nat] :
% 3.82/4.00 ( ( ord_less_nat @ ( plus_plus_nat @ K @ M2 ) @ ( plus_plus_nat @ K @ N2 ) )
% 3.82/4.00 = ( ord_less_nat @ M2 @ N2 ) ) ).
% 3.82/4.00
% 3.82/4.00 % nat_add_left_cancel_less
% 3.82/4.00 thf(fact_95_nat__add__left__cancel__le,axiom,
% 3.82/4.00 ! [K: nat,M2: nat,N2: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M2 ) @ ( plus_plus_nat @ K @ N2 ) )
% 3.82/4.00 = ( ord_less_eq_nat @ M2 @ N2 ) ) ).
% 3.82/4.00
% 3.82/4.00 % nat_add_left_cancel_le
% 3.82/4.00 thf(fact_96_length__list__update,axiom,
% 3.82/4.00 ! [Xs: list_VEBT_VEBT,I: nat,X: vEBT_VEBT] :
% 3.82/4.00 ( ( size_s6755466524823107622T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) )
% 3.82/4.00 = ( size_s6755466524823107622T_VEBT @ Xs ) ) ).
% 3.82/4.00
% 3.82/4.00 % length_list_update
% 3.82/4.00 thf(fact_97_length__list__update,axiom,
% 3.82/4.00 ! [Xs: list_int,I: nat,X: int] :
% 3.82/4.00 ( ( size_size_list_int @ ( list_update_int @ Xs @ I @ X ) )
% 3.82/4.00 = ( size_size_list_int @ Xs ) ) ).
% 3.82/4.00
% 3.82/4.00 % length_list_update
% 3.82/4.00 thf(fact_98_length__list__update,axiom,
% 3.82/4.00 ! [Xs: list_nat,I: nat,X: nat] :
% 3.82/4.00 ( ( size_size_list_nat @ ( list_update_nat @ Xs @ I @ X ) )
% 3.82/4.00 = ( size_size_list_nat @ Xs ) ) ).
% 3.82/4.00
% 3.82/4.00 % length_list_update
% 3.82/4.00 thf(fact_99_less__Suc0,axiom,
% 3.82/4.00 ! [N2: nat] :
% 3.82/4.00 ( ( ord_less_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 3.82/4.00 = ( N2 = zero_zero_nat ) ) ).
% 3.82/4.00
% 3.82/4.00 % less_Suc0
% 3.82/4.00 thf(fact_100_zero__less__Suc,axiom,
% 3.82/4.00 ! [N2: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N2 ) ) ).
% 3.82/4.00
% 3.82/4.00 % zero_less_Suc
% 3.82/4.00 thf(fact_101_add__gr__0,axiom,
% 3.82/4.00 ! [M2: nat,N2: nat] :
% 3.82/4.00 ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M2 @ N2 ) )
% 3.82/4.00 = ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 3.82/4.00 | ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % add_gr_0
% 3.82/4.00 thf(fact_102_list__update__beyond,axiom,
% 3.82/4.00 ! [Xs: list_VEBT_VEBT,I: nat,X: vEBT_VEBT] :
% 3.82/4.00 ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ I )
% 3.82/4.00 => ( ( list_u1324408373059187874T_VEBT @ Xs @ I @ X )
% 3.82/4.00 = Xs ) ) ).
% 3.82/4.00
% 3.82/4.00 % list_update_beyond
% 3.82/4.00 thf(fact_103_list__update__beyond,axiom,
% 3.82/4.00 ! [Xs: list_int,I: nat,X: int] :
% 3.82/4.00 ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ I )
% 3.82/4.00 => ( ( list_update_int @ Xs @ I @ X )
% 3.82/4.00 = Xs ) ) ).
% 3.82/4.00
% 3.82/4.00 % list_update_beyond
% 3.82/4.00 thf(fact_104_list__update__beyond,axiom,
% 3.82/4.00 ! [Xs: list_nat,I: nat,X: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ I )
% 3.82/4.00 => ( ( list_update_nat @ Xs @ I @ X )
% 3.82/4.00 = Xs ) ) ).
% 3.82/4.00
% 3.82/4.00 % list_update_beyond
% 3.82/4.00 thf(fact_105_nth__list__update__eq,axiom,
% 3.82/4.00 ! [I: nat,Xs: list_VEBT_VEBT,X: vEBT_VEBT] :
% 3.82/4.00 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 3.82/4.00 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ I )
% 3.82/4.00 = X ) ) ).
% 3.82/4.00
% 3.82/4.00 % nth_list_update_eq
% 3.82/4.00 thf(fact_106_nth__list__update__eq,axiom,
% 3.82/4.00 ! [I: nat,Xs: list_int,X: int] :
% 3.82/4.00 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 3.82/4.00 => ( ( nth_int @ ( list_update_int @ Xs @ I @ X ) @ I )
% 3.82/4.00 = X ) ) ).
% 3.82/4.00
% 3.82/4.00 % nth_list_update_eq
% 3.82/4.00 thf(fact_107_nth__list__update__eq,axiom,
% 3.82/4.00 ! [I: nat,Xs: list_nat,X: nat] :
% 3.82/4.00 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 3.82/4.00 => ( ( nth_nat @ ( list_update_nat @ Xs @ I @ X ) @ I )
% 3.82/4.00 = X ) ) ).
% 3.82/4.00
% 3.82/4.00 % nth_list_update_eq
% 3.82/4.00 thf(fact_108_set__swap,axiom,
% 3.82/4.00 ! [I: nat,Xs: list_VEBT_VEBT,J: nat] :
% 3.82/4.00 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 3.82/4.00 => ( ( ord_less_nat @ J @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 3.82/4.00 => ( ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ ( nth_VEBT_VEBT @ Xs @ J ) ) @ J @ ( nth_VEBT_VEBT @ Xs @ I ) ) )
% 3.82/4.00 = ( set_VEBT_VEBT2 @ Xs ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % set_swap
% 3.82/4.00 thf(fact_109_set__swap,axiom,
% 3.82/4.00 ! [I: nat,Xs: list_int,J: nat] :
% 3.82/4.00 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 3.82/4.00 => ( ( ord_less_nat @ J @ ( size_size_list_int @ Xs ) )
% 3.82/4.00 => ( ( set_int2 @ ( list_update_int @ ( list_update_int @ Xs @ I @ ( nth_int @ Xs @ J ) ) @ J @ ( nth_int @ Xs @ I ) ) )
% 3.82/4.00 = ( set_int2 @ Xs ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % set_swap
% 3.82/4.00 thf(fact_110_set__swap,axiom,
% 3.82/4.00 ! [I: nat,Xs: list_nat,J: nat] :
% 3.82/4.00 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 3.82/4.00 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs ) )
% 3.82/4.00 => ( ( set_nat2 @ ( list_update_nat @ ( list_update_nat @ Xs @ I @ ( nth_nat @ Xs @ J ) ) @ J @ ( nth_nat @ Xs @ I ) ) )
% 3.82/4.00 = ( set_nat2 @ Xs ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % set_swap
% 3.82/4.00 thf(fact_111_less__natE,axiom,
% 3.82/4.00 ! [M2: nat,N2: nat] :
% 3.82/4.00 ( ( ord_less_nat @ M2 @ N2 )
% 3.82/4.00 => ~ ! [Q2: nat] :
% 3.82/4.00 ( N2
% 3.82/4.00 != ( suc @ ( plus_plus_nat @ M2 @ Q2 ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % less_natE
% 3.82/4.00 thf(fact_112_Ex__less__Suc2,axiom,
% 3.82/4.00 ! [N2: nat,P: nat > $o] :
% 3.82/4.00 ( ( ? [I3: nat] :
% 3.82/4.00 ( ( ord_less_nat @ I3 @ ( suc @ N2 ) )
% 3.82/4.00 & ( P @ I3 ) ) )
% 3.82/4.00 = ( ( P @ zero_zero_nat )
% 3.82/4.00 | ? [I3: nat] :
% 3.82/4.00 ( ( ord_less_nat @ I3 @ N2 )
% 3.82/4.00 & ( P @ ( suc @ I3 ) ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % Ex_less_Suc2
% 3.82/4.00 thf(fact_113_gr0__conv__Suc,axiom,
% 3.82/4.00 ! [N2: nat] :
% 3.82/4.00 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.00 = ( ? [M: nat] :
% 3.82/4.00 ( N2
% 3.82/4.00 = ( suc @ M ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % gr0_conv_Suc
% 3.82/4.00 thf(fact_114_All__less__Suc2,axiom,
% 3.82/4.00 ! [N2: nat,P: nat > $o] :
% 3.82/4.00 ( ( ! [I3: nat] :
% 3.82/4.00 ( ( ord_less_nat @ I3 @ ( suc @ N2 ) )
% 3.82/4.00 => ( P @ I3 ) ) )
% 3.82/4.00 = ( ( P @ zero_zero_nat )
% 3.82/4.00 & ! [I3: nat] :
% 3.82/4.00 ( ( ord_less_nat @ I3 @ N2 )
% 3.82/4.00 => ( P @ ( suc @ I3 ) ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % All_less_Suc2
% 3.82/4.00 thf(fact_115_less__add__Suc1,axiom,
% 3.82/4.00 ! [I: nat,M2: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ I @ M2 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % less_add_Suc1
% 3.82/4.00 thf(fact_116_less__add__Suc2,axiom,
% 3.82/4.00 ! [I: nat,M2: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ M2 @ I ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % less_add_Suc2
% 3.82/4.00 thf(fact_117_gr0__implies__Suc,axiom,
% 3.82/4.00 ! [N2: nat] :
% 3.82/4.00 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.00 => ? [M3: nat] :
% 3.82/4.00 ( N2
% 3.82/4.00 = ( suc @ M3 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % gr0_implies_Suc
% 3.82/4.00 thf(fact_118_less__iff__Suc__add,axiom,
% 3.82/4.00 ( ord_less_nat
% 3.82/4.00 = ( ^ [M: nat,N: nat] :
% 3.82/4.00 ? [K2: nat] :
% 3.82/4.00 ( N
% 3.82/4.00 = ( suc @ ( plus_plus_nat @ M @ K2 ) ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % less_iff_Suc_add
% 3.82/4.00 thf(fact_119_less__imp__Suc__add,axiom,
% 3.82/4.00 ! [M2: nat,N2: nat] :
% 3.82/4.00 ( ( ord_less_nat @ M2 @ N2 )
% 3.82/4.00 => ? [K3: nat] :
% 3.82/4.00 ( N2
% 3.82/4.00 = ( suc @ ( plus_plus_nat @ M2 @ K3 ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % less_imp_Suc_add
% 3.82/4.00 thf(fact_120_Ex__list__of__length,axiom,
% 3.82/4.00 ! [N2: nat] :
% 3.82/4.00 ? [Xs2: list_VEBT_VEBT] :
% 3.82/4.00 ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 3.82/4.00 = N2 ) ).
% 3.82/4.00
% 3.82/4.00 % Ex_list_of_length
% 3.82/4.00 thf(fact_121_Ex__list__of__length,axiom,
% 3.82/4.00 ! [N2: nat] :
% 3.82/4.00 ? [Xs2: list_int] :
% 3.82/4.00 ( ( size_size_list_int @ Xs2 )
% 3.82/4.00 = N2 ) ).
% 3.82/4.00
% 3.82/4.00 % Ex_list_of_length
% 3.82/4.00 thf(fact_122_Ex__list__of__length,axiom,
% 3.82/4.00 ! [N2: nat] :
% 3.82/4.00 ? [Xs2: list_nat] :
% 3.82/4.00 ( ( size_size_list_nat @ Xs2 )
% 3.82/4.00 = N2 ) ).
% 3.82/4.00
% 3.82/4.00 % Ex_list_of_length
% 3.82/4.00 thf(fact_123_neq__if__length__neq,axiom,
% 3.82/4.00 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 3.82/4.00 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 3.82/4.00 != ( size_s6755466524823107622T_VEBT @ Ys ) )
% 3.82/4.00 => ( Xs != Ys ) ) ).
% 3.82/4.00
% 3.82/4.00 % neq_if_length_neq
% 3.82/4.00 thf(fact_124_neq__if__length__neq,axiom,
% 3.82/4.00 ! [Xs: list_int,Ys: list_int] :
% 3.82/4.00 ( ( ( size_size_list_int @ Xs )
% 3.82/4.00 != ( size_size_list_int @ Ys ) )
% 3.82/4.00 => ( Xs != Ys ) ) ).
% 3.82/4.00
% 3.82/4.00 % neq_if_length_neq
% 3.82/4.00 thf(fact_125_neq__if__length__neq,axiom,
% 3.82/4.00 ! [Xs: list_nat,Ys: list_nat] :
% 3.82/4.00 ( ( ( size_size_list_nat @ Xs )
% 3.82/4.00 != ( size_size_list_nat @ Ys ) )
% 3.82/4.00 => ( Xs != Ys ) ) ).
% 3.82/4.00
% 3.82/4.00 % neq_if_length_neq
% 3.82/4.00 thf(fact_126_less__Suc__eq__0__disj,axiom,
% 3.82/4.00 ! [M2: nat,N2: nat] :
% 3.82/4.00 ( ( ord_less_nat @ M2 @ ( suc @ N2 ) )
% 3.82/4.00 = ( ( M2 = zero_zero_nat )
% 3.82/4.00 | ? [J2: nat] :
% 3.82/4.00 ( ( M2
% 3.82/4.00 = ( suc @ J2 ) )
% 3.82/4.00 & ( ord_less_nat @ J2 @ N2 ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % less_Suc_eq_0_disj
% 3.82/4.00 thf(fact_127_less__imp__add__positive,axiom,
% 3.82/4.00 ! [I: nat,J: nat] :
% 3.82/4.00 ( ( ord_less_nat @ I @ J )
% 3.82/4.00 => ? [K3: nat] :
% 3.82/4.00 ( ( ord_less_nat @ zero_zero_nat @ K3 )
% 3.82/4.00 & ( ( plus_plus_nat @ I @ K3 )
% 3.82/4.00 = J ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % less_imp_add_positive
% 3.82/4.00 thf(fact_128_size__neq__size__imp__neq,axiom,
% 3.82/4.00 ! [X: list_VEBT_VEBT,Y: list_VEBT_VEBT] :
% 3.82/4.00 ( ( ( size_s6755466524823107622T_VEBT @ X )
% 3.82/4.00 != ( size_s6755466524823107622T_VEBT @ Y ) )
% 3.82/4.00 => ( X != Y ) ) ).
% 3.82/4.00
% 3.82/4.00 % size_neq_size_imp_neq
% 3.82/4.00 thf(fact_129_size__neq__size__imp__neq,axiom,
% 3.82/4.00 ! [X: num,Y: num] :
% 3.82/4.00 ( ( ( size_size_num @ X )
% 3.82/4.00 != ( size_size_num @ Y ) )
% 3.82/4.00 => ( X != Y ) ) ).
% 3.82/4.00
% 3.82/4.00 % size_neq_size_imp_neq
% 3.82/4.00 thf(fact_130_size__neq__size__imp__neq,axiom,
% 3.82/4.00 ! [X: vEBT_VEBT,Y: vEBT_VEBT] :
% 3.82/4.00 ( ( ( size_size_VEBT_VEBT @ X )
% 3.82/4.00 != ( size_size_VEBT_VEBT @ Y ) )
% 3.82/4.00 => ( X != Y ) ) ).
% 3.82/4.00
% 3.82/4.00 % size_neq_size_imp_neq
% 3.82/4.00 thf(fact_131_size__neq__size__imp__neq,axiom,
% 3.82/4.00 ! [X: list_int,Y: list_int] :
% 3.82/4.00 ( ( ( size_size_list_int @ X )
% 3.82/4.00 != ( size_size_list_int @ Y ) )
% 3.82/4.00 => ( X != Y ) ) ).
% 3.82/4.00
% 3.82/4.00 % size_neq_size_imp_neq
% 3.82/4.00 thf(fact_132_size__neq__size__imp__neq,axiom,
% 3.82/4.00 ! [X: list_nat,Y: list_nat] :
% 3.82/4.00 ( ( ( size_size_list_nat @ X )
% 3.82/4.00 != ( size_size_list_nat @ Y ) )
% 3.82/4.00 => ( X != Y ) ) ).
% 3.82/4.00
% 3.82/4.00 % size_neq_size_imp_neq
% 3.82/4.00 thf(fact_133_not0__implies__Suc,axiom,
% 3.82/4.00 ! [N2: nat] :
% 3.82/4.00 ( ( N2 != zero_zero_nat )
% 3.82/4.00 => ? [M3: nat] :
% 3.82/4.00 ( N2
% 3.82/4.00 = ( suc @ M3 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % not0_implies_Suc
% 3.82/4.00 thf(fact_134_add__eq__self__zero,axiom,
% 3.82/4.00 ! [M2: nat,N2: nat] :
% 3.82/4.00 ( ( ( plus_plus_nat @ M2 @ N2 )
% 3.82/4.00 = M2 )
% 3.82/4.00 => ( N2 = zero_zero_nat ) ) ).
% 3.82/4.00
% 3.82/4.00 % add_eq_self_zero
% 3.82/4.00 thf(fact_135_add__Suc__shift,axiom,
% 3.82/4.00 ! [M2: nat,N2: nat] :
% 3.82/4.00 ( ( plus_plus_nat @ ( suc @ M2 ) @ N2 )
% 3.82/4.00 = ( plus_plus_nat @ M2 @ ( suc @ N2 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % add_Suc_shift
% 3.82/4.00 thf(fact_136_Zero__not__Suc,axiom,
% 3.82/4.00 ! [M2: nat] :
% 3.82/4.00 ( zero_zero_nat
% 3.82/4.00 != ( suc @ M2 ) ) ).
% 3.82/4.00
% 3.82/4.00 % Zero_not_Suc
% 3.82/4.00 thf(fact_137_Zero__neq__Suc,axiom,
% 3.82/4.00 ! [M2: nat] :
% 3.82/4.00 ( zero_zero_nat
% 3.82/4.00 != ( suc @ M2 ) ) ).
% 3.82/4.00
% 3.82/4.00 % Zero_neq_Suc
% 3.82/4.00 thf(fact_138_Suc__neq__Zero,axiom,
% 3.82/4.00 ! [M2: nat] :
% 3.82/4.00 ( ( suc @ M2 )
% 3.82/4.00 != zero_zero_nat ) ).
% 3.82/4.00
% 3.82/4.00 % Suc_neq_Zero
% 3.82/4.00 thf(fact_139_zero__induct,axiom,
% 3.82/4.00 ! [P: nat > $o,K: nat] :
% 3.82/4.00 ( ( P @ K )
% 3.82/4.00 => ( ! [N3: nat] :
% 3.82/4.00 ( ( P @ ( suc @ N3 ) )
% 3.82/4.00 => ( P @ N3 ) )
% 3.82/4.00 => ( P @ zero_zero_nat ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % zero_induct
% 3.82/4.00 thf(fact_140_n__not__Suc__n,axiom,
% 3.82/4.00 ! [N2: nat] :
% 3.82/4.00 ( N2
% 3.82/4.00 != ( suc @ N2 ) ) ).
% 3.82/4.00
% 3.82/4.00 % n_not_Suc_n
% 3.82/4.00 thf(fact_141_diff__induct,axiom,
% 3.82/4.00 ! [P: nat > nat > $o,M2: nat,N2: nat] :
% 3.82/4.00 ( ! [X5: nat] : ( P @ X5 @ zero_zero_nat )
% 3.82/4.00 => ( ! [Y3: nat] : ( P @ zero_zero_nat @ ( suc @ Y3 ) )
% 3.82/4.00 => ( ! [X5: nat,Y3: nat] :
% 3.82/4.00 ( ( P @ X5 @ Y3 )
% 3.82/4.00 => ( P @ ( suc @ X5 ) @ ( suc @ Y3 ) ) )
% 3.82/4.00 => ( P @ M2 @ N2 ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % diff_induct
% 3.82/4.00 thf(fact_142_one__is__add,axiom,
% 3.82/4.00 ! [M2: nat,N2: nat] :
% 3.82/4.00 ( ( ( suc @ zero_zero_nat )
% 3.82/4.00 = ( plus_plus_nat @ M2 @ N2 ) )
% 3.82/4.00 = ( ( ( M2
% 3.82/4.00 = ( suc @ zero_zero_nat ) )
% 3.82/4.00 & ( N2 = zero_zero_nat ) )
% 3.82/4.00 | ( ( M2 = zero_zero_nat )
% 3.82/4.00 & ( N2
% 3.82/4.00 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % one_is_add
% 3.82/4.00 thf(fact_143_nat__induct,axiom,
% 3.82/4.00 ! [P: nat > $o,N2: nat] :
% 3.82/4.00 ( ( P @ zero_zero_nat )
% 3.82/4.00 => ( ! [N3: nat] :
% 3.82/4.00 ( ( P @ N3 )
% 3.82/4.00 => ( P @ ( suc @ N3 ) ) )
% 3.82/4.00 => ( P @ N2 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % nat_induct
% 3.82/4.00 thf(fact_144_Suc__inject,axiom,
% 3.82/4.00 ! [X: nat,Y: nat] :
% 3.82/4.00 ( ( ( suc @ X )
% 3.82/4.00 = ( suc @ Y ) )
% 3.82/4.00 => ( X = Y ) ) ).
% 3.82/4.00
% 3.82/4.00 % Suc_inject
% 3.82/4.00 thf(fact_145_add__is__1,axiom,
% 3.82/4.00 ! [M2: nat,N2: nat] :
% 3.82/4.00 ( ( ( plus_plus_nat @ M2 @ N2 )
% 3.82/4.00 = ( suc @ zero_zero_nat ) )
% 3.82/4.00 = ( ( ( M2
% 3.82/4.00 = ( suc @ zero_zero_nat ) )
% 3.82/4.00 & ( N2 = zero_zero_nat ) )
% 3.82/4.00 | ( ( M2 = zero_zero_nat )
% 3.82/4.00 & ( N2
% 3.82/4.00 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % add_is_1
% 3.82/4.00 thf(fact_146_add__Suc,axiom,
% 3.82/4.00 ! [M2: nat,N2: nat] :
% 3.82/4.00 ( ( plus_plus_nat @ ( suc @ M2 ) @ N2 )
% 3.82/4.00 = ( suc @ ( plus_plus_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % add_Suc
% 3.82/4.00 thf(fact_147_old_Onat_Oexhaust,axiom,
% 3.82/4.00 ! [Y: nat] :
% 3.82/4.00 ( ( Y != zero_zero_nat )
% 3.82/4.00 => ~ ! [Nat3: nat] :
% 3.82/4.00 ( Y
% 3.82/4.00 != ( suc @ Nat3 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % old.nat.exhaust
% 3.82/4.00 thf(fact_148_plus__nat_Oadd__0,axiom,
% 3.82/4.00 ! [N2: nat] :
% 3.82/4.00 ( ( plus_plus_nat @ zero_zero_nat @ N2 )
% 3.82/4.00 = N2 ) ).
% 3.82/4.00
% 3.82/4.00 % plus_nat.add_0
% 3.82/4.00 thf(fact_149_nat__arith_Osuc1,axiom,
% 3.82/4.00 ! [A2: nat,K: nat,A: nat] :
% 3.82/4.00 ( ( A2
% 3.82/4.00 = ( plus_plus_nat @ K @ A ) )
% 3.82/4.00 => ( ( suc @ A2 )
% 3.82/4.00 = ( plus_plus_nat @ K @ ( suc @ A ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % nat_arith.suc1
% 3.82/4.00 thf(fact_150_nat_OdiscI,axiom,
% 3.82/4.00 ! [Nat: nat,X22: nat] :
% 3.82/4.00 ( ( Nat
% 3.82/4.00 = ( suc @ X22 ) )
% 3.82/4.00 => ( Nat != zero_zero_nat ) ) ).
% 3.82/4.00
% 3.82/4.00 % nat.discI
% 3.82/4.00 thf(fact_151_old_Onat_Odistinct_I1_J,axiom,
% 3.82/4.00 ! [Nat2: nat] :
% 3.82/4.00 ( zero_zero_nat
% 3.82/4.00 != ( suc @ Nat2 ) ) ).
% 3.82/4.00
% 3.82/4.00 % old.nat.distinct(1)
% 3.82/4.00 thf(fact_152_old_Onat_Odistinct_I2_J,axiom,
% 3.82/4.00 ! [Nat2: nat] :
% 3.82/4.00 ( ( suc @ Nat2 )
% 3.82/4.00 != zero_zero_nat ) ).
% 3.82/4.00
% 3.82/4.00 % old.nat.distinct(2)
% 3.82/4.00 thf(fact_153_nat_Odistinct_I1_J,axiom,
% 3.82/4.00 ! [X22: nat] :
% 3.82/4.00 ( zero_zero_nat
% 3.82/4.00 != ( suc @ X22 ) ) ).
% 3.82/4.00
% 3.82/4.00 % nat.distinct(1)
% 3.82/4.00 thf(fact_154_not__less__less__Suc__eq,axiom,
% 3.82/4.00 ! [N2: nat,M2: nat] :
% 3.82/4.00 ( ~ ( ord_less_nat @ N2 @ M2 )
% 3.82/4.00 => ( ( ord_less_nat @ N2 @ ( suc @ M2 ) )
% 3.82/4.00 = ( N2 = M2 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % not_less_less_Suc_eq
% 3.82/4.00 thf(fact_155_strict__inc__induct,axiom,
% 3.82/4.00 ! [I: nat,J: nat,P: nat > $o] :
% 3.82/4.00 ( ( ord_less_nat @ I @ J )
% 3.82/4.00 => ( ! [I4: nat] :
% 3.82/4.00 ( ( J
% 3.82/4.00 = ( suc @ I4 ) )
% 3.82/4.00 => ( P @ I4 ) )
% 3.82/4.00 => ( ! [I4: nat] :
% 3.82/4.00 ( ( ord_less_nat @ I4 @ J )
% 3.82/4.00 => ( ( P @ ( suc @ I4 ) )
% 3.82/4.00 => ( P @ I4 ) ) )
% 3.82/4.00 => ( P @ I ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % strict_inc_induct
% 3.82/4.00 thf(fact_156_less__Suc__induct,axiom,
% 3.82/4.00 ! [I: nat,J: nat,P: nat > nat > $o] :
% 3.82/4.00 ( ( ord_less_nat @ I @ J )
% 3.82/4.00 => ( ! [I4: nat] : ( P @ I4 @ ( suc @ I4 ) )
% 3.82/4.00 => ( ! [I4: nat,J3: nat,K3: nat] :
% 3.82/4.00 ( ( ord_less_nat @ I4 @ J3 )
% 3.82/4.00 => ( ( ord_less_nat @ J3 @ K3 )
% 3.82/4.00 => ( ( P @ I4 @ J3 )
% 3.82/4.00 => ( ( P @ J3 @ K3 )
% 3.82/4.00 => ( P @ I4 @ K3 ) ) ) ) )
% 3.82/4.00 => ( P @ I @ J ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % less_Suc_induct
% 3.82/4.00 thf(fact_157_less__trans__Suc,axiom,
% 3.82/4.00 ! [I: nat,J: nat,K: nat] :
% 3.82/4.00 ( ( ord_less_nat @ I @ J )
% 3.82/4.00 => ( ( ord_less_nat @ J @ K )
% 3.82/4.00 => ( ord_less_nat @ ( suc @ I ) @ K ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % less_trans_Suc
% 3.82/4.00 thf(fact_158_Suc__less__SucD,axiom,
% 3.82/4.00 ! [M2: nat,N2: nat] :
% 3.82/4.00 ( ( ord_less_nat @ ( suc @ M2 ) @ ( suc @ N2 ) )
% 3.82/4.00 => ( ord_less_nat @ M2 @ N2 ) ) ).
% 3.82/4.00
% 3.82/4.00 % Suc_less_SucD
% 3.82/4.00 thf(fact_159_less__antisym,axiom,
% 3.82/4.00 ! [N2: nat,M2: nat] :
% 3.82/4.00 ( ~ ( ord_less_nat @ N2 @ M2 )
% 3.82/4.00 => ( ( ord_less_nat @ N2 @ ( suc @ M2 ) )
% 3.82/4.00 => ( M2 = N2 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % less_antisym
% 3.82/4.00 thf(fact_160_Suc__less__eq2,axiom,
% 3.82/4.00 ! [N2: nat,M2: nat] :
% 3.82/4.00 ( ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 3.82/4.00 = ( ? [M4: nat] :
% 3.82/4.00 ( ( M2
% 3.82/4.00 = ( suc @ M4 ) )
% 3.82/4.00 & ( ord_less_nat @ N2 @ M4 ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % Suc_less_eq2
% 3.82/4.00 thf(fact_161_All__less__Suc,axiom,
% 3.82/4.00 ! [N2: nat,P: nat > $o] :
% 3.82/4.00 ( ( ! [I3: nat] :
% 3.82/4.00 ( ( ord_less_nat @ I3 @ ( suc @ N2 ) )
% 3.82/4.00 => ( P @ I3 ) ) )
% 3.82/4.00 = ( ( P @ N2 )
% 3.82/4.00 & ! [I3: nat] :
% 3.82/4.00 ( ( ord_less_nat @ I3 @ N2 )
% 3.82/4.00 => ( P @ I3 ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % All_less_Suc
% 3.82/4.00 thf(fact_162_not__less__eq,axiom,
% 3.82/4.00 ! [M2: nat,N2: nat] :
% 3.82/4.00 ( ( ~ ( ord_less_nat @ M2 @ N2 ) )
% 3.82/4.00 = ( ord_less_nat @ N2 @ ( suc @ M2 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % not_less_eq
% 3.82/4.00 thf(fact_163_less__Suc__eq,axiom,
% 3.82/4.00 ! [M2: nat,N2: nat] :
% 3.82/4.00 ( ( ord_less_nat @ M2 @ ( suc @ N2 ) )
% 3.82/4.00 = ( ( ord_less_nat @ M2 @ N2 )
% 3.82/4.00 | ( M2 = N2 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % less_Suc_eq
% 3.82/4.00 thf(fact_164_Ex__less__Suc,axiom,
% 3.82/4.00 ! [N2: nat,P: nat > $o] :
% 3.82/4.00 ( ( ? [I3: nat] :
% 3.82/4.00 ( ( ord_less_nat @ I3 @ ( suc @ N2 ) )
% 3.82/4.00 & ( P @ I3 ) ) )
% 3.82/4.00 = ( ( P @ N2 )
% 3.82/4.00 | ? [I3: nat] :
% 3.82/4.00 ( ( ord_less_nat @ I3 @ N2 )
% 3.82/4.00 & ( P @ I3 ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % Ex_less_Suc
% 3.82/4.00 thf(fact_165_less__SucI,axiom,
% 3.82/4.00 ! [M2: nat,N2: nat] :
% 3.82/4.00 ( ( ord_less_nat @ M2 @ N2 )
% 3.82/4.00 => ( ord_less_nat @ M2 @ ( suc @ N2 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % less_SucI
% 3.82/4.00 thf(fact_166_less__SucE,axiom,
% 3.82/4.00 ! [M2: nat,N2: nat] :
% 3.82/4.00 ( ( ord_less_nat @ M2 @ ( suc @ N2 ) )
% 3.82/4.00 => ( ~ ( ord_less_nat @ M2 @ N2 )
% 3.82/4.00 => ( M2 = N2 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % less_SucE
% 3.82/4.00 thf(fact_167_Suc__lessI,axiom,
% 3.82/4.00 ! [M2: nat,N2: nat] :
% 3.82/4.00 ( ( ord_less_nat @ M2 @ N2 )
% 3.82/4.00 => ( ( ( suc @ M2 )
% 3.82/4.00 != N2 )
% 3.82/4.00 => ( ord_less_nat @ ( suc @ M2 ) @ N2 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % Suc_lessI
% 3.82/4.00 thf(fact_168_Suc__lessE,axiom,
% 3.82/4.00 ! [I: nat,K: nat] :
% 3.82/4.00 ( ( ord_less_nat @ ( suc @ I ) @ K )
% 3.82/4.00 => ~ ! [J3: nat] :
% 3.82/4.00 ( ( ord_less_nat @ I @ J3 )
% 3.82/4.00 => ( K
% 3.82/4.00 != ( suc @ J3 ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % Suc_lessE
% 3.82/4.00 thf(fact_169_Suc__lessD,axiom,
% 3.82/4.00 ! [M2: nat,N2: nat] :
% 3.82/4.00 ( ( ord_less_nat @ ( suc @ M2 ) @ N2 )
% 3.82/4.00 => ( ord_less_nat @ M2 @ N2 ) ) ).
% 3.82/4.00
% 3.82/4.00 % Suc_lessD
% 3.82/4.00 thf(fact_170_Nat_OlessE,axiom,
% 3.82/4.00 ! [I: nat,K: nat] :
% 3.82/4.00 ( ( ord_less_nat @ I @ K )
% 3.82/4.00 => ( ( K
% 3.82/4.00 != ( suc @ I ) )
% 3.82/4.00 => ~ ! [J3: nat] :
% 3.82/4.00 ( ( ord_less_nat @ I @ J3 )
% 3.82/4.00 => ( K
% 3.82/4.00 != ( suc @ J3 ) ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % Nat.lessE
% 3.82/4.00 thf(fact_171_less__add__eq__less,axiom,
% 3.82/4.00 ! [K: nat,L: nat,M2: nat,N2: nat] :
% 3.82/4.00 ( ( ord_less_nat @ K @ L )
% 3.82/4.00 => ( ( ( plus_plus_nat @ M2 @ L )
% 3.82/4.00 = ( plus_plus_nat @ K @ N2 ) )
% 3.82/4.00 => ( ord_less_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % less_add_eq_less
% 3.82/4.00 thf(fact_172_trans__less__add2,axiom,
% 3.82/4.00 ! [I: nat,J: nat,M2: nat] :
% 3.82/4.00 ( ( ord_less_nat @ I @ J )
% 3.82/4.00 => ( ord_less_nat @ I @ ( plus_plus_nat @ M2 @ J ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % trans_less_add2
% 3.82/4.00 thf(fact_173_trans__less__add1,axiom,
% 3.82/4.00 ! [I: nat,J: nat,M2: nat] :
% 3.82/4.00 ( ( ord_less_nat @ I @ J )
% 3.82/4.00 => ( ord_less_nat @ I @ ( plus_plus_nat @ J @ M2 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % trans_less_add1
% 3.82/4.00 thf(fact_174_add__less__mono1,axiom,
% 3.82/4.00 ! [I: nat,J: nat,K: nat] :
% 3.82/4.00 ( ( ord_less_nat @ I @ J )
% 3.82/4.00 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % add_less_mono1
% 3.82/4.00 thf(fact_175_not__add__less2,axiom,
% 3.82/4.00 ! [J: nat,I: nat] :
% 3.82/4.00 ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I ) @ I ) ).
% 3.82/4.00
% 3.82/4.00 % not_add_less2
% 3.82/4.00 thf(fact_176_not__add__less1,axiom,
% 3.82/4.00 ! [I: nat,J: nat] :
% 3.82/4.00 ~ ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ I ) ).
% 3.82/4.00
% 3.82/4.00 % not_add_less1
% 3.82/4.00 thf(fact_177_add__less__mono,axiom,
% 3.82/4.00 ! [I: nat,J: nat,K: nat,L: nat] :
% 3.82/4.00 ( ( ord_less_nat @ I @ J )
% 3.82/4.00 => ( ( ord_less_nat @ K @ L )
% 3.82/4.00 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % add_less_mono
% 3.82/4.00 thf(fact_178_add__lessD1,axiom,
% 3.82/4.00 ! [I: nat,J: nat,K: nat] :
% 3.82/4.00 ( ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 3.82/4.00 => ( ord_less_nat @ I @ K ) ) ).
% 3.82/4.00
% 3.82/4.00 % add_lessD1
% 3.82/4.00 thf(fact_179_transitive__stepwise__le,axiom,
% 3.82/4.00 ! [M2: nat,N2: nat,R: nat > nat > $o] :
% 3.82/4.00 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.00 => ( ! [X5: nat] : ( R @ X5 @ X5 )
% 3.82/4.00 => ( ! [X5: nat,Y3: nat,Z: nat] :
% 3.82/4.00 ( ( R @ X5 @ Y3 )
% 3.82/4.00 => ( ( R @ Y3 @ Z )
% 3.82/4.00 => ( R @ X5 @ Z ) ) )
% 3.82/4.00 => ( ! [N3: nat] : ( R @ N3 @ ( suc @ N3 ) )
% 3.82/4.00 => ( R @ M2 @ N2 ) ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % transitive_stepwise_le
% 3.82/4.00 thf(fact_180_nat__induct__at__least,axiom,
% 3.82/4.00 ! [M2: nat,N2: nat,P: nat > $o] :
% 3.82/4.00 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.00 => ( ( P @ M2 )
% 3.82/4.00 => ( ! [N3: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ M2 @ N3 )
% 3.82/4.00 => ( ( P @ N3 )
% 3.82/4.00 => ( P @ ( suc @ N3 ) ) ) )
% 3.82/4.00 => ( P @ N2 ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % nat_induct_at_least
% 3.82/4.00 thf(fact_181_full__nat__induct,axiom,
% 3.82/4.00 ! [P: nat > $o,N2: nat] :
% 3.82/4.00 ( ! [N3: nat] :
% 3.82/4.00 ( ! [M5: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ ( suc @ M5 ) @ N3 )
% 3.82/4.00 => ( P @ M5 ) )
% 3.82/4.00 => ( P @ N3 ) )
% 3.82/4.00 => ( P @ N2 ) ) ).
% 3.82/4.00
% 3.82/4.00 % full_nat_induct
% 3.82/4.00 thf(fact_182_not__less__eq__eq,axiom,
% 3.82/4.00 ! [M2: nat,N2: nat] :
% 3.82/4.00 ( ( ~ ( ord_less_eq_nat @ M2 @ N2 ) )
% 3.82/4.00 = ( ord_less_eq_nat @ ( suc @ N2 ) @ M2 ) ) ).
% 3.82/4.00
% 3.82/4.00 % not_less_eq_eq
% 3.82/4.00 thf(fact_183_Suc__n__not__le__n,axiom,
% 3.82/4.00 ! [N2: nat] :
% 3.82/4.00 ~ ( ord_less_eq_nat @ ( suc @ N2 ) @ N2 ) ).
% 3.82/4.00
% 3.82/4.00 % Suc_n_not_le_n
% 3.82/4.00 thf(fact_184_le__Suc__eq,axiom,
% 3.82/4.00 ! [M2: nat,N2: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ M2 @ ( suc @ N2 ) )
% 3.82/4.00 = ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.00 | ( M2
% 3.82/4.00 = ( suc @ N2 ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % le_Suc_eq
% 3.82/4.00 thf(fact_185_Suc__le__D,axiom,
% 3.82/4.00 ! [N2: nat,M6: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ ( suc @ N2 ) @ M6 )
% 3.82/4.00 => ? [M3: nat] :
% 3.82/4.00 ( M6
% 3.82/4.00 = ( suc @ M3 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % Suc_le_D
% 3.82/4.00 thf(fact_186_le__SucI,axiom,
% 3.82/4.00 ! [M2: nat,N2: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.00 => ( ord_less_eq_nat @ M2 @ ( suc @ N2 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % le_SucI
% 3.82/4.00 thf(fact_187_le__SucE,axiom,
% 3.82/4.00 ! [M2: nat,N2: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ M2 @ ( suc @ N2 ) )
% 3.82/4.00 => ( ~ ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.00 => ( M2
% 3.82/4.00 = ( suc @ N2 ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % le_SucE
% 3.82/4.00 thf(fact_188_Suc__leD,axiom,
% 3.82/4.00 ! [M2: nat,N2: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N2 )
% 3.82/4.00 => ( ord_less_eq_nat @ M2 @ N2 ) ) ).
% 3.82/4.00
% 3.82/4.00 % Suc_leD
% 3.82/4.00 thf(fact_189_nat__le__iff__add,axiom,
% 3.82/4.00 ( ord_less_eq_nat
% 3.82/4.00 = ( ^ [M: nat,N: nat] :
% 3.82/4.00 ? [K2: nat] :
% 3.82/4.00 ( N
% 3.82/4.00 = ( plus_plus_nat @ M @ K2 ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % nat_le_iff_add
% 3.82/4.00 thf(fact_190_trans__le__add2,axiom,
% 3.82/4.00 ! [I: nat,J: nat,M2: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ I @ J )
% 3.82/4.00 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ M2 @ J ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % trans_le_add2
% 3.82/4.00 thf(fact_191_trans__le__add1,axiom,
% 3.82/4.00 ! [I: nat,J: nat,M2: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ I @ J )
% 3.82/4.00 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ J @ M2 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % trans_le_add1
% 3.82/4.00 thf(fact_192_add__le__mono1,axiom,
% 3.82/4.00 ! [I: nat,J: nat,K: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ I @ J )
% 3.82/4.00 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % add_le_mono1
% 3.82/4.00 thf(fact_193_add__le__mono,axiom,
% 3.82/4.00 ! [I: nat,J: nat,K: nat,L: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ I @ J )
% 3.82/4.00 => ( ( ord_less_eq_nat @ K @ L )
% 3.82/4.00 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % add_le_mono
% 3.82/4.00 thf(fact_194_le__Suc__ex,axiom,
% 3.82/4.00 ! [K: nat,L: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ K @ L )
% 3.82/4.00 => ? [N3: nat] :
% 3.82/4.00 ( L
% 3.82/4.00 = ( plus_plus_nat @ K @ N3 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % le_Suc_ex
% 3.82/4.00 thf(fact_195_add__leD2,axiom,
% 3.82/4.00 ! [M2: nat,K: nat,N2: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M2 @ K ) @ N2 )
% 3.82/4.00 => ( ord_less_eq_nat @ K @ N2 ) ) ).
% 3.82/4.00
% 3.82/4.00 % add_leD2
% 3.82/4.00 thf(fact_196_add__leD1,axiom,
% 3.82/4.00 ! [M2: nat,K: nat,N2: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M2 @ K ) @ N2 )
% 3.82/4.00 => ( ord_less_eq_nat @ M2 @ N2 ) ) ).
% 3.82/4.00
% 3.82/4.00 % add_leD1
% 3.82/4.00 thf(fact_197_le__add2,axiom,
% 3.82/4.00 ! [N2: nat,M2: nat] : ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ M2 @ N2 ) ) ).
% 3.82/4.00
% 3.82/4.00 % le_add2
% 3.82/4.00 thf(fact_198_le__add1,axiom,
% 3.82/4.00 ! [N2: nat,M2: nat] : ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ N2 @ M2 ) ) ).
% 3.82/4.00
% 3.82/4.00 % le_add1
% 3.82/4.00 thf(fact_199_add__leE,axiom,
% 3.82/4.00 ! [M2: nat,K: nat,N2: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M2 @ K ) @ N2 )
% 3.82/4.00 => ~ ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.00 => ~ ( ord_less_eq_nat @ K @ N2 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % add_leE
% 3.82/4.00 thf(fact_200_infinite__descent0,axiom,
% 3.82/4.00 ! [P: nat > $o,N2: nat] :
% 3.82/4.00 ( ( P @ zero_zero_nat )
% 3.82/4.00 => ( ! [N3: nat] :
% 3.82/4.00 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 3.82/4.00 => ( ~ ( P @ N3 )
% 3.82/4.00 => ? [M5: nat] :
% 3.82/4.00 ( ( ord_less_nat @ M5 @ N3 )
% 3.82/4.00 & ~ ( P @ M5 ) ) ) )
% 3.82/4.00 => ( P @ N2 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % infinite_descent0
% 3.82/4.00 thf(fact_201_gr__implies__not0,axiom,
% 3.82/4.00 ! [M2: nat,N2: nat] :
% 3.82/4.00 ( ( ord_less_nat @ M2 @ N2 )
% 3.82/4.00 => ( N2 != zero_zero_nat ) ) ).
% 3.82/4.00
% 3.82/4.00 % gr_implies_not0
% 3.82/4.00 thf(fact_202_less__zeroE,axiom,
% 3.82/4.00 ! [N2: nat] :
% 3.82/4.00 ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 3.82/4.00
% 3.82/4.00 % less_zeroE
% 3.82/4.00 thf(fact_203_not__less0,axiom,
% 3.82/4.00 ! [N2: nat] :
% 3.82/4.00 ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 3.82/4.00
% 3.82/4.00 % not_less0
% 3.82/4.00 thf(fact_204_not__gr0,axiom,
% 3.82/4.00 ! [N2: nat] :
% 3.82/4.00 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N2 ) )
% 3.82/4.00 = ( N2 = zero_zero_nat ) ) ).
% 3.82/4.00
% 3.82/4.00 % not_gr0
% 3.82/4.00 thf(fact_205_gr0I,axiom,
% 3.82/4.00 ! [N2: nat] :
% 3.82/4.00 ( ( N2 != zero_zero_nat )
% 3.82/4.00 => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 3.82/4.00
% 3.82/4.00 % gr0I
% 3.82/4.00 thf(fact_206_bot__nat__0_Oextremum__strict,axiom,
% 3.82/4.00 ! [A: nat] :
% 3.82/4.00 ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 3.82/4.00
% 3.82/4.00 % bot_nat_0.extremum_strict
% 3.82/4.00 thf(fact_207_le__0__eq,axiom,
% 3.82/4.00 ! [N2: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ N2 @ zero_zero_nat )
% 3.82/4.00 = ( N2 = zero_zero_nat ) ) ).
% 3.82/4.00
% 3.82/4.00 % le_0_eq
% 3.82/4.00 thf(fact_208_bot__nat__0_Oextremum__uniqueI,axiom,
% 3.82/4.00 ! [A: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 3.82/4.00 => ( A = zero_zero_nat ) ) ).
% 3.82/4.00
% 3.82/4.00 % bot_nat_0.extremum_uniqueI
% 3.82/4.00 thf(fact_209_bot__nat__0_Oextremum__unique,axiom,
% 3.82/4.00 ! [A: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 3.82/4.00 = ( A = zero_zero_nat ) ) ).
% 3.82/4.00
% 3.82/4.00 % bot_nat_0.extremum_unique
% 3.82/4.00 thf(fact_210_less__eq__nat_Osimps_I1_J,axiom,
% 3.82/4.00 ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N2 ) ).
% 3.82/4.00
% 3.82/4.00 % less_eq_nat.simps(1)
% 3.82/4.00 thf(fact_211_ex__least__nat__less,axiom,
% 3.82/4.00 ! [P: nat > $o,N2: nat] :
% 3.82/4.00 ( ( P @ N2 )
% 3.82/4.00 => ( ~ ( P @ zero_zero_nat )
% 3.82/4.00 => ? [K3: nat] :
% 3.82/4.00 ( ( ord_less_nat @ K3 @ N2 )
% 3.82/4.00 & ! [I5: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ I5 @ K3 )
% 3.82/4.00 => ~ ( P @ I5 ) )
% 3.82/4.00 & ( P @ ( suc @ K3 ) ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % ex_least_nat_less
% 3.82/4.00 thf(fact_212_length__pos__if__in__set,axiom,
% 3.82/4.00 ! [X: extended_enat,Xs: list_Extended_enat] :
% 3.82/4.00 ( ( member_Extended_enat @ X @ ( set_Extended_enat2 @ Xs ) )
% 3.82/4.00 => ( ord_less_nat @ zero_zero_nat @ ( size_s3941691890525107288d_enat @ Xs ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % length_pos_if_in_set
% 3.82/4.00 thf(fact_213_length__pos__if__in__set,axiom,
% 3.82/4.00 ! [X: real,Xs: list_real] :
% 3.82/4.00 ( ( member_real @ X @ ( set_real2 @ Xs ) )
% 3.82/4.00 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_real @ Xs ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % length_pos_if_in_set
% 3.82/4.00 thf(fact_214_length__pos__if__in__set,axiom,
% 3.82/4.00 ! [X: set_nat,Xs: list_set_nat] :
% 3.82/4.00 ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs ) )
% 3.82/4.00 => ( ord_less_nat @ zero_zero_nat @ ( size_s3254054031482475050et_nat @ Xs ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % length_pos_if_in_set
% 3.82/4.00 thf(fact_215_length__pos__if__in__set,axiom,
% 3.82/4.00 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 3.82/4.00 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 3.82/4.00 => ( ord_less_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % length_pos_if_in_set
% 3.82/4.00 thf(fact_216_length__pos__if__in__set,axiom,
% 3.82/4.00 ! [X: int,Xs: list_int] :
% 3.82/4.00 ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 3.82/4.00 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_int @ Xs ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % length_pos_if_in_set
% 3.82/4.00 thf(fact_217_length__pos__if__in__set,axiom,
% 3.82/4.00 ! [X: nat,Xs: list_nat] :
% 3.82/4.00 ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 3.82/4.00 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % length_pos_if_in_set
% 3.82/4.00 thf(fact_218_length__induct,axiom,
% 3.82/4.00 ! [P: list_VEBT_VEBT > $o,Xs: list_VEBT_VEBT] :
% 3.82/4.00 ( ! [Xs2: list_VEBT_VEBT] :
% 3.82/4.00 ( ! [Ys2: list_VEBT_VEBT] :
% 3.82/4.00 ( ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ Ys2 ) @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 3.82/4.00 => ( P @ Ys2 ) )
% 3.82/4.00 => ( P @ Xs2 ) )
% 3.82/4.00 => ( P @ Xs ) ) ).
% 3.82/4.00
% 3.82/4.00 % length_induct
% 3.82/4.00 thf(fact_219_length__induct,axiom,
% 3.82/4.00 ! [P: list_int > $o,Xs: list_int] :
% 3.82/4.00 ( ! [Xs2: list_int] :
% 3.82/4.00 ( ! [Ys2: list_int] :
% 3.82/4.00 ( ( ord_less_nat @ ( size_size_list_int @ Ys2 ) @ ( size_size_list_int @ Xs2 ) )
% 3.82/4.00 => ( P @ Ys2 ) )
% 3.82/4.00 => ( P @ Xs2 ) )
% 3.82/4.00 => ( P @ Xs ) ) ).
% 3.82/4.00
% 3.82/4.00 % length_induct
% 3.82/4.00 thf(fact_220_length__induct,axiom,
% 3.82/4.00 ! [P: list_nat > $o,Xs: list_nat] :
% 3.82/4.00 ( ! [Xs2: list_nat] :
% 3.82/4.00 ( ! [Ys2: list_nat] :
% 3.82/4.00 ( ( ord_less_nat @ ( size_size_list_nat @ Ys2 ) @ ( size_size_list_nat @ Xs2 ) )
% 3.82/4.00 => ( P @ Ys2 ) )
% 3.82/4.00 => ( P @ Xs2 ) )
% 3.82/4.00 => ( P @ Xs ) ) ).
% 3.82/4.00
% 3.82/4.00 % length_induct
% 3.82/4.00 thf(fact_221_subset__code_I1_J,axiom,
% 3.82/4.00 ! [Xs: list_Extended_enat,B: set_Extended_enat] :
% 3.82/4.00 ( ( ord_le7203529160286727270d_enat @ ( set_Extended_enat2 @ Xs ) @ B )
% 3.82/4.00 = ( ! [X4: extended_enat] :
% 3.82/4.00 ( ( member_Extended_enat @ X4 @ ( set_Extended_enat2 @ Xs ) )
% 3.82/4.00 => ( member_Extended_enat @ X4 @ B ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % subset_code(1)
% 3.82/4.00 thf(fact_222_subset__code_I1_J,axiom,
% 3.82/4.00 ! [Xs: list_real,B: set_real] :
% 3.82/4.00 ( ( ord_less_eq_set_real @ ( set_real2 @ Xs ) @ B )
% 3.82/4.00 = ( ! [X4: real] :
% 3.82/4.00 ( ( member_real @ X4 @ ( set_real2 @ Xs ) )
% 3.82/4.00 => ( member_real @ X4 @ B ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % subset_code(1)
% 3.82/4.00 thf(fact_223_subset__code_I1_J,axiom,
% 3.82/4.00 ! [Xs: list_set_nat,B: set_set_nat] :
% 3.82/4.00 ( ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ Xs ) @ B )
% 3.82/4.00 = ( ! [X4: set_nat] :
% 3.82/4.00 ( ( member_set_nat @ X4 @ ( set_set_nat2 @ Xs ) )
% 3.82/4.00 => ( member_set_nat @ X4 @ B ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % subset_code(1)
% 3.82/4.00 thf(fact_224_subset__code_I1_J,axiom,
% 3.82/4.00 ! [Xs: list_VEBT_VEBT,B: set_VEBT_VEBT] :
% 3.82/4.00 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ B )
% 3.82/4.00 = ( ! [X4: vEBT_VEBT] :
% 3.82/4.00 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs ) )
% 3.82/4.00 => ( member_VEBT_VEBT @ X4 @ B ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % subset_code(1)
% 3.82/4.00 thf(fact_225_subset__code_I1_J,axiom,
% 3.82/4.00 ! [Xs: list_nat,B: set_nat] :
% 3.82/4.00 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ B )
% 3.82/4.00 = ( ! [X4: nat] :
% 3.82/4.00 ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 3.82/4.00 => ( member_nat @ X4 @ B ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % subset_code(1)
% 3.82/4.00 thf(fact_226_subset__code_I1_J,axiom,
% 3.82/4.00 ! [Xs: list_int,B: set_int] :
% 3.82/4.00 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ B )
% 3.82/4.00 = ( ! [X4: int] :
% 3.82/4.00 ( ( member_int @ X4 @ ( set_int2 @ Xs ) )
% 3.82/4.00 => ( member_int @ X4 @ B ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % subset_code(1)
% 3.82/4.00 thf(fact_227_lift__Suc__mono__less__iff,axiom,
% 3.82/4.00 ! [F: nat > nat,N2: nat,M2: nat] :
% 3.82/4.00 ( ! [N3: nat] : ( ord_less_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 3.82/4.00 => ( ( ord_less_nat @ ( F @ N2 ) @ ( F @ M2 ) )
% 3.82/4.00 = ( ord_less_nat @ N2 @ M2 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % lift_Suc_mono_less_iff
% 3.82/4.00 thf(fact_228_lift__Suc__mono__less__iff,axiom,
% 3.82/4.00 ! [F: nat > extended_enat,N2: nat,M2: nat] :
% 3.82/4.00 ( ! [N3: nat] : ( ord_le72135733267957522d_enat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 3.82/4.00 => ( ( ord_le72135733267957522d_enat @ ( F @ N2 ) @ ( F @ M2 ) )
% 3.82/4.00 = ( ord_less_nat @ N2 @ M2 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % lift_Suc_mono_less_iff
% 3.82/4.00 thf(fact_229_lift__Suc__mono__less__iff,axiom,
% 3.82/4.00 ! [F: nat > real,N2: nat,M2: nat] :
% 3.82/4.00 ( ! [N3: nat] : ( ord_less_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 3.82/4.00 => ( ( ord_less_real @ ( F @ N2 ) @ ( F @ M2 ) )
% 3.82/4.00 = ( ord_less_nat @ N2 @ M2 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % lift_Suc_mono_less_iff
% 3.82/4.00 thf(fact_230_lift__Suc__mono__less__iff,axiom,
% 3.82/4.00 ! [F: nat > int,N2: nat,M2: nat] :
% 3.82/4.00 ( ! [N3: nat] : ( ord_less_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 3.82/4.00 => ( ( ord_less_int @ ( F @ N2 ) @ ( F @ M2 ) )
% 3.82/4.00 = ( ord_less_nat @ N2 @ M2 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % lift_Suc_mono_less_iff
% 3.82/4.00 thf(fact_231_lift__Suc__mono__less,axiom,
% 3.82/4.00 ! [F: nat > nat,N2: nat,N4: nat] :
% 3.82/4.00 ( ! [N3: nat] : ( ord_less_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 3.82/4.00 => ( ( ord_less_nat @ N2 @ N4 )
% 3.82/4.00 => ( ord_less_nat @ ( F @ N2 ) @ ( F @ N4 ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % lift_Suc_mono_less
% 3.82/4.00 thf(fact_232_lift__Suc__mono__less,axiom,
% 3.82/4.00 ! [F: nat > extended_enat,N2: nat,N4: nat] :
% 3.82/4.00 ( ! [N3: nat] : ( ord_le72135733267957522d_enat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 3.82/4.00 => ( ( ord_less_nat @ N2 @ N4 )
% 3.82/4.00 => ( ord_le72135733267957522d_enat @ ( F @ N2 ) @ ( F @ N4 ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % lift_Suc_mono_less
% 3.82/4.00 thf(fact_233_lift__Suc__mono__less,axiom,
% 3.82/4.00 ! [F: nat > real,N2: nat,N4: nat] :
% 3.82/4.00 ( ! [N3: nat] : ( ord_less_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 3.82/4.00 => ( ( ord_less_nat @ N2 @ N4 )
% 3.82/4.00 => ( ord_less_real @ ( F @ N2 ) @ ( F @ N4 ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % lift_Suc_mono_less
% 3.82/4.00 thf(fact_234_lift__Suc__mono__less,axiom,
% 3.82/4.00 ! [F: nat > int,N2: nat,N4: nat] :
% 3.82/4.00 ( ! [N3: nat] : ( ord_less_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 3.82/4.00 => ( ( ord_less_nat @ N2 @ N4 )
% 3.82/4.00 => ( ord_less_int @ ( F @ N2 ) @ ( F @ N4 ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % lift_Suc_mono_less
% 3.82/4.00 thf(fact_235_lift__Suc__antimono__le,axiom,
% 3.82/4.00 ! [F: nat > real,N2: nat,N4: nat] :
% 3.82/4.00 ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 3.82/4.00 => ( ( ord_less_eq_nat @ N2 @ N4 )
% 3.82/4.00 => ( ord_less_eq_real @ ( F @ N4 ) @ ( F @ N2 ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % lift_Suc_antimono_le
% 3.82/4.00 thf(fact_236_lift__Suc__antimono__le,axiom,
% 3.82/4.00 ! [F: nat > set_nat,N2: nat,N4: nat] :
% 3.82/4.00 ( ! [N3: nat] : ( ord_less_eq_set_nat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 3.82/4.00 => ( ( ord_less_eq_nat @ N2 @ N4 )
% 3.82/4.00 => ( ord_less_eq_set_nat @ ( F @ N4 ) @ ( F @ N2 ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % lift_Suc_antimono_le
% 3.82/4.00 thf(fact_237_lift__Suc__antimono__le,axiom,
% 3.82/4.00 ! [F: nat > set_int,N2: nat,N4: nat] :
% 3.82/4.00 ( ! [N3: nat] : ( ord_less_eq_set_int @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 3.82/4.00 => ( ( ord_less_eq_nat @ N2 @ N4 )
% 3.82/4.00 => ( ord_less_eq_set_int @ ( F @ N4 ) @ ( F @ N2 ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % lift_Suc_antimono_le
% 3.82/4.00 thf(fact_238_lift__Suc__antimono__le,axiom,
% 3.82/4.00 ! [F: nat > nat,N2: nat,N4: nat] :
% 3.82/4.00 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 3.82/4.00 => ( ( ord_less_eq_nat @ N2 @ N4 )
% 3.82/4.00 => ( ord_less_eq_nat @ ( F @ N4 ) @ ( F @ N2 ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % lift_Suc_antimono_le
% 3.82/4.00 thf(fact_239_lift__Suc__antimono__le,axiom,
% 3.82/4.00 ! [F: nat > int,N2: nat,N4: nat] :
% 3.82/4.00 ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 3.82/4.00 => ( ( ord_less_eq_nat @ N2 @ N4 )
% 3.82/4.00 => ( ord_less_eq_int @ ( F @ N4 ) @ ( F @ N2 ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % lift_Suc_antimono_le
% 3.82/4.00 thf(fact_240_lift__Suc__mono__le,axiom,
% 3.82/4.00 ! [F: nat > real,N2: nat,N4: nat] :
% 3.82/4.00 ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 3.82/4.00 => ( ( ord_less_eq_nat @ N2 @ N4 )
% 3.82/4.00 => ( ord_less_eq_real @ ( F @ N2 ) @ ( F @ N4 ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % lift_Suc_mono_le
% 3.82/4.00 thf(fact_241_lift__Suc__mono__le,axiom,
% 3.82/4.00 ! [F: nat > set_nat,N2: nat,N4: nat] :
% 3.82/4.00 ( ! [N3: nat] : ( ord_less_eq_set_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 3.82/4.00 => ( ( ord_less_eq_nat @ N2 @ N4 )
% 3.82/4.00 => ( ord_less_eq_set_nat @ ( F @ N2 ) @ ( F @ N4 ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % lift_Suc_mono_le
% 3.82/4.00 thf(fact_242_lift__Suc__mono__le,axiom,
% 3.82/4.00 ! [F: nat > set_int,N2: nat,N4: nat] :
% 3.82/4.00 ( ! [N3: nat] : ( ord_less_eq_set_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 3.82/4.00 => ( ( ord_less_eq_nat @ N2 @ N4 )
% 3.82/4.00 => ( ord_less_eq_set_int @ ( F @ N2 ) @ ( F @ N4 ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % lift_Suc_mono_le
% 3.82/4.00 thf(fact_243_lift__Suc__mono__le,axiom,
% 3.82/4.00 ! [F: nat > nat,N2: nat,N4: nat] :
% 3.82/4.00 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 3.82/4.00 => ( ( ord_less_eq_nat @ N2 @ N4 )
% 3.82/4.00 => ( ord_less_eq_nat @ ( F @ N2 ) @ ( F @ N4 ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % lift_Suc_mono_le
% 3.82/4.00 thf(fact_244_lift__Suc__mono__le,axiom,
% 3.82/4.00 ! [F: nat > int,N2: nat,N4: nat] :
% 3.82/4.00 ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 3.82/4.00 => ( ( ord_less_eq_nat @ N2 @ N4 )
% 3.82/4.00 => ( ord_less_eq_int @ ( F @ N2 ) @ ( F @ N4 ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % lift_Suc_mono_le
% 3.82/4.00 thf(fact_245_le__imp__less__Suc,axiom,
% 3.82/4.00 ! [M2: nat,N2: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.00 => ( ord_less_nat @ M2 @ ( suc @ N2 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % le_imp_less_Suc
% 3.82/4.00 thf(fact_246_less__eq__Suc__le,axiom,
% 3.82/4.00 ( ord_less_nat
% 3.82/4.00 = ( ^ [N: nat] : ( ord_less_eq_nat @ ( suc @ N ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % less_eq_Suc_le
% 3.82/4.00 thf(fact_247_less__Suc__eq__le,axiom,
% 3.82/4.00 ! [M2: nat,N2: nat] :
% 3.82/4.00 ( ( ord_less_nat @ M2 @ ( suc @ N2 ) )
% 3.82/4.00 = ( ord_less_eq_nat @ M2 @ N2 ) ) ).
% 3.82/4.00
% 3.82/4.00 % less_Suc_eq_le
% 3.82/4.00 thf(fact_248_le__less__Suc__eq,axiom,
% 3.82/4.00 ! [M2: nat,N2: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.00 => ( ( ord_less_nat @ N2 @ ( suc @ M2 ) )
% 3.82/4.00 = ( N2 = M2 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % le_less_Suc_eq
% 3.82/4.00 thf(fact_249_Suc__le__lessD,axiom,
% 3.82/4.00 ! [M2: nat,N2: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N2 )
% 3.82/4.00 => ( ord_less_nat @ M2 @ N2 ) ) ).
% 3.82/4.00
% 3.82/4.00 % Suc_le_lessD
% 3.82/4.00 thf(fact_250_inc__induct,axiom,
% 3.82/4.00 ! [I: nat,J: nat,P: nat > $o] :
% 3.82/4.00 ( ( ord_less_eq_nat @ I @ J )
% 3.82/4.00 => ( ( P @ J )
% 3.82/4.00 => ( ! [N3: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ I @ N3 )
% 3.82/4.00 => ( ( ord_less_nat @ N3 @ J )
% 3.82/4.00 => ( ( P @ ( suc @ N3 ) )
% 3.82/4.00 => ( P @ N3 ) ) ) )
% 3.82/4.00 => ( P @ I ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % inc_induct
% 3.82/4.00 thf(fact_251_dec__induct,axiom,
% 3.82/4.00 ! [I: nat,J: nat,P: nat > $o] :
% 3.82/4.00 ( ( ord_less_eq_nat @ I @ J )
% 3.82/4.00 => ( ( P @ I )
% 3.82/4.00 => ( ! [N3: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ I @ N3 )
% 3.82/4.00 => ( ( ord_less_nat @ N3 @ J )
% 3.82/4.00 => ( ( P @ N3 )
% 3.82/4.00 => ( P @ ( suc @ N3 ) ) ) ) )
% 3.82/4.00 => ( P @ J ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % dec_induct
% 3.82/4.00 thf(fact_252_Suc__le__eq,axiom,
% 3.82/4.00 ! [M2: nat,N2: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N2 )
% 3.82/4.00 = ( ord_less_nat @ M2 @ N2 ) ) ).
% 3.82/4.00
% 3.82/4.00 % Suc_le_eq
% 3.82/4.00 thf(fact_253_Suc__leI,axiom,
% 3.82/4.00 ! [M2: nat,N2: nat] :
% 3.82/4.00 ( ( ord_less_nat @ M2 @ N2 )
% 3.82/4.00 => ( ord_less_eq_nat @ ( suc @ M2 ) @ N2 ) ) ).
% 3.82/4.00
% 3.82/4.00 % Suc_leI
% 3.82/4.00 thf(fact_254_mono__nat__linear__lb,axiom,
% 3.82/4.00 ! [F: nat > nat,M2: nat,K: nat] :
% 3.82/4.00 ( ! [M3: nat,N3: nat] :
% 3.82/4.00 ( ( ord_less_nat @ M3 @ N3 )
% 3.82/4.00 => ( ord_less_nat @ ( F @ M3 ) @ ( F @ N3 ) ) )
% 3.82/4.00 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M2 ) @ K ) @ ( F @ ( plus_plus_nat @ M2 @ K ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % mono_nat_linear_lb
% 3.82/4.00 thf(fact_255_ex__least__nat__le,axiom,
% 3.82/4.00 ! [P: nat > $o,N2: nat] :
% 3.82/4.00 ( ( P @ N2 )
% 3.82/4.00 => ( ~ ( P @ zero_zero_nat )
% 3.82/4.00 => ? [K3: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ K3 @ N2 )
% 3.82/4.00 & ! [I5: nat] :
% 3.82/4.00 ( ( ord_less_nat @ I5 @ K3 )
% 3.82/4.00 => ~ ( P @ I5 ) )
% 3.82/4.00 & ( P @ K3 ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % ex_least_nat_le
% 3.82/4.00 thf(fact_256_list__eq__iff__nth__eq,axiom,
% 3.82/4.00 ( ( ^ [Y4: list_VEBT_VEBT,Z2: list_VEBT_VEBT] : ( Y4 = Z2 ) )
% 3.82/4.00 = ( ^ [Xs3: list_VEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 3.82/4.00 ( ( ( size_s6755466524823107622T_VEBT @ Xs3 )
% 3.82/4.00 = ( size_s6755466524823107622T_VEBT @ Ys3 ) )
% 3.82/4.00 & ! [I3: nat] :
% 3.82/4.00 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs3 ) )
% 3.82/4.00 => ( ( nth_VEBT_VEBT @ Xs3 @ I3 )
% 3.82/4.00 = ( nth_VEBT_VEBT @ Ys3 @ I3 ) ) ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % list_eq_iff_nth_eq
% 3.82/4.00 thf(fact_257_list__eq__iff__nth__eq,axiom,
% 3.82/4.00 ( ( ^ [Y4: list_int,Z2: list_int] : ( Y4 = Z2 ) )
% 3.82/4.00 = ( ^ [Xs3: list_int,Ys3: list_int] :
% 3.82/4.00 ( ( ( size_size_list_int @ Xs3 )
% 3.82/4.00 = ( size_size_list_int @ Ys3 ) )
% 3.82/4.00 & ! [I3: nat] :
% 3.82/4.00 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs3 ) )
% 3.82/4.00 => ( ( nth_int @ Xs3 @ I3 )
% 3.82/4.00 = ( nth_int @ Ys3 @ I3 ) ) ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % list_eq_iff_nth_eq
% 3.82/4.00 thf(fact_258_list__eq__iff__nth__eq,axiom,
% 3.82/4.00 ( ( ^ [Y4: list_nat,Z2: list_nat] : ( Y4 = Z2 ) )
% 3.82/4.00 = ( ^ [Xs3: list_nat,Ys3: list_nat] :
% 3.82/4.00 ( ( ( size_size_list_nat @ Xs3 )
% 3.82/4.00 = ( size_size_list_nat @ Ys3 ) )
% 3.82/4.00 & ! [I3: nat] :
% 3.82/4.00 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs3 ) )
% 3.82/4.00 => ( ( nth_nat @ Xs3 @ I3 )
% 3.82/4.00 = ( nth_nat @ Ys3 @ I3 ) ) ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % list_eq_iff_nth_eq
% 3.82/4.00 thf(fact_259_Skolem__list__nth,axiom,
% 3.82/4.00 ! [K: nat,P: nat > vEBT_VEBT > $o] :
% 3.82/4.00 ( ( ! [I3: nat] :
% 3.82/4.00 ( ( ord_less_nat @ I3 @ K )
% 3.82/4.00 => ? [X6: vEBT_VEBT] : ( P @ I3 @ X6 ) ) )
% 3.82/4.00 = ( ? [Xs3: list_VEBT_VEBT] :
% 3.82/4.00 ( ( ( size_s6755466524823107622T_VEBT @ Xs3 )
% 3.82/4.00 = K )
% 3.82/4.00 & ! [I3: nat] :
% 3.82/4.00 ( ( ord_less_nat @ I3 @ K )
% 3.82/4.00 => ( P @ I3 @ ( nth_VEBT_VEBT @ Xs3 @ I3 ) ) ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % Skolem_list_nth
% 3.82/4.00 thf(fact_260_Skolem__list__nth,axiom,
% 3.82/4.00 ! [K: nat,P: nat > int > $o] :
% 3.82/4.00 ( ( ! [I3: nat] :
% 3.82/4.00 ( ( ord_less_nat @ I3 @ K )
% 3.82/4.00 => ? [X6: int] : ( P @ I3 @ X6 ) ) )
% 3.82/4.00 = ( ? [Xs3: list_int] :
% 3.82/4.00 ( ( ( size_size_list_int @ Xs3 )
% 3.82/4.00 = K )
% 3.82/4.00 & ! [I3: nat] :
% 3.82/4.00 ( ( ord_less_nat @ I3 @ K )
% 3.82/4.00 => ( P @ I3 @ ( nth_int @ Xs3 @ I3 ) ) ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % Skolem_list_nth
% 3.82/4.00 thf(fact_261_Skolem__list__nth,axiom,
% 3.82/4.00 ! [K: nat,P: nat > nat > $o] :
% 3.82/4.00 ( ( ! [I3: nat] :
% 3.82/4.00 ( ( ord_less_nat @ I3 @ K )
% 3.82/4.00 => ? [X6: nat] : ( P @ I3 @ X6 ) ) )
% 3.82/4.00 = ( ? [Xs3: list_nat] :
% 3.82/4.00 ( ( ( size_size_list_nat @ Xs3 )
% 3.82/4.00 = K )
% 3.82/4.00 & ! [I3: nat] :
% 3.82/4.00 ( ( ord_less_nat @ I3 @ K )
% 3.82/4.00 => ( P @ I3 @ ( nth_nat @ Xs3 @ I3 ) ) ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % Skolem_list_nth
% 3.82/4.00 thf(fact_262_nth__equalityI,axiom,
% 3.82/4.00 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 3.82/4.00 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 3.82/4.00 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 3.82/4.00 => ( ! [I4: nat] :
% 3.82/4.00 ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 3.82/4.00 => ( ( nth_VEBT_VEBT @ Xs @ I4 )
% 3.82/4.00 = ( nth_VEBT_VEBT @ Ys @ I4 ) ) )
% 3.82/4.00 => ( Xs = Ys ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % nth_equalityI
% 3.82/4.00 thf(fact_263_nth__equalityI,axiom,
% 3.82/4.00 ! [Xs: list_int,Ys: list_int] :
% 3.82/4.00 ( ( ( size_size_list_int @ Xs )
% 3.82/4.00 = ( size_size_list_int @ Ys ) )
% 3.82/4.00 => ( ! [I4: nat] :
% 3.82/4.00 ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs ) )
% 3.82/4.00 => ( ( nth_int @ Xs @ I4 )
% 3.82/4.00 = ( nth_int @ Ys @ I4 ) ) )
% 3.82/4.00 => ( Xs = Ys ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % nth_equalityI
% 3.82/4.00 thf(fact_264_nth__equalityI,axiom,
% 3.82/4.00 ! [Xs: list_nat,Ys: list_nat] :
% 3.82/4.00 ( ( ( size_size_list_nat @ Xs )
% 3.82/4.00 = ( size_size_list_nat @ Ys ) )
% 3.82/4.00 => ( ! [I4: nat] :
% 3.82/4.00 ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs ) )
% 3.82/4.00 => ( ( nth_nat @ Xs @ I4 )
% 3.82/4.00 = ( nth_nat @ Ys @ I4 ) ) )
% 3.82/4.00 => ( Xs = Ys ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % nth_equalityI
% 3.82/4.00 thf(fact_265_set__update__subsetI,axiom,
% 3.82/4.00 ! [Xs: list_Extended_enat,A2: set_Extended_enat,X: extended_enat,I: nat] :
% 3.82/4.00 ( ( ord_le7203529160286727270d_enat @ ( set_Extended_enat2 @ Xs ) @ A2 )
% 3.82/4.00 => ( ( member_Extended_enat @ X @ A2 )
% 3.82/4.00 => ( ord_le7203529160286727270d_enat @ ( set_Extended_enat2 @ ( list_u3071683517702156500d_enat @ Xs @ I @ X ) ) @ A2 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % set_update_subsetI
% 3.82/4.00 thf(fact_266_set__update__subsetI,axiom,
% 3.82/4.00 ! [Xs: list_real,A2: set_real,X: real,I: nat] :
% 3.82/4.00 ( ( ord_less_eq_set_real @ ( set_real2 @ Xs ) @ A2 )
% 3.82/4.00 => ( ( member_real @ X @ A2 )
% 3.82/4.00 => ( ord_less_eq_set_real @ ( set_real2 @ ( list_update_real @ Xs @ I @ X ) ) @ A2 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % set_update_subsetI
% 3.82/4.00 thf(fact_267_set__update__subsetI,axiom,
% 3.82/4.00 ! [Xs: list_set_nat,A2: set_set_nat,X: set_nat,I: nat] :
% 3.82/4.00 ( ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ Xs ) @ A2 )
% 3.82/4.00 => ( ( member_set_nat @ X @ A2 )
% 3.82/4.00 => ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ ( list_update_set_nat @ Xs @ I @ X ) ) @ A2 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % set_update_subsetI
% 3.82/4.00 thf(fact_268_set__update__subsetI,axiom,
% 3.82/4.00 ! [Xs: list_VEBT_VEBT,A2: set_VEBT_VEBT,X: vEBT_VEBT,I: nat] :
% 3.82/4.00 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A2 )
% 3.82/4.00 => ( ( member_VEBT_VEBT @ X @ A2 )
% 3.82/4.00 => ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) ) @ A2 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % set_update_subsetI
% 3.82/4.00 thf(fact_269_set__update__subsetI,axiom,
% 3.82/4.00 ! [Xs: list_nat,A2: set_nat,X: nat,I: nat] :
% 3.82/4.00 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A2 )
% 3.82/4.00 => ( ( member_nat @ X @ A2 )
% 3.82/4.00 => ( ord_less_eq_set_nat @ ( set_nat2 @ ( list_update_nat @ Xs @ I @ X ) ) @ A2 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % set_update_subsetI
% 3.82/4.00 thf(fact_270_set__update__subsetI,axiom,
% 3.82/4.00 ! [Xs: list_int,A2: set_int,X: int,I: nat] :
% 3.82/4.00 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A2 )
% 3.82/4.00 => ( ( member_int @ X @ A2 )
% 3.82/4.00 => ( ord_less_eq_set_int @ ( set_int2 @ ( list_update_int @ Xs @ I @ X ) ) @ A2 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % set_update_subsetI
% 3.82/4.00 thf(fact_271_all__set__conv__all__nth,axiom,
% 3.82/4.00 ! [Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 3.82/4.00 ( ( ! [X4: vEBT_VEBT] :
% 3.82/4.00 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs ) )
% 3.82/4.00 => ( P @ X4 ) ) )
% 3.82/4.00 = ( ! [I3: nat] :
% 3.82/4.00 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 3.82/4.00 => ( P @ ( nth_VEBT_VEBT @ Xs @ I3 ) ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % all_set_conv_all_nth
% 3.82/4.00 thf(fact_272_all__set__conv__all__nth,axiom,
% 3.82/4.00 ! [Xs: list_int,P: int > $o] :
% 3.82/4.00 ( ( ! [X4: int] :
% 3.82/4.00 ( ( member_int @ X4 @ ( set_int2 @ Xs ) )
% 3.82/4.00 => ( P @ X4 ) ) )
% 3.82/4.00 = ( ! [I3: nat] :
% 3.82/4.00 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs ) )
% 3.82/4.00 => ( P @ ( nth_int @ Xs @ I3 ) ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % all_set_conv_all_nth
% 3.82/4.00 thf(fact_273_all__set__conv__all__nth,axiom,
% 3.82/4.00 ! [Xs: list_nat,P: nat > $o] :
% 3.82/4.00 ( ( ! [X4: nat] :
% 3.82/4.00 ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 3.82/4.00 => ( P @ X4 ) ) )
% 3.82/4.00 = ( ! [I3: nat] :
% 3.82/4.00 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 3.82/4.00 => ( P @ ( nth_nat @ Xs @ I3 ) ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % all_set_conv_all_nth
% 3.82/4.00 thf(fact_274_all__nth__imp__all__set,axiom,
% 3.82/4.00 ! [Xs: list_Extended_enat,P: extended_enat > $o,X: extended_enat] :
% 3.82/4.00 ( ! [I4: nat] :
% 3.82/4.00 ( ( ord_less_nat @ I4 @ ( size_s3941691890525107288d_enat @ Xs ) )
% 3.82/4.00 => ( P @ ( nth_Extended_enat @ Xs @ I4 ) ) )
% 3.82/4.00 => ( ( member_Extended_enat @ X @ ( set_Extended_enat2 @ Xs ) )
% 3.82/4.00 => ( P @ X ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % all_nth_imp_all_set
% 3.82/4.00 thf(fact_275_all__nth__imp__all__set,axiom,
% 3.82/4.00 ! [Xs: list_real,P: real > $o,X: real] :
% 3.82/4.00 ( ! [I4: nat] :
% 3.82/4.00 ( ( ord_less_nat @ I4 @ ( size_size_list_real @ Xs ) )
% 3.82/4.00 => ( P @ ( nth_real @ Xs @ I4 ) ) )
% 3.82/4.00 => ( ( member_real @ X @ ( set_real2 @ Xs ) )
% 3.82/4.00 => ( P @ X ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % all_nth_imp_all_set
% 3.82/4.00 thf(fact_276_all__nth__imp__all__set,axiom,
% 3.82/4.00 ! [Xs: list_set_nat,P: set_nat > $o,X: set_nat] :
% 3.82/4.00 ( ! [I4: nat] :
% 3.82/4.00 ( ( ord_less_nat @ I4 @ ( size_s3254054031482475050et_nat @ Xs ) )
% 3.82/4.00 => ( P @ ( nth_set_nat @ Xs @ I4 ) ) )
% 3.82/4.00 => ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs ) )
% 3.82/4.00 => ( P @ X ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % all_nth_imp_all_set
% 3.82/4.00 thf(fact_277_all__nth__imp__all__set,axiom,
% 3.82/4.00 ! [Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o,X: vEBT_VEBT] :
% 3.82/4.00 ( ! [I4: nat] :
% 3.82/4.00 ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 3.82/4.00 => ( P @ ( nth_VEBT_VEBT @ Xs @ I4 ) ) )
% 3.82/4.00 => ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 3.82/4.00 => ( P @ X ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % all_nth_imp_all_set
% 3.82/4.00 thf(fact_278_all__nth__imp__all__set,axiom,
% 3.82/4.00 ! [Xs: list_int,P: int > $o,X: int] :
% 3.82/4.00 ( ! [I4: nat] :
% 3.82/4.00 ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs ) )
% 3.82/4.00 => ( P @ ( nth_int @ Xs @ I4 ) ) )
% 3.82/4.00 => ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 3.82/4.00 => ( P @ X ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % all_nth_imp_all_set
% 3.82/4.00 thf(fact_279_all__nth__imp__all__set,axiom,
% 3.82/4.00 ! [Xs: list_nat,P: nat > $o,X: nat] :
% 3.82/4.00 ( ! [I4: nat] :
% 3.82/4.00 ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs ) )
% 3.82/4.00 => ( P @ ( nth_nat @ Xs @ I4 ) ) )
% 3.82/4.00 => ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 3.82/4.00 => ( P @ X ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % all_nth_imp_all_set
% 3.82/4.00 thf(fact_280_in__set__conv__nth,axiom,
% 3.82/4.00 ! [X: extended_enat,Xs: list_Extended_enat] :
% 3.82/4.00 ( ( member_Extended_enat @ X @ ( set_Extended_enat2 @ Xs ) )
% 3.82/4.00 = ( ? [I3: nat] :
% 3.82/4.00 ( ( ord_less_nat @ I3 @ ( size_s3941691890525107288d_enat @ Xs ) )
% 3.82/4.00 & ( ( nth_Extended_enat @ Xs @ I3 )
% 3.82/4.00 = X ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % in_set_conv_nth
% 3.82/4.00 thf(fact_281_in__set__conv__nth,axiom,
% 3.82/4.00 ! [X: real,Xs: list_real] :
% 3.82/4.00 ( ( member_real @ X @ ( set_real2 @ Xs ) )
% 3.82/4.00 = ( ? [I3: nat] :
% 3.82/4.00 ( ( ord_less_nat @ I3 @ ( size_size_list_real @ Xs ) )
% 3.82/4.00 & ( ( nth_real @ Xs @ I3 )
% 3.82/4.00 = X ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % in_set_conv_nth
% 3.82/4.00 thf(fact_282_in__set__conv__nth,axiom,
% 3.82/4.00 ! [X: set_nat,Xs: list_set_nat] :
% 3.82/4.00 ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs ) )
% 3.82/4.00 = ( ? [I3: nat] :
% 3.82/4.00 ( ( ord_less_nat @ I3 @ ( size_s3254054031482475050et_nat @ Xs ) )
% 3.82/4.00 & ( ( nth_set_nat @ Xs @ I3 )
% 3.82/4.00 = X ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % in_set_conv_nth
% 3.82/4.00 thf(fact_283_in__set__conv__nth,axiom,
% 3.82/4.00 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 3.82/4.00 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 3.82/4.00 = ( ? [I3: nat] :
% 3.82/4.00 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 3.82/4.00 & ( ( nth_VEBT_VEBT @ Xs @ I3 )
% 3.82/4.00 = X ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % in_set_conv_nth
% 3.82/4.00 thf(fact_284_in__set__conv__nth,axiom,
% 3.82/4.00 ! [X: int,Xs: list_int] :
% 3.82/4.00 ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 3.82/4.00 = ( ? [I3: nat] :
% 3.82/4.00 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs ) )
% 3.82/4.00 & ( ( nth_int @ Xs @ I3 )
% 3.82/4.00 = X ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % in_set_conv_nth
% 3.82/4.00 thf(fact_285_in__set__conv__nth,axiom,
% 3.82/4.00 ! [X: nat,Xs: list_nat] :
% 3.82/4.00 ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 3.82/4.00 = ( ? [I3: nat] :
% 3.82/4.00 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 3.82/4.00 & ( ( nth_nat @ Xs @ I3 )
% 3.82/4.00 = X ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % in_set_conv_nth
% 3.82/4.00 thf(fact_286_list__ball__nth,axiom,
% 3.82/4.00 ! [N2: nat,Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 3.82/4.00 ( ( ord_less_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 3.82/4.00 => ( ! [X5: vEBT_VEBT] :
% 3.82/4.00 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ Xs ) )
% 3.82/4.00 => ( P @ X5 ) )
% 3.82/4.00 => ( P @ ( nth_VEBT_VEBT @ Xs @ N2 ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % list_ball_nth
% 3.82/4.00 thf(fact_287_list__ball__nth,axiom,
% 3.82/4.00 ! [N2: nat,Xs: list_int,P: int > $o] :
% 3.82/4.00 ( ( ord_less_nat @ N2 @ ( size_size_list_int @ Xs ) )
% 3.82/4.00 => ( ! [X5: int] :
% 3.82/4.00 ( ( member_int @ X5 @ ( set_int2 @ Xs ) )
% 3.82/4.00 => ( P @ X5 ) )
% 3.82/4.00 => ( P @ ( nth_int @ Xs @ N2 ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % list_ball_nth
% 3.82/4.00 thf(fact_288_list__ball__nth,axiom,
% 3.82/4.00 ! [N2: nat,Xs: list_nat,P: nat > $o] :
% 3.82/4.00 ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs ) )
% 3.82/4.00 => ( ! [X5: nat] :
% 3.82/4.00 ( ( member_nat @ X5 @ ( set_nat2 @ Xs ) )
% 3.82/4.00 => ( P @ X5 ) )
% 3.82/4.00 => ( P @ ( nth_nat @ Xs @ N2 ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % list_ball_nth
% 3.82/4.00 thf(fact_289_nth__mem,axiom,
% 3.82/4.00 ! [N2: nat,Xs: list_Extended_enat] :
% 3.82/4.00 ( ( ord_less_nat @ N2 @ ( size_s3941691890525107288d_enat @ Xs ) )
% 3.82/4.00 => ( member_Extended_enat @ ( nth_Extended_enat @ Xs @ N2 ) @ ( set_Extended_enat2 @ Xs ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % nth_mem
% 3.82/4.00 thf(fact_290_nth__mem,axiom,
% 3.82/4.00 ! [N2: nat,Xs: list_real] :
% 3.82/4.00 ( ( ord_less_nat @ N2 @ ( size_size_list_real @ Xs ) )
% 3.82/4.00 => ( member_real @ ( nth_real @ Xs @ N2 ) @ ( set_real2 @ Xs ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % nth_mem
% 3.82/4.00 thf(fact_291_nth__mem,axiom,
% 3.82/4.00 ! [N2: nat,Xs: list_set_nat] :
% 3.82/4.00 ( ( ord_less_nat @ N2 @ ( size_s3254054031482475050et_nat @ Xs ) )
% 3.82/4.00 => ( member_set_nat @ ( nth_set_nat @ Xs @ N2 ) @ ( set_set_nat2 @ Xs ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % nth_mem
% 3.82/4.00 thf(fact_292_nth__mem,axiom,
% 3.82/4.00 ! [N2: nat,Xs: list_VEBT_VEBT] :
% 3.82/4.00 ( ( ord_less_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 3.82/4.00 => ( member_VEBT_VEBT @ ( nth_VEBT_VEBT @ Xs @ N2 ) @ ( set_VEBT_VEBT2 @ Xs ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % nth_mem
% 3.82/4.00 thf(fact_293_nth__mem,axiom,
% 3.82/4.00 ! [N2: nat,Xs: list_int] :
% 3.82/4.00 ( ( ord_less_nat @ N2 @ ( size_size_list_int @ Xs ) )
% 3.82/4.00 => ( member_int @ ( nth_int @ Xs @ N2 ) @ ( set_int2 @ Xs ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % nth_mem
% 3.82/4.00 thf(fact_294_nth__mem,axiom,
% 3.82/4.00 ! [N2: nat,Xs: list_nat] :
% 3.82/4.00 ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs ) )
% 3.82/4.00 => ( member_nat @ ( nth_nat @ Xs @ N2 ) @ ( set_nat2 @ Xs ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % nth_mem
% 3.82/4.00 thf(fact_295_order__antisym__conv,axiom,
% 3.82/4.00 ! [Y: real,X: real] :
% 3.82/4.00 ( ( ord_less_eq_real @ Y @ X )
% 3.82/4.00 => ( ( ord_less_eq_real @ X @ Y )
% 3.82/4.00 = ( X = Y ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % order_antisym_conv
% 3.82/4.00 thf(fact_296_order__antisym__conv,axiom,
% 3.82/4.00 ! [Y: set_nat,X: set_nat] :
% 3.82/4.00 ( ( ord_less_eq_set_nat @ Y @ X )
% 3.82/4.00 => ( ( ord_less_eq_set_nat @ X @ Y )
% 3.82/4.00 = ( X = Y ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % order_antisym_conv
% 3.82/4.00 thf(fact_297_order__antisym__conv,axiom,
% 3.82/4.00 ! [Y: set_int,X: set_int] :
% 3.82/4.00 ( ( ord_less_eq_set_int @ Y @ X )
% 3.82/4.00 => ( ( ord_less_eq_set_int @ X @ Y )
% 3.82/4.00 = ( X = Y ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % order_antisym_conv
% 3.82/4.00 thf(fact_298_order__antisym__conv,axiom,
% 3.82/4.00 ! [Y: nat,X: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ Y @ X )
% 3.82/4.00 => ( ( ord_less_eq_nat @ X @ Y )
% 3.82/4.00 = ( X = Y ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % order_antisym_conv
% 3.82/4.00 thf(fact_299_order__antisym__conv,axiom,
% 3.82/4.00 ! [Y: int,X: int] :
% 3.82/4.00 ( ( ord_less_eq_int @ Y @ X )
% 3.82/4.00 => ( ( ord_less_eq_int @ X @ Y )
% 3.82/4.00 = ( X = Y ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % order_antisym_conv
% 3.82/4.00 thf(fact_300_linorder__le__cases,axiom,
% 3.82/4.00 ! [X: real,Y: real] :
% 3.82/4.00 ( ~ ( ord_less_eq_real @ X @ Y )
% 3.82/4.00 => ( ord_less_eq_real @ Y @ X ) ) ).
% 3.82/4.00
% 3.82/4.00 % linorder_le_cases
% 3.82/4.00 thf(fact_301_linorder__le__cases,axiom,
% 3.82/4.00 ! [X: nat,Y: nat] :
% 3.82/4.00 ( ~ ( ord_less_eq_nat @ X @ Y )
% 3.82/4.00 => ( ord_less_eq_nat @ Y @ X ) ) ).
% 3.82/4.00
% 3.82/4.00 % linorder_le_cases
% 3.82/4.00 thf(fact_302_linorder__le__cases,axiom,
% 3.82/4.00 ! [X: int,Y: int] :
% 3.82/4.00 ( ~ ( ord_less_eq_int @ X @ Y )
% 3.82/4.00 => ( ord_less_eq_int @ Y @ X ) ) ).
% 3.82/4.00
% 3.82/4.00 % linorder_le_cases
% 3.82/4.00 thf(fact_303_ord__le__eq__subst,axiom,
% 3.82/4.00 ! [A: real,B2: real,F: real > real,C: real] :
% 3.82/4.00 ( ( ord_less_eq_real @ A @ B2 )
% 3.82/4.00 => ( ( ( F @ B2 )
% 3.82/4.00 = C )
% 3.82/4.00 => ( ! [X5: real,Y3: real] :
% 3.82/4.00 ( ( ord_less_eq_real @ X5 @ Y3 )
% 3.82/4.00 => ( ord_less_eq_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.00 => ( ord_less_eq_real @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % ord_le_eq_subst
% 3.82/4.00 thf(fact_304_ord__le__eq__subst,axiom,
% 3.82/4.00 ! [A: real,B2: real,F: real > nat,C: nat] :
% 3.82/4.00 ( ( ord_less_eq_real @ A @ B2 )
% 3.82/4.00 => ( ( ( F @ B2 )
% 3.82/4.00 = C )
% 3.82/4.00 => ( ! [X5: real,Y3: real] :
% 3.82/4.00 ( ( ord_less_eq_real @ X5 @ Y3 )
% 3.82/4.00 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.00 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % ord_le_eq_subst
% 3.82/4.00 thf(fact_305_ord__le__eq__subst,axiom,
% 3.82/4.00 ! [A: real,B2: real,F: real > int,C: int] :
% 3.82/4.00 ( ( ord_less_eq_real @ A @ B2 )
% 3.82/4.00 => ( ( ( F @ B2 )
% 3.82/4.00 = C )
% 3.82/4.00 => ( ! [X5: real,Y3: real] :
% 3.82/4.00 ( ( ord_less_eq_real @ X5 @ Y3 )
% 3.82/4.00 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.00 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % ord_le_eq_subst
% 3.82/4.00 thf(fact_306_ord__le__eq__subst,axiom,
% 3.82/4.00 ! [A: nat,B2: nat,F: nat > real,C: real] :
% 3.82/4.00 ( ( ord_less_eq_nat @ A @ B2 )
% 3.82/4.00 => ( ( ( F @ B2 )
% 3.82/4.00 = C )
% 3.82/4.00 => ( ! [X5: nat,Y3: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 3.82/4.00 => ( ord_less_eq_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.00 => ( ord_less_eq_real @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % ord_le_eq_subst
% 3.82/4.00 thf(fact_307_ord__le__eq__subst,axiom,
% 3.82/4.00 ! [A: nat,B2: nat,F: nat > nat,C: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ A @ B2 )
% 3.82/4.00 => ( ( ( F @ B2 )
% 3.82/4.00 = C )
% 3.82/4.00 => ( ! [X5: nat,Y3: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 3.82/4.00 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.00 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % ord_le_eq_subst
% 3.82/4.00 thf(fact_308_ord__le__eq__subst,axiom,
% 3.82/4.00 ! [A: nat,B2: nat,F: nat > int,C: int] :
% 3.82/4.00 ( ( ord_less_eq_nat @ A @ B2 )
% 3.82/4.00 => ( ( ( F @ B2 )
% 3.82/4.00 = C )
% 3.82/4.00 => ( ! [X5: nat,Y3: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 3.82/4.00 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.00 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % ord_le_eq_subst
% 3.82/4.00 thf(fact_309_ord__le__eq__subst,axiom,
% 3.82/4.00 ! [A: int,B2: int,F: int > real,C: real] :
% 3.82/4.00 ( ( ord_less_eq_int @ A @ B2 )
% 3.82/4.00 => ( ( ( F @ B2 )
% 3.82/4.00 = C )
% 3.82/4.00 => ( ! [X5: int,Y3: int] :
% 3.82/4.00 ( ( ord_less_eq_int @ X5 @ Y3 )
% 3.82/4.00 => ( ord_less_eq_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.00 => ( ord_less_eq_real @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % ord_le_eq_subst
% 3.82/4.00 thf(fact_310_ord__le__eq__subst,axiom,
% 3.82/4.00 ! [A: int,B2: int,F: int > nat,C: nat] :
% 3.82/4.00 ( ( ord_less_eq_int @ A @ B2 )
% 3.82/4.00 => ( ( ( F @ B2 )
% 3.82/4.00 = C )
% 3.82/4.00 => ( ! [X5: int,Y3: int] :
% 3.82/4.00 ( ( ord_less_eq_int @ X5 @ Y3 )
% 3.82/4.00 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.00 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % ord_le_eq_subst
% 3.82/4.00 thf(fact_311_ord__le__eq__subst,axiom,
% 3.82/4.00 ! [A: int,B2: int,F: int > int,C: int] :
% 3.82/4.00 ( ( ord_less_eq_int @ A @ B2 )
% 3.82/4.00 => ( ( ( F @ B2 )
% 3.82/4.00 = C )
% 3.82/4.00 => ( ! [X5: int,Y3: int] :
% 3.82/4.00 ( ( ord_less_eq_int @ X5 @ Y3 )
% 3.82/4.00 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.00 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % ord_le_eq_subst
% 3.82/4.00 thf(fact_312_ord__le__eq__subst,axiom,
% 3.82/4.00 ! [A: real,B2: real,F: real > set_nat,C: set_nat] :
% 3.82/4.00 ( ( ord_less_eq_real @ A @ B2 )
% 3.82/4.00 => ( ( ( F @ B2 )
% 3.82/4.00 = C )
% 3.82/4.00 => ( ! [X5: real,Y3: real] :
% 3.82/4.00 ( ( ord_less_eq_real @ X5 @ Y3 )
% 3.82/4.00 => ( ord_less_eq_set_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.00 => ( ord_less_eq_set_nat @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % ord_le_eq_subst
% 3.82/4.00 thf(fact_313_ord__eq__le__subst,axiom,
% 3.82/4.00 ! [A: real,F: real > real,B2: real,C: real] :
% 3.82/4.00 ( ( A
% 3.82/4.00 = ( F @ B2 ) )
% 3.82/4.00 => ( ( ord_less_eq_real @ B2 @ C )
% 3.82/4.00 => ( ! [X5: real,Y3: real] :
% 3.82/4.00 ( ( ord_less_eq_real @ X5 @ Y3 )
% 3.82/4.00 => ( ord_less_eq_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.00 => ( ord_less_eq_real @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % ord_eq_le_subst
% 3.82/4.00 thf(fact_314_ord__eq__le__subst,axiom,
% 3.82/4.00 ! [A: nat,F: real > nat,B2: real,C: real] :
% 3.82/4.00 ( ( A
% 3.82/4.00 = ( F @ B2 ) )
% 3.82/4.00 => ( ( ord_less_eq_real @ B2 @ C )
% 3.82/4.00 => ( ! [X5: real,Y3: real] :
% 3.82/4.00 ( ( ord_less_eq_real @ X5 @ Y3 )
% 3.82/4.00 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.00 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % ord_eq_le_subst
% 3.82/4.00 thf(fact_315_ord__eq__le__subst,axiom,
% 3.82/4.00 ! [A: int,F: real > int,B2: real,C: real] :
% 3.82/4.00 ( ( A
% 3.82/4.00 = ( F @ B2 ) )
% 3.82/4.00 => ( ( ord_less_eq_real @ B2 @ C )
% 3.82/4.00 => ( ! [X5: real,Y3: real] :
% 3.82/4.00 ( ( ord_less_eq_real @ X5 @ Y3 )
% 3.82/4.00 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.00 => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % ord_eq_le_subst
% 3.82/4.00 thf(fact_316_ord__eq__le__subst,axiom,
% 3.82/4.00 ! [A: real,F: nat > real,B2: nat,C: nat] :
% 3.82/4.00 ( ( A
% 3.82/4.00 = ( F @ B2 ) )
% 3.82/4.00 => ( ( ord_less_eq_nat @ B2 @ C )
% 3.82/4.00 => ( ! [X5: nat,Y3: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 3.82/4.00 => ( ord_less_eq_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.00 => ( ord_less_eq_real @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % ord_eq_le_subst
% 3.82/4.00 thf(fact_317_ord__eq__le__subst,axiom,
% 3.82/4.00 ! [A: nat,F: nat > nat,B2: nat,C: nat] :
% 3.82/4.00 ( ( A
% 3.82/4.00 = ( F @ B2 ) )
% 3.82/4.00 => ( ( ord_less_eq_nat @ B2 @ C )
% 3.82/4.00 => ( ! [X5: nat,Y3: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 3.82/4.00 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.00 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % ord_eq_le_subst
% 3.82/4.00 thf(fact_318_ord__eq__le__subst,axiom,
% 3.82/4.00 ! [A: int,F: nat > int,B2: nat,C: nat] :
% 3.82/4.00 ( ( A
% 3.82/4.00 = ( F @ B2 ) )
% 3.82/4.00 => ( ( ord_less_eq_nat @ B2 @ C )
% 3.82/4.00 => ( ! [X5: nat,Y3: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 3.82/4.00 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.00 => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % ord_eq_le_subst
% 3.82/4.00 thf(fact_319_ord__eq__le__subst,axiom,
% 3.82/4.00 ! [A: real,F: int > real,B2: int,C: int] :
% 3.82/4.00 ( ( A
% 3.82/4.00 = ( F @ B2 ) )
% 3.82/4.00 => ( ( ord_less_eq_int @ B2 @ C )
% 3.82/4.00 => ( ! [X5: int,Y3: int] :
% 3.82/4.00 ( ( ord_less_eq_int @ X5 @ Y3 )
% 3.82/4.00 => ( ord_less_eq_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.00 => ( ord_less_eq_real @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % ord_eq_le_subst
% 3.82/4.00 thf(fact_320_ord__eq__le__subst,axiom,
% 3.82/4.00 ! [A: nat,F: int > nat,B2: int,C: int] :
% 3.82/4.00 ( ( A
% 3.82/4.00 = ( F @ B2 ) )
% 3.82/4.00 => ( ( ord_less_eq_int @ B2 @ C )
% 3.82/4.00 => ( ! [X5: int,Y3: int] :
% 3.82/4.00 ( ( ord_less_eq_int @ X5 @ Y3 )
% 3.82/4.00 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.00 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % ord_eq_le_subst
% 3.82/4.00 thf(fact_321_ord__eq__le__subst,axiom,
% 3.82/4.00 ! [A: int,F: int > int,B2: int,C: int] :
% 3.82/4.00 ( ( A
% 3.82/4.00 = ( F @ B2 ) )
% 3.82/4.00 => ( ( ord_less_eq_int @ B2 @ C )
% 3.82/4.00 => ( ! [X5: int,Y3: int] :
% 3.82/4.00 ( ( ord_less_eq_int @ X5 @ Y3 )
% 3.82/4.00 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.00 => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % ord_eq_le_subst
% 3.82/4.00 thf(fact_322_ord__eq__le__subst,axiom,
% 3.82/4.00 ! [A: set_nat,F: real > set_nat,B2: real,C: real] :
% 3.82/4.00 ( ( A
% 3.82/4.00 = ( F @ B2 ) )
% 3.82/4.00 => ( ( ord_less_eq_real @ B2 @ C )
% 3.82/4.00 => ( ! [X5: real,Y3: real] :
% 3.82/4.00 ( ( ord_less_eq_real @ X5 @ Y3 )
% 3.82/4.00 => ( ord_less_eq_set_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.00 => ( ord_less_eq_set_nat @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % ord_eq_le_subst
% 3.82/4.00 thf(fact_323_linorder__linear,axiom,
% 3.82/4.00 ! [X: real,Y: real] :
% 3.82/4.00 ( ( ord_less_eq_real @ X @ Y )
% 3.82/4.00 | ( ord_less_eq_real @ Y @ X ) ) ).
% 3.82/4.00
% 3.82/4.00 % linorder_linear
% 3.82/4.00 thf(fact_324_linorder__linear,axiom,
% 3.82/4.00 ! [X: nat,Y: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ X @ Y )
% 3.82/4.00 | ( ord_less_eq_nat @ Y @ X ) ) ).
% 3.82/4.00
% 3.82/4.00 % linorder_linear
% 3.82/4.00 thf(fact_325_linorder__linear,axiom,
% 3.82/4.00 ! [X: int,Y: int] :
% 3.82/4.00 ( ( ord_less_eq_int @ X @ Y )
% 3.82/4.00 | ( ord_less_eq_int @ Y @ X ) ) ).
% 3.82/4.00
% 3.82/4.00 % linorder_linear
% 3.82/4.00 thf(fact_326_order__eq__refl,axiom,
% 3.82/4.00 ! [X: real,Y: real] :
% 3.82/4.00 ( ( X = Y )
% 3.82/4.00 => ( ord_less_eq_real @ X @ Y ) ) ).
% 3.82/4.00
% 3.82/4.00 % order_eq_refl
% 3.82/4.00 thf(fact_327_order__eq__refl,axiom,
% 3.82/4.00 ! [X: set_nat,Y: set_nat] :
% 3.82/4.00 ( ( X = Y )
% 3.82/4.00 => ( ord_less_eq_set_nat @ X @ Y ) ) ).
% 3.82/4.00
% 3.82/4.00 % order_eq_refl
% 3.82/4.00 thf(fact_328_order__eq__refl,axiom,
% 3.82/4.00 ! [X: set_int,Y: set_int] :
% 3.82/4.00 ( ( X = Y )
% 3.82/4.00 => ( ord_less_eq_set_int @ X @ Y ) ) ).
% 3.82/4.00
% 3.82/4.00 % order_eq_refl
% 3.82/4.00 thf(fact_329_order__eq__refl,axiom,
% 3.82/4.00 ! [X: nat,Y: nat] :
% 3.82/4.00 ( ( X = Y )
% 3.82/4.00 => ( ord_less_eq_nat @ X @ Y ) ) ).
% 3.82/4.00
% 3.82/4.00 % order_eq_refl
% 3.82/4.00 thf(fact_330_order__eq__refl,axiom,
% 3.82/4.00 ! [X: int,Y: int] :
% 3.82/4.00 ( ( X = Y )
% 3.82/4.00 => ( ord_less_eq_int @ X @ Y ) ) ).
% 3.82/4.00
% 3.82/4.00 % order_eq_refl
% 3.82/4.00 thf(fact_331_order__subst2,axiom,
% 3.82/4.00 ! [A: real,B2: real,F: real > real,C: real] :
% 3.82/4.00 ( ( ord_less_eq_real @ A @ B2 )
% 3.82/4.00 => ( ( ord_less_eq_real @ ( F @ B2 ) @ C )
% 3.82/4.00 => ( ! [X5: real,Y3: real] :
% 3.82/4.00 ( ( ord_less_eq_real @ X5 @ Y3 )
% 3.82/4.00 => ( ord_less_eq_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.00 => ( ord_less_eq_real @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % order_subst2
% 3.82/4.00 thf(fact_332_order__subst2,axiom,
% 3.82/4.00 ! [A: real,B2: real,F: real > nat,C: nat] :
% 3.82/4.00 ( ( ord_less_eq_real @ A @ B2 )
% 3.82/4.00 => ( ( ord_less_eq_nat @ ( F @ B2 ) @ C )
% 3.82/4.00 => ( ! [X5: real,Y3: real] :
% 3.82/4.00 ( ( ord_less_eq_real @ X5 @ Y3 )
% 3.82/4.00 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.00 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % order_subst2
% 3.82/4.00 thf(fact_333_order__subst2,axiom,
% 3.82/4.00 ! [A: real,B2: real,F: real > int,C: int] :
% 3.82/4.00 ( ( ord_less_eq_real @ A @ B2 )
% 3.82/4.00 => ( ( ord_less_eq_int @ ( F @ B2 ) @ C )
% 3.82/4.00 => ( ! [X5: real,Y3: real] :
% 3.82/4.00 ( ( ord_less_eq_real @ X5 @ Y3 )
% 3.82/4.00 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.00 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % order_subst2
% 3.82/4.00 thf(fact_334_order__subst2,axiom,
% 3.82/4.00 ! [A: nat,B2: nat,F: nat > real,C: real] :
% 3.82/4.00 ( ( ord_less_eq_nat @ A @ B2 )
% 3.82/4.00 => ( ( ord_less_eq_real @ ( F @ B2 ) @ C )
% 3.82/4.00 => ( ! [X5: nat,Y3: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 3.82/4.00 => ( ord_less_eq_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.00 => ( ord_less_eq_real @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % order_subst2
% 3.82/4.00 thf(fact_335_order__subst2,axiom,
% 3.82/4.00 ! [A: nat,B2: nat,F: nat > nat,C: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ A @ B2 )
% 3.82/4.00 => ( ( ord_less_eq_nat @ ( F @ B2 ) @ C )
% 3.82/4.00 => ( ! [X5: nat,Y3: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 3.82/4.00 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.00 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % order_subst2
% 3.82/4.00 thf(fact_336_order__subst2,axiom,
% 3.82/4.00 ! [A: nat,B2: nat,F: nat > int,C: int] :
% 3.82/4.00 ( ( ord_less_eq_nat @ A @ B2 )
% 3.82/4.00 => ( ( ord_less_eq_int @ ( F @ B2 ) @ C )
% 3.82/4.00 => ( ! [X5: nat,Y3: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 3.82/4.00 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.00 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % order_subst2
% 3.82/4.00 thf(fact_337_order__subst2,axiom,
% 3.82/4.00 ! [A: int,B2: int,F: int > real,C: real] :
% 3.82/4.00 ( ( ord_less_eq_int @ A @ B2 )
% 3.82/4.00 => ( ( ord_less_eq_real @ ( F @ B2 ) @ C )
% 3.82/4.00 => ( ! [X5: int,Y3: int] :
% 3.82/4.00 ( ( ord_less_eq_int @ X5 @ Y3 )
% 3.82/4.00 => ( ord_less_eq_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.00 => ( ord_less_eq_real @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % order_subst2
% 3.82/4.00 thf(fact_338_order__subst2,axiom,
% 3.82/4.00 ! [A: int,B2: int,F: int > nat,C: nat] :
% 3.82/4.00 ( ( ord_less_eq_int @ A @ B2 )
% 3.82/4.00 => ( ( ord_less_eq_nat @ ( F @ B2 ) @ C )
% 3.82/4.00 => ( ! [X5: int,Y3: int] :
% 3.82/4.00 ( ( ord_less_eq_int @ X5 @ Y3 )
% 3.82/4.00 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.00 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % order_subst2
% 3.82/4.00 thf(fact_339_order__subst2,axiom,
% 3.82/4.00 ! [A: int,B2: int,F: int > int,C: int] :
% 3.82/4.00 ( ( ord_less_eq_int @ A @ B2 )
% 3.82/4.00 => ( ( ord_less_eq_int @ ( F @ B2 ) @ C )
% 3.82/4.00 => ( ! [X5: int,Y3: int] :
% 3.82/4.00 ( ( ord_less_eq_int @ X5 @ Y3 )
% 3.82/4.00 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.00 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % order_subst2
% 3.82/4.00 thf(fact_340_order__subst2,axiom,
% 3.82/4.00 ! [A: real,B2: real,F: real > set_nat,C: set_nat] :
% 3.82/4.00 ( ( ord_less_eq_real @ A @ B2 )
% 3.82/4.00 => ( ( ord_less_eq_set_nat @ ( F @ B2 ) @ C )
% 3.82/4.00 => ( ! [X5: real,Y3: real] :
% 3.82/4.00 ( ( ord_less_eq_real @ X5 @ Y3 )
% 3.82/4.00 => ( ord_less_eq_set_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.00 => ( ord_less_eq_set_nat @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % order_subst2
% 3.82/4.00 thf(fact_341_order__subst1,axiom,
% 3.82/4.00 ! [A: real,F: real > real,B2: real,C: real] :
% 3.82/4.00 ( ( ord_less_eq_real @ A @ ( F @ B2 ) )
% 3.82/4.00 => ( ( ord_less_eq_real @ B2 @ C )
% 3.82/4.00 => ( ! [X5: real,Y3: real] :
% 3.82/4.00 ( ( ord_less_eq_real @ X5 @ Y3 )
% 3.82/4.00 => ( ord_less_eq_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.00 => ( ord_less_eq_real @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % order_subst1
% 3.82/4.00 thf(fact_342_order__subst1,axiom,
% 3.82/4.00 ! [A: real,F: nat > real,B2: nat,C: nat] :
% 3.82/4.00 ( ( ord_less_eq_real @ A @ ( F @ B2 ) )
% 3.82/4.00 => ( ( ord_less_eq_nat @ B2 @ C )
% 3.82/4.00 => ( ! [X5: nat,Y3: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 3.82/4.00 => ( ord_less_eq_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.00 => ( ord_less_eq_real @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % order_subst1
% 3.82/4.00 thf(fact_343_order__subst1,axiom,
% 3.82/4.00 ! [A: real,F: int > real,B2: int,C: int] :
% 3.82/4.00 ( ( ord_less_eq_real @ A @ ( F @ B2 ) )
% 3.82/4.00 => ( ( ord_less_eq_int @ B2 @ C )
% 3.82/4.00 => ( ! [X5: int,Y3: int] :
% 3.82/4.00 ( ( ord_less_eq_int @ X5 @ Y3 )
% 3.82/4.00 => ( ord_less_eq_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.00 => ( ord_less_eq_real @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % order_subst1
% 3.82/4.00 thf(fact_344_order__subst1,axiom,
% 3.82/4.00 ! [A: nat,F: real > nat,B2: real,C: real] :
% 3.82/4.00 ( ( ord_less_eq_nat @ A @ ( F @ B2 ) )
% 3.82/4.00 => ( ( ord_less_eq_real @ B2 @ C )
% 3.82/4.00 => ( ! [X5: real,Y3: real] :
% 3.82/4.00 ( ( ord_less_eq_real @ X5 @ Y3 )
% 3.82/4.00 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.00 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % order_subst1
% 3.82/4.00 thf(fact_345_order__subst1,axiom,
% 3.82/4.00 ! [A: nat,F: nat > nat,B2: nat,C: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ A @ ( F @ B2 ) )
% 3.82/4.00 => ( ( ord_less_eq_nat @ B2 @ C )
% 3.82/4.00 => ( ! [X5: nat,Y3: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 3.82/4.00 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.00 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % order_subst1
% 3.82/4.00 thf(fact_346_order__subst1,axiom,
% 3.82/4.00 ! [A: nat,F: int > nat,B2: int,C: int] :
% 3.82/4.00 ( ( ord_less_eq_nat @ A @ ( F @ B2 ) )
% 3.82/4.00 => ( ( ord_less_eq_int @ B2 @ C )
% 3.82/4.00 => ( ! [X5: int,Y3: int] :
% 3.82/4.00 ( ( ord_less_eq_int @ X5 @ Y3 )
% 3.82/4.00 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.00 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % order_subst1
% 3.82/4.00 thf(fact_347_order__subst1,axiom,
% 3.82/4.00 ! [A: int,F: real > int,B2: real,C: real] :
% 3.82/4.00 ( ( ord_less_eq_int @ A @ ( F @ B2 ) )
% 3.82/4.00 => ( ( ord_less_eq_real @ B2 @ C )
% 3.82/4.00 => ( ! [X5: real,Y3: real] :
% 3.82/4.00 ( ( ord_less_eq_real @ X5 @ Y3 )
% 3.82/4.00 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.00 => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % order_subst1
% 3.82/4.00 thf(fact_348_order__subst1,axiom,
% 3.82/4.00 ! [A: int,F: nat > int,B2: nat,C: nat] :
% 3.82/4.00 ( ( ord_less_eq_int @ A @ ( F @ B2 ) )
% 3.82/4.00 => ( ( ord_less_eq_nat @ B2 @ C )
% 3.82/4.00 => ( ! [X5: nat,Y3: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 3.82/4.00 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.00 => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % order_subst1
% 3.82/4.00 thf(fact_349_order__subst1,axiom,
% 3.82/4.00 ! [A: int,F: int > int,B2: int,C: int] :
% 3.82/4.00 ( ( ord_less_eq_int @ A @ ( F @ B2 ) )
% 3.82/4.00 => ( ( ord_less_eq_int @ B2 @ C )
% 3.82/4.00 => ( ! [X5: int,Y3: int] :
% 3.82/4.00 ( ( ord_less_eq_int @ X5 @ Y3 )
% 3.82/4.00 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.00 => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % order_subst1
% 3.82/4.00 thf(fact_350_order__subst1,axiom,
% 3.82/4.00 ! [A: real,F: set_nat > real,B2: set_nat,C: set_nat] :
% 3.82/4.00 ( ( ord_less_eq_real @ A @ ( F @ B2 ) )
% 3.82/4.00 => ( ( ord_less_eq_set_nat @ B2 @ C )
% 3.82/4.00 => ( ! [X5: set_nat,Y3: set_nat] :
% 3.82/4.00 ( ( ord_less_eq_set_nat @ X5 @ Y3 )
% 3.82/4.00 => ( ord_less_eq_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.00 => ( ord_less_eq_real @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % order_subst1
% 3.82/4.00 thf(fact_351_Orderings_Oorder__eq__iff,axiom,
% 3.82/4.00 ( ( ^ [Y4: real,Z2: real] : ( Y4 = Z2 ) )
% 3.82/4.00 = ( ^ [A3: real,B3: real] :
% 3.82/4.00 ( ( ord_less_eq_real @ A3 @ B3 )
% 3.82/4.00 & ( ord_less_eq_real @ B3 @ A3 ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % Orderings.order_eq_iff
% 3.82/4.00 thf(fact_352_Orderings_Oorder__eq__iff,axiom,
% 3.82/4.00 ( ( ^ [Y4: set_nat,Z2: set_nat] : ( Y4 = Z2 ) )
% 3.82/4.00 = ( ^ [A3: set_nat,B3: set_nat] :
% 3.82/4.00 ( ( ord_less_eq_set_nat @ A3 @ B3 )
% 3.82/4.00 & ( ord_less_eq_set_nat @ B3 @ A3 ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % Orderings.order_eq_iff
% 3.82/4.00 thf(fact_353_Orderings_Oorder__eq__iff,axiom,
% 3.82/4.00 ( ( ^ [Y4: set_int,Z2: set_int] : ( Y4 = Z2 ) )
% 3.82/4.00 = ( ^ [A3: set_int,B3: set_int] :
% 3.82/4.00 ( ( ord_less_eq_set_int @ A3 @ B3 )
% 3.82/4.00 & ( ord_less_eq_set_int @ B3 @ A3 ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % Orderings.order_eq_iff
% 3.82/4.00 thf(fact_354_Orderings_Oorder__eq__iff,axiom,
% 3.82/4.00 ( ( ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 3.82/4.00 = ( ^ [A3: nat,B3: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ A3 @ B3 )
% 3.82/4.00 & ( ord_less_eq_nat @ B3 @ A3 ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % Orderings.order_eq_iff
% 3.82/4.00 thf(fact_355_Orderings_Oorder__eq__iff,axiom,
% 3.82/4.00 ( ( ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 3.82/4.00 = ( ^ [A3: int,B3: int] :
% 3.82/4.00 ( ( ord_less_eq_int @ A3 @ B3 )
% 3.82/4.00 & ( ord_less_eq_int @ B3 @ A3 ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % Orderings.order_eq_iff
% 3.82/4.00 thf(fact_356_antisym,axiom,
% 3.82/4.00 ! [A: real,B2: real] :
% 3.82/4.00 ( ( ord_less_eq_real @ A @ B2 )
% 3.82/4.00 => ( ( ord_less_eq_real @ B2 @ A )
% 3.82/4.00 => ( A = B2 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % antisym
% 3.82/4.00 thf(fact_357_antisym,axiom,
% 3.82/4.00 ! [A: set_nat,B2: set_nat] :
% 3.82/4.00 ( ( ord_less_eq_set_nat @ A @ B2 )
% 3.82/4.00 => ( ( ord_less_eq_set_nat @ B2 @ A )
% 3.82/4.00 => ( A = B2 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % antisym
% 3.82/4.00 thf(fact_358_antisym,axiom,
% 3.82/4.00 ! [A: set_int,B2: set_int] :
% 3.82/4.00 ( ( ord_less_eq_set_int @ A @ B2 )
% 3.82/4.00 => ( ( ord_less_eq_set_int @ B2 @ A )
% 3.82/4.00 => ( A = B2 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % antisym
% 3.82/4.00 thf(fact_359_antisym,axiom,
% 3.82/4.00 ! [A: nat,B2: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ A @ B2 )
% 3.82/4.00 => ( ( ord_less_eq_nat @ B2 @ A )
% 3.82/4.00 => ( A = B2 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % antisym
% 3.82/4.00 thf(fact_360_antisym,axiom,
% 3.82/4.00 ! [A: int,B2: int] :
% 3.82/4.00 ( ( ord_less_eq_int @ A @ B2 )
% 3.82/4.00 => ( ( ord_less_eq_int @ B2 @ A )
% 3.82/4.00 => ( A = B2 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % antisym
% 3.82/4.00 thf(fact_361_dual__order_Otrans,axiom,
% 3.82/4.00 ! [B2: real,A: real,C: real] :
% 3.82/4.00 ( ( ord_less_eq_real @ B2 @ A )
% 3.82/4.00 => ( ( ord_less_eq_real @ C @ B2 )
% 3.82/4.00 => ( ord_less_eq_real @ C @ A ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % dual_order.trans
% 3.82/4.00 thf(fact_362_dual__order_Otrans,axiom,
% 3.82/4.00 ! [B2: set_nat,A: set_nat,C: set_nat] :
% 3.82/4.00 ( ( ord_less_eq_set_nat @ B2 @ A )
% 3.82/4.00 => ( ( ord_less_eq_set_nat @ C @ B2 )
% 3.82/4.00 => ( ord_less_eq_set_nat @ C @ A ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % dual_order.trans
% 3.82/4.00 thf(fact_363_dual__order_Otrans,axiom,
% 3.82/4.00 ! [B2: set_int,A: set_int,C: set_int] :
% 3.82/4.00 ( ( ord_less_eq_set_int @ B2 @ A )
% 3.82/4.00 => ( ( ord_less_eq_set_int @ C @ B2 )
% 3.82/4.00 => ( ord_less_eq_set_int @ C @ A ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % dual_order.trans
% 3.82/4.00 thf(fact_364_dual__order_Otrans,axiom,
% 3.82/4.00 ! [B2: nat,A: nat,C: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ B2 @ A )
% 3.82/4.00 => ( ( ord_less_eq_nat @ C @ B2 )
% 3.82/4.00 => ( ord_less_eq_nat @ C @ A ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % dual_order.trans
% 3.82/4.00 thf(fact_365_dual__order_Otrans,axiom,
% 3.82/4.00 ! [B2: int,A: int,C: int] :
% 3.82/4.00 ( ( ord_less_eq_int @ B2 @ A )
% 3.82/4.00 => ( ( ord_less_eq_int @ C @ B2 )
% 3.82/4.00 => ( ord_less_eq_int @ C @ A ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % dual_order.trans
% 3.82/4.00 thf(fact_366_dual__order_Oantisym,axiom,
% 3.82/4.00 ! [B2: real,A: real] :
% 3.82/4.00 ( ( ord_less_eq_real @ B2 @ A )
% 3.82/4.00 => ( ( ord_less_eq_real @ A @ B2 )
% 3.82/4.00 => ( A = B2 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % dual_order.antisym
% 3.82/4.00 thf(fact_367_dual__order_Oantisym,axiom,
% 3.82/4.00 ! [B2: set_nat,A: set_nat] :
% 3.82/4.00 ( ( ord_less_eq_set_nat @ B2 @ A )
% 3.82/4.00 => ( ( ord_less_eq_set_nat @ A @ B2 )
% 3.82/4.00 => ( A = B2 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % dual_order.antisym
% 3.82/4.00 thf(fact_368_dual__order_Oantisym,axiom,
% 3.82/4.00 ! [B2: set_int,A: set_int] :
% 3.82/4.00 ( ( ord_less_eq_set_int @ B2 @ A )
% 3.82/4.00 => ( ( ord_less_eq_set_int @ A @ B2 )
% 3.82/4.00 => ( A = B2 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % dual_order.antisym
% 3.82/4.00 thf(fact_369_dual__order_Oantisym,axiom,
% 3.82/4.00 ! [B2: nat,A: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ B2 @ A )
% 3.82/4.00 => ( ( ord_less_eq_nat @ A @ B2 )
% 3.82/4.00 => ( A = B2 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % dual_order.antisym
% 3.82/4.00 thf(fact_370_dual__order_Oantisym,axiom,
% 3.82/4.00 ! [B2: int,A: int] :
% 3.82/4.00 ( ( ord_less_eq_int @ B2 @ A )
% 3.82/4.00 => ( ( ord_less_eq_int @ A @ B2 )
% 3.82/4.00 => ( A = B2 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % dual_order.antisym
% 3.82/4.00 thf(fact_371_dual__order_Oeq__iff,axiom,
% 3.82/4.00 ( ( ^ [Y4: real,Z2: real] : ( Y4 = Z2 ) )
% 3.82/4.00 = ( ^ [A3: real,B3: real] :
% 3.82/4.00 ( ( ord_less_eq_real @ B3 @ A3 )
% 3.82/4.00 & ( ord_less_eq_real @ A3 @ B3 ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % dual_order.eq_iff
% 3.82/4.00 thf(fact_372_dual__order_Oeq__iff,axiom,
% 3.82/4.00 ( ( ^ [Y4: set_nat,Z2: set_nat] : ( Y4 = Z2 ) )
% 3.82/4.00 = ( ^ [A3: set_nat,B3: set_nat] :
% 3.82/4.00 ( ( ord_less_eq_set_nat @ B3 @ A3 )
% 3.82/4.00 & ( ord_less_eq_set_nat @ A3 @ B3 ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % dual_order.eq_iff
% 3.82/4.00 thf(fact_373_dual__order_Oeq__iff,axiom,
% 3.82/4.00 ( ( ^ [Y4: set_int,Z2: set_int] : ( Y4 = Z2 ) )
% 3.82/4.00 = ( ^ [A3: set_int,B3: set_int] :
% 3.82/4.00 ( ( ord_less_eq_set_int @ B3 @ A3 )
% 3.82/4.00 & ( ord_less_eq_set_int @ A3 @ B3 ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % dual_order.eq_iff
% 3.82/4.00 thf(fact_374_dual__order_Oeq__iff,axiom,
% 3.82/4.00 ( ( ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 3.82/4.00 = ( ^ [A3: nat,B3: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ B3 @ A3 )
% 3.82/4.00 & ( ord_less_eq_nat @ A3 @ B3 ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % dual_order.eq_iff
% 3.82/4.00 thf(fact_375_dual__order_Oeq__iff,axiom,
% 3.82/4.00 ( ( ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 3.82/4.00 = ( ^ [A3: int,B3: int] :
% 3.82/4.00 ( ( ord_less_eq_int @ B3 @ A3 )
% 3.82/4.00 & ( ord_less_eq_int @ A3 @ B3 ) ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % dual_order.eq_iff
% 3.82/4.00 thf(fact_376_linorder__wlog,axiom,
% 3.82/4.00 ! [P: real > real > $o,A: real,B2: real] :
% 3.82/4.00 ( ! [A4: real,B4: real] :
% 3.82/4.00 ( ( ord_less_eq_real @ A4 @ B4 )
% 3.82/4.00 => ( P @ A4 @ B4 ) )
% 3.82/4.00 => ( ! [A4: real,B4: real] :
% 3.82/4.00 ( ( P @ B4 @ A4 )
% 3.82/4.00 => ( P @ A4 @ B4 ) )
% 3.82/4.00 => ( P @ A @ B2 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % linorder_wlog
% 3.82/4.00 thf(fact_377_linorder__wlog,axiom,
% 3.82/4.00 ! [P: nat > nat > $o,A: nat,B2: nat] :
% 3.82/4.00 ( ! [A4: nat,B4: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ A4 @ B4 )
% 3.82/4.00 => ( P @ A4 @ B4 ) )
% 3.82/4.00 => ( ! [A4: nat,B4: nat] :
% 3.82/4.00 ( ( P @ B4 @ A4 )
% 3.82/4.00 => ( P @ A4 @ B4 ) )
% 3.82/4.00 => ( P @ A @ B2 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % linorder_wlog
% 3.82/4.00 thf(fact_378_linorder__wlog,axiom,
% 3.82/4.00 ! [P: int > int > $o,A: int,B2: int] :
% 3.82/4.00 ( ! [A4: int,B4: int] :
% 3.82/4.00 ( ( ord_less_eq_int @ A4 @ B4 )
% 3.82/4.00 => ( P @ A4 @ B4 ) )
% 3.82/4.00 => ( ! [A4: int,B4: int] :
% 3.82/4.00 ( ( P @ B4 @ A4 )
% 3.82/4.00 => ( P @ A4 @ B4 ) )
% 3.82/4.00 => ( P @ A @ B2 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % linorder_wlog
% 3.82/4.00 thf(fact_379_order__trans,axiom,
% 3.82/4.00 ! [X: real,Y: real,Z3: real] :
% 3.82/4.00 ( ( ord_less_eq_real @ X @ Y )
% 3.82/4.00 => ( ( ord_less_eq_real @ Y @ Z3 )
% 3.82/4.00 => ( ord_less_eq_real @ X @ Z3 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % order_trans
% 3.82/4.00 thf(fact_380_order__trans,axiom,
% 3.82/4.00 ! [X: set_nat,Y: set_nat,Z3: set_nat] :
% 3.82/4.00 ( ( ord_less_eq_set_nat @ X @ Y )
% 3.82/4.00 => ( ( ord_less_eq_set_nat @ Y @ Z3 )
% 3.82/4.00 => ( ord_less_eq_set_nat @ X @ Z3 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % order_trans
% 3.82/4.00 thf(fact_381_order__trans,axiom,
% 3.82/4.00 ! [X: set_int,Y: set_int,Z3: set_int] :
% 3.82/4.00 ( ( ord_less_eq_set_int @ X @ Y )
% 3.82/4.00 => ( ( ord_less_eq_set_int @ Y @ Z3 )
% 3.82/4.00 => ( ord_less_eq_set_int @ X @ Z3 ) ) ) ).
% 3.82/4.00
% 3.82/4.00 % order_trans
% 3.82/4.00 thf(fact_382_order__trans,axiom,
% 3.82/4.00 ! [X: nat,Y: nat,Z3: nat] :
% 3.82/4.00 ( ( ord_less_eq_nat @ X @ Y )
% 3.82/4.00 => ( ( ord_less_eq_nat @ Y @ Z3 )
% 3.82/4.00 => ( ord_less_eq_nat @ X @ Z3 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_trans
% 3.82/4.01 thf(fact_383_order__trans,axiom,
% 3.82/4.01 ! [X: int,Y: int,Z3: int] :
% 3.82/4.01 ( ( ord_less_eq_int @ X @ Y )
% 3.82/4.01 => ( ( ord_less_eq_int @ Y @ Z3 )
% 3.82/4.01 => ( ord_less_eq_int @ X @ Z3 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_trans
% 3.82/4.01 thf(fact_384_order_Otrans,axiom,
% 3.82/4.01 ! [A: real,B2: real,C: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ A @ B2 )
% 3.82/4.01 => ( ( ord_less_eq_real @ B2 @ C )
% 3.82/4.01 => ( ord_less_eq_real @ A @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.trans
% 3.82/4.01 thf(fact_385_order_Otrans,axiom,
% 3.82/4.01 ! [A: set_nat,B2: set_nat,C: set_nat] :
% 3.82/4.01 ( ( ord_less_eq_set_nat @ A @ B2 )
% 3.82/4.01 => ( ( ord_less_eq_set_nat @ B2 @ C )
% 3.82/4.01 => ( ord_less_eq_set_nat @ A @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.trans
% 3.82/4.01 thf(fact_386_order_Otrans,axiom,
% 3.82/4.01 ! [A: set_int,B2: set_int,C: set_int] :
% 3.82/4.01 ( ( ord_less_eq_set_int @ A @ B2 )
% 3.82/4.01 => ( ( ord_less_eq_set_int @ B2 @ C )
% 3.82/4.01 => ( ord_less_eq_set_int @ A @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.trans
% 3.82/4.01 thf(fact_387_order_Otrans,axiom,
% 3.82/4.01 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ A @ B2 )
% 3.82/4.01 => ( ( ord_less_eq_nat @ B2 @ C )
% 3.82/4.01 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.trans
% 3.82/4.01 thf(fact_388_order_Otrans,axiom,
% 3.82/4.01 ! [A: int,B2: int,C: int] :
% 3.82/4.01 ( ( ord_less_eq_int @ A @ B2 )
% 3.82/4.01 => ( ( ord_less_eq_int @ B2 @ C )
% 3.82/4.01 => ( ord_less_eq_int @ A @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.trans
% 3.82/4.01 thf(fact_389_order__antisym,axiom,
% 3.82/4.01 ! [X: real,Y: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ X @ Y )
% 3.82/4.01 => ( ( ord_less_eq_real @ Y @ X )
% 3.82/4.01 => ( X = Y ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_antisym
% 3.82/4.01 thf(fact_390_order__antisym,axiom,
% 3.82/4.01 ! [X: set_nat,Y: set_nat] :
% 3.82/4.01 ( ( ord_less_eq_set_nat @ X @ Y )
% 3.82/4.01 => ( ( ord_less_eq_set_nat @ Y @ X )
% 3.82/4.01 => ( X = Y ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_antisym
% 3.82/4.01 thf(fact_391_order__antisym,axiom,
% 3.82/4.01 ! [X: set_int,Y: set_int] :
% 3.82/4.01 ( ( ord_less_eq_set_int @ X @ Y )
% 3.82/4.01 => ( ( ord_less_eq_set_int @ Y @ X )
% 3.82/4.01 => ( X = Y ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_antisym
% 3.82/4.01 thf(fact_392_order__antisym,axiom,
% 3.82/4.01 ! [X: nat,Y: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ X @ Y )
% 3.82/4.01 => ( ( ord_less_eq_nat @ Y @ X )
% 3.82/4.01 => ( X = Y ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_antisym
% 3.82/4.01 thf(fact_393_order__antisym,axiom,
% 3.82/4.01 ! [X: int,Y: int] :
% 3.82/4.01 ( ( ord_less_eq_int @ X @ Y )
% 3.82/4.01 => ( ( ord_less_eq_int @ Y @ X )
% 3.82/4.01 => ( X = Y ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_antisym
% 3.82/4.01 thf(fact_394_ord__le__eq__trans,axiom,
% 3.82/4.01 ! [A: real,B2: real,C: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ A @ B2 )
% 3.82/4.01 => ( ( B2 = C )
% 3.82/4.01 => ( ord_less_eq_real @ A @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % ord_le_eq_trans
% 3.82/4.01 thf(fact_395_ord__le__eq__trans,axiom,
% 3.82/4.01 ! [A: set_nat,B2: set_nat,C: set_nat] :
% 3.82/4.01 ( ( ord_less_eq_set_nat @ A @ B2 )
% 3.82/4.01 => ( ( B2 = C )
% 3.82/4.01 => ( ord_less_eq_set_nat @ A @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % ord_le_eq_trans
% 3.82/4.01 thf(fact_396_ord__le__eq__trans,axiom,
% 3.82/4.01 ! [A: set_int,B2: set_int,C: set_int] :
% 3.82/4.01 ( ( ord_less_eq_set_int @ A @ B2 )
% 3.82/4.01 => ( ( B2 = C )
% 3.82/4.01 => ( ord_less_eq_set_int @ A @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % ord_le_eq_trans
% 3.82/4.01 thf(fact_397_ord__le__eq__trans,axiom,
% 3.82/4.01 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ A @ B2 )
% 3.82/4.01 => ( ( B2 = C )
% 3.82/4.01 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % ord_le_eq_trans
% 3.82/4.01 thf(fact_398_ord__le__eq__trans,axiom,
% 3.82/4.01 ! [A: int,B2: int,C: int] :
% 3.82/4.01 ( ( ord_less_eq_int @ A @ B2 )
% 3.82/4.01 => ( ( B2 = C )
% 3.82/4.01 => ( ord_less_eq_int @ A @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % ord_le_eq_trans
% 3.82/4.01 thf(fact_399_ord__eq__le__trans,axiom,
% 3.82/4.01 ! [A: real,B2: real,C: real] :
% 3.82/4.01 ( ( A = B2 )
% 3.82/4.01 => ( ( ord_less_eq_real @ B2 @ C )
% 3.82/4.01 => ( ord_less_eq_real @ A @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % ord_eq_le_trans
% 3.82/4.01 thf(fact_400_ord__eq__le__trans,axiom,
% 3.82/4.01 ! [A: set_nat,B2: set_nat,C: set_nat] :
% 3.82/4.01 ( ( A = B2 )
% 3.82/4.01 => ( ( ord_less_eq_set_nat @ B2 @ C )
% 3.82/4.01 => ( ord_less_eq_set_nat @ A @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % ord_eq_le_trans
% 3.82/4.01 thf(fact_401_ord__eq__le__trans,axiom,
% 3.82/4.01 ! [A: set_int,B2: set_int,C: set_int] :
% 3.82/4.01 ( ( A = B2 )
% 3.82/4.01 => ( ( ord_less_eq_set_int @ B2 @ C )
% 3.82/4.01 => ( ord_less_eq_set_int @ A @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % ord_eq_le_trans
% 3.82/4.01 thf(fact_402_ord__eq__le__trans,axiom,
% 3.82/4.01 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.01 ( ( A = B2 )
% 3.82/4.01 => ( ( ord_less_eq_nat @ B2 @ C )
% 3.82/4.01 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % ord_eq_le_trans
% 3.82/4.01 thf(fact_403_ord__eq__le__trans,axiom,
% 3.82/4.01 ! [A: int,B2: int,C: int] :
% 3.82/4.01 ( ( A = B2 )
% 3.82/4.01 => ( ( ord_less_eq_int @ B2 @ C )
% 3.82/4.01 => ( ord_less_eq_int @ A @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % ord_eq_le_trans
% 3.82/4.01 thf(fact_404_order__class_Oorder__eq__iff,axiom,
% 3.82/4.01 ( ( ^ [Y4: real,Z2: real] : ( Y4 = Z2 ) )
% 3.82/4.01 = ( ^ [X4: real,Y5: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ X4 @ Y5 )
% 3.82/4.01 & ( ord_less_eq_real @ Y5 @ X4 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_class.order_eq_iff
% 3.82/4.01 thf(fact_405_order__class_Oorder__eq__iff,axiom,
% 3.82/4.01 ( ( ^ [Y4: set_nat,Z2: set_nat] : ( Y4 = Z2 ) )
% 3.82/4.01 = ( ^ [X4: set_nat,Y5: set_nat] :
% 3.82/4.01 ( ( ord_less_eq_set_nat @ X4 @ Y5 )
% 3.82/4.01 & ( ord_less_eq_set_nat @ Y5 @ X4 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_class.order_eq_iff
% 3.82/4.01 thf(fact_406_order__class_Oorder__eq__iff,axiom,
% 3.82/4.01 ( ( ^ [Y4: set_int,Z2: set_int] : ( Y4 = Z2 ) )
% 3.82/4.01 = ( ^ [X4: set_int,Y5: set_int] :
% 3.82/4.01 ( ( ord_less_eq_set_int @ X4 @ Y5 )
% 3.82/4.01 & ( ord_less_eq_set_int @ Y5 @ X4 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_class.order_eq_iff
% 3.82/4.01 thf(fact_407_order__class_Oorder__eq__iff,axiom,
% 3.82/4.01 ( ( ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 3.82/4.01 = ( ^ [X4: nat,Y5: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ X4 @ Y5 )
% 3.82/4.01 & ( ord_less_eq_nat @ Y5 @ X4 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_class.order_eq_iff
% 3.82/4.01 thf(fact_408_order__class_Oorder__eq__iff,axiom,
% 3.82/4.01 ( ( ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 3.82/4.01 = ( ^ [X4: int,Y5: int] :
% 3.82/4.01 ( ( ord_less_eq_int @ X4 @ Y5 )
% 3.82/4.01 & ( ord_less_eq_int @ Y5 @ X4 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_class.order_eq_iff
% 3.82/4.01 thf(fact_409_le__cases3,axiom,
% 3.82/4.01 ! [X: real,Y: real,Z3: real] :
% 3.82/4.01 ( ( ( ord_less_eq_real @ X @ Y )
% 3.82/4.01 => ~ ( ord_less_eq_real @ Y @ Z3 ) )
% 3.82/4.01 => ( ( ( ord_less_eq_real @ Y @ X )
% 3.82/4.01 => ~ ( ord_less_eq_real @ X @ Z3 ) )
% 3.82/4.01 => ( ( ( ord_less_eq_real @ X @ Z3 )
% 3.82/4.01 => ~ ( ord_less_eq_real @ Z3 @ Y ) )
% 3.82/4.01 => ( ( ( ord_less_eq_real @ Z3 @ Y )
% 3.82/4.01 => ~ ( ord_less_eq_real @ Y @ X ) )
% 3.82/4.01 => ( ( ( ord_less_eq_real @ Y @ Z3 )
% 3.82/4.01 => ~ ( ord_less_eq_real @ Z3 @ X ) )
% 3.82/4.01 => ~ ( ( ord_less_eq_real @ Z3 @ X )
% 3.82/4.01 => ~ ( ord_less_eq_real @ X @ Y ) ) ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % le_cases3
% 3.82/4.01 thf(fact_410_le__cases3,axiom,
% 3.82/4.01 ! [X: nat,Y: nat,Z3: nat] :
% 3.82/4.01 ( ( ( ord_less_eq_nat @ X @ Y )
% 3.82/4.01 => ~ ( ord_less_eq_nat @ Y @ Z3 ) )
% 3.82/4.01 => ( ( ( ord_less_eq_nat @ Y @ X )
% 3.82/4.01 => ~ ( ord_less_eq_nat @ X @ Z3 ) )
% 3.82/4.01 => ( ( ( ord_less_eq_nat @ X @ Z3 )
% 3.82/4.01 => ~ ( ord_less_eq_nat @ Z3 @ Y ) )
% 3.82/4.01 => ( ( ( ord_less_eq_nat @ Z3 @ Y )
% 3.82/4.01 => ~ ( ord_less_eq_nat @ Y @ X ) )
% 3.82/4.01 => ( ( ( ord_less_eq_nat @ Y @ Z3 )
% 3.82/4.01 => ~ ( ord_less_eq_nat @ Z3 @ X ) )
% 3.82/4.01 => ~ ( ( ord_less_eq_nat @ Z3 @ X )
% 3.82/4.01 => ~ ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % le_cases3
% 3.82/4.01 thf(fact_411_le__cases3,axiom,
% 3.82/4.01 ! [X: int,Y: int,Z3: int] :
% 3.82/4.01 ( ( ( ord_less_eq_int @ X @ Y )
% 3.82/4.01 => ~ ( ord_less_eq_int @ Y @ Z3 ) )
% 3.82/4.01 => ( ( ( ord_less_eq_int @ Y @ X )
% 3.82/4.01 => ~ ( ord_less_eq_int @ X @ Z3 ) )
% 3.82/4.01 => ( ( ( ord_less_eq_int @ X @ Z3 )
% 3.82/4.01 => ~ ( ord_less_eq_int @ Z3 @ Y ) )
% 3.82/4.01 => ( ( ( ord_less_eq_int @ Z3 @ Y )
% 3.82/4.01 => ~ ( ord_less_eq_int @ Y @ X ) )
% 3.82/4.01 => ( ( ( ord_less_eq_int @ Y @ Z3 )
% 3.82/4.01 => ~ ( ord_less_eq_int @ Z3 @ X ) )
% 3.82/4.01 => ~ ( ( ord_less_eq_int @ Z3 @ X )
% 3.82/4.01 => ~ ( ord_less_eq_int @ X @ Y ) ) ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % le_cases3
% 3.82/4.01 thf(fact_412_nle__le,axiom,
% 3.82/4.01 ! [A: real,B2: real] :
% 3.82/4.01 ( ( ~ ( ord_less_eq_real @ A @ B2 ) )
% 3.82/4.01 = ( ( ord_less_eq_real @ B2 @ A )
% 3.82/4.01 & ( B2 != A ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % nle_le
% 3.82/4.01 thf(fact_413_nle__le,axiom,
% 3.82/4.01 ! [A: nat,B2: nat] :
% 3.82/4.01 ( ( ~ ( ord_less_eq_nat @ A @ B2 ) )
% 3.82/4.01 = ( ( ord_less_eq_nat @ B2 @ A )
% 3.82/4.01 & ( B2 != A ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % nle_le
% 3.82/4.01 thf(fact_414_nle__le,axiom,
% 3.82/4.01 ! [A: int,B2: int] :
% 3.82/4.01 ( ( ~ ( ord_less_eq_int @ A @ B2 ) )
% 3.82/4.01 = ( ( ord_less_eq_int @ B2 @ A )
% 3.82/4.01 & ( B2 != A ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % nle_le
% 3.82/4.01 thf(fact_415_set__update__memI,axiom,
% 3.82/4.01 ! [N2: nat,Xs: list_Extended_enat,X: extended_enat] :
% 3.82/4.01 ( ( ord_less_nat @ N2 @ ( size_s3941691890525107288d_enat @ Xs ) )
% 3.82/4.01 => ( member_Extended_enat @ X @ ( set_Extended_enat2 @ ( list_u3071683517702156500d_enat @ Xs @ N2 @ X ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % set_update_memI
% 3.82/4.01 thf(fact_416_set__update__memI,axiom,
% 3.82/4.01 ! [N2: nat,Xs: list_real,X: real] :
% 3.82/4.01 ( ( ord_less_nat @ N2 @ ( size_size_list_real @ Xs ) )
% 3.82/4.01 => ( member_real @ X @ ( set_real2 @ ( list_update_real @ Xs @ N2 @ X ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % set_update_memI
% 3.82/4.01 thf(fact_417_set__update__memI,axiom,
% 3.82/4.01 ! [N2: nat,Xs: list_set_nat,X: set_nat] :
% 3.82/4.01 ( ( ord_less_nat @ N2 @ ( size_s3254054031482475050et_nat @ Xs ) )
% 3.82/4.01 => ( member_set_nat @ X @ ( set_set_nat2 @ ( list_update_set_nat @ Xs @ N2 @ X ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % set_update_memI
% 3.82/4.01 thf(fact_418_set__update__memI,axiom,
% 3.82/4.01 ! [N2: nat,Xs: list_VEBT_VEBT,X: vEBT_VEBT] :
% 3.82/4.01 ( ( ord_less_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 3.82/4.01 => ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs @ N2 @ X ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % set_update_memI
% 3.82/4.01 thf(fact_419_set__update__memI,axiom,
% 3.82/4.01 ! [N2: nat,Xs: list_int,X: int] :
% 3.82/4.01 ( ( ord_less_nat @ N2 @ ( size_size_list_int @ Xs ) )
% 3.82/4.01 => ( member_int @ X @ ( set_int2 @ ( list_update_int @ Xs @ N2 @ X ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % set_update_memI
% 3.82/4.01 thf(fact_420_set__update__memI,axiom,
% 3.82/4.01 ! [N2: nat,Xs: list_nat,X: nat] :
% 3.82/4.01 ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs ) )
% 3.82/4.01 => ( member_nat @ X @ ( set_nat2 @ ( list_update_nat @ Xs @ N2 @ X ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % set_update_memI
% 3.82/4.01 thf(fact_421_order__less__imp__not__less,axiom,
% 3.82/4.01 ! [X: nat,Y: nat] :
% 3.82/4.01 ( ( ord_less_nat @ X @ Y )
% 3.82/4.01 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_imp_not_less
% 3.82/4.01 thf(fact_422_order__less__imp__not__less,axiom,
% 3.82/4.01 ! [X: extended_enat,Y: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ X @ Y )
% 3.82/4.01 => ~ ( ord_le72135733267957522d_enat @ Y @ X ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_imp_not_less
% 3.82/4.01 thf(fact_423_order__less__imp__not__less,axiom,
% 3.82/4.01 ! [X: real,Y: real] :
% 3.82/4.01 ( ( ord_less_real @ X @ Y )
% 3.82/4.01 => ~ ( ord_less_real @ Y @ X ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_imp_not_less
% 3.82/4.01 thf(fact_424_order__less__imp__not__less,axiom,
% 3.82/4.01 ! [X: int,Y: int] :
% 3.82/4.01 ( ( ord_less_int @ X @ Y )
% 3.82/4.01 => ~ ( ord_less_int @ Y @ X ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_imp_not_less
% 3.82/4.01 thf(fact_425_order__less__imp__not__eq2,axiom,
% 3.82/4.01 ! [X: nat,Y: nat] :
% 3.82/4.01 ( ( ord_less_nat @ X @ Y )
% 3.82/4.01 => ( Y != X ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_imp_not_eq2
% 3.82/4.01 thf(fact_426_order__less__imp__not__eq2,axiom,
% 3.82/4.01 ! [X: extended_enat,Y: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ X @ Y )
% 3.82/4.01 => ( Y != X ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_imp_not_eq2
% 3.82/4.01 thf(fact_427_order__less__imp__not__eq2,axiom,
% 3.82/4.01 ! [X: real,Y: real] :
% 3.82/4.01 ( ( ord_less_real @ X @ Y )
% 3.82/4.01 => ( Y != X ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_imp_not_eq2
% 3.82/4.01 thf(fact_428_order__less__imp__not__eq2,axiom,
% 3.82/4.01 ! [X: int,Y: int] :
% 3.82/4.01 ( ( ord_less_int @ X @ Y )
% 3.82/4.01 => ( Y != X ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_imp_not_eq2
% 3.82/4.01 thf(fact_429_order__less__imp__not__eq,axiom,
% 3.82/4.01 ! [X: nat,Y: nat] :
% 3.82/4.01 ( ( ord_less_nat @ X @ Y )
% 3.82/4.01 => ( X != Y ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_imp_not_eq
% 3.82/4.01 thf(fact_430_order__less__imp__not__eq,axiom,
% 3.82/4.01 ! [X: extended_enat,Y: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ X @ Y )
% 3.82/4.01 => ( X != Y ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_imp_not_eq
% 3.82/4.01 thf(fact_431_order__less__imp__not__eq,axiom,
% 3.82/4.01 ! [X: real,Y: real] :
% 3.82/4.01 ( ( ord_less_real @ X @ Y )
% 3.82/4.01 => ( X != Y ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_imp_not_eq
% 3.82/4.01 thf(fact_432_order__less__imp__not__eq,axiom,
% 3.82/4.01 ! [X: int,Y: int] :
% 3.82/4.01 ( ( ord_less_int @ X @ Y )
% 3.82/4.01 => ( X != Y ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_imp_not_eq
% 3.82/4.01 thf(fact_433_linorder__less__linear,axiom,
% 3.82/4.01 ! [X: nat,Y: nat] :
% 3.82/4.01 ( ( ord_less_nat @ X @ Y )
% 3.82/4.01 | ( X = Y )
% 3.82/4.01 | ( ord_less_nat @ Y @ X ) ) ).
% 3.82/4.01
% 3.82/4.01 % linorder_less_linear
% 3.82/4.01 thf(fact_434_linorder__less__linear,axiom,
% 3.82/4.01 ! [X: extended_enat,Y: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ X @ Y )
% 3.82/4.01 | ( X = Y )
% 3.82/4.01 | ( ord_le72135733267957522d_enat @ Y @ X ) ) ).
% 3.82/4.01
% 3.82/4.01 % linorder_less_linear
% 3.82/4.01 thf(fact_435_linorder__less__linear,axiom,
% 3.82/4.01 ! [X: real,Y: real] :
% 3.82/4.01 ( ( ord_less_real @ X @ Y )
% 3.82/4.01 | ( X = Y )
% 3.82/4.01 | ( ord_less_real @ Y @ X ) ) ).
% 3.82/4.01
% 3.82/4.01 % linorder_less_linear
% 3.82/4.01 thf(fact_436_linorder__less__linear,axiom,
% 3.82/4.01 ! [X: int,Y: int] :
% 3.82/4.01 ( ( ord_less_int @ X @ Y )
% 3.82/4.01 | ( X = Y )
% 3.82/4.01 | ( ord_less_int @ Y @ X ) ) ).
% 3.82/4.01
% 3.82/4.01 % linorder_less_linear
% 3.82/4.01 thf(fact_437_order__less__imp__triv,axiom,
% 3.82/4.01 ! [X: nat,Y: nat,P: $o] :
% 3.82/4.01 ( ( ord_less_nat @ X @ Y )
% 3.82/4.01 => ( ( ord_less_nat @ Y @ X )
% 3.82/4.01 => P ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_imp_triv
% 3.82/4.01 thf(fact_438_order__less__imp__triv,axiom,
% 3.82/4.01 ! [X: extended_enat,Y: extended_enat,P: $o] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ X @ Y )
% 3.82/4.01 => ( ( ord_le72135733267957522d_enat @ Y @ X )
% 3.82/4.01 => P ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_imp_triv
% 3.82/4.01 thf(fact_439_order__less__imp__triv,axiom,
% 3.82/4.01 ! [X: real,Y: real,P: $o] :
% 3.82/4.01 ( ( ord_less_real @ X @ Y )
% 3.82/4.01 => ( ( ord_less_real @ Y @ X )
% 3.82/4.01 => P ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_imp_triv
% 3.82/4.01 thf(fact_440_order__less__imp__triv,axiom,
% 3.82/4.01 ! [X: int,Y: int,P: $o] :
% 3.82/4.01 ( ( ord_less_int @ X @ Y )
% 3.82/4.01 => ( ( ord_less_int @ Y @ X )
% 3.82/4.01 => P ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_imp_triv
% 3.82/4.01 thf(fact_441_order__less__not__sym,axiom,
% 3.82/4.01 ! [X: nat,Y: nat] :
% 3.82/4.01 ( ( ord_less_nat @ X @ Y )
% 3.82/4.01 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_not_sym
% 3.82/4.01 thf(fact_442_order__less__not__sym,axiom,
% 3.82/4.01 ! [X: extended_enat,Y: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ X @ Y )
% 3.82/4.01 => ~ ( ord_le72135733267957522d_enat @ Y @ X ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_not_sym
% 3.82/4.01 thf(fact_443_order__less__not__sym,axiom,
% 3.82/4.01 ! [X: real,Y: real] :
% 3.82/4.01 ( ( ord_less_real @ X @ Y )
% 3.82/4.01 => ~ ( ord_less_real @ Y @ X ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_not_sym
% 3.82/4.01 thf(fact_444_order__less__not__sym,axiom,
% 3.82/4.01 ! [X: int,Y: int] :
% 3.82/4.01 ( ( ord_less_int @ X @ Y )
% 3.82/4.01 => ~ ( ord_less_int @ Y @ X ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_not_sym
% 3.82/4.01 thf(fact_445_order__less__subst2,axiom,
% 3.82/4.01 ! [A: nat,B2: nat,F: nat > nat,C: nat] :
% 3.82/4.01 ( ( ord_less_nat @ A @ B2 )
% 3.82/4.01 => ( ( ord_less_nat @ ( F @ B2 ) @ C )
% 3.82/4.01 => ( ! [X5: nat,Y3: nat] :
% 3.82/4.01 ( ( ord_less_nat @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_subst2
% 3.82/4.01 thf(fact_446_order__less__subst2,axiom,
% 3.82/4.01 ! [A: nat,B2: nat,F: nat > extended_enat,C: extended_enat] :
% 3.82/4.01 ( ( ord_less_nat @ A @ B2 )
% 3.82/4.01 => ( ( ord_le72135733267957522d_enat @ ( F @ B2 ) @ C )
% 3.82/4.01 => ( ! [X5: nat,Y3: nat] :
% 3.82/4.01 ( ( ord_less_nat @ X5 @ Y3 )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_subst2
% 3.82/4.01 thf(fact_447_order__less__subst2,axiom,
% 3.82/4.01 ! [A: nat,B2: nat,F: nat > real,C: real] :
% 3.82/4.01 ( ( ord_less_nat @ A @ B2 )
% 3.82/4.01 => ( ( ord_less_real @ ( F @ B2 ) @ C )
% 3.82/4.01 => ( ! [X5: nat,Y3: nat] :
% 3.82/4.01 ( ( ord_less_nat @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_subst2
% 3.82/4.01 thf(fact_448_order__less__subst2,axiom,
% 3.82/4.01 ! [A: nat,B2: nat,F: nat > int,C: int] :
% 3.82/4.01 ( ( ord_less_nat @ A @ B2 )
% 3.82/4.01 => ( ( ord_less_int @ ( F @ B2 ) @ C )
% 3.82/4.01 => ( ! [X5: nat,Y3: nat] :
% 3.82/4.01 ( ( ord_less_nat @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_subst2
% 3.82/4.01 thf(fact_449_order__less__subst2,axiom,
% 3.82/4.01 ! [A: extended_enat,B2: extended_enat,F: extended_enat > nat,C: nat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ A @ B2 )
% 3.82/4.01 => ( ( ord_less_nat @ ( F @ B2 ) @ C )
% 3.82/4.01 => ( ! [X5: extended_enat,Y3: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_subst2
% 3.82/4.01 thf(fact_450_order__less__subst2,axiom,
% 3.82/4.01 ! [A: extended_enat,B2: extended_enat,F: extended_enat > extended_enat,C: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ A @ B2 )
% 3.82/4.01 => ( ( ord_le72135733267957522d_enat @ ( F @ B2 ) @ C )
% 3.82/4.01 => ( ! [X5: extended_enat,Y3: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ X5 @ Y3 )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_subst2
% 3.82/4.01 thf(fact_451_order__less__subst2,axiom,
% 3.82/4.01 ! [A: extended_enat,B2: extended_enat,F: extended_enat > real,C: real] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ A @ B2 )
% 3.82/4.01 => ( ( ord_less_real @ ( F @ B2 ) @ C )
% 3.82/4.01 => ( ! [X5: extended_enat,Y3: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_subst2
% 3.82/4.01 thf(fact_452_order__less__subst2,axiom,
% 3.82/4.01 ! [A: extended_enat,B2: extended_enat,F: extended_enat > int,C: int] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ A @ B2 )
% 3.82/4.01 => ( ( ord_less_int @ ( F @ B2 ) @ C )
% 3.82/4.01 => ( ! [X5: extended_enat,Y3: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_subst2
% 3.82/4.01 thf(fact_453_order__less__subst2,axiom,
% 3.82/4.01 ! [A: real,B2: real,F: real > nat,C: nat] :
% 3.82/4.01 ( ( ord_less_real @ A @ B2 )
% 3.82/4.01 => ( ( ord_less_nat @ ( F @ B2 ) @ C )
% 3.82/4.01 => ( ! [X5: real,Y3: real] :
% 3.82/4.01 ( ( ord_less_real @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_subst2
% 3.82/4.01 thf(fact_454_order__less__subst2,axiom,
% 3.82/4.01 ! [A: real,B2: real,F: real > extended_enat,C: extended_enat] :
% 3.82/4.01 ( ( ord_less_real @ A @ B2 )
% 3.82/4.01 => ( ( ord_le72135733267957522d_enat @ ( F @ B2 ) @ C )
% 3.82/4.01 => ( ! [X5: real,Y3: real] :
% 3.82/4.01 ( ( ord_less_real @ X5 @ Y3 )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_subst2
% 3.82/4.01 thf(fact_455_order__less__subst1,axiom,
% 3.82/4.01 ! [A: nat,F: nat > nat,B2: nat,C: nat] :
% 3.82/4.01 ( ( ord_less_nat @ A @ ( F @ B2 ) )
% 3.82/4.01 => ( ( ord_less_nat @ B2 @ C )
% 3.82/4.01 => ( ! [X5: nat,Y3: nat] :
% 3.82/4.01 ( ( ord_less_nat @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_subst1
% 3.82/4.01 thf(fact_456_order__less__subst1,axiom,
% 3.82/4.01 ! [A: nat,F: extended_enat > nat,B2: extended_enat,C: extended_enat] :
% 3.82/4.01 ( ( ord_less_nat @ A @ ( F @ B2 ) )
% 3.82/4.01 => ( ( ord_le72135733267957522d_enat @ B2 @ C )
% 3.82/4.01 => ( ! [X5: extended_enat,Y3: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_subst1
% 3.82/4.01 thf(fact_457_order__less__subst1,axiom,
% 3.82/4.01 ! [A: nat,F: real > nat,B2: real,C: real] :
% 3.82/4.01 ( ( ord_less_nat @ A @ ( F @ B2 ) )
% 3.82/4.01 => ( ( ord_less_real @ B2 @ C )
% 3.82/4.01 => ( ! [X5: real,Y3: real] :
% 3.82/4.01 ( ( ord_less_real @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_subst1
% 3.82/4.01 thf(fact_458_order__less__subst1,axiom,
% 3.82/4.01 ! [A: nat,F: int > nat,B2: int,C: int] :
% 3.82/4.01 ( ( ord_less_nat @ A @ ( F @ B2 ) )
% 3.82/4.01 => ( ( ord_less_int @ B2 @ C )
% 3.82/4.01 => ( ! [X5: int,Y3: int] :
% 3.82/4.01 ( ( ord_less_int @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_subst1
% 3.82/4.01 thf(fact_459_order__less__subst1,axiom,
% 3.82/4.01 ! [A: extended_enat,F: nat > extended_enat,B2: nat,C: nat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ A @ ( F @ B2 ) )
% 3.82/4.01 => ( ( ord_less_nat @ B2 @ C )
% 3.82/4.01 => ( ! [X5: nat,Y3: nat] :
% 3.82/4.01 ( ( ord_less_nat @ X5 @ Y3 )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_subst1
% 3.82/4.01 thf(fact_460_order__less__subst1,axiom,
% 3.82/4.01 ! [A: extended_enat,F: extended_enat > extended_enat,B2: extended_enat,C: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ A @ ( F @ B2 ) )
% 3.82/4.01 => ( ( ord_le72135733267957522d_enat @ B2 @ C )
% 3.82/4.01 => ( ! [X5: extended_enat,Y3: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ X5 @ Y3 )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_subst1
% 3.82/4.01 thf(fact_461_order__less__subst1,axiom,
% 3.82/4.01 ! [A: extended_enat,F: real > extended_enat,B2: real,C: real] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ A @ ( F @ B2 ) )
% 3.82/4.01 => ( ( ord_less_real @ B2 @ C )
% 3.82/4.01 => ( ! [X5: real,Y3: real] :
% 3.82/4.01 ( ( ord_less_real @ X5 @ Y3 )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_subst1
% 3.82/4.01 thf(fact_462_order__less__subst1,axiom,
% 3.82/4.01 ! [A: extended_enat,F: int > extended_enat,B2: int,C: int] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ A @ ( F @ B2 ) )
% 3.82/4.01 => ( ( ord_less_int @ B2 @ C )
% 3.82/4.01 => ( ! [X5: int,Y3: int] :
% 3.82/4.01 ( ( ord_less_int @ X5 @ Y3 )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_subst1
% 3.82/4.01 thf(fact_463_order__less__subst1,axiom,
% 3.82/4.01 ! [A: real,F: nat > real,B2: nat,C: nat] :
% 3.82/4.01 ( ( ord_less_real @ A @ ( F @ B2 ) )
% 3.82/4.01 => ( ( ord_less_nat @ B2 @ C )
% 3.82/4.01 => ( ! [X5: nat,Y3: nat] :
% 3.82/4.01 ( ( ord_less_nat @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_subst1
% 3.82/4.01 thf(fact_464_order__less__subst1,axiom,
% 3.82/4.01 ! [A: real,F: extended_enat > real,B2: extended_enat,C: extended_enat] :
% 3.82/4.01 ( ( ord_less_real @ A @ ( F @ B2 ) )
% 3.82/4.01 => ( ( ord_le72135733267957522d_enat @ B2 @ C )
% 3.82/4.01 => ( ! [X5: extended_enat,Y3: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_subst1
% 3.82/4.01 thf(fact_465_order__less__irrefl,axiom,
% 3.82/4.01 ! [X: nat] :
% 3.82/4.01 ~ ( ord_less_nat @ X @ X ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_irrefl
% 3.82/4.01 thf(fact_466_order__less__irrefl,axiom,
% 3.82/4.01 ! [X: extended_enat] :
% 3.82/4.01 ~ ( ord_le72135733267957522d_enat @ X @ X ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_irrefl
% 3.82/4.01 thf(fact_467_order__less__irrefl,axiom,
% 3.82/4.01 ! [X: real] :
% 3.82/4.01 ~ ( ord_less_real @ X @ X ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_irrefl
% 3.82/4.01 thf(fact_468_order__less__irrefl,axiom,
% 3.82/4.01 ! [X: int] :
% 3.82/4.01 ~ ( ord_less_int @ X @ X ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_irrefl
% 3.82/4.01 thf(fact_469_ord__less__eq__subst,axiom,
% 3.82/4.01 ! [A: nat,B2: nat,F: nat > nat,C: nat] :
% 3.82/4.01 ( ( ord_less_nat @ A @ B2 )
% 3.82/4.01 => ( ( ( F @ B2 )
% 3.82/4.01 = C )
% 3.82/4.01 => ( ! [X5: nat,Y3: nat] :
% 3.82/4.01 ( ( ord_less_nat @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % ord_less_eq_subst
% 3.82/4.01 thf(fact_470_ord__less__eq__subst,axiom,
% 3.82/4.01 ! [A: nat,B2: nat,F: nat > extended_enat,C: extended_enat] :
% 3.82/4.01 ( ( ord_less_nat @ A @ B2 )
% 3.82/4.01 => ( ( ( F @ B2 )
% 3.82/4.01 = C )
% 3.82/4.01 => ( ! [X5: nat,Y3: nat] :
% 3.82/4.01 ( ( ord_less_nat @ X5 @ Y3 )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % ord_less_eq_subst
% 3.82/4.01 thf(fact_471_ord__less__eq__subst,axiom,
% 3.82/4.01 ! [A: nat,B2: nat,F: nat > real,C: real] :
% 3.82/4.01 ( ( ord_less_nat @ A @ B2 )
% 3.82/4.01 => ( ( ( F @ B2 )
% 3.82/4.01 = C )
% 3.82/4.01 => ( ! [X5: nat,Y3: nat] :
% 3.82/4.01 ( ( ord_less_nat @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % ord_less_eq_subst
% 3.82/4.01 thf(fact_472_ord__less__eq__subst,axiom,
% 3.82/4.01 ! [A: nat,B2: nat,F: nat > int,C: int] :
% 3.82/4.01 ( ( ord_less_nat @ A @ B2 )
% 3.82/4.01 => ( ( ( F @ B2 )
% 3.82/4.01 = C )
% 3.82/4.01 => ( ! [X5: nat,Y3: nat] :
% 3.82/4.01 ( ( ord_less_nat @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % ord_less_eq_subst
% 3.82/4.01 thf(fact_473_ord__less__eq__subst,axiom,
% 3.82/4.01 ! [A: extended_enat,B2: extended_enat,F: extended_enat > nat,C: nat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ A @ B2 )
% 3.82/4.01 => ( ( ( F @ B2 )
% 3.82/4.01 = C )
% 3.82/4.01 => ( ! [X5: extended_enat,Y3: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % ord_less_eq_subst
% 3.82/4.01 thf(fact_474_ord__less__eq__subst,axiom,
% 3.82/4.01 ! [A: extended_enat,B2: extended_enat,F: extended_enat > extended_enat,C: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ A @ B2 )
% 3.82/4.01 => ( ( ( F @ B2 )
% 3.82/4.01 = C )
% 3.82/4.01 => ( ! [X5: extended_enat,Y3: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ X5 @ Y3 )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % ord_less_eq_subst
% 3.82/4.01 thf(fact_475_ord__less__eq__subst,axiom,
% 3.82/4.01 ! [A: extended_enat,B2: extended_enat,F: extended_enat > real,C: real] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ A @ B2 )
% 3.82/4.01 => ( ( ( F @ B2 )
% 3.82/4.01 = C )
% 3.82/4.01 => ( ! [X5: extended_enat,Y3: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % ord_less_eq_subst
% 3.82/4.01 thf(fact_476_ord__less__eq__subst,axiom,
% 3.82/4.01 ! [A: extended_enat,B2: extended_enat,F: extended_enat > int,C: int] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ A @ B2 )
% 3.82/4.01 => ( ( ( F @ B2 )
% 3.82/4.01 = C )
% 3.82/4.01 => ( ! [X5: extended_enat,Y3: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % ord_less_eq_subst
% 3.82/4.01 thf(fact_477_ord__less__eq__subst,axiom,
% 3.82/4.01 ! [A: real,B2: real,F: real > nat,C: nat] :
% 3.82/4.01 ( ( ord_less_real @ A @ B2 )
% 3.82/4.01 => ( ( ( F @ B2 )
% 3.82/4.01 = C )
% 3.82/4.01 => ( ! [X5: real,Y3: real] :
% 3.82/4.01 ( ( ord_less_real @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % ord_less_eq_subst
% 3.82/4.01 thf(fact_478_ord__less__eq__subst,axiom,
% 3.82/4.01 ! [A: real,B2: real,F: real > extended_enat,C: extended_enat] :
% 3.82/4.01 ( ( ord_less_real @ A @ B2 )
% 3.82/4.01 => ( ( ( F @ B2 )
% 3.82/4.01 = C )
% 3.82/4.01 => ( ! [X5: real,Y3: real] :
% 3.82/4.01 ( ( ord_less_real @ X5 @ Y3 )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % ord_less_eq_subst
% 3.82/4.01 thf(fact_479_ord__eq__less__subst,axiom,
% 3.82/4.01 ! [A: nat,F: nat > nat,B2: nat,C: nat] :
% 3.82/4.01 ( ( A
% 3.82/4.01 = ( F @ B2 ) )
% 3.82/4.01 => ( ( ord_less_nat @ B2 @ C )
% 3.82/4.01 => ( ! [X5: nat,Y3: nat] :
% 3.82/4.01 ( ( ord_less_nat @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % ord_eq_less_subst
% 3.82/4.01 thf(fact_480_ord__eq__less__subst,axiom,
% 3.82/4.01 ! [A: extended_enat,F: nat > extended_enat,B2: nat,C: nat] :
% 3.82/4.01 ( ( A
% 3.82/4.01 = ( F @ B2 ) )
% 3.82/4.01 => ( ( ord_less_nat @ B2 @ C )
% 3.82/4.01 => ( ! [X5: nat,Y3: nat] :
% 3.82/4.01 ( ( ord_less_nat @ X5 @ Y3 )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % ord_eq_less_subst
% 3.82/4.01 thf(fact_481_ord__eq__less__subst,axiom,
% 3.82/4.01 ! [A: real,F: nat > real,B2: nat,C: nat] :
% 3.82/4.01 ( ( A
% 3.82/4.01 = ( F @ B2 ) )
% 3.82/4.01 => ( ( ord_less_nat @ B2 @ C )
% 3.82/4.01 => ( ! [X5: nat,Y3: nat] :
% 3.82/4.01 ( ( ord_less_nat @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % ord_eq_less_subst
% 3.82/4.01 thf(fact_482_ord__eq__less__subst,axiom,
% 3.82/4.01 ! [A: int,F: nat > int,B2: nat,C: nat] :
% 3.82/4.01 ( ( A
% 3.82/4.01 = ( F @ B2 ) )
% 3.82/4.01 => ( ( ord_less_nat @ B2 @ C )
% 3.82/4.01 => ( ! [X5: nat,Y3: nat] :
% 3.82/4.01 ( ( ord_less_nat @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % ord_eq_less_subst
% 3.82/4.01 thf(fact_483_ord__eq__less__subst,axiom,
% 3.82/4.01 ! [A: nat,F: extended_enat > nat,B2: extended_enat,C: extended_enat] :
% 3.82/4.01 ( ( A
% 3.82/4.01 = ( F @ B2 ) )
% 3.82/4.01 => ( ( ord_le72135733267957522d_enat @ B2 @ C )
% 3.82/4.01 => ( ! [X5: extended_enat,Y3: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % ord_eq_less_subst
% 3.82/4.01 thf(fact_484_ord__eq__less__subst,axiom,
% 3.82/4.01 ! [A: extended_enat,F: extended_enat > extended_enat,B2: extended_enat,C: extended_enat] :
% 3.82/4.01 ( ( A
% 3.82/4.01 = ( F @ B2 ) )
% 3.82/4.01 => ( ( ord_le72135733267957522d_enat @ B2 @ C )
% 3.82/4.01 => ( ! [X5: extended_enat,Y3: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ X5 @ Y3 )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % ord_eq_less_subst
% 3.82/4.01 thf(fact_485_ord__eq__less__subst,axiom,
% 3.82/4.01 ! [A: real,F: extended_enat > real,B2: extended_enat,C: extended_enat] :
% 3.82/4.01 ( ( A
% 3.82/4.01 = ( F @ B2 ) )
% 3.82/4.01 => ( ( ord_le72135733267957522d_enat @ B2 @ C )
% 3.82/4.01 => ( ! [X5: extended_enat,Y3: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % ord_eq_less_subst
% 3.82/4.01 thf(fact_486_ord__eq__less__subst,axiom,
% 3.82/4.01 ! [A: int,F: extended_enat > int,B2: extended_enat,C: extended_enat] :
% 3.82/4.01 ( ( A
% 3.82/4.01 = ( F @ B2 ) )
% 3.82/4.01 => ( ( ord_le72135733267957522d_enat @ B2 @ C )
% 3.82/4.01 => ( ! [X5: extended_enat,Y3: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % ord_eq_less_subst
% 3.82/4.01 thf(fact_487_ord__eq__less__subst,axiom,
% 3.82/4.01 ! [A: nat,F: real > nat,B2: real,C: real] :
% 3.82/4.01 ( ( A
% 3.82/4.01 = ( F @ B2 ) )
% 3.82/4.01 => ( ( ord_less_real @ B2 @ C )
% 3.82/4.01 => ( ! [X5: real,Y3: real] :
% 3.82/4.01 ( ( ord_less_real @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % ord_eq_less_subst
% 3.82/4.01 thf(fact_488_ord__eq__less__subst,axiom,
% 3.82/4.01 ! [A: extended_enat,F: real > extended_enat,B2: real,C: real] :
% 3.82/4.01 ( ( A
% 3.82/4.01 = ( F @ B2 ) )
% 3.82/4.01 => ( ( ord_less_real @ B2 @ C )
% 3.82/4.01 => ( ! [X5: real,Y3: real] :
% 3.82/4.01 ( ( ord_less_real @ X5 @ Y3 )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % ord_eq_less_subst
% 3.82/4.01 thf(fact_489_order__less__trans,axiom,
% 3.82/4.01 ! [X: nat,Y: nat,Z3: nat] :
% 3.82/4.01 ( ( ord_less_nat @ X @ Y )
% 3.82/4.01 => ( ( ord_less_nat @ Y @ Z3 )
% 3.82/4.01 => ( ord_less_nat @ X @ Z3 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_trans
% 3.82/4.01 thf(fact_490_order__less__trans,axiom,
% 3.82/4.01 ! [X: extended_enat,Y: extended_enat,Z3: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ X @ Y )
% 3.82/4.01 => ( ( ord_le72135733267957522d_enat @ Y @ Z3 )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ X @ Z3 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_trans
% 3.82/4.01 thf(fact_491_order__less__trans,axiom,
% 3.82/4.01 ! [X: real,Y: real,Z3: real] :
% 3.82/4.01 ( ( ord_less_real @ X @ Y )
% 3.82/4.01 => ( ( ord_less_real @ Y @ Z3 )
% 3.82/4.01 => ( ord_less_real @ X @ Z3 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_trans
% 3.82/4.01 thf(fact_492_order__less__trans,axiom,
% 3.82/4.01 ! [X: int,Y: int,Z3: int] :
% 3.82/4.01 ( ( ord_less_int @ X @ Y )
% 3.82/4.01 => ( ( ord_less_int @ Y @ Z3 )
% 3.82/4.01 => ( ord_less_int @ X @ Z3 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_trans
% 3.82/4.01 thf(fact_493_order__less__asym_H,axiom,
% 3.82/4.01 ! [A: nat,B2: nat] :
% 3.82/4.01 ( ( ord_less_nat @ A @ B2 )
% 3.82/4.01 => ~ ( ord_less_nat @ B2 @ A ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_asym'
% 3.82/4.01 thf(fact_494_order__less__asym_H,axiom,
% 3.82/4.01 ! [A: extended_enat,B2: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ A @ B2 )
% 3.82/4.01 => ~ ( ord_le72135733267957522d_enat @ B2 @ A ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_asym'
% 3.82/4.01 thf(fact_495_order__less__asym_H,axiom,
% 3.82/4.01 ! [A: real,B2: real] :
% 3.82/4.01 ( ( ord_less_real @ A @ B2 )
% 3.82/4.01 => ~ ( ord_less_real @ B2 @ A ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_asym'
% 3.82/4.01 thf(fact_496_order__less__asym_H,axiom,
% 3.82/4.01 ! [A: int,B2: int] :
% 3.82/4.01 ( ( ord_less_int @ A @ B2 )
% 3.82/4.01 => ~ ( ord_less_int @ B2 @ A ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_asym'
% 3.82/4.01 thf(fact_497_linorder__neq__iff,axiom,
% 3.82/4.01 ! [X: nat,Y: nat] :
% 3.82/4.01 ( ( X != Y )
% 3.82/4.01 = ( ( ord_less_nat @ X @ Y )
% 3.82/4.01 | ( ord_less_nat @ Y @ X ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % linorder_neq_iff
% 3.82/4.01 thf(fact_498_linorder__neq__iff,axiom,
% 3.82/4.01 ! [X: extended_enat,Y: extended_enat] :
% 3.82/4.01 ( ( X != Y )
% 3.82/4.01 = ( ( ord_le72135733267957522d_enat @ X @ Y )
% 3.82/4.01 | ( ord_le72135733267957522d_enat @ Y @ X ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % linorder_neq_iff
% 3.82/4.01 thf(fact_499_linorder__neq__iff,axiom,
% 3.82/4.01 ! [X: real,Y: real] :
% 3.82/4.01 ( ( X != Y )
% 3.82/4.01 = ( ( ord_less_real @ X @ Y )
% 3.82/4.01 | ( ord_less_real @ Y @ X ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % linorder_neq_iff
% 3.82/4.01 thf(fact_500_linorder__neq__iff,axiom,
% 3.82/4.01 ! [X: int,Y: int] :
% 3.82/4.01 ( ( X != Y )
% 3.82/4.01 = ( ( ord_less_int @ X @ Y )
% 3.82/4.01 | ( ord_less_int @ Y @ X ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % linorder_neq_iff
% 3.82/4.01 thf(fact_501_order__less__asym,axiom,
% 3.82/4.01 ! [X: nat,Y: nat] :
% 3.82/4.01 ( ( ord_less_nat @ X @ Y )
% 3.82/4.01 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_asym
% 3.82/4.01 thf(fact_502_order__less__asym,axiom,
% 3.82/4.01 ! [X: extended_enat,Y: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ X @ Y )
% 3.82/4.01 => ~ ( ord_le72135733267957522d_enat @ Y @ X ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_asym
% 3.82/4.01 thf(fact_503_order__less__asym,axiom,
% 3.82/4.01 ! [X: real,Y: real] :
% 3.82/4.01 ( ( ord_less_real @ X @ Y )
% 3.82/4.01 => ~ ( ord_less_real @ Y @ X ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_asym
% 3.82/4.01 thf(fact_504_order__less__asym,axiom,
% 3.82/4.01 ! [X: int,Y: int] :
% 3.82/4.01 ( ( ord_less_int @ X @ Y )
% 3.82/4.01 => ~ ( ord_less_int @ Y @ X ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_asym
% 3.82/4.01 thf(fact_505_linorder__neqE,axiom,
% 3.82/4.01 ! [X: nat,Y: nat] :
% 3.82/4.01 ( ( X != Y )
% 3.82/4.01 => ( ~ ( ord_less_nat @ X @ Y )
% 3.82/4.01 => ( ord_less_nat @ Y @ X ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % linorder_neqE
% 3.82/4.01 thf(fact_506_linorder__neqE,axiom,
% 3.82/4.01 ! [X: extended_enat,Y: extended_enat] :
% 3.82/4.01 ( ( X != Y )
% 3.82/4.01 => ( ~ ( ord_le72135733267957522d_enat @ X @ Y )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ Y @ X ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % linorder_neqE
% 3.82/4.01 thf(fact_507_linorder__neqE,axiom,
% 3.82/4.01 ! [X: real,Y: real] :
% 3.82/4.01 ( ( X != Y )
% 3.82/4.01 => ( ~ ( ord_less_real @ X @ Y )
% 3.82/4.01 => ( ord_less_real @ Y @ X ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % linorder_neqE
% 3.82/4.01 thf(fact_508_linorder__neqE,axiom,
% 3.82/4.01 ! [X: int,Y: int] :
% 3.82/4.01 ( ( X != Y )
% 3.82/4.01 => ( ~ ( ord_less_int @ X @ Y )
% 3.82/4.01 => ( ord_less_int @ Y @ X ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % linorder_neqE
% 3.82/4.01 thf(fact_509_dual__order_Ostrict__implies__not__eq,axiom,
% 3.82/4.01 ! [B2: nat,A: nat] :
% 3.82/4.01 ( ( ord_less_nat @ B2 @ A )
% 3.82/4.01 => ( A != B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.strict_implies_not_eq
% 3.82/4.01 thf(fact_510_dual__order_Ostrict__implies__not__eq,axiom,
% 3.82/4.01 ! [B2: extended_enat,A: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ B2 @ A )
% 3.82/4.01 => ( A != B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.strict_implies_not_eq
% 3.82/4.01 thf(fact_511_dual__order_Ostrict__implies__not__eq,axiom,
% 3.82/4.01 ! [B2: real,A: real] :
% 3.82/4.01 ( ( ord_less_real @ B2 @ A )
% 3.82/4.01 => ( A != B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.strict_implies_not_eq
% 3.82/4.01 thf(fact_512_dual__order_Ostrict__implies__not__eq,axiom,
% 3.82/4.01 ! [B2: int,A: int] :
% 3.82/4.01 ( ( ord_less_int @ B2 @ A )
% 3.82/4.01 => ( A != B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.strict_implies_not_eq
% 3.82/4.01 thf(fact_513_order_Ostrict__implies__not__eq,axiom,
% 3.82/4.01 ! [A: nat,B2: nat] :
% 3.82/4.01 ( ( ord_less_nat @ A @ B2 )
% 3.82/4.01 => ( A != B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.strict_implies_not_eq
% 3.82/4.01 thf(fact_514_order_Ostrict__implies__not__eq,axiom,
% 3.82/4.01 ! [A: extended_enat,B2: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ A @ B2 )
% 3.82/4.01 => ( A != B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.strict_implies_not_eq
% 3.82/4.01 thf(fact_515_order_Ostrict__implies__not__eq,axiom,
% 3.82/4.01 ! [A: real,B2: real] :
% 3.82/4.01 ( ( ord_less_real @ A @ B2 )
% 3.82/4.01 => ( A != B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.strict_implies_not_eq
% 3.82/4.01 thf(fact_516_order_Ostrict__implies__not__eq,axiom,
% 3.82/4.01 ! [A: int,B2: int] :
% 3.82/4.01 ( ( ord_less_int @ A @ B2 )
% 3.82/4.01 => ( A != B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.strict_implies_not_eq
% 3.82/4.01 thf(fact_517_dual__order_Ostrict__trans,axiom,
% 3.82/4.01 ! [B2: nat,A: nat,C: nat] :
% 3.82/4.01 ( ( ord_less_nat @ B2 @ A )
% 3.82/4.01 => ( ( ord_less_nat @ C @ B2 )
% 3.82/4.01 => ( ord_less_nat @ C @ A ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.strict_trans
% 3.82/4.01 thf(fact_518_dual__order_Ostrict__trans,axiom,
% 3.82/4.01 ! [B2: extended_enat,A: extended_enat,C: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ B2 @ A )
% 3.82/4.01 => ( ( ord_le72135733267957522d_enat @ C @ B2 )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ C @ A ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.strict_trans
% 3.82/4.01 thf(fact_519_dual__order_Ostrict__trans,axiom,
% 3.82/4.01 ! [B2: real,A: real,C: real] :
% 3.82/4.01 ( ( ord_less_real @ B2 @ A )
% 3.82/4.01 => ( ( ord_less_real @ C @ B2 )
% 3.82/4.01 => ( ord_less_real @ C @ A ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.strict_trans
% 3.82/4.01 thf(fact_520_dual__order_Ostrict__trans,axiom,
% 3.82/4.01 ! [B2: int,A: int,C: int] :
% 3.82/4.01 ( ( ord_less_int @ B2 @ A )
% 3.82/4.01 => ( ( ord_less_int @ C @ B2 )
% 3.82/4.01 => ( ord_less_int @ C @ A ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.strict_trans
% 3.82/4.01 thf(fact_521_not__less__iff__gr__or__eq,axiom,
% 3.82/4.01 ! [X: nat,Y: nat] :
% 3.82/4.01 ( ( ~ ( ord_less_nat @ X @ Y ) )
% 3.82/4.01 = ( ( ord_less_nat @ Y @ X )
% 3.82/4.01 | ( X = Y ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % not_less_iff_gr_or_eq
% 3.82/4.01 thf(fact_522_not__less__iff__gr__or__eq,axiom,
% 3.82/4.01 ! [X: extended_enat,Y: extended_enat] :
% 3.82/4.01 ( ( ~ ( ord_le72135733267957522d_enat @ X @ Y ) )
% 3.82/4.01 = ( ( ord_le72135733267957522d_enat @ Y @ X )
% 3.82/4.01 | ( X = Y ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % not_less_iff_gr_or_eq
% 3.82/4.01 thf(fact_523_not__less__iff__gr__or__eq,axiom,
% 3.82/4.01 ! [X: real,Y: real] :
% 3.82/4.01 ( ( ~ ( ord_less_real @ X @ Y ) )
% 3.82/4.01 = ( ( ord_less_real @ Y @ X )
% 3.82/4.01 | ( X = Y ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % not_less_iff_gr_or_eq
% 3.82/4.01 thf(fact_524_not__less__iff__gr__or__eq,axiom,
% 3.82/4.01 ! [X: int,Y: int] :
% 3.82/4.01 ( ( ~ ( ord_less_int @ X @ Y ) )
% 3.82/4.01 = ( ( ord_less_int @ Y @ X )
% 3.82/4.01 | ( X = Y ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % not_less_iff_gr_or_eq
% 3.82/4.01 thf(fact_525_order_Ostrict__trans,axiom,
% 3.82/4.01 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.01 ( ( ord_less_nat @ A @ B2 )
% 3.82/4.01 => ( ( ord_less_nat @ B2 @ C )
% 3.82/4.01 => ( ord_less_nat @ A @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.strict_trans
% 3.82/4.01 thf(fact_526_order_Ostrict__trans,axiom,
% 3.82/4.01 ! [A: extended_enat,B2: extended_enat,C: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ A @ B2 )
% 3.82/4.01 => ( ( ord_le72135733267957522d_enat @ B2 @ C )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ A @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.strict_trans
% 3.82/4.01 thf(fact_527_order_Ostrict__trans,axiom,
% 3.82/4.01 ! [A: real,B2: real,C: real] :
% 3.82/4.01 ( ( ord_less_real @ A @ B2 )
% 3.82/4.01 => ( ( ord_less_real @ B2 @ C )
% 3.82/4.01 => ( ord_less_real @ A @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.strict_trans
% 3.82/4.01 thf(fact_528_order_Ostrict__trans,axiom,
% 3.82/4.01 ! [A: int,B2: int,C: int] :
% 3.82/4.01 ( ( ord_less_int @ A @ B2 )
% 3.82/4.01 => ( ( ord_less_int @ B2 @ C )
% 3.82/4.01 => ( ord_less_int @ A @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.strict_trans
% 3.82/4.01 thf(fact_529_linorder__less__wlog,axiom,
% 3.82/4.01 ! [P: nat > nat > $o,A: nat,B2: nat] :
% 3.82/4.01 ( ! [A4: nat,B4: nat] :
% 3.82/4.01 ( ( ord_less_nat @ A4 @ B4 )
% 3.82/4.01 => ( P @ A4 @ B4 ) )
% 3.82/4.01 => ( ! [A4: nat] : ( P @ A4 @ A4 )
% 3.82/4.01 => ( ! [A4: nat,B4: nat] :
% 3.82/4.01 ( ( P @ B4 @ A4 )
% 3.82/4.01 => ( P @ A4 @ B4 ) )
% 3.82/4.01 => ( P @ A @ B2 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % linorder_less_wlog
% 3.82/4.01 thf(fact_530_linorder__less__wlog,axiom,
% 3.82/4.01 ! [P: extended_enat > extended_enat > $o,A: extended_enat,B2: extended_enat] :
% 3.82/4.01 ( ! [A4: extended_enat,B4: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ A4 @ B4 )
% 3.82/4.01 => ( P @ A4 @ B4 ) )
% 3.82/4.01 => ( ! [A4: extended_enat] : ( P @ A4 @ A4 )
% 3.82/4.01 => ( ! [A4: extended_enat,B4: extended_enat] :
% 3.82/4.01 ( ( P @ B4 @ A4 )
% 3.82/4.01 => ( P @ A4 @ B4 ) )
% 3.82/4.01 => ( P @ A @ B2 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % linorder_less_wlog
% 3.82/4.01 thf(fact_531_linorder__less__wlog,axiom,
% 3.82/4.01 ! [P: real > real > $o,A: real,B2: real] :
% 3.82/4.01 ( ! [A4: real,B4: real] :
% 3.82/4.01 ( ( ord_less_real @ A4 @ B4 )
% 3.82/4.01 => ( P @ A4 @ B4 ) )
% 3.82/4.01 => ( ! [A4: real] : ( P @ A4 @ A4 )
% 3.82/4.01 => ( ! [A4: real,B4: real] :
% 3.82/4.01 ( ( P @ B4 @ A4 )
% 3.82/4.01 => ( P @ A4 @ B4 ) )
% 3.82/4.01 => ( P @ A @ B2 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % linorder_less_wlog
% 3.82/4.01 thf(fact_532_linorder__less__wlog,axiom,
% 3.82/4.01 ! [P: int > int > $o,A: int,B2: int] :
% 3.82/4.01 ( ! [A4: int,B4: int] :
% 3.82/4.01 ( ( ord_less_int @ A4 @ B4 )
% 3.82/4.01 => ( P @ A4 @ B4 ) )
% 3.82/4.01 => ( ! [A4: int] : ( P @ A4 @ A4 )
% 3.82/4.01 => ( ! [A4: int,B4: int] :
% 3.82/4.01 ( ( P @ B4 @ A4 )
% 3.82/4.01 => ( P @ A4 @ B4 ) )
% 3.82/4.01 => ( P @ A @ B2 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % linorder_less_wlog
% 3.82/4.01 thf(fact_533_exists__least__iff,axiom,
% 3.82/4.01 ( ( ^ [P2: nat > $o] :
% 3.82/4.01 ? [X7: nat] : ( P2 @ X7 ) )
% 3.82/4.01 = ( ^ [P3: nat > $o] :
% 3.82/4.01 ? [N: nat] :
% 3.82/4.01 ( ( P3 @ N )
% 3.82/4.01 & ! [M: nat] :
% 3.82/4.01 ( ( ord_less_nat @ M @ N )
% 3.82/4.01 => ~ ( P3 @ M ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % exists_least_iff
% 3.82/4.01 thf(fact_534_exists__least__iff,axiom,
% 3.82/4.01 ( ( ^ [P2: extended_enat > $o] :
% 3.82/4.01 ? [X7: extended_enat] : ( P2 @ X7 ) )
% 3.82/4.01 = ( ^ [P3: extended_enat > $o] :
% 3.82/4.01 ? [N: extended_enat] :
% 3.82/4.01 ( ( P3 @ N )
% 3.82/4.01 & ! [M: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ M @ N )
% 3.82/4.01 => ~ ( P3 @ M ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % exists_least_iff
% 3.82/4.01 thf(fact_535_dual__order_Oirrefl,axiom,
% 3.82/4.01 ! [A: nat] :
% 3.82/4.01 ~ ( ord_less_nat @ A @ A ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.irrefl
% 3.82/4.01 thf(fact_536_dual__order_Oirrefl,axiom,
% 3.82/4.01 ! [A: extended_enat] :
% 3.82/4.01 ~ ( ord_le72135733267957522d_enat @ A @ A ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.irrefl
% 3.82/4.01 thf(fact_537_dual__order_Oirrefl,axiom,
% 3.82/4.01 ! [A: real] :
% 3.82/4.01 ~ ( ord_less_real @ A @ A ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.irrefl
% 3.82/4.01 thf(fact_538_dual__order_Oirrefl,axiom,
% 3.82/4.01 ! [A: int] :
% 3.82/4.01 ~ ( ord_less_int @ A @ A ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.irrefl
% 3.82/4.01 thf(fact_539_dual__order_Oasym,axiom,
% 3.82/4.01 ! [B2: nat,A: nat] :
% 3.82/4.01 ( ( ord_less_nat @ B2 @ A )
% 3.82/4.01 => ~ ( ord_less_nat @ A @ B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.asym
% 3.82/4.01 thf(fact_540_dual__order_Oasym,axiom,
% 3.82/4.01 ! [B2: extended_enat,A: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ B2 @ A )
% 3.82/4.01 => ~ ( ord_le72135733267957522d_enat @ A @ B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.asym
% 3.82/4.01 thf(fact_541_dual__order_Oasym,axiom,
% 3.82/4.01 ! [B2: real,A: real] :
% 3.82/4.01 ( ( ord_less_real @ B2 @ A )
% 3.82/4.01 => ~ ( ord_less_real @ A @ B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.asym
% 3.82/4.01 thf(fact_542_dual__order_Oasym,axiom,
% 3.82/4.01 ! [B2: int,A: int] :
% 3.82/4.01 ( ( ord_less_int @ B2 @ A )
% 3.82/4.01 => ~ ( ord_less_int @ A @ B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.asym
% 3.82/4.01 thf(fact_543_linorder__cases,axiom,
% 3.82/4.01 ! [X: nat,Y: nat] :
% 3.82/4.01 ( ~ ( ord_less_nat @ X @ Y )
% 3.82/4.01 => ( ( X != Y )
% 3.82/4.01 => ( ord_less_nat @ Y @ X ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % linorder_cases
% 3.82/4.01 thf(fact_544_linorder__cases,axiom,
% 3.82/4.01 ! [X: extended_enat,Y: extended_enat] :
% 3.82/4.01 ( ~ ( ord_le72135733267957522d_enat @ X @ Y )
% 3.82/4.01 => ( ( X != Y )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ Y @ X ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % linorder_cases
% 3.82/4.01 thf(fact_545_linorder__cases,axiom,
% 3.82/4.01 ! [X: real,Y: real] :
% 3.82/4.01 ( ~ ( ord_less_real @ X @ Y )
% 3.82/4.01 => ( ( X != Y )
% 3.82/4.01 => ( ord_less_real @ Y @ X ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % linorder_cases
% 3.82/4.01 thf(fact_546_linorder__cases,axiom,
% 3.82/4.01 ! [X: int,Y: int] :
% 3.82/4.01 ( ~ ( ord_less_int @ X @ Y )
% 3.82/4.01 => ( ( X != Y )
% 3.82/4.01 => ( ord_less_int @ Y @ X ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % linorder_cases
% 3.82/4.01 thf(fact_547_antisym__conv3,axiom,
% 3.82/4.01 ! [Y: nat,X: nat] :
% 3.82/4.01 ( ~ ( ord_less_nat @ Y @ X )
% 3.82/4.01 => ( ( ~ ( ord_less_nat @ X @ Y ) )
% 3.82/4.01 = ( X = Y ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % antisym_conv3
% 3.82/4.01 thf(fact_548_antisym__conv3,axiom,
% 3.82/4.01 ! [Y: extended_enat,X: extended_enat] :
% 3.82/4.01 ( ~ ( ord_le72135733267957522d_enat @ Y @ X )
% 3.82/4.01 => ( ( ~ ( ord_le72135733267957522d_enat @ X @ Y ) )
% 3.82/4.01 = ( X = Y ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % antisym_conv3
% 3.82/4.01 thf(fact_549_antisym__conv3,axiom,
% 3.82/4.01 ! [Y: real,X: real] :
% 3.82/4.01 ( ~ ( ord_less_real @ Y @ X )
% 3.82/4.01 => ( ( ~ ( ord_less_real @ X @ Y ) )
% 3.82/4.01 = ( X = Y ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % antisym_conv3
% 3.82/4.01 thf(fact_550_antisym__conv3,axiom,
% 3.82/4.01 ! [Y: int,X: int] :
% 3.82/4.01 ( ~ ( ord_less_int @ Y @ X )
% 3.82/4.01 => ( ( ~ ( ord_less_int @ X @ Y ) )
% 3.82/4.01 = ( X = Y ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % antisym_conv3
% 3.82/4.01 thf(fact_551_less__induct,axiom,
% 3.82/4.01 ! [P: nat > $o,A: nat] :
% 3.82/4.01 ( ! [X5: nat] :
% 3.82/4.01 ( ! [Y6: nat] :
% 3.82/4.01 ( ( ord_less_nat @ Y6 @ X5 )
% 3.82/4.01 => ( P @ Y6 ) )
% 3.82/4.01 => ( P @ X5 ) )
% 3.82/4.01 => ( P @ A ) ) ).
% 3.82/4.01
% 3.82/4.01 % less_induct
% 3.82/4.01 thf(fact_552_less__induct,axiom,
% 3.82/4.01 ! [P: extended_enat > $o,A: extended_enat] :
% 3.82/4.01 ( ! [X5: extended_enat] :
% 3.82/4.01 ( ! [Y6: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ Y6 @ X5 )
% 3.82/4.01 => ( P @ Y6 ) )
% 3.82/4.01 => ( P @ X5 ) )
% 3.82/4.01 => ( P @ A ) ) ).
% 3.82/4.01
% 3.82/4.01 % less_induct
% 3.82/4.01 thf(fact_553_ord__less__eq__trans,axiom,
% 3.82/4.01 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.01 ( ( ord_less_nat @ A @ B2 )
% 3.82/4.01 => ( ( B2 = C )
% 3.82/4.01 => ( ord_less_nat @ A @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % ord_less_eq_trans
% 3.82/4.01 thf(fact_554_ord__less__eq__trans,axiom,
% 3.82/4.01 ! [A: extended_enat,B2: extended_enat,C: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ A @ B2 )
% 3.82/4.01 => ( ( B2 = C )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ A @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % ord_less_eq_trans
% 3.82/4.01 thf(fact_555_ord__less__eq__trans,axiom,
% 3.82/4.01 ! [A: real,B2: real,C: real] :
% 3.82/4.01 ( ( ord_less_real @ A @ B2 )
% 3.82/4.01 => ( ( B2 = C )
% 3.82/4.01 => ( ord_less_real @ A @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % ord_less_eq_trans
% 3.82/4.01 thf(fact_556_ord__less__eq__trans,axiom,
% 3.82/4.01 ! [A: int,B2: int,C: int] :
% 3.82/4.01 ( ( ord_less_int @ A @ B2 )
% 3.82/4.01 => ( ( B2 = C )
% 3.82/4.01 => ( ord_less_int @ A @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % ord_less_eq_trans
% 3.82/4.01 thf(fact_557_ord__eq__less__trans,axiom,
% 3.82/4.01 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.01 ( ( A = B2 )
% 3.82/4.01 => ( ( ord_less_nat @ B2 @ C )
% 3.82/4.01 => ( ord_less_nat @ A @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % ord_eq_less_trans
% 3.82/4.01 thf(fact_558_ord__eq__less__trans,axiom,
% 3.82/4.01 ! [A: extended_enat,B2: extended_enat,C: extended_enat] :
% 3.82/4.01 ( ( A = B2 )
% 3.82/4.01 => ( ( ord_le72135733267957522d_enat @ B2 @ C )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ A @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % ord_eq_less_trans
% 3.82/4.01 thf(fact_559_ord__eq__less__trans,axiom,
% 3.82/4.01 ! [A: real,B2: real,C: real] :
% 3.82/4.01 ( ( A = B2 )
% 3.82/4.01 => ( ( ord_less_real @ B2 @ C )
% 3.82/4.01 => ( ord_less_real @ A @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % ord_eq_less_trans
% 3.82/4.01 thf(fact_560_ord__eq__less__trans,axiom,
% 3.82/4.01 ! [A: int,B2: int,C: int] :
% 3.82/4.01 ( ( A = B2 )
% 3.82/4.01 => ( ( ord_less_int @ B2 @ C )
% 3.82/4.01 => ( ord_less_int @ A @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % ord_eq_less_trans
% 3.82/4.01 thf(fact_561_order_Oasym,axiom,
% 3.82/4.01 ! [A: nat,B2: nat] :
% 3.82/4.01 ( ( ord_less_nat @ A @ B2 )
% 3.82/4.01 => ~ ( ord_less_nat @ B2 @ A ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.asym
% 3.82/4.01 thf(fact_562_order_Oasym,axiom,
% 3.82/4.01 ! [A: extended_enat,B2: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ A @ B2 )
% 3.82/4.01 => ~ ( ord_le72135733267957522d_enat @ B2 @ A ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.asym
% 3.82/4.01 thf(fact_563_order_Oasym,axiom,
% 3.82/4.01 ! [A: real,B2: real] :
% 3.82/4.01 ( ( ord_less_real @ A @ B2 )
% 3.82/4.01 => ~ ( ord_less_real @ B2 @ A ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.asym
% 3.82/4.01 thf(fact_564_order_Oasym,axiom,
% 3.82/4.01 ! [A: int,B2: int] :
% 3.82/4.01 ( ( ord_less_int @ A @ B2 )
% 3.82/4.01 => ~ ( ord_less_int @ B2 @ A ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.asym
% 3.82/4.01 thf(fact_565_less__imp__neq,axiom,
% 3.82/4.01 ! [X: nat,Y: nat] :
% 3.82/4.01 ( ( ord_less_nat @ X @ Y )
% 3.82/4.01 => ( X != Y ) ) ).
% 3.82/4.01
% 3.82/4.01 % less_imp_neq
% 3.82/4.01 thf(fact_566_less__imp__neq,axiom,
% 3.82/4.01 ! [X: extended_enat,Y: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ X @ Y )
% 3.82/4.01 => ( X != Y ) ) ).
% 3.82/4.01
% 3.82/4.01 % less_imp_neq
% 3.82/4.01 thf(fact_567_less__imp__neq,axiom,
% 3.82/4.01 ! [X: real,Y: real] :
% 3.82/4.01 ( ( ord_less_real @ X @ Y )
% 3.82/4.01 => ( X != Y ) ) ).
% 3.82/4.01
% 3.82/4.01 % less_imp_neq
% 3.82/4.01 thf(fact_568_less__imp__neq,axiom,
% 3.82/4.01 ! [X: int,Y: int] :
% 3.82/4.01 ( ( ord_less_int @ X @ Y )
% 3.82/4.01 => ( X != Y ) ) ).
% 3.82/4.01
% 3.82/4.01 % less_imp_neq
% 3.82/4.01 thf(fact_569_dense,axiom,
% 3.82/4.01 ! [X: real,Y: real] :
% 3.82/4.01 ( ( ord_less_real @ X @ Y )
% 3.82/4.01 => ? [Z: real] :
% 3.82/4.01 ( ( ord_less_real @ X @ Z )
% 3.82/4.01 & ( ord_less_real @ Z @ Y ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % dense
% 3.82/4.01 thf(fact_570_gt__ex,axiom,
% 3.82/4.01 ! [X: nat] :
% 3.82/4.01 ? [X_12: nat] : ( ord_less_nat @ X @ X_12 ) ).
% 3.82/4.01
% 3.82/4.01 % gt_ex
% 3.82/4.01 thf(fact_571_gt__ex,axiom,
% 3.82/4.01 ! [X: real] :
% 3.82/4.01 ? [X_12: real] : ( ord_less_real @ X @ X_12 ) ).
% 3.82/4.01
% 3.82/4.01 % gt_ex
% 3.82/4.01 thf(fact_572_gt__ex,axiom,
% 3.82/4.01 ! [X: int] :
% 3.82/4.01 ? [X_12: int] : ( ord_less_int @ X @ X_12 ) ).
% 3.82/4.01
% 3.82/4.01 % gt_ex
% 3.82/4.01 thf(fact_573_lt__ex,axiom,
% 3.82/4.01 ! [X: real] :
% 3.82/4.01 ? [Y3: real] : ( ord_less_real @ Y3 @ X ) ).
% 3.82/4.01
% 3.82/4.01 % lt_ex
% 3.82/4.01 thf(fact_574_lt__ex,axiom,
% 3.82/4.01 ! [X: int] :
% 3.82/4.01 ? [Y3: int] : ( ord_less_int @ Y3 @ X ) ).
% 3.82/4.01
% 3.82/4.01 % lt_ex
% 3.82/4.01 thf(fact_575_nth__list__update,axiom,
% 3.82/4.01 ! [I: nat,Xs: list_VEBT_VEBT,J: nat,X: vEBT_VEBT] :
% 3.82/4.01 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 3.82/4.01 => ( ( ( I = J )
% 3.82/4.01 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ J )
% 3.82/4.01 = X ) )
% 3.82/4.01 & ( ( I != J )
% 3.82/4.01 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ J )
% 3.82/4.01 = ( nth_VEBT_VEBT @ Xs @ J ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % nth_list_update
% 3.82/4.01 thf(fact_576_nth__list__update,axiom,
% 3.82/4.01 ! [I: nat,Xs: list_int,J: nat,X: int] :
% 3.82/4.01 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 3.82/4.01 => ( ( ( I = J )
% 3.82/4.01 => ( ( nth_int @ ( list_update_int @ Xs @ I @ X ) @ J )
% 3.82/4.01 = X ) )
% 3.82/4.01 & ( ( I != J )
% 3.82/4.01 => ( ( nth_int @ ( list_update_int @ Xs @ I @ X ) @ J )
% 3.82/4.01 = ( nth_int @ Xs @ J ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % nth_list_update
% 3.82/4.01 thf(fact_577_nth__list__update,axiom,
% 3.82/4.01 ! [I: nat,Xs: list_nat,J: nat,X: nat] :
% 3.82/4.01 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 3.82/4.01 => ( ( ( I = J )
% 3.82/4.01 => ( ( nth_nat @ ( list_update_nat @ Xs @ I @ X ) @ J )
% 3.82/4.01 = X ) )
% 3.82/4.01 & ( ( I != J )
% 3.82/4.01 => ( ( nth_nat @ ( list_update_nat @ Xs @ I @ X ) @ J )
% 3.82/4.01 = ( nth_nat @ Xs @ J ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % nth_list_update
% 3.82/4.01 thf(fact_578_list__update__same__conv,axiom,
% 3.82/4.01 ! [I: nat,Xs: list_VEBT_VEBT,X: vEBT_VEBT] :
% 3.82/4.01 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 3.82/4.01 => ( ( ( list_u1324408373059187874T_VEBT @ Xs @ I @ X )
% 3.82/4.01 = Xs )
% 3.82/4.01 = ( ( nth_VEBT_VEBT @ Xs @ I )
% 3.82/4.01 = X ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % list_update_same_conv
% 3.82/4.01 thf(fact_579_list__update__same__conv,axiom,
% 3.82/4.01 ! [I: nat,Xs: list_int,X: int] :
% 3.82/4.01 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 3.82/4.01 => ( ( ( list_update_int @ Xs @ I @ X )
% 3.82/4.01 = Xs )
% 3.82/4.01 = ( ( nth_int @ Xs @ I )
% 3.82/4.01 = X ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % list_update_same_conv
% 3.82/4.01 thf(fact_580_list__update__same__conv,axiom,
% 3.82/4.01 ! [I: nat,Xs: list_nat,X: nat] :
% 3.82/4.01 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 3.82/4.01 => ( ( ( list_update_nat @ Xs @ I @ X )
% 3.82/4.01 = Xs )
% 3.82/4.01 = ( ( nth_nat @ Xs @ I )
% 3.82/4.01 = X ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % list_update_same_conv
% 3.82/4.01 thf(fact_581_linorder__neqE__nat,axiom,
% 3.82/4.01 ! [X: nat,Y: nat] :
% 3.82/4.01 ( ( X != Y )
% 3.82/4.01 => ( ~ ( ord_less_nat @ X @ Y )
% 3.82/4.01 => ( ord_less_nat @ Y @ X ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % linorder_neqE_nat
% 3.82/4.01 thf(fact_582_infinite__descent,axiom,
% 3.82/4.01 ! [P: nat > $o,N2: nat] :
% 3.82/4.01 ( ! [N3: nat] :
% 3.82/4.01 ( ~ ( P @ N3 )
% 3.82/4.01 => ? [M5: nat] :
% 3.82/4.01 ( ( ord_less_nat @ M5 @ N3 )
% 3.82/4.01 & ~ ( P @ M5 ) ) )
% 3.82/4.01 => ( P @ N2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % infinite_descent
% 3.82/4.01 thf(fact_583_nat__less__induct,axiom,
% 3.82/4.01 ! [P: nat > $o,N2: nat] :
% 3.82/4.01 ( ! [N3: nat] :
% 3.82/4.01 ( ! [M5: nat] :
% 3.82/4.01 ( ( ord_less_nat @ M5 @ N3 )
% 3.82/4.01 => ( P @ M5 ) )
% 3.82/4.01 => ( P @ N3 ) )
% 3.82/4.01 => ( P @ N2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % nat_less_induct
% 3.82/4.01 thf(fact_584_less__irrefl__nat,axiom,
% 3.82/4.01 ! [N2: nat] :
% 3.82/4.01 ~ ( ord_less_nat @ N2 @ N2 ) ).
% 3.82/4.01
% 3.82/4.01 % less_irrefl_nat
% 3.82/4.01 thf(fact_585_less__not__refl3,axiom,
% 3.82/4.01 ! [S: nat,T: nat] :
% 3.82/4.01 ( ( ord_less_nat @ S @ T )
% 3.82/4.01 => ( S != T ) ) ).
% 3.82/4.01
% 3.82/4.01 % less_not_refl3
% 3.82/4.01 thf(fact_586_less__not__refl2,axiom,
% 3.82/4.01 ! [N2: nat,M2: nat] :
% 3.82/4.01 ( ( ord_less_nat @ N2 @ M2 )
% 3.82/4.01 => ( M2 != N2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % less_not_refl2
% 3.82/4.01 thf(fact_587_less__not__refl,axiom,
% 3.82/4.01 ! [N2: nat] :
% 3.82/4.01 ~ ( ord_less_nat @ N2 @ N2 ) ).
% 3.82/4.01
% 3.82/4.01 % less_not_refl
% 3.82/4.01 thf(fact_588_nat__neq__iff,axiom,
% 3.82/4.01 ! [M2: nat,N2: nat] :
% 3.82/4.01 ( ( M2 != N2 )
% 3.82/4.01 = ( ( ord_less_nat @ M2 @ N2 )
% 3.82/4.01 | ( ord_less_nat @ N2 @ M2 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % nat_neq_iff
% 3.82/4.01 thf(fact_589_Nat_Oex__has__greatest__nat,axiom,
% 3.82/4.01 ! [P: nat > $o,K: nat,B2: nat] :
% 3.82/4.01 ( ( P @ K )
% 3.82/4.01 => ( ! [Y3: nat] :
% 3.82/4.01 ( ( P @ Y3 )
% 3.82/4.01 => ( ord_less_eq_nat @ Y3 @ B2 ) )
% 3.82/4.01 => ? [X5: nat] :
% 3.82/4.01 ( ( P @ X5 )
% 3.82/4.01 & ! [Y6: nat] :
% 3.82/4.01 ( ( P @ Y6 )
% 3.82/4.01 => ( ord_less_eq_nat @ Y6 @ X5 ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % Nat.ex_has_greatest_nat
% 3.82/4.01 thf(fact_590_nat__le__linear,axiom,
% 3.82/4.01 ! [M2: nat,N2: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.01 | ( ord_less_eq_nat @ N2 @ M2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % nat_le_linear
% 3.82/4.01 thf(fact_591_le__antisym,axiom,
% 3.82/4.01 ! [M2: nat,N2: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.01 => ( ( ord_less_eq_nat @ N2 @ M2 )
% 3.82/4.01 => ( M2 = N2 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % le_antisym
% 3.82/4.01 thf(fact_592_eq__imp__le,axiom,
% 3.82/4.01 ! [M2: nat,N2: nat] :
% 3.82/4.01 ( ( M2 = N2 )
% 3.82/4.01 => ( ord_less_eq_nat @ M2 @ N2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % eq_imp_le
% 3.82/4.01 thf(fact_593_le__trans,axiom,
% 3.82/4.01 ! [I: nat,J: nat,K: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ I @ J )
% 3.82/4.01 => ( ( ord_less_eq_nat @ J @ K )
% 3.82/4.01 => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % le_trans
% 3.82/4.01 thf(fact_594_le__refl,axiom,
% 3.82/4.01 ! [N2: nat] : ( ord_less_eq_nat @ N2 @ N2 ) ).
% 3.82/4.01
% 3.82/4.01 % le_refl
% 3.82/4.01 thf(fact_595_order__le__imp__less__or__eq,axiom,
% 3.82/4.01 ! [X: extended_enat,Y: extended_enat] :
% 3.82/4.01 ( ( ord_le2932123472753598470d_enat @ X @ Y )
% 3.82/4.01 => ( ( ord_le72135733267957522d_enat @ X @ Y )
% 3.82/4.01 | ( X = Y ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_le_imp_less_or_eq
% 3.82/4.01 thf(fact_596_order__le__imp__less__or__eq,axiom,
% 3.82/4.01 ! [X: real,Y: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ X @ Y )
% 3.82/4.01 => ( ( ord_less_real @ X @ Y )
% 3.82/4.01 | ( X = Y ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_le_imp_less_or_eq
% 3.82/4.01 thf(fact_597_order__le__imp__less__or__eq,axiom,
% 3.82/4.01 ! [X: set_nat,Y: set_nat] :
% 3.82/4.01 ( ( ord_less_eq_set_nat @ X @ Y )
% 3.82/4.01 => ( ( ord_less_set_nat @ X @ Y )
% 3.82/4.01 | ( X = Y ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_le_imp_less_or_eq
% 3.82/4.01 thf(fact_598_order__le__imp__less__or__eq,axiom,
% 3.82/4.01 ! [X: set_int,Y: set_int] :
% 3.82/4.01 ( ( ord_less_eq_set_int @ X @ Y )
% 3.82/4.01 => ( ( ord_less_set_int @ X @ Y )
% 3.82/4.01 | ( X = Y ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_le_imp_less_or_eq
% 3.82/4.01 thf(fact_599_order__le__imp__less__or__eq,axiom,
% 3.82/4.01 ! [X: nat,Y: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ X @ Y )
% 3.82/4.01 => ( ( ord_less_nat @ X @ Y )
% 3.82/4.01 | ( X = Y ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_le_imp_less_or_eq
% 3.82/4.01 thf(fact_600_order__le__imp__less__or__eq,axiom,
% 3.82/4.01 ! [X: int,Y: int] :
% 3.82/4.01 ( ( ord_less_eq_int @ X @ Y )
% 3.82/4.01 => ( ( ord_less_int @ X @ Y )
% 3.82/4.01 | ( X = Y ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_le_imp_less_or_eq
% 3.82/4.01 thf(fact_601_linorder__le__less__linear,axiom,
% 3.82/4.01 ! [X: extended_enat,Y: extended_enat] :
% 3.82/4.01 ( ( ord_le2932123472753598470d_enat @ X @ Y )
% 3.82/4.01 | ( ord_le72135733267957522d_enat @ Y @ X ) ) ).
% 3.82/4.01
% 3.82/4.01 % linorder_le_less_linear
% 3.82/4.01 thf(fact_602_linorder__le__less__linear,axiom,
% 3.82/4.01 ! [X: real,Y: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ X @ Y )
% 3.82/4.01 | ( ord_less_real @ Y @ X ) ) ).
% 3.82/4.01
% 3.82/4.01 % linorder_le_less_linear
% 3.82/4.01 thf(fact_603_linorder__le__less__linear,axiom,
% 3.82/4.01 ! [X: nat,Y: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ X @ Y )
% 3.82/4.01 | ( ord_less_nat @ Y @ X ) ) ).
% 3.82/4.01
% 3.82/4.01 % linorder_le_less_linear
% 3.82/4.01 thf(fact_604_linorder__le__less__linear,axiom,
% 3.82/4.01 ! [X: int,Y: int] :
% 3.82/4.01 ( ( ord_less_eq_int @ X @ Y )
% 3.82/4.01 | ( ord_less_int @ Y @ X ) ) ).
% 3.82/4.01
% 3.82/4.01 % linorder_le_less_linear
% 3.82/4.01 thf(fact_605_order__less__le__subst2,axiom,
% 3.82/4.01 ! [A: nat,B2: nat,F: nat > extended_enat,C: extended_enat] :
% 3.82/4.01 ( ( ord_less_nat @ A @ B2 )
% 3.82/4.01 => ( ( ord_le2932123472753598470d_enat @ ( F @ B2 ) @ C )
% 3.82/4.01 => ( ! [X5: nat,Y3: nat] :
% 3.82/4.01 ( ( ord_less_nat @ X5 @ Y3 )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_le_subst2
% 3.82/4.01 thf(fact_606_order__less__le__subst2,axiom,
% 3.82/4.01 ! [A: extended_enat,B2: extended_enat,F: extended_enat > extended_enat,C: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ A @ B2 )
% 3.82/4.01 => ( ( ord_le2932123472753598470d_enat @ ( F @ B2 ) @ C )
% 3.82/4.01 => ( ! [X5: extended_enat,Y3: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ X5 @ Y3 )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_le_subst2
% 3.82/4.01 thf(fact_607_order__less__le__subst2,axiom,
% 3.82/4.01 ! [A: real,B2: real,F: real > extended_enat,C: extended_enat] :
% 3.82/4.01 ( ( ord_less_real @ A @ B2 )
% 3.82/4.01 => ( ( ord_le2932123472753598470d_enat @ ( F @ B2 ) @ C )
% 3.82/4.01 => ( ! [X5: real,Y3: real] :
% 3.82/4.01 ( ( ord_less_real @ X5 @ Y3 )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_le_subst2
% 3.82/4.01 thf(fact_608_order__less__le__subst2,axiom,
% 3.82/4.01 ! [A: int,B2: int,F: int > extended_enat,C: extended_enat] :
% 3.82/4.01 ( ( ord_less_int @ A @ B2 )
% 3.82/4.01 => ( ( ord_le2932123472753598470d_enat @ ( F @ B2 ) @ C )
% 3.82/4.01 => ( ! [X5: int,Y3: int] :
% 3.82/4.01 ( ( ord_less_int @ X5 @ Y3 )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_le_subst2
% 3.82/4.01 thf(fact_609_order__less__le__subst2,axiom,
% 3.82/4.01 ! [A: nat,B2: nat,F: nat > real,C: real] :
% 3.82/4.01 ( ( ord_less_nat @ A @ B2 )
% 3.82/4.01 => ( ( ord_less_eq_real @ ( F @ B2 ) @ C )
% 3.82/4.01 => ( ! [X5: nat,Y3: nat] :
% 3.82/4.01 ( ( ord_less_nat @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_le_subst2
% 3.82/4.01 thf(fact_610_order__less__le__subst2,axiom,
% 3.82/4.01 ! [A: extended_enat,B2: extended_enat,F: extended_enat > real,C: real] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ A @ B2 )
% 3.82/4.01 => ( ( ord_less_eq_real @ ( F @ B2 ) @ C )
% 3.82/4.01 => ( ! [X5: extended_enat,Y3: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_le_subst2
% 3.82/4.01 thf(fact_611_order__less__le__subst2,axiom,
% 3.82/4.01 ! [A: real,B2: real,F: real > real,C: real] :
% 3.82/4.01 ( ( ord_less_real @ A @ B2 )
% 3.82/4.01 => ( ( ord_less_eq_real @ ( F @ B2 ) @ C )
% 3.82/4.01 => ( ! [X5: real,Y3: real] :
% 3.82/4.01 ( ( ord_less_real @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_le_subst2
% 3.82/4.01 thf(fact_612_order__less__le__subst2,axiom,
% 3.82/4.01 ! [A: int,B2: int,F: int > real,C: real] :
% 3.82/4.01 ( ( ord_less_int @ A @ B2 )
% 3.82/4.01 => ( ( ord_less_eq_real @ ( F @ B2 ) @ C )
% 3.82/4.01 => ( ! [X5: int,Y3: int] :
% 3.82/4.01 ( ( ord_less_int @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_le_subst2
% 3.82/4.01 thf(fact_613_order__less__le__subst2,axiom,
% 3.82/4.01 ! [A: nat,B2: nat,F: nat > nat,C: nat] :
% 3.82/4.01 ( ( ord_less_nat @ A @ B2 )
% 3.82/4.01 => ( ( ord_less_eq_nat @ ( F @ B2 ) @ C )
% 3.82/4.01 => ( ! [X5: nat,Y3: nat] :
% 3.82/4.01 ( ( ord_less_nat @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_le_subst2
% 3.82/4.01 thf(fact_614_order__less__le__subst2,axiom,
% 3.82/4.01 ! [A: extended_enat,B2: extended_enat,F: extended_enat > nat,C: nat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ A @ B2 )
% 3.82/4.01 => ( ( ord_less_eq_nat @ ( F @ B2 ) @ C )
% 3.82/4.01 => ( ! [X5: extended_enat,Y3: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_le_subst2
% 3.82/4.01 thf(fact_615_order__less__le__subst1,axiom,
% 3.82/4.01 ! [A: extended_enat,F: real > extended_enat,B2: real,C: real] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ A @ ( F @ B2 ) )
% 3.82/4.01 => ( ( ord_less_eq_real @ B2 @ C )
% 3.82/4.01 => ( ! [X5: real,Y3: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ X5 @ Y3 )
% 3.82/4.01 => ( ord_le2932123472753598470d_enat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_le_subst1
% 3.82/4.01 thf(fact_616_order__less__le__subst1,axiom,
% 3.82/4.01 ! [A: real,F: real > real,B2: real,C: real] :
% 3.82/4.01 ( ( ord_less_real @ A @ ( F @ B2 ) )
% 3.82/4.01 => ( ( ord_less_eq_real @ B2 @ C )
% 3.82/4.01 => ( ! [X5: real,Y3: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_eq_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_le_subst1
% 3.82/4.01 thf(fact_617_order__less__le__subst1,axiom,
% 3.82/4.01 ! [A: nat,F: real > nat,B2: real,C: real] :
% 3.82/4.01 ( ( ord_less_nat @ A @ ( F @ B2 ) )
% 3.82/4.01 => ( ( ord_less_eq_real @ B2 @ C )
% 3.82/4.01 => ( ! [X5: real,Y3: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_le_subst1
% 3.82/4.01 thf(fact_618_order__less__le__subst1,axiom,
% 3.82/4.01 ! [A: int,F: real > int,B2: real,C: real] :
% 3.82/4.01 ( ( ord_less_int @ A @ ( F @ B2 ) )
% 3.82/4.01 => ( ( ord_less_eq_real @ B2 @ C )
% 3.82/4.01 => ( ! [X5: real,Y3: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_le_subst1
% 3.82/4.01 thf(fact_619_order__less__le__subst1,axiom,
% 3.82/4.01 ! [A: extended_enat,F: nat > extended_enat,B2: nat,C: nat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ A @ ( F @ B2 ) )
% 3.82/4.01 => ( ( ord_less_eq_nat @ B2 @ C )
% 3.82/4.01 => ( ! [X5: nat,Y3: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 3.82/4.01 => ( ord_le2932123472753598470d_enat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_le_subst1
% 3.82/4.01 thf(fact_620_order__less__le__subst1,axiom,
% 3.82/4.01 ! [A: real,F: nat > real,B2: nat,C: nat] :
% 3.82/4.01 ( ( ord_less_real @ A @ ( F @ B2 ) )
% 3.82/4.01 => ( ( ord_less_eq_nat @ B2 @ C )
% 3.82/4.01 => ( ! [X5: nat,Y3: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_eq_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_le_subst1
% 3.82/4.01 thf(fact_621_order__less__le__subst1,axiom,
% 3.82/4.01 ! [A: nat,F: nat > nat,B2: nat,C: nat] :
% 3.82/4.01 ( ( ord_less_nat @ A @ ( F @ B2 ) )
% 3.82/4.01 => ( ( ord_less_eq_nat @ B2 @ C )
% 3.82/4.01 => ( ! [X5: nat,Y3: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_le_subst1
% 3.82/4.01 thf(fact_622_order__less__le__subst1,axiom,
% 3.82/4.01 ! [A: int,F: nat > int,B2: nat,C: nat] :
% 3.82/4.01 ( ( ord_less_int @ A @ ( F @ B2 ) )
% 3.82/4.01 => ( ( ord_less_eq_nat @ B2 @ C )
% 3.82/4.01 => ( ! [X5: nat,Y3: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_le_subst1
% 3.82/4.01 thf(fact_623_order__less__le__subst1,axiom,
% 3.82/4.01 ! [A: extended_enat,F: int > extended_enat,B2: int,C: int] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ A @ ( F @ B2 ) )
% 3.82/4.01 => ( ( ord_less_eq_int @ B2 @ C )
% 3.82/4.01 => ( ! [X5: int,Y3: int] :
% 3.82/4.01 ( ( ord_less_eq_int @ X5 @ Y3 )
% 3.82/4.01 => ( ord_le2932123472753598470d_enat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_le_subst1
% 3.82/4.01 thf(fact_624_order__less__le__subst1,axiom,
% 3.82/4.01 ! [A: real,F: int > real,B2: int,C: int] :
% 3.82/4.01 ( ( ord_less_real @ A @ ( F @ B2 ) )
% 3.82/4.01 => ( ( ord_less_eq_int @ B2 @ C )
% 3.82/4.01 => ( ! [X5: int,Y3: int] :
% 3.82/4.01 ( ( ord_less_eq_int @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_eq_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_le_subst1
% 3.82/4.01 thf(fact_625_order__le__less__subst2,axiom,
% 3.82/4.01 ! [A: real,B2: real,F: real > extended_enat,C: extended_enat] :
% 3.82/4.01 ( ( ord_less_eq_real @ A @ B2 )
% 3.82/4.01 => ( ( ord_le72135733267957522d_enat @ ( F @ B2 ) @ C )
% 3.82/4.01 => ( ! [X5: real,Y3: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ X5 @ Y3 )
% 3.82/4.01 => ( ord_le2932123472753598470d_enat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_le_less_subst2
% 3.82/4.01 thf(fact_626_order__le__less__subst2,axiom,
% 3.82/4.01 ! [A: real,B2: real,F: real > real,C: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ A @ B2 )
% 3.82/4.01 => ( ( ord_less_real @ ( F @ B2 ) @ C )
% 3.82/4.01 => ( ! [X5: real,Y3: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_eq_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_le_less_subst2
% 3.82/4.01 thf(fact_627_order__le__less__subst2,axiom,
% 3.82/4.01 ! [A: real,B2: real,F: real > nat,C: nat] :
% 3.82/4.01 ( ( ord_less_eq_real @ A @ B2 )
% 3.82/4.01 => ( ( ord_less_nat @ ( F @ B2 ) @ C )
% 3.82/4.01 => ( ! [X5: real,Y3: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_le_less_subst2
% 3.82/4.01 thf(fact_628_order__le__less__subst2,axiom,
% 3.82/4.01 ! [A: real,B2: real,F: real > int,C: int] :
% 3.82/4.01 ( ( ord_less_eq_real @ A @ B2 )
% 3.82/4.01 => ( ( ord_less_int @ ( F @ B2 ) @ C )
% 3.82/4.01 => ( ! [X5: real,Y3: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_le_less_subst2
% 3.82/4.01 thf(fact_629_order__le__less__subst2,axiom,
% 3.82/4.01 ! [A: nat,B2: nat,F: nat > extended_enat,C: extended_enat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ A @ B2 )
% 3.82/4.01 => ( ( ord_le72135733267957522d_enat @ ( F @ B2 ) @ C )
% 3.82/4.01 => ( ! [X5: nat,Y3: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 3.82/4.01 => ( ord_le2932123472753598470d_enat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_le_less_subst2
% 3.82/4.01 thf(fact_630_order__le__less__subst2,axiom,
% 3.82/4.01 ! [A: nat,B2: nat,F: nat > real,C: real] :
% 3.82/4.01 ( ( ord_less_eq_nat @ A @ B2 )
% 3.82/4.01 => ( ( ord_less_real @ ( F @ B2 ) @ C )
% 3.82/4.01 => ( ! [X5: nat,Y3: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_eq_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_le_less_subst2
% 3.82/4.01 thf(fact_631_order__le__less__subst2,axiom,
% 3.82/4.01 ! [A: nat,B2: nat,F: nat > nat,C: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ A @ B2 )
% 3.82/4.01 => ( ( ord_less_nat @ ( F @ B2 ) @ C )
% 3.82/4.01 => ( ! [X5: nat,Y3: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_le_less_subst2
% 3.82/4.01 thf(fact_632_order__le__less__subst2,axiom,
% 3.82/4.01 ! [A: nat,B2: nat,F: nat > int,C: int] :
% 3.82/4.01 ( ( ord_less_eq_nat @ A @ B2 )
% 3.82/4.01 => ( ( ord_less_int @ ( F @ B2 ) @ C )
% 3.82/4.01 => ( ! [X5: nat,Y3: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_le_less_subst2
% 3.82/4.01 thf(fact_633_order__le__less__subst2,axiom,
% 3.82/4.01 ! [A: int,B2: int,F: int > extended_enat,C: extended_enat] :
% 3.82/4.01 ( ( ord_less_eq_int @ A @ B2 )
% 3.82/4.01 => ( ( ord_le72135733267957522d_enat @ ( F @ B2 ) @ C )
% 3.82/4.01 => ( ! [X5: int,Y3: int] :
% 3.82/4.01 ( ( ord_less_eq_int @ X5 @ Y3 )
% 3.82/4.01 => ( ord_le2932123472753598470d_enat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_le_less_subst2
% 3.82/4.01 thf(fact_634_order__le__less__subst2,axiom,
% 3.82/4.01 ! [A: int,B2: int,F: int > real,C: real] :
% 3.82/4.01 ( ( ord_less_eq_int @ A @ B2 )
% 3.82/4.01 => ( ( ord_less_real @ ( F @ B2 ) @ C )
% 3.82/4.01 => ( ! [X5: int,Y3: int] :
% 3.82/4.01 ( ( ord_less_eq_int @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_eq_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_le_less_subst2
% 3.82/4.01 thf(fact_635_order__le__less__subst1,axiom,
% 3.82/4.01 ! [A: extended_enat,F: nat > extended_enat,B2: nat,C: nat] :
% 3.82/4.01 ( ( ord_le2932123472753598470d_enat @ A @ ( F @ B2 ) )
% 3.82/4.01 => ( ( ord_less_nat @ B2 @ C )
% 3.82/4.01 => ( ! [X5: nat,Y3: nat] :
% 3.82/4.01 ( ( ord_less_nat @ X5 @ Y3 )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_le_less_subst1
% 3.82/4.01 thf(fact_636_order__le__less__subst1,axiom,
% 3.82/4.01 ! [A: extended_enat,F: extended_enat > extended_enat,B2: extended_enat,C: extended_enat] :
% 3.82/4.01 ( ( ord_le2932123472753598470d_enat @ A @ ( F @ B2 ) )
% 3.82/4.01 => ( ( ord_le72135733267957522d_enat @ B2 @ C )
% 3.82/4.01 => ( ! [X5: extended_enat,Y3: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ X5 @ Y3 )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_le_less_subst1
% 3.82/4.01 thf(fact_637_order__le__less__subst1,axiom,
% 3.82/4.01 ! [A: extended_enat,F: real > extended_enat,B2: real,C: real] :
% 3.82/4.01 ( ( ord_le2932123472753598470d_enat @ A @ ( F @ B2 ) )
% 3.82/4.01 => ( ( ord_less_real @ B2 @ C )
% 3.82/4.01 => ( ! [X5: real,Y3: real] :
% 3.82/4.01 ( ( ord_less_real @ X5 @ Y3 )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_le_less_subst1
% 3.82/4.01 thf(fact_638_order__le__less__subst1,axiom,
% 3.82/4.01 ! [A: extended_enat,F: int > extended_enat,B2: int,C: int] :
% 3.82/4.01 ( ( ord_le2932123472753598470d_enat @ A @ ( F @ B2 ) )
% 3.82/4.01 => ( ( ord_less_int @ B2 @ C )
% 3.82/4.01 => ( ! [X5: int,Y3: int] :
% 3.82/4.01 ( ( ord_less_int @ X5 @ Y3 )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_le_less_subst1
% 3.82/4.01 thf(fact_639_order__le__less__subst1,axiom,
% 3.82/4.01 ! [A: real,F: nat > real,B2: nat,C: nat] :
% 3.82/4.01 ( ( ord_less_eq_real @ A @ ( F @ B2 ) )
% 3.82/4.01 => ( ( ord_less_nat @ B2 @ C )
% 3.82/4.01 => ( ! [X5: nat,Y3: nat] :
% 3.82/4.01 ( ( ord_less_nat @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_le_less_subst1
% 3.82/4.01 thf(fact_640_order__le__less__subst1,axiom,
% 3.82/4.01 ! [A: real,F: extended_enat > real,B2: extended_enat,C: extended_enat] :
% 3.82/4.01 ( ( ord_less_eq_real @ A @ ( F @ B2 ) )
% 3.82/4.01 => ( ( ord_le72135733267957522d_enat @ B2 @ C )
% 3.82/4.01 => ( ! [X5: extended_enat,Y3: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_le_less_subst1
% 3.82/4.01 thf(fact_641_order__le__less__subst1,axiom,
% 3.82/4.01 ! [A: real,F: real > real,B2: real,C: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ A @ ( F @ B2 ) )
% 3.82/4.01 => ( ( ord_less_real @ B2 @ C )
% 3.82/4.01 => ( ! [X5: real,Y3: real] :
% 3.82/4.01 ( ( ord_less_real @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_le_less_subst1
% 3.82/4.01 thf(fact_642_order__le__less__subst1,axiom,
% 3.82/4.01 ! [A: real,F: int > real,B2: int,C: int] :
% 3.82/4.01 ( ( ord_less_eq_real @ A @ ( F @ B2 ) )
% 3.82/4.01 => ( ( ord_less_int @ B2 @ C )
% 3.82/4.01 => ( ! [X5: int,Y3: int] :
% 3.82/4.01 ( ( ord_less_int @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_le_less_subst1
% 3.82/4.01 thf(fact_643_order__le__less__subst1,axiom,
% 3.82/4.01 ! [A: nat,F: nat > nat,B2: nat,C: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ A @ ( F @ B2 ) )
% 3.82/4.01 => ( ( ord_less_nat @ B2 @ C )
% 3.82/4.01 => ( ! [X5: nat,Y3: nat] :
% 3.82/4.01 ( ( ord_less_nat @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_le_less_subst1
% 3.82/4.01 thf(fact_644_order__le__less__subst1,axiom,
% 3.82/4.01 ! [A: nat,F: extended_enat > nat,B2: extended_enat,C: extended_enat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ A @ ( F @ B2 ) )
% 3.82/4.01 => ( ( ord_le72135733267957522d_enat @ B2 @ C )
% 3.82/4.01 => ( ! [X5: extended_enat,Y3: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ X5 @ Y3 )
% 3.82/4.01 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 3.82/4.01 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_le_less_subst1
% 3.82/4.01 thf(fact_645_order__less__le__trans,axiom,
% 3.82/4.01 ! [X: extended_enat,Y: extended_enat,Z3: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ X @ Y )
% 3.82/4.01 => ( ( ord_le2932123472753598470d_enat @ Y @ Z3 )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ X @ Z3 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_le_trans
% 3.82/4.01 thf(fact_646_order__less__le__trans,axiom,
% 3.82/4.01 ! [X: real,Y: real,Z3: real] :
% 3.82/4.01 ( ( ord_less_real @ X @ Y )
% 3.82/4.01 => ( ( ord_less_eq_real @ Y @ Z3 )
% 3.82/4.01 => ( ord_less_real @ X @ Z3 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_le_trans
% 3.82/4.01 thf(fact_647_order__less__le__trans,axiom,
% 3.82/4.01 ! [X: set_nat,Y: set_nat,Z3: set_nat] :
% 3.82/4.01 ( ( ord_less_set_nat @ X @ Y )
% 3.82/4.01 => ( ( ord_less_eq_set_nat @ Y @ Z3 )
% 3.82/4.01 => ( ord_less_set_nat @ X @ Z3 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_le_trans
% 3.82/4.01 thf(fact_648_order__less__le__trans,axiom,
% 3.82/4.01 ! [X: set_int,Y: set_int,Z3: set_int] :
% 3.82/4.01 ( ( ord_less_set_int @ X @ Y )
% 3.82/4.01 => ( ( ord_less_eq_set_int @ Y @ Z3 )
% 3.82/4.01 => ( ord_less_set_int @ X @ Z3 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_le_trans
% 3.82/4.01 thf(fact_649_order__less__le__trans,axiom,
% 3.82/4.01 ! [X: nat,Y: nat,Z3: nat] :
% 3.82/4.01 ( ( ord_less_nat @ X @ Y )
% 3.82/4.01 => ( ( ord_less_eq_nat @ Y @ Z3 )
% 3.82/4.01 => ( ord_less_nat @ X @ Z3 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_le_trans
% 3.82/4.01 thf(fact_650_order__less__le__trans,axiom,
% 3.82/4.01 ! [X: int,Y: int,Z3: int] :
% 3.82/4.01 ( ( ord_less_int @ X @ Y )
% 3.82/4.01 => ( ( ord_less_eq_int @ Y @ Z3 )
% 3.82/4.01 => ( ord_less_int @ X @ Z3 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_le_trans
% 3.82/4.01 thf(fact_651_order__le__less__trans,axiom,
% 3.82/4.01 ! [X: extended_enat,Y: extended_enat,Z3: extended_enat] :
% 3.82/4.01 ( ( ord_le2932123472753598470d_enat @ X @ Y )
% 3.82/4.01 => ( ( ord_le72135733267957522d_enat @ Y @ Z3 )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ X @ Z3 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_le_less_trans
% 3.82/4.01 thf(fact_652_order__le__less__trans,axiom,
% 3.82/4.01 ! [X: real,Y: real,Z3: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ X @ Y )
% 3.82/4.01 => ( ( ord_less_real @ Y @ Z3 )
% 3.82/4.01 => ( ord_less_real @ X @ Z3 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_le_less_trans
% 3.82/4.01 thf(fact_653_order__le__less__trans,axiom,
% 3.82/4.01 ! [X: set_nat,Y: set_nat,Z3: set_nat] :
% 3.82/4.01 ( ( ord_less_eq_set_nat @ X @ Y )
% 3.82/4.01 => ( ( ord_less_set_nat @ Y @ Z3 )
% 3.82/4.01 => ( ord_less_set_nat @ X @ Z3 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_le_less_trans
% 3.82/4.01 thf(fact_654_order__le__less__trans,axiom,
% 3.82/4.01 ! [X: set_int,Y: set_int,Z3: set_int] :
% 3.82/4.01 ( ( ord_less_eq_set_int @ X @ Y )
% 3.82/4.01 => ( ( ord_less_set_int @ Y @ Z3 )
% 3.82/4.01 => ( ord_less_set_int @ X @ Z3 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_le_less_trans
% 3.82/4.01 thf(fact_655_order__le__less__trans,axiom,
% 3.82/4.01 ! [X: nat,Y: nat,Z3: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ X @ Y )
% 3.82/4.01 => ( ( ord_less_nat @ Y @ Z3 )
% 3.82/4.01 => ( ord_less_nat @ X @ Z3 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_le_less_trans
% 3.82/4.01 thf(fact_656_order__le__less__trans,axiom,
% 3.82/4.01 ! [X: int,Y: int,Z3: int] :
% 3.82/4.01 ( ( ord_less_eq_int @ X @ Y )
% 3.82/4.01 => ( ( ord_less_int @ Y @ Z3 )
% 3.82/4.01 => ( ord_less_int @ X @ Z3 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_le_less_trans
% 3.82/4.01 thf(fact_657_order__neq__le__trans,axiom,
% 3.82/4.01 ! [A: extended_enat,B2: extended_enat] :
% 3.82/4.01 ( ( A != B2 )
% 3.82/4.01 => ( ( ord_le2932123472753598470d_enat @ A @ B2 )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ A @ B2 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_neq_le_trans
% 3.82/4.01 thf(fact_658_order__neq__le__trans,axiom,
% 3.82/4.01 ! [A: real,B2: real] :
% 3.82/4.01 ( ( A != B2 )
% 3.82/4.01 => ( ( ord_less_eq_real @ A @ B2 )
% 3.82/4.01 => ( ord_less_real @ A @ B2 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_neq_le_trans
% 3.82/4.01 thf(fact_659_order__neq__le__trans,axiom,
% 3.82/4.01 ! [A: set_nat,B2: set_nat] :
% 3.82/4.01 ( ( A != B2 )
% 3.82/4.01 => ( ( ord_less_eq_set_nat @ A @ B2 )
% 3.82/4.01 => ( ord_less_set_nat @ A @ B2 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_neq_le_trans
% 3.82/4.01 thf(fact_660_order__neq__le__trans,axiom,
% 3.82/4.01 ! [A: set_int,B2: set_int] :
% 3.82/4.01 ( ( A != B2 )
% 3.82/4.01 => ( ( ord_less_eq_set_int @ A @ B2 )
% 3.82/4.01 => ( ord_less_set_int @ A @ B2 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_neq_le_trans
% 3.82/4.01 thf(fact_661_order__neq__le__trans,axiom,
% 3.82/4.01 ! [A: nat,B2: nat] :
% 3.82/4.01 ( ( A != B2 )
% 3.82/4.01 => ( ( ord_less_eq_nat @ A @ B2 )
% 3.82/4.01 => ( ord_less_nat @ A @ B2 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_neq_le_trans
% 3.82/4.01 thf(fact_662_order__neq__le__trans,axiom,
% 3.82/4.01 ! [A: int,B2: int] :
% 3.82/4.01 ( ( A != B2 )
% 3.82/4.01 => ( ( ord_less_eq_int @ A @ B2 )
% 3.82/4.01 => ( ord_less_int @ A @ B2 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_neq_le_trans
% 3.82/4.01 thf(fact_663_order__le__neq__trans,axiom,
% 3.82/4.01 ! [A: extended_enat,B2: extended_enat] :
% 3.82/4.01 ( ( ord_le2932123472753598470d_enat @ A @ B2 )
% 3.82/4.01 => ( ( A != B2 )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ A @ B2 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_le_neq_trans
% 3.82/4.01 thf(fact_664_order__le__neq__trans,axiom,
% 3.82/4.01 ! [A: real,B2: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ A @ B2 )
% 3.82/4.01 => ( ( A != B2 )
% 3.82/4.01 => ( ord_less_real @ A @ B2 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_le_neq_trans
% 3.82/4.01 thf(fact_665_order__le__neq__trans,axiom,
% 3.82/4.01 ! [A: set_nat,B2: set_nat] :
% 3.82/4.01 ( ( ord_less_eq_set_nat @ A @ B2 )
% 3.82/4.01 => ( ( A != B2 )
% 3.82/4.01 => ( ord_less_set_nat @ A @ B2 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_le_neq_trans
% 3.82/4.01 thf(fact_666_order__le__neq__trans,axiom,
% 3.82/4.01 ! [A: set_int,B2: set_int] :
% 3.82/4.01 ( ( ord_less_eq_set_int @ A @ B2 )
% 3.82/4.01 => ( ( A != B2 )
% 3.82/4.01 => ( ord_less_set_int @ A @ B2 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_le_neq_trans
% 3.82/4.01 thf(fact_667_order__le__neq__trans,axiom,
% 3.82/4.01 ! [A: nat,B2: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ A @ B2 )
% 3.82/4.01 => ( ( A != B2 )
% 3.82/4.01 => ( ord_less_nat @ A @ B2 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_le_neq_trans
% 3.82/4.01 thf(fact_668_order__le__neq__trans,axiom,
% 3.82/4.01 ! [A: int,B2: int] :
% 3.82/4.01 ( ( ord_less_eq_int @ A @ B2 )
% 3.82/4.01 => ( ( A != B2 )
% 3.82/4.01 => ( ord_less_int @ A @ B2 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_le_neq_trans
% 3.82/4.01 thf(fact_669_order__less__imp__le,axiom,
% 3.82/4.01 ! [X: extended_enat,Y: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ X @ Y )
% 3.82/4.01 => ( ord_le2932123472753598470d_enat @ X @ Y ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_imp_le
% 3.82/4.01 thf(fact_670_order__less__imp__le,axiom,
% 3.82/4.01 ! [X: real,Y: real] :
% 3.82/4.01 ( ( ord_less_real @ X @ Y )
% 3.82/4.01 => ( ord_less_eq_real @ X @ Y ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_imp_le
% 3.82/4.01 thf(fact_671_order__less__imp__le,axiom,
% 3.82/4.01 ! [X: set_nat,Y: set_nat] :
% 3.82/4.01 ( ( ord_less_set_nat @ X @ Y )
% 3.82/4.01 => ( ord_less_eq_set_nat @ X @ Y ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_imp_le
% 3.82/4.01 thf(fact_672_order__less__imp__le,axiom,
% 3.82/4.01 ! [X: set_int,Y: set_int] :
% 3.82/4.01 ( ( ord_less_set_int @ X @ Y )
% 3.82/4.01 => ( ord_less_eq_set_int @ X @ Y ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_imp_le
% 3.82/4.01 thf(fact_673_order__less__imp__le,axiom,
% 3.82/4.01 ! [X: nat,Y: nat] :
% 3.82/4.01 ( ( ord_less_nat @ X @ Y )
% 3.82/4.01 => ( ord_less_eq_nat @ X @ Y ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_imp_le
% 3.82/4.01 thf(fact_674_order__less__imp__le,axiom,
% 3.82/4.01 ! [X: int,Y: int] :
% 3.82/4.01 ( ( ord_less_int @ X @ Y )
% 3.82/4.01 => ( ord_less_eq_int @ X @ Y ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_imp_le
% 3.82/4.01 thf(fact_675_linorder__not__less,axiom,
% 3.82/4.01 ! [X: extended_enat,Y: extended_enat] :
% 3.82/4.01 ( ( ~ ( ord_le72135733267957522d_enat @ X @ Y ) )
% 3.82/4.01 = ( ord_le2932123472753598470d_enat @ Y @ X ) ) ).
% 3.82/4.01
% 3.82/4.01 % linorder_not_less
% 3.82/4.01 thf(fact_676_linorder__not__less,axiom,
% 3.82/4.01 ! [X: real,Y: real] :
% 3.82/4.01 ( ( ~ ( ord_less_real @ X @ Y ) )
% 3.82/4.01 = ( ord_less_eq_real @ Y @ X ) ) ).
% 3.82/4.01
% 3.82/4.01 % linorder_not_less
% 3.82/4.01 thf(fact_677_linorder__not__less,axiom,
% 3.82/4.01 ! [X: nat,Y: nat] :
% 3.82/4.01 ( ( ~ ( ord_less_nat @ X @ Y ) )
% 3.82/4.01 = ( ord_less_eq_nat @ Y @ X ) ) ).
% 3.82/4.01
% 3.82/4.01 % linorder_not_less
% 3.82/4.01 thf(fact_678_linorder__not__less,axiom,
% 3.82/4.01 ! [X: int,Y: int] :
% 3.82/4.01 ( ( ~ ( ord_less_int @ X @ Y ) )
% 3.82/4.01 = ( ord_less_eq_int @ Y @ X ) ) ).
% 3.82/4.01
% 3.82/4.01 % linorder_not_less
% 3.82/4.01 thf(fact_679_linorder__not__le,axiom,
% 3.82/4.01 ! [X: extended_enat,Y: extended_enat] :
% 3.82/4.01 ( ( ~ ( ord_le2932123472753598470d_enat @ X @ Y ) )
% 3.82/4.01 = ( ord_le72135733267957522d_enat @ Y @ X ) ) ).
% 3.82/4.01
% 3.82/4.01 % linorder_not_le
% 3.82/4.01 thf(fact_680_linorder__not__le,axiom,
% 3.82/4.01 ! [X: real,Y: real] :
% 3.82/4.01 ( ( ~ ( ord_less_eq_real @ X @ Y ) )
% 3.82/4.01 = ( ord_less_real @ Y @ X ) ) ).
% 3.82/4.01
% 3.82/4.01 % linorder_not_le
% 3.82/4.01 thf(fact_681_linorder__not__le,axiom,
% 3.82/4.01 ! [X: nat,Y: nat] :
% 3.82/4.01 ( ( ~ ( ord_less_eq_nat @ X @ Y ) )
% 3.82/4.01 = ( ord_less_nat @ Y @ X ) ) ).
% 3.82/4.01
% 3.82/4.01 % linorder_not_le
% 3.82/4.01 thf(fact_682_linorder__not__le,axiom,
% 3.82/4.01 ! [X: int,Y: int] :
% 3.82/4.01 ( ( ~ ( ord_less_eq_int @ X @ Y ) )
% 3.82/4.01 = ( ord_less_int @ Y @ X ) ) ).
% 3.82/4.01
% 3.82/4.01 % linorder_not_le
% 3.82/4.01 thf(fact_683_order__less__le,axiom,
% 3.82/4.01 ( ord_le72135733267957522d_enat
% 3.82/4.01 = ( ^ [X4: extended_enat,Y5: extended_enat] :
% 3.82/4.01 ( ( ord_le2932123472753598470d_enat @ X4 @ Y5 )
% 3.82/4.01 & ( X4 != Y5 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_le
% 3.82/4.01 thf(fact_684_order__less__le,axiom,
% 3.82/4.01 ( ord_less_real
% 3.82/4.01 = ( ^ [X4: real,Y5: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ X4 @ Y5 )
% 3.82/4.01 & ( X4 != Y5 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_le
% 3.82/4.01 thf(fact_685_order__less__le,axiom,
% 3.82/4.01 ( ord_less_set_nat
% 3.82/4.01 = ( ^ [X4: set_nat,Y5: set_nat] :
% 3.82/4.01 ( ( ord_less_eq_set_nat @ X4 @ Y5 )
% 3.82/4.01 & ( X4 != Y5 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_le
% 3.82/4.01 thf(fact_686_order__less__le,axiom,
% 3.82/4.01 ( ord_less_set_int
% 3.82/4.01 = ( ^ [X4: set_int,Y5: set_int] :
% 3.82/4.01 ( ( ord_less_eq_set_int @ X4 @ Y5 )
% 3.82/4.01 & ( X4 != Y5 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_le
% 3.82/4.01 thf(fact_687_order__less__le,axiom,
% 3.82/4.01 ( ord_less_nat
% 3.82/4.01 = ( ^ [X4: nat,Y5: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ X4 @ Y5 )
% 3.82/4.01 & ( X4 != Y5 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_le
% 3.82/4.01 thf(fact_688_order__less__le,axiom,
% 3.82/4.01 ( ord_less_int
% 3.82/4.01 = ( ^ [X4: int,Y5: int] :
% 3.82/4.01 ( ( ord_less_eq_int @ X4 @ Y5 )
% 3.82/4.01 & ( X4 != Y5 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_less_le
% 3.82/4.01 thf(fact_689_order__le__less,axiom,
% 3.82/4.01 ( ord_le2932123472753598470d_enat
% 3.82/4.01 = ( ^ [X4: extended_enat,Y5: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ X4 @ Y5 )
% 3.82/4.01 | ( X4 = Y5 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_le_less
% 3.82/4.01 thf(fact_690_order__le__less,axiom,
% 3.82/4.01 ( ord_less_eq_real
% 3.82/4.01 = ( ^ [X4: real,Y5: real] :
% 3.82/4.01 ( ( ord_less_real @ X4 @ Y5 )
% 3.82/4.01 | ( X4 = Y5 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_le_less
% 3.82/4.01 thf(fact_691_order__le__less,axiom,
% 3.82/4.01 ( ord_less_eq_set_nat
% 3.82/4.01 = ( ^ [X4: set_nat,Y5: set_nat] :
% 3.82/4.01 ( ( ord_less_set_nat @ X4 @ Y5 )
% 3.82/4.01 | ( X4 = Y5 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_le_less
% 3.82/4.01 thf(fact_692_order__le__less,axiom,
% 3.82/4.01 ( ord_less_eq_set_int
% 3.82/4.01 = ( ^ [X4: set_int,Y5: set_int] :
% 3.82/4.01 ( ( ord_less_set_int @ X4 @ Y5 )
% 3.82/4.01 | ( X4 = Y5 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_le_less
% 3.82/4.01 thf(fact_693_order__le__less,axiom,
% 3.82/4.01 ( ord_less_eq_nat
% 3.82/4.01 = ( ^ [X4: nat,Y5: nat] :
% 3.82/4.01 ( ( ord_less_nat @ X4 @ Y5 )
% 3.82/4.01 | ( X4 = Y5 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_le_less
% 3.82/4.01 thf(fact_694_order__le__less,axiom,
% 3.82/4.01 ( ord_less_eq_int
% 3.82/4.01 = ( ^ [X4: int,Y5: int] :
% 3.82/4.01 ( ( ord_less_int @ X4 @ Y5 )
% 3.82/4.01 | ( X4 = Y5 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order_le_less
% 3.82/4.01 thf(fact_695_dual__order_Ostrict__implies__order,axiom,
% 3.82/4.01 ! [B2: extended_enat,A: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ B2 @ A )
% 3.82/4.01 => ( ord_le2932123472753598470d_enat @ B2 @ A ) ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.strict_implies_order
% 3.82/4.01 thf(fact_696_dual__order_Ostrict__implies__order,axiom,
% 3.82/4.01 ! [B2: real,A: real] :
% 3.82/4.01 ( ( ord_less_real @ B2 @ A )
% 3.82/4.01 => ( ord_less_eq_real @ B2 @ A ) ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.strict_implies_order
% 3.82/4.01 thf(fact_697_dual__order_Ostrict__implies__order,axiom,
% 3.82/4.01 ! [B2: set_nat,A: set_nat] :
% 3.82/4.01 ( ( ord_less_set_nat @ B2 @ A )
% 3.82/4.01 => ( ord_less_eq_set_nat @ B2 @ A ) ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.strict_implies_order
% 3.82/4.01 thf(fact_698_dual__order_Ostrict__implies__order,axiom,
% 3.82/4.01 ! [B2: set_int,A: set_int] :
% 3.82/4.01 ( ( ord_less_set_int @ B2 @ A )
% 3.82/4.01 => ( ord_less_eq_set_int @ B2 @ A ) ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.strict_implies_order
% 3.82/4.01 thf(fact_699_dual__order_Ostrict__implies__order,axiom,
% 3.82/4.01 ! [B2: nat,A: nat] :
% 3.82/4.01 ( ( ord_less_nat @ B2 @ A )
% 3.82/4.01 => ( ord_less_eq_nat @ B2 @ A ) ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.strict_implies_order
% 3.82/4.01 thf(fact_700_dual__order_Ostrict__implies__order,axiom,
% 3.82/4.01 ! [B2: int,A: int] :
% 3.82/4.01 ( ( ord_less_int @ B2 @ A )
% 3.82/4.01 => ( ord_less_eq_int @ B2 @ A ) ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.strict_implies_order
% 3.82/4.01 thf(fact_701_order_Ostrict__implies__order,axiom,
% 3.82/4.01 ! [A: extended_enat,B2: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ A @ B2 )
% 3.82/4.01 => ( ord_le2932123472753598470d_enat @ A @ B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.strict_implies_order
% 3.82/4.01 thf(fact_702_order_Ostrict__implies__order,axiom,
% 3.82/4.01 ! [A: real,B2: real] :
% 3.82/4.01 ( ( ord_less_real @ A @ B2 )
% 3.82/4.01 => ( ord_less_eq_real @ A @ B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.strict_implies_order
% 3.82/4.01 thf(fact_703_order_Ostrict__implies__order,axiom,
% 3.82/4.01 ! [A: set_nat,B2: set_nat] :
% 3.82/4.01 ( ( ord_less_set_nat @ A @ B2 )
% 3.82/4.01 => ( ord_less_eq_set_nat @ A @ B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.strict_implies_order
% 3.82/4.01 thf(fact_704_order_Ostrict__implies__order,axiom,
% 3.82/4.01 ! [A: set_int,B2: set_int] :
% 3.82/4.01 ( ( ord_less_set_int @ A @ B2 )
% 3.82/4.01 => ( ord_less_eq_set_int @ A @ B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.strict_implies_order
% 3.82/4.01 thf(fact_705_order_Ostrict__implies__order,axiom,
% 3.82/4.01 ! [A: nat,B2: nat] :
% 3.82/4.01 ( ( ord_less_nat @ A @ B2 )
% 3.82/4.01 => ( ord_less_eq_nat @ A @ B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.strict_implies_order
% 3.82/4.01 thf(fact_706_order_Ostrict__implies__order,axiom,
% 3.82/4.01 ! [A: int,B2: int] :
% 3.82/4.01 ( ( ord_less_int @ A @ B2 )
% 3.82/4.01 => ( ord_less_eq_int @ A @ B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.strict_implies_order
% 3.82/4.01 thf(fact_707_dual__order_Ostrict__iff__not,axiom,
% 3.82/4.01 ( ord_le72135733267957522d_enat
% 3.82/4.01 = ( ^ [B3: extended_enat,A3: extended_enat] :
% 3.82/4.01 ( ( ord_le2932123472753598470d_enat @ B3 @ A3 )
% 3.82/4.01 & ~ ( ord_le2932123472753598470d_enat @ A3 @ B3 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.strict_iff_not
% 3.82/4.01 thf(fact_708_dual__order_Ostrict__iff__not,axiom,
% 3.82/4.01 ( ord_less_real
% 3.82/4.01 = ( ^ [B3: real,A3: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ B3 @ A3 )
% 3.82/4.01 & ~ ( ord_less_eq_real @ A3 @ B3 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.strict_iff_not
% 3.82/4.01 thf(fact_709_dual__order_Ostrict__iff__not,axiom,
% 3.82/4.01 ( ord_less_set_nat
% 3.82/4.01 = ( ^ [B3: set_nat,A3: set_nat] :
% 3.82/4.01 ( ( ord_less_eq_set_nat @ B3 @ A3 )
% 3.82/4.01 & ~ ( ord_less_eq_set_nat @ A3 @ B3 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.strict_iff_not
% 3.82/4.01 thf(fact_710_dual__order_Ostrict__iff__not,axiom,
% 3.82/4.01 ( ord_less_set_int
% 3.82/4.01 = ( ^ [B3: set_int,A3: set_int] :
% 3.82/4.01 ( ( ord_less_eq_set_int @ B3 @ A3 )
% 3.82/4.01 & ~ ( ord_less_eq_set_int @ A3 @ B3 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.strict_iff_not
% 3.82/4.01 thf(fact_711_dual__order_Ostrict__iff__not,axiom,
% 3.82/4.01 ( ord_less_nat
% 3.82/4.01 = ( ^ [B3: nat,A3: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ B3 @ A3 )
% 3.82/4.01 & ~ ( ord_less_eq_nat @ A3 @ B3 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.strict_iff_not
% 3.82/4.01 thf(fact_712_dual__order_Ostrict__iff__not,axiom,
% 3.82/4.01 ( ord_less_int
% 3.82/4.01 = ( ^ [B3: int,A3: int] :
% 3.82/4.01 ( ( ord_less_eq_int @ B3 @ A3 )
% 3.82/4.01 & ~ ( ord_less_eq_int @ A3 @ B3 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.strict_iff_not
% 3.82/4.01 thf(fact_713_dual__order_Ostrict__trans2,axiom,
% 3.82/4.01 ! [B2: extended_enat,A: extended_enat,C: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ B2 @ A )
% 3.82/4.01 => ( ( ord_le2932123472753598470d_enat @ C @ B2 )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ C @ A ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.strict_trans2
% 3.82/4.01 thf(fact_714_dual__order_Ostrict__trans2,axiom,
% 3.82/4.01 ! [B2: real,A: real,C: real] :
% 3.82/4.01 ( ( ord_less_real @ B2 @ A )
% 3.82/4.01 => ( ( ord_less_eq_real @ C @ B2 )
% 3.82/4.01 => ( ord_less_real @ C @ A ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.strict_trans2
% 3.82/4.01 thf(fact_715_dual__order_Ostrict__trans2,axiom,
% 3.82/4.01 ! [B2: set_nat,A: set_nat,C: set_nat] :
% 3.82/4.01 ( ( ord_less_set_nat @ B2 @ A )
% 3.82/4.01 => ( ( ord_less_eq_set_nat @ C @ B2 )
% 3.82/4.01 => ( ord_less_set_nat @ C @ A ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.strict_trans2
% 3.82/4.01 thf(fact_716_dual__order_Ostrict__trans2,axiom,
% 3.82/4.01 ! [B2: set_int,A: set_int,C: set_int] :
% 3.82/4.01 ( ( ord_less_set_int @ B2 @ A )
% 3.82/4.01 => ( ( ord_less_eq_set_int @ C @ B2 )
% 3.82/4.01 => ( ord_less_set_int @ C @ A ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.strict_trans2
% 3.82/4.01 thf(fact_717_dual__order_Ostrict__trans2,axiom,
% 3.82/4.01 ! [B2: nat,A: nat,C: nat] :
% 3.82/4.01 ( ( ord_less_nat @ B2 @ A )
% 3.82/4.01 => ( ( ord_less_eq_nat @ C @ B2 )
% 3.82/4.01 => ( ord_less_nat @ C @ A ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.strict_trans2
% 3.82/4.01 thf(fact_718_dual__order_Ostrict__trans2,axiom,
% 3.82/4.01 ! [B2: int,A: int,C: int] :
% 3.82/4.01 ( ( ord_less_int @ B2 @ A )
% 3.82/4.01 => ( ( ord_less_eq_int @ C @ B2 )
% 3.82/4.01 => ( ord_less_int @ C @ A ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.strict_trans2
% 3.82/4.01 thf(fact_719_dual__order_Ostrict__trans1,axiom,
% 3.82/4.01 ! [B2: extended_enat,A: extended_enat,C: extended_enat] :
% 3.82/4.01 ( ( ord_le2932123472753598470d_enat @ B2 @ A )
% 3.82/4.01 => ( ( ord_le72135733267957522d_enat @ C @ B2 )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ C @ A ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.strict_trans1
% 3.82/4.01 thf(fact_720_dual__order_Ostrict__trans1,axiom,
% 3.82/4.01 ! [B2: real,A: real,C: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ B2 @ A )
% 3.82/4.01 => ( ( ord_less_real @ C @ B2 )
% 3.82/4.01 => ( ord_less_real @ C @ A ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.strict_trans1
% 3.82/4.01 thf(fact_721_dual__order_Ostrict__trans1,axiom,
% 3.82/4.01 ! [B2: set_nat,A: set_nat,C: set_nat] :
% 3.82/4.01 ( ( ord_less_eq_set_nat @ B2 @ A )
% 3.82/4.01 => ( ( ord_less_set_nat @ C @ B2 )
% 3.82/4.01 => ( ord_less_set_nat @ C @ A ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.strict_trans1
% 3.82/4.01 thf(fact_722_dual__order_Ostrict__trans1,axiom,
% 3.82/4.01 ! [B2: set_int,A: set_int,C: set_int] :
% 3.82/4.01 ( ( ord_less_eq_set_int @ B2 @ A )
% 3.82/4.01 => ( ( ord_less_set_int @ C @ B2 )
% 3.82/4.01 => ( ord_less_set_int @ C @ A ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.strict_trans1
% 3.82/4.01 thf(fact_723_dual__order_Ostrict__trans1,axiom,
% 3.82/4.01 ! [B2: nat,A: nat,C: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ B2 @ A )
% 3.82/4.01 => ( ( ord_less_nat @ C @ B2 )
% 3.82/4.01 => ( ord_less_nat @ C @ A ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.strict_trans1
% 3.82/4.01 thf(fact_724_dual__order_Ostrict__trans1,axiom,
% 3.82/4.01 ! [B2: int,A: int,C: int] :
% 3.82/4.01 ( ( ord_less_eq_int @ B2 @ A )
% 3.82/4.01 => ( ( ord_less_int @ C @ B2 )
% 3.82/4.01 => ( ord_less_int @ C @ A ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.strict_trans1
% 3.82/4.01 thf(fact_725_dual__order_Ostrict__iff__order,axiom,
% 3.82/4.01 ( ord_le72135733267957522d_enat
% 3.82/4.01 = ( ^ [B3: extended_enat,A3: extended_enat] :
% 3.82/4.01 ( ( ord_le2932123472753598470d_enat @ B3 @ A3 )
% 3.82/4.01 & ( A3 != B3 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.strict_iff_order
% 3.82/4.01 thf(fact_726_dual__order_Ostrict__iff__order,axiom,
% 3.82/4.01 ( ord_less_real
% 3.82/4.01 = ( ^ [B3: real,A3: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ B3 @ A3 )
% 3.82/4.01 & ( A3 != B3 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.strict_iff_order
% 3.82/4.01 thf(fact_727_dual__order_Ostrict__iff__order,axiom,
% 3.82/4.01 ( ord_less_set_nat
% 3.82/4.01 = ( ^ [B3: set_nat,A3: set_nat] :
% 3.82/4.01 ( ( ord_less_eq_set_nat @ B3 @ A3 )
% 3.82/4.01 & ( A3 != B3 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.strict_iff_order
% 3.82/4.01 thf(fact_728_dual__order_Ostrict__iff__order,axiom,
% 3.82/4.01 ( ord_less_set_int
% 3.82/4.01 = ( ^ [B3: set_int,A3: set_int] :
% 3.82/4.01 ( ( ord_less_eq_set_int @ B3 @ A3 )
% 3.82/4.01 & ( A3 != B3 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.strict_iff_order
% 3.82/4.01 thf(fact_729_dual__order_Ostrict__iff__order,axiom,
% 3.82/4.01 ( ord_less_nat
% 3.82/4.01 = ( ^ [B3: nat,A3: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ B3 @ A3 )
% 3.82/4.01 & ( A3 != B3 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.strict_iff_order
% 3.82/4.01 thf(fact_730_dual__order_Ostrict__iff__order,axiom,
% 3.82/4.01 ( ord_less_int
% 3.82/4.01 = ( ^ [B3: int,A3: int] :
% 3.82/4.01 ( ( ord_less_eq_int @ B3 @ A3 )
% 3.82/4.01 & ( A3 != B3 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.strict_iff_order
% 3.82/4.01 thf(fact_731_dual__order_Oorder__iff__strict,axiom,
% 3.82/4.01 ( ord_le2932123472753598470d_enat
% 3.82/4.01 = ( ^ [B3: extended_enat,A3: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ B3 @ A3 )
% 3.82/4.01 | ( A3 = B3 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.order_iff_strict
% 3.82/4.01 thf(fact_732_dual__order_Oorder__iff__strict,axiom,
% 3.82/4.01 ( ord_less_eq_real
% 3.82/4.01 = ( ^ [B3: real,A3: real] :
% 3.82/4.01 ( ( ord_less_real @ B3 @ A3 )
% 3.82/4.01 | ( A3 = B3 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.order_iff_strict
% 3.82/4.01 thf(fact_733_dual__order_Oorder__iff__strict,axiom,
% 3.82/4.01 ( ord_less_eq_set_nat
% 3.82/4.01 = ( ^ [B3: set_nat,A3: set_nat] :
% 3.82/4.01 ( ( ord_less_set_nat @ B3 @ A3 )
% 3.82/4.01 | ( A3 = B3 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.order_iff_strict
% 3.82/4.01 thf(fact_734_dual__order_Oorder__iff__strict,axiom,
% 3.82/4.01 ( ord_less_eq_set_int
% 3.82/4.01 = ( ^ [B3: set_int,A3: set_int] :
% 3.82/4.01 ( ( ord_less_set_int @ B3 @ A3 )
% 3.82/4.01 | ( A3 = B3 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.order_iff_strict
% 3.82/4.01 thf(fact_735_dual__order_Oorder__iff__strict,axiom,
% 3.82/4.01 ( ord_less_eq_nat
% 3.82/4.01 = ( ^ [B3: nat,A3: nat] :
% 3.82/4.01 ( ( ord_less_nat @ B3 @ A3 )
% 3.82/4.01 | ( A3 = B3 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.order_iff_strict
% 3.82/4.01 thf(fact_736_dual__order_Oorder__iff__strict,axiom,
% 3.82/4.01 ( ord_less_eq_int
% 3.82/4.01 = ( ^ [B3: int,A3: int] :
% 3.82/4.01 ( ( ord_less_int @ B3 @ A3 )
% 3.82/4.01 | ( A3 = B3 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % dual_order.order_iff_strict
% 3.82/4.01 thf(fact_737_dense__le__bounded,axiom,
% 3.82/4.01 ! [X: real,Y: real,Z3: real] :
% 3.82/4.01 ( ( ord_less_real @ X @ Y )
% 3.82/4.01 => ( ! [W: real] :
% 3.82/4.01 ( ( ord_less_real @ X @ W )
% 3.82/4.01 => ( ( ord_less_real @ W @ Y )
% 3.82/4.01 => ( ord_less_eq_real @ W @ Z3 ) ) )
% 3.82/4.01 => ( ord_less_eq_real @ Y @ Z3 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % dense_le_bounded
% 3.82/4.01 thf(fact_738_dense__ge__bounded,axiom,
% 3.82/4.01 ! [Z3: real,X: real,Y: real] :
% 3.82/4.01 ( ( ord_less_real @ Z3 @ X )
% 3.82/4.01 => ( ! [W: real] :
% 3.82/4.01 ( ( ord_less_real @ Z3 @ W )
% 3.82/4.01 => ( ( ord_less_real @ W @ X )
% 3.82/4.01 => ( ord_less_eq_real @ Y @ W ) ) )
% 3.82/4.01 => ( ord_less_eq_real @ Y @ Z3 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % dense_ge_bounded
% 3.82/4.01 thf(fact_739_order_Ostrict__iff__not,axiom,
% 3.82/4.01 ( ord_le72135733267957522d_enat
% 3.82/4.01 = ( ^ [A3: extended_enat,B3: extended_enat] :
% 3.82/4.01 ( ( ord_le2932123472753598470d_enat @ A3 @ B3 )
% 3.82/4.01 & ~ ( ord_le2932123472753598470d_enat @ B3 @ A3 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.strict_iff_not
% 3.82/4.01 thf(fact_740_order_Ostrict__iff__not,axiom,
% 3.82/4.01 ( ord_less_real
% 3.82/4.01 = ( ^ [A3: real,B3: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ A3 @ B3 )
% 3.82/4.01 & ~ ( ord_less_eq_real @ B3 @ A3 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.strict_iff_not
% 3.82/4.01 thf(fact_741_order_Ostrict__iff__not,axiom,
% 3.82/4.01 ( ord_less_set_nat
% 3.82/4.01 = ( ^ [A3: set_nat,B3: set_nat] :
% 3.82/4.01 ( ( ord_less_eq_set_nat @ A3 @ B3 )
% 3.82/4.01 & ~ ( ord_less_eq_set_nat @ B3 @ A3 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.strict_iff_not
% 3.82/4.01 thf(fact_742_order_Ostrict__iff__not,axiom,
% 3.82/4.01 ( ord_less_set_int
% 3.82/4.01 = ( ^ [A3: set_int,B3: set_int] :
% 3.82/4.01 ( ( ord_less_eq_set_int @ A3 @ B3 )
% 3.82/4.01 & ~ ( ord_less_eq_set_int @ B3 @ A3 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.strict_iff_not
% 3.82/4.01 thf(fact_743_order_Ostrict__iff__not,axiom,
% 3.82/4.01 ( ord_less_nat
% 3.82/4.01 = ( ^ [A3: nat,B3: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ A3 @ B3 )
% 3.82/4.01 & ~ ( ord_less_eq_nat @ B3 @ A3 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.strict_iff_not
% 3.82/4.01 thf(fact_744_order_Ostrict__iff__not,axiom,
% 3.82/4.01 ( ord_less_int
% 3.82/4.01 = ( ^ [A3: int,B3: int] :
% 3.82/4.01 ( ( ord_less_eq_int @ A3 @ B3 )
% 3.82/4.01 & ~ ( ord_less_eq_int @ B3 @ A3 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.strict_iff_not
% 3.82/4.01 thf(fact_745_order_Ostrict__trans2,axiom,
% 3.82/4.01 ! [A: extended_enat,B2: extended_enat,C: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ A @ B2 )
% 3.82/4.01 => ( ( ord_le2932123472753598470d_enat @ B2 @ C )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ A @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.strict_trans2
% 3.82/4.01 thf(fact_746_order_Ostrict__trans2,axiom,
% 3.82/4.01 ! [A: real,B2: real,C: real] :
% 3.82/4.01 ( ( ord_less_real @ A @ B2 )
% 3.82/4.01 => ( ( ord_less_eq_real @ B2 @ C )
% 3.82/4.01 => ( ord_less_real @ A @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.strict_trans2
% 3.82/4.01 thf(fact_747_order_Ostrict__trans2,axiom,
% 3.82/4.01 ! [A: set_nat,B2: set_nat,C: set_nat] :
% 3.82/4.01 ( ( ord_less_set_nat @ A @ B2 )
% 3.82/4.01 => ( ( ord_less_eq_set_nat @ B2 @ C )
% 3.82/4.01 => ( ord_less_set_nat @ A @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.strict_trans2
% 3.82/4.01 thf(fact_748_order_Ostrict__trans2,axiom,
% 3.82/4.01 ! [A: set_int,B2: set_int,C: set_int] :
% 3.82/4.01 ( ( ord_less_set_int @ A @ B2 )
% 3.82/4.01 => ( ( ord_less_eq_set_int @ B2 @ C )
% 3.82/4.01 => ( ord_less_set_int @ A @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.strict_trans2
% 3.82/4.01 thf(fact_749_order_Ostrict__trans2,axiom,
% 3.82/4.01 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.01 ( ( ord_less_nat @ A @ B2 )
% 3.82/4.01 => ( ( ord_less_eq_nat @ B2 @ C )
% 3.82/4.01 => ( ord_less_nat @ A @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.strict_trans2
% 3.82/4.01 thf(fact_750_order_Ostrict__trans2,axiom,
% 3.82/4.01 ! [A: int,B2: int,C: int] :
% 3.82/4.01 ( ( ord_less_int @ A @ B2 )
% 3.82/4.01 => ( ( ord_less_eq_int @ B2 @ C )
% 3.82/4.01 => ( ord_less_int @ A @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.strict_trans2
% 3.82/4.01 thf(fact_751_order_Ostrict__trans1,axiom,
% 3.82/4.01 ! [A: extended_enat,B2: extended_enat,C: extended_enat] :
% 3.82/4.01 ( ( ord_le2932123472753598470d_enat @ A @ B2 )
% 3.82/4.01 => ( ( ord_le72135733267957522d_enat @ B2 @ C )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ A @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.strict_trans1
% 3.82/4.01 thf(fact_752_order_Ostrict__trans1,axiom,
% 3.82/4.01 ! [A: real,B2: real,C: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ A @ B2 )
% 3.82/4.01 => ( ( ord_less_real @ B2 @ C )
% 3.82/4.01 => ( ord_less_real @ A @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.strict_trans1
% 3.82/4.01 thf(fact_753_order_Ostrict__trans1,axiom,
% 3.82/4.01 ! [A: set_nat,B2: set_nat,C: set_nat] :
% 3.82/4.01 ( ( ord_less_eq_set_nat @ A @ B2 )
% 3.82/4.01 => ( ( ord_less_set_nat @ B2 @ C )
% 3.82/4.01 => ( ord_less_set_nat @ A @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.strict_trans1
% 3.82/4.01 thf(fact_754_order_Ostrict__trans1,axiom,
% 3.82/4.01 ! [A: set_int,B2: set_int,C: set_int] :
% 3.82/4.01 ( ( ord_less_eq_set_int @ A @ B2 )
% 3.82/4.01 => ( ( ord_less_set_int @ B2 @ C )
% 3.82/4.01 => ( ord_less_set_int @ A @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.strict_trans1
% 3.82/4.01 thf(fact_755_order_Ostrict__trans1,axiom,
% 3.82/4.01 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ A @ B2 )
% 3.82/4.01 => ( ( ord_less_nat @ B2 @ C )
% 3.82/4.01 => ( ord_less_nat @ A @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.strict_trans1
% 3.82/4.01 thf(fact_756_order_Ostrict__trans1,axiom,
% 3.82/4.01 ! [A: int,B2: int,C: int] :
% 3.82/4.01 ( ( ord_less_eq_int @ A @ B2 )
% 3.82/4.01 => ( ( ord_less_int @ B2 @ C )
% 3.82/4.01 => ( ord_less_int @ A @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.strict_trans1
% 3.82/4.01 thf(fact_757_order_Ostrict__iff__order,axiom,
% 3.82/4.01 ( ord_le72135733267957522d_enat
% 3.82/4.01 = ( ^ [A3: extended_enat,B3: extended_enat] :
% 3.82/4.01 ( ( ord_le2932123472753598470d_enat @ A3 @ B3 )
% 3.82/4.01 & ( A3 != B3 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.strict_iff_order
% 3.82/4.01 thf(fact_758_order_Ostrict__iff__order,axiom,
% 3.82/4.01 ( ord_less_real
% 3.82/4.01 = ( ^ [A3: real,B3: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ A3 @ B3 )
% 3.82/4.01 & ( A3 != B3 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.strict_iff_order
% 3.82/4.01 thf(fact_759_order_Ostrict__iff__order,axiom,
% 3.82/4.01 ( ord_less_set_nat
% 3.82/4.01 = ( ^ [A3: set_nat,B3: set_nat] :
% 3.82/4.01 ( ( ord_less_eq_set_nat @ A3 @ B3 )
% 3.82/4.01 & ( A3 != B3 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.strict_iff_order
% 3.82/4.01 thf(fact_760_order_Ostrict__iff__order,axiom,
% 3.82/4.01 ( ord_less_set_int
% 3.82/4.01 = ( ^ [A3: set_int,B3: set_int] :
% 3.82/4.01 ( ( ord_less_eq_set_int @ A3 @ B3 )
% 3.82/4.01 & ( A3 != B3 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.strict_iff_order
% 3.82/4.01 thf(fact_761_order_Ostrict__iff__order,axiom,
% 3.82/4.01 ( ord_less_nat
% 3.82/4.01 = ( ^ [A3: nat,B3: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ A3 @ B3 )
% 3.82/4.01 & ( A3 != B3 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.strict_iff_order
% 3.82/4.01 thf(fact_762_order_Ostrict__iff__order,axiom,
% 3.82/4.01 ( ord_less_int
% 3.82/4.01 = ( ^ [A3: int,B3: int] :
% 3.82/4.01 ( ( ord_less_eq_int @ A3 @ B3 )
% 3.82/4.01 & ( A3 != B3 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.strict_iff_order
% 3.82/4.01 thf(fact_763_order_Oorder__iff__strict,axiom,
% 3.82/4.01 ( ord_le2932123472753598470d_enat
% 3.82/4.01 = ( ^ [A3: extended_enat,B3: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ A3 @ B3 )
% 3.82/4.01 | ( A3 = B3 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.order_iff_strict
% 3.82/4.01 thf(fact_764_order_Oorder__iff__strict,axiom,
% 3.82/4.01 ( ord_less_eq_real
% 3.82/4.01 = ( ^ [A3: real,B3: real] :
% 3.82/4.01 ( ( ord_less_real @ A3 @ B3 )
% 3.82/4.01 | ( A3 = B3 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.order_iff_strict
% 3.82/4.01 thf(fact_765_order_Oorder__iff__strict,axiom,
% 3.82/4.01 ( ord_less_eq_set_nat
% 3.82/4.01 = ( ^ [A3: set_nat,B3: set_nat] :
% 3.82/4.01 ( ( ord_less_set_nat @ A3 @ B3 )
% 3.82/4.01 | ( A3 = B3 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.order_iff_strict
% 3.82/4.01 thf(fact_766_order_Oorder__iff__strict,axiom,
% 3.82/4.01 ( ord_less_eq_set_int
% 3.82/4.01 = ( ^ [A3: set_int,B3: set_int] :
% 3.82/4.01 ( ( ord_less_set_int @ A3 @ B3 )
% 3.82/4.01 | ( A3 = B3 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.order_iff_strict
% 3.82/4.01 thf(fact_767_order_Oorder__iff__strict,axiom,
% 3.82/4.01 ( ord_less_eq_nat
% 3.82/4.01 = ( ^ [A3: nat,B3: nat] :
% 3.82/4.01 ( ( ord_less_nat @ A3 @ B3 )
% 3.82/4.01 | ( A3 = B3 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.order_iff_strict
% 3.82/4.01 thf(fact_768_order_Oorder__iff__strict,axiom,
% 3.82/4.01 ( ord_less_eq_int
% 3.82/4.01 = ( ^ [A3: int,B3: int] :
% 3.82/4.01 ( ( ord_less_int @ A3 @ B3 )
% 3.82/4.01 | ( A3 = B3 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % order.order_iff_strict
% 3.82/4.01 thf(fact_769_not__le__imp__less,axiom,
% 3.82/4.01 ! [Y: extended_enat,X: extended_enat] :
% 3.82/4.01 ( ~ ( ord_le2932123472753598470d_enat @ Y @ X )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ X @ Y ) ) ).
% 3.82/4.01
% 3.82/4.01 % not_le_imp_less
% 3.82/4.01 thf(fact_770_not__le__imp__less,axiom,
% 3.82/4.01 ! [Y: real,X: real] :
% 3.82/4.01 ( ~ ( ord_less_eq_real @ Y @ X )
% 3.82/4.01 => ( ord_less_real @ X @ Y ) ) ).
% 3.82/4.01
% 3.82/4.01 % not_le_imp_less
% 3.82/4.01 thf(fact_771_not__le__imp__less,axiom,
% 3.82/4.01 ! [Y: nat,X: nat] :
% 3.82/4.01 ( ~ ( ord_less_eq_nat @ Y @ X )
% 3.82/4.01 => ( ord_less_nat @ X @ Y ) ) ).
% 3.82/4.01
% 3.82/4.01 % not_le_imp_less
% 3.82/4.01 thf(fact_772_not__le__imp__less,axiom,
% 3.82/4.01 ! [Y: int,X: int] :
% 3.82/4.01 ( ~ ( ord_less_eq_int @ Y @ X )
% 3.82/4.01 => ( ord_less_int @ X @ Y ) ) ).
% 3.82/4.01
% 3.82/4.01 % not_le_imp_less
% 3.82/4.01 thf(fact_773_less__le__not__le,axiom,
% 3.82/4.01 ( ord_le72135733267957522d_enat
% 3.82/4.01 = ( ^ [X4: extended_enat,Y5: extended_enat] :
% 3.82/4.01 ( ( ord_le2932123472753598470d_enat @ X4 @ Y5 )
% 3.82/4.01 & ~ ( ord_le2932123472753598470d_enat @ Y5 @ X4 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % less_le_not_le
% 3.82/4.01 thf(fact_774_less__le__not__le,axiom,
% 3.82/4.01 ( ord_less_real
% 3.82/4.01 = ( ^ [X4: real,Y5: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ X4 @ Y5 )
% 3.82/4.01 & ~ ( ord_less_eq_real @ Y5 @ X4 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % less_le_not_le
% 3.82/4.01 thf(fact_775_less__le__not__le,axiom,
% 3.82/4.01 ( ord_less_set_nat
% 3.82/4.01 = ( ^ [X4: set_nat,Y5: set_nat] :
% 3.82/4.01 ( ( ord_less_eq_set_nat @ X4 @ Y5 )
% 3.82/4.01 & ~ ( ord_less_eq_set_nat @ Y5 @ X4 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % less_le_not_le
% 3.82/4.01 thf(fact_776_less__le__not__le,axiom,
% 3.82/4.01 ( ord_less_set_int
% 3.82/4.01 = ( ^ [X4: set_int,Y5: set_int] :
% 3.82/4.01 ( ( ord_less_eq_set_int @ X4 @ Y5 )
% 3.82/4.01 & ~ ( ord_less_eq_set_int @ Y5 @ X4 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % less_le_not_le
% 3.82/4.01 thf(fact_777_less__le__not__le,axiom,
% 3.82/4.01 ( ord_less_nat
% 3.82/4.01 = ( ^ [X4: nat,Y5: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ X4 @ Y5 )
% 3.82/4.01 & ~ ( ord_less_eq_nat @ Y5 @ X4 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % less_le_not_le
% 3.82/4.01 thf(fact_778_less__le__not__le,axiom,
% 3.82/4.01 ( ord_less_int
% 3.82/4.01 = ( ^ [X4: int,Y5: int] :
% 3.82/4.01 ( ( ord_less_eq_int @ X4 @ Y5 )
% 3.82/4.01 & ~ ( ord_less_eq_int @ Y5 @ X4 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % less_le_not_le
% 3.82/4.01 thf(fact_779_dense__le,axiom,
% 3.82/4.01 ! [Y: real,Z3: real] :
% 3.82/4.01 ( ! [X5: real] :
% 3.82/4.01 ( ( ord_less_real @ X5 @ Y )
% 3.82/4.01 => ( ord_less_eq_real @ X5 @ Z3 ) )
% 3.82/4.01 => ( ord_less_eq_real @ Y @ Z3 ) ) ).
% 3.82/4.01
% 3.82/4.01 % dense_le
% 3.82/4.01 thf(fact_780_dense__ge,axiom,
% 3.82/4.01 ! [Z3: real,Y: real] :
% 3.82/4.01 ( ! [X5: real] :
% 3.82/4.01 ( ( ord_less_real @ Z3 @ X5 )
% 3.82/4.01 => ( ord_less_eq_real @ Y @ X5 ) )
% 3.82/4.01 => ( ord_less_eq_real @ Y @ Z3 ) ) ).
% 3.82/4.01
% 3.82/4.01 % dense_ge
% 3.82/4.01 thf(fact_781_antisym__conv2,axiom,
% 3.82/4.01 ! [X: extended_enat,Y: extended_enat] :
% 3.82/4.01 ( ( ord_le2932123472753598470d_enat @ X @ Y )
% 3.82/4.01 => ( ( ~ ( ord_le72135733267957522d_enat @ X @ Y ) )
% 3.82/4.01 = ( X = Y ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % antisym_conv2
% 3.82/4.01 thf(fact_782_antisym__conv2,axiom,
% 3.82/4.01 ! [X: real,Y: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ X @ Y )
% 3.82/4.01 => ( ( ~ ( ord_less_real @ X @ Y ) )
% 3.82/4.01 = ( X = Y ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % antisym_conv2
% 3.82/4.01 thf(fact_783_antisym__conv2,axiom,
% 3.82/4.01 ! [X: set_nat,Y: set_nat] :
% 3.82/4.01 ( ( ord_less_eq_set_nat @ X @ Y )
% 3.82/4.01 => ( ( ~ ( ord_less_set_nat @ X @ Y ) )
% 3.82/4.01 = ( X = Y ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % antisym_conv2
% 3.82/4.01 thf(fact_784_antisym__conv2,axiom,
% 3.82/4.01 ! [X: set_int,Y: set_int] :
% 3.82/4.01 ( ( ord_less_eq_set_int @ X @ Y )
% 3.82/4.01 => ( ( ~ ( ord_less_set_int @ X @ Y ) )
% 3.82/4.01 = ( X = Y ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % antisym_conv2
% 3.82/4.01 thf(fact_785_antisym__conv2,axiom,
% 3.82/4.01 ! [X: nat,Y: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ X @ Y )
% 3.82/4.01 => ( ( ~ ( ord_less_nat @ X @ Y ) )
% 3.82/4.01 = ( X = Y ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % antisym_conv2
% 3.82/4.01 thf(fact_786_antisym__conv2,axiom,
% 3.82/4.01 ! [X: int,Y: int] :
% 3.82/4.01 ( ( ord_less_eq_int @ X @ Y )
% 3.82/4.01 => ( ( ~ ( ord_less_int @ X @ Y ) )
% 3.82/4.01 = ( X = Y ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % antisym_conv2
% 3.82/4.01 thf(fact_787_antisym__conv1,axiom,
% 3.82/4.01 ! [X: extended_enat,Y: extended_enat] :
% 3.82/4.01 ( ~ ( ord_le72135733267957522d_enat @ X @ Y )
% 3.82/4.01 => ( ( ord_le2932123472753598470d_enat @ X @ Y )
% 3.82/4.01 = ( X = Y ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % antisym_conv1
% 3.82/4.01 thf(fact_788_antisym__conv1,axiom,
% 3.82/4.01 ! [X: real,Y: real] :
% 3.82/4.01 ( ~ ( ord_less_real @ X @ Y )
% 3.82/4.01 => ( ( ord_less_eq_real @ X @ Y )
% 3.82/4.01 = ( X = Y ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % antisym_conv1
% 3.82/4.01 thf(fact_789_antisym__conv1,axiom,
% 3.82/4.01 ! [X: set_nat,Y: set_nat] :
% 3.82/4.01 ( ~ ( ord_less_set_nat @ X @ Y )
% 3.82/4.01 => ( ( ord_less_eq_set_nat @ X @ Y )
% 3.82/4.01 = ( X = Y ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % antisym_conv1
% 3.82/4.01 thf(fact_790_antisym__conv1,axiom,
% 3.82/4.01 ! [X: set_int,Y: set_int] :
% 3.82/4.01 ( ~ ( ord_less_set_int @ X @ Y )
% 3.82/4.01 => ( ( ord_less_eq_set_int @ X @ Y )
% 3.82/4.01 = ( X = Y ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % antisym_conv1
% 3.82/4.01 thf(fact_791_antisym__conv1,axiom,
% 3.82/4.01 ! [X: nat,Y: nat] :
% 3.82/4.01 ( ~ ( ord_less_nat @ X @ Y )
% 3.82/4.01 => ( ( ord_less_eq_nat @ X @ Y )
% 3.82/4.01 = ( X = Y ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % antisym_conv1
% 3.82/4.01 thf(fact_792_antisym__conv1,axiom,
% 3.82/4.01 ! [X: int,Y: int] :
% 3.82/4.01 ( ~ ( ord_less_int @ X @ Y )
% 3.82/4.01 => ( ( ord_less_eq_int @ X @ Y )
% 3.82/4.01 = ( X = Y ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % antisym_conv1
% 3.82/4.01 thf(fact_793_nless__le,axiom,
% 3.82/4.01 ! [A: extended_enat,B2: extended_enat] :
% 3.82/4.01 ( ( ~ ( ord_le72135733267957522d_enat @ A @ B2 ) )
% 3.82/4.01 = ( ~ ( ord_le2932123472753598470d_enat @ A @ B2 )
% 3.82/4.01 | ( A = B2 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % nless_le
% 3.82/4.01 thf(fact_794_nless__le,axiom,
% 3.82/4.01 ! [A: real,B2: real] :
% 3.82/4.01 ( ( ~ ( ord_less_real @ A @ B2 ) )
% 3.82/4.01 = ( ~ ( ord_less_eq_real @ A @ B2 )
% 3.82/4.01 | ( A = B2 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % nless_le
% 3.82/4.01 thf(fact_795_nless__le,axiom,
% 3.82/4.01 ! [A: set_nat,B2: set_nat] :
% 3.82/4.01 ( ( ~ ( ord_less_set_nat @ A @ B2 ) )
% 3.82/4.01 = ( ~ ( ord_less_eq_set_nat @ A @ B2 )
% 3.82/4.01 | ( A = B2 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % nless_le
% 3.82/4.01 thf(fact_796_nless__le,axiom,
% 3.82/4.01 ! [A: set_int,B2: set_int] :
% 3.82/4.01 ( ( ~ ( ord_less_set_int @ A @ B2 ) )
% 3.82/4.01 = ( ~ ( ord_less_eq_set_int @ A @ B2 )
% 3.82/4.01 | ( A = B2 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % nless_le
% 3.82/4.01 thf(fact_797_nless__le,axiom,
% 3.82/4.01 ! [A: nat,B2: nat] :
% 3.82/4.01 ( ( ~ ( ord_less_nat @ A @ B2 ) )
% 3.82/4.01 = ( ~ ( ord_less_eq_nat @ A @ B2 )
% 3.82/4.01 | ( A = B2 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % nless_le
% 3.82/4.01 thf(fact_798_nless__le,axiom,
% 3.82/4.01 ! [A: int,B2: int] :
% 3.82/4.01 ( ( ~ ( ord_less_int @ A @ B2 ) )
% 3.82/4.01 = ( ~ ( ord_less_eq_int @ A @ B2 )
% 3.82/4.01 | ( A = B2 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % nless_le
% 3.82/4.01 thf(fact_799_leI,axiom,
% 3.82/4.01 ! [X: extended_enat,Y: extended_enat] :
% 3.82/4.01 ( ~ ( ord_le72135733267957522d_enat @ X @ Y )
% 3.82/4.01 => ( ord_le2932123472753598470d_enat @ Y @ X ) ) ).
% 3.82/4.01
% 3.82/4.01 % leI
% 3.82/4.01 thf(fact_800_leI,axiom,
% 3.82/4.01 ! [X: real,Y: real] :
% 3.82/4.01 ( ~ ( ord_less_real @ X @ Y )
% 3.82/4.01 => ( ord_less_eq_real @ Y @ X ) ) ).
% 3.82/4.01
% 3.82/4.01 % leI
% 3.82/4.01 thf(fact_801_leI,axiom,
% 3.82/4.01 ! [X: nat,Y: nat] :
% 3.82/4.01 ( ~ ( ord_less_nat @ X @ Y )
% 3.82/4.01 => ( ord_less_eq_nat @ Y @ X ) ) ).
% 3.82/4.01
% 3.82/4.01 % leI
% 3.82/4.01 thf(fact_802_leI,axiom,
% 3.82/4.01 ! [X: int,Y: int] :
% 3.82/4.01 ( ~ ( ord_less_int @ X @ Y )
% 3.82/4.01 => ( ord_less_eq_int @ Y @ X ) ) ).
% 3.82/4.01
% 3.82/4.01 % leI
% 3.82/4.01 thf(fact_803_leD,axiom,
% 3.82/4.01 ! [Y: extended_enat,X: extended_enat] :
% 3.82/4.01 ( ( ord_le2932123472753598470d_enat @ Y @ X )
% 3.82/4.01 => ~ ( ord_le72135733267957522d_enat @ X @ Y ) ) ).
% 3.82/4.01
% 3.82/4.01 % leD
% 3.82/4.01 thf(fact_804_leD,axiom,
% 3.82/4.01 ! [Y: real,X: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ Y @ X )
% 3.82/4.01 => ~ ( ord_less_real @ X @ Y ) ) ).
% 3.82/4.01
% 3.82/4.01 % leD
% 3.82/4.01 thf(fact_805_leD,axiom,
% 3.82/4.01 ! [Y: set_nat,X: set_nat] :
% 3.82/4.01 ( ( ord_less_eq_set_nat @ Y @ X )
% 3.82/4.01 => ~ ( ord_less_set_nat @ X @ Y ) ) ).
% 3.82/4.01
% 3.82/4.01 % leD
% 3.82/4.01 thf(fact_806_leD,axiom,
% 3.82/4.01 ! [Y: set_int,X: set_int] :
% 3.82/4.01 ( ( ord_less_eq_set_int @ Y @ X )
% 3.82/4.01 => ~ ( ord_less_set_int @ X @ Y ) ) ).
% 3.82/4.01
% 3.82/4.01 % leD
% 3.82/4.01 thf(fact_807_leD,axiom,
% 3.82/4.01 ! [Y: nat,X: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ Y @ X )
% 3.82/4.01 => ~ ( ord_less_nat @ X @ Y ) ) ).
% 3.82/4.01
% 3.82/4.01 % leD
% 3.82/4.01 thf(fact_808_leD,axiom,
% 3.82/4.01 ! [Y: int,X: int] :
% 3.82/4.01 ( ( ord_less_eq_int @ Y @ X )
% 3.82/4.01 => ~ ( ord_less_int @ X @ Y ) ) ).
% 3.82/4.01
% 3.82/4.01 % leD
% 3.82/4.01 thf(fact_809_less__mono__imp__le__mono,axiom,
% 3.82/4.01 ! [F: nat > nat,I: nat,J: nat] :
% 3.82/4.01 ( ! [I4: nat,J3: nat] :
% 3.82/4.01 ( ( ord_less_nat @ I4 @ J3 )
% 3.82/4.01 => ( ord_less_nat @ ( F @ I4 ) @ ( F @ J3 ) ) )
% 3.82/4.01 => ( ( ord_less_eq_nat @ I @ J )
% 3.82/4.01 => ( ord_less_eq_nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % less_mono_imp_le_mono
% 3.82/4.01 thf(fact_810_le__neq__implies__less,axiom,
% 3.82/4.01 ! [M2: nat,N2: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.01 => ( ( M2 != N2 )
% 3.82/4.01 => ( ord_less_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % le_neq_implies_less
% 3.82/4.01 thf(fact_811_less__or__eq__imp__le,axiom,
% 3.82/4.01 ! [M2: nat,N2: nat] :
% 3.82/4.01 ( ( ( ord_less_nat @ M2 @ N2 )
% 3.82/4.01 | ( M2 = N2 ) )
% 3.82/4.01 => ( ord_less_eq_nat @ M2 @ N2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % less_or_eq_imp_le
% 3.82/4.01 thf(fact_812_le__eq__less__or__eq,axiom,
% 3.82/4.01 ( ord_less_eq_nat
% 3.82/4.01 = ( ^ [M: nat,N: nat] :
% 3.82/4.01 ( ( ord_less_nat @ M @ N )
% 3.82/4.01 | ( M = N ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % le_eq_less_or_eq
% 3.82/4.01 thf(fact_813_buildup__gives__valid,axiom,
% 3.82/4.01 ! [N2: nat] :
% 3.82/4.01 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.01 => ( vEBT_invar_vebt @ ( vEBT_vebt_buildup @ N2 ) @ N2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % buildup_gives_valid
% 3.82/4.01 thf(fact_814_add__less__same__cancel1,axiom,
% 3.82/4.01 ! [B2: nat,A: nat] :
% 3.82/4.01 ( ( ord_less_nat @ ( plus_plus_nat @ B2 @ A ) @ B2 )
% 3.82/4.01 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_less_same_cancel1
% 3.82/4.01 thf(fact_815_add__less__same__cancel1,axiom,
% 3.82/4.01 ! [B2: real,A: real] :
% 3.82/4.01 ( ( ord_less_real @ ( plus_plus_real @ B2 @ A ) @ B2 )
% 3.82/4.01 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_less_same_cancel1
% 3.82/4.01 thf(fact_816_add__less__same__cancel1,axiom,
% 3.82/4.01 ! [B2: int,A: int] :
% 3.82/4.01 ( ( ord_less_int @ ( plus_plus_int @ B2 @ A ) @ B2 )
% 3.82/4.01 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_less_same_cancel1
% 3.82/4.01 thf(fact_817_add__less__same__cancel2,axiom,
% 3.82/4.01 ! [A: nat,B2: nat] :
% 3.82/4.01 ( ( ord_less_nat @ ( plus_plus_nat @ A @ B2 ) @ B2 )
% 3.82/4.01 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_less_same_cancel2
% 3.82/4.01 thf(fact_818_add__less__same__cancel2,axiom,
% 3.82/4.01 ! [A: real,B2: real] :
% 3.82/4.01 ( ( ord_less_real @ ( plus_plus_real @ A @ B2 ) @ B2 )
% 3.82/4.01 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_less_same_cancel2
% 3.82/4.01 thf(fact_819_add__less__same__cancel2,axiom,
% 3.82/4.01 ! [A: int,B2: int] :
% 3.82/4.01 ( ( ord_less_int @ ( plus_plus_int @ A @ B2 ) @ B2 )
% 3.82/4.01 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_less_same_cancel2
% 3.82/4.01 thf(fact_820_less__add__same__cancel1,axiom,
% 3.82/4.01 ! [A: nat,B2: nat] :
% 3.82/4.01 ( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B2 ) )
% 3.82/4.01 = ( ord_less_nat @ zero_zero_nat @ B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % less_add_same_cancel1
% 3.82/4.01 thf(fact_821_less__add__same__cancel1,axiom,
% 3.82/4.01 ! [A: real,B2: real] :
% 3.82/4.01 ( ( ord_less_real @ A @ ( plus_plus_real @ A @ B2 ) )
% 3.82/4.01 = ( ord_less_real @ zero_zero_real @ B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % less_add_same_cancel1
% 3.82/4.01 thf(fact_822_less__add__same__cancel1,axiom,
% 3.82/4.01 ! [A: int,B2: int] :
% 3.82/4.01 ( ( ord_less_int @ A @ ( plus_plus_int @ A @ B2 ) )
% 3.82/4.01 = ( ord_less_int @ zero_zero_int @ B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % less_add_same_cancel1
% 3.82/4.01 thf(fact_823_less__add__same__cancel2,axiom,
% 3.82/4.01 ! [A: nat,B2: nat] :
% 3.82/4.01 ( ( ord_less_nat @ A @ ( plus_plus_nat @ B2 @ A ) )
% 3.82/4.01 = ( ord_less_nat @ zero_zero_nat @ B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % less_add_same_cancel2
% 3.82/4.01 thf(fact_824_less__add__same__cancel2,axiom,
% 3.82/4.01 ! [A: real,B2: real] :
% 3.82/4.01 ( ( ord_less_real @ A @ ( plus_plus_real @ B2 @ A ) )
% 3.82/4.01 = ( ord_less_real @ zero_zero_real @ B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % less_add_same_cancel2
% 3.82/4.01 thf(fact_825_less__add__same__cancel2,axiom,
% 3.82/4.01 ! [A: int,B2: int] :
% 3.82/4.01 ( ( ord_less_int @ A @ ( plus_plus_int @ B2 @ A ) )
% 3.82/4.01 = ( ord_less_int @ zero_zero_int @ B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % less_add_same_cancel2
% 3.82/4.01 thf(fact_826_double__add__less__zero__iff__single__add__less__zero,axiom,
% 3.82/4.01 ! [A: real] :
% 3.82/4.01 ( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 3.82/4.01 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 3.82/4.01
% 3.82/4.01 % double_add_less_zero_iff_single_add_less_zero
% 3.82/4.01 thf(fact_827_double__add__less__zero__iff__single__add__less__zero,axiom,
% 3.82/4.01 ! [A: int] :
% 3.82/4.01 ( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 3.82/4.01 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 3.82/4.01
% 3.82/4.01 % double_add_less_zero_iff_single_add_less_zero
% 3.82/4.01 thf(fact_828_zero__less__double__add__iff__zero__less__single__add,axiom,
% 3.82/4.01 ! [A: real] :
% 3.82/4.01 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 3.82/4.01 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 3.82/4.01
% 3.82/4.01 % zero_less_double_add_iff_zero_less_single_add
% 3.82/4.01 thf(fact_829_zero__less__double__add__iff__zero__less__single__add,axiom,
% 3.82/4.01 ! [A: int] :
% 3.82/4.01 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 3.82/4.01 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 3.82/4.01
% 3.82/4.01 % zero_less_double_add_iff_zero_less_single_add
% 3.82/4.01 thf(fact_830_add__le__same__cancel1,axiom,
% 3.82/4.01 ! [B2: real,A: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ ( plus_plus_real @ B2 @ A ) @ B2 )
% 3.82/4.01 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_le_same_cancel1
% 3.82/4.01 thf(fact_831_add__le__same__cancel1,axiom,
% 3.82/4.01 ! [B2: nat,A: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ ( plus_plus_nat @ B2 @ A ) @ B2 )
% 3.82/4.01 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_le_same_cancel1
% 3.82/4.01 thf(fact_832_add__le__same__cancel1,axiom,
% 3.82/4.01 ! [B2: int,A: int] :
% 3.82/4.01 ( ( ord_less_eq_int @ ( plus_plus_int @ B2 @ A ) @ B2 )
% 3.82/4.01 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_le_same_cancel1
% 3.82/4.01 thf(fact_833_add__le__same__cancel2,axiom,
% 3.82/4.01 ! [A: real,B2: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B2 ) @ B2 )
% 3.82/4.01 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_le_same_cancel2
% 3.82/4.01 thf(fact_834_add__le__same__cancel2,axiom,
% 3.82/4.01 ! [A: nat,B2: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B2 ) @ B2 )
% 3.82/4.01 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_le_same_cancel2
% 3.82/4.01 thf(fact_835_add__le__same__cancel2,axiom,
% 3.82/4.01 ! [A: int,B2: int] :
% 3.82/4.01 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ B2 ) @ B2 )
% 3.82/4.01 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_le_same_cancel2
% 3.82/4.01 thf(fact_836_le__add__same__cancel1,axiom,
% 3.82/4.01 ! [A: real,B2: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ A @ B2 ) )
% 3.82/4.01 = ( ord_less_eq_real @ zero_zero_real @ B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % le_add_same_cancel1
% 3.82/4.01 thf(fact_837_le__add__same__cancel1,axiom,
% 3.82/4.01 ! [A: nat,B2: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B2 ) )
% 3.82/4.01 = ( ord_less_eq_nat @ zero_zero_nat @ B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % le_add_same_cancel1
% 3.82/4.01 thf(fact_838_le__add__same__cancel1,axiom,
% 3.82/4.01 ! [A: int,B2: int] :
% 3.82/4.01 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ A @ B2 ) )
% 3.82/4.01 = ( ord_less_eq_int @ zero_zero_int @ B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % le_add_same_cancel1
% 3.82/4.01 thf(fact_839_le__add__same__cancel2,axiom,
% 3.82/4.01 ! [A: real,B2: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ B2 @ A ) )
% 3.82/4.01 = ( ord_less_eq_real @ zero_zero_real @ B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % le_add_same_cancel2
% 3.82/4.01 thf(fact_840_le__add__same__cancel2,axiom,
% 3.82/4.01 ! [A: nat,B2: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B2 @ A ) )
% 3.82/4.01 = ( ord_less_eq_nat @ zero_zero_nat @ B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % le_add_same_cancel2
% 3.82/4.01 thf(fact_841_le__add__same__cancel2,axiom,
% 3.82/4.01 ! [A: int,B2: int] :
% 3.82/4.01 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ B2 @ A ) )
% 3.82/4.01 = ( ord_less_eq_int @ zero_zero_int @ B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % le_add_same_cancel2
% 3.82/4.01 thf(fact_842_double__add__le__zero__iff__single__add__le__zero,axiom,
% 3.82/4.01 ! [A: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 3.82/4.01 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 3.82/4.01
% 3.82/4.01 % double_add_le_zero_iff_single_add_le_zero
% 3.82/4.01 thf(fact_843_double__add__le__zero__iff__single__add__le__zero,axiom,
% 3.82/4.01 ! [A: int] :
% 3.82/4.01 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 3.82/4.01 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 3.82/4.01
% 3.82/4.01 % double_add_le_zero_iff_single_add_le_zero
% 3.82/4.01 thf(fact_844_add__left__cancel,axiom,
% 3.82/4.01 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.01 ( ( ( plus_plus_nat @ A @ B2 )
% 3.82/4.01 = ( plus_plus_nat @ A @ C ) )
% 3.82/4.01 = ( B2 = C ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_left_cancel
% 3.82/4.01 thf(fact_845_add__left__cancel,axiom,
% 3.82/4.01 ! [A: int,B2: int,C: int] :
% 3.82/4.01 ( ( ( plus_plus_int @ A @ B2 )
% 3.82/4.01 = ( plus_plus_int @ A @ C ) )
% 3.82/4.01 = ( B2 = C ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_left_cancel
% 3.82/4.01 thf(fact_846_add__left__cancel,axiom,
% 3.82/4.01 ! [A: real,B2: real,C: real] :
% 3.82/4.01 ( ( ( plus_plus_real @ A @ B2 )
% 3.82/4.01 = ( plus_plus_real @ A @ C ) )
% 3.82/4.01 = ( B2 = C ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_left_cancel
% 3.82/4.01 thf(fact_847_add__right__cancel,axiom,
% 3.82/4.01 ! [B2: nat,A: nat,C: nat] :
% 3.82/4.01 ( ( ( plus_plus_nat @ B2 @ A )
% 3.82/4.01 = ( plus_plus_nat @ C @ A ) )
% 3.82/4.01 = ( B2 = C ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_right_cancel
% 3.82/4.01 thf(fact_848_add__right__cancel,axiom,
% 3.82/4.01 ! [B2: int,A: int,C: int] :
% 3.82/4.01 ( ( ( plus_plus_int @ B2 @ A )
% 3.82/4.01 = ( plus_plus_int @ C @ A ) )
% 3.82/4.01 = ( B2 = C ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_right_cancel
% 3.82/4.01 thf(fact_849_add__right__cancel,axiom,
% 3.82/4.01 ! [B2: real,A: real,C: real] :
% 3.82/4.01 ( ( ( plus_plus_real @ B2 @ A )
% 3.82/4.01 = ( plus_plus_real @ C @ A ) )
% 3.82/4.01 = ( B2 = C ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_right_cancel
% 3.82/4.01 thf(fact_850_le__zero__eq,axiom,
% 3.82/4.01 ! [N2: extended_enat] :
% 3.82/4.01 ( ( ord_le2932123472753598470d_enat @ N2 @ zero_z5237406670263579293d_enat )
% 3.82/4.01 = ( N2 = zero_z5237406670263579293d_enat ) ) ).
% 3.82/4.01
% 3.82/4.01 % le_zero_eq
% 3.82/4.01 thf(fact_851_le__zero__eq,axiom,
% 3.82/4.01 ! [N2: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ N2 @ zero_zero_nat )
% 3.82/4.01 = ( N2 = zero_zero_nat ) ) ).
% 3.82/4.01
% 3.82/4.01 % le_zero_eq
% 3.82/4.01 thf(fact_852_not__gr__zero,axiom,
% 3.82/4.01 ! [N2: nat] :
% 3.82/4.01 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N2 ) )
% 3.82/4.01 = ( N2 = zero_zero_nat ) ) ).
% 3.82/4.01
% 3.82/4.01 % not_gr_zero
% 3.82/4.01 thf(fact_853_not__gr__zero,axiom,
% 3.82/4.01 ! [N2: extended_enat] :
% 3.82/4.01 ( ( ~ ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N2 ) )
% 3.82/4.01 = ( N2 = zero_z5237406670263579293d_enat ) ) ).
% 3.82/4.01
% 3.82/4.01 % not_gr_zero
% 3.82/4.01 thf(fact_854_add__le__cancel__left,axiom,
% 3.82/4.01 ! [C: real,A: real,B2: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B2 ) )
% 3.82/4.01 = ( ord_less_eq_real @ A @ B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_le_cancel_left
% 3.82/4.01 thf(fact_855_add__le__cancel__left,axiom,
% 3.82/4.01 ! [C: nat,A: nat,B2: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B2 ) )
% 3.82/4.01 = ( ord_less_eq_nat @ A @ B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_le_cancel_left
% 3.82/4.01 thf(fact_856_add__le__cancel__left,axiom,
% 3.82/4.01 ! [C: int,A: int,B2: int] :
% 3.82/4.01 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B2 ) )
% 3.82/4.01 = ( ord_less_eq_int @ A @ B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_le_cancel_left
% 3.82/4.01 thf(fact_857_add__le__cancel__right,axiom,
% 3.82/4.01 ! [A: real,C: real,B2: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B2 @ C ) )
% 3.82/4.01 = ( ord_less_eq_real @ A @ B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_le_cancel_right
% 3.82/4.01 thf(fact_858_add__le__cancel__right,axiom,
% 3.82/4.01 ! [A: nat,C: nat,B2: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B2 @ C ) )
% 3.82/4.01 = ( ord_less_eq_nat @ A @ B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_le_cancel_right
% 3.82/4.01 thf(fact_859_add__le__cancel__right,axiom,
% 3.82/4.01 ! [A: int,C: int,B2: int] :
% 3.82/4.01 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B2 @ C ) )
% 3.82/4.01 = ( ord_less_eq_int @ A @ B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_le_cancel_right
% 3.82/4.01 thf(fact_860_add_Oright__neutral,axiom,
% 3.82/4.01 ! [A: nat] :
% 3.82/4.01 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 3.82/4.01 = A ) ).
% 3.82/4.01
% 3.82/4.01 % add.right_neutral
% 3.82/4.01 thf(fact_861_add_Oright__neutral,axiom,
% 3.82/4.01 ! [A: real] :
% 3.82/4.01 ( ( plus_plus_real @ A @ zero_zero_real )
% 3.82/4.01 = A ) ).
% 3.82/4.01
% 3.82/4.01 % add.right_neutral
% 3.82/4.01 thf(fact_862_add_Oright__neutral,axiom,
% 3.82/4.01 ! [A: int] :
% 3.82/4.01 ( ( plus_plus_int @ A @ zero_zero_int )
% 3.82/4.01 = A ) ).
% 3.82/4.01
% 3.82/4.01 % add.right_neutral
% 3.82/4.01 thf(fact_863_add_Oright__neutral,axiom,
% 3.82/4.01 ! [A: complex] :
% 3.82/4.01 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 3.82/4.01 = A ) ).
% 3.82/4.01
% 3.82/4.01 % add.right_neutral
% 3.82/4.01 thf(fact_864_add_Oright__neutral,axiom,
% 3.82/4.01 ! [A: extended_enat] :
% 3.82/4.01 ( ( plus_p3455044024723400733d_enat @ A @ zero_z5237406670263579293d_enat )
% 3.82/4.01 = A ) ).
% 3.82/4.01
% 3.82/4.01 % add.right_neutral
% 3.82/4.01 thf(fact_865_double__zero__sym,axiom,
% 3.82/4.01 ! [A: real] :
% 3.82/4.01 ( ( zero_zero_real
% 3.82/4.01 = ( plus_plus_real @ A @ A ) )
% 3.82/4.01 = ( A = zero_zero_real ) ) ).
% 3.82/4.01
% 3.82/4.01 % double_zero_sym
% 3.82/4.01 thf(fact_866_double__zero__sym,axiom,
% 3.82/4.01 ! [A: int] :
% 3.82/4.01 ( ( zero_zero_int
% 3.82/4.01 = ( plus_plus_int @ A @ A ) )
% 3.82/4.01 = ( A = zero_zero_int ) ) ).
% 3.82/4.01
% 3.82/4.01 % double_zero_sym
% 3.82/4.01 thf(fact_867_add__cancel__left__left,axiom,
% 3.82/4.01 ! [B2: nat,A: nat] :
% 3.82/4.01 ( ( ( plus_plus_nat @ B2 @ A )
% 3.82/4.01 = A )
% 3.82/4.01 = ( B2 = zero_zero_nat ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_cancel_left_left
% 3.82/4.01 thf(fact_868_add__cancel__left__left,axiom,
% 3.82/4.01 ! [B2: real,A: real] :
% 3.82/4.01 ( ( ( plus_plus_real @ B2 @ A )
% 3.82/4.01 = A )
% 3.82/4.01 = ( B2 = zero_zero_real ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_cancel_left_left
% 3.82/4.01 thf(fact_869_add__cancel__left__left,axiom,
% 3.82/4.01 ! [B2: int,A: int] :
% 3.82/4.01 ( ( ( plus_plus_int @ B2 @ A )
% 3.82/4.01 = A )
% 3.82/4.01 = ( B2 = zero_zero_int ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_cancel_left_left
% 3.82/4.01 thf(fact_870_add__cancel__left__left,axiom,
% 3.82/4.01 ! [B2: complex,A: complex] :
% 3.82/4.01 ( ( ( plus_plus_complex @ B2 @ A )
% 3.82/4.01 = A )
% 3.82/4.01 = ( B2 = zero_zero_complex ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_cancel_left_left
% 3.82/4.01 thf(fact_871_add__cancel__left__right,axiom,
% 3.82/4.01 ! [A: nat,B2: nat] :
% 3.82/4.01 ( ( ( plus_plus_nat @ A @ B2 )
% 3.82/4.01 = A )
% 3.82/4.01 = ( B2 = zero_zero_nat ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_cancel_left_right
% 3.82/4.01 thf(fact_872_add__cancel__left__right,axiom,
% 3.82/4.01 ! [A: real,B2: real] :
% 3.82/4.01 ( ( ( plus_plus_real @ A @ B2 )
% 3.82/4.01 = A )
% 3.82/4.01 = ( B2 = zero_zero_real ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_cancel_left_right
% 3.82/4.01 thf(fact_873_add__cancel__left__right,axiom,
% 3.82/4.01 ! [A: int,B2: int] :
% 3.82/4.01 ( ( ( plus_plus_int @ A @ B2 )
% 3.82/4.01 = A )
% 3.82/4.01 = ( B2 = zero_zero_int ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_cancel_left_right
% 3.82/4.01 thf(fact_874_add__cancel__left__right,axiom,
% 3.82/4.01 ! [A: complex,B2: complex] :
% 3.82/4.01 ( ( ( plus_plus_complex @ A @ B2 )
% 3.82/4.01 = A )
% 3.82/4.01 = ( B2 = zero_zero_complex ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_cancel_left_right
% 3.82/4.01 thf(fact_875_add__cancel__right__left,axiom,
% 3.82/4.01 ! [A: nat,B2: nat] :
% 3.82/4.01 ( ( A
% 3.82/4.01 = ( plus_plus_nat @ B2 @ A ) )
% 3.82/4.01 = ( B2 = zero_zero_nat ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_cancel_right_left
% 3.82/4.01 thf(fact_876_add__cancel__right__left,axiom,
% 3.82/4.01 ! [A: real,B2: real] :
% 3.82/4.01 ( ( A
% 3.82/4.01 = ( plus_plus_real @ B2 @ A ) )
% 3.82/4.01 = ( B2 = zero_zero_real ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_cancel_right_left
% 3.82/4.01 thf(fact_877_add__cancel__right__left,axiom,
% 3.82/4.01 ! [A: int,B2: int] :
% 3.82/4.01 ( ( A
% 3.82/4.01 = ( plus_plus_int @ B2 @ A ) )
% 3.82/4.01 = ( B2 = zero_zero_int ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_cancel_right_left
% 3.82/4.01 thf(fact_878_add__cancel__right__left,axiom,
% 3.82/4.01 ! [A: complex,B2: complex] :
% 3.82/4.01 ( ( A
% 3.82/4.01 = ( plus_plus_complex @ B2 @ A ) )
% 3.82/4.01 = ( B2 = zero_zero_complex ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_cancel_right_left
% 3.82/4.01 thf(fact_879_add__cancel__right__right,axiom,
% 3.82/4.01 ! [A: nat,B2: nat] :
% 3.82/4.01 ( ( A
% 3.82/4.01 = ( plus_plus_nat @ A @ B2 ) )
% 3.82/4.01 = ( B2 = zero_zero_nat ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_cancel_right_right
% 3.82/4.01 thf(fact_880_add__cancel__right__right,axiom,
% 3.82/4.01 ! [A: real,B2: real] :
% 3.82/4.01 ( ( A
% 3.82/4.01 = ( plus_plus_real @ A @ B2 ) )
% 3.82/4.01 = ( B2 = zero_zero_real ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_cancel_right_right
% 3.82/4.01 thf(fact_881_add__cancel__right__right,axiom,
% 3.82/4.01 ! [A: int,B2: int] :
% 3.82/4.01 ( ( A
% 3.82/4.01 = ( plus_plus_int @ A @ B2 ) )
% 3.82/4.01 = ( B2 = zero_zero_int ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_cancel_right_right
% 3.82/4.01 thf(fact_882_add__cancel__right__right,axiom,
% 3.82/4.01 ! [A: complex,B2: complex] :
% 3.82/4.01 ( ( A
% 3.82/4.01 = ( plus_plus_complex @ A @ B2 ) )
% 3.82/4.01 = ( B2 = zero_zero_complex ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_cancel_right_right
% 3.82/4.01 thf(fact_883_add__eq__0__iff__both__eq__0,axiom,
% 3.82/4.01 ! [X: nat,Y: nat] :
% 3.82/4.01 ( ( ( plus_plus_nat @ X @ Y )
% 3.82/4.01 = zero_zero_nat )
% 3.82/4.01 = ( ( X = zero_zero_nat )
% 3.82/4.01 & ( Y = zero_zero_nat ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_eq_0_iff_both_eq_0
% 3.82/4.01 thf(fact_884_add__eq__0__iff__both__eq__0,axiom,
% 3.82/4.01 ! [X: extended_enat,Y: extended_enat] :
% 3.82/4.01 ( ( ( plus_p3455044024723400733d_enat @ X @ Y )
% 3.82/4.01 = zero_z5237406670263579293d_enat )
% 3.82/4.01 = ( ( X = zero_z5237406670263579293d_enat )
% 3.82/4.01 & ( Y = zero_z5237406670263579293d_enat ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_eq_0_iff_both_eq_0
% 3.82/4.01 thf(fact_885_zero__eq__add__iff__both__eq__0,axiom,
% 3.82/4.01 ! [X: nat,Y: nat] :
% 3.82/4.01 ( ( zero_zero_nat
% 3.82/4.01 = ( plus_plus_nat @ X @ Y ) )
% 3.82/4.01 = ( ( X = zero_zero_nat )
% 3.82/4.01 & ( Y = zero_zero_nat ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % zero_eq_add_iff_both_eq_0
% 3.82/4.01 thf(fact_886_zero__eq__add__iff__both__eq__0,axiom,
% 3.82/4.01 ! [X: extended_enat,Y: extended_enat] :
% 3.82/4.01 ( ( zero_z5237406670263579293d_enat
% 3.82/4.01 = ( plus_p3455044024723400733d_enat @ X @ Y ) )
% 3.82/4.01 = ( ( X = zero_z5237406670263579293d_enat )
% 3.82/4.01 & ( Y = zero_z5237406670263579293d_enat ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % zero_eq_add_iff_both_eq_0
% 3.82/4.01 thf(fact_887_add__0,axiom,
% 3.82/4.01 ! [A: nat] :
% 3.82/4.01 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 3.82/4.01 = A ) ).
% 3.82/4.01
% 3.82/4.01 % add_0
% 3.82/4.01 thf(fact_888_add__0,axiom,
% 3.82/4.01 ! [A: real] :
% 3.82/4.01 ( ( plus_plus_real @ zero_zero_real @ A )
% 3.82/4.01 = A ) ).
% 3.82/4.01
% 3.82/4.01 % add_0
% 3.82/4.01 thf(fact_889_add__0,axiom,
% 3.82/4.01 ! [A: int] :
% 3.82/4.01 ( ( plus_plus_int @ zero_zero_int @ A )
% 3.82/4.01 = A ) ).
% 3.82/4.01
% 3.82/4.01 % add_0
% 3.82/4.01 thf(fact_890_add__0,axiom,
% 3.82/4.01 ! [A: complex] :
% 3.82/4.01 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 3.82/4.01 = A ) ).
% 3.82/4.01
% 3.82/4.01 % add_0
% 3.82/4.01 thf(fact_891_add__0,axiom,
% 3.82/4.01 ! [A: extended_enat] :
% 3.82/4.01 ( ( plus_p3455044024723400733d_enat @ zero_z5237406670263579293d_enat @ A )
% 3.82/4.01 = A ) ).
% 3.82/4.01
% 3.82/4.01 % add_0
% 3.82/4.01 thf(fact_892_add__less__cancel__left,axiom,
% 3.82/4.01 ! [C: nat,A: nat,B2: nat] :
% 3.82/4.01 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B2 ) )
% 3.82/4.01 = ( ord_less_nat @ A @ B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_less_cancel_left
% 3.82/4.01 thf(fact_893_add__less__cancel__left,axiom,
% 3.82/4.01 ! [C: real,A: real,B2: real] :
% 3.82/4.01 ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B2 ) )
% 3.82/4.01 = ( ord_less_real @ A @ B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_less_cancel_left
% 3.82/4.01 thf(fact_894_add__less__cancel__left,axiom,
% 3.82/4.01 ! [C: int,A: int,B2: int] :
% 3.82/4.01 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B2 ) )
% 3.82/4.01 = ( ord_less_int @ A @ B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_less_cancel_left
% 3.82/4.01 thf(fact_895_add__less__cancel__right,axiom,
% 3.82/4.01 ! [A: nat,C: nat,B2: nat] :
% 3.82/4.01 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B2 @ C ) )
% 3.82/4.01 = ( ord_less_nat @ A @ B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_less_cancel_right
% 3.82/4.01 thf(fact_896_add__less__cancel__right,axiom,
% 3.82/4.01 ! [A: real,C: real,B2: real] :
% 3.82/4.01 ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B2 @ C ) )
% 3.82/4.01 = ( ord_less_real @ A @ B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_less_cancel_right
% 3.82/4.01 thf(fact_897_add__less__cancel__right,axiom,
% 3.82/4.01 ! [A: int,C: int,B2: int] :
% 3.82/4.01 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B2 @ C ) )
% 3.82/4.01 = ( ord_less_int @ A @ B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_less_cancel_right
% 3.82/4.01 thf(fact_898_zero__le__double__add__iff__zero__le__single__add,axiom,
% 3.82/4.01 ! [A: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 3.82/4.01 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 3.82/4.01
% 3.82/4.01 % zero_le_double_add_iff_zero_le_single_add
% 3.82/4.01 thf(fact_899_zero__le__double__add__iff__zero__le__single__add,axiom,
% 3.82/4.01 ! [A: int] :
% 3.82/4.01 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 3.82/4.01 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 3.82/4.01
% 3.82/4.01 % zero_le_double_add_iff_zero_le_single_add
% 3.82/4.01 thf(fact_900_zero__reorient,axiom,
% 3.82/4.01 ! [X: nat] :
% 3.82/4.01 ( ( zero_zero_nat = X )
% 3.82/4.01 = ( X = zero_zero_nat ) ) ).
% 3.82/4.01
% 3.82/4.01 % zero_reorient
% 3.82/4.01 thf(fact_901_zero__reorient,axiom,
% 3.82/4.01 ! [X: real] :
% 3.82/4.01 ( ( zero_zero_real = X )
% 3.82/4.01 = ( X = zero_zero_real ) ) ).
% 3.82/4.01
% 3.82/4.01 % zero_reorient
% 3.82/4.01 thf(fact_902_zero__reorient,axiom,
% 3.82/4.01 ! [X: int] :
% 3.82/4.01 ( ( zero_zero_int = X )
% 3.82/4.01 = ( X = zero_zero_int ) ) ).
% 3.82/4.01
% 3.82/4.01 % zero_reorient
% 3.82/4.01 thf(fact_903_zero__reorient,axiom,
% 3.82/4.01 ! [X: complex] :
% 3.82/4.01 ( ( zero_zero_complex = X )
% 3.82/4.01 = ( X = zero_zero_complex ) ) ).
% 3.82/4.01
% 3.82/4.01 % zero_reorient
% 3.82/4.01 thf(fact_904_zero__reorient,axiom,
% 3.82/4.01 ! [X: extended_enat] :
% 3.82/4.01 ( ( zero_z5237406670263579293d_enat = X )
% 3.82/4.01 = ( X = zero_z5237406670263579293d_enat ) ) ).
% 3.82/4.01
% 3.82/4.01 % zero_reorient
% 3.82/4.01 thf(fact_905_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 3.82/4.01 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.01 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B2 ) @ C )
% 3.82/4.01 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B2 @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % ab_semigroup_add_class.add_ac(1)
% 3.82/4.01 thf(fact_906_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 3.82/4.01 ! [A: int,B2: int,C: int] :
% 3.82/4.01 ( ( plus_plus_int @ ( plus_plus_int @ A @ B2 ) @ C )
% 3.82/4.01 = ( plus_plus_int @ A @ ( plus_plus_int @ B2 @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % ab_semigroup_add_class.add_ac(1)
% 3.82/4.01 thf(fact_907_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 3.82/4.01 ! [A: real,B2: real,C: real] :
% 3.82/4.01 ( ( plus_plus_real @ ( plus_plus_real @ A @ B2 ) @ C )
% 3.82/4.01 = ( plus_plus_real @ A @ ( plus_plus_real @ B2 @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % ab_semigroup_add_class.add_ac(1)
% 3.82/4.01 thf(fact_908_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 3.82/4.01 ! [A: extended_enat,B2: extended_enat,C: extended_enat] :
% 3.82/4.01 ( ( plus_p3455044024723400733d_enat @ ( plus_p3455044024723400733d_enat @ A @ B2 ) @ C )
% 3.82/4.01 = ( plus_p3455044024723400733d_enat @ A @ ( plus_p3455044024723400733d_enat @ B2 @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % ab_semigroup_add_class.add_ac(1)
% 3.82/4.01 thf(fact_909_add__mono__thms__linordered__semiring_I4_J,axiom,
% 3.82/4.01 ! [I: nat,J: nat,K: nat,L: nat] :
% 3.82/4.01 ( ( ( I = J )
% 3.82/4.01 & ( K = L ) )
% 3.82/4.01 => ( ( plus_plus_nat @ I @ K )
% 3.82/4.01 = ( plus_plus_nat @ J @ L ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_mono_thms_linordered_semiring(4)
% 3.82/4.01 thf(fact_910_add__mono__thms__linordered__semiring_I4_J,axiom,
% 3.82/4.01 ! [I: int,J: int,K: int,L: int] :
% 3.82/4.01 ( ( ( I = J )
% 3.82/4.01 & ( K = L ) )
% 3.82/4.01 => ( ( plus_plus_int @ I @ K )
% 3.82/4.01 = ( plus_plus_int @ J @ L ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_mono_thms_linordered_semiring(4)
% 3.82/4.01 thf(fact_911_add__mono__thms__linordered__semiring_I4_J,axiom,
% 3.82/4.01 ! [I: real,J: real,K: real,L: real] :
% 3.82/4.01 ( ( ( I = J )
% 3.82/4.01 & ( K = L ) )
% 3.82/4.01 => ( ( plus_plus_real @ I @ K )
% 3.82/4.01 = ( plus_plus_real @ J @ L ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_mono_thms_linordered_semiring(4)
% 3.82/4.01 thf(fact_912_add__mono__thms__linordered__semiring_I4_J,axiom,
% 3.82/4.01 ! [I: extended_enat,J: extended_enat,K: extended_enat,L: extended_enat] :
% 3.82/4.01 ( ( ( I = J )
% 3.82/4.01 & ( K = L ) )
% 3.82/4.01 => ( ( plus_p3455044024723400733d_enat @ I @ K )
% 3.82/4.01 = ( plus_p3455044024723400733d_enat @ J @ L ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_mono_thms_linordered_semiring(4)
% 3.82/4.01 thf(fact_913_group__cancel_Oadd1,axiom,
% 3.82/4.01 ! [A2: nat,K: nat,A: nat,B2: nat] :
% 3.82/4.01 ( ( A2
% 3.82/4.01 = ( plus_plus_nat @ K @ A ) )
% 3.82/4.01 => ( ( plus_plus_nat @ A2 @ B2 )
% 3.82/4.01 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B2 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % group_cancel.add1
% 3.82/4.01 thf(fact_914_group__cancel_Oadd1,axiom,
% 3.82/4.01 ! [A2: int,K: int,A: int,B2: int] :
% 3.82/4.01 ( ( A2
% 3.82/4.01 = ( plus_plus_int @ K @ A ) )
% 3.82/4.01 => ( ( plus_plus_int @ A2 @ B2 )
% 3.82/4.01 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B2 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % group_cancel.add1
% 3.82/4.01 thf(fact_915_group__cancel_Oadd1,axiom,
% 3.82/4.01 ! [A2: real,K: real,A: real,B2: real] :
% 3.82/4.01 ( ( A2
% 3.82/4.01 = ( plus_plus_real @ K @ A ) )
% 3.82/4.01 => ( ( plus_plus_real @ A2 @ B2 )
% 3.82/4.01 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B2 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % group_cancel.add1
% 3.82/4.01 thf(fact_916_group__cancel_Oadd1,axiom,
% 3.82/4.01 ! [A2: extended_enat,K: extended_enat,A: extended_enat,B2: extended_enat] :
% 3.82/4.01 ( ( A2
% 3.82/4.01 = ( plus_p3455044024723400733d_enat @ K @ A ) )
% 3.82/4.01 => ( ( plus_p3455044024723400733d_enat @ A2 @ B2 )
% 3.82/4.01 = ( plus_p3455044024723400733d_enat @ K @ ( plus_p3455044024723400733d_enat @ A @ B2 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % group_cancel.add1
% 3.82/4.01 thf(fact_917_group__cancel_Oadd2,axiom,
% 3.82/4.01 ! [B: nat,K: nat,B2: nat,A: nat] :
% 3.82/4.01 ( ( B
% 3.82/4.01 = ( plus_plus_nat @ K @ B2 ) )
% 3.82/4.01 => ( ( plus_plus_nat @ A @ B )
% 3.82/4.01 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B2 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % group_cancel.add2
% 3.82/4.01 thf(fact_918_group__cancel_Oadd2,axiom,
% 3.82/4.01 ! [B: int,K: int,B2: int,A: int] :
% 3.82/4.01 ( ( B
% 3.82/4.01 = ( plus_plus_int @ K @ B2 ) )
% 3.82/4.01 => ( ( plus_plus_int @ A @ B )
% 3.82/4.01 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B2 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % group_cancel.add2
% 3.82/4.01 thf(fact_919_group__cancel_Oadd2,axiom,
% 3.82/4.01 ! [B: real,K: real,B2: real,A: real] :
% 3.82/4.01 ( ( B
% 3.82/4.01 = ( plus_plus_real @ K @ B2 ) )
% 3.82/4.01 => ( ( plus_plus_real @ A @ B )
% 3.82/4.01 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B2 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % group_cancel.add2
% 3.82/4.01 thf(fact_920_group__cancel_Oadd2,axiom,
% 3.82/4.01 ! [B: extended_enat,K: extended_enat,B2: extended_enat,A: extended_enat] :
% 3.82/4.01 ( ( B
% 3.82/4.01 = ( plus_p3455044024723400733d_enat @ K @ B2 ) )
% 3.82/4.01 => ( ( plus_p3455044024723400733d_enat @ A @ B )
% 3.82/4.01 = ( plus_p3455044024723400733d_enat @ K @ ( plus_p3455044024723400733d_enat @ A @ B2 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % group_cancel.add2
% 3.82/4.01 thf(fact_921_add_Oassoc,axiom,
% 3.82/4.01 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.01 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B2 ) @ C )
% 3.82/4.01 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B2 @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add.assoc
% 3.82/4.01 thf(fact_922_add_Oassoc,axiom,
% 3.82/4.01 ! [A: int,B2: int,C: int] :
% 3.82/4.01 ( ( plus_plus_int @ ( plus_plus_int @ A @ B2 ) @ C )
% 3.82/4.01 = ( plus_plus_int @ A @ ( plus_plus_int @ B2 @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add.assoc
% 3.82/4.01 thf(fact_923_add_Oassoc,axiom,
% 3.82/4.01 ! [A: real,B2: real,C: real] :
% 3.82/4.01 ( ( plus_plus_real @ ( plus_plus_real @ A @ B2 ) @ C )
% 3.82/4.01 = ( plus_plus_real @ A @ ( plus_plus_real @ B2 @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add.assoc
% 3.82/4.01 thf(fact_924_add_Oassoc,axiom,
% 3.82/4.01 ! [A: extended_enat,B2: extended_enat,C: extended_enat] :
% 3.82/4.01 ( ( plus_p3455044024723400733d_enat @ ( plus_p3455044024723400733d_enat @ A @ B2 ) @ C )
% 3.82/4.01 = ( plus_p3455044024723400733d_enat @ A @ ( plus_p3455044024723400733d_enat @ B2 @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add.assoc
% 3.82/4.01 thf(fact_925_add_Oleft__cancel,axiom,
% 3.82/4.01 ! [A: int,B2: int,C: int] :
% 3.82/4.01 ( ( ( plus_plus_int @ A @ B2 )
% 3.82/4.01 = ( plus_plus_int @ A @ C ) )
% 3.82/4.01 = ( B2 = C ) ) ).
% 3.82/4.01
% 3.82/4.01 % add.left_cancel
% 3.82/4.01 thf(fact_926_add_Oleft__cancel,axiom,
% 3.82/4.01 ! [A: real,B2: real,C: real] :
% 3.82/4.01 ( ( ( plus_plus_real @ A @ B2 )
% 3.82/4.01 = ( plus_plus_real @ A @ C ) )
% 3.82/4.01 = ( B2 = C ) ) ).
% 3.82/4.01
% 3.82/4.01 % add.left_cancel
% 3.82/4.01 thf(fact_927_add_Oright__cancel,axiom,
% 3.82/4.01 ! [B2: int,A: int,C: int] :
% 3.82/4.01 ( ( ( plus_plus_int @ B2 @ A )
% 3.82/4.01 = ( plus_plus_int @ C @ A ) )
% 3.82/4.01 = ( B2 = C ) ) ).
% 3.82/4.01
% 3.82/4.01 % add.right_cancel
% 3.82/4.01 thf(fact_928_add_Oright__cancel,axiom,
% 3.82/4.01 ! [B2: real,A: real,C: real] :
% 3.82/4.01 ( ( ( plus_plus_real @ B2 @ A )
% 3.82/4.01 = ( plus_plus_real @ C @ A ) )
% 3.82/4.01 = ( B2 = C ) ) ).
% 3.82/4.01
% 3.82/4.01 % add.right_cancel
% 3.82/4.01 thf(fact_929_add_Ocommute,axiom,
% 3.82/4.01 ( plus_plus_nat
% 3.82/4.01 = ( ^ [A3: nat,B3: nat] : ( plus_plus_nat @ B3 @ A3 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add.commute
% 3.82/4.01 thf(fact_930_add_Ocommute,axiom,
% 3.82/4.01 ( plus_plus_int
% 3.82/4.01 = ( ^ [A3: int,B3: int] : ( plus_plus_int @ B3 @ A3 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add.commute
% 3.82/4.01 thf(fact_931_add_Ocommute,axiom,
% 3.82/4.01 ( plus_plus_real
% 3.82/4.01 = ( ^ [A3: real,B3: real] : ( plus_plus_real @ B3 @ A3 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add.commute
% 3.82/4.01 thf(fact_932_add_Ocommute,axiom,
% 3.82/4.01 ( plus_p3455044024723400733d_enat
% 3.82/4.01 = ( ^ [A3: extended_enat,B3: extended_enat] : ( plus_p3455044024723400733d_enat @ B3 @ A3 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add.commute
% 3.82/4.01 thf(fact_933_add_Oleft__commute,axiom,
% 3.82/4.01 ! [B2: nat,A: nat,C: nat] :
% 3.82/4.01 ( ( plus_plus_nat @ B2 @ ( plus_plus_nat @ A @ C ) )
% 3.82/4.01 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B2 @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add.left_commute
% 3.82/4.01 thf(fact_934_add_Oleft__commute,axiom,
% 3.82/4.01 ! [B2: int,A: int,C: int] :
% 3.82/4.01 ( ( plus_plus_int @ B2 @ ( plus_plus_int @ A @ C ) )
% 3.82/4.01 = ( plus_plus_int @ A @ ( plus_plus_int @ B2 @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add.left_commute
% 3.82/4.01 thf(fact_935_add_Oleft__commute,axiom,
% 3.82/4.01 ! [B2: real,A: real,C: real] :
% 3.82/4.01 ( ( plus_plus_real @ B2 @ ( plus_plus_real @ A @ C ) )
% 3.82/4.01 = ( plus_plus_real @ A @ ( plus_plus_real @ B2 @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add.left_commute
% 3.82/4.01 thf(fact_936_add_Oleft__commute,axiom,
% 3.82/4.01 ! [B2: extended_enat,A: extended_enat,C: extended_enat] :
% 3.82/4.01 ( ( plus_p3455044024723400733d_enat @ B2 @ ( plus_p3455044024723400733d_enat @ A @ C ) )
% 3.82/4.01 = ( plus_p3455044024723400733d_enat @ A @ ( plus_p3455044024723400733d_enat @ B2 @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add.left_commute
% 3.82/4.01 thf(fact_937_add__left__imp__eq,axiom,
% 3.82/4.01 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.01 ( ( ( plus_plus_nat @ A @ B2 )
% 3.82/4.01 = ( plus_plus_nat @ A @ C ) )
% 3.82/4.01 => ( B2 = C ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_left_imp_eq
% 3.82/4.01 thf(fact_938_add__left__imp__eq,axiom,
% 3.82/4.01 ! [A: int,B2: int,C: int] :
% 3.82/4.01 ( ( ( plus_plus_int @ A @ B2 )
% 3.82/4.01 = ( plus_plus_int @ A @ C ) )
% 3.82/4.01 => ( B2 = C ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_left_imp_eq
% 3.82/4.01 thf(fact_939_add__left__imp__eq,axiom,
% 3.82/4.01 ! [A: real,B2: real,C: real] :
% 3.82/4.01 ( ( ( plus_plus_real @ A @ B2 )
% 3.82/4.01 = ( plus_plus_real @ A @ C ) )
% 3.82/4.01 => ( B2 = C ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_left_imp_eq
% 3.82/4.01 thf(fact_940_add__right__imp__eq,axiom,
% 3.82/4.01 ! [B2: nat,A: nat,C: nat] :
% 3.82/4.01 ( ( ( plus_plus_nat @ B2 @ A )
% 3.82/4.01 = ( plus_plus_nat @ C @ A ) )
% 3.82/4.01 => ( B2 = C ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_right_imp_eq
% 3.82/4.01 thf(fact_941_add__right__imp__eq,axiom,
% 3.82/4.01 ! [B2: int,A: int,C: int] :
% 3.82/4.01 ( ( ( plus_plus_int @ B2 @ A )
% 3.82/4.01 = ( plus_plus_int @ C @ A ) )
% 3.82/4.01 => ( B2 = C ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_right_imp_eq
% 3.82/4.01 thf(fact_942_add__right__imp__eq,axiom,
% 3.82/4.01 ! [B2: real,A: real,C: real] :
% 3.82/4.01 ( ( ( plus_plus_real @ B2 @ A )
% 3.82/4.01 = ( plus_plus_real @ C @ A ) )
% 3.82/4.01 => ( B2 = C ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_right_imp_eq
% 3.82/4.01 thf(fact_943_zero__le,axiom,
% 3.82/4.01 ! [X: extended_enat] : ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ X ) ).
% 3.82/4.01
% 3.82/4.01 % zero_le
% 3.82/4.01 thf(fact_944_zero__le,axiom,
% 3.82/4.01 ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) ).
% 3.82/4.01
% 3.82/4.01 % zero_le
% 3.82/4.01 thf(fact_945_gr__zeroI,axiom,
% 3.82/4.01 ! [N2: nat] :
% 3.82/4.01 ( ( N2 != zero_zero_nat )
% 3.82/4.01 => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % gr_zeroI
% 3.82/4.01 thf(fact_946_gr__zeroI,axiom,
% 3.82/4.01 ! [N2: extended_enat] :
% 3.82/4.01 ( ( N2 != zero_z5237406670263579293d_enat )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % gr_zeroI
% 3.82/4.01 thf(fact_947_not__less__zero,axiom,
% 3.82/4.01 ! [N2: nat] :
% 3.82/4.01 ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 3.82/4.01
% 3.82/4.01 % not_less_zero
% 3.82/4.01 thf(fact_948_not__less__zero,axiom,
% 3.82/4.01 ! [N2: extended_enat] :
% 3.82/4.01 ~ ( ord_le72135733267957522d_enat @ N2 @ zero_z5237406670263579293d_enat ) ).
% 3.82/4.01
% 3.82/4.01 % not_less_zero
% 3.82/4.01 thf(fact_949_gr__implies__not__zero,axiom,
% 3.82/4.01 ! [M2: nat,N2: nat] :
% 3.82/4.01 ( ( ord_less_nat @ M2 @ N2 )
% 3.82/4.01 => ( N2 != zero_zero_nat ) ) ).
% 3.82/4.01
% 3.82/4.01 % gr_implies_not_zero
% 3.82/4.01 thf(fact_950_gr__implies__not__zero,axiom,
% 3.82/4.01 ! [M2: extended_enat,N2: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ M2 @ N2 )
% 3.82/4.01 => ( N2 != zero_z5237406670263579293d_enat ) ) ).
% 3.82/4.01
% 3.82/4.01 % gr_implies_not_zero
% 3.82/4.01 thf(fact_951_zero__less__iff__neq__zero,axiom,
% 3.82/4.01 ! [N2: nat] :
% 3.82/4.01 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.01 = ( N2 != zero_zero_nat ) ) ).
% 3.82/4.01
% 3.82/4.01 % zero_less_iff_neq_zero
% 3.82/4.01 thf(fact_952_zero__less__iff__neq__zero,axiom,
% 3.82/4.01 ! [N2: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N2 )
% 3.82/4.01 = ( N2 != zero_z5237406670263579293d_enat ) ) ).
% 3.82/4.01
% 3.82/4.01 % zero_less_iff_neq_zero
% 3.82/4.01 thf(fact_953_add__mono__thms__linordered__semiring_I3_J,axiom,
% 3.82/4.01 ! [I: extended_enat,J: extended_enat,K: extended_enat,L: extended_enat] :
% 3.82/4.01 ( ( ( ord_le2932123472753598470d_enat @ I @ J )
% 3.82/4.01 & ( K = L ) )
% 3.82/4.01 => ( ord_le2932123472753598470d_enat @ ( plus_p3455044024723400733d_enat @ I @ K ) @ ( plus_p3455044024723400733d_enat @ J @ L ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_mono_thms_linordered_semiring(3)
% 3.82/4.01 thf(fact_954_add__mono__thms__linordered__semiring_I3_J,axiom,
% 3.82/4.01 ! [I: real,J: real,K: real,L: real] :
% 3.82/4.01 ( ( ( ord_less_eq_real @ I @ J )
% 3.82/4.01 & ( K = L ) )
% 3.82/4.01 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_mono_thms_linordered_semiring(3)
% 3.82/4.01 thf(fact_955_add__mono__thms__linordered__semiring_I3_J,axiom,
% 3.82/4.01 ! [I: nat,J: nat,K: nat,L: nat] :
% 3.82/4.01 ( ( ( ord_less_eq_nat @ I @ J )
% 3.82/4.01 & ( K = L ) )
% 3.82/4.01 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_mono_thms_linordered_semiring(3)
% 3.82/4.01 thf(fact_956_add__mono__thms__linordered__semiring_I3_J,axiom,
% 3.82/4.01 ! [I: int,J: int,K: int,L: int] :
% 3.82/4.01 ( ( ( ord_less_eq_int @ I @ J )
% 3.82/4.01 & ( K = L ) )
% 3.82/4.01 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_mono_thms_linordered_semiring(3)
% 3.82/4.01 thf(fact_957_add__mono__thms__linordered__semiring_I2_J,axiom,
% 3.82/4.01 ! [I: extended_enat,J: extended_enat,K: extended_enat,L: extended_enat] :
% 3.82/4.01 ( ( ( I = J )
% 3.82/4.01 & ( ord_le2932123472753598470d_enat @ K @ L ) )
% 3.82/4.01 => ( ord_le2932123472753598470d_enat @ ( plus_p3455044024723400733d_enat @ I @ K ) @ ( plus_p3455044024723400733d_enat @ J @ L ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_mono_thms_linordered_semiring(2)
% 3.82/4.01 thf(fact_958_add__mono__thms__linordered__semiring_I2_J,axiom,
% 3.82/4.01 ! [I: real,J: real,K: real,L: real] :
% 3.82/4.01 ( ( ( I = J )
% 3.82/4.01 & ( ord_less_eq_real @ K @ L ) )
% 3.82/4.01 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_mono_thms_linordered_semiring(2)
% 3.82/4.01 thf(fact_959_add__mono__thms__linordered__semiring_I2_J,axiom,
% 3.82/4.01 ! [I: nat,J: nat,K: nat,L: nat] :
% 3.82/4.01 ( ( ( I = J )
% 3.82/4.01 & ( ord_less_eq_nat @ K @ L ) )
% 3.82/4.01 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_mono_thms_linordered_semiring(2)
% 3.82/4.01 thf(fact_960_add__mono__thms__linordered__semiring_I2_J,axiom,
% 3.82/4.01 ! [I: int,J: int,K: int,L: int] :
% 3.82/4.01 ( ( ( I = J )
% 3.82/4.01 & ( ord_less_eq_int @ K @ L ) )
% 3.82/4.01 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_mono_thms_linordered_semiring(2)
% 3.82/4.01 thf(fact_961_add__mono__thms__linordered__semiring_I1_J,axiom,
% 3.82/4.01 ! [I: extended_enat,J: extended_enat,K: extended_enat,L: extended_enat] :
% 3.82/4.01 ( ( ( ord_le2932123472753598470d_enat @ I @ J )
% 3.82/4.01 & ( ord_le2932123472753598470d_enat @ K @ L ) )
% 3.82/4.01 => ( ord_le2932123472753598470d_enat @ ( plus_p3455044024723400733d_enat @ I @ K ) @ ( plus_p3455044024723400733d_enat @ J @ L ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_mono_thms_linordered_semiring(1)
% 3.82/4.01 thf(fact_962_add__mono__thms__linordered__semiring_I1_J,axiom,
% 3.82/4.01 ! [I: real,J: real,K: real,L: real] :
% 3.82/4.01 ( ( ( ord_less_eq_real @ I @ J )
% 3.82/4.01 & ( ord_less_eq_real @ K @ L ) )
% 3.82/4.01 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_mono_thms_linordered_semiring(1)
% 3.82/4.01 thf(fact_963_add__mono__thms__linordered__semiring_I1_J,axiom,
% 3.82/4.01 ! [I: nat,J: nat,K: nat,L: nat] :
% 3.82/4.01 ( ( ( ord_less_eq_nat @ I @ J )
% 3.82/4.01 & ( ord_less_eq_nat @ K @ L ) )
% 3.82/4.01 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_mono_thms_linordered_semiring(1)
% 3.82/4.01 thf(fact_964_add__mono__thms__linordered__semiring_I1_J,axiom,
% 3.82/4.01 ! [I: int,J: int,K: int,L: int] :
% 3.82/4.01 ( ( ( ord_less_eq_int @ I @ J )
% 3.82/4.01 & ( ord_less_eq_int @ K @ L ) )
% 3.82/4.01 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_mono_thms_linordered_semiring(1)
% 3.82/4.01 thf(fact_965_add__mono,axiom,
% 3.82/4.01 ! [A: extended_enat,B2: extended_enat,C: extended_enat,D: extended_enat] :
% 3.82/4.01 ( ( ord_le2932123472753598470d_enat @ A @ B2 )
% 3.82/4.01 => ( ( ord_le2932123472753598470d_enat @ C @ D )
% 3.82/4.01 => ( ord_le2932123472753598470d_enat @ ( plus_p3455044024723400733d_enat @ A @ C ) @ ( plus_p3455044024723400733d_enat @ B2 @ D ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_mono
% 3.82/4.01 thf(fact_966_add__mono,axiom,
% 3.82/4.01 ! [A: real,B2: real,C: real,D: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ A @ B2 )
% 3.82/4.01 => ( ( ord_less_eq_real @ C @ D )
% 3.82/4.01 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B2 @ D ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_mono
% 3.82/4.01 thf(fact_967_add__mono,axiom,
% 3.82/4.01 ! [A: nat,B2: nat,C: nat,D: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ A @ B2 )
% 3.82/4.01 => ( ( ord_less_eq_nat @ C @ D )
% 3.82/4.01 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B2 @ D ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_mono
% 3.82/4.01 thf(fact_968_add__mono,axiom,
% 3.82/4.01 ! [A: int,B2: int,C: int,D: int] :
% 3.82/4.01 ( ( ord_less_eq_int @ A @ B2 )
% 3.82/4.01 => ( ( ord_less_eq_int @ C @ D )
% 3.82/4.01 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B2 @ D ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_mono
% 3.82/4.01 thf(fact_969_add__left__mono,axiom,
% 3.82/4.01 ! [A: extended_enat,B2: extended_enat,C: extended_enat] :
% 3.82/4.01 ( ( ord_le2932123472753598470d_enat @ A @ B2 )
% 3.82/4.01 => ( ord_le2932123472753598470d_enat @ ( plus_p3455044024723400733d_enat @ C @ A ) @ ( plus_p3455044024723400733d_enat @ C @ B2 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_left_mono
% 3.82/4.01 thf(fact_970_add__left__mono,axiom,
% 3.82/4.01 ! [A: real,B2: real,C: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ A @ B2 )
% 3.82/4.01 => ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B2 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_left_mono
% 3.82/4.01 thf(fact_971_add__left__mono,axiom,
% 3.82/4.01 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ A @ B2 )
% 3.82/4.01 => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B2 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_left_mono
% 3.82/4.01 thf(fact_972_add__left__mono,axiom,
% 3.82/4.01 ! [A: int,B2: int,C: int] :
% 3.82/4.01 ( ( ord_less_eq_int @ A @ B2 )
% 3.82/4.01 => ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B2 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_left_mono
% 3.82/4.01 thf(fact_973_less__eqE,axiom,
% 3.82/4.01 ! [A: extended_enat,B2: extended_enat] :
% 3.82/4.01 ( ( ord_le2932123472753598470d_enat @ A @ B2 )
% 3.82/4.01 => ~ ! [C2: extended_enat] :
% 3.82/4.01 ( B2
% 3.82/4.01 != ( plus_p3455044024723400733d_enat @ A @ C2 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % less_eqE
% 3.82/4.01 thf(fact_974_less__eqE,axiom,
% 3.82/4.01 ! [A: nat,B2: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ A @ B2 )
% 3.82/4.01 => ~ ! [C2: nat] :
% 3.82/4.01 ( B2
% 3.82/4.01 != ( plus_plus_nat @ A @ C2 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % less_eqE
% 3.82/4.01 thf(fact_975_add__right__mono,axiom,
% 3.82/4.01 ! [A: extended_enat,B2: extended_enat,C: extended_enat] :
% 3.82/4.01 ( ( ord_le2932123472753598470d_enat @ A @ B2 )
% 3.82/4.01 => ( ord_le2932123472753598470d_enat @ ( plus_p3455044024723400733d_enat @ A @ C ) @ ( plus_p3455044024723400733d_enat @ B2 @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_right_mono
% 3.82/4.01 thf(fact_976_add__right__mono,axiom,
% 3.82/4.01 ! [A: real,B2: real,C: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ A @ B2 )
% 3.82/4.01 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B2 @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_right_mono
% 3.82/4.01 thf(fact_977_add__right__mono,axiom,
% 3.82/4.01 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ A @ B2 )
% 3.82/4.01 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B2 @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_right_mono
% 3.82/4.01 thf(fact_978_add__right__mono,axiom,
% 3.82/4.01 ! [A: int,B2: int,C: int] :
% 3.82/4.01 ( ( ord_less_eq_int @ A @ B2 )
% 3.82/4.01 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B2 @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_right_mono
% 3.82/4.01 thf(fact_979_le__iff__add,axiom,
% 3.82/4.01 ( ord_le2932123472753598470d_enat
% 3.82/4.01 = ( ^ [A3: extended_enat,B3: extended_enat] :
% 3.82/4.01 ? [C3: extended_enat] :
% 3.82/4.01 ( B3
% 3.82/4.01 = ( plus_p3455044024723400733d_enat @ A3 @ C3 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % le_iff_add
% 3.82/4.01 thf(fact_980_le__iff__add,axiom,
% 3.82/4.01 ( ord_less_eq_nat
% 3.82/4.01 = ( ^ [A3: nat,B3: nat] :
% 3.82/4.01 ? [C3: nat] :
% 3.82/4.01 ( B3
% 3.82/4.01 = ( plus_plus_nat @ A3 @ C3 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % le_iff_add
% 3.82/4.01 thf(fact_981_add__le__imp__le__left,axiom,
% 3.82/4.01 ! [C: real,A: real,B2: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B2 ) )
% 3.82/4.01 => ( ord_less_eq_real @ A @ B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_le_imp_le_left
% 3.82/4.01 thf(fact_982_add__le__imp__le__left,axiom,
% 3.82/4.01 ! [C: nat,A: nat,B2: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B2 ) )
% 3.82/4.01 => ( ord_less_eq_nat @ A @ B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_le_imp_le_left
% 3.82/4.01 thf(fact_983_add__le__imp__le__left,axiom,
% 3.82/4.01 ! [C: int,A: int,B2: int] :
% 3.82/4.01 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B2 ) )
% 3.82/4.01 => ( ord_less_eq_int @ A @ B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_le_imp_le_left
% 3.82/4.01 thf(fact_984_add__le__imp__le__right,axiom,
% 3.82/4.01 ! [A: real,C: real,B2: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B2 @ C ) )
% 3.82/4.01 => ( ord_less_eq_real @ A @ B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_le_imp_le_right
% 3.82/4.01 thf(fact_985_add__le__imp__le__right,axiom,
% 3.82/4.01 ! [A: nat,C: nat,B2: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B2 @ C ) )
% 3.82/4.01 => ( ord_less_eq_nat @ A @ B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_le_imp_le_right
% 3.82/4.01 thf(fact_986_add__le__imp__le__right,axiom,
% 3.82/4.01 ! [A: int,C: int,B2: int] :
% 3.82/4.01 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B2 @ C ) )
% 3.82/4.01 => ( ord_less_eq_int @ A @ B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_le_imp_le_right
% 3.82/4.01 thf(fact_987_comm__monoid__add__class_Oadd__0,axiom,
% 3.82/4.01 ! [A: nat] :
% 3.82/4.01 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 3.82/4.01 = A ) ).
% 3.82/4.01
% 3.82/4.01 % comm_monoid_add_class.add_0
% 3.82/4.01 thf(fact_988_comm__monoid__add__class_Oadd__0,axiom,
% 3.82/4.01 ! [A: real] :
% 3.82/4.01 ( ( plus_plus_real @ zero_zero_real @ A )
% 3.82/4.01 = A ) ).
% 3.82/4.01
% 3.82/4.01 % comm_monoid_add_class.add_0
% 3.82/4.01 thf(fact_989_comm__monoid__add__class_Oadd__0,axiom,
% 3.82/4.01 ! [A: int] :
% 3.82/4.01 ( ( plus_plus_int @ zero_zero_int @ A )
% 3.82/4.01 = A ) ).
% 3.82/4.01
% 3.82/4.01 % comm_monoid_add_class.add_0
% 3.82/4.01 thf(fact_990_comm__monoid__add__class_Oadd__0,axiom,
% 3.82/4.01 ! [A: complex] :
% 3.82/4.01 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 3.82/4.01 = A ) ).
% 3.82/4.01
% 3.82/4.01 % comm_monoid_add_class.add_0
% 3.82/4.01 thf(fact_991_comm__monoid__add__class_Oadd__0,axiom,
% 3.82/4.01 ! [A: extended_enat] :
% 3.82/4.01 ( ( plus_p3455044024723400733d_enat @ zero_z5237406670263579293d_enat @ A )
% 3.82/4.01 = A ) ).
% 3.82/4.01
% 3.82/4.01 % comm_monoid_add_class.add_0
% 3.82/4.01 thf(fact_992_add_Ocomm__neutral,axiom,
% 3.82/4.01 ! [A: nat] :
% 3.82/4.01 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 3.82/4.01 = A ) ).
% 3.82/4.01
% 3.82/4.01 % add.comm_neutral
% 3.82/4.01 thf(fact_993_add_Ocomm__neutral,axiom,
% 3.82/4.01 ! [A: real] :
% 3.82/4.01 ( ( plus_plus_real @ A @ zero_zero_real )
% 3.82/4.01 = A ) ).
% 3.82/4.01
% 3.82/4.01 % add.comm_neutral
% 3.82/4.01 thf(fact_994_add_Ocomm__neutral,axiom,
% 3.82/4.01 ! [A: int] :
% 3.82/4.01 ( ( plus_plus_int @ A @ zero_zero_int )
% 3.82/4.01 = A ) ).
% 3.82/4.01
% 3.82/4.01 % add.comm_neutral
% 3.82/4.01 thf(fact_995_add_Ocomm__neutral,axiom,
% 3.82/4.01 ! [A: complex] :
% 3.82/4.01 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 3.82/4.01 = A ) ).
% 3.82/4.01
% 3.82/4.01 % add.comm_neutral
% 3.82/4.01 thf(fact_996_add_Ocomm__neutral,axiom,
% 3.82/4.01 ! [A: extended_enat] :
% 3.82/4.01 ( ( plus_p3455044024723400733d_enat @ A @ zero_z5237406670263579293d_enat )
% 3.82/4.01 = A ) ).
% 3.82/4.01
% 3.82/4.01 % add.comm_neutral
% 3.82/4.01 thf(fact_997_add_Ogroup__left__neutral,axiom,
% 3.82/4.01 ! [A: real] :
% 3.82/4.01 ( ( plus_plus_real @ zero_zero_real @ A )
% 3.82/4.01 = A ) ).
% 3.82/4.01
% 3.82/4.01 % add.group_left_neutral
% 3.82/4.01 thf(fact_998_add_Ogroup__left__neutral,axiom,
% 3.82/4.01 ! [A: int] :
% 3.82/4.01 ( ( plus_plus_int @ zero_zero_int @ A )
% 3.82/4.01 = A ) ).
% 3.82/4.01
% 3.82/4.01 % add.group_left_neutral
% 3.82/4.01 thf(fact_999_add_Ogroup__left__neutral,axiom,
% 3.82/4.01 ! [A: complex] :
% 3.82/4.01 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 3.82/4.01 = A ) ).
% 3.82/4.01
% 3.82/4.01 % add.group_left_neutral
% 3.82/4.01 thf(fact_1000_add__mono__thms__linordered__field_I5_J,axiom,
% 3.82/4.01 ! [I: nat,J: nat,K: nat,L: nat] :
% 3.82/4.01 ( ( ( ord_less_nat @ I @ J )
% 3.82/4.01 & ( ord_less_nat @ K @ L ) )
% 3.82/4.01 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_mono_thms_linordered_field(5)
% 3.82/4.01 thf(fact_1001_add__mono__thms__linordered__field_I5_J,axiom,
% 3.82/4.01 ! [I: real,J: real,K: real,L: real] :
% 3.82/4.01 ( ( ( ord_less_real @ I @ J )
% 3.82/4.01 & ( ord_less_real @ K @ L ) )
% 3.82/4.01 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_mono_thms_linordered_field(5)
% 3.82/4.01 thf(fact_1002_add__mono__thms__linordered__field_I5_J,axiom,
% 3.82/4.01 ! [I: int,J: int,K: int,L: int] :
% 3.82/4.01 ( ( ( ord_less_int @ I @ J )
% 3.82/4.01 & ( ord_less_int @ K @ L ) )
% 3.82/4.01 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_mono_thms_linordered_field(5)
% 3.82/4.01 thf(fact_1003_add__mono__thms__linordered__field_I2_J,axiom,
% 3.82/4.01 ! [I: nat,J: nat,K: nat,L: nat] :
% 3.82/4.01 ( ( ( I = J )
% 3.82/4.01 & ( ord_less_nat @ K @ L ) )
% 3.82/4.01 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_mono_thms_linordered_field(2)
% 3.82/4.01 thf(fact_1004_add__mono__thms__linordered__field_I2_J,axiom,
% 3.82/4.01 ! [I: real,J: real,K: real,L: real] :
% 3.82/4.01 ( ( ( I = J )
% 3.82/4.01 & ( ord_less_real @ K @ L ) )
% 3.82/4.01 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_mono_thms_linordered_field(2)
% 3.82/4.01 thf(fact_1005_add__mono__thms__linordered__field_I2_J,axiom,
% 3.82/4.01 ! [I: int,J: int,K: int,L: int] :
% 3.82/4.01 ( ( ( I = J )
% 3.82/4.01 & ( ord_less_int @ K @ L ) )
% 3.82/4.01 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_mono_thms_linordered_field(2)
% 3.82/4.01 thf(fact_1006_add__mono__thms__linordered__field_I1_J,axiom,
% 3.82/4.01 ! [I: nat,J: nat,K: nat,L: nat] :
% 3.82/4.01 ( ( ( ord_less_nat @ I @ J )
% 3.82/4.01 & ( K = L ) )
% 3.82/4.01 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_mono_thms_linordered_field(1)
% 3.82/4.01 thf(fact_1007_add__mono__thms__linordered__field_I1_J,axiom,
% 3.82/4.01 ! [I: real,J: real,K: real,L: real] :
% 3.82/4.01 ( ( ( ord_less_real @ I @ J )
% 3.82/4.01 & ( K = L ) )
% 3.82/4.01 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_mono_thms_linordered_field(1)
% 3.82/4.01 thf(fact_1008_add__mono__thms__linordered__field_I1_J,axiom,
% 3.82/4.01 ! [I: int,J: int,K: int,L: int] :
% 3.82/4.01 ( ( ( ord_less_int @ I @ J )
% 3.82/4.01 & ( K = L ) )
% 3.82/4.01 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_mono_thms_linordered_field(1)
% 3.82/4.01 thf(fact_1009_add__strict__mono,axiom,
% 3.82/4.01 ! [A: nat,B2: nat,C: nat,D: nat] :
% 3.82/4.01 ( ( ord_less_nat @ A @ B2 )
% 3.82/4.01 => ( ( ord_less_nat @ C @ D )
% 3.82/4.01 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B2 @ D ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_strict_mono
% 3.82/4.01 thf(fact_1010_add__strict__mono,axiom,
% 3.82/4.01 ! [A: extended_enat,B2: extended_enat,C: extended_enat,D: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ A @ B2 )
% 3.82/4.01 => ( ( ord_le72135733267957522d_enat @ C @ D )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ ( plus_p3455044024723400733d_enat @ A @ C ) @ ( plus_p3455044024723400733d_enat @ B2 @ D ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_strict_mono
% 3.82/4.01 thf(fact_1011_add__strict__mono,axiom,
% 3.82/4.01 ! [A: real,B2: real,C: real,D: real] :
% 3.82/4.01 ( ( ord_less_real @ A @ B2 )
% 3.82/4.01 => ( ( ord_less_real @ C @ D )
% 3.82/4.01 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B2 @ D ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_strict_mono
% 3.82/4.01 thf(fact_1012_add__strict__mono,axiom,
% 3.82/4.01 ! [A: int,B2: int,C: int,D: int] :
% 3.82/4.01 ( ( ord_less_int @ A @ B2 )
% 3.82/4.01 => ( ( ord_less_int @ C @ D )
% 3.82/4.01 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B2 @ D ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_strict_mono
% 3.82/4.01 thf(fact_1013_add__strict__left__mono,axiom,
% 3.82/4.01 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.01 ( ( ord_less_nat @ A @ B2 )
% 3.82/4.01 => ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B2 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_strict_left_mono
% 3.82/4.01 thf(fact_1014_add__strict__left__mono,axiom,
% 3.82/4.01 ! [A: real,B2: real,C: real] :
% 3.82/4.01 ( ( ord_less_real @ A @ B2 )
% 3.82/4.01 => ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B2 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_strict_left_mono
% 3.82/4.01 thf(fact_1015_add__strict__left__mono,axiom,
% 3.82/4.01 ! [A: int,B2: int,C: int] :
% 3.82/4.01 ( ( ord_less_int @ A @ B2 )
% 3.82/4.01 => ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B2 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_strict_left_mono
% 3.82/4.01 thf(fact_1016_add__strict__right__mono,axiom,
% 3.82/4.01 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.01 ( ( ord_less_nat @ A @ B2 )
% 3.82/4.01 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B2 @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_strict_right_mono
% 3.82/4.01 thf(fact_1017_add__strict__right__mono,axiom,
% 3.82/4.01 ! [A: real,B2: real,C: real] :
% 3.82/4.01 ( ( ord_less_real @ A @ B2 )
% 3.82/4.01 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B2 @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_strict_right_mono
% 3.82/4.01 thf(fact_1018_add__strict__right__mono,axiom,
% 3.82/4.01 ! [A: int,B2: int,C: int] :
% 3.82/4.01 ( ( ord_less_int @ A @ B2 )
% 3.82/4.01 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B2 @ C ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_strict_right_mono
% 3.82/4.01 thf(fact_1019_add__less__imp__less__left,axiom,
% 3.82/4.01 ! [C: nat,A: nat,B2: nat] :
% 3.82/4.01 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B2 ) )
% 3.82/4.01 => ( ord_less_nat @ A @ B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_less_imp_less_left
% 3.82/4.01 thf(fact_1020_add__less__imp__less__left,axiom,
% 3.82/4.01 ! [C: real,A: real,B2: real] :
% 3.82/4.01 ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B2 ) )
% 3.82/4.01 => ( ord_less_real @ A @ B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_less_imp_less_left
% 3.82/4.01 thf(fact_1021_add__less__imp__less__left,axiom,
% 3.82/4.01 ! [C: int,A: int,B2: int] :
% 3.82/4.01 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B2 ) )
% 3.82/4.01 => ( ord_less_int @ A @ B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_less_imp_less_left
% 3.82/4.01 thf(fact_1022_add__less__imp__less__right,axiom,
% 3.82/4.01 ! [A: nat,C: nat,B2: nat] :
% 3.82/4.01 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B2 @ C ) )
% 3.82/4.01 => ( ord_less_nat @ A @ B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_less_imp_less_right
% 3.82/4.01 thf(fact_1023_add__less__imp__less__right,axiom,
% 3.82/4.01 ! [A: real,C: real,B2: real] :
% 3.82/4.01 ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B2 @ C ) )
% 3.82/4.01 => ( ord_less_real @ A @ B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_less_imp_less_right
% 3.82/4.01 thf(fact_1024_add__less__imp__less__right,axiom,
% 3.82/4.01 ! [A: int,C: int,B2: int] :
% 3.82/4.01 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B2 @ C ) )
% 3.82/4.01 => ( ord_less_int @ A @ B2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_less_imp_less_right
% 3.82/4.01 thf(fact_1025_add__nonpos__eq__0__iff,axiom,
% 3.82/4.01 ! [X: extended_enat,Y: extended_enat] :
% 3.82/4.01 ( ( ord_le2932123472753598470d_enat @ X @ zero_z5237406670263579293d_enat )
% 3.82/4.01 => ( ( ord_le2932123472753598470d_enat @ Y @ zero_z5237406670263579293d_enat )
% 3.82/4.01 => ( ( ( plus_p3455044024723400733d_enat @ X @ Y )
% 3.82/4.01 = zero_z5237406670263579293d_enat )
% 3.82/4.01 = ( ( X = zero_z5237406670263579293d_enat )
% 3.82/4.01 & ( Y = zero_z5237406670263579293d_enat ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_nonpos_eq_0_iff
% 3.82/4.01 thf(fact_1026_add__nonpos__eq__0__iff,axiom,
% 3.82/4.01 ! [X: real,Y: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 3.82/4.01 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 3.82/4.01 => ( ( ( plus_plus_real @ X @ Y )
% 3.82/4.01 = zero_zero_real )
% 3.82/4.01 = ( ( X = zero_zero_real )
% 3.82/4.01 & ( Y = zero_zero_real ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_nonpos_eq_0_iff
% 3.82/4.01 thf(fact_1027_add__nonpos__eq__0__iff,axiom,
% 3.82/4.01 ! [X: nat,Y: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ X @ zero_zero_nat )
% 3.82/4.01 => ( ( ord_less_eq_nat @ Y @ zero_zero_nat )
% 3.82/4.01 => ( ( ( plus_plus_nat @ X @ Y )
% 3.82/4.01 = zero_zero_nat )
% 3.82/4.01 = ( ( X = zero_zero_nat )
% 3.82/4.01 & ( Y = zero_zero_nat ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_nonpos_eq_0_iff
% 3.82/4.01 thf(fact_1028_add__nonpos__eq__0__iff,axiom,
% 3.82/4.01 ! [X: int,Y: int] :
% 3.82/4.01 ( ( ord_less_eq_int @ X @ zero_zero_int )
% 3.82/4.01 => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 3.82/4.01 => ( ( ( plus_plus_int @ X @ Y )
% 3.82/4.01 = zero_zero_int )
% 3.82/4.01 = ( ( X = zero_zero_int )
% 3.82/4.01 & ( Y = zero_zero_int ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_nonpos_eq_0_iff
% 3.82/4.01 thf(fact_1029_add__nonneg__eq__0__iff,axiom,
% 3.82/4.01 ! [X: extended_enat,Y: extended_enat] :
% 3.82/4.01 ( ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ X )
% 3.82/4.01 => ( ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ Y )
% 3.82/4.01 => ( ( ( plus_p3455044024723400733d_enat @ X @ Y )
% 3.82/4.01 = zero_z5237406670263579293d_enat )
% 3.82/4.01 = ( ( X = zero_z5237406670263579293d_enat )
% 3.82/4.01 & ( Y = zero_z5237406670263579293d_enat ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_nonneg_eq_0_iff
% 3.82/4.01 thf(fact_1030_add__nonneg__eq__0__iff,axiom,
% 3.82/4.01 ! [X: real,Y: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 3.82/4.01 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 3.82/4.01 => ( ( ( plus_plus_real @ X @ Y )
% 3.82/4.01 = zero_zero_real )
% 3.82/4.01 = ( ( X = zero_zero_real )
% 3.82/4.01 & ( Y = zero_zero_real ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_nonneg_eq_0_iff
% 3.82/4.01 thf(fact_1031_add__nonneg__eq__0__iff,axiom,
% 3.82/4.01 ! [X: nat,Y: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 3.82/4.01 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 3.82/4.01 => ( ( ( plus_plus_nat @ X @ Y )
% 3.82/4.01 = zero_zero_nat )
% 3.82/4.01 = ( ( X = zero_zero_nat )
% 3.82/4.01 & ( Y = zero_zero_nat ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_nonneg_eq_0_iff
% 3.82/4.01 thf(fact_1032_add__nonneg__eq__0__iff,axiom,
% 3.82/4.01 ! [X: int,Y: int] :
% 3.82/4.01 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 3.82/4.01 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 3.82/4.01 => ( ( ( plus_plus_int @ X @ Y )
% 3.82/4.01 = zero_zero_int )
% 3.82/4.01 = ( ( X = zero_zero_int )
% 3.82/4.01 & ( Y = zero_zero_int ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_nonneg_eq_0_iff
% 3.82/4.01 thf(fact_1033_add__nonpos__nonpos,axiom,
% 3.82/4.01 ! [A: extended_enat,B2: extended_enat] :
% 3.82/4.01 ( ( ord_le2932123472753598470d_enat @ A @ zero_z5237406670263579293d_enat )
% 3.82/4.01 => ( ( ord_le2932123472753598470d_enat @ B2 @ zero_z5237406670263579293d_enat )
% 3.82/4.01 => ( ord_le2932123472753598470d_enat @ ( plus_p3455044024723400733d_enat @ A @ B2 ) @ zero_z5237406670263579293d_enat ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_nonpos_nonpos
% 3.82/4.01 thf(fact_1034_add__nonpos__nonpos,axiom,
% 3.82/4.01 ! [A: real,B2: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 3.82/4.01 => ( ( ord_less_eq_real @ B2 @ zero_zero_real )
% 3.82/4.01 => ( ord_less_eq_real @ ( plus_plus_real @ A @ B2 ) @ zero_zero_real ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_nonpos_nonpos
% 3.82/4.01 thf(fact_1035_add__nonpos__nonpos,axiom,
% 3.82/4.01 ! [A: nat,B2: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 3.82/4.01 => ( ( ord_less_eq_nat @ B2 @ zero_zero_nat )
% 3.82/4.01 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B2 ) @ zero_zero_nat ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_nonpos_nonpos
% 3.82/4.01 thf(fact_1036_add__nonpos__nonpos,axiom,
% 3.82/4.01 ! [A: int,B2: int] :
% 3.82/4.01 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 3.82/4.01 => ( ( ord_less_eq_int @ B2 @ zero_zero_int )
% 3.82/4.01 => ( ord_less_eq_int @ ( plus_plus_int @ A @ B2 ) @ zero_zero_int ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_nonpos_nonpos
% 3.82/4.01 thf(fact_1037_add__nonneg__nonneg,axiom,
% 3.82/4.01 ! [A: extended_enat,B2: extended_enat] :
% 3.82/4.01 ( ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ A )
% 3.82/4.01 => ( ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ B2 )
% 3.82/4.01 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( plus_p3455044024723400733d_enat @ A @ B2 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_nonneg_nonneg
% 3.82/4.01 thf(fact_1038_add__nonneg__nonneg,axiom,
% 3.82/4.01 ! [A: real,B2: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 3.82/4.01 => ( ( ord_less_eq_real @ zero_zero_real @ B2 )
% 3.82/4.01 => ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ B2 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_nonneg_nonneg
% 3.82/4.01 thf(fact_1039_add__nonneg__nonneg,axiom,
% 3.82/4.01 ! [A: nat,B2: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 3.82/4.01 => ( ( ord_less_eq_nat @ zero_zero_nat @ B2 )
% 3.82/4.01 => ( ord_less_eq_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B2 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_nonneg_nonneg
% 3.82/4.01 thf(fact_1040_add__nonneg__nonneg,axiom,
% 3.82/4.01 ! [A: int,B2: int] :
% 3.82/4.01 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 3.82/4.01 => ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 3.82/4.01 => ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ B2 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_nonneg_nonneg
% 3.82/4.01 thf(fact_1041_add__increasing2,axiom,
% 3.82/4.01 ! [C: extended_enat,B2: extended_enat,A: extended_enat] :
% 3.82/4.01 ( ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ C )
% 3.82/4.01 => ( ( ord_le2932123472753598470d_enat @ B2 @ A )
% 3.82/4.01 => ( ord_le2932123472753598470d_enat @ B2 @ ( plus_p3455044024723400733d_enat @ A @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_increasing2
% 3.82/4.01 thf(fact_1042_add__increasing2,axiom,
% 3.82/4.01 ! [C: real,B2: real,A: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ zero_zero_real @ C )
% 3.82/4.01 => ( ( ord_less_eq_real @ B2 @ A )
% 3.82/4.01 => ( ord_less_eq_real @ B2 @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_increasing2
% 3.82/4.01 thf(fact_1043_add__increasing2,axiom,
% 3.82/4.01 ! [C: nat,B2: nat,A: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 3.82/4.01 => ( ( ord_less_eq_nat @ B2 @ A )
% 3.82/4.01 => ( ord_less_eq_nat @ B2 @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_increasing2
% 3.82/4.01 thf(fact_1044_add__increasing2,axiom,
% 3.82/4.01 ! [C: int,B2: int,A: int] :
% 3.82/4.01 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 3.82/4.01 => ( ( ord_less_eq_int @ B2 @ A )
% 3.82/4.01 => ( ord_less_eq_int @ B2 @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_increasing2
% 3.82/4.01 thf(fact_1045_add__decreasing2,axiom,
% 3.82/4.01 ! [C: extended_enat,A: extended_enat,B2: extended_enat] :
% 3.82/4.01 ( ( ord_le2932123472753598470d_enat @ C @ zero_z5237406670263579293d_enat )
% 3.82/4.01 => ( ( ord_le2932123472753598470d_enat @ A @ B2 )
% 3.82/4.01 => ( ord_le2932123472753598470d_enat @ ( plus_p3455044024723400733d_enat @ A @ C ) @ B2 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_decreasing2
% 3.82/4.01 thf(fact_1046_add__decreasing2,axiom,
% 3.82/4.01 ! [C: real,A: real,B2: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ C @ zero_zero_real )
% 3.82/4.01 => ( ( ord_less_eq_real @ A @ B2 )
% 3.82/4.01 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B2 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_decreasing2
% 3.82/4.01 thf(fact_1047_add__decreasing2,axiom,
% 3.82/4.01 ! [C: nat,A: nat,B2: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ C @ zero_zero_nat )
% 3.82/4.01 => ( ( ord_less_eq_nat @ A @ B2 )
% 3.82/4.01 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B2 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_decreasing2
% 3.82/4.01 thf(fact_1048_add__decreasing2,axiom,
% 3.82/4.01 ! [C: int,A: int,B2: int] :
% 3.82/4.01 ( ( ord_less_eq_int @ C @ zero_zero_int )
% 3.82/4.01 => ( ( ord_less_eq_int @ A @ B2 )
% 3.82/4.01 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B2 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_decreasing2
% 3.82/4.01 thf(fact_1049_add__increasing,axiom,
% 3.82/4.01 ! [A: extended_enat,B2: extended_enat,C: extended_enat] :
% 3.82/4.01 ( ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ A )
% 3.82/4.01 => ( ( ord_le2932123472753598470d_enat @ B2 @ C )
% 3.82/4.01 => ( ord_le2932123472753598470d_enat @ B2 @ ( plus_p3455044024723400733d_enat @ A @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_increasing
% 3.82/4.01 thf(fact_1050_add__increasing,axiom,
% 3.82/4.01 ! [A: real,B2: real,C: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 3.82/4.01 => ( ( ord_less_eq_real @ B2 @ C )
% 3.82/4.01 => ( ord_less_eq_real @ B2 @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_increasing
% 3.82/4.01 thf(fact_1051_add__increasing,axiom,
% 3.82/4.01 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 3.82/4.01 => ( ( ord_less_eq_nat @ B2 @ C )
% 3.82/4.01 => ( ord_less_eq_nat @ B2 @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_increasing
% 3.82/4.01 thf(fact_1052_add__increasing,axiom,
% 3.82/4.01 ! [A: int,B2: int,C: int] :
% 3.82/4.01 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 3.82/4.01 => ( ( ord_less_eq_int @ B2 @ C )
% 3.82/4.01 => ( ord_less_eq_int @ B2 @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_increasing
% 3.82/4.01 thf(fact_1053_add__decreasing,axiom,
% 3.82/4.01 ! [A: extended_enat,C: extended_enat,B2: extended_enat] :
% 3.82/4.01 ( ( ord_le2932123472753598470d_enat @ A @ zero_z5237406670263579293d_enat )
% 3.82/4.01 => ( ( ord_le2932123472753598470d_enat @ C @ B2 )
% 3.82/4.01 => ( ord_le2932123472753598470d_enat @ ( plus_p3455044024723400733d_enat @ A @ C ) @ B2 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_decreasing
% 3.82/4.01 thf(fact_1054_add__decreasing,axiom,
% 3.82/4.01 ! [A: real,C: real,B2: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 3.82/4.01 => ( ( ord_less_eq_real @ C @ B2 )
% 3.82/4.01 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B2 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_decreasing
% 3.82/4.01 thf(fact_1055_add__decreasing,axiom,
% 3.82/4.01 ! [A: nat,C: nat,B2: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 3.82/4.01 => ( ( ord_less_eq_nat @ C @ B2 )
% 3.82/4.01 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B2 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_decreasing
% 3.82/4.01 thf(fact_1056_add__decreasing,axiom,
% 3.82/4.01 ! [A: int,C: int,B2: int] :
% 3.82/4.01 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 3.82/4.01 => ( ( ord_less_eq_int @ C @ B2 )
% 3.82/4.01 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B2 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_decreasing
% 3.82/4.01 thf(fact_1057_add__mono__thms__linordered__field_I4_J,axiom,
% 3.82/4.01 ! [I: real,J: real,K: real,L: real] :
% 3.82/4.01 ( ( ( ord_less_eq_real @ I @ J )
% 3.82/4.01 & ( ord_less_real @ K @ L ) )
% 3.82/4.01 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_mono_thms_linordered_field(4)
% 3.82/4.01 thf(fact_1058_add__mono__thms__linordered__field_I4_J,axiom,
% 3.82/4.01 ! [I: nat,J: nat,K: nat,L: nat] :
% 3.82/4.01 ( ( ( ord_less_eq_nat @ I @ J )
% 3.82/4.01 & ( ord_less_nat @ K @ L ) )
% 3.82/4.01 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_mono_thms_linordered_field(4)
% 3.82/4.01 thf(fact_1059_add__mono__thms__linordered__field_I4_J,axiom,
% 3.82/4.01 ! [I: int,J: int,K: int,L: int] :
% 3.82/4.01 ( ( ( ord_less_eq_int @ I @ J )
% 3.82/4.01 & ( ord_less_int @ K @ L ) )
% 3.82/4.01 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_mono_thms_linordered_field(4)
% 3.82/4.01 thf(fact_1060_add__mono__thms__linordered__field_I3_J,axiom,
% 3.82/4.01 ! [I: real,J: real,K: real,L: real] :
% 3.82/4.01 ( ( ( ord_less_real @ I @ J )
% 3.82/4.01 & ( ord_less_eq_real @ K @ L ) )
% 3.82/4.01 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_mono_thms_linordered_field(3)
% 3.82/4.01 thf(fact_1061_add__mono__thms__linordered__field_I3_J,axiom,
% 3.82/4.01 ! [I: nat,J: nat,K: nat,L: nat] :
% 3.82/4.01 ( ( ( ord_less_nat @ I @ J )
% 3.82/4.01 & ( ord_less_eq_nat @ K @ L ) )
% 3.82/4.01 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_mono_thms_linordered_field(3)
% 3.82/4.01 thf(fact_1062_add__mono__thms__linordered__field_I3_J,axiom,
% 3.82/4.01 ! [I: int,J: int,K: int,L: int] :
% 3.82/4.01 ( ( ( ord_less_int @ I @ J )
% 3.82/4.01 & ( ord_less_eq_int @ K @ L ) )
% 3.82/4.01 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_mono_thms_linordered_field(3)
% 3.82/4.01 thf(fact_1063_add__le__less__mono,axiom,
% 3.82/4.01 ! [A: real,B2: real,C: real,D: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ A @ B2 )
% 3.82/4.01 => ( ( ord_less_real @ C @ D )
% 3.82/4.01 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B2 @ D ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_le_less_mono
% 3.82/4.01 thf(fact_1064_add__le__less__mono,axiom,
% 3.82/4.01 ! [A: nat,B2: nat,C: nat,D: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ A @ B2 )
% 3.82/4.01 => ( ( ord_less_nat @ C @ D )
% 3.82/4.01 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B2 @ D ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_le_less_mono
% 3.82/4.01 thf(fact_1065_add__le__less__mono,axiom,
% 3.82/4.01 ! [A: int,B2: int,C: int,D: int] :
% 3.82/4.01 ( ( ord_less_eq_int @ A @ B2 )
% 3.82/4.01 => ( ( ord_less_int @ C @ D )
% 3.82/4.01 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B2 @ D ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_le_less_mono
% 3.82/4.01 thf(fact_1066_add__less__le__mono,axiom,
% 3.82/4.01 ! [A: real,B2: real,C: real,D: real] :
% 3.82/4.01 ( ( ord_less_real @ A @ B2 )
% 3.82/4.01 => ( ( ord_less_eq_real @ C @ D )
% 3.82/4.01 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B2 @ D ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_less_le_mono
% 3.82/4.01 thf(fact_1067_add__less__le__mono,axiom,
% 3.82/4.01 ! [A: nat,B2: nat,C: nat,D: nat] :
% 3.82/4.01 ( ( ord_less_nat @ A @ B2 )
% 3.82/4.01 => ( ( ord_less_eq_nat @ C @ D )
% 3.82/4.01 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B2 @ D ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_less_le_mono
% 3.82/4.01 thf(fact_1068_add__less__le__mono,axiom,
% 3.82/4.01 ! [A: int,B2: int,C: int,D: int] :
% 3.82/4.01 ( ( ord_less_int @ A @ B2 )
% 3.82/4.01 => ( ( ord_less_eq_int @ C @ D )
% 3.82/4.01 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B2 @ D ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_less_le_mono
% 3.82/4.01 thf(fact_1069_pos__add__strict,axiom,
% 3.82/4.01 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.01 ( ( ord_less_nat @ zero_zero_nat @ A )
% 3.82/4.01 => ( ( ord_less_nat @ B2 @ C )
% 3.82/4.01 => ( ord_less_nat @ B2 @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % pos_add_strict
% 3.82/4.01 thf(fact_1070_pos__add__strict,axiom,
% 3.82/4.01 ! [A: extended_enat,B2: extended_enat,C: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ A )
% 3.82/4.01 => ( ( ord_le72135733267957522d_enat @ B2 @ C )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ B2 @ ( plus_p3455044024723400733d_enat @ A @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % pos_add_strict
% 3.82/4.01 thf(fact_1071_pos__add__strict,axiom,
% 3.82/4.01 ! [A: real,B2: real,C: real] :
% 3.82/4.01 ( ( ord_less_real @ zero_zero_real @ A )
% 3.82/4.01 => ( ( ord_less_real @ B2 @ C )
% 3.82/4.01 => ( ord_less_real @ B2 @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % pos_add_strict
% 3.82/4.01 thf(fact_1072_pos__add__strict,axiom,
% 3.82/4.01 ! [A: int,B2: int,C: int] :
% 3.82/4.01 ( ( ord_less_int @ zero_zero_int @ A )
% 3.82/4.01 => ( ( ord_less_int @ B2 @ C )
% 3.82/4.01 => ( ord_less_int @ B2 @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % pos_add_strict
% 3.82/4.01 thf(fact_1073_canonically__ordered__monoid__add__class_OlessE,axiom,
% 3.82/4.01 ! [A: nat,B2: nat] :
% 3.82/4.01 ( ( ord_less_nat @ A @ B2 )
% 3.82/4.01 => ~ ! [C2: nat] :
% 3.82/4.01 ( ( B2
% 3.82/4.01 = ( plus_plus_nat @ A @ C2 ) )
% 3.82/4.01 => ( C2 = zero_zero_nat ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % canonically_ordered_monoid_add_class.lessE
% 3.82/4.01 thf(fact_1074_canonically__ordered__monoid__add__class_OlessE,axiom,
% 3.82/4.01 ! [A: extended_enat,B2: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ A @ B2 )
% 3.82/4.01 => ~ ! [C2: extended_enat] :
% 3.82/4.01 ( ( B2
% 3.82/4.01 = ( plus_p3455044024723400733d_enat @ A @ C2 ) )
% 3.82/4.01 => ( C2 = zero_z5237406670263579293d_enat ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % canonically_ordered_monoid_add_class.lessE
% 3.82/4.01 thf(fact_1075_add__pos__pos,axiom,
% 3.82/4.01 ! [A: nat,B2: nat] :
% 3.82/4.01 ( ( ord_less_nat @ zero_zero_nat @ A )
% 3.82/4.01 => ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 3.82/4.01 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B2 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_pos_pos
% 3.82/4.01 thf(fact_1076_add__pos__pos,axiom,
% 3.82/4.01 ! [A: extended_enat,B2: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ A )
% 3.82/4.01 => ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ B2 )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( plus_p3455044024723400733d_enat @ A @ B2 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_pos_pos
% 3.82/4.01 thf(fact_1077_add__pos__pos,axiom,
% 3.82/4.01 ! [A: real,B2: real] :
% 3.82/4.01 ( ( ord_less_real @ zero_zero_real @ A )
% 3.82/4.01 => ( ( ord_less_real @ zero_zero_real @ B2 )
% 3.82/4.01 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B2 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_pos_pos
% 3.82/4.01 thf(fact_1078_add__pos__pos,axiom,
% 3.82/4.01 ! [A: int,B2: int] :
% 3.82/4.01 ( ( ord_less_int @ zero_zero_int @ A )
% 3.82/4.01 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 3.82/4.01 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B2 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_pos_pos
% 3.82/4.01 thf(fact_1079_add__neg__neg,axiom,
% 3.82/4.01 ! [A: nat,B2: nat] :
% 3.82/4.01 ( ( ord_less_nat @ A @ zero_zero_nat )
% 3.82/4.01 => ( ( ord_less_nat @ B2 @ zero_zero_nat )
% 3.82/4.01 => ( ord_less_nat @ ( plus_plus_nat @ A @ B2 ) @ zero_zero_nat ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_neg_neg
% 3.82/4.01 thf(fact_1080_add__neg__neg,axiom,
% 3.82/4.01 ! [A: extended_enat,B2: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ A @ zero_z5237406670263579293d_enat )
% 3.82/4.01 => ( ( ord_le72135733267957522d_enat @ B2 @ zero_z5237406670263579293d_enat )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ ( plus_p3455044024723400733d_enat @ A @ B2 ) @ zero_z5237406670263579293d_enat ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_neg_neg
% 3.82/4.01 thf(fact_1081_add__neg__neg,axiom,
% 3.82/4.01 ! [A: real,B2: real] :
% 3.82/4.01 ( ( ord_less_real @ A @ zero_zero_real )
% 3.82/4.01 => ( ( ord_less_real @ B2 @ zero_zero_real )
% 3.82/4.01 => ( ord_less_real @ ( plus_plus_real @ A @ B2 ) @ zero_zero_real ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_neg_neg
% 3.82/4.01 thf(fact_1082_add__neg__neg,axiom,
% 3.82/4.01 ! [A: int,B2: int] :
% 3.82/4.01 ( ( ord_less_int @ A @ zero_zero_int )
% 3.82/4.01 => ( ( ord_less_int @ B2 @ zero_zero_int )
% 3.82/4.01 => ( ord_less_int @ ( plus_plus_int @ A @ B2 ) @ zero_zero_int ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_neg_neg
% 3.82/4.01 thf(fact_1083_add__neg__nonpos,axiom,
% 3.82/4.01 ! [A: extended_enat,B2: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ A @ zero_z5237406670263579293d_enat )
% 3.82/4.01 => ( ( ord_le2932123472753598470d_enat @ B2 @ zero_z5237406670263579293d_enat )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ ( plus_p3455044024723400733d_enat @ A @ B2 ) @ zero_z5237406670263579293d_enat ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_neg_nonpos
% 3.82/4.01 thf(fact_1084_add__neg__nonpos,axiom,
% 3.82/4.01 ! [A: real,B2: real] :
% 3.82/4.01 ( ( ord_less_real @ A @ zero_zero_real )
% 3.82/4.01 => ( ( ord_less_eq_real @ B2 @ zero_zero_real )
% 3.82/4.01 => ( ord_less_real @ ( plus_plus_real @ A @ B2 ) @ zero_zero_real ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_neg_nonpos
% 3.82/4.01 thf(fact_1085_add__neg__nonpos,axiom,
% 3.82/4.01 ! [A: nat,B2: nat] :
% 3.82/4.01 ( ( ord_less_nat @ A @ zero_zero_nat )
% 3.82/4.01 => ( ( ord_less_eq_nat @ B2 @ zero_zero_nat )
% 3.82/4.01 => ( ord_less_nat @ ( plus_plus_nat @ A @ B2 ) @ zero_zero_nat ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_neg_nonpos
% 3.82/4.01 thf(fact_1086_add__neg__nonpos,axiom,
% 3.82/4.01 ! [A: int,B2: int] :
% 3.82/4.01 ( ( ord_less_int @ A @ zero_zero_int )
% 3.82/4.01 => ( ( ord_less_eq_int @ B2 @ zero_zero_int )
% 3.82/4.01 => ( ord_less_int @ ( plus_plus_int @ A @ B2 ) @ zero_zero_int ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_neg_nonpos
% 3.82/4.01 thf(fact_1087_add__nonneg__pos,axiom,
% 3.82/4.01 ! [A: extended_enat,B2: extended_enat] :
% 3.82/4.01 ( ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ A )
% 3.82/4.01 => ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ B2 )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( plus_p3455044024723400733d_enat @ A @ B2 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_nonneg_pos
% 3.82/4.01 thf(fact_1088_add__nonneg__pos,axiom,
% 3.82/4.01 ! [A: real,B2: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 3.82/4.01 => ( ( ord_less_real @ zero_zero_real @ B2 )
% 3.82/4.01 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B2 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_nonneg_pos
% 3.82/4.01 thf(fact_1089_add__nonneg__pos,axiom,
% 3.82/4.01 ! [A: nat,B2: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 3.82/4.01 => ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 3.82/4.01 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B2 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_nonneg_pos
% 3.82/4.01 thf(fact_1090_add__nonneg__pos,axiom,
% 3.82/4.01 ! [A: int,B2: int] :
% 3.82/4.01 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 3.82/4.01 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 3.82/4.01 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B2 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_nonneg_pos
% 3.82/4.01 thf(fact_1091_add__nonpos__neg,axiom,
% 3.82/4.01 ! [A: extended_enat,B2: extended_enat] :
% 3.82/4.01 ( ( ord_le2932123472753598470d_enat @ A @ zero_z5237406670263579293d_enat )
% 3.82/4.01 => ( ( ord_le72135733267957522d_enat @ B2 @ zero_z5237406670263579293d_enat )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ ( plus_p3455044024723400733d_enat @ A @ B2 ) @ zero_z5237406670263579293d_enat ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_nonpos_neg
% 3.82/4.01 thf(fact_1092_add__nonpos__neg,axiom,
% 3.82/4.01 ! [A: real,B2: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 3.82/4.01 => ( ( ord_less_real @ B2 @ zero_zero_real )
% 3.82/4.01 => ( ord_less_real @ ( plus_plus_real @ A @ B2 ) @ zero_zero_real ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_nonpos_neg
% 3.82/4.01 thf(fact_1093_add__nonpos__neg,axiom,
% 3.82/4.01 ! [A: nat,B2: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 3.82/4.01 => ( ( ord_less_nat @ B2 @ zero_zero_nat )
% 3.82/4.01 => ( ord_less_nat @ ( plus_plus_nat @ A @ B2 ) @ zero_zero_nat ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_nonpos_neg
% 3.82/4.01 thf(fact_1094_add__nonpos__neg,axiom,
% 3.82/4.01 ! [A: int,B2: int] :
% 3.82/4.01 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 3.82/4.01 => ( ( ord_less_int @ B2 @ zero_zero_int )
% 3.82/4.01 => ( ord_less_int @ ( plus_plus_int @ A @ B2 ) @ zero_zero_int ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_nonpos_neg
% 3.82/4.01 thf(fact_1095_add__pos__nonneg,axiom,
% 3.82/4.01 ! [A: extended_enat,B2: extended_enat] :
% 3.82/4.01 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ A )
% 3.82/4.01 => ( ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ B2 )
% 3.82/4.01 => ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( plus_p3455044024723400733d_enat @ A @ B2 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_pos_nonneg
% 3.82/4.01 thf(fact_1096_add__pos__nonneg,axiom,
% 3.82/4.01 ! [A: real,B2: real] :
% 3.82/4.01 ( ( ord_less_real @ zero_zero_real @ A )
% 3.82/4.01 => ( ( ord_less_eq_real @ zero_zero_real @ B2 )
% 3.82/4.01 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B2 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_pos_nonneg
% 3.82/4.01 thf(fact_1097_add__pos__nonneg,axiom,
% 3.82/4.01 ! [A: nat,B2: nat] :
% 3.82/4.01 ( ( ord_less_nat @ zero_zero_nat @ A )
% 3.82/4.01 => ( ( ord_less_eq_nat @ zero_zero_nat @ B2 )
% 3.82/4.01 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B2 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_pos_nonneg
% 3.82/4.01 thf(fact_1098_add__pos__nonneg,axiom,
% 3.82/4.01 ! [A: int,B2: int] :
% 3.82/4.01 ( ( ord_less_int @ zero_zero_int @ A )
% 3.82/4.01 => ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 3.82/4.01 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B2 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_pos_nonneg
% 3.82/4.01 thf(fact_1099_add__strict__increasing,axiom,
% 3.82/4.01 ! [A: real,B2: real,C: real] :
% 3.82/4.01 ( ( ord_less_real @ zero_zero_real @ A )
% 3.82/4.01 => ( ( ord_less_eq_real @ B2 @ C )
% 3.82/4.01 => ( ord_less_real @ B2 @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_strict_increasing
% 3.82/4.01 thf(fact_1100_add__strict__increasing,axiom,
% 3.82/4.01 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.01 ( ( ord_less_nat @ zero_zero_nat @ A )
% 3.82/4.01 => ( ( ord_less_eq_nat @ B2 @ C )
% 3.82/4.01 => ( ord_less_nat @ B2 @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_strict_increasing
% 3.82/4.01 thf(fact_1101_add__strict__increasing,axiom,
% 3.82/4.01 ! [A: int,B2: int,C: int] :
% 3.82/4.01 ( ( ord_less_int @ zero_zero_int @ A )
% 3.82/4.01 => ( ( ord_less_eq_int @ B2 @ C )
% 3.82/4.01 => ( ord_less_int @ B2 @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_strict_increasing
% 3.82/4.01 thf(fact_1102_add__strict__increasing2,axiom,
% 3.82/4.01 ! [A: real,B2: real,C: real] :
% 3.82/4.01 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 3.82/4.01 => ( ( ord_less_real @ B2 @ C )
% 3.82/4.01 => ( ord_less_real @ B2 @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_strict_increasing2
% 3.82/4.01 thf(fact_1103_add__strict__increasing2,axiom,
% 3.82/4.01 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 3.82/4.01 => ( ( ord_less_nat @ B2 @ C )
% 3.82/4.01 => ( ord_less_nat @ B2 @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_strict_increasing2
% 3.82/4.01 thf(fact_1104_add__strict__increasing2,axiom,
% 3.82/4.01 ! [A: int,B2: int,C: int] :
% 3.82/4.01 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 3.82/4.01 => ( ( ord_less_int @ B2 @ C )
% 3.82/4.01 => ( ord_less_int @ B2 @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_strict_increasing2
% 3.82/4.01 thf(fact_1105_double__eq__0__iff,axiom,
% 3.82/4.01 ! [A: real] :
% 3.82/4.01 ( ( ( plus_plus_real @ A @ A )
% 3.82/4.01 = zero_zero_real )
% 3.82/4.01 = ( A = zero_zero_real ) ) ).
% 3.82/4.01
% 3.82/4.01 % double_eq_0_iff
% 3.82/4.01 thf(fact_1106_double__eq__0__iff,axiom,
% 3.82/4.01 ! [A: int] :
% 3.82/4.01 ( ( ( plus_plus_int @ A @ A )
% 3.82/4.01 = zero_zero_int )
% 3.82/4.01 = ( A = zero_zero_int ) ) ).
% 3.82/4.01
% 3.82/4.01 % double_eq_0_iff
% 3.82/4.01 thf(fact_1107_buildup__nothing__in__leaf,axiom,
% 3.82/4.01 ! [N2: nat,X: nat] :
% 3.82/4.01 ~ ( vEBT_V5719532721284313246member @ ( vEBT_vebt_buildup @ N2 ) @ X ) ).
% 3.82/4.01
% 3.82/4.01 % buildup_nothing_in_leaf
% 3.82/4.01 thf(fact_1108_field__le__epsilon,axiom,
% 3.82/4.01 ! [X: real,Y: real] :
% 3.82/4.01 ( ! [E: real] :
% 3.82/4.01 ( ( ord_less_real @ zero_zero_real @ E )
% 3.82/4.01 => ( ord_less_eq_real @ X @ ( plus_plus_real @ Y @ E ) ) )
% 3.82/4.01 => ( ord_less_eq_real @ X @ Y ) ) ).
% 3.82/4.01
% 3.82/4.01 % field_le_epsilon
% 3.82/4.01 thf(fact_1109_add__less__zeroD,axiom,
% 3.82/4.01 ! [X: real,Y: real] :
% 3.82/4.01 ( ( ord_less_real @ ( plus_plus_real @ X @ Y ) @ zero_zero_real )
% 3.82/4.01 => ( ( ord_less_real @ X @ zero_zero_real )
% 3.82/4.01 | ( ord_less_real @ Y @ zero_zero_real ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_less_zeroD
% 3.82/4.01 thf(fact_1110_add__less__zeroD,axiom,
% 3.82/4.01 ! [X: int,Y: int] :
% 3.82/4.01 ( ( ord_less_int @ ( plus_plus_int @ X @ Y ) @ zero_zero_int )
% 3.82/4.01 => ( ( ord_less_int @ X @ zero_zero_int )
% 3.82/4.01 | ( ord_less_int @ Y @ zero_zero_int ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % add_less_zeroD
% 3.82/4.01 thf(fact_1111_buildup__gives__empty,axiom,
% 3.82/4.01 ! [N2: nat] :
% 3.82/4.01 ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_buildup @ N2 ) )
% 3.82/4.01 = bot_bot_set_nat ) ).
% 3.82/4.01
% 3.82/4.01 % buildup_gives_empty
% 3.82/4.01 thf(fact_1112_subsetI,axiom,
% 3.82/4.01 ! [A2: set_Extended_enat,B: set_Extended_enat] :
% 3.82/4.01 ( ! [X5: extended_enat] :
% 3.82/4.01 ( ( member_Extended_enat @ X5 @ A2 )
% 3.82/4.01 => ( member_Extended_enat @ X5 @ B ) )
% 3.82/4.01 => ( ord_le7203529160286727270d_enat @ A2 @ B ) ) ).
% 3.82/4.01
% 3.82/4.01 % subsetI
% 3.82/4.01 thf(fact_1113_subsetI,axiom,
% 3.82/4.01 ! [A2: set_real,B: set_real] :
% 3.82/4.01 ( ! [X5: real] :
% 3.82/4.01 ( ( member_real @ X5 @ A2 )
% 3.82/4.01 => ( member_real @ X5 @ B ) )
% 3.82/4.01 => ( ord_less_eq_set_real @ A2 @ B ) ) ).
% 3.82/4.01
% 3.82/4.01 % subsetI
% 3.82/4.01 thf(fact_1114_subsetI,axiom,
% 3.82/4.01 ! [A2: set_set_nat,B: set_set_nat] :
% 3.82/4.01 ( ! [X5: set_nat] :
% 3.82/4.01 ( ( member_set_nat @ X5 @ A2 )
% 3.82/4.01 => ( member_set_nat @ X5 @ B ) )
% 3.82/4.01 => ( ord_le6893508408891458716et_nat @ A2 @ B ) ) ).
% 3.82/4.01
% 3.82/4.01 % subsetI
% 3.82/4.01 thf(fact_1115_subsetI,axiom,
% 3.82/4.01 ! [A2: set_nat,B: set_nat] :
% 3.82/4.01 ( ! [X5: nat] :
% 3.82/4.01 ( ( member_nat @ X5 @ A2 )
% 3.82/4.01 => ( member_nat @ X5 @ B ) )
% 3.82/4.01 => ( ord_less_eq_set_nat @ A2 @ B ) ) ).
% 3.82/4.01
% 3.82/4.01 % subsetI
% 3.82/4.01 thf(fact_1116_subsetI,axiom,
% 3.82/4.01 ! [A2: set_int,B: set_int] :
% 3.82/4.01 ( ! [X5: int] :
% 3.82/4.01 ( ( member_int @ X5 @ A2 )
% 3.82/4.01 => ( member_int @ X5 @ B ) )
% 3.82/4.01 => ( ord_less_eq_set_int @ A2 @ B ) ) ).
% 3.82/4.01
% 3.82/4.01 % subsetI
% 3.82/4.01 thf(fact_1117_psubsetI,axiom,
% 3.82/4.01 ! [A2: set_nat,B: set_nat] :
% 3.82/4.01 ( ( ord_less_eq_set_nat @ A2 @ B )
% 3.82/4.01 => ( ( A2 != B )
% 3.82/4.01 => ( ord_less_set_nat @ A2 @ B ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % psubsetI
% 3.82/4.01 thf(fact_1118_psubsetI,axiom,
% 3.82/4.01 ! [A2: set_int,B: set_int] :
% 3.82/4.01 ( ( ord_less_eq_set_int @ A2 @ B )
% 3.82/4.01 => ( ( A2 != B )
% 3.82/4.01 => ( ord_less_set_int @ A2 @ B ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % psubsetI
% 3.82/4.01 thf(fact_1119_subset__antisym,axiom,
% 3.82/4.01 ! [A2: set_nat,B: set_nat] :
% 3.82/4.01 ( ( ord_less_eq_set_nat @ A2 @ B )
% 3.82/4.01 => ( ( ord_less_eq_set_nat @ B @ A2 )
% 3.82/4.01 => ( A2 = B ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % subset_antisym
% 3.82/4.01 thf(fact_1120_subset__antisym,axiom,
% 3.82/4.01 ! [A2: set_int,B: set_int] :
% 3.82/4.01 ( ( ord_less_eq_set_int @ A2 @ B )
% 3.82/4.01 => ( ( ord_less_eq_set_int @ B @ A2 )
% 3.82/4.01 => ( A2 = B ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % subset_antisym
% 3.82/4.01 thf(fact_1121_buildup__nothing__in__min__max,axiom,
% 3.82/4.01 ! [N2: nat,X: nat] :
% 3.82/4.01 ~ ( vEBT_VEBT_membermima @ ( vEBT_vebt_buildup @ N2 ) @ X ) ).
% 3.82/4.01
% 3.82/4.01 % buildup_nothing_in_min_max
% 3.82/4.01 thf(fact_1122_set__vebt__finite,axiom,
% 3.82/4.01 ! [T: vEBT_VEBT,N2: nat] :
% 3.82/4.01 ( ( vEBT_invar_vebt @ T @ N2 )
% 3.82/4.01 => ( finite_finite_nat @ ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % set_vebt_finite
% 3.82/4.01 thf(fact_1123_both__member__options__def,axiom,
% 3.82/4.01 ( vEBT_V8194947554948674370ptions
% 3.82/4.01 = ( ^ [T2: vEBT_VEBT,X4: nat] :
% 3.82/4.01 ( ( vEBT_V5719532721284313246member @ T2 @ X4 )
% 3.82/4.01 | ( vEBT_VEBT_membermima @ T2 @ X4 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % both_member_options_def
% 3.82/4.01 thf(fact_1124_empty__Collect__eq,axiom,
% 3.82/4.01 ! [P: list_nat > $o] :
% 3.82/4.01 ( ( bot_bot_set_list_nat
% 3.82/4.01 = ( collect_list_nat @ P ) )
% 3.82/4.01 = ( ! [X4: list_nat] :
% 3.82/4.01 ~ ( P @ X4 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % empty_Collect_eq
% 3.82/4.01 thf(fact_1125_empty__Collect__eq,axiom,
% 3.82/4.01 ! [P: set_nat > $o] :
% 3.82/4.01 ( ( bot_bot_set_set_nat
% 3.82/4.01 = ( collect_set_nat @ P ) )
% 3.82/4.01 = ( ! [X4: set_nat] :
% 3.82/4.01 ~ ( P @ X4 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % empty_Collect_eq
% 3.82/4.01 thf(fact_1126_empty__Collect__eq,axiom,
% 3.82/4.01 ! [P: extended_enat > $o] :
% 3.82/4.01 ( ( bot_bo7653980558646680370d_enat
% 3.82/4.01 = ( collec4429806609662206161d_enat @ P ) )
% 3.82/4.01 = ( ! [X4: extended_enat] :
% 3.82/4.01 ~ ( P @ X4 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % empty_Collect_eq
% 3.82/4.01 thf(fact_1127_empty__Collect__eq,axiom,
% 3.82/4.01 ! [P: real > $o] :
% 3.82/4.01 ( ( bot_bot_set_real
% 3.82/4.01 = ( collect_real @ P ) )
% 3.82/4.01 = ( ! [X4: real] :
% 3.82/4.01 ~ ( P @ X4 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % empty_Collect_eq
% 3.82/4.01 thf(fact_1128_empty__Collect__eq,axiom,
% 3.82/4.01 ! [P: nat > $o] :
% 3.82/4.01 ( ( bot_bot_set_nat
% 3.82/4.01 = ( collect_nat @ P ) )
% 3.82/4.01 = ( ! [X4: nat] :
% 3.82/4.01 ~ ( P @ X4 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % empty_Collect_eq
% 3.82/4.01 thf(fact_1129_empty__Collect__eq,axiom,
% 3.82/4.01 ! [P: int > $o] :
% 3.82/4.01 ( ( bot_bot_set_int
% 3.82/4.01 = ( collect_int @ P ) )
% 3.82/4.01 = ( ! [X4: int] :
% 3.82/4.01 ~ ( P @ X4 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % empty_Collect_eq
% 3.82/4.01 thf(fact_1130_Collect__empty__eq,axiom,
% 3.82/4.01 ! [P: list_nat > $o] :
% 3.82/4.01 ( ( ( collect_list_nat @ P )
% 3.82/4.01 = bot_bot_set_list_nat )
% 3.82/4.01 = ( ! [X4: list_nat] :
% 3.82/4.01 ~ ( P @ X4 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % Collect_empty_eq
% 3.82/4.01 thf(fact_1131_Collect__empty__eq,axiom,
% 3.82/4.01 ! [P: set_nat > $o] :
% 3.82/4.01 ( ( ( collect_set_nat @ P )
% 3.82/4.01 = bot_bot_set_set_nat )
% 3.82/4.01 = ( ! [X4: set_nat] :
% 3.82/4.01 ~ ( P @ X4 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % Collect_empty_eq
% 3.82/4.01 thf(fact_1132_Collect__empty__eq,axiom,
% 3.82/4.01 ! [P: extended_enat > $o] :
% 3.82/4.01 ( ( ( collec4429806609662206161d_enat @ P )
% 3.82/4.01 = bot_bo7653980558646680370d_enat )
% 3.82/4.01 = ( ! [X4: extended_enat] :
% 3.82/4.01 ~ ( P @ X4 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % Collect_empty_eq
% 3.82/4.01 thf(fact_1133_Collect__empty__eq,axiom,
% 3.82/4.01 ! [P: real > $o] :
% 3.82/4.01 ( ( ( collect_real @ P )
% 3.82/4.01 = bot_bot_set_real )
% 3.82/4.01 = ( ! [X4: real] :
% 3.82/4.01 ~ ( P @ X4 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % Collect_empty_eq
% 3.82/4.01 thf(fact_1134_Collect__empty__eq,axiom,
% 3.82/4.01 ! [P: nat > $o] :
% 3.82/4.01 ( ( ( collect_nat @ P )
% 3.82/4.01 = bot_bot_set_nat )
% 3.82/4.01 = ( ! [X4: nat] :
% 3.82/4.01 ~ ( P @ X4 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % Collect_empty_eq
% 3.82/4.01 thf(fact_1135_Collect__empty__eq,axiom,
% 3.82/4.01 ! [P: int > $o] :
% 3.82/4.01 ( ( ( collect_int @ P )
% 3.82/4.01 = bot_bot_set_int )
% 3.82/4.01 = ( ! [X4: int] :
% 3.82/4.01 ~ ( P @ X4 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % Collect_empty_eq
% 3.82/4.01 thf(fact_1136_all__not__in__conv,axiom,
% 3.82/4.01 ! [A2: set_set_nat] :
% 3.82/4.01 ( ( ! [X4: set_nat] :
% 3.82/4.01 ~ ( member_set_nat @ X4 @ A2 ) )
% 3.82/4.01 = ( A2 = bot_bot_set_set_nat ) ) ).
% 3.82/4.01
% 3.82/4.01 % all_not_in_conv
% 3.82/4.01 thf(fact_1137_all__not__in__conv,axiom,
% 3.82/4.01 ! [A2: set_Extended_enat] :
% 3.82/4.01 ( ( ! [X4: extended_enat] :
% 3.82/4.01 ~ ( member_Extended_enat @ X4 @ A2 ) )
% 3.82/4.01 = ( A2 = bot_bo7653980558646680370d_enat ) ) ).
% 3.82/4.01
% 3.82/4.01 % all_not_in_conv
% 3.82/4.01 thf(fact_1138_all__not__in__conv,axiom,
% 3.82/4.01 ! [A2: set_real] :
% 3.82/4.01 ( ( ! [X4: real] :
% 3.82/4.01 ~ ( member_real @ X4 @ A2 ) )
% 3.82/4.01 = ( A2 = bot_bot_set_real ) ) ).
% 3.82/4.01
% 3.82/4.01 % all_not_in_conv
% 3.82/4.01 thf(fact_1139_all__not__in__conv,axiom,
% 3.82/4.01 ! [A2: set_nat] :
% 3.82/4.01 ( ( ! [X4: nat] :
% 3.82/4.01 ~ ( member_nat @ X4 @ A2 ) )
% 3.82/4.01 = ( A2 = bot_bot_set_nat ) ) ).
% 3.82/4.01
% 3.82/4.01 % all_not_in_conv
% 3.82/4.01 thf(fact_1140_all__not__in__conv,axiom,
% 3.82/4.01 ! [A2: set_int] :
% 3.82/4.01 ( ( ! [X4: int] :
% 3.82/4.01 ~ ( member_int @ X4 @ A2 ) )
% 3.82/4.01 = ( A2 = bot_bot_set_int ) ) ).
% 3.82/4.01
% 3.82/4.01 % all_not_in_conv
% 3.82/4.01 thf(fact_1141_empty__iff,axiom,
% 3.82/4.01 ! [C: set_nat] :
% 3.82/4.01 ~ ( member_set_nat @ C @ bot_bot_set_set_nat ) ).
% 3.82/4.01
% 3.82/4.01 % empty_iff
% 3.82/4.01 thf(fact_1142_empty__iff,axiom,
% 3.82/4.01 ! [C: extended_enat] :
% 3.82/4.01 ~ ( member_Extended_enat @ C @ bot_bo7653980558646680370d_enat ) ).
% 3.82/4.01
% 3.82/4.01 % empty_iff
% 3.82/4.01 thf(fact_1143_empty__iff,axiom,
% 3.82/4.01 ! [C: real] :
% 3.82/4.01 ~ ( member_real @ C @ bot_bot_set_real ) ).
% 3.82/4.01
% 3.82/4.01 % empty_iff
% 3.82/4.01 thf(fact_1144_empty__iff,axiom,
% 3.82/4.01 ! [C: nat] :
% 3.82/4.01 ~ ( member_nat @ C @ bot_bot_set_nat ) ).
% 3.82/4.01
% 3.82/4.01 % empty_iff
% 3.82/4.01 thf(fact_1145_empty__iff,axiom,
% 3.82/4.01 ! [C: int] :
% 3.82/4.01 ~ ( member_int @ C @ bot_bot_set_int ) ).
% 3.82/4.01
% 3.82/4.01 % empty_iff
% 3.82/4.01 thf(fact_1146_member__valid__both__member__options,axiom,
% 3.82/4.01 ! [Tree: vEBT_VEBT,N2: nat,X: nat] :
% 3.82/4.01 ( ( vEBT_invar_vebt @ Tree @ N2 )
% 3.82/4.01 => ( ( vEBT_vebt_member @ Tree @ X )
% 3.82/4.01 => ( ( vEBT_V5719532721284313246member @ Tree @ X )
% 3.82/4.01 | ( vEBT_VEBT_membermima @ Tree @ X ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % member_valid_both_member_options
% 3.82/4.01 thf(fact_1147_empty__subsetI,axiom,
% 3.82/4.01 ! [A2: set_Extended_enat] : ( ord_le7203529160286727270d_enat @ bot_bo7653980558646680370d_enat @ A2 ) ).
% 3.82/4.01
% 3.82/4.01 % empty_subsetI
% 3.82/4.01 thf(fact_1148_empty__subsetI,axiom,
% 3.82/4.01 ! [A2: set_real] : ( ord_less_eq_set_real @ bot_bot_set_real @ A2 ) ).
% 3.82/4.01
% 3.82/4.01 % empty_subsetI
% 3.82/4.01 thf(fact_1149_empty__subsetI,axiom,
% 3.82/4.01 ! [A2: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A2 ) ).
% 3.82/4.01
% 3.82/4.01 % empty_subsetI
% 3.82/4.01 thf(fact_1150_empty__subsetI,axiom,
% 3.82/4.01 ! [A2: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A2 ) ).
% 3.82/4.01
% 3.82/4.01 % empty_subsetI
% 3.82/4.01 thf(fact_1151_subset__empty,axiom,
% 3.82/4.01 ! [A2: set_Extended_enat] :
% 3.82/4.01 ( ( ord_le7203529160286727270d_enat @ A2 @ bot_bo7653980558646680370d_enat )
% 3.82/4.01 = ( A2 = bot_bo7653980558646680370d_enat ) ) ).
% 3.82/4.01
% 3.82/4.01 % subset_empty
% 3.82/4.01 thf(fact_1152_subset__empty,axiom,
% 3.82/4.01 ! [A2: set_real] :
% 3.82/4.01 ( ( ord_less_eq_set_real @ A2 @ bot_bot_set_real )
% 3.82/4.01 = ( A2 = bot_bot_set_real ) ) ).
% 3.82/4.01
% 3.82/4.01 % subset_empty
% 3.82/4.01 thf(fact_1153_subset__empty,axiom,
% 3.82/4.01 ! [A2: set_nat] :
% 3.82/4.01 ( ( ord_less_eq_set_nat @ A2 @ bot_bot_set_nat )
% 3.82/4.01 = ( A2 = bot_bot_set_nat ) ) ).
% 3.82/4.01
% 3.82/4.01 % subset_empty
% 3.82/4.01 thf(fact_1154_subset__empty,axiom,
% 3.82/4.01 ! [A2: set_int] :
% 3.82/4.01 ( ( ord_less_eq_set_int @ A2 @ bot_bot_set_int )
% 3.82/4.01 = ( A2 = bot_bot_set_int ) ) ).
% 3.82/4.01
% 3.82/4.01 % subset_empty
% 3.82/4.01 thf(fact_1155_List_Ofinite__set,axiom,
% 3.82/4.01 ! [Xs: list_VEBT_VEBT] : ( finite5795047828879050333T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) ) ).
% 3.82/4.01
% 3.82/4.01 % List.finite_set
% 3.82/4.01 thf(fact_1156_List_Ofinite__set,axiom,
% 3.82/4.01 ! [Xs: list_nat] : ( finite_finite_nat @ ( set_nat2 @ Xs ) ) ).
% 3.82/4.01
% 3.82/4.01 % List.finite_set
% 3.82/4.01 thf(fact_1157_List_Ofinite__set,axiom,
% 3.82/4.01 ! [Xs: list_complex] : ( finite3207457112153483333omplex @ ( set_complex2 @ Xs ) ) ).
% 3.82/4.01
% 3.82/4.01 % List.finite_set
% 3.82/4.01 thf(fact_1158_List_Ofinite__set,axiom,
% 3.82/4.01 ! [Xs: list_int] : ( finite_finite_int @ ( set_int2 @ Xs ) ) ).
% 3.82/4.01
% 3.82/4.01 % List.finite_set
% 3.82/4.01 thf(fact_1159_List_Ofinite__set,axiom,
% 3.82/4.01 ! [Xs: list_Extended_enat] : ( finite4001608067531595151d_enat @ ( set_Extended_enat2 @ Xs ) ) ).
% 3.82/4.01
% 3.82/4.01 % List.finite_set
% 3.82/4.01 thf(fact_1160_ex__min__if__finite,axiom,
% 3.82/4.01 ! [S2: set_nat] :
% 3.82/4.01 ( ( finite_finite_nat @ S2 )
% 3.82/4.01 => ( ( S2 != bot_bot_set_nat )
% 3.82/4.01 => ? [X5: nat] :
% 3.82/4.01 ( ( member_nat @ X5 @ S2 )
% 3.82/4.01 & ~ ? [Xa: nat] :
% 3.82/4.01 ( ( member_nat @ Xa @ S2 )
% 3.82/4.01 & ( ord_less_nat @ Xa @ X5 ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % ex_min_if_finite
% 3.82/4.01 thf(fact_1161_ex__min__if__finite,axiom,
% 3.82/4.01 ! [S2: set_Extended_enat] :
% 3.82/4.01 ( ( finite4001608067531595151d_enat @ S2 )
% 3.82/4.01 => ( ( S2 != bot_bo7653980558646680370d_enat )
% 3.82/4.01 => ? [X5: extended_enat] :
% 3.82/4.01 ( ( member_Extended_enat @ X5 @ S2 )
% 3.82/4.01 & ~ ? [Xa: extended_enat] :
% 3.82/4.01 ( ( member_Extended_enat @ Xa @ S2 )
% 3.82/4.01 & ( ord_le72135733267957522d_enat @ Xa @ X5 ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % ex_min_if_finite
% 3.82/4.01 thf(fact_1162_ex__min__if__finite,axiom,
% 3.82/4.01 ! [S2: set_real] :
% 3.82/4.01 ( ( finite_finite_real @ S2 )
% 3.82/4.01 => ( ( S2 != bot_bot_set_real )
% 3.82/4.01 => ? [X5: real] :
% 3.82/4.01 ( ( member_real @ X5 @ S2 )
% 3.82/4.01 & ~ ? [Xa: real] :
% 3.82/4.01 ( ( member_real @ Xa @ S2 )
% 3.82/4.01 & ( ord_less_real @ Xa @ X5 ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % ex_min_if_finite
% 3.82/4.01 thf(fact_1163_ex__min__if__finite,axiom,
% 3.82/4.01 ! [S2: set_int] :
% 3.82/4.01 ( ( finite_finite_int @ S2 )
% 3.82/4.01 => ( ( S2 != bot_bot_set_int )
% 3.82/4.01 => ? [X5: int] :
% 3.82/4.01 ( ( member_int @ X5 @ S2 )
% 3.82/4.01 & ~ ? [Xa: int] :
% 3.82/4.01 ( ( member_int @ Xa @ S2 )
% 3.82/4.01 & ( ord_less_int @ Xa @ X5 ) ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % ex_min_if_finite
% 3.82/4.01 thf(fact_1164_not__psubset__empty,axiom,
% 3.82/4.01 ! [A2: set_Extended_enat] :
% 3.82/4.01 ~ ( ord_le2529575680413868914d_enat @ A2 @ bot_bo7653980558646680370d_enat ) ).
% 3.82/4.01
% 3.82/4.01 % not_psubset_empty
% 3.82/4.01 thf(fact_1165_not__psubset__empty,axiom,
% 3.82/4.01 ! [A2: set_real] :
% 3.82/4.01 ~ ( ord_less_set_real @ A2 @ bot_bot_set_real ) ).
% 3.82/4.01
% 3.82/4.01 % not_psubset_empty
% 3.82/4.01 thf(fact_1166_not__psubset__empty,axiom,
% 3.82/4.01 ! [A2: set_nat] :
% 3.82/4.01 ~ ( ord_less_set_nat @ A2 @ bot_bot_set_nat ) ).
% 3.82/4.01
% 3.82/4.01 % not_psubset_empty
% 3.82/4.01 thf(fact_1167_not__psubset__empty,axiom,
% 3.82/4.01 ! [A2: set_int] :
% 3.82/4.01 ~ ( ord_less_set_int @ A2 @ bot_bot_set_int ) ).
% 3.82/4.01
% 3.82/4.01 % not_psubset_empty
% 3.82/4.01 thf(fact_1168_psubsetD,axiom,
% 3.82/4.01 ! [A2: set_Extended_enat,B: set_Extended_enat,C: extended_enat] :
% 3.82/4.01 ( ( ord_le2529575680413868914d_enat @ A2 @ B )
% 3.82/4.01 => ( ( member_Extended_enat @ C @ A2 )
% 3.82/4.01 => ( member_Extended_enat @ C @ B ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % psubsetD
% 3.82/4.01 thf(fact_1169_psubsetD,axiom,
% 3.82/4.01 ! [A2: set_real,B: set_real,C: real] :
% 3.82/4.01 ( ( ord_less_set_real @ A2 @ B )
% 3.82/4.01 => ( ( member_real @ C @ A2 )
% 3.82/4.01 => ( member_real @ C @ B ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % psubsetD
% 3.82/4.01 thf(fact_1170_psubsetD,axiom,
% 3.82/4.01 ! [A2: set_set_nat,B: set_set_nat,C: set_nat] :
% 3.82/4.01 ( ( ord_less_set_set_nat @ A2 @ B )
% 3.82/4.01 => ( ( member_set_nat @ C @ A2 )
% 3.82/4.01 => ( member_set_nat @ C @ B ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % psubsetD
% 3.82/4.01 thf(fact_1171_psubsetD,axiom,
% 3.82/4.01 ! [A2: set_nat,B: set_nat,C: nat] :
% 3.82/4.01 ( ( ord_less_set_nat @ A2 @ B )
% 3.82/4.01 => ( ( member_nat @ C @ A2 )
% 3.82/4.01 => ( member_nat @ C @ B ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % psubsetD
% 3.82/4.01 thf(fact_1172_psubsetD,axiom,
% 3.82/4.01 ! [A2: set_int,B: set_int,C: int] :
% 3.82/4.01 ( ( ord_less_set_int @ A2 @ B )
% 3.82/4.01 => ( ( member_int @ C @ A2 )
% 3.82/4.01 => ( member_int @ C @ B ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % psubsetD
% 3.82/4.01 thf(fact_1173_infinite__growing,axiom,
% 3.82/4.01 ! [X8: set_nat] :
% 3.82/4.01 ( ( X8 != bot_bot_set_nat )
% 3.82/4.01 => ( ! [X5: nat] :
% 3.82/4.01 ( ( member_nat @ X5 @ X8 )
% 3.82/4.01 => ? [Xa: nat] :
% 3.82/4.01 ( ( member_nat @ Xa @ X8 )
% 3.82/4.01 & ( ord_less_nat @ X5 @ Xa ) ) )
% 3.82/4.01 => ~ ( finite_finite_nat @ X8 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % infinite_growing
% 3.82/4.01 thf(fact_1174_infinite__growing,axiom,
% 3.82/4.01 ! [X8: set_Extended_enat] :
% 3.82/4.01 ( ( X8 != bot_bo7653980558646680370d_enat )
% 3.82/4.01 => ( ! [X5: extended_enat] :
% 3.82/4.01 ( ( member_Extended_enat @ X5 @ X8 )
% 3.82/4.01 => ? [Xa: extended_enat] :
% 3.82/4.01 ( ( member_Extended_enat @ Xa @ X8 )
% 3.82/4.01 & ( ord_le72135733267957522d_enat @ X5 @ Xa ) ) )
% 3.82/4.01 => ~ ( finite4001608067531595151d_enat @ X8 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % infinite_growing
% 3.82/4.01 thf(fact_1175_infinite__growing,axiom,
% 3.82/4.01 ! [X8: set_real] :
% 3.82/4.01 ( ( X8 != bot_bot_set_real )
% 3.82/4.01 => ( ! [X5: real] :
% 3.82/4.01 ( ( member_real @ X5 @ X8 )
% 3.82/4.01 => ? [Xa: real] :
% 3.82/4.01 ( ( member_real @ Xa @ X8 )
% 3.82/4.01 & ( ord_less_real @ X5 @ Xa ) ) )
% 3.82/4.01 => ~ ( finite_finite_real @ X8 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % infinite_growing
% 3.82/4.01 thf(fact_1176_infinite__growing,axiom,
% 3.82/4.01 ! [X8: set_int] :
% 3.82/4.01 ( ( X8 != bot_bot_set_int )
% 3.82/4.01 => ( ! [X5: int] :
% 3.82/4.01 ( ( member_int @ X5 @ X8 )
% 3.82/4.01 => ? [Xa: int] :
% 3.82/4.01 ( ( member_int @ Xa @ X8 )
% 3.82/4.01 & ( ord_less_int @ X5 @ Xa ) ) )
% 3.82/4.01 => ~ ( finite_finite_int @ X8 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % infinite_growing
% 3.82/4.01 thf(fact_1177_ex__in__conv,axiom,
% 3.82/4.01 ! [A2: set_set_nat] :
% 3.82/4.01 ( ( ? [X4: set_nat] : ( member_set_nat @ X4 @ A2 ) )
% 3.82/4.01 = ( A2 != bot_bot_set_set_nat ) ) ).
% 3.82/4.01
% 3.82/4.01 % ex_in_conv
% 3.82/4.01 thf(fact_1178_ex__in__conv,axiom,
% 3.82/4.01 ! [A2: set_Extended_enat] :
% 3.82/4.01 ( ( ? [X4: extended_enat] : ( member_Extended_enat @ X4 @ A2 ) )
% 3.82/4.01 = ( A2 != bot_bo7653980558646680370d_enat ) ) ).
% 3.82/4.01
% 3.82/4.01 % ex_in_conv
% 3.82/4.01 thf(fact_1179_ex__in__conv,axiom,
% 3.82/4.01 ! [A2: set_real] :
% 3.82/4.01 ( ( ? [X4: real] : ( member_real @ X4 @ A2 ) )
% 3.82/4.01 = ( A2 != bot_bot_set_real ) ) ).
% 3.82/4.01
% 3.82/4.01 % ex_in_conv
% 3.82/4.01 thf(fact_1180_ex__in__conv,axiom,
% 3.82/4.01 ! [A2: set_nat] :
% 3.82/4.01 ( ( ? [X4: nat] : ( member_nat @ X4 @ A2 ) )
% 3.82/4.01 = ( A2 != bot_bot_set_nat ) ) ).
% 3.82/4.01
% 3.82/4.01 % ex_in_conv
% 3.82/4.01 thf(fact_1181_ex__in__conv,axiom,
% 3.82/4.01 ! [A2: set_int] :
% 3.82/4.01 ( ( ? [X4: int] : ( member_int @ X4 @ A2 ) )
% 3.82/4.01 = ( A2 != bot_bot_set_int ) ) ).
% 3.82/4.01
% 3.82/4.01 % ex_in_conv
% 3.82/4.01 thf(fact_1182_equals0I,axiom,
% 3.82/4.01 ! [A2: set_set_nat] :
% 3.82/4.01 ( ! [Y3: set_nat] :
% 3.82/4.01 ~ ( member_set_nat @ Y3 @ A2 )
% 3.82/4.01 => ( A2 = bot_bot_set_set_nat ) ) ).
% 3.82/4.01
% 3.82/4.01 % equals0I
% 3.82/4.01 thf(fact_1183_equals0I,axiom,
% 3.82/4.01 ! [A2: set_Extended_enat] :
% 3.82/4.01 ( ! [Y3: extended_enat] :
% 3.82/4.01 ~ ( member_Extended_enat @ Y3 @ A2 )
% 3.82/4.01 => ( A2 = bot_bo7653980558646680370d_enat ) ) ).
% 3.82/4.01
% 3.82/4.01 % equals0I
% 3.82/4.01 thf(fact_1184_equals0I,axiom,
% 3.82/4.01 ! [A2: set_real] :
% 3.82/4.01 ( ! [Y3: real] :
% 3.82/4.01 ~ ( member_real @ Y3 @ A2 )
% 3.82/4.01 => ( A2 = bot_bot_set_real ) ) ).
% 3.82/4.01
% 3.82/4.01 % equals0I
% 3.82/4.01 thf(fact_1185_equals0I,axiom,
% 3.82/4.01 ! [A2: set_nat] :
% 3.82/4.01 ( ! [Y3: nat] :
% 3.82/4.01 ~ ( member_nat @ Y3 @ A2 )
% 3.82/4.01 => ( A2 = bot_bot_set_nat ) ) ).
% 3.82/4.01
% 3.82/4.01 % equals0I
% 3.82/4.01 thf(fact_1186_equals0I,axiom,
% 3.82/4.01 ! [A2: set_int] :
% 3.82/4.01 ( ! [Y3: int] :
% 3.82/4.01 ~ ( member_int @ Y3 @ A2 )
% 3.82/4.01 => ( A2 = bot_bot_set_int ) ) ).
% 3.82/4.01
% 3.82/4.01 % equals0I
% 3.82/4.01 thf(fact_1187_equals0D,axiom,
% 3.82/4.01 ! [A2: set_set_nat,A: set_nat] :
% 3.82/4.01 ( ( A2 = bot_bot_set_set_nat )
% 3.82/4.01 => ~ ( member_set_nat @ A @ A2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % equals0D
% 3.82/4.01 thf(fact_1188_equals0D,axiom,
% 3.82/4.01 ! [A2: set_Extended_enat,A: extended_enat] :
% 3.82/4.01 ( ( A2 = bot_bo7653980558646680370d_enat )
% 3.82/4.01 => ~ ( member_Extended_enat @ A @ A2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % equals0D
% 3.82/4.01 thf(fact_1189_equals0D,axiom,
% 3.82/4.01 ! [A2: set_real,A: real] :
% 3.82/4.01 ( ( A2 = bot_bot_set_real )
% 3.82/4.01 => ~ ( member_real @ A @ A2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % equals0D
% 3.82/4.01 thf(fact_1190_equals0D,axiom,
% 3.82/4.01 ! [A2: set_nat,A: nat] :
% 3.82/4.01 ( ( A2 = bot_bot_set_nat )
% 3.82/4.01 => ~ ( member_nat @ A @ A2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % equals0D
% 3.82/4.01 thf(fact_1191_equals0D,axiom,
% 3.82/4.01 ! [A2: set_int,A: int] :
% 3.82/4.01 ( ( A2 = bot_bot_set_int )
% 3.82/4.01 => ~ ( member_int @ A @ A2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % equals0D
% 3.82/4.01 thf(fact_1192_emptyE,axiom,
% 3.82/4.01 ! [A: set_nat] :
% 3.82/4.01 ~ ( member_set_nat @ A @ bot_bot_set_set_nat ) ).
% 3.82/4.01
% 3.82/4.01 % emptyE
% 3.82/4.01 thf(fact_1193_emptyE,axiom,
% 3.82/4.01 ! [A: extended_enat] :
% 3.82/4.01 ~ ( member_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ).
% 3.82/4.01
% 3.82/4.01 % emptyE
% 3.82/4.01 thf(fact_1194_emptyE,axiom,
% 3.82/4.01 ! [A: real] :
% 3.82/4.01 ~ ( member_real @ A @ bot_bot_set_real ) ).
% 3.82/4.01
% 3.82/4.01 % emptyE
% 3.82/4.01 thf(fact_1195_emptyE,axiom,
% 3.82/4.01 ! [A: nat] :
% 3.82/4.01 ~ ( member_nat @ A @ bot_bot_set_nat ) ).
% 3.82/4.01
% 3.82/4.01 % emptyE
% 3.82/4.01 thf(fact_1196_emptyE,axiom,
% 3.82/4.01 ! [A: int] :
% 3.82/4.01 ~ ( member_int @ A @ bot_bot_set_int ) ).
% 3.82/4.01
% 3.82/4.01 % emptyE
% 3.82/4.01 thf(fact_1197_bot_Oextremum__uniqueI,axiom,
% 3.82/4.01 ! [A: set_Extended_enat] :
% 3.82/4.01 ( ( ord_le7203529160286727270d_enat @ A @ bot_bo7653980558646680370d_enat )
% 3.82/4.01 => ( A = bot_bo7653980558646680370d_enat ) ) ).
% 3.82/4.01
% 3.82/4.01 % bot.extremum_uniqueI
% 3.82/4.01 thf(fact_1198_bot_Oextremum__uniqueI,axiom,
% 3.82/4.01 ! [A: set_real] :
% 3.82/4.01 ( ( ord_less_eq_set_real @ A @ bot_bot_set_real )
% 3.82/4.01 => ( A = bot_bot_set_real ) ) ).
% 3.82/4.01
% 3.82/4.01 % bot.extremum_uniqueI
% 3.82/4.01 thf(fact_1199_bot_Oextremum__uniqueI,axiom,
% 3.82/4.01 ! [A: set_nat] :
% 3.82/4.01 ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 3.82/4.01 => ( A = bot_bot_set_nat ) ) ).
% 3.82/4.01
% 3.82/4.01 % bot.extremum_uniqueI
% 3.82/4.01 thf(fact_1200_bot_Oextremum__uniqueI,axiom,
% 3.82/4.01 ! [A: set_int] :
% 3.82/4.01 ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 3.82/4.01 => ( A = bot_bot_set_int ) ) ).
% 3.82/4.01
% 3.82/4.01 % bot.extremum_uniqueI
% 3.82/4.01 thf(fact_1201_bot_Oextremum__uniqueI,axiom,
% 3.82/4.01 ! [A: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 3.82/4.01 => ( A = bot_bot_nat ) ) ).
% 3.82/4.01
% 3.82/4.01 % bot.extremum_uniqueI
% 3.82/4.01 thf(fact_1202_bot_Oextremum__unique,axiom,
% 3.82/4.01 ! [A: set_Extended_enat] :
% 3.82/4.01 ( ( ord_le7203529160286727270d_enat @ A @ bot_bo7653980558646680370d_enat )
% 3.82/4.01 = ( A = bot_bo7653980558646680370d_enat ) ) ).
% 3.82/4.01
% 3.82/4.01 % bot.extremum_unique
% 3.82/4.01 thf(fact_1203_bot_Oextremum__unique,axiom,
% 3.82/4.01 ! [A: set_real] :
% 3.82/4.01 ( ( ord_less_eq_set_real @ A @ bot_bot_set_real )
% 3.82/4.01 = ( A = bot_bot_set_real ) ) ).
% 3.82/4.01
% 3.82/4.01 % bot.extremum_unique
% 3.82/4.01 thf(fact_1204_bot_Oextremum__unique,axiom,
% 3.82/4.01 ! [A: set_nat] :
% 3.82/4.01 ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 3.82/4.01 = ( A = bot_bot_set_nat ) ) ).
% 3.82/4.01
% 3.82/4.01 % bot.extremum_unique
% 3.82/4.01 thf(fact_1205_bot_Oextremum__unique,axiom,
% 3.82/4.01 ! [A: set_int] :
% 3.82/4.01 ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 3.82/4.01 = ( A = bot_bot_set_int ) ) ).
% 3.82/4.01
% 3.82/4.01 % bot.extremum_unique
% 3.82/4.01 thf(fact_1206_bot_Oextremum__unique,axiom,
% 3.82/4.01 ! [A: nat] :
% 3.82/4.01 ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 3.82/4.01 = ( A = bot_bot_nat ) ) ).
% 3.82/4.01
% 3.82/4.01 % bot.extremum_unique
% 3.82/4.01 thf(fact_1207_bot_Oextremum,axiom,
% 3.82/4.01 ! [A: set_Extended_enat] : ( ord_le7203529160286727270d_enat @ bot_bo7653980558646680370d_enat @ A ) ).
% 3.82/4.01
% 3.82/4.01 % bot.extremum
% 3.82/4.01 thf(fact_1208_bot_Oextremum,axiom,
% 3.82/4.01 ! [A: set_real] : ( ord_less_eq_set_real @ bot_bot_set_real @ A ) ).
% 3.82/4.01
% 3.82/4.01 % bot.extremum
% 3.82/4.01 thf(fact_1209_bot_Oextremum,axiom,
% 3.82/4.01 ! [A: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A ) ).
% 3.82/4.01
% 3.82/4.01 % bot.extremum
% 3.82/4.01 thf(fact_1210_bot_Oextremum,axiom,
% 3.82/4.01 ! [A: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A ) ).
% 3.82/4.01
% 3.82/4.01 % bot.extremum
% 3.82/4.01 thf(fact_1211_bot_Oextremum,axiom,
% 3.82/4.01 ! [A: nat] : ( ord_less_eq_nat @ bot_bot_nat @ A ) ).
% 3.82/4.01
% 3.82/4.01 % bot.extremum
% 3.82/4.01 thf(fact_1212_bot_Onot__eq__extremum,axiom,
% 3.82/4.01 ! [A: set_Extended_enat] :
% 3.82/4.01 ( ( A != bot_bo7653980558646680370d_enat )
% 3.82/4.01 = ( ord_le2529575680413868914d_enat @ bot_bo7653980558646680370d_enat @ A ) ) ).
% 3.82/4.01
% 3.82/4.01 % bot.not_eq_extremum
% 3.82/4.01 thf(fact_1213_bot_Onot__eq__extremum,axiom,
% 3.82/4.01 ! [A: set_real] :
% 3.82/4.01 ( ( A != bot_bot_set_real )
% 3.82/4.01 = ( ord_less_set_real @ bot_bot_set_real @ A ) ) ).
% 3.82/4.01
% 3.82/4.01 % bot.not_eq_extremum
% 3.82/4.01 thf(fact_1214_bot_Onot__eq__extremum,axiom,
% 3.82/4.01 ! [A: set_nat] :
% 3.82/4.01 ( ( A != bot_bot_set_nat )
% 3.82/4.01 = ( ord_less_set_nat @ bot_bot_set_nat @ A ) ) ).
% 3.82/4.01
% 3.82/4.01 % bot.not_eq_extremum
% 3.82/4.01 thf(fact_1215_bot_Onot__eq__extremum,axiom,
% 3.82/4.01 ! [A: set_int] :
% 3.82/4.01 ( ( A != bot_bot_set_int )
% 3.82/4.01 = ( ord_less_set_int @ bot_bot_set_int @ A ) ) ).
% 3.82/4.01
% 3.82/4.01 % bot.not_eq_extremum
% 3.82/4.01 thf(fact_1216_bot_Onot__eq__extremum,axiom,
% 3.82/4.01 ! [A: nat] :
% 3.82/4.01 ( ( A != bot_bot_nat )
% 3.82/4.01 = ( ord_less_nat @ bot_bot_nat @ A ) ) ).
% 3.82/4.01
% 3.82/4.01 % bot.not_eq_extremum
% 3.82/4.01 thf(fact_1217_bot_Onot__eq__extremum,axiom,
% 3.82/4.01 ! [A: extended_enat] :
% 3.82/4.01 ( ( A != bot_bo4199563552545308370d_enat )
% 3.82/4.01 = ( ord_le72135733267957522d_enat @ bot_bo4199563552545308370d_enat @ A ) ) ).
% 3.82/4.01
% 3.82/4.01 % bot.not_eq_extremum
% 3.82/4.01 thf(fact_1218_bot_Oextremum__strict,axiom,
% 3.82/4.01 ! [A: set_Extended_enat] :
% 3.82/4.01 ~ ( ord_le2529575680413868914d_enat @ A @ bot_bo7653980558646680370d_enat ) ).
% 3.82/4.01
% 3.82/4.01 % bot.extremum_strict
% 3.82/4.01 thf(fact_1219_bot_Oextremum__strict,axiom,
% 3.82/4.01 ! [A: set_real] :
% 3.82/4.01 ~ ( ord_less_set_real @ A @ bot_bot_set_real ) ).
% 3.82/4.01
% 3.82/4.01 % bot.extremum_strict
% 3.82/4.01 thf(fact_1220_bot_Oextremum__strict,axiom,
% 3.82/4.01 ! [A: set_nat] :
% 3.82/4.01 ~ ( ord_less_set_nat @ A @ bot_bot_set_nat ) ).
% 3.82/4.01
% 3.82/4.01 % bot.extremum_strict
% 3.82/4.01 thf(fact_1221_bot_Oextremum__strict,axiom,
% 3.82/4.01 ! [A: set_int] :
% 3.82/4.01 ~ ( ord_less_set_int @ A @ bot_bot_set_int ) ).
% 3.82/4.01
% 3.82/4.01 % bot.extremum_strict
% 3.82/4.01 thf(fact_1222_bot_Oextremum__strict,axiom,
% 3.82/4.01 ! [A: nat] :
% 3.82/4.01 ~ ( ord_less_nat @ A @ bot_bot_nat ) ).
% 3.82/4.01
% 3.82/4.01 % bot.extremum_strict
% 3.82/4.01 thf(fact_1223_bot_Oextremum__strict,axiom,
% 3.82/4.01 ! [A: extended_enat] :
% 3.82/4.01 ~ ( ord_le72135733267957522d_enat @ A @ bot_bo4199563552545308370d_enat ) ).
% 3.82/4.01
% 3.82/4.01 % bot.extremum_strict
% 3.82/4.01 thf(fact_1224_finite__list,axiom,
% 3.82/4.01 ! [A2: set_VEBT_VEBT] :
% 3.82/4.01 ( ( finite5795047828879050333T_VEBT @ A2 )
% 3.82/4.01 => ? [Xs2: list_VEBT_VEBT] :
% 3.82/4.01 ( ( set_VEBT_VEBT2 @ Xs2 )
% 3.82/4.01 = A2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % finite_list
% 3.82/4.01 thf(fact_1225_finite__list,axiom,
% 3.82/4.01 ! [A2: set_nat] :
% 3.82/4.01 ( ( finite_finite_nat @ A2 )
% 3.82/4.01 => ? [Xs2: list_nat] :
% 3.82/4.01 ( ( set_nat2 @ Xs2 )
% 3.82/4.01 = A2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % finite_list
% 3.82/4.01 thf(fact_1226_finite__list,axiom,
% 3.82/4.01 ! [A2: set_complex] :
% 3.82/4.01 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.01 => ? [Xs2: list_complex] :
% 3.82/4.01 ( ( set_complex2 @ Xs2 )
% 3.82/4.01 = A2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % finite_list
% 3.82/4.01 thf(fact_1227_finite__list,axiom,
% 3.82/4.01 ! [A2: set_int] :
% 3.82/4.01 ( ( finite_finite_int @ A2 )
% 3.82/4.01 => ? [Xs2: list_int] :
% 3.82/4.01 ( ( set_int2 @ Xs2 )
% 3.82/4.01 = A2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % finite_list
% 3.82/4.01 thf(fact_1228_finite__list,axiom,
% 3.82/4.01 ! [A2: set_Extended_enat] :
% 3.82/4.01 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.01 => ? [Xs2: list_Extended_enat] :
% 3.82/4.01 ( ( set_Extended_enat2 @ Xs2 )
% 3.82/4.01 = A2 ) ) ).
% 3.82/4.01
% 3.82/4.01 % finite_list
% 3.82/4.01 thf(fact_1229_linorder__neqE__linordered__idom,axiom,
% 3.82/4.01 ! [X: real,Y: real] :
% 3.82/4.01 ( ( X != Y )
% 3.82/4.01 => ( ~ ( ord_less_real @ X @ Y )
% 3.82/4.01 => ( ord_less_real @ Y @ X ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % linorder_neqE_linordered_idom
% 3.82/4.01 thf(fact_1230_linorder__neqE__linordered__idom,axiom,
% 3.82/4.01 ! [X: int,Y: int] :
% 3.82/4.01 ( ( X != Y )
% 3.82/4.01 => ( ~ ( ord_less_int @ X @ Y )
% 3.82/4.01 => ( ord_less_int @ Y @ X ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % linorder_neqE_linordered_idom
% 3.82/4.01 thf(fact_1231_linordered__field__no__ub,axiom,
% 3.82/4.01 ! [X2: real] :
% 3.82/4.01 ? [X_12: real] : ( ord_less_real @ X2 @ X_12 ) ).
% 3.82/4.01
% 3.82/4.01 % linordered_field_no_ub
% 3.82/4.01 thf(fact_1232_linordered__field__no__lb,axiom,
% 3.82/4.01 ! [X2: real] :
% 3.82/4.01 ? [Y3: real] : ( ord_less_real @ Y3 @ X2 ) ).
% 3.82/4.01
% 3.82/4.01 % linordered_field_no_lb
% 3.82/4.01 thf(fact_1233_subset__iff__psubset__eq,axiom,
% 3.82/4.01 ( ord_less_eq_set_nat
% 3.82/4.01 = ( ^ [A5: set_nat,B5: set_nat] :
% 3.82/4.01 ( ( ord_less_set_nat @ A5 @ B5 )
% 3.82/4.01 | ( A5 = B5 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % subset_iff_psubset_eq
% 3.82/4.01 thf(fact_1234_subset__iff__psubset__eq,axiom,
% 3.82/4.01 ( ord_less_eq_set_int
% 3.82/4.01 = ( ^ [A5: set_int,B5: set_int] :
% 3.82/4.01 ( ( ord_less_set_int @ A5 @ B5 )
% 3.82/4.01 | ( A5 = B5 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % subset_iff_psubset_eq
% 3.82/4.01 thf(fact_1235_subset__psubset__trans,axiom,
% 3.82/4.01 ! [A2: set_nat,B: set_nat,C4: set_nat] :
% 3.82/4.01 ( ( ord_less_eq_set_nat @ A2 @ B )
% 3.82/4.01 => ( ( ord_less_set_nat @ B @ C4 )
% 3.82/4.01 => ( ord_less_set_nat @ A2 @ C4 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % subset_psubset_trans
% 3.82/4.01 thf(fact_1236_subset__psubset__trans,axiom,
% 3.82/4.01 ! [A2: set_int,B: set_int,C4: set_int] :
% 3.82/4.01 ( ( ord_less_eq_set_int @ A2 @ B )
% 3.82/4.01 => ( ( ord_less_set_int @ B @ C4 )
% 3.82/4.01 => ( ord_less_set_int @ A2 @ C4 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % subset_psubset_trans
% 3.82/4.01 thf(fact_1237_subset__not__subset__eq,axiom,
% 3.82/4.01 ( ord_less_set_nat
% 3.82/4.01 = ( ^ [A5: set_nat,B5: set_nat] :
% 3.82/4.01 ( ( ord_less_eq_set_nat @ A5 @ B5 )
% 3.82/4.01 & ~ ( ord_less_eq_set_nat @ B5 @ A5 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % subset_not_subset_eq
% 3.82/4.01 thf(fact_1238_subset__not__subset__eq,axiom,
% 3.82/4.01 ( ord_less_set_int
% 3.82/4.01 = ( ^ [A5: set_int,B5: set_int] :
% 3.82/4.01 ( ( ord_less_eq_set_int @ A5 @ B5 )
% 3.82/4.01 & ~ ( ord_less_eq_set_int @ B5 @ A5 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % subset_not_subset_eq
% 3.82/4.01 thf(fact_1239_psubset__subset__trans,axiom,
% 3.82/4.01 ! [A2: set_nat,B: set_nat,C4: set_nat] :
% 3.82/4.01 ( ( ord_less_set_nat @ A2 @ B )
% 3.82/4.01 => ( ( ord_less_eq_set_nat @ B @ C4 )
% 3.82/4.01 => ( ord_less_set_nat @ A2 @ C4 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % psubset_subset_trans
% 3.82/4.01 thf(fact_1240_psubset__subset__trans,axiom,
% 3.82/4.01 ! [A2: set_int,B: set_int,C4: set_int] :
% 3.82/4.01 ( ( ord_less_set_int @ A2 @ B )
% 3.82/4.01 => ( ( ord_less_eq_set_int @ B @ C4 )
% 3.82/4.01 => ( ord_less_set_int @ A2 @ C4 ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % psubset_subset_trans
% 3.82/4.01 thf(fact_1241_psubset__imp__subset,axiom,
% 3.82/4.01 ! [A2: set_nat,B: set_nat] :
% 3.82/4.01 ( ( ord_less_set_nat @ A2 @ B )
% 3.82/4.01 => ( ord_less_eq_set_nat @ A2 @ B ) ) ).
% 3.82/4.01
% 3.82/4.01 % psubset_imp_subset
% 3.82/4.01 thf(fact_1242_psubset__imp__subset,axiom,
% 3.82/4.01 ! [A2: set_int,B: set_int] :
% 3.82/4.01 ( ( ord_less_set_int @ A2 @ B )
% 3.82/4.01 => ( ord_less_eq_set_int @ A2 @ B ) ) ).
% 3.82/4.01
% 3.82/4.01 % psubset_imp_subset
% 3.82/4.01 thf(fact_1243_Collect__mono__iff,axiom,
% 3.82/4.01 ! [P: real > $o,Q: real > $o] :
% 3.82/4.01 ( ( ord_less_eq_set_real @ ( collect_real @ P ) @ ( collect_real @ Q ) )
% 3.82/4.01 = ( ! [X4: real] :
% 3.82/4.01 ( ( P @ X4 )
% 3.82/4.01 => ( Q @ X4 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % Collect_mono_iff
% 3.82/4.01 thf(fact_1244_Collect__mono__iff,axiom,
% 3.82/4.01 ! [P: list_nat > $o,Q: list_nat > $o] :
% 3.82/4.01 ( ( ord_le6045566169113846134st_nat @ ( collect_list_nat @ P ) @ ( collect_list_nat @ Q ) )
% 3.82/4.01 = ( ! [X4: list_nat] :
% 3.82/4.01 ( ( P @ X4 )
% 3.82/4.01 => ( Q @ X4 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % Collect_mono_iff
% 3.82/4.01 thf(fact_1245_Collect__mono__iff,axiom,
% 3.82/4.01 ! [P: set_nat > $o,Q: set_nat > $o] :
% 3.82/4.01 ( ( ord_le6893508408891458716et_nat @ ( collect_set_nat @ P ) @ ( collect_set_nat @ Q ) )
% 3.82/4.01 = ( ! [X4: set_nat] :
% 3.82/4.01 ( ( P @ X4 )
% 3.82/4.01 => ( Q @ X4 ) ) ) ) ).
% 3.82/4.01
% 3.82/4.01 % Collect_mono_iff
% 3.82/4.01 thf(fact_1246_Collect__mono__iff,axiom,
% 3.82/4.01 ! [P: nat > $o,Q: nat > $o] :
% 3.82/4.01 ( ( ord_less_eq_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) )
% 3.82/4.02 = ( ! [X4: nat] :
% 3.82/4.02 ( ( P @ X4 )
% 3.82/4.02 => ( Q @ X4 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % Collect_mono_iff
% 3.82/4.02 thf(fact_1247_Collect__mono__iff,axiom,
% 3.82/4.02 ! [P: int > $o,Q: int > $o] :
% 3.82/4.02 ( ( ord_less_eq_set_int @ ( collect_int @ P ) @ ( collect_int @ Q ) )
% 3.82/4.02 = ( ! [X4: int] :
% 3.82/4.02 ( ( P @ X4 )
% 3.82/4.02 => ( Q @ X4 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % Collect_mono_iff
% 3.82/4.02 thf(fact_1248_set__eq__subset,axiom,
% 3.82/4.02 ( ( ^ [Y4: set_nat,Z2: set_nat] : ( Y4 = Z2 ) )
% 3.82/4.02 = ( ^ [A5: set_nat,B5: set_nat] :
% 3.82/4.02 ( ( ord_less_eq_set_nat @ A5 @ B5 )
% 3.82/4.02 & ( ord_less_eq_set_nat @ B5 @ A5 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % set_eq_subset
% 3.82/4.02 thf(fact_1249_set__eq__subset,axiom,
% 3.82/4.02 ( ( ^ [Y4: set_int,Z2: set_int] : ( Y4 = Z2 ) )
% 3.82/4.02 = ( ^ [A5: set_int,B5: set_int] :
% 3.82/4.02 ( ( ord_less_eq_set_int @ A5 @ B5 )
% 3.82/4.02 & ( ord_less_eq_set_int @ B5 @ A5 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % set_eq_subset
% 3.82/4.02 thf(fact_1250_subset__trans,axiom,
% 3.82/4.02 ! [A2: set_nat,B: set_nat,C4: set_nat] :
% 3.82/4.02 ( ( ord_less_eq_set_nat @ A2 @ B )
% 3.82/4.02 => ( ( ord_less_eq_set_nat @ B @ C4 )
% 3.82/4.02 => ( ord_less_eq_set_nat @ A2 @ C4 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % subset_trans
% 3.82/4.02 thf(fact_1251_subset__trans,axiom,
% 3.82/4.02 ! [A2: set_int,B: set_int,C4: set_int] :
% 3.82/4.02 ( ( ord_less_eq_set_int @ A2 @ B )
% 3.82/4.02 => ( ( ord_less_eq_set_int @ B @ C4 )
% 3.82/4.02 => ( ord_less_eq_set_int @ A2 @ C4 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % subset_trans
% 3.82/4.02 thf(fact_1252_Collect__mono,axiom,
% 3.82/4.02 ! [P: real > $o,Q: real > $o] :
% 3.82/4.02 ( ! [X5: real] :
% 3.82/4.02 ( ( P @ X5 )
% 3.82/4.02 => ( Q @ X5 ) )
% 3.82/4.02 => ( ord_less_eq_set_real @ ( collect_real @ P ) @ ( collect_real @ Q ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % Collect_mono
% 3.82/4.02 thf(fact_1253_Collect__mono,axiom,
% 3.82/4.02 ! [P: list_nat > $o,Q: list_nat > $o] :
% 3.82/4.02 ( ! [X5: list_nat] :
% 3.82/4.02 ( ( P @ X5 )
% 3.82/4.02 => ( Q @ X5 ) )
% 3.82/4.02 => ( ord_le6045566169113846134st_nat @ ( collect_list_nat @ P ) @ ( collect_list_nat @ Q ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % Collect_mono
% 3.82/4.02 thf(fact_1254_Collect__mono,axiom,
% 3.82/4.02 ! [P: set_nat > $o,Q: set_nat > $o] :
% 3.82/4.02 ( ! [X5: set_nat] :
% 3.82/4.02 ( ( P @ X5 )
% 3.82/4.02 => ( Q @ X5 ) )
% 3.82/4.02 => ( ord_le6893508408891458716et_nat @ ( collect_set_nat @ P ) @ ( collect_set_nat @ Q ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % Collect_mono
% 3.82/4.02 thf(fact_1255_Collect__mono,axiom,
% 3.82/4.02 ! [P: nat > $o,Q: nat > $o] :
% 3.82/4.02 ( ! [X5: nat] :
% 3.82/4.02 ( ( P @ X5 )
% 3.82/4.02 => ( Q @ X5 ) )
% 3.82/4.02 => ( ord_less_eq_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % Collect_mono
% 3.82/4.02 thf(fact_1256_Collect__mono,axiom,
% 3.82/4.02 ! [P: int > $o,Q: int > $o] :
% 3.82/4.02 ( ! [X5: int] :
% 3.82/4.02 ( ( P @ X5 )
% 3.82/4.02 => ( Q @ X5 ) )
% 3.82/4.02 => ( ord_less_eq_set_int @ ( collect_int @ P ) @ ( collect_int @ Q ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % Collect_mono
% 3.82/4.02 thf(fact_1257_subset__refl,axiom,
% 3.82/4.02 ! [A2: set_nat] : ( ord_less_eq_set_nat @ A2 @ A2 ) ).
% 3.82/4.02
% 3.82/4.02 % subset_refl
% 3.82/4.02 thf(fact_1258_subset__refl,axiom,
% 3.82/4.02 ! [A2: set_int] : ( ord_less_eq_set_int @ A2 @ A2 ) ).
% 3.82/4.02
% 3.82/4.02 % subset_refl
% 3.82/4.02 thf(fact_1259_subset__iff,axiom,
% 3.82/4.02 ( ord_le7203529160286727270d_enat
% 3.82/4.02 = ( ^ [A5: set_Extended_enat,B5: set_Extended_enat] :
% 3.82/4.02 ! [T2: extended_enat] :
% 3.82/4.02 ( ( member_Extended_enat @ T2 @ A5 )
% 3.82/4.02 => ( member_Extended_enat @ T2 @ B5 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % subset_iff
% 3.82/4.02 thf(fact_1260_subset__iff,axiom,
% 3.82/4.02 ( ord_less_eq_set_real
% 3.82/4.02 = ( ^ [A5: set_real,B5: set_real] :
% 3.82/4.02 ! [T2: real] :
% 3.82/4.02 ( ( member_real @ T2 @ A5 )
% 3.82/4.02 => ( member_real @ T2 @ B5 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % subset_iff
% 3.82/4.02 thf(fact_1261_subset__iff,axiom,
% 3.82/4.02 ( ord_le6893508408891458716et_nat
% 3.82/4.02 = ( ^ [A5: set_set_nat,B5: set_set_nat] :
% 3.82/4.02 ! [T2: set_nat] :
% 3.82/4.02 ( ( member_set_nat @ T2 @ A5 )
% 3.82/4.02 => ( member_set_nat @ T2 @ B5 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % subset_iff
% 3.82/4.02 thf(fact_1262_subset__iff,axiom,
% 3.82/4.02 ( ord_less_eq_set_nat
% 3.82/4.02 = ( ^ [A5: set_nat,B5: set_nat] :
% 3.82/4.02 ! [T2: nat] :
% 3.82/4.02 ( ( member_nat @ T2 @ A5 )
% 3.82/4.02 => ( member_nat @ T2 @ B5 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % subset_iff
% 3.82/4.02 thf(fact_1263_subset__iff,axiom,
% 3.82/4.02 ( ord_less_eq_set_int
% 3.82/4.02 = ( ^ [A5: set_int,B5: set_int] :
% 3.82/4.02 ! [T2: int] :
% 3.82/4.02 ( ( member_int @ T2 @ A5 )
% 3.82/4.02 => ( member_int @ T2 @ B5 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % subset_iff
% 3.82/4.02 thf(fact_1264_psubset__eq,axiom,
% 3.82/4.02 ( ord_less_set_nat
% 3.82/4.02 = ( ^ [A5: set_nat,B5: set_nat] :
% 3.82/4.02 ( ( ord_less_eq_set_nat @ A5 @ B5 )
% 3.82/4.02 & ( A5 != B5 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % psubset_eq
% 3.82/4.02 thf(fact_1265_psubset__eq,axiom,
% 3.82/4.02 ( ord_less_set_int
% 3.82/4.02 = ( ^ [A5: set_int,B5: set_int] :
% 3.82/4.02 ( ( ord_less_eq_set_int @ A5 @ B5 )
% 3.82/4.02 & ( A5 != B5 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % psubset_eq
% 3.82/4.02 thf(fact_1266_equalityD2,axiom,
% 3.82/4.02 ! [A2: set_nat,B: set_nat] :
% 3.82/4.02 ( ( A2 = B )
% 3.82/4.02 => ( ord_less_eq_set_nat @ B @ A2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % equalityD2
% 3.82/4.02 thf(fact_1267_equalityD2,axiom,
% 3.82/4.02 ! [A2: set_int,B: set_int] :
% 3.82/4.02 ( ( A2 = B )
% 3.82/4.02 => ( ord_less_eq_set_int @ B @ A2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % equalityD2
% 3.82/4.02 thf(fact_1268_equalityD1,axiom,
% 3.82/4.02 ! [A2: set_nat,B: set_nat] :
% 3.82/4.02 ( ( A2 = B )
% 3.82/4.02 => ( ord_less_eq_set_nat @ A2 @ B ) ) ).
% 3.82/4.02
% 3.82/4.02 % equalityD1
% 3.82/4.02 thf(fact_1269_equalityD1,axiom,
% 3.82/4.02 ! [A2: set_int,B: set_int] :
% 3.82/4.02 ( ( A2 = B )
% 3.82/4.02 => ( ord_less_eq_set_int @ A2 @ B ) ) ).
% 3.82/4.02
% 3.82/4.02 % equalityD1
% 3.82/4.02 thf(fact_1270_subset__eq,axiom,
% 3.82/4.02 ( ord_le7203529160286727270d_enat
% 3.82/4.02 = ( ^ [A5: set_Extended_enat,B5: set_Extended_enat] :
% 3.82/4.02 ! [X4: extended_enat] :
% 3.82/4.02 ( ( member_Extended_enat @ X4 @ A5 )
% 3.82/4.02 => ( member_Extended_enat @ X4 @ B5 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % subset_eq
% 3.82/4.02 thf(fact_1271_subset__eq,axiom,
% 3.82/4.02 ( ord_less_eq_set_real
% 3.82/4.02 = ( ^ [A5: set_real,B5: set_real] :
% 3.82/4.02 ! [X4: real] :
% 3.82/4.02 ( ( member_real @ X4 @ A5 )
% 3.82/4.02 => ( member_real @ X4 @ B5 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % subset_eq
% 3.82/4.02 thf(fact_1272_subset__eq,axiom,
% 3.82/4.02 ( ord_le6893508408891458716et_nat
% 3.82/4.02 = ( ^ [A5: set_set_nat,B5: set_set_nat] :
% 3.82/4.02 ! [X4: set_nat] :
% 3.82/4.02 ( ( member_set_nat @ X4 @ A5 )
% 3.82/4.02 => ( member_set_nat @ X4 @ B5 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % subset_eq
% 3.82/4.02 thf(fact_1273_subset__eq,axiom,
% 3.82/4.02 ( ord_less_eq_set_nat
% 3.82/4.02 = ( ^ [A5: set_nat,B5: set_nat] :
% 3.82/4.02 ! [X4: nat] :
% 3.82/4.02 ( ( member_nat @ X4 @ A5 )
% 3.82/4.02 => ( member_nat @ X4 @ B5 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % subset_eq
% 3.82/4.02 thf(fact_1274_subset__eq,axiom,
% 3.82/4.02 ( ord_less_eq_set_int
% 3.82/4.02 = ( ^ [A5: set_int,B5: set_int] :
% 3.82/4.02 ! [X4: int] :
% 3.82/4.02 ( ( member_int @ X4 @ A5 )
% 3.82/4.02 => ( member_int @ X4 @ B5 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % subset_eq
% 3.82/4.02 thf(fact_1275_equalityE,axiom,
% 3.82/4.02 ! [A2: set_nat,B: set_nat] :
% 3.82/4.02 ( ( A2 = B )
% 3.82/4.02 => ~ ( ( ord_less_eq_set_nat @ A2 @ B )
% 3.82/4.02 => ~ ( ord_less_eq_set_nat @ B @ A2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % equalityE
% 3.82/4.02 thf(fact_1276_equalityE,axiom,
% 3.82/4.02 ! [A2: set_int,B: set_int] :
% 3.82/4.02 ( ( A2 = B )
% 3.82/4.02 => ~ ( ( ord_less_eq_set_int @ A2 @ B )
% 3.82/4.02 => ~ ( ord_less_eq_set_int @ B @ A2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % equalityE
% 3.82/4.02 thf(fact_1277_psubsetE,axiom,
% 3.82/4.02 ! [A2: set_nat,B: set_nat] :
% 3.82/4.02 ( ( ord_less_set_nat @ A2 @ B )
% 3.82/4.02 => ~ ( ( ord_less_eq_set_nat @ A2 @ B )
% 3.82/4.02 => ( ord_less_eq_set_nat @ B @ A2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % psubsetE
% 3.82/4.02 thf(fact_1278_psubsetE,axiom,
% 3.82/4.02 ! [A2: set_int,B: set_int] :
% 3.82/4.02 ( ( ord_less_set_int @ A2 @ B )
% 3.82/4.02 => ~ ( ( ord_less_eq_set_int @ A2 @ B )
% 3.82/4.02 => ( ord_less_eq_set_int @ B @ A2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % psubsetE
% 3.82/4.02 thf(fact_1279_subsetD,axiom,
% 3.82/4.02 ! [A2: set_Extended_enat,B: set_Extended_enat,C: extended_enat] :
% 3.82/4.02 ( ( ord_le7203529160286727270d_enat @ A2 @ B )
% 3.82/4.02 => ( ( member_Extended_enat @ C @ A2 )
% 3.82/4.02 => ( member_Extended_enat @ C @ B ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % subsetD
% 3.82/4.02 thf(fact_1280_subsetD,axiom,
% 3.82/4.02 ! [A2: set_real,B: set_real,C: real] :
% 3.82/4.02 ( ( ord_less_eq_set_real @ A2 @ B )
% 3.82/4.02 => ( ( member_real @ C @ A2 )
% 3.82/4.02 => ( member_real @ C @ B ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % subsetD
% 3.82/4.02 thf(fact_1281_subsetD,axiom,
% 3.82/4.02 ! [A2: set_set_nat,B: set_set_nat,C: set_nat] :
% 3.82/4.02 ( ( ord_le6893508408891458716et_nat @ A2 @ B )
% 3.82/4.02 => ( ( member_set_nat @ C @ A2 )
% 3.82/4.02 => ( member_set_nat @ C @ B ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % subsetD
% 3.82/4.02 thf(fact_1282_subsetD,axiom,
% 3.82/4.02 ! [A2: set_nat,B: set_nat,C: nat] :
% 3.82/4.02 ( ( ord_less_eq_set_nat @ A2 @ B )
% 3.82/4.02 => ( ( member_nat @ C @ A2 )
% 3.82/4.02 => ( member_nat @ C @ B ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % subsetD
% 3.82/4.02 thf(fact_1283_subsetD,axiom,
% 3.82/4.02 ! [A2: set_int,B: set_int,C: int] :
% 3.82/4.02 ( ( ord_less_eq_set_int @ A2 @ B )
% 3.82/4.02 => ( ( member_int @ C @ A2 )
% 3.82/4.02 => ( member_int @ C @ B ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % subsetD
% 3.82/4.02 thf(fact_1284_in__mono,axiom,
% 3.82/4.02 ! [A2: set_Extended_enat,B: set_Extended_enat,X: extended_enat] :
% 3.82/4.02 ( ( ord_le7203529160286727270d_enat @ A2 @ B )
% 3.82/4.02 => ( ( member_Extended_enat @ X @ A2 )
% 3.82/4.02 => ( member_Extended_enat @ X @ B ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % in_mono
% 3.82/4.02 thf(fact_1285_in__mono,axiom,
% 3.82/4.02 ! [A2: set_real,B: set_real,X: real] :
% 3.82/4.02 ( ( ord_less_eq_set_real @ A2 @ B )
% 3.82/4.02 => ( ( member_real @ X @ A2 )
% 3.82/4.02 => ( member_real @ X @ B ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % in_mono
% 3.82/4.02 thf(fact_1286_in__mono,axiom,
% 3.82/4.02 ! [A2: set_set_nat,B: set_set_nat,X: set_nat] :
% 3.82/4.02 ( ( ord_le6893508408891458716et_nat @ A2 @ B )
% 3.82/4.02 => ( ( member_set_nat @ X @ A2 )
% 3.82/4.02 => ( member_set_nat @ X @ B ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % in_mono
% 3.82/4.02 thf(fact_1287_in__mono,axiom,
% 3.82/4.02 ! [A2: set_nat,B: set_nat,X: nat] :
% 3.82/4.02 ( ( ord_less_eq_set_nat @ A2 @ B )
% 3.82/4.02 => ( ( member_nat @ X @ A2 )
% 3.82/4.02 => ( member_nat @ X @ B ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % in_mono
% 3.82/4.02 thf(fact_1288_in__mono,axiom,
% 3.82/4.02 ! [A2: set_int,B: set_int,X: int] :
% 3.82/4.02 ( ( ord_less_eq_set_int @ A2 @ B )
% 3.82/4.02 => ( ( member_int @ X @ A2 )
% 3.82/4.02 => ( member_int @ X @ B ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % in_mono
% 3.82/4.02 thf(fact_1289_finite__has__maximal,axiom,
% 3.82/4.02 ! [A2: set_Extended_enat] :
% 3.82/4.02 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.02 => ( ( A2 != bot_bo7653980558646680370d_enat )
% 3.82/4.02 => ? [X5: extended_enat] :
% 3.82/4.02 ( ( member_Extended_enat @ X5 @ A2 )
% 3.82/4.02 & ! [Xa: extended_enat] :
% 3.82/4.02 ( ( member_Extended_enat @ Xa @ A2 )
% 3.82/4.02 => ( ( ord_le2932123472753598470d_enat @ X5 @ Xa )
% 3.82/4.02 => ( X5 = Xa ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % finite_has_maximal
% 3.82/4.02 thf(fact_1290_finite__has__maximal,axiom,
% 3.82/4.02 ! [A2: set_real] :
% 3.82/4.02 ( ( finite_finite_real @ A2 )
% 3.82/4.02 => ( ( A2 != bot_bot_set_real )
% 3.82/4.02 => ? [X5: real] :
% 3.82/4.02 ( ( member_real @ X5 @ A2 )
% 3.82/4.02 & ! [Xa: real] :
% 3.82/4.02 ( ( member_real @ Xa @ A2 )
% 3.82/4.02 => ( ( ord_less_eq_real @ X5 @ Xa )
% 3.82/4.02 => ( X5 = Xa ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % finite_has_maximal
% 3.82/4.02 thf(fact_1291_finite__has__maximal,axiom,
% 3.82/4.02 ! [A2: set_set_nat] :
% 3.82/4.02 ( ( finite1152437895449049373et_nat @ A2 )
% 3.82/4.02 => ( ( A2 != bot_bot_set_set_nat )
% 3.82/4.02 => ? [X5: set_nat] :
% 3.82/4.02 ( ( member_set_nat @ X5 @ A2 )
% 3.82/4.02 & ! [Xa: set_nat] :
% 3.82/4.02 ( ( member_set_nat @ Xa @ A2 )
% 3.82/4.02 => ( ( ord_less_eq_set_nat @ X5 @ Xa )
% 3.82/4.02 => ( X5 = Xa ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % finite_has_maximal
% 3.82/4.02 thf(fact_1292_finite__has__maximal,axiom,
% 3.82/4.02 ! [A2: set_set_int] :
% 3.82/4.02 ( ( finite6197958912794628473et_int @ A2 )
% 3.82/4.02 => ( ( A2 != bot_bot_set_set_int )
% 3.82/4.02 => ? [X5: set_int] :
% 3.82/4.02 ( ( member_set_int @ X5 @ A2 )
% 3.82/4.02 & ! [Xa: set_int] :
% 3.82/4.02 ( ( member_set_int @ Xa @ A2 )
% 3.82/4.02 => ( ( ord_less_eq_set_int @ X5 @ Xa )
% 3.82/4.02 => ( X5 = Xa ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % finite_has_maximal
% 3.82/4.02 thf(fact_1293_finite__has__maximal,axiom,
% 3.82/4.02 ! [A2: set_nat] :
% 3.82/4.02 ( ( finite_finite_nat @ A2 )
% 3.82/4.02 => ( ( A2 != bot_bot_set_nat )
% 3.82/4.02 => ? [X5: nat] :
% 3.82/4.02 ( ( member_nat @ X5 @ A2 )
% 3.82/4.02 & ! [Xa: nat] :
% 3.82/4.02 ( ( member_nat @ Xa @ A2 )
% 3.82/4.02 => ( ( ord_less_eq_nat @ X5 @ Xa )
% 3.82/4.02 => ( X5 = Xa ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % finite_has_maximal
% 3.82/4.02 thf(fact_1294_finite__has__maximal,axiom,
% 3.82/4.02 ! [A2: set_int] :
% 3.82/4.02 ( ( finite_finite_int @ A2 )
% 3.82/4.02 => ( ( A2 != bot_bot_set_int )
% 3.82/4.02 => ? [X5: int] :
% 3.82/4.02 ( ( member_int @ X5 @ A2 )
% 3.82/4.02 & ! [Xa: int] :
% 3.82/4.02 ( ( member_int @ Xa @ A2 )
% 3.82/4.02 => ( ( ord_less_eq_int @ X5 @ Xa )
% 3.82/4.02 => ( X5 = Xa ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % finite_has_maximal
% 3.82/4.02 thf(fact_1295_finite__has__minimal,axiom,
% 3.82/4.02 ! [A2: set_Extended_enat] :
% 3.82/4.02 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.02 => ( ( A2 != bot_bo7653980558646680370d_enat )
% 3.82/4.02 => ? [X5: extended_enat] :
% 3.82/4.02 ( ( member_Extended_enat @ X5 @ A2 )
% 3.82/4.02 & ! [Xa: extended_enat] :
% 3.82/4.02 ( ( member_Extended_enat @ Xa @ A2 )
% 3.82/4.02 => ( ( ord_le2932123472753598470d_enat @ Xa @ X5 )
% 3.82/4.02 => ( X5 = Xa ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % finite_has_minimal
% 3.82/4.02 thf(fact_1296_finite__has__minimal,axiom,
% 3.82/4.02 ! [A2: set_real] :
% 3.82/4.02 ( ( finite_finite_real @ A2 )
% 3.82/4.02 => ( ( A2 != bot_bot_set_real )
% 3.82/4.02 => ? [X5: real] :
% 3.82/4.02 ( ( member_real @ X5 @ A2 )
% 3.82/4.02 & ! [Xa: real] :
% 3.82/4.02 ( ( member_real @ Xa @ A2 )
% 3.82/4.02 => ( ( ord_less_eq_real @ Xa @ X5 )
% 3.82/4.02 => ( X5 = Xa ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % finite_has_minimal
% 3.82/4.02 thf(fact_1297_finite__has__minimal,axiom,
% 3.82/4.02 ! [A2: set_set_nat] :
% 3.82/4.02 ( ( finite1152437895449049373et_nat @ A2 )
% 3.82/4.02 => ( ( A2 != bot_bot_set_set_nat )
% 3.82/4.02 => ? [X5: set_nat] :
% 3.82/4.02 ( ( member_set_nat @ X5 @ A2 )
% 3.82/4.02 & ! [Xa: set_nat] :
% 3.82/4.02 ( ( member_set_nat @ Xa @ A2 )
% 3.82/4.02 => ( ( ord_less_eq_set_nat @ Xa @ X5 )
% 3.82/4.02 => ( X5 = Xa ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % finite_has_minimal
% 3.82/4.02 thf(fact_1298_finite__has__minimal,axiom,
% 3.82/4.02 ! [A2: set_set_int] :
% 3.82/4.02 ( ( finite6197958912794628473et_int @ A2 )
% 3.82/4.02 => ( ( A2 != bot_bot_set_set_int )
% 3.82/4.02 => ? [X5: set_int] :
% 3.82/4.02 ( ( member_set_int @ X5 @ A2 )
% 3.82/4.02 & ! [Xa: set_int] :
% 3.82/4.02 ( ( member_set_int @ Xa @ A2 )
% 3.82/4.02 => ( ( ord_less_eq_set_int @ Xa @ X5 )
% 3.82/4.02 => ( X5 = Xa ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % finite_has_minimal
% 3.82/4.02 thf(fact_1299_finite__has__minimal,axiom,
% 3.82/4.02 ! [A2: set_nat] :
% 3.82/4.02 ( ( finite_finite_nat @ A2 )
% 3.82/4.02 => ( ( A2 != bot_bot_set_nat )
% 3.82/4.02 => ? [X5: nat] :
% 3.82/4.02 ( ( member_nat @ X5 @ A2 )
% 3.82/4.02 & ! [Xa: nat] :
% 3.82/4.02 ( ( member_nat @ Xa @ A2 )
% 3.82/4.02 => ( ( ord_less_eq_nat @ Xa @ X5 )
% 3.82/4.02 => ( X5 = Xa ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % finite_has_minimal
% 3.82/4.02 thf(fact_1300_finite__has__minimal,axiom,
% 3.82/4.02 ! [A2: set_int] :
% 3.82/4.02 ( ( finite_finite_int @ A2 )
% 3.82/4.02 => ( ( A2 != bot_bot_set_int )
% 3.82/4.02 => ? [X5: int] :
% 3.82/4.02 ( ( member_int @ X5 @ A2 )
% 3.82/4.02 & ! [Xa: int] :
% 3.82/4.02 ( ( member_int @ Xa @ A2 )
% 3.82/4.02 => ( ( ord_less_eq_int @ Xa @ X5 )
% 3.82/4.02 => ( X5 = Xa ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % finite_has_minimal
% 3.82/4.02 thf(fact_1301_finite__nat__set__iff__bounded__le,axiom,
% 3.82/4.02 ( finite_finite_nat
% 3.82/4.02 = ( ^ [N5: set_nat] :
% 3.82/4.02 ? [M: nat] :
% 3.82/4.02 ! [X4: nat] :
% 3.82/4.02 ( ( member_nat @ X4 @ N5 )
% 3.82/4.02 => ( ord_less_eq_nat @ X4 @ M ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % finite_nat_set_iff_bounded_le
% 3.82/4.02 thf(fact_1302_infinite__nat__iff__unbounded__le,axiom,
% 3.82/4.02 ! [S2: set_nat] :
% 3.82/4.02 ( ( ~ ( finite_finite_nat @ S2 ) )
% 3.82/4.02 = ( ! [M: nat] :
% 3.82/4.02 ? [N: nat] :
% 3.82/4.02 ( ( ord_less_eq_nat @ M @ N )
% 3.82/4.02 & ( member_nat @ N @ S2 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % infinite_nat_iff_unbounded_le
% 3.82/4.02 thf(fact_1303_finite__nat__set__iff__bounded,axiom,
% 3.82/4.02 ( finite_finite_nat
% 3.82/4.02 = ( ^ [N5: set_nat] :
% 3.82/4.02 ? [M: nat] :
% 3.82/4.02 ! [X4: nat] :
% 3.82/4.02 ( ( member_nat @ X4 @ N5 )
% 3.82/4.02 => ( ord_less_nat @ X4 @ M ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % finite_nat_set_iff_bounded
% 3.82/4.02 thf(fact_1304_infinite__nat__iff__unbounded,axiom,
% 3.82/4.02 ! [S2: set_nat] :
% 3.82/4.02 ( ( ~ ( finite_finite_nat @ S2 ) )
% 3.82/4.02 = ( ! [M: nat] :
% 3.82/4.02 ? [N: nat] :
% 3.82/4.02 ( ( ord_less_nat @ M @ N )
% 3.82/4.02 & ( member_nat @ N @ S2 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % infinite_nat_iff_unbounded
% 3.82/4.02 thf(fact_1305_bounded__nat__set__is__finite,axiom,
% 3.82/4.02 ! [N6: set_nat,N2: nat] :
% 3.82/4.02 ( ! [X5: nat] :
% 3.82/4.02 ( ( member_nat @ X5 @ N6 )
% 3.82/4.02 => ( ord_less_nat @ X5 @ N2 ) )
% 3.82/4.02 => ( finite_finite_nat @ N6 ) ) ).
% 3.82/4.02
% 3.82/4.02 % bounded_nat_set_is_finite
% 3.82/4.02 thf(fact_1306_unbounded__k__infinite,axiom,
% 3.82/4.02 ! [K: nat,S2: set_nat] :
% 3.82/4.02 ( ! [M3: nat] :
% 3.82/4.02 ( ( ord_less_nat @ K @ M3 )
% 3.82/4.02 => ? [N7: nat] :
% 3.82/4.02 ( ( ord_less_nat @ M3 @ N7 )
% 3.82/4.02 & ( member_nat @ N7 @ S2 ) ) )
% 3.82/4.02 => ~ ( finite_finite_nat @ S2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % unbounded_k_infinite
% 3.82/4.02 thf(fact_1307_finite__psubset__induct,axiom,
% 3.82/4.02 ! [A2: set_nat,P: set_nat > $o] :
% 3.82/4.02 ( ( finite_finite_nat @ A2 )
% 3.82/4.02 => ( ! [A6: set_nat] :
% 3.82/4.02 ( ( finite_finite_nat @ A6 )
% 3.82/4.02 => ( ! [B6: set_nat] :
% 3.82/4.02 ( ( ord_less_set_nat @ B6 @ A6 )
% 3.82/4.02 => ( P @ B6 ) )
% 3.82/4.02 => ( P @ A6 ) ) )
% 3.82/4.02 => ( P @ A2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % finite_psubset_induct
% 3.82/4.02 thf(fact_1308_finite__psubset__induct,axiom,
% 3.82/4.02 ! [A2: set_complex,P: set_complex > $o] :
% 3.82/4.02 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.02 => ( ! [A6: set_complex] :
% 3.82/4.02 ( ( finite3207457112153483333omplex @ A6 )
% 3.82/4.02 => ( ! [B6: set_complex] :
% 3.82/4.02 ( ( ord_less_set_complex @ B6 @ A6 )
% 3.82/4.02 => ( P @ B6 ) )
% 3.82/4.02 => ( P @ A6 ) ) )
% 3.82/4.02 => ( P @ A2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % finite_psubset_induct
% 3.82/4.02 thf(fact_1309_finite__psubset__induct,axiom,
% 3.82/4.02 ! [A2: set_int,P: set_int > $o] :
% 3.82/4.02 ( ( finite_finite_int @ A2 )
% 3.82/4.02 => ( ! [A6: set_int] :
% 3.82/4.02 ( ( finite_finite_int @ A6 )
% 3.82/4.02 => ( ! [B6: set_int] :
% 3.82/4.02 ( ( ord_less_set_int @ B6 @ A6 )
% 3.82/4.02 => ( P @ B6 ) )
% 3.82/4.02 => ( P @ A6 ) ) )
% 3.82/4.02 => ( P @ A2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % finite_psubset_induct
% 3.82/4.02 thf(fact_1310_finite__psubset__induct,axiom,
% 3.82/4.02 ! [A2: set_Extended_enat,P: set_Extended_enat > $o] :
% 3.82/4.02 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.02 => ( ! [A6: set_Extended_enat] :
% 3.82/4.02 ( ( finite4001608067531595151d_enat @ A6 )
% 3.82/4.02 => ( ! [B6: set_Extended_enat] :
% 3.82/4.02 ( ( ord_le2529575680413868914d_enat @ B6 @ A6 )
% 3.82/4.02 => ( P @ B6 ) )
% 3.82/4.02 => ( P @ A6 ) ) )
% 3.82/4.02 => ( P @ A2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % finite_psubset_induct
% 3.82/4.02 thf(fact_1311_arg__min__if__finite_I2_J,axiom,
% 3.82/4.02 ! [S2: set_complex,F: complex > nat] :
% 3.82/4.02 ( ( finite3207457112153483333omplex @ S2 )
% 3.82/4.02 => ( ( S2 != bot_bot_set_complex )
% 3.82/4.02 => ~ ? [X2: complex] :
% 3.82/4.02 ( ( member_complex @ X2 @ S2 )
% 3.82/4.02 & ( ord_less_nat @ ( F @ X2 ) @ ( F @ ( lattic5364784637807008409ex_nat @ F @ S2 ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % arg_min_if_finite(2)
% 3.82/4.02 thf(fact_1312_arg__min__if__finite_I2_J,axiom,
% 3.82/4.02 ! [S2: set_Extended_enat,F: extended_enat > nat] :
% 3.82/4.02 ( ( finite4001608067531595151d_enat @ S2 )
% 3.82/4.02 => ( ( S2 != bot_bo7653980558646680370d_enat )
% 3.82/4.02 => ~ ? [X2: extended_enat] :
% 3.82/4.02 ( ( member_Extended_enat @ X2 @ S2 )
% 3.82/4.02 & ( ord_less_nat @ ( F @ X2 ) @ ( F @ ( lattic3845382081240766429at_nat @ F @ S2 ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % arg_min_if_finite(2)
% 3.82/4.02 thf(fact_1313_arg__min__if__finite_I2_J,axiom,
% 3.82/4.02 ! [S2: set_real,F: real > nat] :
% 3.82/4.02 ( ( finite_finite_real @ S2 )
% 3.82/4.02 => ( ( S2 != bot_bot_set_real )
% 3.82/4.02 => ~ ? [X2: real] :
% 3.82/4.02 ( ( member_real @ X2 @ S2 )
% 3.82/4.02 & ( ord_less_nat @ ( F @ X2 ) @ ( F @ ( lattic5055836439445974935al_nat @ F @ S2 ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % arg_min_if_finite(2)
% 3.82/4.02 thf(fact_1314_arg__min__if__finite_I2_J,axiom,
% 3.82/4.02 ! [S2: set_nat,F: nat > nat] :
% 3.82/4.02 ( ( finite_finite_nat @ S2 )
% 3.82/4.02 => ( ( S2 != bot_bot_set_nat )
% 3.82/4.02 => ~ ? [X2: nat] :
% 3.82/4.02 ( ( member_nat @ X2 @ S2 )
% 3.82/4.02 & ( ord_less_nat @ ( F @ X2 ) @ ( F @ ( lattic7446932960582359483at_nat @ F @ S2 ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % arg_min_if_finite(2)
% 3.82/4.02 thf(fact_1315_arg__min__if__finite_I2_J,axiom,
% 3.82/4.02 ! [S2: set_int,F: int > nat] :
% 3.82/4.02 ( ( finite_finite_int @ S2 )
% 3.82/4.02 => ( ( S2 != bot_bot_set_int )
% 3.82/4.02 => ~ ? [X2: int] :
% 3.82/4.02 ( ( member_int @ X2 @ S2 )
% 3.82/4.02 & ( ord_less_nat @ ( F @ X2 ) @ ( F @ ( lattic8446286672483414039nt_nat @ F @ S2 ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % arg_min_if_finite(2)
% 3.82/4.02 thf(fact_1316_arg__min__if__finite_I2_J,axiom,
% 3.82/4.02 ! [S2: set_complex,F: complex > extended_enat] :
% 3.82/4.02 ( ( finite3207457112153483333omplex @ S2 )
% 3.82/4.02 => ( ( S2 != bot_bot_set_complex )
% 3.82/4.02 => ~ ? [X2: complex] :
% 3.82/4.02 ( ( member_complex @ X2 @ S2 )
% 3.82/4.02 & ( ord_le72135733267957522d_enat @ ( F @ X2 ) @ ( F @ ( lattic7796887085614042845d_enat @ F @ S2 ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % arg_min_if_finite(2)
% 3.82/4.02 thf(fact_1317_arg__min__if__finite_I2_J,axiom,
% 3.82/4.02 ! [S2: set_Extended_enat,F: extended_enat > extended_enat] :
% 3.82/4.02 ( ( finite4001608067531595151d_enat @ S2 )
% 3.82/4.02 => ( ( S2 != bot_bo7653980558646680370d_enat )
% 3.82/4.02 => ~ ? [X2: extended_enat] :
% 3.82/4.02 ( ( member_Extended_enat @ X2 @ S2 )
% 3.82/4.02 & ( ord_le72135733267957522d_enat @ ( F @ X2 ) @ ( F @ ( lattic1996716550891908761d_enat @ F @ S2 ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % arg_min_if_finite(2)
% 3.82/4.02 thf(fact_1318_arg__min__if__finite_I2_J,axiom,
% 3.82/4.02 ! [S2: set_real,F: real > extended_enat] :
% 3.82/4.02 ( ( finite_finite_real @ S2 )
% 3.82/4.02 => ( ( S2 != bot_bot_set_real )
% 3.82/4.02 => ~ ? [X2: real] :
% 3.82/4.02 ( ( member_real @ X2 @ S2 )
% 3.82/4.02 & ( ord_le72135733267957522d_enat @ ( F @ X2 ) @ ( F @ ( lattic9066027731366277983d_enat @ F @ S2 ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % arg_min_if_finite(2)
% 3.82/4.02 thf(fact_1319_arg__min__if__finite_I2_J,axiom,
% 3.82/4.02 ! [S2: set_nat,F: nat > extended_enat] :
% 3.82/4.02 ( ( finite_finite_nat @ S2 )
% 3.82/4.02 => ( ( S2 != bot_bot_set_nat )
% 3.82/4.02 => ~ ? [X2: nat] :
% 3.82/4.02 ( ( member_nat @ X2 @ S2 )
% 3.82/4.02 & ( ord_le72135733267957522d_enat @ ( F @ X2 ) @ ( F @ ( lattic8926238025367240251d_enat @ F @ S2 ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % arg_min_if_finite(2)
% 3.82/4.02 thf(fact_1320_arg__min__if__finite_I2_J,axiom,
% 3.82/4.02 ! [S2: set_int,F: int > extended_enat] :
% 3.82/4.02 ( ( finite_finite_int @ S2 )
% 3.82/4.02 => ( ( S2 != bot_bot_set_int )
% 3.82/4.02 => ~ ? [X2: int] :
% 3.82/4.02 ( ( member_int @ X2 @ S2 )
% 3.82/4.02 & ( ord_le72135733267957522d_enat @ ( F @ X2 ) @ ( F @ ( lattic6042659972569420511d_enat @ F @ S2 ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % arg_min_if_finite(2)
% 3.82/4.02 thf(fact_1321_bot__set__def,axiom,
% 3.82/4.02 ( bot_bot_set_list_nat
% 3.82/4.02 = ( collect_list_nat @ bot_bot_list_nat_o ) ) ).
% 3.82/4.02
% 3.82/4.02 % bot_set_def
% 3.82/4.02 thf(fact_1322_bot__set__def,axiom,
% 3.82/4.02 ( bot_bot_set_set_nat
% 3.82/4.02 = ( collect_set_nat @ bot_bot_set_nat_o ) ) ).
% 3.82/4.02
% 3.82/4.02 % bot_set_def
% 3.82/4.02 thf(fact_1323_bot__set__def,axiom,
% 3.82/4.02 ( bot_bo7653980558646680370d_enat
% 3.82/4.02 = ( collec4429806609662206161d_enat @ bot_bo1954855461789132331enat_o ) ) ).
% 3.82/4.02
% 3.82/4.02 % bot_set_def
% 3.82/4.02 thf(fact_1324_bot__set__def,axiom,
% 3.82/4.02 ( bot_bot_set_real
% 3.82/4.02 = ( collect_real @ bot_bot_real_o ) ) ).
% 3.82/4.02
% 3.82/4.02 % bot_set_def
% 3.82/4.02 thf(fact_1325_bot__set__def,axiom,
% 3.82/4.02 ( bot_bot_set_nat
% 3.82/4.02 = ( collect_nat @ bot_bot_nat_o ) ) ).
% 3.82/4.02
% 3.82/4.02 % bot_set_def
% 3.82/4.02 thf(fact_1326_bot__set__def,axiom,
% 3.82/4.02 ( bot_bot_set_int
% 3.82/4.02 = ( collect_int @ bot_bot_int_o ) ) ).
% 3.82/4.02
% 3.82/4.02 % bot_set_def
% 3.82/4.02 thf(fact_1327_bot__nat__def,axiom,
% 3.82/4.02 bot_bot_nat = zero_zero_nat ).
% 3.82/4.02
% 3.82/4.02 % bot_nat_def
% 3.82/4.02 thf(fact_1328_finite__maxlen,axiom,
% 3.82/4.02 ! [M7: set_list_VEBT_VEBT] :
% 3.82/4.02 ( ( finite3004134309566078307T_VEBT @ M7 )
% 3.82/4.02 => ? [N3: nat] :
% 3.82/4.02 ! [X2: list_VEBT_VEBT] :
% 3.82/4.02 ( ( member2936631157270082147T_VEBT @ X2 @ M7 )
% 3.82/4.02 => ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ X2 ) @ N3 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % finite_maxlen
% 3.82/4.02 thf(fact_1329_finite__maxlen,axiom,
% 3.82/4.02 ! [M7: set_list_int] :
% 3.82/4.02 ( ( finite3922522038869484883st_int @ M7 )
% 3.82/4.02 => ? [N3: nat] :
% 3.82/4.02 ! [X2: list_int] :
% 3.82/4.02 ( ( member_list_int @ X2 @ M7 )
% 3.82/4.02 => ( ord_less_nat @ ( size_size_list_int @ X2 ) @ N3 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % finite_maxlen
% 3.82/4.02 thf(fact_1330_finite__maxlen,axiom,
% 3.82/4.02 ! [M7: set_list_nat] :
% 3.82/4.02 ( ( finite8100373058378681591st_nat @ M7 )
% 3.82/4.02 => ? [N3: nat] :
% 3.82/4.02 ! [X2: list_nat] :
% 3.82/4.02 ( ( member_list_nat @ X2 @ M7 )
% 3.82/4.02 => ( ord_less_nat @ ( size_size_list_nat @ X2 ) @ N3 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % finite_maxlen
% 3.82/4.02 thf(fact_1331_bounded__Max__nat,axiom,
% 3.82/4.02 ! [P: nat > $o,X: nat,M7: nat] :
% 3.82/4.02 ( ( P @ X )
% 3.82/4.02 => ( ! [X5: nat] :
% 3.82/4.02 ( ( P @ X5 )
% 3.82/4.02 => ( ord_less_eq_nat @ X5 @ M7 ) )
% 3.82/4.02 => ~ ! [M3: nat] :
% 3.82/4.02 ( ( P @ M3 )
% 3.82/4.02 => ~ ! [X2: nat] :
% 3.82/4.02 ( ( P @ X2 )
% 3.82/4.02 => ( ord_less_eq_nat @ X2 @ M3 ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % bounded_Max_nat
% 3.82/4.02 thf(fact_1332_finite__has__maximal2,axiom,
% 3.82/4.02 ! [A2: set_Extended_enat,A: extended_enat] :
% 3.82/4.02 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.02 => ( ( member_Extended_enat @ A @ A2 )
% 3.82/4.02 => ? [X5: extended_enat] :
% 3.82/4.02 ( ( member_Extended_enat @ X5 @ A2 )
% 3.82/4.02 & ( ord_le2932123472753598470d_enat @ A @ X5 )
% 3.82/4.02 & ! [Xa: extended_enat] :
% 3.82/4.02 ( ( member_Extended_enat @ Xa @ A2 )
% 3.82/4.02 => ( ( ord_le2932123472753598470d_enat @ X5 @ Xa )
% 3.82/4.02 => ( X5 = Xa ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % finite_has_maximal2
% 3.82/4.02 thf(fact_1333_finite__has__maximal2,axiom,
% 3.82/4.02 ! [A2: set_real,A: real] :
% 3.82/4.02 ( ( finite_finite_real @ A2 )
% 3.82/4.02 => ( ( member_real @ A @ A2 )
% 3.82/4.02 => ? [X5: real] :
% 3.82/4.02 ( ( member_real @ X5 @ A2 )
% 3.82/4.02 & ( ord_less_eq_real @ A @ X5 )
% 3.82/4.02 & ! [Xa: real] :
% 3.82/4.02 ( ( member_real @ Xa @ A2 )
% 3.82/4.02 => ( ( ord_less_eq_real @ X5 @ Xa )
% 3.82/4.02 => ( X5 = Xa ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % finite_has_maximal2
% 3.82/4.02 thf(fact_1334_finite__has__maximal2,axiom,
% 3.82/4.02 ! [A2: set_set_nat,A: set_nat] :
% 3.82/4.02 ( ( finite1152437895449049373et_nat @ A2 )
% 3.82/4.02 => ( ( member_set_nat @ A @ A2 )
% 3.82/4.02 => ? [X5: set_nat] :
% 3.82/4.02 ( ( member_set_nat @ X5 @ A2 )
% 3.82/4.02 & ( ord_less_eq_set_nat @ A @ X5 )
% 3.82/4.02 & ! [Xa: set_nat] :
% 3.82/4.02 ( ( member_set_nat @ Xa @ A2 )
% 3.82/4.02 => ( ( ord_less_eq_set_nat @ X5 @ Xa )
% 3.82/4.02 => ( X5 = Xa ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % finite_has_maximal2
% 3.82/4.02 thf(fact_1335_finite__has__maximal2,axiom,
% 3.82/4.02 ! [A2: set_set_int,A: set_int] :
% 3.82/4.02 ( ( finite6197958912794628473et_int @ A2 )
% 3.82/4.02 => ( ( member_set_int @ A @ A2 )
% 3.82/4.02 => ? [X5: set_int] :
% 3.82/4.02 ( ( member_set_int @ X5 @ A2 )
% 3.82/4.02 & ( ord_less_eq_set_int @ A @ X5 )
% 3.82/4.02 & ! [Xa: set_int] :
% 3.82/4.02 ( ( member_set_int @ Xa @ A2 )
% 3.82/4.02 => ( ( ord_less_eq_set_int @ X5 @ Xa )
% 3.82/4.02 => ( X5 = Xa ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % finite_has_maximal2
% 3.82/4.02 thf(fact_1336_finite__has__maximal2,axiom,
% 3.82/4.02 ! [A2: set_nat,A: nat] :
% 3.82/4.02 ( ( finite_finite_nat @ A2 )
% 3.82/4.02 => ( ( member_nat @ A @ A2 )
% 3.82/4.02 => ? [X5: nat] :
% 3.82/4.02 ( ( member_nat @ X5 @ A2 )
% 3.82/4.02 & ( ord_less_eq_nat @ A @ X5 )
% 3.82/4.02 & ! [Xa: nat] :
% 3.82/4.02 ( ( member_nat @ Xa @ A2 )
% 3.82/4.02 => ( ( ord_less_eq_nat @ X5 @ Xa )
% 3.82/4.02 => ( X5 = Xa ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % finite_has_maximal2
% 3.82/4.02 thf(fact_1337_finite__has__maximal2,axiom,
% 3.82/4.02 ! [A2: set_int,A: int] :
% 3.82/4.02 ( ( finite_finite_int @ A2 )
% 3.82/4.02 => ( ( member_int @ A @ A2 )
% 3.82/4.02 => ? [X5: int] :
% 3.82/4.02 ( ( member_int @ X5 @ A2 )
% 3.82/4.02 & ( ord_less_eq_int @ A @ X5 )
% 3.82/4.02 & ! [Xa: int] :
% 3.82/4.02 ( ( member_int @ Xa @ A2 )
% 3.82/4.02 => ( ( ord_less_eq_int @ X5 @ Xa )
% 3.82/4.02 => ( X5 = Xa ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % finite_has_maximal2
% 3.82/4.02 thf(fact_1338_finite__has__minimal2,axiom,
% 3.82/4.02 ! [A2: set_Extended_enat,A: extended_enat] :
% 3.82/4.02 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.02 => ( ( member_Extended_enat @ A @ A2 )
% 3.82/4.02 => ? [X5: extended_enat] :
% 3.82/4.02 ( ( member_Extended_enat @ X5 @ A2 )
% 3.82/4.02 & ( ord_le2932123472753598470d_enat @ X5 @ A )
% 3.82/4.02 & ! [Xa: extended_enat] :
% 3.82/4.02 ( ( member_Extended_enat @ Xa @ A2 )
% 3.82/4.02 => ( ( ord_le2932123472753598470d_enat @ Xa @ X5 )
% 3.82/4.02 => ( X5 = Xa ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % finite_has_minimal2
% 3.82/4.02 thf(fact_1339_finite__has__minimal2,axiom,
% 3.82/4.02 ! [A2: set_real,A: real] :
% 3.82/4.02 ( ( finite_finite_real @ A2 )
% 3.82/4.02 => ( ( member_real @ A @ A2 )
% 3.82/4.02 => ? [X5: real] :
% 3.82/4.02 ( ( member_real @ X5 @ A2 )
% 3.82/4.02 & ( ord_less_eq_real @ X5 @ A )
% 3.82/4.02 & ! [Xa: real] :
% 3.82/4.02 ( ( member_real @ Xa @ A2 )
% 3.82/4.02 => ( ( ord_less_eq_real @ Xa @ X5 )
% 3.82/4.02 => ( X5 = Xa ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % finite_has_minimal2
% 3.82/4.02 thf(fact_1340_finite__has__minimal2,axiom,
% 3.82/4.02 ! [A2: set_set_nat,A: set_nat] :
% 3.82/4.02 ( ( finite1152437895449049373et_nat @ A2 )
% 3.82/4.02 => ( ( member_set_nat @ A @ A2 )
% 3.82/4.02 => ? [X5: set_nat] :
% 3.82/4.02 ( ( member_set_nat @ X5 @ A2 )
% 3.82/4.02 & ( ord_less_eq_set_nat @ X5 @ A )
% 3.82/4.02 & ! [Xa: set_nat] :
% 3.82/4.02 ( ( member_set_nat @ Xa @ A2 )
% 3.82/4.02 => ( ( ord_less_eq_set_nat @ Xa @ X5 )
% 3.82/4.02 => ( X5 = Xa ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % finite_has_minimal2
% 3.82/4.02 thf(fact_1341_finite__has__minimal2,axiom,
% 3.82/4.02 ! [A2: set_set_int,A: set_int] :
% 3.82/4.02 ( ( finite6197958912794628473et_int @ A2 )
% 3.82/4.02 => ( ( member_set_int @ A @ A2 )
% 3.82/4.02 => ? [X5: set_int] :
% 3.82/4.02 ( ( member_set_int @ X5 @ A2 )
% 3.82/4.02 & ( ord_less_eq_set_int @ X5 @ A )
% 3.82/4.02 & ! [Xa: set_int] :
% 3.82/4.02 ( ( member_set_int @ Xa @ A2 )
% 3.82/4.02 => ( ( ord_less_eq_set_int @ Xa @ X5 )
% 3.82/4.02 => ( X5 = Xa ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % finite_has_minimal2
% 3.82/4.02 thf(fact_1342_finite__has__minimal2,axiom,
% 3.82/4.02 ! [A2: set_nat,A: nat] :
% 3.82/4.02 ( ( finite_finite_nat @ A2 )
% 3.82/4.02 => ( ( member_nat @ A @ A2 )
% 3.82/4.02 => ? [X5: nat] :
% 3.82/4.02 ( ( member_nat @ X5 @ A2 )
% 3.82/4.02 & ( ord_less_eq_nat @ X5 @ A )
% 3.82/4.02 & ! [Xa: nat] :
% 3.82/4.02 ( ( member_nat @ Xa @ A2 )
% 3.82/4.02 => ( ( ord_less_eq_nat @ Xa @ X5 )
% 3.82/4.02 => ( X5 = Xa ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % finite_has_minimal2
% 3.82/4.02 thf(fact_1343_finite__has__minimal2,axiom,
% 3.82/4.02 ! [A2: set_int,A: int] :
% 3.82/4.02 ( ( finite_finite_int @ A2 )
% 3.82/4.02 => ( ( member_int @ A @ A2 )
% 3.82/4.02 => ? [X5: int] :
% 3.82/4.02 ( ( member_int @ X5 @ A2 )
% 3.82/4.02 & ( ord_less_eq_int @ X5 @ A )
% 3.82/4.02 & ! [Xa: int] :
% 3.82/4.02 ( ( member_int @ Xa @ A2 )
% 3.82/4.02 => ( ( ord_less_eq_int @ Xa @ X5 )
% 3.82/4.02 => ( X5 = Xa ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % finite_has_minimal2
% 3.82/4.02 thf(fact_1344_finite_OemptyI,axiom,
% 3.82/4.02 finite3207457112153483333omplex @ bot_bot_set_complex ).
% 3.82/4.02
% 3.82/4.02 % finite.emptyI
% 3.82/4.02 thf(fact_1345_finite_OemptyI,axiom,
% 3.82/4.02 finite4001608067531595151d_enat @ bot_bo7653980558646680370d_enat ).
% 3.82/4.02
% 3.82/4.02 % finite.emptyI
% 3.82/4.02 thf(fact_1346_finite_OemptyI,axiom,
% 3.82/4.02 finite_finite_real @ bot_bot_set_real ).
% 3.82/4.02
% 3.82/4.02 % finite.emptyI
% 3.82/4.02 thf(fact_1347_finite_OemptyI,axiom,
% 3.82/4.02 finite_finite_nat @ bot_bot_set_nat ).
% 3.82/4.02
% 3.82/4.02 % finite.emptyI
% 3.82/4.02 thf(fact_1348_finite_OemptyI,axiom,
% 3.82/4.02 finite_finite_int @ bot_bot_set_int ).
% 3.82/4.02
% 3.82/4.02 % finite.emptyI
% 3.82/4.02 thf(fact_1349_infinite__imp__nonempty,axiom,
% 3.82/4.02 ! [S2: set_complex] :
% 3.82/4.02 ( ~ ( finite3207457112153483333omplex @ S2 )
% 3.82/4.02 => ( S2 != bot_bot_set_complex ) ) ).
% 3.82/4.02
% 3.82/4.02 % infinite_imp_nonempty
% 3.82/4.02 thf(fact_1350_infinite__imp__nonempty,axiom,
% 3.82/4.02 ! [S2: set_Extended_enat] :
% 3.82/4.02 ( ~ ( finite4001608067531595151d_enat @ S2 )
% 3.82/4.02 => ( S2 != bot_bo7653980558646680370d_enat ) ) ).
% 3.82/4.02
% 3.82/4.02 % infinite_imp_nonempty
% 3.82/4.02 thf(fact_1351_infinite__imp__nonempty,axiom,
% 3.82/4.02 ! [S2: set_real] :
% 3.82/4.02 ( ~ ( finite_finite_real @ S2 )
% 3.82/4.02 => ( S2 != bot_bot_set_real ) ) ).
% 3.82/4.02
% 3.82/4.02 % infinite_imp_nonempty
% 3.82/4.02 thf(fact_1352_infinite__imp__nonempty,axiom,
% 3.82/4.02 ! [S2: set_nat] :
% 3.82/4.02 ( ~ ( finite_finite_nat @ S2 )
% 3.82/4.02 => ( S2 != bot_bot_set_nat ) ) ).
% 3.82/4.02
% 3.82/4.02 % infinite_imp_nonempty
% 3.82/4.02 thf(fact_1353_infinite__imp__nonempty,axiom,
% 3.82/4.02 ! [S2: set_int] :
% 3.82/4.02 ( ~ ( finite_finite_int @ S2 )
% 3.82/4.02 => ( S2 != bot_bot_set_int ) ) ).
% 3.82/4.02
% 3.82/4.02 % infinite_imp_nonempty
% 3.82/4.02 thf(fact_1354_finite__transitivity__chain,axiom,
% 3.82/4.02 ! [A2: set_set_nat,R: set_nat > set_nat > $o] :
% 3.82/4.02 ( ( finite1152437895449049373et_nat @ A2 )
% 3.82/4.02 => ( ! [X5: set_nat] :
% 3.82/4.02 ~ ( R @ X5 @ X5 )
% 3.82/4.02 => ( ! [X5: set_nat,Y3: set_nat,Z: set_nat] :
% 3.82/4.02 ( ( R @ X5 @ Y3 )
% 3.82/4.02 => ( ( R @ Y3 @ Z )
% 3.82/4.02 => ( R @ X5 @ Z ) ) )
% 3.82/4.02 => ( ! [X5: set_nat] :
% 3.82/4.02 ( ( member_set_nat @ X5 @ A2 )
% 3.82/4.02 => ? [Y6: set_nat] :
% 3.82/4.02 ( ( member_set_nat @ Y6 @ A2 )
% 3.82/4.02 & ( R @ X5 @ Y6 ) ) )
% 3.82/4.02 => ( A2 = bot_bot_set_set_nat ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % finite_transitivity_chain
% 3.82/4.02 thf(fact_1355_finite__transitivity__chain,axiom,
% 3.82/4.02 ! [A2: set_complex,R: complex > complex > $o] :
% 3.82/4.02 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.02 => ( ! [X5: complex] :
% 3.82/4.02 ~ ( R @ X5 @ X5 )
% 3.82/4.02 => ( ! [X5: complex,Y3: complex,Z: complex] :
% 3.82/4.02 ( ( R @ X5 @ Y3 )
% 3.82/4.02 => ( ( R @ Y3 @ Z )
% 3.82/4.02 => ( R @ X5 @ Z ) ) )
% 3.82/4.02 => ( ! [X5: complex] :
% 3.82/4.02 ( ( member_complex @ X5 @ A2 )
% 3.82/4.02 => ? [Y6: complex] :
% 3.82/4.02 ( ( member_complex @ Y6 @ A2 )
% 3.82/4.02 & ( R @ X5 @ Y6 ) ) )
% 3.82/4.02 => ( A2 = bot_bot_set_complex ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % finite_transitivity_chain
% 3.82/4.02 thf(fact_1356_finite__transitivity__chain,axiom,
% 3.82/4.02 ! [A2: set_Extended_enat,R: extended_enat > extended_enat > $o] :
% 3.82/4.02 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.02 => ( ! [X5: extended_enat] :
% 3.82/4.02 ~ ( R @ X5 @ X5 )
% 3.82/4.02 => ( ! [X5: extended_enat,Y3: extended_enat,Z: extended_enat] :
% 3.82/4.02 ( ( R @ X5 @ Y3 )
% 3.82/4.02 => ( ( R @ Y3 @ Z )
% 3.82/4.02 => ( R @ X5 @ Z ) ) )
% 3.82/4.02 => ( ! [X5: extended_enat] :
% 3.82/4.02 ( ( member_Extended_enat @ X5 @ A2 )
% 3.82/4.02 => ? [Y6: extended_enat] :
% 3.82/4.02 ( ( member_Extended_enat @ Y6 @ A2 )
% 3.82/4.02 & ( R @ X5 @ Y6 ) ) )
% 3.82/4.02 => ( A2 = bot_bo7653980558646680370d_enat ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % finite_transitivity_chain
% 3.82/4.02 thf(fact_1357_finite__transitivity__chain,axiom,
% 3.82/4.02 ! [A2: set_real,R: real > real > $o] :
% 3.82/4.02 ( ( finite_finite_real @ A2 )
% 3.82/4.02 => ( ! [X5: real] :
% 3.82/4.02 ~ ( R @ X5 @ X5 )
% 3.82/4.02 => ( ! [X5: real,Y3: real,Z: real] :
% 3.82/4.02 ( ( R @ X5 @ Y3 )
% 3.82/4.02 => ( ( R @ Y3 @ Z )
% 3.82/4.02 => ( R @ X5 @ Z ) ) )
% 3.82/4.02 => ( ! [X5: real] :
% 3.82/4.02 ( ( member_real @ X5 @ A2 )
% 3.82/4.02 => ? [Y6: real] :
% 3.82/4.02 ( ( member_real @ Y6 @ A2 )
% 3.82/4.02 & ( R @ X5 @ Y6 ) ) )
% 3.82/4.02 => ( A2 = bot_bot_set_real ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % finite_transitivity_chain
% 3.82/4.02 thf(fact_1358_finite__transitivity__chain,axiom,
% 3.82/4.02 ! [A2: set_nat,R: nat > nat > $o] :
% 3.82/4.02 ( ( finite_finite_nat @ A2 )
% 3.82/4.02 => ( ! [X5: nat] :
% 3.82/4.02 ~ ( R @ X5 @ X5 )
% 3.82/4.02 => ( ! [X5: nat,Y3: nat,Z: nat] :
% 3.82/4.02 ( ( R @ X5 @ Y3 )
% 3.82/4.02 => ( ( R @ Y3 @ Z )
% 3.82/4.02 => ( R @ X5 @ Z ) ) )
% 3.82/4.02 => ( ! [X5: nat] :
% 3.82/4.02 ( ( member_nat @ X5 @ A2 )
% 3.82/4.02 => ? [Y6: nat] :
% 3.82/4.02 ( ( member_nat @ Y6 @ A2 )
% 3.82/4.02 & ( R @ X5 @ Y6 ) ) )
% 3.82/4.02 => ( A2 = bot_bot_set_nat ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % finite_transitivity_chain
% 3.82/4.02 thf(fact_1359_finite__transitivity__chain,axiom,
% 3.82/4.02 ! [A2: set_int,R: int > int > $o] :
% 3.82/4.02 ( ( finite_finite_int @ A2 )
% 3.82/4.02 => ( ! [X5: int] :
% 3.82/4.02 ~ ( R @ X5 @ X5 )
% 3.82/4.02 => ( ! [X5: int,Y3: int,Z: int] :
% 3.82/4.02 ( ( R @ X5 @ Y3 )
% 3.82/4.02 => ( ( R @ Y3 @ Z )
% 3.82/4.02 => ( R @ X5 @ Z ) ) )
% 3.82/4.02 => ( ! [X5: int] :
% 3.82/4.02 ( ( member_int @ X5 @ A2 )
% 3.82/4.02 => ? [Y6: int] :
% 3.82/4.02 ( ( member_int @ Y6 @ A2 )
% 3.82/4.02 & ( R @ X5 @ Y6 ) ) )
% 3.82/4.02 => ( A2 = bot_bot_set_int ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % finite_transitivity_chain
% 3.82/4.02 thf(fact_1360_finite__subset,axiom,
% 3.82/4.02 ! [A2: set_complex,B: set_complex] :
% 3.82/4.02 ( ( ord_le211207098394363844omplex @ A2 @ B )
% 3.82/4.02 => ( ( finite3207457112153483333omplex @ B )
% 3.82/4.02 => ( finite3207457112153483333omplex @ A2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % finite_subset
% 3.82/4.02 thf(fact_1361_finite__subset,axiom,
% 3.82/4.02 ! [A2: set_Extended_enat,B: set_Extended_enat] :
% 3.82/4.02 ( ( ord_le7203529160286727270d_enat @ A2 @ B )
% 3.82/4.02 => ( ( finite4001608067531595151d_enat @ B )
% 3.82/4.02 => ( finite4001608067531595151d_enat @ A2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % finite_subset
% 3.82/4.02 thf(fact_1362_finite__subset,axiom,
% 3.82/4.02 ! [A2: set_nat,B: set_nat] :
% 3.82/4.02 ( ( ord_less_eq_set_nat @ A2 @ B )
% 3.82/4.02 => ( ( finite_finite_nat @ B )
% 3.82/4.02 => ( finite_finite_nat @ A2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % finite_subset
% 3.82/4.02 thf(fact_1363_finite__subset,axiom,
% 3.82/4.02 ! [A2: set_int,B: set_int] :
% 3.82/4.02 ( ( ord_less_eq_set_int @ A2 @ B )
% 3.82/4.02 => ( ( finite_finite_int @ B )
% 3.82/4.02 => ( finite_finite_int @ A2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % finite_subset
% 3.82/4.02 thf(fact_1364_infinite__super,axiom,
% 3.82/4.02 ! [S2: set_complex,T3: set_complex] :
% 3.82/4.02 ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 3.82/4.02 => ( ~ ( finite3207457112153483333omplex @ S2 )
% 3.82/4.02 => ~ ( finite3207457112153483333omplex @ T3 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % infinite_super
% 3.82/4.02 thf(fact_1365_infinite__super,axiom,
% 3.82/4.02 ! [S2: set_Extended_enat,T3: set_Extended_enat] :
% 3.82/4.02 ( ( ord_le7203529160286727270d_enat @ S2 @ T3 )
% 3.82/4.02 => ( ~ ( finite4001608067531595151d_enat @ S2 )
% 3.82/4.02 => ~ ( finite4001608067531595151d_enat @ T3 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % infinite_super
% 3.82/4.02 thf(fact_1366_infinite__super,axiom,
% 3.82/4.02 ! [S2: set_nat,T3: set_nat] :
% 3.82/4.02 ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 3.82/4.02 => ( ~ ( finite_finite_nat @ S2 )
% 3.82/4.02 => ~ ( finite_finite_nat @ T3 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % infinite_super
% 3.82/4.02 thf(fact_1367_infinite__super,axiom,
% 3.82/4.02 ! [S2: set_int,T3: set_int] :
% 3.82/4.02 ( ( ord_less_eq_set_int @ S2 @ T3 )
% 3.82/4.02 => ( ~ ( finite_finite_int @ S2 )
% 3.82/4.02 => ~ ( finite_finite_int @ T3 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % infinite_super
% 3.82/4.02 thf(fact_1368_rev__finite__subset,axiom,
% 3.82/4.02 ! [B: set_complex,A2: set_complex] :
% 3.82/4.02 ( ( finite3207457112153483333omplex @ B )
% 3.82/4.02 => ( ( ord_le211207098394363844omplex @ A2 @ B )
% 3.82/4.02 => ( finite3207457112153483333omplex @ A2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % rev_finite_subset
% 3.82/4.02 thf(fact_1369_rev__finite__subset,axiom,
% 3.82/4.02 ! [B: set_Extended_enat,A2: set_Extended_enat] :
% 3.82/4.02 ( ( finite4001608067531595151d_enat @ B )
% 3.82/4.02 => ( ( ord_le7203529160286727270d_enat @ A2 @ B )
% 3.82/4.02 => ( finite4001608067531595151d_enat @ A2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % rev_finite_subset
% 3.82/4.02 thf(fact_1370_rev__finite__subset,axiom,
% 3.82/4.02 ! [B: set_nat,A2: set_nat] :
% 3.82/4.02 ( ( finite_finite_nat @ B )
% 3.82/4.02 => ( ( ord_less_eq_set_nat @ A2 @ B )
% 3.82/4.02 => ( finite_finite_nat @ A2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % rev_finite_subset
% 3.82/4.02 thf(fact_1371_rev__finite__subset,axiom,
% 3.82/4.02 ! [B: set_int,A2: set_int] :
% 3.82/4.02 ( ( finite_finite_int @ B )
% 3.82/4.02 => ( ( ord_less_eq_set_int @ A2 @ B )
% 3.82/4.02 => ( finite_finite_int @ A2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % rev_finite_subset
% 3.82/4.02 thf(fact_1372_arg__min__least,axiom,
% 3.82/4.02 ! [S2: set_complex,Y: complex,F: complex > real] :
% 3.82/4.02 ( ( finite3207457112153483333omplex @ S2 )
% 3.82/4.02 => ( ( S2 != bot_bot_set_complex )
% 3.82/4.02 => ( ( member_complex @ Y @ S2 )
% 3.82/4.02 => ( ord_less_eq_real @ ( F @ ( lattic8794016678065449205x_real @ F @ S2 ) ) @ ( F @ Y ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % arg_min_least
% 3.82/4.02 thf(fact_1373_arg__min__least,axiom,
% 3.82/4.02 ! [S2: set_Extended_enat,Y: extended_enat,F: extended_enat > real] :
% 3.82/4.02 ( ( finite4001608067531595151d_enat @ S2 )
% 3.82/4.02 => ( ( S2 != bot_bo7653980558646680370d_enat )
% 3.82/4.02 => ( ( member_Extended_enat @ Y @ S2 )
% 3.82/4.02 => ( ord_less_eq_real @ ( F @ ( lattic1189837152898106425t_real @ F @ S2 ) ) @ ( F @ Y ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % arg_min_least
% 3.82/4.02 thf(fact_1374_arg__min__least,axiom,
% 3.82/4.02 ! [S2: set_real,Y: real,F: real > real] :
% 3.82/4.02 ( ( finite_finite_real @ S2 )
% 3.82/4.02 => ( ( S2 != bot_bot_set_real )
% 3.82/4.02 => ( ( member_real @ Y @ S2 )
% 3.82/4.02 => ( ord_less_eq_real @ ( F @ ( lattic8440615504127631091l_real @ F @ S2 ) ) @ ( F @ Y ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % arg_min_least
% 3.82/4.02 thf(fact_1375_arg__min__least,axiom,
% 3.82/4.02 ! [S2: set_nat,Y: nat,F: nat > real] :
% 3.82/4.02 ( ( finite_finite_nat @ S2 )
% 3.82/4.02 => ( ( S2 != bot_bot_set_nat )
% 3.82/4.02 => ( ( member_nat @ Y @ S2 )
% 3.82/4.02 => ( ord_less_eq_real @ ( F @ ( lattic488527866317076247t_real @ F @ S2 ) ) @ ( F @ Y ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % arg_min_least
% 3.82/4.02 thf(fact_1376_arg__min__least,axiom,
% 3.82/4.02 ! [S2: set_int,Y: int,F: int > real] :
% 3.82/4.02 ( ( finite_finite_int @ S2 )
% 3.82/4.02 => ( ( S2 != bot_bot_set_int )
% 3.82/4.02 => ( ( member_int @ Y @ S2 )
% 3.82/4.02 => ( ord_less_eq_real @ ( F @ ( lattic2675449441010098035t_real @ F @ S2 ) ) @ ( F @ Y ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % arg_min_least
% 3.82/4.02 thf(fact_1377_arg__min__least,axiom,
% 3.82/4.02 ! [S2: set_complex,Y: complex,F: complex > nat] :
% 3.82/4.02 ( ( finite3207457112153483333omplex @ S2 )
% 3.82/4.02 => ( ( S2 != bot_bot_set_complex )
% 3.82/4.02 => ( ( member_complex @ Y @ S2 )
% 3.82/4.02 => ( ord_less_eq_nat @ ( F @ ( lattic5364784637807008409ex_nat @ F @ S2 ) ) @ ( F @ Y ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % arg_min_least
% 3.82/4.02 thf(fact_1378_arg__min__least,axiom,
% 3.82/4.02 ! [S2: set_Extended_enat,Y: extended_enat,F: extended_enat > nat] :
% 3.82/4.02 ( ( finite4001608067531595151d_enat @ S2 )
% 3.82/4.02 => ( ( S2 != bot_bo7653980558646680370d_enat )
% 3.82/4.02 => ( ( member_Extended_enat @ Y @ S2 )
% 3.82/4.02 => ( ord_less_eq_nat @ ( F @ ( lattic3845382081240766429at_nat @ F @ S2 ) ) @ ( F @ Y ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % arg_min_least
% 3.82/4.02 thf(fact_1379_arg__min__least,axiom,
% 3.82/4.02 ! [S2: set_real,Y: real,F: real > nat] :
% 3.82/4.02 ( ( finite_finite_real @ S2 )
% 3.82/4.02 => ( ( S2 != bot_bot_set_real )
% 3.82/4.02 => ( ( member_real @ Y @ S2 )
% 3.82/4.02 => ( ord_less_eq_nat @ ( F @ ( lattic5055836439445974935al_nat @ F @ S2 ) ) @ ( F @ Y ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % arg_min_least
% 3.82/4.02 thf(fact_1380_arg__min__least,axiom,
% 3.82/4.02 ! [S2: set_nat,Y: nat,F: nat > nat] :
% 3.82/4.02 ( ( finite_finite_nat @ S2 )
% 3.82/4.02 => ( ( S2 != bot_bot_set_nat )
% 3.82/4.02 => ( ( member_nat @ Y @ S2 )
% 3.82/4.02 => ( ord_less_eq_nat @ ( F @ ( lattic7446932960582359483at_nat @ F @ S2 ) ) @ ( F @ Y ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % arg_min_least
% 3.82/4.02 thf(fact_1381_arg__min__least,axiom,
% 3.82/4.02 ! [S2: set_int,Y: int,F: int > nat] :
% 3.82/4.02 ( ( finite_finite_int @ S2 )
% 3.82/4.02 => ( ( S2 != bot_bot_set_int )
% 3.82/4.02 => ( ( member_int @ Y @ S2 )
% 3.82/4.02 => ( ord_less_eq_nat @ ( F @ ( lattic8446286672483414039nt_nat @ F @ S2 ) ) @ ( F @ Y ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % arg_min_least
% 3.82/4.02 thf(fact_1382_Euclid__induct,axiom,
% 3.82/4.02 ! [P: nat > nat > $o,A: nat,B2: nat] :
% 3.82/4.02 ( ! [A4: nat,B4: nat] :
% 3.82/4.02 ( ( P @ A4 @ B4 )
% 3.82/4.02 = ( P @ B4 @ A4 ) )
% 3.82/4.02 => ( ! [A4: nat] : ( P @ A4 @ zero_zero_nat )
% 3.82/4.02 => ( ! [A4: nat,B4: nat] :
% 3.82/4.02 ( ( P @ A4 @ B4 )
% 3.82/4.02 => ( P @ A4 @ ( plus_plus_nat @ A4 @ B4 ) ) )
% 3.82/4.02 => ( P @ A @ B2 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % Euclid_induct
% 3.82/4.02 thf(fact_1383_nat__descend__induct,axiom,
% 3.82/4.02 ! [N2: nat,P: nat > $o,M2: nat] :
% 3.82/4.02 ( ! [K3: nat] :
% 3.82/4.02 ( ( ord_less_nat @ N2 @ K3 )
% 3.82/4.02 => ( P @ K3 ) )
% 3.82/4.02 => ( ! [K3: nat] :
% 3.82/4.02 ( ( ord_less_eq_nat @ K3 @ N2 )
% 3.82/4.02 => ( ! [I5: nat] :
% 3.82/4.02 ( ( ord_less_nat @ K3 @ I5 )
% 3.82/4.02 => ( P @ I5 ) )
% 3.82/4.02 => ( P @ K3 ) ) )
% 3.82/4.02 => ( P @ M2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % nat_descend_induct
% 3.82/4.02 thf(fact_1384_subset__emptyI,axiom,
% 3.82/4.02 ! [A2: set_set_nat] :
% 3.82/4.02 ( ! [X5: set_nat] :
% 3.82/4.02 ~ ( member_set_nat @ X5 @ A2 )
% 3.82/4.02 => ( ord_le6893508408891458716et_nat @ A2 @ bot_bot_set_set_nat ) ) ).
% 3.82/4.02
% 3.82/4.02 % subset_emptyI
% 3.82/4.02 thf(fact_1385_subset__emptyI,axiom,
% 3.82/4.02 ! [A2: set_Extended_enat] :
% 3.82/4.02 ( ! [X5: extended_enat] :
% 3.82/4.02 ~ ( member_Extended_enat @ X5 @ A2 )
% 3.82/4.02 => ( ord_le7203529160286727270d_enat @ A2 @ bot_bo7653980558646680370d_enat ) ) ).
% 3.82/4.02
% 3.82/4.02 % subset_emptyI
% 3.82/4.02 thf(fact_1386_subset__emptyI,axiom,
% 3.82/4.02 ! [A2: set_real] :
% 3.82/4.02 ( ! [X5: real] :
% 3.82/4.02 ~ ( member_real @ X5 @ A2 )
% 3.82/4.02 => ( ord_less_eq_set_real @ A2 @ bot_bot_set_real ) ) ).
% 3.82/4.02
% 3.82/4.02 % subset_emptyI
% 3.82/4.02 thf(fact_1387_subset__emptyI,axiom,
% 3.82/4.02 ! [A2: set_nat] :
% 3.82/4.02 ( ! [X5: nat] :
% 3.82/4.02 ~ ( member_nat @ X5 @ A2 )
% 3.82/4.02 => ( ord_less_eq_set_nat @ A2 @ bot_bot_set_nat ) ) ).
% 3.82/4.02
% 3.82/4.02 % subset_emptyI
% 3.82/4.02 thf(fact_1388_subset__emptyI,axiom,
% 3.82/4.02 ! [A2: set_int] :
% 3.82/4.02 ( ! [X5: int] :
% 3.82/4.02 ~ ( member_int @ X5 @ A2 )
% 3.82/4.02 => ( ord_less_eq_set_int @ A2 @ bot_bot_set_int ) ) ).
% 3.82/4.02
% 3.82/4.02 % subset_emptyI
% 3.82/4.02 thf(fact_1389_list__decode_Ocases,axiom,
% 3.82/4.02 ! [X: nat] :
% 3.82/4.02 ( ( X != zero_zero_nat )
% 3.82/4.02 => ~ ! [N3: nat] :
% 3.82/4.02 ( X
% 3.82/4.02 != ( suc @ N3 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % list_decode.cases
% 3.82/4.02 thf(fact_1390_vebt__buildup_Ocases,axiom,
% 3.82/4.02 ! [X: nat] :
% 3.82/4.02 ( ( X != zero_zero_nat )
% 3.82/4.02 => ( ( X
% 3.82/4.02 != ( suc @ zero_zero_nat ) )
% 3.82/4.02 => ~ ! [Va: nat] :
% 3.82/4.02 ( X
% 3.82/4.02 != ( suc @ ( suc @ Va ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % vebt_buildup.cases
% 3.82/4.02 thf(fact_1391_exists__least__lemma,axiom,
% 3.82/4.02 ! [P: nat > $o] :
% 3.82/4.02 ( ~ ( P @ zero_zero_nat )
% 3.82/4.02 => ( ? [X_1: nat] : ( P @ X_1 )
% 3.82/4.02 => ? [N3: nat] :
% 3.82/4.02 ( ~ ( P @ N3 )
% 3.82/4.02 & ( P @ ( suc @ N3 ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % exists_least_lemma
% 3.82/4.02 thf(fact_1392_add__0__iff,axiom,
% 3.82/4.02 ! [B2: nat,A: nat] :
% 3.82/4.02 ( ( B2
% 3.82/4.02 = ( plus_plus_nat @ B2 @ A ) )
% 3.82/4.02 = ( A = zero_zero_nat ) ) ).
% 3.82/4.02
% 3.82/4.02 % add_0_iff
% 3.82/4.02 thf(fact_1393_add__0__iff,axiom,
% 3.82/4.02 ! [B2: real,A: real] :
% 3.82/4.02 ( ( B2
% 3.82/4.02 = ( plus_plus_real @ B2 @ A ) )
% 3.82/4.02 = ( A = zero_zero_real ) ) ).
% 3.82/4.02
% 3.82/4.02 % add_0_iff
% 3.82/4.02 thf(fact_1394_add__0__iff,axiom,
% 3.82/4.02 ! [B2: int,A: int] :
% 3.82/4.02 ( ( B2
% 3.82/4.02 = ( plus_plus_int @ B2 @ A ) )
% 3.82/4.02 = ( A = zero_zero_int ) ) ).
% 3.82/4.02
% 3.82/4.02 % add_0_iff
% 3.82/4.02 thf(fact_1395_add__0__iff,axiom,
% 3.82/4.02 ! [B2: complex,A: complex] :
% 3.82/4.02 ( ( B2
% 3.82/4.02 = ( plus_plus_complex @ B2 @ A ) )
% 3.82/4.02 = ( A = zero_zero_complex ) ) ).
% 3.82/4.02
% 3.82/4.02 % add_0_iff
% 3.82/4.02 thf(fact_1396_verit__sum__simplify,axiom,
% 3.82/4.02 ! [A: nat] :
% 3.82/4.02 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 3.82/4.02 = A ) ).
% 3.82/4.02
% 3.82/4.02 % verit_sum_simplify
% 3.82/4.02 thf(fact_1397_verit__sum__simplify,axiom,
% 3.82/4.02 ! [A: real] :
% 3.82/4.02 ( ( plus_plus_real @ A @ zero_zero_real )
% 3.82/4.02 = A ) ).
% 3.82/4.02
% 3.82/4.02 % verit_sum_simplify
% 3.82/4.02 thf(fact_1398_verit__sum__simplify,axiom,
% 3.82/4.02 ! [A: int] :
% 3.82/4.02 ( ( plus_plus_int @ A @ zero_zero_int )
% 3.82/4.02 = A ) ).
% 3.82/4.02
% 3.82/4.02 % verit_sum_simplify
% 3.82/4.02 thf(fact_1399_verit__sum__simplify,axiom,
% 3.82/4.02 ! [A: complex] :
% 3.82/4.02 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 3.82/4.02 = A ) ).
% 3.82/4.02
% 3.82/4.02 % verit_sum_simplify
% 3.82/4.02 thf(fact_1400_less__numeral__extra_I3_J,axiom,
% 3.82/4.02 ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 3.82/4.02
% 3.82/4.02 % less_numeral_extra(3)
% 3.82/4.02 thf(fact_1401_less__numeral__extra_I3_J,axiom,
% 3.82/4.02 ~ ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ zero_z5237406670263579293d_enat ) ).
% 3.82/4.02
% 3.82/4.02 % less_numeral_extra(3)
% 3.82/4.02 thf(fact_1402_less__numeral__extra_I3_J,axiom,
% 3.82/4.02 ~ ( ord_less_real @ zero_zero_real @ zero_zero_real ) ).
% 3.82/4.02
% 3.82/4.02 % less_numeral_extra(3)
% 3.82/4.02 thf(fact_1403_less__numeral__extra_I3_J,axiom,
% 3.82/4.02 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 3.82/4.02
% 3.82/4.02 % less_numeral_extra(3)
% 3.82/4.02 thf(fact_1404_field__lbound__gt__zero,axiom,
% 3.82/4.02 ! [D1: real,D2: real] :
% 3.82/4.02 ( ( ord_less_real @ zero_zero_real @ D1 )
% 3.82/4.02 => ( ( ord_less_real @ zero_zero_real @ D2 )
% 3.82/4.02 => ? [E: real] :
% 3.82/4.02 ( ( ord_less_real @ zero_zero_real @ E )
% 3.82/4.02 & ( ord_less_real @ E @ D1 )
% 3.82/4.02 & ( ord_less_real @ E @ D2 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % field_lbound_gt_zero
% 3.82/4.02 thf(fact_1405_verit__la__disequality,axiom,
% 3.82/4.02 ! [A: real,B2: real] :
% 3.82/4.02 ( ( A = B2 )
% 3.82/4.02 | ~ ( ord_less_eq_real @ A @ B2 )
% 3.82/4.02 | ~ ( ord_less_eq_real @ B2 @ A ) ) ).
% 3.82/4.02
% 3.82/4.02 % verit_la_disequality
% 3.82/4.02 thf(fact_1406_verit__la__disequality,axiom,
% 3.82/4.02 ! [A: nat,B2: nat] :
% 3.82/4.02 ( ( A = B2 )
% 3.82/4.02 | ~ ( ord_less_eq_nat @ A @ B2 )
% 3.82/4.02 | ~ ( ord_less_eq_nat @ B2 @ A ) ) ).
% 3.82/4.02
% 3.82/4.02 % verit_la_disequality
% 3.82/4.02 thf(fact_1407_verit__la__disequality,axiom,
% 3.82/4.02 ! [A: int,B2: int] :
% 3.82/4.02 ( ( A = B2 )
% 3.82/4.02 | ~ ( ord_less_eq_int @ A @ B2 )
% 3.82/4.02 | ~ ( ord_less_eq_int @ B2 @ A ) ) ).
% 3.82/4.02
% 3.82/4.02 % verit_la_disequality
% 3.82/4.02 thf(fact_1408_verit__comp__simplify1_I2_J,axiom,
% 3.82/4.02 ! [A: real] : ( ord_less_eq_real @ A @ A ) ).
% 3.82/4.02
% 3.82/4.02 % verit_comp_simplify1(2)
% 3.82/4.02 thf(fact_1409_verit__comp__simplify1_I2_J,axiom,
% 3.82/4.02 ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ) ).
% 3.82/4.02
% 3.82/4.02 % verit_comp_simplify1(2)
% 3.82/4.02 thf(fact_1410_verit__comp__simplify1_I2_J,axiom,
% 3.82/4.02 ! [A: set_int] : ( ord_less_eq_set_int @ A @ A ) ).
% 3.82/4.02
% 3.82/4.02 % verit_comp_simplify1(2)
% 3.82/4.02 thf(fact_1411_verit__comp__simplify1_I2_J,axiom,
% 3.82/4.02 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 3.82/4.02
% 3.82/4.02 % verit_comp_simplify1(2)
% 3.82/4.02 thf(fact_1412_verit__comp__simplify1_I2_J,axiom,
% 3.82/4.02 ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 3.82/4.02
% 3.82/4.02 % verit_comp_simplify1(2)
% 3.82/4.02 thf(fact_1413_verit__comp__simplify1_I1_J,axiom,
% 3.82/4.02 ! [A: nat] :
% 3.82/4.02 ~ ( ord_less_nat @ A @ A ) ).
% 3.82/4.02
% 3.82/4.02 % verit_comp_simplify1(1)
% 3.82/4.02 thf(fact_1414_verit__comp__simplify1_I1_J,axiom,
% 3.82/4.02 ! [A: extended_enat] :
% 3.82/4.02 ~ ( ord_le72135733267957522d_enat @ A @ A ) ).
% 3.82/4.02
% 3.82/4.02 % verit_comp_simplify1(1)
% 3.82/4.02 thf(fact_1415_verit__comp__simplify1_I1_J,axiom,
% 3.82/4.02 ! [A: real] :
% 3.82/4.02 ~ ( ord_less_real @ A @ A ) ).
% 3.82/4.02
% 3.82/4.02 % verit_comp_simplify1(1)
% 3.82/4.02 thf(fact_1416_verit__comp__simplify1_I1_J,axiom,
% 3.82/4.02 ! [A: int] :
% 3.82/4.02 ~ ( ord_less_int @ A @ A ) ).
% 3.82/4.02
% 3.82/4.02 % verit_comp_simplify1(1)
% 3.82/4.02 thf(fact_1417_is__num__normalize_I1_J,axiom,
% 3.82/4.02 ! [A: int,B2: int,C: int] :
% 3.82/4.02 ( ( plus_plus_int @ ( plus_plus_int @ A @ B2 ) @ C )
% 3.82/4.02 = ( plus_plus_int @ A @ ( plus_plus_int @ B2 @ C ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % is_num_normalize(1)
% 3.82/4.02 thf(fact_1418_is__num__normalize_I1_J,axiom,
% 3.82/4.02 ! [A: real,B2: real,C: real] :
% 3.82/4.02 ( ( plus_plus_real @ ( plus_plus_real @ A @ B2 ) @ C )
% 3.82/4.02 = ( plus_plus_real @ A @ ( plus_plus_real @ B2 @ C ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % is_num_normalize(1)
% 3.82/4.02 thf(fact_1419_le__numeral__extra_I3_J,axiom,
% 3.82/4.02 ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ zero_z5237406670263579293d_enat ).
% 3.82/4.02
% 3.82/4.02 % le_numeral_extra(3)
% 3.82/4.02 thf(fact_1420_le__numeral__extra_I3_J,axiom,
% 3.82/4.02 ord_less_eq_real @ zero_zero_real @ zero_zero_real ).
% 3.82/4.02
% 3.82/4.02 % le_numeral_extra(3)
% 3.82/4.02 thf(fact_1421_le__numeral__extra_I3_J,axiom,
% 3.82/4.02 ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 3.82/4.02
% 3.82/4.02 % le_numeral_extra(3)
% 3.82/4.02 thf(fact_1422_le__numeral__extra_I3_J,axiom,
% 3.82/4.02 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 3.82/4.02
% 3.82/4.02 % le_numeral_extra(3)
% 3.82/4.02 thf(fact_1423_verit__comp__simplify1_I3_J,axiom,
% 3.82/4.02 ! [B7: extended_enat,A7: extended_enat] :
% 3.82/4.02 ( ( ~ ( ord_le2932123472753598470d_enat @ B7 @ A7 ) )
% 3.82/4.02 = ( ord_le72135733267957522d_enat @ A7 @ B7 ) ) ).
% 3.82/4.02
% 3.82/4.02 % verit_comp_simplify1(3)
% 3.82/4.02 thf(fact_1424_verit__comp__simplify1_I3_J,axiom,
% 3.82/4.02 ! [B7: real,A7: real] :
% 3.82/4.02 ( ( ~ ( ord_less_eq_real @ B7 @ A7 ) )
% 3.82/4.02 = ( ord_less_real @ A7 @ B7 ) ) ).
% 3.82/4.02
% 3.82/4.02 % verit_comp_simplify1(3)
% 3.82/4.02 thf(fact_1425_verit__comp__simplify1_I3_J,axiom,
% 3.82/4.02 ! [B7: nat,A7: nat] :
% 3.82/4.02 ( ( ~ ( ord_less_eq_nat @ B7 @ A7 ) )
% 3.82/4.02 = ( ord_less_nat @ A7 @ B7 ) ) ).
% 3.82/4.02
% 3.82/4.02 % verit_comp_simplify1(3)
% 3.82/4.02 thf(fact_1426_verit__comp__simplify1_I3_J,axiom,
% 3.82/4.02 ! [B7: int,A7: int] :
% 3.82/4.02 ( ( ~ ( ord_less_eq_int @ B7 @ A7 ) )
% 3.82/4.02 = ( ord_less_int @ A7 @ B7 ) ) ).
% 3.82/4.02
% 3.82/4.02 % verit_comp_simplify1(3)
% 3.82/4.02 thf(fact_1427_Collect__empty__eq__bot,axiom,
% 3.82/4.02 ! [P: list_nat > $o] :
% 3.82/4.02 ( ( ( collect_list_nat @ P )
% 3.82/4.02 = bot_bot_set_list_nat )
% 3.82/4.02 = ( P = bot_bot_list_nat_o ) ) ).
% 3.82/4.02
% 3.82/4.02 % Collect_empty_eq_bot
% 3.82/4.02 thf(fact_1428_Collect__empty__eq__bot,axiom,
% 3.82/4.02 ! [P: set_nat > $o] :
% 3.82/4.02 ( ( ( collect_set_nat @ P )
% 3.82/4.02 = bot_bot_set_set_nat )
% 3.82/4.02 = ( P = bot_bot_set_nat_o ) ) ).
% 3.82/4.02
% 3.82/4.02 % Collect_empty_eq_bot
% 3.82/4.02 thf(fact_1429_Collect__empty__eq__bot,axiom,
% 3.82/4.02 ! [P: extended_enat > $o] :
% 3.82/4.02 ( ( ( collec4429806609662206161d_enat @ P )
% 3.82/4.02 = bot_bo7653980558646680370d_enat )
% 3.82/4.02 = ( P = bot_bo1954855461789132331enat_o ) ) ).
% 3.82/4.02
% 3.82/4.02 % Collect_empty_eq_bot
% 3.82/4.02 thf(fact_1430_Collect__empty__eq__bot,axiom,
% 3.82/4.02 ! [P: real > $o] :
% 3.82/4.02 ( ( ( collect_real @ P )
% 3.82/4.02 = bot_bot_set_real )
% 3.82/4.02 = ( P = bot_bot_real_o ) ) ).
% 3.82/4.02
% 3.82/4.02 % Collect_empty_eq_bot
% 3.82/4.02 thf(fact_1431_Collect__empty__eq__bot,axiom,
% 3.82/4.02 ! [P: nat > $o] :
% 3.82/4.02 ( ( ( collect_nat @ P )
% 3.82/4.02 = bot_bot_set_nat )
% 3.82/4.02 = ( P = bot_bot_nat_o ) ) ).
% 3.82/4.02
% 3.82/4.02 % Collect_empty_eq_bot
% 3.82/4.02 thf(fact_1432_Collect__empty__eq__bot,axiom,
% 3.82/4.02 ! [P: int > $o] :
% 3.82/4.02 ( ( ( collect_int @ P )
% 3.82/4.02 = bot_bot_set_int )
% 3.82/4.02 = ( P = bot_bot_int_o ) ) ).
% 3.82/4.02
% 3.82/4.02 % Collect_empty_eq_bot
% 3.82/4.02 thf(fact_1433_bot__empty__eq,axiom,
% 3.82/4.02 ( bot_bot_set_nat_o
% 3.82/4.02 = ( ^ [X4: set_nat] : ( member_set_nat @ X4 @ bot_bot_set_set_nat ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % bot_empty_eq
% 3.82/4.02 thf(fact_1434_bot__empty__eq,axiom,
% 3.82/4.02 ( bot_bo1954855461789132331enat_o
% 3.82/4.02 = ( ^ [X4: extended_enat] : ( member_Extended_enat @ X4 @ bot_bo7653980558646680370d_enat ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % bot_empty_eq
% 3.82/4.02 thf(fact_1435_bot__empty__eq,axiom,
% 3.82/4.02 ( bot_bot_real_o
% 3.82/4.02 = ( ^ [X4: real] : ( member_real @ X4 @ bot_bot_set_real ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % bot_empty_eq
% 3.82/4.02 thf(fact_1436_bot__empty__eq,axiom,
% 3.82/4.02 ( bot_bot_nat_o
% 3.82/4.02 = ( ^ [X4: nat] : ( member_nat @ X4 @ bot_bot_set_nat ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % bot_empty_eq
% 3.82/4.02 thf(fact_1437_bot__empty__eq,axiom,
% 3.82/4.02 ( bot_bot_int_o
% 3.82/4.02 = ( ^ [X4: int] : ( member_int @ X4 @ bot_bot_set_int ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % bot_empty_eq
% 3.82/4.02 thf(fact_1438_triangle__Suc,axiom,
% 3.82/4.02 ! [N2: nat] :
% 3.82/4.02 ( ( nat_triangle @ ( suc @ N2 ) )
% 3.82/4.02 = ( plus_plus_nat @ ( nat_triangle @ N2 ) @ ( suc @ N2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % triangle_Suc
% 3.82/4.02 thf(fact_1439_complete__interval,axiom,
% 3.82/4.02 ! [A: extended_enat,B2: extended_enat,P: extended_enat > $o] :
% 3.82/4.02 ( ( ord_le72135733267957522d_enat @ A @ B2 )
% 3.82/4.02 => ( ( P @ A )
% 3.82/4.02 => ( ~ ( P @ B2 )
% 3.82/4.02 => ? [C2: extended_enat] :
% 3.82/4.02 ( ( ord_le2932123472753598470d_enat @ A @ C2 )
% 3.82/4.02 & ( ord_le2932123472753598470d_enat @ C2 @ B2 )
% 3.82/4.02 & ! [X2: extended_enat] :
% 3.82/4.02 ( ( ( ord_le2932123472753598470d_enat @ A @ X2 )
% 3.82/4.02 & ( ord_le72135733267957522d_enat @ X2 @ C2 ) )
% 3.82/4.02 => ( P @ X2 ) )
% 3.82/4.02 & ! [D3: extended_enat] :
% 3.82/4.02 ( ! [X5: extended_enat] :
% 3.82/4.02 ( ( ( ord_le2932123472753598470d_enat @ A @ X5 )
% 3.82/4.02 & ( ord_le72135733267957522d_enat @ X5 @ D3 ) )
% 3.82/4.02 => ( P @ X5 ) )
% 3.82/4.02 => ( ord_le2932123472753598470d_enat @ D3 @ C2 ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % complete_interval
% 3.82/4.02 thf(fact_1440_complete__interval,axiom,
% 3.82/4.02 ! [A: real,B2: real,P: real > $o] :
% 3.82/4.02 ( ( ord_less_real @ A @ B2 )
% 3.82/4.02 => ( ( P @ A )
% 3.82/4.02 => ( ~ ( P @ B2 )
% 3.82/4.02 => ? [C2: real] :
% 3.82/4.02 ( ( ord_less_eq_real @ A @ C2 )
% 3.82/4.02 & ( ord_less_eq_real @ C2 @ B2 )
% 3.82/4.02 & ! [X2: real] :
% 3.82/4.02 ( ( ( ord_less_eq_real @ A @ X2 )
% 3.82/4.02 & ( ord_less_real @ X2 @ C2 ) )
% 3.82/4.02 => ( P @ X2 ) )
% 3.82/4.02 & ! [D3: real] :
% 3.82/4.02 ( ! [X5: real] :
% 3.82/4.02 ( ( ( ord_less_eq_real @ A @ X5 )
% 3.82/4.02 & ( ord_less_real @ X5 @ D3 ) )
% 3.82/4.02 => ( P @ X5 ) )
% 3.82/4.02 => ( ord_less_eq_real @ D3 @ C2 ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % complete_interval
% 3.82/4.02 thf(fact_1441_complete__interval,axiom,
% 3.82/4.02 ! [A: nat,B2: nat,P: nat > $o] :
% 3.82/4.02 ( ( ord_less_nat @ A @ B2 )
% 3.82/4.02 => ( ( P @ A )
% 3.82/4.02 => ( ~ ( P @ B2 )
% 3.82/4.02 => ? [C2: nat] :
% 3.82/4.02 ( ( ord_less_eq_nat @ A @ C2 )
% 3.82/4.02 & ( ord_less_eq_nat @ C2 @ B2 )
% 3.82/4.02 & ! [X2: nat] :
% 3.82/4.02 ( ( ( ord_less_eq_nat @ A @ X2 )
% 3.82/4.02 & ( ord_less_nat @ X2 @ C2 ) )
% 3.82/4.02 => ( P @ X2 ) )
% 3.82/4.02 & ! [D3: nat] :
% 3.82/4.02 ( ! [X5: nat] :
% 3.82/4.02 ( ( ( ord_less_eq_nat @ A @ X5 )
% 3.82/4.02 & ( ord_less_nat @ X5 @ D3 ) )
% 3.82/4.02 => ( P @ X5 ) )
% 3.82/4.02 => ( ord_less_eq_nat @ D3 @ C2 ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % complete_interval
% 3.82/4.02 thf(fact_1442_complete__interval,axiom,
% 3.82/4.02 ! [A: int,B2: int,P: int > $o] :
% 3.82/4.02 ( ( ord_less_int @ A @ B2 )
% 3.82/4.02 => ( ( P @ A )
% 3.82/4.02 => ( ~ ( P @ B2 )
% 3.82/4.02 => ? [C2: int] :
% 3.82/4.02 ( ( ord_less_eq_int @ A @ C2 )
% 3.82/4.02 & ( ord_less_eq_int @ C2 @ B2 )
% 3.82/4.02 & ! [X2: int] :
% 3.82/4.02 ( ( ( ord_less_eq_int @ A @ X2 )
% 3.82/4.02 & ( ord_less_int @ X2 @ C2 ) )
% 3.82/4.02 => ( P @ X2 ) )
% 3.82/4.02 & ! [D3: int] :
% 3.82/4.02 ( ! [X5: int] :
% 3.82/4.02 ( ( ( ord_less_eq_int @ A @ X5 )
% 3.82/4.02 & ( ord_less_int @ X5 @ D3 ) )
% 3.82/4.02 => ( P @ X5 ) )
% 3.82/4.02 => ( ord_less_eq_int @ D3 @ C2 ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % complete_interval
% 3.82/4.02 thf(fact_1443_pinf_I6_J,axiom,
% 3.82/4.02 ! [T: extended_enat] :
% 3.82/4.02 ? [Z: extended_enat] :
% 3.82/4.02 ! [X2: extended_enat] :
% 3.82/4.02 ( ( ord_le72135733267957522d_enat @ Z @ X2 )
% 3.82/4.02 => ~ ( ord_le2932123472753598470d_enat @ X2 @ T ) ) ).
% 3.82/4.02
% 3.82/4.02 % pinf(6)
% 3.82/4.02 thf(fact_1444_pinf_I6_J,axiom,
% 3.82/4.02 ! [T: real] :
% 3.82/4.02 ? [Z: real] :
% 3.82/4.02 ! [X2: real] :
% 3.82/4.02 ( ( ord_less_real @ Z @ X2 )
% 3.82/4.02 => ~ ( ord_less_eq_real @ X2 @ T ) ) ).
% 3.82/4.02
% 3.82/4.02 % pinf(6)
% 3.82/4.02 thf(fact_1445_pinf_I6_J,axiom,
% 3.82/4.02 ! [T: nat] :
% 3.82/4.02 ? [Z: nat] :
% 3.82/4.02 ! [X2: nat] :
% 3.82/4.02 ( ( ord_less_nat @ Z @ X2 )
% 3.82/4.02 => ~ ( ord_less_eq_nat @ X2 @ T ) ) ).
% 3.82/4.02
% 3.82/4.02 % pinf(6)
% 3.82/4.02 thf(fact_1446_pinf_I6_J,axiom,
% 3.82/4.02 ! [T: int] :
% 3.82/4.02 ? [Z: int] :
% 3.82/4.02 ! [X2: int] :
% 3.82/4.02 ( ( ord_less_int @ Z @ X2 )
% 3.82/4.02 => ~ ( ord_less_eq_int @ X2 @ T ) ) ).
% 3.82/4.02
% 3.82/4.02 % pinf(6)
% 3.82/4.02 thf(fact_1447_pinf_I8_J,axiom,
% 3.82/4.02 ! [T: extended_enat] :
% 3.82/4.02 ? [Z: extended_enat] :
% 3.82/4.02 ! [X2: extended_enat] :
% 3.82/4.02 ( ( ord_le72135733267957522d_enat @ Z @ X2 )
% 3.82/4.02 => ( ord_le2932123472753598470d_enat @ T @ X2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % pinf(8)
% 3.82/4.02 thf(fact_1448_pinf_I8_J,axiom,
% 3.82/4.02 ! [T: real] :
% 3.82/4.02 ? [Z: real] :
% 3.82/4.02 ! [X2: real] :
% 3.82/4.02 ( ( ord_less_real @ Z @ X2 )
% 3.82/4.02 => ( ord_less_eq_real @ T @ X2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % pinf(8)
% 3.82/4.02 thf(fact_1449_pinf_I8_J,axiom,
% 3.82/4.02 ! [T: nat] :
% 3.82/4.02 ? [Z: nat] :
% 3.82/4.02 ! [X2: nat] :
% 3.82/4.02 ( ( ord_less_nat @ Z @ X2 )
% 3.82/4.02 => ( ord_less_eq_nat @ T @ X2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % pinf(8)
% 3.82/4.02 thf(fact_1450_pinf_I8_J,axiom,
% 3.82/4.02 ! [T: int] :
% 3.82/4.02 ? [Z: int] :
% 3.82/4.02 ! [X2: int] :
% 3.82/4.02 ( ( ord_less_int @ Z @ X2 )
% 3.82/4.02 => ( ord_less_eq_int @ T @ X2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % pinf(8)
% 3.82/4.02 thf(fact_1451_minf_I6_J,axiom,
% 3.82/4.02 ! [T: extended_enat] :
% 3.82/4.02 ? [Z: extended_enat] :
% 3.82/4.02 ! [X2: extended_enat] :
% 3.82/4.02 ( ( ord_le72135733267957522d_enat @ X2 @ Z )
% 3.82/4.02 => ( ord_le2932123472753598470d_enat @ X2 @ T ) ) ).
% 3.82/4.02
% 3.82/4.02 % minf(6)
% 3.82/4.02 thf(fact_1452_minf_I6_J,axiom,
% 3.82/4.02 ! [T: real] :
% 3.82/4.02 ? [Z: real] :
% 3.82/4.02 ! [X2: real] :
% 3.82/4.02 ( ( ord_less_real @ X2 @ Z )
% 3.82/4.02 => ( ord_less_eq_real @ X2 @ T ) ) ).
% 3.82/4.02
% 3.82/4.02 % minf(6)
% 3.82/4.02 thf(fact_1453_minf_I6_J,axiom,
% 3.82/4.02 ! [T: nat] :
% 3.82/4.02 ? [Z: nat] :
% 3.82/4.02 ! [X2: nat] :
% 3.82/4.02 ( ( ord_less_nat @ X2 @ Z )
% 3.82/4.02 => ( ord_less_eq_nat @ X2 @ T ) ) ).
% 3.82/4.02
% 3.82/4.02 % minf(6)
% 3.82/4.02 thf(fact_1454_minf_I6_J,axiom,
% 3.82/4.02 ! [T: int] :
% 3.82/4.02 ? [Z: int] :
% 3.82/4.02 ! [X2: int] :
% 3.82/4.02 ( ( ord_less_int @ X2 @ Z )
% 3.82/4.02 => ( ord_less_eq_int @ X2 @ T ) ) ).
% 3.82/4.02
% 3.82/4.02 % minf(6)
% 3.82/4.02 thf(fact_1455_minf_I8_J,axiom,
% 3.82/4.02 ! [T: extended_enat] :
% 3.82/4.02 ? [Z: extended_enat] :
% 3.82/4.02 ! [X2: extended_enat] :
% 3.82/4.02 ( ( ord_le72135733267957522d_enat @ X2 @ Z )
% 3.82/4.02 => ~ ( ord_le2932123472753598470d_enat @ T @ X2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % minf(8)
% 3.82/4.02 thf(fact_1456_minf_I8_J,axiom,
% 3.82/4.02 ! [T: real] :
% 3.82/4.02 ? [Z: real] :
% 3.82/4.02 ! [X2: real] :
% 3.82/4.02 ( ( ord_less_real @ X2 @ Z )
% 3.82/4.02 => ~ ( ord_less_eq_real @ T @ X2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % minf(8)
% 3.82/4.02 thf(fact_1457_minf_I8_J,axiom,
% 3.82/4.02 ! [T: nat] :
% 3.82/4.02 ? [Z: nat] :
% 3.82/4.02 ! [X2: nat] :
% 3.82/4.02 ( ( ord_less_nat @ X2 @ Z )
% 3.82/4.02 => ~ ( ord_less_eq_nat @ T @ X2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % minf(8)
% 3.82/4.02 thf(fact_1458_minf_I8_J,axiom,
% 3.82/4.02 ! [T: int] :
% 3.82/4.02 ? [Z: int] :
% 3.82/4.02 ! [X2: int] :
% 3.82/4.02 ( ( ord_less_int @ X2 @ Z )
% 3.82/4.02 => ~ ( ord_less_eq_int @ T @ X2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % minf(8)
% 3.82/4.02 thf(fact_1459_count__notin,axiom,
% 3.82/4.02 ! [X: extended_enat,Xs: list_Extended_enat] :
% 3.82/4.02 ( ~ ( member_Extended_enat @ X @ ( set_Extended_enat2 @ Xs ) )
% 3.82/4.02 => ( ( count_101369445342291426d_enat @ Xs @ X )
% 3.82/4.02 = zero_zero_nat ) ) ).
% 3.82/4.02
% 3.82/4.02 % count_notin
% 3.82/4.02 thf(fact_1460_count__notin,axiom,
% 3.82/4.02 ! [X: real,Xs: list_real] :
% 3.82/4.02 ( ~ ( member_real @ X @ ( set_real2 @ Xs ) )
% 3.82/4.02 => ( ( count_list_real @ Xs @ X )
% 3.82/4.02 = zero_zero_nat ) ) ).
% 3.82/4.02
% 3.82/4.02 % count_notin
% 3.82/4.02 thf(fact_1461_count__notin,axiom,
% 3.82/4.02 ! [X: set_nat,Xs: list_set_nat] :
% 3.82/4.02 ( ~ ( member_set_nat @ X @ ( set_set_nat2 @ Xs ) )
% 3.82/4.02 => ( ( count_list_set_nat @ Xs @ X )
% 3.82/4.02 = zero_zero_nat ) ) ).
% 3.82/4.02
% 3.82/4.02 % count_notin
% 3.82/4.02 thf(fact_1462_count__notin,axiom,
% 3.82/4.02 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 3.82/4.02 ( ~ ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 3.82/4.02 => ( ( count_list_VEBT_VEBT @ Xs @ X )
% 3.82/4.02 = zero_zero_nat ) ) ).
% 3.82/4.02
% 3.82/4.02 % count_notin
% 3.82/4.02 thf(fact_1463_count__notin,axiom,
% 3.82/4.02 ! [X: int,Xs: list_int] :
% 3.82/4.02 ( ~ ( member_int @ X @ ( set_int2 @ Xs ) )
% 3.82/4.02 => ( ( count_list_int @ Xs @ X )
% 3.82/4.02 = zero_zero_nat ) ) ).
% 3.82/4.02
% 3.82/4.02 % count_notin
% 3.82/4.02 thf(fact_1464_count__notin,axiom,
% 3.82/4.02 ! [X: nat,Xs: list_nat] :
% 3.82/4.02 ( ~ ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 3.82/4.02 => ( ( count_list_nat @ Xs @ X )
% 3.82/4.02 = zero_zero_nat ) ) ).
% 3.82/4.02
% 3.82/4.02 % count_notin
% 3.82/4.02 thf(fact_1465__C10_C,axiom,
% 3.82/4.02 ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
% 3.82/4.02 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ xa @ ( ord_max_nat @ mi @ ma ) ) ) @ deg @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) @ ( vEBT_VEBT_low @ mi @ na ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) ) @ ( vEBT_vebt_insert @ summary @ ( vEBT_VEBT_high @ mi @ na ) ) @ summary ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % "10"
% 3.82/4.02 thf(fact_1466_deg__deg__n,axiom,
% 3.82/4.02 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N2: nat] :
% 3.82/4.02 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ N2 )
% 3.82/4.02 => ( Deg = N2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % deg_deg_n
% 3.82/4.02 thf(fact_1467_deg__SUcn__Node,axiom,
% 3.82/4.02 ! [Tree: vEBT_VEBT,N2: nat] :
% 3.82/4.02 ( ( vEBT_invar_vebt @ Tree @ ( suc @ ( suc @ N2 ) ) )
% 3.82/4.02 => ? [Info2: option4927543243414619207at_nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 3.82/4.02 ( Tree
% 3.82/4.02 = ( vEBT_Node @ Info2 @ ( suc @ ( suc @ N2 ) ) @ TreeList3 @ S3 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % deg_SUcn_Node
% 3.82/4.02 thf(fact_1468_mi__eq__ma__no__ch,axiom,
% 3.82/4.02 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 3.82/4.02 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg )
% 3.82/4.02 => ( ( Mi = Ma )
% 3.82/4.02 => ( ! [X2: vEBT_VEBT] :
% 3.82/4.02 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 3.82/4.02 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X_1 ) )
% 3.82/4.02 & ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % mi_eq_ma_no_ch
% 3.82/4.02 thf(fact_1469_max__bot2,axiom,
% 3.82/4.02 ! [X: set_Extended_enat] :
% 3.82/4.02 ( ( ord_ma4205026669011143323d_enat @ X @ bot_bo7653980558646680370d_enat )
% 3.82/4.02 = X ) ).
% 3.82/4.02
% 3.82/4.02 % max_bot2
% 3.82/4.02 thf(fact_1470_max__bot2,axiom,
% 3.82/4.02 ! [X: set_real] :
% 3.82/4.02 ( ( ord_max_set_real @ X @ bot_bot_set_real )
% 3.82/4.02 = X ) ).
% 3.82/4.02
% 3.82/4.02 % max_bot2
% 3.82/4.02 thf(fact_1471_max__bot2,axiom,
% 3.82/4.02 ! [X: set_nat] :
% 3.82/4.02 ( ( ord_max_set_nat @ X @ bot_bot_set_nat )
% 3.82/4.02 = X ) ).
% 3.82/4.02
% 3.82/4.02 % max_bot2
% 3.82/4.02 thf(fact_1472_max__bot2,axiom,
% 3.82/4.02 ! [X: set_int] :
% 3.82/4.02 ( ( ord_max_set_int @ X @ bot_bot_set_int )
% 3.82/4.02 = X ) ).
% 3.82/4.02
% 3.82/4.02 % max_bot2
% 3.82/4.02 thf(fact_1473_max__bot2,axiom,
% 3.82/4.02 ! [X: nat] :
% 3.82/4.02 ( ( ord_max_nat @ X @ bot_bot_nat )
% 3.82/4.02 = X ) ).
% 3.82/4.02
% 3.82/4.02 % max_bot2
% 3.82/4.02 thf(fact_1474_max__bot,axiom,
% 3.82/4.02 ! [X: set_Extended_enat] :
% 3.82/4.02 ( ( ord_ma4205026669011143323d_enat @ bot_bo7653980558646680370d_enat @ X )
% 3.82/4.02 = X ) ).
% 3.82/4.02
% 3.82/4.02 % max_bot
% 3.82/4.02 thf(fact_1475_max__bot,axiom,
% 3.82/4.02 ! [X: set_real] :
% 3.82/4.02 ( ( ord_max_set_real @ bot_bot_set_real @ X )
% 3.82/4.02 = X ) ).
% 3.82/4.02
% 3.82/4.02 % max_bot
% 3.82/4.02 thf(fact_1476_max__bot,axiom,
% 3.82/4.02 ! [X: set_nat] :
% 3.82/4.02 ( ( ord_max_set_nat @ bot_bot_set_nat @ X )
% 3.82/4.02 = X ) ).
% 3.82/4.02
% 3.82/4.02 % max_bot
% 3.82/4.02 thf(fact_1477_max__bot,axiom,
% 3.82/4.02 ! [X: set_int] :
% 3.82/4.02 ( ( ord_max_set_int @ bot_bot_set_int @ X )
% 3.82/4.02 = X ) ).
% 3.82/4.02
% 3.82/4.02 % max_bot
% 3.82/4.02 thf(fact_1478_max__bot,axiom,
% 3.82/4.02 ! [X: nat] :
% 3.82/4.02 ( ( ord_max_nat @ bot_bot_nat @ X )
% 3.82/4.02 = X ) ).
% 3.82/4.02
% 3.82/4.02 % max_bot
% 3.82/4.02 thf(fact_1479_max__Suc__Suc,axiom,
% 3.82/4.02 ! [M2: nat,N2: nat] :
% 3.82/4.02 ( ( ord_max_nat @ ( suc @ M2 ) @ ( suc @ N2 ) )
% 3.82/4.02 = ( suc @ ( ord_max_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max_Suc_Suc
% 3.82/4.02 thf(fact_1480_max__nat_Oeq__neutr__iff,axiom,
% 3.82/4.02 ! [A: nat,B2: nat] :
% 3.82/4.02 ( ( ( ord_max_nat @ A @ B2 )
% 3.82/4.02 = zero_zero_nat )
% 3.82/4.02 = ( ( A = zero_zero_nat )
% 3.82/4.02 & ( B2 = zero_zero_nat ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max_nat.eq_neutr_iff
% 3.82/4.02 thf(fact_1481_max__nat_Oleft__neutral,axiom,
% 3.82/4.02 ! [A: nat] :
% 3.82/4.02 ( ( ord_max_nat @ zero_zero_nat @ A )
% 3.82/4.02 = A ) ).
% 3.82/4.02
% 3.82/4.02 % max_nat.left_neutral
% 3.82/4.02 thf(fact_1482_max__nat_Oneutr__eq__iff,axiom,
% 3.82/4.02 ! [A: nat,B2: nat] :
% 3.82/4.02 ( ( zero_zero_nat
% 3.82/4.02 = ( ord_max_nat @ A @ B2 ) )
% 3.82/4.02 = ( ( A = zero_zero_nat )
% 3.82/4.02 & ( B2 = zero_zero_nat ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max_nat.neutr_eq_iff
% 3.82/4.02 thf(fact_1483_max__nat_Oright__neutral,axiom,
% 3.82/4.02 ! [A: nat] :
% 3.82/4.02 ( ( ord_max_nat @ A @ zero_zero_nat )
% 3.82/4.02 = A ) ).
% 3.82/4.02
% 3.82/4.02 % max_nat.right_neutral
% 3.82/4.02 thf(fact_1484_max__0L,axiom,
% 3.82/4.02 ! [N2: nat] :
% 3.82/4.02 ( ( ord_max_nat @ zero_zero_nat @ N2 )
% 3.82/4.02 = N2 ) ).
% 3.82/4.02
% 3.82/4.02 % max_0L
% 3.82/4.02 thf(fact_1485_max__0R,axiom,
% 3.82/4.02 ! [N2: nat] :
% 3.82/4.02 ( ( ord_max_nat @ N2 @ zero_zero_nat )
% 3.82/4.02 = N2 ) ).
% 3.82/4.02
% 3.82/4.02 % max_0R
% 3.82/4.02 thf(fact_1486_triangle__0,axiom,
% 3.82/4.02 ( ( nat_triangle @ zero_zero_nat )
% 3.82/4.02 = zero_zero_nat ) ).
% 3.82/4.02
% 3.82/4.02 % triangle_0
% 3.82/4.02 thf(fact_1487_VEBT__internal_Omembermima_Osimps_I3_J,axiom,
% 3.82/4.02 ! [Mi: nat,Ma: nat,Va2: list_VEBT_VEBT,Vb: vEBT_VEBT,X: nat] :
% 3.82/4.02 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ Va2 @ Vb ) @ X )
% 3.82/4.02 = ( ( X = Mi )
% 3.82/4.02 | ( X = Ma ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % VEBT_internal.membermima.simps(3)
% 3.82/4.02 thf(fact_1488_max__def,axiom,
% 3.82/4.02 ( ord_max_real
% 3.82/4.02 = ( ^ [A3: real,B3: real] : ( if_real @ ( ord_less_eq_real @ A3 @ B3 ) @ B3 @ A3 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max_def
% 3.82/4.02 thf(fact_1489_max__def,axiom,
% 3.82/4.02 ( ord_max_set_nat
% 3.82/4.02 = ( ^ [A3: set_nat,B3: set_nat] : ( if_set_nat @ ( ord_less_eq_set_nat @ A3 @ B3 ) @ B3 @ A3 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max_def
% 3.82/4.02 thf(fact_1490_max__def,axiom,
% 3.82/4.02 ( ord_max_set_int
% 3.82/4.02 = ( ^ [A3: set_int,B3: set_int] : ( if_set_int @ ( ord_less_eq_set_int @ A3 @ B3 ) @ B3 @ A3 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max_def
% 3.82/4.02 thf(fact_1491_max__def,axiom,
% 3.82/4.02 ( ord_max_nat
% 3.82/4.02 = ( ^ [A3: nat,B3: nat] : ( if_nat @ ( ord_less_eq_nat @ A3 @ B3 ) @ B3 @ A3 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max_def
% 3.82/4.02 thf(fact_1492_max__def,axiom,
% 3.82/4.02 ( ord_max_int
% 3.82/4.02 = ( ^ [A3: int,B3: int] : ( if_int @ ( ord_less_eq_int @ A3 @ B3 ) @ B3 @ A3 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max_def
% 3.82/4.02 thf(fact_1493_max__absorb1,axiom,
% 3.82/4.02 ! [Y: real,X: real] :
% 3.82/4.02 ( ( ord_less_eq_real @ Y @ X )
% 3.82/4.02 => ( ( ord_max_real @ X @ Y )
% 3.82/4.02 = X ) ) ).
% 3.82/4.02
% 3.82/4.02 % max_absorb1
% 3.82/4.02 thf(fact_1494_max__absorb1,axiom,
% 3.82/4.02 ! [Y: set_nat,X: set_nat] :
% 3.82/4.02 ( ( ord_less_eq_set_nat @ Y @ X )
% 3.82/4.02 => ( ( ord_max_set_nat @ X @ Y )
% 3.82/4.02 = X ) ) ).
% 3.82/4.02
% 3.82/4.02 % max_absorb1
% 3.82/4.02 thf(fact_1495_max__absorb1,axiom,
% 3.82/4.02 ! [Y: set_int,X: set_int] :
% 3.82/4.02 ( ( ord_less_eq_set_int @ Y @ X )
% 3.82/4.02 => ( ( ord_max_set_int @ X @ Y )
% 3.82/4.02 = X ) ) ).
% 3.82/4.02
% 3.82/4.02 % max_absorb1
% 3.82/4.02 thf(fact_1496_max__absorb1,axiom,
% 3.82/4.02 ! [Y: nat,X: nat] :
% 3.82/4.02 ( ( ord_less_eq_nat @ Y @ X )
% 3.82/4.02 => ( ( ord_max_nat @ X @ Y )
% 3.82/4.02 = X ) ) ).
% 3.82/4.02
% 3.82/4.02 % max_absorb1
% 3.82/4.02 thf(fact_1497_max__absorb1,axiom,
% 3.82/4.02 ! [Y: int,X: int] :
% 3.82/4.02 ( ( ord_less_eq_int @ Y @ X )
% 3.82/4.02 => ( ( ord_max_int @ X @ Y )
% 3.82/4.02 = X ) ) ).
% 3.82/4.02
% 3.82/4.02 % max_absorb1
% 3.82/4.02 thf(fact_1498_max__absorb2,axiom,
% 3.82/4.02 ! [X: real,Y: real] :
% 3.82/4.02 ( ( ord_less_eq_real @ X @ Y )
% 3.82/4.02 => ( ( ord_max_real @ X @ Y )
% 3.82/4.02 = Y ) ) ).
% 3.82/4.02
% 3.82/4.02 % max_absorb2
% 3.82/4.02 thf(fact_1499_max__absorb2,axiom,
% 3.82/4.02 ! [X: set_nat,Y: set_nat] :
% 3.82/4.02 ( ( ord_less_eq_set_nat @ X @ Y )
% 3.82/4.02 => ( ( ord_max_set_nat @ X @ Y )
% 3.82/4.02 = Y ) ) ).
% 3.82/4.02
% 3.82/4.02 % max_absorb2
% 3.82/4.02 thf(fact_1500_max__absorb2,axiom,
% 3.82/4.02 ! [X: set_int,Y: set_int] :
% 3.82/4.02 ( ( ord_less_eq_set_int @ X @ Y )
% 3.82/4.02 => ( ( ord_max_set_int @ X @ Y )
% 3.82/4.02 = Y ) ) ).
% 3.82/4.02
% 3.82/4.02 % max_absorb2
% 3.82/4.02 thf(fact_1501_max__absorb2,axiom,
% 3.82/4.02 ! [X: nat,Y: nat] :
% 3.82/4.02 ( ( ord_less_eq_nat @ X @ Y )
% 3.82/4.02 => ( ( ord_max_nat @ X @ Y )
% 3.82/4.02 = Y ) ) ).
% 3.82/4.02
% 3.82/4.02 % max_absorb2
% 3.82/4.02 thf(fact_1502_max__absorb2,axiom,
% 3.82/4.02 ! [X: int,Y: int] :
% 3.82/4.02 ( ( ord_less_eq_int @ X @ Y )
% 3.82/4.02 => ( ( ord_max_int @ X @ Y )
% 3.82/4.02 = Y ) ) ).
% 3.82/4.02
% 3.82/4.02 % max_absorb2
% 3.82/4.02 thf(fact_1503_max__add__distrib__left,axiom,
% 3.82/4.02 ! [X: real,Y: real,Z3: real] :
% 3.82/4.02 ( ( plus_plus_real @ ( ord_max_real @ X @ Y ) @ Z3 )
% 3.82/4.02 = ( ord_max_real @ ( plus_plus_real @ X @ Z3 ) @ ( plus_plus_real @ Y @ Z3 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max_add_distrib_left
% 3.82/4.02 thf(fact_1504_max__add__distrib__left,axiom,
% 3.82/4.02 ! [X: nat,Y: nat,Z3: nat] :
% 3.82/4.02 ( ( plus_plus_nat @ ( ord_max_nat @ X @ Y ) @ Z3 )
% 3.82/4.02 = ( ord_max_nat @ ( plus_plus_nat @ X @ Z3 ) @ ( plus_plus_nat @ Y @ Z3 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max_add_distrib_left
% 3.82/4.02 thf(fact_1505_max__add__distrib__left,axiom,
% 3.82/4.02 ! [X: int,Y: int,Z3: int] :
% 3.82/4.02 ( ( plus_plus_int @ ( ord_max_int @ X @ Y ) @ Z3 )
% 3.82/4.02 = ( ord_max_int @ ( plus_plus_int @ X @ Z3 ) @ ( plus_plus_int @ Y @ Z3 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max_add_distrib_left
% 3.82/4.02 thf(fact_1506_max__add__distrib__right,axiom,
% 3.82/4.02 ! [X: real,Y: real,Z3: real] :
% 3.82/4.02 ( ( plus_plus_real @ X @ ( ord_max_real @ Y @ Z3 ) )
% 3.82/4.02 = ( ord_max_real @ ( plus_plus_real @ X @ Y ) @ ( plus_plus_real @ X @ Z3 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max_add_distrib_right
% 3.82/4.02 thf(fact_1507_max__add__distrib__right,axiom,
% 3.82/4.02 ! [X: nat,Y: nat,Z3: nat] :
% 3.82/4.02 ( ( plus_plus_nat @ X @ ( ord_max_nat @ Y @ Z3 ) )
% 3.82/4.02 = ( ord_max_nat @ ( plus_plus_nat @ X @ Y ) @ ( plus_plus_nat @ X @ Z3 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max_add_distrib_right
% 3.82/4.02 thf(fact_1508_max__add__distrib__right,axiom,
% 3.82/4.02 ! [X: int,Y: int,Z3: int] :
% 3.82/4.02 ( ( plus_plus_int @ X @ ( ord_max_int @ Y @ Z3 ) )
% 3.82/4.02 = ( ord_max_int @ ( plus_plus_int @ X @ Y ) @ ( plus_plus_int @ X @ Z3 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max_add_distrib_right
% 3.82/4.02 thf(fact_1509_nat__add__max__left,axiom,
% 3.82/4.02 ! [M2: nat,N2: nat,Q3: nat] :
% 3.82/4.02 ( ( plus_plus_nat @ ( ord_max_nat @ M2 @ N2 ) @ Q3 )
% 3.82/4.02 = ( ord_max_nat @ ( plus_plus_nat @ M2 @ Q3 ) @ ( plus_plus_nat @ N2 @ Q3 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % nat_add_max_left
% 3.82/4.02 thf(fact_1510_nat__add__max__right,axiom,
% 3.82/4.02 ! [M2: nat,N2: nat,Q3: nat] :
% 3.82/4.02 ( ( plus_plus_nat @ M2 @ ( ord_max_nat @ N2 @ Q3 ) )
% 3.82/4.02 = ( ord_max_nat @ ( plus_plus_nat @ M2 @ N2 ) @ ( plus_plus_nat @ M2 @ Q3 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % nat_add_max_right
% 3.82/4.02 thf(fact_1511_VEBT__internal_Onaive__member_Osimps_I2_J,axiom,
% 3.82/4.02 ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,Ux: nat] :
% 3.82/4.02 ~ ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) @ Ux ) ).
% 3.82/4.02
% 3.82/4.02 % VEBT_internal.naive_member.simps(2)
% 3.82/4.02 thf(fact_1512_minf_I7_J,axiom,
% 3.82/4.02 ! [T: nat] :
% 3.82/4.02 ? [Z: nat] :
% 3.82/4.02 ! [X2: nat] :
% 3.82/4.02 ( ( ord_less_nat @ X2 @ Z )
% 3.82/4.02 => ~ ( ord_less_nat @ T @ X2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % minf(7)
% 3.82/4.02 thf(fact_1513_minf_I7_J,axiom,
% 3.82/4.02 ! [T: extended_enat] :
% 3.82/4.02 ? [Z: extended_enat] :
% 3.82/4.02 ! [X2: extended_enat] :
% 3.82/4.02 ( ( ord_le72135733267957522d_enat @ X2 @ Z )
% 3.82/4.02 => ~ ( ord_le72135733267957522d_enat @ T @ X2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % minf(7)
% 3.82/4.02 thf(fact_1514_minf_I7_J,axiom,
% 3.82/4.02 ! [T: real] :
% 3.82/4.02 ? [Z: real] :
% 3.82/4.02 ! [X2: real] :
% 3.82/4.02 ( ( ord_less_real @ X2 @ Z )
% 3.82/4.02 => ~ ( ord_less_real @ T @ X2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % minf(7)
% 3.82/4.02 thf(fact_1515_minf_I7_J,axiom,
% 3.82/4.02 ! [T: int] :
% 3.82/4.02 ? [Z: int] :
% 3.82/4.02 ! [X2: int] :
% 3.82/4.02 ( ( ord_less_int @ X2 @ Z )
% 3.82/4.02 => ~ ( ord_less_int @ T @ X2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % minf(7)
% 3.82/4.02 thf(fact_1516_minf_I5_J,axiom,
% 3.82/4.02 ! [T: nat] :
% 3.82/4.02 ? [Z: nat] :
% 3.82/4.02 ! [X2: nat] :
% 3.82/4.02 ( ( ord_less_nat @ X2 @ Z )
% 3.82/4.02 => ( ord_less_nat @ X2 @ T ) ) ).
% 3.82/4.02
% 3.82/4.02 % minf(5)
% 3.82/4.02 thf(fact_1517_minf_I5_J,axiom,
% 3.82/4.02 ! [T: extended_enat] :
% 3.82/4.02 ? [Z: extended_enat] :
% 3.82/4.02 ! [X2: extended_enat] :
% 3.82/4.02 ( ( ord_le72135733267957522d_enat @ X2 @ Z )
% 3.82/4.02 => ( ord_le72135733267957522d_enat @ X2 @ T ) ) ).
% 3.82/4.02
% 3.82/4.02 % minf(5)
% 3.82/4.02 thf(fact_1518_minf_I5_J,axiom,
% 3.82/4.02 ! [T: real] :
% 3.82/4.02 ? [Z: real] :
% 3.82/4.02 ! [X2: real] :
% 3.82/4.02 ( ( ord_less_real @ X2 @ Z )
% 3.82/4.02 => ( ord_less_real @ X2 @ T ) ) ).
% 3.82/4.02
% 3.82/4.02 % minf(5)
% 3.82/4.02 thf(fact_1519_minf_I5_J,axiom,
% 3.82/4.02 ! [T: int] :
% 3.82/4.02 ? [Z: int] :
% 3.82/4.02 ! [X2: int] :
% 3.82/4.02 ( ( ord_less_int @ X2 @ Z )
% 3.82/4.02 => ( ord_less_int @ X2 @ T ) ) ).
% 3.82/4.02
% 3.82/4.02 % minf(5)
% 3.82/4.02 thf(fact_1520_minf_I4_J,axiom,
% 3.82/4.02 ! [T: nat] :
% 3.82/4.02 ? [Z: nat] :
% 3.82/4.02 ! [X2: nat] :
% 3.82/4.02 ( ( ord_less_nat @ X2 @ Z )
% 3.82/4.02 => ( X2 != T ) ) ).
% 3.82/4.02
% 3.82/4.02 % minf(4)
% 3.82/4.02 thf(fact_1521_minf_I4_J,axiom,
% 3.82/4.02 ! [T: extended_enat] :
% 3.82/4.02 ? [Z: extended_enat] :
% 3.82/4.02 ! [X2: extended_enat] :
% 3.82/4.02 ( ( ord_le72135733267957522d_enat @ X2 @ Z )
% 3.82/4.02 => ( X2 != T ) ) ).
% 3.82/4.02
% 3.82/4.02 % minf(4)
% 3.82/4.02 thf(fact_1522_minf_I4_J,axiom,
% 3.82/4.02 ! [T: real] :
% 3.82/4.02 ? [Z: real] :
% 3.82/4.02 ! [X2: real] :
% 3.82/4.02 ( ( ord_less_real @ X2 @ Z )
% 3.82/4.02 => ( X2 != T ) ) ).
% 3.82/4.02
% 3.82/4.02 % minf(4)
% 3.82/4.02 thf(fact_1523_minf_I4_J,axiom,
% 3.82/4.02 ! [T: int] :
% 3.82/4.02 ? [Z: int] :
% 3.82/4.02 ! [X2: int] :
% 3.82/4.02 ( ( ord_less_int @ X2 @ Z )
% 3.82/4.02 => ( X2 != T ) ) ).
% 3.82/4.02
% 3.82/4.02 % minf(4)
% 3.82/4.02 thf(fact_1524_minf_I3_J,axiom,
% 3.82/4.02 ! [T: nat] :
% 3.82/4.02 ? [Z: nat] :
% 3.82/4.02 ! [X2: nat] :
% 3.82/4.02 ( ( ord_less_nat @ X2 @ Z )
% 3.82/4.02 => ( X2 != T ) ) ).
% 3.82/4.02
% 3.82/4.02 % minf(3)
% 3.82/4.02 thf(fact_1525_minf_I3_J,axiom,
% 3.82/4.02 ! [T: extended_enat] :
% 3.82/4.02 ? [Z: extended_enat] :
% 3.82/4.02 ! [X2: extended_enat] :
% 3.82/4.02 ( ( ord_le72135733267957522d_enat @ X2 @ Z )
% 3.82/4.02 => ( X2 != T ) ) ).
% 3.82/4.02
% 3.82/4.02 % minf(3)
% 3.82/4.02 thf(fact_1526_minf_I3_J,axiom,
% 3.82/4.02 ! [T: real] :
% 3.82/4.02 ? [Z: real] :
% 3.82/4.02 ! [X2: real] :
% 3.82/4.02 ( ( ord_less_real @ X2 @ Z )
% 3.82/4.02 => ( X2 != T ) ) ).
% 3.82/4.02
% 3.82/4.02 % minf(3)
% 3.82/4.02 thf(fact_1527_minf_I3_J,axiom,
% 3.82/4.02 ! [T: int] :
% 3.82/4.02 ? [Z: int] :
% 3.82/4.02 ! [X2: int] :
% 3.82/4.02 ( ( ord_less_int @ X2 @ Z )
% 3.82/4.02 => ( X2 != T ) ) ).
% 3.82/4.02
% 3.82/4.02 % minf(3)
% 3.82/4.02 thf(fact_1528_minf_I2_J,axiom,
% 3.82/4.02 ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q4: nat > $o] :
% 3.82/4.02 ( ? [Z4: nat] :
% 3.82/4.02 ! [X5: nat] :
% 3.82/4.02 ( ( ord_less_nat @ X5 @ Z4 )
% 3.82/4.02 => ( ( P @ X5 )
% 3.82/4.02 = ( P4 @ X5 ) ) )
% 3.82/4.02 => ( ? [Z4: nat] :
% 3.82/4.02 ! [X5: nat] :
% 3.82/4.02 ( ( ord_less_nat @ X5 @ Z4 )
% 3.82/4.02 => ( ( Q @ X5 )
% 3.82/4.02 = ( Q4 @ X5 ) ) )
% 3.82/4.02 => ? [Z: nat] :
% 3.82/4.02 ! [X2: nat] :
% 3.82/4.02 ( ( ord_less_nat @ X2 @ Z )
% 3.82/4.02 => ( ( ( P @ X2 )
% 3.82/4.02 | ( Q @ X2 ) )
% 3.82/4.02 = ( ( P4 @ X2 )
% 3.82/4.02 | ( Q4 @ X2 ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % minf(2)
% 3.82/4.02 thf(fact_1529_minf_I2_J,axiom,
% 3.82/4.02 ! [P: extended_enat > $o,P4: extended_enat > $o,Q: extended_enat > $o,Q4: extended_enat > $o] :
% 3.82/4.02 ( ? [Z4: extended_enat] :
% 3.82/4.02 ! [X5: extended_enat] :
% 3.82/4.02 ( ( ord_le72135733267957522d_enat @ X5 @ Z4 )
% 3.82/4.02 => ( ( P @ X5 )
% 3.82/4.02 = ( P4 @ X5 ) ) )
% 3.82/4.02 => ( ? [Z4: extended_enat] :
% 3.82/4.02 ! [X5: extended_enat] :
% 3.82/4.02 ( ( ord_le72135733267957522d_enat @ X5 @ Z4 )
% 3.82/4.02 => ( ( Q @ X5 )
% 3.82/4.02 = ( Q4 @ X5 ) ) )
% 3.82/4.02 => ? [Z: extended_enat] :
% 3.82/4.02 ! [X2: extended_enat] :
% 3.82/4.02 ( ( ord_le72135733267957522d_enat @ X2 @ Z )
% 3.82/4.02 => ( ( ( P @ X2 )
% 3.82/4.02 | ( Q @ X2 ) )
% 3.82/4.02 = ( ( P4 @ X2 )
% 3.82/4.02 | ( Q4 @ X2 ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % minf(2)
% 3.82/4.02 thf(fact_1530_minf_I2_J,axiom,
% 3.82/4.02 ! [P: real > $o,P4: real > $o,Q: real > $o,Q4: real > $o] :
% 3.82/4.02 ( ? [Z4: real] :
% 3.82/4.02 ! [X5: real] :
% 3.82/4.02 ( ( ord_less_real @ X5 @ Z4 )
% 3.82/4.02 => ( ( P @ X5 )
% 3.82/4.02 = ( P4 @ X5 ) ) )
% 3.82/4.02 => ( ? [Z4: real] :
% 3.82/4.02 ! [X5: real] :
% 3.82/4.02 ( ( ord_less_real @ X5 @ Z4 )
% 3.82/4.02 => ( ( Q @ X5 )
% 3.82/4.02 = ( Q4 @ X5 ) ) )
% 3.82/4.02 => ? [Z: real] :
% 3.82/4.02 ! [X2: real] :
% 3.82/4.02 ( ( ord_less_real @ X2 @ Z )
% 3.82/4.02 => ( ( ( P @ X2 )
% 3.82/4.02 | ( Q @ X2 ) )
% 3.82/4.02 = ( ( P4 @ X2 )
% 3.82/4.02 | ( Q4 @ X2 ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % minf(2)
% 3.82/4.02 thf(fact_1531_minf_I2_J,axiom,
% 3.82/4.02 ! [P: int > $o,P4: int > $o,Q: int > $o,Q4: int > $o] :
% 3.82/4.02 ( ? [Z4: int] :
% 3.82/4.02 ! [X5: int] :
% 3.82/4.02 ( ( ord_less_int @ X5 @ Z4 )
% 3.82/4.02 => ( ( P @ X5 )
% 3.82/4.02 = ( P4 @ X5 ) ) )
% 3.82/4.02 => ( ? [Z4: int] :
% 3.82/4.02 ! [X5: int] :
% 3.82/4.02 ( ( ord_less_int @ X5 @ Z4 )
% 3.82/4.02 => ( ( Q @ X5 )
% 3.82/4.02 = ( Q4 @ X5 ) ) )
% 3.82/4.02 => ? [Z: int] :
% 3.82/4.02 ! [X2: int] :
% 3.82/4.02 ( ( ord_less_int @ X2 @ Z )
% 3.82/4.02 => ( ( ( P @ X2 )
% 3.82/4.02 | ( Q @ X2 ) )
% 3.82/4.02 = ( ( P4 @ X2 )
% 3.82/4.02 | ( Q4 @ X2 ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % minf(2)
% 3.82/4.02 thf(fact_1532_minf_I1_J,axiom,
% 3.82/4.02 ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q4: nat > $o] :
% 3.82/4.02 ( ? [Z4: nat] :
% 3.82/4.02 ! [X5: nat] :
% 3.82/4.02 ( ( ord_less_nat @ X5 @ Z4 )
% 3.82/4.02 => ( ( P @ X5 )
% 3.82/4.02 = ( P4 @ X5 ) ) )
% 3.82/4.02 => ( ? [Z4: nat] :
% 3.82/4.02 ! [X5: nat] :
% 3.82/4.02 ( ( ord_less_nat @ X5 @ Z4 )
% 3.82/4.02 => ( ( Q @ X5 )
% 3.82/4.02 = ( Q4 @ X5 ) ) )
% 3.82/4.02 => ? [Z: nat] :
% 3.82/4.02 ! [X2: nat] :
% 3.82/4.02 ( ( ord_less_nat @ X2 @ Z )
% 3.82/4.02 => ( ( ( P @ X2 )
% 3.82/4.02 & ( Q @ X2 ) )
% 3.82/4.02 = ( ( P4 @ X2 )
% 3.82/4.02 & ( Q4 @ X2 ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % minf(1)
% 3.82/4.02 thf(fact_1533_minf_I1_J,axiom,
% 3.82/4.02 ! [P: extended_enat > $o,P4: extended_enat > $o,Q: extended_enat > $o,Q4: extended_enat > $o] :
% 3.82/4.02 ( ? [Z4: extended_enat] :
% 3.82/4.02 ! [X5: extended_enat] :
% 3.82/4.02 ( ( ord_le72135733267957522d_enat @ X5 @ Z4 )
% 3.82/4.02 => ( ( P @ X5 )
% 3.82/4.02 = ( P4 @ X5 ) ) )
% 3.82/4.02 => ( ? [Z4: extended_enat] :
% 3.82/4.02 ! [X5: extended_enat] :
% 3.82/4.02 ( ( ord_le72135733267957522d_enat @ X5 @ Z4 )
% 3.82/4.02 => ( ( Q @ X5 )
% 3.82/4.02 = ( Q4 @ X5 ) ) )
% 3.82/4.02 => ? [Z: extended_enat] :
% 3.82/4.02 ! [X2: extended_enat] :
% 3.82/4.02 ( ( ord_le72135733267957522d_enat @ X2 @ Z )
% 3.82/4.02 => ( ( ( P @ X2 )
% 3.82/4.02 & ( Q @ X2 ) )
% 3.82/4.02 = ( ( P4 @ X2 )
% 3.82/4.02 & ( Q4 @ X2 ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % minf(1)
% 3.82/4.02 thf(fact_1534_minf_I1_J,axiom,
% 3.82/4.02 ! [P: real > $o,P4: real > $o,Q: real > $o,Q4: real > $o] :
% 3.82/4.02 ( ? [Z4: real] :
% 3.82/4.02 ! [X5: real] :
% 3.82/4.02 ( ( ord_less_real @ X5 @ Z4 )
% 3.82/4.02 => ( ( P @ X5 )
% 3.82/4.02 = ( P4 @ X5 ) ) )
% 3.82/4.02 => ( ? [Z4: real] :
% 3.82/4.02 ! [X5: real] :
% 3.82/4.02 ( ( ord_less_real @ X5 @ Z4 )
% 3.82/4.02 => ( ( Q @ X5 )
% 3.82/4.02 = ( Q4 @ X5 ) ) )
% 3.82/4.02 => ? [Z: real] :
% 3.82/4.02 ! [X2: real] :
% 3.82/4.02 ( ( ord_less_real @ X2 @ Z )
% 3.82/4.02 => ( ( ( P @ X2 )
% 3.82/4.02 & ( Q @ X2 ) )
% 3.82/4.02 = ( ( P4 @ X2 )
% 3.82/4.02 & ( Q4 @ X2 ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % minf(1)
% 3.82/4.02 thf(fact_1535_minf_I1_J,axiom,
% 3.82/4.02 ! [P: int > $o,P4: int > $o,Q: int > $o,Q4: int > $o] :
% 3.82/4.02 ( ? [Z4: int] :
% 3.82/4.02 ! [X5: int] :
% 3.82/4.02 ( ( ord_less_int @ X5 @ Z4 )
% 3.82/4.02 => ( ( P @ X5 )
% 3.82/4.02 = ( P4 @ X5 ) ) )
% 3.82/4.02 => ( ? [Z4: int] :
% 3.82/4.02 ! [X5: int] :
% 3.82/4.02 ( ( ord_less_int @ X5 @ Z4 )
% 3.82/4.02 => ( ( Q @ X5 )
% 3.82/4.02 = ( Q4 @ X5 ) ) )
% 3.82/4.02 => ? [Z: int] :
% 3.82/4.02 ! [X2: int] :
% 3.82/4.02 ( ( ord_less_int @ X2 @ Z )
% 3.82/4.02 => ( ( ( P @ X2 )
% 3.82/4.02 & ( Q @ X2 ) )
% 3.82/4.02 = ( ( P4 @ X2 )
% 3.82/4.02 & ( Q4 @ X2 ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % minf(1)
% 3.82/4.02 thf(fact_1536_pinf_I7_J,axiom,
% 3.82/4.02 ! [T: nat] :
% 3.82/4.02 ? [Z: nat] :
% 3.82/4.02 ! [X2: nat] :
% 3.82/4.02 ( ( ord_less_nat @ Z @ X2 )
% 3.82/4.02 => ( ord_less_nat @ T @ X2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % pinf(7)
% 3.82/4.02 thf(fact_1537_pinf_I7_J,axiom,
% 3.82/4.02 ! [T: extended_enat] :
% 3.82/4.02 ? [Z: extended_enat] :
% 3.82/4.02 ! [X2: extended_enat] :
% 3.82/4.02 ( ( ord_le72135733267957522d_enat @ Z @ X2 )
% 3.82/4.02 => ( ord_le72135733267957522d_enat @ T @ X2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % pinf(7)
% 3.82/4.02 thf(fact_1538_pinf_I7_J,axiom,
% 3.82/4.02 ! [T: real] :
% 3.82/4.02 ? [Z: real] :
% 3.82/4.02 ! [X2: real] :
% 3.82/4.02 ( ( ord_less_real @ Z @ X2 )
% 3.82/4.02 => ( ord_less_real @ T @ X2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % pinf(7)
% 3.82/4.02 thf(fact_1539_pinf_I7_J,axiom,
% 3.82/4.02 ! [T: int] :
% 3.82/4.02 ? [Z: int] :
% 3.82/4.02 ! [X2: int] :
% 3.82/4.02 ( ( ord_less_int @ Z @ X2 )
% 3.82/4.02 => ( ord_less_int @ T @ X2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % pinf(7)
% 3.82/4.02 thf(fact_1540_pinf_I5_J,axiom,
% 3.82/4.02 ! [T: nat] :
% 3.82/4.02 ? [Z: nat] :
% 3.82/4.02 ! [X2: nat] :
% 3.82/4.02 ( ( ord_less_nat @ Z @ X2 )
% 3.82/4.02 => ~ ( ord_less_nat @ X2 @ T ) ) ).
% 3.82/4.02
% 3.82/4.02 % pinf(5)
% 3.82/4.02 thf(fact_1541_pinf_I5_J,axiom,
% 3.82/4.02 ! [T: extended_enat] :
% 3.82/4.02 ? [Z: extended_enat] :
% 3.82/4.02 ! [X2: extended_enat] :
% 3.82/4.02 ( ( ord_le72135733267957522d_enat @ Z @ X2 )
% 3.82/4.02 => ~ ( ord_le72135733267957522d_enat @ X2 @ T ) ) ).
% 3.82/4.02
% 3.82/4.02 % pinf(5)
% 3.82/4.02 thf(fact_1542_pinf_I5_J,axiom,
% 3.82/4.02 ! [T: real] :
% 3.82/4.02 ? [Z: real] :
% 3.82/4.02 ! [X2: real] :
% 3.82/4.02 ( ( ord_less_real @ Z @ X2 )
% 3.82/4.02 => ~ ( ord_less_real @ X2 @ T ) ) ).
% 3.82/4.02
% 3.82/4.02 % pinf(5)
% 3.82/4.02 thf(fact_1543_pinf_I5_J,axiom,
% 3.82/4.02 ! [T: int] :
% 3.82/4.02 ? [Z: int] :
% 3.82/4.02 ! [X2: int] :
% 3.82/4.02 ( ( ord_less_int @ Z @ X2 )
% 3.82/4.02 => ~ ( ord_less_int @ X2 @ T ) ) ).
% 3.82/4.02
% 3.82/4.02 % pinf(5)
% 3.82/4.02 thf(fact_1544_pinf_I4_J,axiom,
% 3.82/4.02 ! [T: nat] :
% 3.82/4.02 ? [Z: nat] :
% 3.82/4.02 ! [X2: nat] :
% 3.82/4.02 ( ( ord_less_nat @ Z @ X2 )
% 3.82/4.02 => ( X2 != T ) ) ).
% 3.82/4.02
% 3.82/4.02 % pinf(4)
% 3.82/4.02 thf(fact_1545_pinf_I4_J,axiom,
% 3.82/4.02 ! [T: extended_enat] :
% 3.82/4.02 ? [Z: extended_enat] :
% 3.82/4.02 ! [X2: extended_enat] :
% 3.82/4.02 ( ( ord_le72135733267957522d_enat @ Z @ X2 )
% 3.82/4.02 => ( X2 != T ) ) ).
% 3.82/4.02
% 3.82/4.02 % pinf(4)
% 3.82/4.02 thf(fact_1546_pinf_I4_J,axiom,
% 3.82/4.02 ! [T: real] :
% 3.82/4.02 ? [Z: real] :
% 3.82/4.02 ! [X2: real] :
% 3.82/4.02 ( ( ord_less_real @ Z @ X2 )
% 3.82/4.02 => ( X2 != T ) ) ).
% 3.82/4.02
% 3.82/4.02 % pinf(4)
% 3.82/4.02 thf(fact_1547_pinf_I4_J,axiom,
% 3.82/4.02 ! [T: int] :
% 3.82/4.02 ? [Z: int] :
% 3.82/4.02 ! [X2: int] :
% 3.82/4.02 ( ( ord_less_int @ Z @ X2 )
% 3.82/4.02 => ( X2 != T ) ) ).
% 3.82/4.02
% 3.82/4.02 % pinf(4)
% 3.82/4.02 thf(fact_1548_pinf_I3_J,axiom,
% 3.82/4.02 ! [T: nat] :
% 3.82/4.02 ? [Z: nat] :
% 3.82/4.02 ! [X2: nat] :
% 3.82/4.02 ( ( ord_less_nat @ Z @ X2 )
% 3.82/4.02 => ( X2 != T ) ) ).
% 3.82/4.02
% 3.82/4.02 % pinf(3)
% 3.82/4.02 thf(fact_1549_pinf_I3_J,axiom,
% 3.82/4.02 ! [T: extended_enat] :
% 3.82/4.02 ? [Z: extended_enat] :
% 3.82/4.02 ! [X2: extended_enat] :
% 3.82/4.02 ( ( ord_le72135733267957522d_enat @ Z @ X2 )
% 3.82/4.02 => ( X2 != T ) ) ).
% 3.82/4.02
% 3.82/4.02 % pinf(3)
% 3.82/4.02 thf(fact_1550_pinf_I3_J,axiom,
% 3.82/4.02 ! [T: real] :
% 3.82/4.02 ? [Z: real] :
% 3.82/4.02 ! [X2: real] :
% 3.82/4.02 ( ( ord_less_real @ Z @ X2 )
% 3.82/4.02 => ( X2 != T ) ) ).
% 3.82/4.02
% 3.82/4.02 % pinf(3)
% 3.82/4.02 thf(fact_1551_pinf_I3_J,axiom,
% 3.82/4.02 ! [T: int] :
% 3.82/4.02 ? [Z: int] :
% 3.82/4.02 ! [X2: int] :
% 3.82/4.02 ( ( ord_less_int @ Z @ X2 )
% 3.82/4.02 => ( X2 != T ) ) ).
% 3.82/4.02
% 3.82/4.02 % pinf(3)
% 3.82/4.02 thf(fact_1552_pinf_I2_J,axiom,
% 3.82/4.02 ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q4: nat > $o] :
% 3.82/4.02 ( ? [Z4: nat] :
% 3.82/4.02 ! [X5: nat] :
% 3.82/4.02 ( ( ord_less_nat @ Z4 @ X5 )
% 3.82/4.02 => ( ( P @ X5 )
% 3.82/4.02 = ( P4 @ X5 ) ) )
% 3.82/4.02 => ( ? [Z4: nat] :
% 3.82/4.02 ! [X5: nat] :
% 3.82/4.02 ( ( ord_less_nat @ Z4 @ X5 )
% 3.82/4.02 => ( ( Q @ X5 )
% 3.82/4.02 = ( Q4 @ X5 ) ) )
% 3.82/4.02 => ? [Z: nat] :
% 3.82/4.02 ! [X2: nat] :
% 3.82/4.02 ( ( ord_less_nat @ Z @ X2 )
% 3.82/4.02 => ( ( ( P @ X2 )
% 3.82/4.02 | ( Q @ X2 ) )
% 3.82/4.02 = ( ( P4 @ X2 )
% 3.82/4.02 | ( Q4 @ X2 ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % pinf(2)
% 3.82/4.02 thf(fact_1553_pinf_I2_J,axiom,
% 3.82/4.02 ! [P: extended_enat > $o,P4: extended_enat > $o,Q: extended_enat > $o,Q4: extended_enat > $o] :
% 3.82/4.02 ( ? [Z4: extended_enat] :
% 3.82/4.02 ! [X5: extended_enat] :
% 3.82/4.02 ( ( ord_le72135733267957522d_enat @ Z4 @ X5 )
% 3.82/4.02 => ( ( P @ X5 )
% 3.82/4.02 = ( P4 @ X5 ) ) )
% 3.82/4.02 => ( ? [Z4: extended_enat] :
% 3.82/4.02 ! [X5: extended_enat] :
% 3.82/4.02 ( ( ord_le72135733267957522d_enat @ Z4 @ X5 )
% 3.82/4.02 => ( ( Q @ X5 )
% 3.82/4.02 = ( Q4 @ X5 ) ) )
% 3.82/4.02 => ? [Z: extended_enat] :
% 3.82/4.02 ! [X2: extended_enat] :
% 3.82/4.02 ( ( ord_le72135733267957522d_enat @ Z @ X2 )
% 3.82/4.02 => ( ( ( P @ X2 )
% 3.82/4.02 | ( Q @ X2 ) )
% 3.82/4.02 = ( ( P4 @ X2 )
% 3.82/4.02 | ( Q4 @ X2 ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % pinf(2)
% 3.82/4.02 thf(fact_1554_pinf_I2_J,axiom,
% 3.82/4.02 ! [P: real > $o,P4: real > $o,Q: real > $o,Q4: real > $o] :
% 3.82/4.02 ( ? [Z4: real] :
% 3.82/4.02 ! [X5: real] :
% 3.82/4.02 ( ( ord_less_real @ Z4 @ X5 )
% 3.82/4.02 => ( ( P @ X5 )
% 3.82/4.02 = ( P4 @ X5 ) ) )
% 3.82/4.02 => ( ? [Z4: real] :
% 3.82/4.02 ! [X5: real] :
% 3.82/4.02 ( ( ord_less_real @ Z4 @ X5 )
% 3.82/4.02 => ( ( Q @ X5 )
% 3.82/4.02 = ( Q4 @ X5 ) ) )
% 3.82/4.02 => ? [Z: real] :
% 3.82/4.02 ! [X2: real] :
% 3.82/4.02 ( ( ord_less_real @ Z @ X2 )
% 3.82/4.02 => ( ( ( P @ X2 )
% 3.82/4.02 | ( Q @ X2 ) )
% 3.82/4.02 = ( ( P4 @ X2 )
% 3.82/4.02 | ( Q4 @ X2 ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % pinf(2)
% 3.82/4.02 thf(fact_1555_pinf_I2_J,axiom,
% 3.82/4.02 ! [P: int > $o,P4: int > $o,Q: int > $o,Q4: int > $o] :
% 3.82/4.02 ( ? [Z4: int] :
% 3.82/4.02 ! [X5: int] :
% 3.82/4.02 ( ( ord_less_int @ Z4 @ X5 )
% 3.82/4.02 => ( ( P @ X5 )
% 3.82/4.02 = ( P4 @ X5 ) ) )
% 3.82/4.02 => ( ? [Z4: int] :
% 3.82/4.02 ! [X5: int] :
% 3.82/4.02 ( ( ord_less_int @ Z4 @ X5 )
% 3.82/4.02 => ( ( Q @ X5 )
% 3.82/4.02 = ( Q4 @ X5 ) ) )
% 3.82/4.02 => ? [Z: int] :
% 3.82/4.02 ! [X2: int] :
% 3.82/4.02 ( ( ord_less_int @ Z @ X2 )
% 3.82/4.02 => ( ( ( P @ X2 )
% 3.82/4.02 | ( Q @ X2 ) )
% 3.82/4.02 = ( ( P4 @ X2 )
% 3.82/4.02 | ( Q4 @ X2 ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % pinf(2)
% 3.82/4.02 thf(fact_1556_pinf_I1_J,axiom,
% 3.82/4.02 ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q4: nat > $o] :
% 3.82/4.02 ( ? [Z4: nat] :
% 3.82/4.02 ! [X5: nat] :
% 3.82/4.02 ( ( ord_less_nat @ Z4 @ X5 )
% 3.82/4.02 => ( ( P @ X5 )
% 3.82/4.02 = ( P4 @ X5 ) ) )
% 3.82/4.02 => ( ? [Z4: nat] :
% 3.82/4.02 ! [X5: nat] :
% 3.82/4.02 ( ( ord_less_nat @ Z4 @ X5 )
% 3.82/4.02 => ( ( Q @ X5 )
% 3.82/4.02 = ( Q4 @ X5 ) ) )
% 3.82/4.02 => ? [Z: nat] :
% 3.82/4.02 ! [X2: nat] :
% 3.82/4.02 ( ( ord_less_nat @ Z @ X2 )
% 3.82/4.02 => ( ( ( P @ X2 )
% 3.82/4.02 & ( Q @ X2 ) )
% 3.82/4.02 = ( ( P4 @ X2 )
% 3.82/4.02 & ( Q4 @ X2 ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % pinf(1)
% 3.82/4.02 thf(fact_1557_pinf_I1_J,axiom,
% 3.82/4.02 ! [P: extended_enat > $o,P4: extended_enat > $o,Q: extended_enat > $o,Q4: extended_enat > $o] :
% 3.82/4.02 ( ? [Z4: extended_enat] :
% 3.82/4.02 ! [X5: extended_enat] :
% 3.82/4.02 ( ( ord_le72135733267957522d_enat @ Z4 @ X5 )
% 3.82/4.02 => ( ( P @ X5 )
% 3.82/4.02 = ( P4 @ X5 ) ) )
% 3.82/4.02 => ( ? [Z4: extended_enat] :
% 3.82/4.02 ! [X5: extended_enat] :
% 3.82/4.02 ( ( ord_le72135733267957522d_enat @ Z4 @ X5 )
% 3.82/4.02 => ( ( Q @ X5 )
% 3.82/4.02 = ( Q4 @ X5 ) ) )
% 3.82/4.02 => ? [Z: extended_enat] :
% 3.82/4.02 ! [X2: extended_enat] :
% 3.82/4.02 ( ( ord_le72135733267957522d_enat @ Z @ X2 )
% 3.82/4.02 => ( ( ( P @ X2 )
% 3.82/4.02 & ( Q @ X2 ) )
% 3.82/4.02 = ( ( P4 @ X2 )
% 3.82/4.02 & ( Q4 @ X2 ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % pinf(1)
% 3.82/4.02 thf(fact_1558_pinf_I1_J,axiom,
% 3.82/4.02 ! [P: real > $o,P4: real > $o,Q: real > $o,Q4: real > $o] :
% 3.82/4.02 ( ? [Z4: real] :
% 3.82/4.02 ! [X5: real] :
% 3.82/4.02 ( ( ord_less_real @ Z4 @ X5 )
% 3.82/4.02 => ( ( P @ X5 )
% 3.82/4.02 = ( P4 @ X5 ) ) )
% 3.82/4.02 => ( ? [Z4: real] :
% 3.82/4.02 ! [X5: real] :
% 3.82/4.02 ( ( ord_less_real @ Z4 @ X5 )
% 3.82/4.02 => ( ( Q @ X5 )
% 3.82/4.02 = ( Q4 @ X5 ) ) )
% 3.82/4.02 => ? [Z: real] :
% 3.82/4.02 ! [X2: real] :
% 3.82/4.02 ( ( ord_less_real @ Z @ X2 )
% 3.82/4.02 => ( ( ( P @ X2 )
% 3.82/4.02 & ( Q @ X2 ) )
% 3.82/4.02 = ( ( P4 @ X2 )
% 3.82/4.02 & ( Q4 @ X2 ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % pinf(1)
% 3.82/4.02 thf(fact_1559_pinf_I1_J,axiom,
% 3.82/4.02 ! [P: int > $o,P4: int > $o,Q: int > $o,Q4: int > $o] :
% 3.82/4.02 ( ? [Z4: int] :
% 3.82/4.02 ! [X5: int] :
% 3.82/4.02 ( ( ord_less_int @ Z4 @ X5 )
% 3.82/4.02 => ( ( P @ X5 )
% 3.82/4.02 = ( P4 @ X5 ) ) )
% 3.82/4.02 => ( ? [Z4: int] :
% 3.82/4.02 ! [X5: int] :
% 3.82/4.02 ( ( ord_less_int @ Z4 @ X5 )
% 3.82/4.02 => ( ( Q @ X5 )
% 3.82/4.02 = ( Q4 @ X5 ) ) )
% 3.82/4.02 => ? [Z: int] :
% 3.82/4.02 ! [X2: int] :
% 3.82/4.02 ( ( ord_less_int @ Z @ X2 )
% 3.82/4.02 => ( ( ( P @ X2 )
% 3.82/4.02 & ( Q @ X2 ) )
% 3.82/4.02 = ( ( P4 @ X2 )
% 3.82/4.02 & ( Q4 @ X2 ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % pinf(1)
% 3.82/4.02 thf(fact_1560_ex__gt__or__lt,axiom,
% 3.82/4.02 ! [A: real] :
% 3.82/4.02 ? [B4: real] :
% 3.82/4.02 ( ( ord_less_real @ A @ B4 )
% 3.82/4.02 | ( ord_less_real @ B4 @ A ) ) ).
% 3.82/4.02
% 3.82/4.02 % ex_gt_or_lt
% 3.82/4.02 thf(fact_1561_count__le__length,axiom,
% 3.82/4.02 ! [Xs: list_VEBT_VEBT,X: vEBT_VEBT] : ( ord_less_eq_nat @ ( count_list_VEBT_VEBT @ Xs @ X ) @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ).
% 3.82/4.02
% 3.82/4.02 % count_le_length
% 3.82/4.02 thf(fact_1562_count__le__length,axiom,
% 3.82/4.02 ! [Xs: list_int,X: int] : ( ord_less_eq_nat @ ( count_list_int @ Xs @ X ) @ ( size_size_list_int @ Xs ) ) ).
% 3.82/4.02
% 3.82/4.02 % count_le_length
% 3.82/4.02 thf(fact_1563_count__le__length,axiom,
% 3.82/4.02 ! [Xs: list_nat,X: nat] : ( ord_less_eq_nat @ ( count_list_nat @ Xs @ X ) @ ( size_size_list_nat @ Xs ) ) ).
% 3.82/4.02
% 3.82/4.02 % count_le_length
% 3.82/4.02 thf(fact_1564_vebt__member_Osimps_I4_J,axiom,
% 3.82/4.02 ! [V: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT,X: nat] :
% 3.82/4.02 ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc ) @ X ) ).
% 3.82/4.02
% 3.82/4.02 % vebt_member.simps(4)
% 3.82/4.02 thf(fact_1565_max_Oabsorb3,axiom,
% 3.82/4.02 ! [B2: nat,A: nat] :
% 3.82/4.02 ( ( ord_less_nat @ B2 @ A )
% 3.82/4.02 => ( ( ord_max_nat @ A @ B2 )
% 3.82/4.02 = A ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.absorb3
% 3.82/4.02 thf(fact_1566_max_Oabsorb3,axiom,
% 3.82/4.02 ! [B2: extended_enat,A: extended_enat] :
% 3.82/4.02 ( ( ord_le72135733267957522d_enat @ B2 @ A )
% 3.82/4.02 => ( ( ord_ma741700101516333627d_enat @ A @ B2 )
% 3.82/4.02 = A ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.absorb3
% 3.82/4.02 thf(fact_1567_max_Oabsorb3,axiom,
% 3.82/4.02 ! [B2: real,A: real] :
% 3.82/4.02 ( ( ord_less_real @ B2 @ A )
% 3.82/4.02 => ( ( ord_max_real @ A @ B2 )
% 3.82/4.02 = A ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.absorb3
% 3.82/4.02 thf(fact_1568_max_Oabsorb3,axiom,
% 3.82/4.02 ! [B2: int,A: int] :
% 3.82/4.02 ( ( ord_less_int @ B2 @ A )
% 3.82/4.02 => ( ( ord_max_int @ A @ B2 )
% 3.82/4.02 = A ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.absorb3
% 3.82/4.02 thf(fact_1569_max_Oabsorb4,axiom,
% 3.82/4.02 ! [A: nat,B2: nat] :
% 3.82/4.02 ( ( ord_less_nat @ A @ B2 )
% 3.82/4.02 => ( ( ord_max_nat @ A @ B2 )
% 3.82/4.02 = B2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.absorb4
% 3.82/4.02 thf(fact_1570_max_Oabsorb4,axiom,
% 3.82/4.02 ! [A: extended_enat,B2: extended_enat] :
% 3.82/4.02 ( ( ord_le72135733267957522d_enat @ A @ B2 )
% 3.82/4.02 => ( ( ord_ma741700101516333627d_enat @ A @ B2 )
% 3.82/4.02 = B2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.absorb4
% 3.82/4.02 thf(fact_1571_max_Oabsorb4,axiom,
% 3.82/4.02 ! [A: real,B2: real] :
% 3.82/4.02 ( ( ord_less_real @ A @ B2 )
% 3.82/4.02 => ( ( ord_max_real @ A @ B2 )
% 3.82/4.02 = B2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.absorb4
% 3.82/4.02 thf(fact_1572_max_Oabsorb4,axiom,
% 3.82/4.02 ! [A: int,B2: int] :
% 3.82/4.02 ( ( ord_less_int @ A @ B2 )
% 3.82/4.02 => ( ( ord_max_int @ A @ B2 )
% 3.82/4.02 = B2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.absorb4
% 3.82/4.02 thf(fact_1573_max__less__iff__conj,axiom,
% 3.82/4.02 ! [X: nat,Y: nat,Z3: nat] :
% 3.82/4.02 ( ( ord_less_nat @ ( ord_max_nat @ X @ Y ) @ Z3 )
% 3.82/4.02 = ( ( ord_less_nat @ X @ Z3 )
% 3.82/4.02 & ( ord_less_nat @ Y @ Z3 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max_less_iff_conj
% 3.82/4.02 thf(fact_1574_max__less__iff__conj,axiom,
% 3.82/4.02 ! [X: extended_enat,Y: extended_enat,Z3: extended_enat] :
% 3.82/4.02 ( ( ord_le72135733267957522d_enat @ ( ord_ma741700101516333627d_enat @ X @ Y ) @ Z3 )
% 3.82/4.02 = ( ( ord_le72135733267957522d_enat @ X @ Z3 )
% 3.82/4.02 & ( ord_le72135733267957522d_enat @ Y @ Z3 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max_less_iff_conj
% 3.82/4.02 thf(fact_1575_max__less__iff__conj,axiom,
% 3.82/4.02 ! [X: real,Y: real,Z3: real] :
% 3.82/4.02 ( ( ord_less_real @ ( ord_max_real @ X @ Y ) @ Z3 )
% 3.82/4.02 = ( ( ord_less_real @ X @ Z3 )
% 3.82/4.02 & ( ord_less_real @ Y @ Z3 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max_less_iff_conj
% 3.82/4.02 thf(fact_1576_max__less__iff__conj,axiom,
% 3.82/4.02 ! [X: int,Y: int,Z3: int] :
% 3.82/4.02 ( ( ord_less_int @ ( ord_max_int @ X @ Y ) @ Z3 )
% 3.82/4.02 = ( ( ord_less_int @ X @ Z3 )
% 3.82/4.02 & ( ord_less_int @ Y @ Z3 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max_less_iff_conj
% 3.82/4.02 thf(fact_1577_max_Oabsorb1,axiom,
% 3.82/4.02 ! [B2: real,A: real] :
% 3.82/4.02 ( ( ord_less_eq_real @ B2 @ A )
% 3.82/4.02 => ( ( ord_max_real @ A @ B2 )
% 3.82/4.02 = A ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.absorb1
% 3.82/4.02 thf(fact_1578_max_Oabsorb1,axiom,
% 3.82/4.02 ! [B2: nat,A: nat] :
% 3.82/4.02 ( ( ord_less_eq_nat @ B2 @ A )
% 3.82/4.02 => ( ( ord_max_nat @ A @ B2 )
% 3.82/4.02 = A ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.absorb1
% 3.82/4.02 thf(fact_1579_max_Oabsorb1,axiom,
% 3.82/4.02 ! [B2: int,A: int] :
% 3.82/4.02 ( ( ord_less_eq_int @ B2 @ A )
% 3.82/4.02 => ( ( ord_max_int @ A @ B2 )
% 3.82/4.02 = A ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.absorb1
% 3.82/4.02 thf(fact_1580_max_Oabsorb2,axiom,
% 3.82/4.02 ! [A: real,B2: real] :
% 3.82/4.02 ( ( ord_less_eq_real @ A @ B2 )
% 3.82/4.02 => ( ( ord_max_real @ A @ B2 )
% 3.82/4.02 = B2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.absorb2
% 3.82/4.02 thf(fact_1581_max_Oabsorb2,axiom,
% 3.82/4.02 ! [A: nat,B2: nat] :
% 3.82/4.02 ( ( ord_less_eq_nat @ A @ B2 )
% 3.82/4.02 => ( ( ord_max_nat @ A @ B2 )
% 3.82/4.02 = B2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.absorb2
% 3.82/4.02 thf(fact_1582_max_Oabsorb2,axiom,
% 3.82/4.02 ! [A: int,B2: int] :
% 3.82/4.02 ( ( ord_less_eq_int @ A @ B2 )
% 3.82/4.02 => ( ( ord_max_int @ A @ B2 )
% 3.82/4.02 = B2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.absorb2
% 3.82/4.02 thf(fact_1583_max_Obounded__iff,axiom,
% 3.82/4.02 ! [B2: real,C: real,A: real] :
% 3.82/4.02 ( ( ord_less_eq_real @ ( ord_max_real @ B2 @ C ) @ A )
% 3.82/4.02 = ( ( ord_less_eq_real @ B2 @ A )
% 3.82/4.02 & ( ord_less_eq_real @ C @ A ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.bounded_iff
% 3.82/4.02 thf(fact_1584_max_Obounded__iff,axiom,
% 3.82/4.02 ! [B2: nat,C: nat,A: nat] :
% 3.82/4.02 ( ( ord_less_eq_nat @ ( ord_max_nat @ B2 @ C ) @ A )
% 3.82/4.02 = ( ( ord_less_eq_nat @ B2 @ A )
% 3.82/4.02 & ( ord_less_eq_nat @ C @ A ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.bounded_iff
% 3.82/4.02 thf(fact_1585_max_Obounded__iff,axiom,
% 3.82/4.02 ! [B2: int,C: int,A: int] :
% 3.82/4.02 ( ( ord_less_eq_int @ ( ord_max_int @ B2 @ C ) @ A )
% 3.82/4.02 = ( ( ord_less_eq_int @ B2 @ A )
% 3.82/4.02 & ( ord_less_eq_int @ C @ A ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.bounded_iff
% 3.82/4.02 thf(fact_1586_vebt__member_Osimps_I3_J,axiom,
% 3.82/4.02 ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,X: nat] :
% 3.82/4.02 ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz ) @ X ) ).
% 3.82/4.02
% 3.82/4.02 % vebt_member.simps(3)
% 3.82/4.02 thf(fact_1587_vebt__insert_Osimps_I3_J,axiom,
% 3.82/4.02 ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT,X: nat] :
% 3.82/4.02 ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S ) @ X )
% 3.82/4.02 = ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S ) ) ).
% 3.82/4.02
% 3.82/4.02 % vebt_insert.simps(3)
% 3.82/4.02 thf(fact_1588_VEBT__internal_OminNull_Osimps_I5_J,axiom,
% 3.82/4.02 ! [Uz: product_prod_nat_nat,Va2: nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 3.82/4.02 ~ ( vEBT_VEBT_minNull @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz ) @ Va2 @ Vb @ Vc ) ) ).
% 3.82/4.02
% 3.82/4.02 % VEBT_internal.minNull.simps(5)
% 3.82/4.02 thf(fact_1589_max_OcoboundedI2,axiom,
% 3.82/4.02 ! [C: real,B2: real,A: real] :
% 3.82/4.02 ( ( ord_less_eq_real @ C @ B2 )
% 3.82/4.02 => ( ord_less_eq_real @ C @ ( ord_max_real @ A @ B2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.coboundedI2
% 3.82/4.02 thf(fact_1590_max_OcoboundedI2,axiom,
% 3.82/4.02 ! [C: nat,B2: nat,A: nat] :
% 3.82/4.02 ( ( ord_less_eq_nat @ C @ B2 )
% 3.82/4.02 => ( ord_less_eq_nat @ C @ ( ord_max_nat @ A @ B2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.coboundedI2
% 3.82/4.02 thf(fact_1591_max_OcoboundedI2,axiom,
% 3.82/4.02 ! [C: int,B2: int,A: int] :
% 3.82/4.02 ( ( ord_less_eq_int @ C @ B2 )
% 3.82/4.02 => ( ord_less_eq_int @ C @ ( ord_max_int @ A @ B2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.coboundedI2
% 3.82/4.02 thf(fact_1592_max_OcoboundedI1,axiom,
% 3.82/4.02 ! [C: real,A: real,B2: real] :
% 3.82/4.02 ( ( ord_less_eq_real @ C @ A )
% 3.82/4.02 => ( ord_less_eq_real @ C @ ( ord_max_real @ A @ B2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.coboundedI1
% 3.82/4.02 thf(fact_1593_max_OcoboundedI1,axiom,
% 3.82/4.02 ! [C: nat,A: nat,B2: nat] :
% 3.82/4.02 ( ( ord_less_eq_nat @ C @ A )
% 3.82/4.02 => ( ord_less_eq_nat @ C @ ( ord_max_nat @ A @ B2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.coboundedI1
% 3.82/4.02 thf(fact_1594_max_OcoboundedI1,axiom,
% 3.82/4.02 ! [C: int,A: int,B2: int] :
% 3.82/4.02 ( ( ord_less_eq_int @ C @ A )
% 3.82/4.02 => ( ord_less_eq_int @ C @ ( ord_max_int @ A @ B2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.coboundedI1
% 3.82/4.02 thf(fact_1595_max_Oabsorb__iff2,axiom,
% 3.82/4.02 ( ord_less_eq_real
% 3.82/4.02 = ( ^ [A3: real,B3: real] :
% 3.82/4.02 ( ( ord_max_real @ A3 @ B3 )
% 3.82/4.02 = B3 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.absorb_iff2
% 3.82/4.02 thf(fact_1596_max_Oabsorb__iff2,axiom,
% 3.82/4.02 ( ord_less_eq_nat
% 3.82/4.02 = ( ^ [A3: nat,B3: nat] :
% 3.82/4.02 ( ( ord_max_nat @ A3 @ B3 )
% 3.82/4.02 = B3 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.absorb_iff2
% 3.82/4.02 thf(fact_1597_max_Oabsorb__iff2,axiom,
% 3.82/4.02 ( ord_less_eq_int
% 3.82/4.02 = ( ^ [A3: int,B3: int] :
% 3.82/4.02 ( ( ord_max_int @ A3 @ B3 )
% 3.82/4.02 = B3 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.absorb_iff2
% 3.82/4.02 thf(fact_1598_max_Oabsorb__iff1,axiom,
% 3.82/4.02 ( ord_less_eq_real
% 3.82/4.02 = ( ^ [B3: real,A3: real] :
% 3.82/4.02 ( ( ord_max_real @ A3 @ B3 )
% 3.82/4.02 = A3 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.absorb_iff1
% 3.82/4.02 thf(fact_1599_max_Oabsorb__iff1,axiom,
% 3.82/4.02 ( ord_less_eq_nat
% 3.82/4.02 = ( ^ [B3: nat,A3: nat] :
% 3.82/4.02 ( ( ord_max_nat @ A3 @ B3 )
% 3.82/4.02 = A3 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.absorb_iff1
% 3.82/4.02 thf(fact_1600_max_Oabsorb__iff1,axiom,
% 3.82/4.02 ( ord_less_eq_int
% 3.82/4.02 = ( ^ [B3: int,A3: int] :
% 3.82/4.02 ( ( ord_max_int @ A3 @ B3 )
% 3.82/4.02 = A3 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.absorb_iff1
% 3.82/4.02 thf(fact_1601_le__max__iff__disj,axiom,
% 3.82/4.02 ! [Z3: real,X: real,Y: real] :
% 3.82/4.02 ( ( ord_less_eq_real @ Z3 @ ( ord_max_real @ X @ Y ) )
% 3.82/4.02 = ( ( ord_less_eq_real @ Z3 @ X )
% 3.82/4.02 | ( ord_less_eq_real @ Z3 @ Y ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % le_max_iff_disj
% 3.82/4.02 thf(fact_1602_le__max__iff__disj,axiom,
% 3.82/4.02 ! [Z3: nat,X: nat,Y: nat] :
% 3.82/4.02 ( ( ord_less_eq_nat @ Z3 @ ( ord_max_nat @ X @ Y ) )
% 3.82/4.02 = ( ( ord_less_eq_nat @ Z3 @ X )
% 3.82/4.02 | ( ord_less_eq_nat @ Z3 @ Y ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % le_max_iff_disj
% 3.82/4.02 thf(fact_1603_le__max__iff__disj,axiom,
% 3.82/4.02 ! [Z3: int,X: int,Y: int] :
% 3.82/4.02 ( ( ord_less_eq_int @ Z3 @ ( ord_max_int @ X @ Y ) )
% 3.82/4.02 = ( ( ord_less_eq_int @ Z3 @ X )
% 3.82/4.02 | ( ord_less_eq_int @ Z3 @ Y ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % le_max_iff_disj
% 3.82/4.02 thf(fact_1604_max_Ocobounded2,axiom,
% 3.82/4.02 ! [B2: real,A: real] : ( ord_less_eq_real @ B2 @ ( ord_max_real @ A @ B2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.cobounded2
% 3.82/4.02 thf(fact_1605_max_Ocobounded2,axiom,
% 3.82/4.02 ! [B2: nat,A: nat] : ( ord_less_eq_nat @ B2 @ ( ord_max_nat @ A @ B2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.cobounded2
% 3.82/4.02 thf(fact_1606_max_Ocobounded2,axiom,
% 3.82/4.02 ! [B2: int,A: int] : ( ord_less_eq_int @ B2 @ ( ord_max_int @ A @ B2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.cobounded2
% 3.82/4.02 thf(fact_1607_max_Ocobounded1,axiom,
% 3.82/4.02 ! [A: real,B2: real] : ( ord_less_eq_real @ A @ ( ord_max_real @ A @ B2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.cobounded1
% 3.82/4.02 thf(fact_1608_max_Ocobounded1,axiom,
% 3.82/4.02 ! [A: nat,B2: nat] : ( ord_less_eq_nat @ A @ ( ord_max_nat @ A @ B2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.cobounded1
% 3.82/4.02 thf(fact_1609_max_Ocobounded1,axiom,
% 3.82/4.02 ! [A: int,B2: int] : ( ord_less_eq_int @ A @ ( ord_max_int @ A @ B2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.cobounded1
% 3.82/4.02 thf(fact_1610_max_Oorder__iff,axiom,
% 3.82/4.02 ( ord_less_eq_real
% 3.82/4.02 = ( ^ [B3: real,A3: real] :
% 3.82/4.02 ( A3
% 3.82/4.02 = ( ord_max_real @ A3 @ B3 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.order_iff
% 3.82/4.02 thf(fact_1611_max_Oorder__iff,axiom,
% 3.82/4.02 ( ord_less_eq_nat
% 3.82/4.02 = ( ^ [B3: nat,A3: nat] :
% 3.82/4.02 ( A3
% 3.82/4.02 = ( ord_max_nat @ A3 @ B3 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.order_iff
% 3.82/4.02 thf(fact_1612_max_Oorder__iff,axiom,
% 3.82/4.02 ( ord_less_eq_int
% 3.82/4.02 = ( ^ [B3: int,A3: int] :
% 3.82/4.02 ( A3
% 3.82/4.02 = ( ord_max_int @ A3 @ B3 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.order_iff
% 3.82/4.02 thf(fact_1613_max_OboundedI,axiom,
% 3.82/4.02 ! [B2: real,A: real,C: real] :
% 3.82/4.02 ( ( ord_less_eq_real @ B2 @ A )
% 3.82/4.02 => ( ( ord_less_eq_real @ C @ A )
% 3.82/4.02 => ( ord_less_eq_real @ ( ord_max_real @ B2 @ C ) @ A ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.boundedI
% 3.82/4.02 thf(fact_1614_max_OboundedI,axiom,
% 3.82/4.02 ! [B2: nat,A: nat,C: nat] :
% 3.82/4.02 ( ( ord_less_eq_nat @ B2 @ A )
% 3.82/4.02 => ( ( ord_less_eq_nat @ C @ A )
% 3.82/4.02 => ( ord_less_eq_nat @ ( ord_max_nat @ B2 @ C ) @ A ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.boundedI
% 3.82/4.02 thf(fact_1615_max_OboundedI,axiom,
% 3.82/4.02 ! [B2: int,A: int,C: int] :
% 3.82/4.02 ( ( ord_less_eq_int @ B2 @ A )
% 3.82/4.02 => ( ( ord_less_eq_int @ C @ A )
% 3.82/4.02 => ( ord_less_eq_int @ ( ord_max_int @ B2 @ C ) @ A ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.boundedI
% 3.82/4.02 thf(fact_1616_max_OboundedE,axiom,
% 3.82/4.02 ! [B2: real,C: real,A: real] :
% 3.82/4.02 ( ( ord_less_eq_real @ ( ord_max_real @ B2 @ C ) @ A )
% 3.82/4.02 => ~ ( ( ord_less_eq_real @ B2 @ A )
% 3.82/4.02 => ~ ( ord_less_eq_real @ C @ A ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.boundedE
% 3.82/4.02 thf(fact_1617_max_OboundedE,axiom,
% 3.82/4.02 ! [B2: nat,C: nat,A: nat] :
% 3.82/4.02 ( ( ord_less_eq_nat @ ( ord_max_nat @ B2 @ C ) @ A )
% 3.82/4.02 => ~ ( ( ord_less_eq_nat @ B2 @ A )
% 3.82/4.02 => ~ ( ord_less_eq_nat @ C @ A ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.boundedE
% 3.82/4.02 thf(fact_1618_max_OboundedE,axiom,
% 3.82/4.02 ! [B2: int,C: int,A: int] :
% 3.82/4.02 ( ( ord_less_eq_int @ ( ord_max_int @ B2 @ C ) @ A )
% 3.82/4.02 => ~ ( ( ord_less_eq_int @ B2 @ A )
% 3.82/4.02 => ~ ( ord_less_eq_int @ C @ A ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.boundedE
% 3.82/4.02 thf(fact_1619_max_OorderI,axiom,
% 3.82/4.02 ! [A: real,B2: real] :
% 3.82/4.02 ( ( A
% 3.82/4.02 = ( ord_max_real @ A @ B2 ) )
% 3.82/4.02 => ( ord_less_eq_real @ B2 @ A ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.orderI
% 3.82/4.02 thf(fact_1620_max_OorderI,axiom,
% 3.82/4.02 ! [A: nat,B2: nat] :
% 3.82/4.02 ( ( A
% 3.82/4.02 = ( ord_max_nat @ A @ B2 ) )
% 3.82/4.02 => ( ord_less_eq_nat @ B2 @ A ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.orderI
% 3.82/4.02 thf(fact_1621_max_OorderI,axiom,
% 3.82/4.02 ! [A: int,B2: int] :
% 3.82/4.02 ( ( A
% 3.82/4.02 = ( ord_max_int @ A @ B2 ) )
% 3.82/4.02 => ( ord_less_eq_int @ B2 @ A ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.orderI
% 3.82/4.02 thf(fact_1622_max_OorderE,axiom,
% 3.82/4.02 ! [B2: real,A: real] :
% 3.82/4.02 ( ( ord_less_eq_real @ B2 @ A )
% 3.82/4.02 => ( A
% 3.82/4.02 = ( ord_max_real @ A @ B2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.orderE
% 3.82/4.02 thf(fact_1623_max_OorderE,axiom,
% 3.82/4.02 ! [B2: nat,A: nat] :
% 3.82/4.02 ( ( ord_less_eq_nat @ B2 @ A )
% 3.82/4.02 => ( A
% 3.82/4.02 = ( ord_max_nat @ A @ B2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.orderE
% 3.82/4.02 thf(fact_1624_max_OorderE,axiom,
% 3.82/4.02 ! [B2: int,A: int] :
% 3.82/4.02 ( ( ord_less_eq_int @ B2 @ A )
% 3.82/4.02 => ( A
% 3.82/4.02 = ( ord_max_int @ A @ B2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.orderE
% 3.82/4.02 thf(fact_1625_max_Omono,axiom,
% 3.82/4.02 ! [C: real,A: real,D: real,B2: real] :
% 3.82/4.02 ( ( ord_less_eq_real @ C @ A )
% 3.82/4.02 => ( ( ord_less_eq_real @ D @ B2 )
% 3.82/4.02 => ( ord_less_eq_real @ ( ord_max_real @ C @ D ) @ ( ord_max_real @ A @ B2 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.mono
% 3.82/4.02 thf(fact_1626_max_Omono,axiom,
% 3.82/4.02 ! [C: nat,A: nat,D: nat,B2: nat] :
% 3.82/4.02 ( ( ord_less_eq_nat @ C @ A )
% 3.82/4.02 => ( ( ord_less_eq_nat @ D @ B2 )
% 3.82/4.02 => ( ord_less_eq_nat @ ( ord_max_nat @ C @ D ) @ ( ord_max_nat @ A @ B2 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.mono
% 3.82/4.02 thf(fact_1627_max_Omono,axiom,
% 3.82/4.02 ! [C: int,A: int,D: int,B2: int] :
% 3.82/4.02 ( ( ord_less_eq_int @ C @ A )
% 3.82/4.02 => ( ( ord_less_eq_int @ D @ B2 )
% 3.82/4.02 => ( ord_less_eq_int @ ( ord_max_int @ C @ D ) @ ( ord_max_int @ A @ B2 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.mono
% 3.82/4.02 thf(fact_1628_max_Ostrict__coboundedI2,axiom,
% 3.82/4.02 ! [C: nat,B2: nat,A: nat] :
% 3.82/4.02 ( ( ord_less_nat @ C @ B2 )
% 3.82/4.02 => ( ord_less_nat @ C @ ( ord_max_nat @ A @ B2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.strict_coboundedI2
% 3.82/4.02 thf(fact_1629_max_Ostrict__coboundedI2,axiom,
% 3.82/4.02 ! [C: extended_enat,B2: extended_enat,A: extended_enat] :
% 3.82/4.02 ( ( ord_le72135733267957522d_enat @ C @ B2 )
% 3.82/4.02 => ( ord_le72135733267957522d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.strict_coboundedI2
% 3.82/4.02 thf(fact_1630_max_Ostrict__coboundedI2,axiom,
% 3.82/4.02 ! [C: real,B2: real,A: real] :
% 3.82/4.02 ( ( ord_less_real @ C @ B2 )
% 3.82/4.02 => ( ord_less_real @ C @ ( ord_max_real @ A @ B2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.strict_coboundedI2
% 3.82/4.02 thf(fact_1631_max_Ostrict__coboundedI2,axiom,
% 3.82/4.02 ! [C: int,B2: int,A: int] :
% 3.82/4.02 ( ( ord_less_int @ C @ B2 )
% 3.82/4.02 => ( ord_less_int @ C @ ( ord_max_int @ A @ B2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.strict_coboundedI2
% 3.82/4.02 thf(fact_1632_max_Ostrict__coboundedI1,axiom,
% 3.82/4.02 ! [C: nat,A: nat,B2: nat] :
% 3.82/4.02 ( ( ord_less_nat @ C @ A )
% 3.82/4.02 => ( ord_less_nat @ C @ ( ord_max_nat @ A @ B2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.strict_coboundedI1
% 3.82/4.02 thf(fact_1633_max_Ostrict__coboundedI1,axiom,
% 3.82/4.02 ! [C: extended_enat,A: extended_enat,B2: extended_enat] :
% 3.82/4.02 ( ( ord_le72135733267957522d_enat @ C @ A )
% 3.82/4.02 => ( ord_le72135733267957522d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.strict_coboundedI1
% 3.82/4.02 thf(fact_1634_max_Ostrict__coboundedI1,axiom,
% 3.82/4.02 ! [C: real,A: real,B2: real] :
% 3.82/4.02 ( ( ord_less_real @ C @ A )
% 3.82/4.02 => ( ord_less_real @ C @ ( ord_max_real @ A @ B2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.strict_coboundedI1
% 3.82/4.02 thf(fact_1635_max_Ostrict__coboundedI1,axiom,
% 3.82/4.02 ! [C: int,A: int,B2: int] :
% 3.82/4.02 ( ( ord_less_int @ C @ A )
% 3.82/4.02 => ( ord_less_int @ C @ ( ord_max_int @ A @ B2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.strict_coboundedI1
% 3.82/4.02 thf(fact_1636_max_Ostrict__order__iff,axiom,
% 3.82/4.02 ( ord_less_nat
% 3.82/4.02 = ( ^ [B3: nat,A3: nat] :
% 3.82/4.02 ( ( A3
% 3.82/4.02 = ( ord_max_nat @ A3 @ B3 ) )
% 3.82/4.02 & ( A3 != B3 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.strict_order_iff
% 3.82/4.02 thf(fact_1637_max_Ostrict__order__iff,axiom,
% 3.82/4.02 ( ord_le72135733267957522d_enat
% 3.82/4.02 = ( ^ [B3: extended_enat,A3: extended_enat] :
% 3.82/4.02 ( ( A3
% 3.82/4.02 = ( ord_ma741700101516333627d_enat @ A3 @ B3 ) )
% 3.82/4.02 & ( A3 != B3 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.strict_order_iff
% 3.82/4.02 thf(fact_1638_max_Ostrict__order__iff,axiom,
% 3.82/4.02 ( ord_less_real
% 3.82/4.02 = ( ^ [B3: real,A3: real] :
% 3.82/4.02 ( ( A3
% 3.82/4.02 = ( ord_max_real @ A3 @ B3 ) )
% 3.82/4.02 & ( A3 != B3 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.strict_order_iff
% 3.82/4.02 thf(fact_1639_max_Ostrict__order__iff,axiom,
% 3.82/4.02 ( ord_less_int
% 3.82/4.02 = ( ^ [B3: int,A3: int] :
% 3.82/4.02 ( ( A3
% 3.82/4.02 = ( ord_max_int @ A3 @ B3 ) )
% 3.82/4.02 & ( A3 != B3 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.strict_order_iff
% 3.82/4.02 thf(fact_1640_max_Ostrict__boundedE,axiom,
% 3.82/4.02 ! [B2: nat,C: nat,A: nat] :
% 3.82/4.02 ( ( ord_less_nat @ ( ord_max_nat @ B2 @ C ) @ A )
% 3.82/4.02 => ~ ( ( ord_less_nat @ B2 @ A )
% 3.82/4.02 => ~ ( ord_less_nat @ C @ A ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.strict_boundedE
% 3.82/4.02 thf(fact_1641_max_Ostrict__boundedE,axiom,
% 3.82/4.02 ! [B2: extended_enat,C: extended_enat,A: extended_enat] :
% 3.82/4.02 ( ( ord_le72135733267957522d_enat @ ( ord_ma741700101516333627d_enat @ B2 @ C ) @ A )
% 3.82/4.02 => ~ ( ( ord_le72135733267957522d_enat @ B2 @ A )
% 3.82/4.02 => ~ ( ord_le72135733267957522d_enat @ C @ A ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.strict_boundedE
% 3.82/4.02 thf(fact_1642_max_Ostrict__boundedE,axiom,
% 3.82/4.02 ! [B2: real,C: real,A: real] :
% 3.82/4.02 ( ( ord_less_real @ ( ord_max_real @ B2 @ C ) @ A )
% 3.82/4.02 => ~ ( ( ord_less_real @ B2 @ A )
% 3.82/4.02 => ~ ( ord_less_real @ C @ A ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.strict_boundedE
% 3.82/4.02 thf(fact_1643_max_Ostrict__boundedE,axiom,
% 3.82/4.02 ! [B2: int,C: int,A: int] :
% 3.82/4.02 ( ( ord_less_int @ ( ord_max_int @ B2 @ C ) @ A )
% 3.82/4.02 => ~ ( ( ord_less_int @ B2 @ A )
% 3.82/4.02 => ~ ( ord_less_int @ C @ A ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max.strict_boundedE
% 3.82/4.02 thf(fact_1644_less__max__iff__disj,axiom,
% 3.82/4.02 ! [Z3: nat,X: nat,Y: nat] :
% 3.82/4.02 ( ( ord_less_nat @ Z3 @ ( ord_max_nat @ X @ Y ) )
% 3.82/4.02 = ( ( ord_less_nat @ Z3 @ X )
% 3.82/4.02 | ( ord_less_nat @ Z3 @ Y ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % less_max_iff_disj
% 3.82/4.02 thf(fact_1645_less__max__iff__disj,axiom,
% 3.82/4.02 ! [Z3: extended_enat,X: extended_enat,Y: extended_enat] :
% 3.82/4.02 ( ( ord_le72135733267957522d_enat @ Z3 @ ( ord_ma741700101516333627d_enat @ X @ Y ) )
% 3.82/4.02 = ( ( ord_le72135733267957522d_enat @ Z3 @ X )
% 3.82/4.02 | ( ord_le72135733267957522d_enat @ Z3 @ Y ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % less_max_iff_disj
% 3.82/4.02 thf(fact_1646_less__max__iff__disj,axiom,
% 3.82/4.02 ! [Z3: real,X: real,Y: real] :
% 3.82/4.02 ( ( ord_less_real @ Z3 @ ( ord_max_real @ X @ Y ) )
% 3.82/4.02 = ( ( ord_less_real @ Z3 @ X )
% 3.82/4.02 | ( ord_less_real @ Z3 @ Y ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % less_max_iff_disj
% 3.82/4.02 thf(fact_1647_less__max__iff__disj,axiom,
% 3.82/4.02 ! [Z3: int,X: int,Y: int] :
% 3.82/4.02 ( ( ord_less_int @ Z3 @ ( ord_max_int @ X @ Y ) )
% 3.82/4.02 = ( ( ord_less_int @ Z3 @ X )
% 3.82/4.02 | ( ord_less_int @ Z3 @ Y ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % less_max_iff_disj
% 3.82/4.02 thf(fact_1648_vebt__insert_Osimps_I2_J,axiom,
% 3.82/4.02 ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT,X: nat] :
% 3.82/4.02 ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S ) @ X )
% 3.82/4.02 = ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S ) ) ).
% 3.82/4.02
% 3.82/4.02 % vebt_insert.simps(2)
% 3.82/4.02 thf(fact_1649_option_Osize_I4_J,axiom,
% 3.82/4.02 ! [X22: product_prod_nat_nat] :
% 3.82/4.02 ( ( size_s170228958280169651at_nat @ ( some_P7363390416028606310at_nat @ X22 ) )
% 3.82/4.02 = ( suc @ zero_zero_nat ) ) ).
% 3.82/4.02
% 3.82/4.02 % option.size(4)
% 3.82/4.02 thf(fact_1650_option_Osize_I4_J,axiom,
% 3.82/4.02 ! [X22: num] :
% 3.82/4.02 ( ( size_size_option_num @ ( some_num @ X22 ) )
% 3.82/4.02 = ( suc @ zero_zero_nat ) ) ).
% 3.82/4.02
% 3.82/4.02 % option.size(4)
% 3.82/4.02 thf(fact_1651_nth__enumerate__eq,axiom,
% 3.82/4.02 ! [M2: nat,Xs: list_VEBT_VEBT,N2: nat] :
% 3.82/4.02 ( ( ord_less_nat @ M2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 3.82/4.02 => ( ( nth_Pr744662078594809490T_VEBT @ ( enumerate_VEBT_VEBT @ N2 @ Xs ) @ M2 )
% 3.82/4.02 = ( produc599794634098209291T_VEBT @ ( plus_plus_nat @ N2 @ M2 ) @ ( nth_VEBT_VEBT @ Xs @ M2 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % nth_enumerate_eq
% 3.82/4.02 thf(fact_1652_nth__enumerate__eq,axiom,
% 3.82/4.02 ! [M2: nat,Xs: list_int,N2: nat] :
% 3.82/4.02 ( ( ord_less_nat @ M2 @ ( size_size_list_int @ Xs ) )
% 3.82/4.02 => ( ( nth_Pr3440142176431000676at_int @ ( enumerate_int @ N2 @ Xs ) @ M2 )
% 3.82/4.02 = ( product_Pair_nat_int @ ( plus_plus_nat @ N2 @ M2 ) @ ( nth_int @ Xs @ M2 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % nth_enumerate_eq
% 3.82/4.02 thf(fact_1653_nth__enumerate__eq,axiom,
% 3.82/4.02 ! [M2: nat,Xs: list_nat,N2: nat] :
% 3.82/4.02 ( ( ord_less_nat @ M2 @ ( size_size_list_nat @ Xs ) )
% 3.82/4.02 => ( ( nth_Pr7617993195940197384at_nat @ ( enumerate_nat @ N2 @ Xs ) @ M2 )
% 3.82/4.02 = ( product_Pair_nat_nat @ ( plus_plus_nat @ N2 @ M2 ) @ ( nth_nat @ Xs @ M2 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % nth_enumerate_eq
% 3.82/4.02 thf(fact_1654_find__Some__iff2,axiom,
% 3.82/4.02 ! [X: product_prod_nat_nat,P: product_prod_nat_nat > $o,Xs: list_P6011104703257516679at_nat] :
% 3.82/4.02 ( ( ( some_P7363390416028606310at_nat @ X )
% 3.82/4.02 = ( find_P8199882355184865565at_nat @ P @ Xs ) )
% 3.82/4.02 = ( ? [I3: nat] :
% 3.82/4.02 ( ( ord_less_nat @ I3 @ ( size_s5460976970255530739at_nat @ Xs ) )
% 3.82/4.02 & ( P @ ( nth_Pr7617993195940197384at_nat @ Xs @ I3 ) )
% 3.82/4.02 & ( X
% 3.82/4.02 = ( nth_Pr7617993195940197384at_nat @ Xs @ I3 ) )
% 3.82/4.02 & ! [J2: nat] :
% 3.82/4.02 ( ( ord_less_nat @ J2 @ I3 )
% 3.82/4.02 => ~ ( P @ ( nth_Pr7617993195940197384at_nat @ Xs @ J2 ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % find_Some_iff2
% 3.82/4.02 thf(fact_1655_find__Some__iff2,axiom,
% 3.82/4.02 ! [X: num,P: num > $o,Xs: list_num] :
% 3.82/4.02 ( ( ( some_num @ X )
% 3.82/4.02 = ( find_num @ P @ Xs ) )
% 3.82/4.02 = ( ? [I3: nat] :
% 3.82/4.02 ( ( ord_less_nat @ I3 @ ( size_size_list_num @ Xs ) )
% 3.82/4.02 & ( P @ ( nth_num @ Xs @ I3 ) )
% 3.82/4.02 & ( X
% 3.82/4.02 = ( nth_num @ Xs @ I3 ) )
% 3.82/4.02 & ! [J2: nat] :
% 3.82/4.02 ( ( ord_less_nat @ J2 @ I3 )
% 3.82/4.02 => ~ ( P @ ( nth_num @ Xs @ J2 ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % find_Some_iff2
% 3.82/4.02 thf(fact_1656_find__Some__iff2,axiom,
% 3.82/4.02 ! [X: vEBT_VEBT,P: vEBT_VEBT > $o,Xs: list_VEBT_VEBT] :
% 3.82/4.02 ( ( ( some_VEBT_VEBT @ X )
% 3.82/4.02 = ( find_VEBT_VEBT @ P @ Xs ) )
% 3.82/4.02 = ( ? [I3: nat] :
% 3.82/4.02 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 3.82/4.02 & ( P @ ( nth_VEBT_VEBT @ Xs @ I3 ) )
% 3.82/4.02 & ( X
% 3.82/4.02 = ( nth_VEBT_VEBT @ Xs @ I3 ) )
% 3.82/4.02 & ! [J2: nat] :
% 3.82/4.02 ( ( ord_less_nat @ J2 @ I3 )
% 3.82/4.02 => ~ ( P @ ( nth_VEBT_VEBT @ Xs @ J2 ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % find_Some_iff2
% 3.82/4.02 thf(fact_1657_find__Some__iff2,axiom,
% 3.82/4.02 ! [X: int,P: int > $o,Xs: list_int] :
% 3.82/4.02 ( ( ( some_int @ X )
% 3.82/4.02 = ( find_int @ P @ Xs ) )
% 3.82/4.02 = ( ? [I3: nat] :
% 3.82/4.02 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs ) )
% 3.82/4.02 & ( P @ ( nth_int @ Xs @ I3 ) )
% 3.82/4.02 & ( X
% 3.82/4.02 = ( nth_int @ Xs @ I3 ) )
% 3.82/4.02 & ! [J2: nat] :
% 3.82/4.02 ( ( ord_less_nat @ J2 @ I3 )
% 3.82/4.02 => ~ ( P @ ( nth_int @ Xs @ J2 ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % find_Some_iff2
% 3.82/4.02 thf(fact_1658_find__Some__iff2,axiom,
% 3.82/4.02 ! [X: nat,P: nat > $o,Xs: list_nat] :
% 3.82/4.02 ( ( ( some_nat @ X )
% 3.82/4.02 = ( find_nat @ P @ Xs ) )
% 3.82/4.02 = ( ? [I3: nat] :
% 3.82/4.02 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 3.82/4.02 & ( P @ ( nth_nat @ Xs @ I3 ) )
% 3.82/4.02 & ( X
% 3.82/4.02 = ( nth_nat @ Xs @ I3 ) )
% 3.82/4.02 & ! [J2: nat] :
% 3.82/4.02 ( ( ord_less_nat @ J2 @ I3 )
% 3.82/4.02 => ~ ( P @ ( nth_nat @ Xs @ J2 ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % find_Some_iff2
% 3.82/4.02 thf(fact_1659_find__Some__iff,axiom,
% 3.82/4.02 ! [P: product_prod_nat_nat > $o,Xs: list_P6011104703257516679at_nat,X: product_prod_nat_nat] :
% 3.82/4.02 ( ( ( find_P8199882355184865565at_nat @ P @ Xs )
% 3.82/4.02 = ( some_P7363390416028606310at_nat @ X ) )
% 3.82/4.02 = ( ? [I3: nat] :
% 3.82/4.02 ( ( ord_less_nat @ I3 @ ( size_s5460976970255530739at_nat @ Xs ) )
% 3.82/4.02 & ( P @ ( nth_Pr7617993195940197384at_nat @ Xs @ I3 ) )
% 3.82/4.02 & ( X
% 3.82/4.02 = ( nth_Pr7617993195940197384at_nat @ Xs @ I3 ) )
% 3.82/4.02 & ! [J2: nat] :
% 3.82/4.02 ( ( ord_less_nat @ J2 @ I3 )
% 3.82/4.02 => ~ ( P @ ( nth_Pr7617993195940197384at_nat @ Xs @ J2 ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % find_Some_iff
% 3.82/4.02 thf(fact_1660_find__Some__iff,axiom,
% 3.82/4.02 ! [P: num > $o,Xs: list_num,X: num] :
% 3.82/4.02 ( ( ( find_num @ P @ Xs )
% 3.82/4.02 = ( some_num @ X ) )
% 3.82/4.02 = ( ? [I3: nat] :
% 3.82/4.02 ( ( ord_less_nat @ I3 @ ( size_size_list_num @ Xs ) )
% 3.82/4.02 & ( P @ ( nth_num @ Xs @ I3 ) )
% 3.82/4.02 & ( X
% 3.82/4.02 = ( nth_num @ Xs @ I3 ) )
% 3.82/4.02 & ! [J2: nat] :
% 3.82/4.02 ( ( ord_less_nat @ J2 @ I3 )
% 3.82/4.02 => ~ ( P @ ( nth_num @ Xs @ J2 ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % find_Some_iff
% 3.82/4.02 thf(fact_1661_find__Some__iff,axiom,
% 3.82/4.02 ! [P: vEBT_VEBT > $o,Xs: list_VEBT_VEBT,X: vEBT_VEBT] :
% 3.82/4.02 ( ( ( find_VEBT_VEBT @ P @ Xs )
% 3.82/4.02 = ( some_VEBT_VEBT @ X ) )
% 3.82/4.02 = ( ? [I3: nat] :
% 3.82/4.02 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 3.82/4.02 & ( P @ ( nth_VEBT_VEBT @ Xs @ I3 ) )
% 3.82/4.02 & ( X
% 3.82/4.02 = ( nth_VEBT_VEBT @ Xs @ I3 ) )
% 3.82/4.02 & ! [J2: nat] :
% 3.82/4.02 ( ( ord_less_nat @ J2 @ I3 )
% 3.82/4.02 => ~ ( P @ ( nth_VEBT_VEBT @ Xs @ J2 ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % find_Some_iff
% 3.82/4.02 thf(fact_1662_find__Some__iff,axiom,
% 3.82/4.02 ! [P: int > $o,Xs: list_int,X: int] :
% 3.82/4.02 ( ( ( find_int @ P @ Xs )
% 3.82/4.02 = ( some_int @ X ) )
% 3.82/4.02 = ( ? [I3: nat] :
% 3.82/4.02 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs ) )
% 3.82/4.02 & ( P @ ( nth_int @ Xs @ I3 ) )
% 3.82/4.02 & ( X
% 3.82/4.02 = ( nth_int @ Xs @ I3 ) )
% 3.82/4.02 & ! [J2: nat] :
% 3.82/4.02 ( ( ord_less_nat @ J2 @ I3 )
% 3.82/4.02 => ~ ( P @ ( nth_int @ Xs @ J2 ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % find_Some_iff
% 3.82/4.02 thf(fact_1663_find__Some__iff,axiom,
% 3.82/4.02 ! [P: nat > $o,Xs: list_nat,X: nat] :
% 3.82/4.02 ( ( ( find_nat @ P @ Xs )
% 3.82/4.02 = ( some_nat @ X ) )
% 3.82/4.02 = ( ? [I3: nat] :
% 3.82/4.02 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 3.82/4.02 & ( P @ ( nth_nat @ Xs @ I3 ) )
% 3.82/4.02 & ( X
% 3.82/4.02 = ( nth_nat @ Xs @ I3 ) )
% 3.82/4.02 & ! [J2: nat] :
% 3.82/4.02 ( ( ord_less_nat @ J2 @ I3 )
% 3.82/4.02 => ~ ( P @ ( nth_nat @ Xs @ J2 ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % find_Some_iff
% 3.82/4.02 thf(fact_1664__C7_C,axiom,
% 3.82/4.02 ( ( mi != ma )
% 3.82/4.02 => ! [I5: nat] :
% 3.82/4.02 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 3.82/4.02 => ( ( ( ( vEBT_VEBT_high @ ma @ na )
% 3.82/4.02 = I5 )
% 3.82/4.02 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I5 ) @ ( vEBT_VEBT_low @ ma @ na ) ) )
% 3.82/4.02 & ! [Y6: nat] :
% 3.82/4.02 ( ( ( ( vEBT_VEBT_high @ Y6 @ na )
% 3.82/4.02 = I5 )
% 3.82/4.02 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I5 ) @ ( vEBT_VEBT_low @ Y6 @ na ) ) )
% 3.82/4.02 => ( ( ord_less_nat @ mi @ Y6 )
% 3.82/4.02 & ( ord_less_eq_nat @ Y6 @ ma ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % "7"
% 3.82/4.02 thf(fact_1665_listrel1__iff__update,axiom,
% 3.82/4.02 ! [Xs: list_P6011104703257516679at_nat,Ys: list_P6011104703257516679at_nat,R2: set_Pr8693737435421807431at_nat] :
% 3.82/4.02 ( ( member6693912407220327184at_nat @ ( produc5943733680697469783at_nat @ Xs @ Ys ) @ ( listre4828114922151135584at_nat @ R2 ) )
% 3.82/4.02 = ( ? [Y5: product_prod_nat_nat,N: nat] :
% 3.82/4.02 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( nth_Pr7617993195940197384at_nat @ Xs @ N ) @ Y5 ) @ R2 )
% 3.82/4.02 & ( ord_less_nat @ N @ ( size_s5460976970255530739at_nat @ Xs ) )
% 3.82/4.02 & ( Ys
% 3.82/4.02 = ( list_u6180841689913720943at_nat @ Xs @ N @ Y5 ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % listrel1_iff_update
% 3.82/4.02 thf(fact_1666_listrel1__iff__update,axiom,
% 3.82/4.02 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT,R2: set_Pr6192946355708809607T_VEBT] :
% 3.82/4.02 ( ( member4439316823752958928T_VEBT @ ( produc3897820843166775703T_VEBT @ Xs @ Ys ) @ ( listrel1_VEBT_VEBT @ R2 ) )
% 3.82/4.02 = ( ? [Y5: vEBT_VEBT,N: nat] :
% 3.82/4.02 ( ( member568628332442017744T_VEBT @ ( produc537772716801021591T_VEBT @ ( nth_VEBT_VEBT @ Xs @ N ) @ Y5 ) @ R2 )
% 3.82/4.02 & ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 3.82/4.02 & ( Ys
% 3.82/4.02 = ( list_u1324408373059187874T_VEBT @ Xs @ N @ Y5 ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % listrel1_iff_update
% 3.82/4.02 thf(fact_1667_listrel1__iff__update,axiom,
% 3.82/4.02 ! [Xs: list_int,Ys: list_int,R2: set_Pr958786334691620121nt_int] :
% 3.82/4.02 ( ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Xs @ Ys ) @ ( listrel1_int @ R2 ) )
% 3.82/4.02 = ( ? [Y5: int,N: nat] :
% 3.82/4.02 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ ( nth_int @ Xs @ N ) @ Y5 ) @ R2 )
% 3.82/4.02 & ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 3.82/4.02 & ( Ys
% 3.82/4.02 = ( list_update_int @ Xs @ N @ Y5 ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % listrel1_iff_update
% 3.82/4.02 thf(fact_1668_listrel1__iff__update,axiom,
% 3.82/4.02 ! [Xs: list_nat,Ys: list_nat,R2: set_Pr1261947904930325089at_nat] :
% 3.82/4.02 ( ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Xs @ Ys ) @ ( listrel1_nat @ R2 ) )
% 3.82/4.02 = ( ? [Y5: nat,N: nat] :
% 3.82/4.02 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ ( nth_nat @ Xs @ N ) @ Y5 ) @ R2 )
% 3.82/4.02 & ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 3.82/4.02 & ( Ys
% 3.82/4.02 = ( list_update_nat @ Xs @ N @ Y5 ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % listrel1_iff_update
% 3.82/4.02 thf(fact_1669_option_Osize__gen_I2_J,axiom,
% 3.82/4.02 ! [X: product_prod_nat_nat > nat,X22: product_prod_nat_nat] :
% 3.82/4.02 ( ( size_o8335143837870341156at_nat @ X @ ( some_P7363390416028606310at_nat @ X22 ) )
% 3.82/4.02 = ( plus_plus_nat @ ( X @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % option.size_gen(2)
% 3.82/4.02 thf(fact_1670_option_Osize__gen_I2_J,axiom,
% 3.82/4.02 ! [X: num > nat,X22: num] :
% 3.82/4.02 ( ( size_option_num @ X @ ( some_num @ X22 ) )
% 3.82/4.02 = ( plus_plus_nat @ ( X @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % option.size_gen(2)
% 3.82/4.02 thf(fact_1671_intind,axiom,
% 3.82/4.02 ! [I: nat,N2: nat,P: nat > $o,X: nat] :
% 3.82/4.02 ( ( ord_less_nat @ I @ N2 )
% 3.82/4.02 => ( ( P @ X )
% 3.82/4.02 => ( P @ ( nth_nat @ ( replicate_nat @ N2 @ X ) @ I ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % intind
% 3.82/4.02 thf(fact_1672_intind,axiom,
% 3.82/4.02 ! [I: nat,N2: nat,P: int > $o,X: int] :
% 3.82/4.02 ( ( ord_less_nat @ I @ N2 )
% 3.82/4.02 => ( ( P @ X )
% 3.82/4.02 => ( P @ ( nth_int @ ( replicate_int @ N2 @ X ) @ I ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % intind
% 3.82/4.02 thf(fact_1673_intind,axiom,
% 3.82/4.02 ! [I: nat,N2: nat,P: vEBT_VEBT > $o,X: vEBT_VEBT] :
% 3.82/4.02 ( ( ord_less_nat @ I @ N2 )
% 3.82/4.02 => ( ( P @ X )
% 3.82/4.02 => ( P @ ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N2 @ X ) @ I ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % intind
% 3.82/4.02 thf(fact_1674_vebt__insert_Osimps_I4_J,axiom,
% 3.82/4.02 ! [V: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 3.82/4.02 ( ( vEBT_vebt_insert @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList2 @ Summary ) @ X )
% 3.82/4.02 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X @ X ) ) @ ( suc @ ( suc @ V ) ) @ TreeList2 @ Summary ) ) ).
% 3.82/4.02
% 3.82/4.02 % vebt_insert.simps(4)
% 3.82/4.02 thf(fact_1675_gen__length__def,axiom,
% 3.82/4.02 ( gen_length_VEBT_VEBT
% 3.82/4.02 = ( ^ [N: nat,Xs3: list_VEBT_VEBT] : ( plus_plus_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs3 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % gen_length_def
% 3.82/4.02 thf(fact_1676_gen__length__def,axiom,
% 3.82/4.02 ( gen_length_int
% 3.82/4.02 = ( ^ [N: nat,Xs3: list_int] : ( plus_plus_nat @ N @ ( size_size_list_int @ Xs3 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % gen_length_def
% 3.82/4.02 thf(fact_1677_gen__length__def,axiom,
% 3.82/4.02 ( gen_length_nat
% 3.82/4.02 = ( ^ [N: nat,Xs3: list_nat] : ( plus_plus_nat @ N @ ( size_size_list_nat @ Xs3 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % gen_length_def
% 3.82/4.02 thf(fact_1678__C2_C,axiom,
% 3.82/4.02 ( ( size_s6755466524823107622T_VEBT @ treeList )
% 3.82/4.02 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ).
% 3.82/4.02
% 3.82/4.02 % "2"
% 3.82/4.02 thf(fact_1679__C5_Ohyps_C_I8_J,axiom,
% 3.82/4.02 ord_less_nat @ ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ).
% 3.82/4.02
% 3.82/4.02 % "5.hyps"(8)
% 3.82/4.02 thf(fact_1680__C5_Oprems_C,axiom,
% 3.82/4.02 ord_less_nat @ xa @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ).
% 3.82/4.02
% 3.82/4.02 % "5.prems"
% 3.82/4.02 thf(fact_1681__092_060open_062i_A_060_A2_A_094_Am_092_060close_062,axiom,
% 3.82/4.02 ord_less_nat @ i @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ).
% 3.82/4.02
% 3.82/4.02 % \<open>i < 2 ^ m\<close>
% 3.82/4.02 thf(fact_1682__C5_OIH_C_I1_J,axiom,
% 3.82/4.02 ! [X2: vEBT_VEBT] :
% 3.82/4.02 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ treeList ) )
% 3.82/4.02 => ( ( vEBT_invar_vebt @ X2 @ na )
% 3.82/4.02 & ! [Xa: nat] :
% 3.82/4.02 ( ( ord_less_nat @ Xa @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) )
% 3.82/4.02 => ( vEBT_invar_vebt @ ( vEBT_vebt_insert @ X2 @ Xa ) @ na ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % "5.IH"(1)
% 3.82/4.02 thf(fact_1683__C4_C,axiom,
% 3.82/4.02 ! [I5: nat] :
% 3.82/4.02 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 3.82/4.02 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I5 ) @ X6 ) )
% 3.82/4.02 = ( vEBT_V8194947554948674370ptions @ summary @ I5 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % "4"
% 3.82/4.02 thf(fact_1684_high__bound__aux,axiom,
% 3.82/4.02 ! [Ma: nat,N2: nat,M2: nat] :
% 3.82/4.02 ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M2 ) ) )
% 3.82/4.02 => ( ord_less_nat @ ( vEBT_VEBT_high @ Ma @ N2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % high_bound_aux
% 3.82/4.02 thf(fact_1685_member__bound,axiom,
% 3.82/4.02 ! [Tree: vEBT_VEBT,X: nat,N2: nat] :
% 3.82/4.02 ( ( vEBT_vebt_member @ Tree @ X )
% 3.82/4.02 => ( ( vEBT_invar_vebt @ Tree @ N2 )
% 3.82/4.02 => ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % member_bound
% 3.82/4.02 thf(fact_1686_numeral__le__iff,axiom,
% 3.82/4.02 ! [M2: num,N2: num] :
% 3.82/4.02 ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M2 ) @ ( numera1916890842035813515d_enat @ N2 ) )
% 3.82/4.02 = ( ord_less_eq_num @ M2 @ N2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % numeral_le_iff
% 3.82/4.02 thf(fact_1687_numeral__le__iff,axiom,
% 3.82/4.02 ! [M2: num,N2: num] :
% 3.82/4.02 ( ( ord_less_eq_real @ ( numeral_numeral_real @ M2 ) @ ( numeral_numeral_real @ N2 ) )
% 3.82/4.02 = ( ord_less_eq_num @ M2 @ N2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % numeral_le_iff
% 3.82/4.02 thf(fact_1688_numeral__le__iff,axiom,
% 3.82/4.02 ! [M2: num,N2: num] :
% 3.82/4.02 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N2 ) )
% 3.82/4.02 = ( ord_less_eq_num @ M2 @ N2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % numeral_le_iff
% 3.82/4.02 thf(fact_1689_numeral__le__iff,axiom,
% 3.82/4.02 ! [M2: num,N2: num] :
% 3.82/4.02 ( ( ord_less_eq_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N2 ) )
% 3.82/4.02 = ( ord_less_eq_num @ M2 @ N2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % numeral_le_iff
% 3.82/4.02 thf(fact_1690_numeral__less__iff,axiom,
% 3.82/4.02 ! [M2: num,N2: num] :
% 3.82/4.02 ( ( ord_less_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N2 ) )
% 3.82/4.02 = ( ord_less_num @ M2 @ N2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % numeral_less_iff
% 3.82/4.02 thf(fact_1691_numeral__less__iff,axiom,
% 3.82/4.02 ! [M2: num,N2: num] :
% 3.82/4.02 ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M2 ) @ ( numera1916890842035813515d_enat @ N2 ) )
% 3.82/4.02 = ( ord_less_num @ M2 @ N2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % numeral_less_iff
% 3.82/4.02 thf(fact_1692_numeral__less__iff,axiom,
% 3.82/4.02 ! [M2: num,N2: num] :
% 3.82/4.02 ( ( ord_less_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N2 ) )
% 3.82/4.02 = ( ord_less_num @ M2 @ N2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % numeral_less_iff
% 3.82/4.02 thf(fact_1693_numeral__less__iff,axiom,
% 3.82/4.02 ! [M2: num,N2: num] :
% 3.82/4.02 ( ( ord_less_real @ ( numeral_numeral_real @ M2 ) @ ( numeral_numeral_real @ N2 ) )
% 3.82/4.02 = ( ord_less_num @ M2 @ N2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % numeral_less_iff
% 3.82/4.02 thf(fact_1694_numeral__plus__numeral,axiom,
% 3.82/4.02 ! [M2: num,N2: num] :
% 3.82/4.02 ( ( plus_plus_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N2 ) )
% 3.82/4.02 = ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % numeral_plus_numeral
% 3.82/4.02 thf(fact_1695_numeral__plus__numeral,axiom,
% 3.82/4.02 ! [M2: num,N2: num] :
% 3.82/4.02 ( ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ M2 ) @ ( numera1916890842035813515d_enat @ N2 ) )
% 3.82/4.02 = ( numera1916890842035813515d_enat @ ( plus_plus_num @ M2 @ N2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % numeral_plus_numeral
% 3.82/4.02 thf(fact_1696_numeral__plus__numeral,axiom,
% 3.82/4.02 ! [M2: num,N2: num] :
% 3.82/4.02 ( ( plus_plus_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N2 ) )
% 3.82/4.02 = ( numeral_numeral_int @ ( plus_plus_num @ M2 @ N2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % numeral_plus_numeral
% 3.82/4.02 thf(fact_1697_numeral__plus__numeral,axiom,
% 3.82/4.02 ! [M2: num,N2: num] :
% 3.82/4.02 ( ( plus_plus_real @ ( numeral_numeral_real @ M2 ) @ ( numeral_numeral_real @ N2 ) )
% 3.82/4.02 = ( numeral_numeral_real @ ( plus_plus_num @ M2 @ N2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % numeral_plus_numeral
% 3.82/4.02 thf(fact_1698_add__numeral__left,axiom,
% 3.82/4.02 ! [V: num,W2: num,Z3: nat] :
% 3.82/4.02 ( ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ W2 ) @ Z3 ) )
% 3.82/4.02 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ W2 ) ) @ Z3 ) ) ).
% 3.82/4.02
% 3.82/4.02 % add_numeral_left
% 3.82/4.02 thf(fact_1699_add__numeral__left,axiom,
% 3.82/4.02 ! [V: num,W2: num,Z3: extended_enat] :
% 3.82/4.02 ( ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ V ) @ ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ W2 ) @ Z3 ) )
% 3.82/4.02 = ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ ( plus_plus_num @ V @ W2 ) ) @ Z3 ) ) ).
% 3.82/4.02
% 3.82/4.02 % add_numeral_left
% 3.82/4.02 thf(fact_1700_add__numeral__left,axiom,
% 3.82/4.02 ! [V: num,W2: num,Z3: int] :
% 3.82/4.02 ( ( plus_plus_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ ( numeral_numeral_int @ W2 ) @ Z3 ) )
% 3.82/4.02 = ( plus_plus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W2 ) ) @ Z3 ) ) ).
% 3.82/4.02
% 3.82/4.02 % add_numeral_left
% 3.82/4.02 thf(fact_1701_add__numeral__left,axiom,
% 3.82/4.02 ! [V: num,W2: num,Z3: real] :
% 3.82/4.02 ( ( plus_plus_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ ( numeral_numeral_real @ W2 ) @ Z3 ) )
% 3.82/4.02 = ( plus_plus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W2 ) ) @ Z3 ) ) ).
% 3.82/4.02
% 3.82/4.02 % add_numeral_left
% 3.82/4.02 thf(fact_1702_insert__simp__mima,axiom,
% 3.82/4.02 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 3.82/4.02 ( ( ( X = Mi )
% 3.82/4.02 | ( X = Ma ) )
% 3.82/4.02 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 3.82/4.02 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 3.82/4.02 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % insert_simp_mima
% 3.82/4.02 thf(fact_1703_valid__insert__both__member__options__add,axiom,
% 3.82/4.02 ! [T: vEBT_VEBT,N2: nat,X: nat] :
% 3.82/4.02 ( ( vEBT_invar_vebt @ T @ N2 )
% 3.82/4.02 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 3.82/4.02 => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ X ) @ X ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % valid_insert_both_member_options_add
% 3.82/4.02 thf(fact_1704_valid__insert__both__member__options__pres,axiom,
% 3.82/4.02 ! [T: vEBT_VEBT,N2: nat,X: nat,Y: nat] :
% 3.82/4.02 ( ( vEBT_invar_vebt @ T @ N2 )
% 3.82/4.02 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 3.82/4.02 => ( ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 3.82/4.02 => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 3.82/4.02 => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ Y ) @ X ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % valid_insert_both_member_options_pres
% 3.82/4.02 thf(fact_1705_post__member__pre__member,axiom,
% 3.82/4.02 ! [T: vEBT_VEBT,N2: nat,X: nat,Y: nat] :
% 3.82/4.02 ( ( vEBT_invar_vebt @ T @ N2 )
% 3.82/4.02 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 3.82/4.02 => ( ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 3.82/4.02 => ( ( vEBT_vebt_member @ ( vEBT_vebt_insert @ T @ X ) @ Y )
% 3.82/4.02 => ( ( vEBT_vebt_member @ T @ Y )
% 3.82/4.02 | ( X = Y ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % post_member_pre_member
% 3.82/4.02 thf(fact_1706_replicate__eq__replicate,axiom,
% 3.82/4.02 ! [M2: nat,X: vEBT_VEBT,N2: nat,Y: vEBT_VEBT] :
% 3.82/4.02 ( ( ( replicate_VEBT_VEBT @ M2 @ X )
% 3.82/4.02 = ( replicate_VEBT_VEBT @ N2 @ Y ) )
% 3.82/4.02 = ( ( M2 = N2 )
% 3.82/4.02 & ( ( M2 != zero_zero_nat )
% 3.82/4.02 => ( X = Y ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % replicate_eq_replicate
% 3.82/4.02 thf(fact_1707_length__replicate,axiom,
% 3.82/4.02 ! [N2: nat,X: vEBT_VEBT] :
% 3.82/4.02 ( ( size_s6755466524823107622T_VEBT @ ( replicate_VEBT_VEBT @ N2 @ X ) )
% 3.82/4.02 = N2 ) ).
% 3.82/4.02
% 3.82/4.02 % length_replicate
% 3.82/4.02 thf(fact_1708_length__replicate,axiom,
% 3.82/4.02 ! [N2: nat,X: int] :
% 3.82/4.02 ( ( size_size_list_int @ ( replicate_int @ N2 @ X ) )
% 3.82/4.02 = N2 ) ).
% 3.82/4.02
% 3.82/4.02 % length_replicate
% 3.82/4.02 thf(fact_1709_length__replicate,axiom,
% 3.82/4.02 ! [N2: nat,X: nat] :
% 3.82/4.02 ( ( size_size_list_nat @ ( replicate_nat @ N2 @ X ) )
% 3.82/4.02 = N2 ) ).
% 3.82/4.02
% 3.82/4.02 % length_replicate
% 3.82/4.02 thf(fact_1710_length__enumerate,axiom,
% 3.82/4.02 ! [N2: nat,Xs: list_VEBT_VEBT] :
% 3.82/4.02 ( ( size_s4762443039079500285T_VEBT @ ( enumerate_VEBT_VEBT @ N2 @ Xs ) )
% 3.82/4.02 = ( size_s6755466524823107622T_VEBT @ Xs ) ) ).
% 3.82/4.02
% 3.82/4.02 % length_enumerate
% 3.82/4.02 thf(fact_1711_length__enumerate,axiom,
% 3.82/4.02 ! [N2: nat,Xs: list_int] :
% 3.82/4.02 ( ( size_s2970893825323803983at_int @ ( enumerate_int @ N2 @ Xs ) )
% 3.82/4.02 = ( size_size_list_int @ Xs ) ) ).
% 3.82/4.02
% 3.82/4.02 % length_enumerate
% 3.82/4.02 thf(fact_1712_length__enumerate,axiom,
% 3.82/4.02 ! [N2: nat,Xs: list_nat] :
% 3.82/4.02 ( ( size_s5460976970255530739at_nat @ ( enumerate_nat @ N2 @ Xs ) )
% 3.82/4.02 = ( size_size_list_nat @ Xs ) ) ).
% 3.82/4.02
% 3.82/4.02 % length_enumerate
% 3.82/4.02 thf(fact_1713_mi__ma__2__deg,axiom,
% 3.82/4.02 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N2: nat] :
% 3.82/4.02 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N2 )
% 3.82/4.02 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 3.82/4.02 & ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % mi_ma_2_deg
% 3.82/4.02 thf(fact_1714__C5_OIH_C_I2_J,axiom,
% 3.82/4.02 ! [X: nat] :
% 3.82/4.02 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 3.82/4.02 => ( vEBT_invar_vebt @ ( vEBT_vebt_insert @ summary @ X ) @ m ) ) ).
% 3.82/4.02
% 3.82/4.02 % "5.IH"(2)
% 3.82/4.02 thf(fact_1715_Suc__numeral,axiom,
% 3.82/4.02 ! [N2: num] :
% 3.82/4.02 ( ( suc @ ( numeral_numeral_nat @ N2 ) )
% 3.82/4.02 = ( numeral_numeral_nat @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % Suc_numeral
% 3.82/4.02 thf(fact_1716_max__number__of_I1_J,axiom,
% 3.82/4.02 ! [U: num,V: num] :
% 3.82/4.02 ( ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 3.82/4.02 => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 3.82/4.02 = ( numera1916890842035813515d_enat @ V ) ) )
% 3.82/4.02 & ( ~ ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 3.82/4.02 => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 3.82/4.02 = ( numera1916890842035813515d_enat @ U ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max_number_of(1)
% 3.82/4.02 thf(fact_1717_max__number__of_I1_J,axiom,
% 3.82/4.02 ! [U: num,V: num] :
% 3.82/4.02 ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 3.82/4.02 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 3.82/4.02 = ( numeral_numeral_real @ V ) ) )
% 3.82/4.02 & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 3.82/4.02 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 3.82/4.02 = ( numeral_numeral_real @ U ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max_number_of(1)
% 3.82/4.02 thf(fact_1718_max__number__of_I1_J,axiom,
% 3.82/4.02 ! [U: num,V: num] :
% 3.82/4.02 ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 3.82/4.02 => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 3.82/4.02 = ( numeral_numeral_nat @ V ) ) )
% 3.82/4.02 & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 3.82/4.02 => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 3.82/4.02 = ( numeral_numeral_nat @ U ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max_number_of(1)
% 3.82/4.02 thf(fact_1719_max__number__of_I1_J,axiom,
% 3.82/4.02 ! [U: num,V: num] :
% 3.82/4.02 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 3.82/4.02 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 3.82/4.02 = ( numeral_numeral_int @ V ) ) )
% 3.82/4.02 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 3.82/4.02 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 3.82/4.02 = ( numeral_numeral_int @ U ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % max_number_of(1)
% 3.82/4.02 thf(fact_1720_max__0__1_I4_J,axiom,
% 3.82/4.02 ! [X: num] :
% 3.82/4.02 ( ( ord_max_nat @ ( numeral_numeral_nat @ X ) @ zero_zero_nat )
% 3.82/4.02 = ( numeral_numeral_nat @ X ) ) ).
% 3.82/4.02
% 3.82/4.02 % max_0_1(4)
% 3.82/4.02 thf(fact_1721_max__0__1_I4_J,axiom,
% 3.82/4.02 ! [X: num] :
% 3.82/4.02 ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X ) @ zero_z5237406670263579293d_enat )
% 3.82/4.02 = ( numera1916890842035813515d_enat @ X ) ) ).
% 3.82/4.02
% 3.82/4.02 % max_0_1(4)
% 3.82/4.02 thf(fact_1722_max__0__1_I4_J,axiom,
% 3.82/4.02 ! [X: num] :
% 3.82/4.02 ( ( ord_max_int @ ( numeral_numeral_int @ X ) @ zero_zero_int )
% 3.82/4.02 = ( numeral_numeral_int @ X ) ) ).
% 3.82/4.02
% 3.82/4.02 % max_0_1(4)
% 3.82/4.02 thf(fact_1723_max__0__1_I4_J,axiom,
% 3.82/4.02 ! [X: num] :
% 3.82/4.02 ( ( ord_max_real @ ( numeral_numeral_real @ X ) @ zero_zero_real )
% 3.82/4.02 = ( numeral_numeral_real @ X ) ) ).
% 3.82/4.02
% 3.82/4.02 % max_0_1(4)
% 3.82/4.02 thf(fact_1724_max__0__1_I3_J,axiom,
% 3.82/4.02 ! [X: num] :
% 3.82/4.02 ( ( ord_max_nat @ zero_zero_nat @ ( numeral_numeral_nat @ X ) )
% 3.82/4.02 = ( numeral_numeral_nat @ X ) ) ).
% 3.82/4.02
% 3.82/4.02 % max_0_1(3)
% 3.82/4.02 thf(fact_1725_max__0__1_I3_J,axiom,
% 3.82/4.02 ! [X: num] :
% 3.82/4.02 ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ ( numera1916890842035813515d_enat @ X ) )
% 3.82/4.02 = ( numera1916890842035813515d_enat @ X ) ) ).
% 3.82/4.02
% 3.82/4.02 % max_0_1(3)
% 3.82/4.02 thf(fact_1726_max__0__1_I3_J,axiom,
% 3.82/4.02 ! [X: num] :
% 3.82/4.02 ( ( ord_max_int @ zero_zero_int @ ( numeral_numeral_int @ X ) )
% 3.82/4.02 = ( numeral_numeral_int @ X ) ) ).
% 3.82/4.02
% 3.82/4.02 % max_0_1(3)
% 3.82/4.02 thf(fact_1727_max__0__1_I3_J,axiom,
% 3.82/4.02 ! [X: num] :
% 3.82/4.02 ( ( ord_max_real @ zero_zero_real @ ( numeral_numeral_real @ X ) )
% 3.82/4.02 = ( numeral_numeral_real @ X ) ) ).
% 3.82/4.02
% 3.82/4.02 % max_0_1(3)
% 3.82/4.02 thf(fact_1728__C6_C,axiom,
% 3.82/4.02 ( ( ord_less_eq_nat @ mi @ ma )
% 3.82/4.02 & ( ord_less_nat @ ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % "6"
% 3.82/4.02 thf(fact_1729_myIHs,axiom,
% 3.82/4.02 ! [X: vEBT_VEBT,Xa2: nat] :
% 3.82/4.02 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ treeList ) )
% 3.82/4.02 => ( ( vEBT_invar_vebt @ X @ na )
% 3.82/4.02 => ( ( ord_less_nat @ Xa2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) )
% 3.82/4.02 => ( vEBT_invar_vebt @ ( vEBT_vebt_insert @ X @ Xa2 ) @ na ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % myIHs
% 3.82/4.02 thf(fact_1730_in__set__replicate,axiom,
% 3.82/4.02 ! [X: extended_enat,N2: nat,Y: extended_enat] :
% 3.82/4.02 ( ( member_Extended_enat @ X @ ( set_Extended_enat2 @ ( replic7216382294607269926d_enat @ N2 @ Y ) ) )
% 3.82/4.02 = ( ( X = Y )
% 3.82/4.02 & ( N2 != zero_zero_nat ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % in_set_replicate
% 3.82/4.02 thf(fact_1731_in__set__replicate,axiom,
% 3.82/4.02 ! [X: real,N2: nat,Y: real] :
% 3.82/4.02 ( ( member_real @ X @ ( set_real2 @ ( replicate_real @ N2 @ Y ) ) )
% 3.82/4.02 = ( ( X = Y )
% 3.82/4.02 & ( N2 != zero_zero_nat ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % in_set_replicate
% 3.82/4.02 thf(fact_1732_in__set__replicate,axiom,
% 3.82/4.02 ! [X: set_nat,N2: nat,Y: set_nat] :
% 3.82/4.02 ( ( member_set_nat @ X @ ( set_set_nat2 @ ( replicate_set_nat @ N2 @ Y ) ) )
% 3.82/4.02 = ( ( X = Y )
% 3.82/4.02 & ( N2 != zero_zero_nat ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % in_set_replicate
% 3.82/4.02 thf(fact_1733_in__set__replicate,axiom,
% 3.82/4.02 ! [X: int,N2: nat,Y: int] :
% 3.82/4.02 ( ( member_int @ X @ ( set_int2 @ ( replicate_int @ N2 @ Y ) ) )
% 3.82/4.02 = ( ( X = Y )
% 3.82/4.02 & ( N2 != zero_zero_nat ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % in_set_replicate
% 3.82/4.02 thf(fact_1734_in__set__replicate,axiom,
% 3.82/4.02 ! [X: nat,N2: nat,Y: nat] :
% 3.82/4.02 ( ( member_nat @ X @ ( set_nat2 @ ( replicate_nat @ N2 @ Y ) ) )
% 3.82/4.02 = ( ( X = Y )
% 3.82/4.02 & ( N2 != zero_zero_nat ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % in_set_replicate
% 3.82/4.02 thf(fact_1735_in__set__replicate,axiom,
% 3.82/4.02 ! [X: vEBT_VEBT,N2: nat,Y: vEBT_VEBT] :
% 3.82/4.02 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N2 @ Y ) ) )
% 3.82/4.02 = ( ( X = Y )
% 3.82/4.02 & ( N2 != zero_zero_nat ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % in_set_replicate
% 3.82/4.02 thf(fact_1736_Bex__set__replicate,axiom,
% 3.82/4.02 ! [N2: nat,A: int,P: int > $o] :
% 3.82/4.02 ( ( ? [X4: int] :
% 3.82/4.02 ( ( member_int @ X4 @ ( set_int2 @ ( replicate_int @ N2 @ A ) ) )
% 3.82/4.02 & ( P @ X4 ) ) )
% 3.82/4.02 = ( ( P @ A )
% 3.82/4.02 & ( N2 != zero_zero_nat ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % Bex_set_replicate
% 3.82/4.02 thf(fact_1737_Bex__set__replicate,axiom,
% 3.82/4.02 ! [N2: nat,A: nat,P: nat > $o] :
% 3.82/4.02 ( ( ? [X4: nat] :
% 3.82/4.02 ( ( member_nat @ X4 @ ( set_nat2 @ ( replicate_nat @ N2 @ A ) ) )
% 3.82/4.02 & ( P @ X4 ) ) )
% 3.82/4.02 = ( ( P @ A )
% 3.82/4.02 & ( N2 != zero_zero_nat ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % Bex_set_replicate
% 3.82/4.02 thf(fact_1738_Bex__set__replicate,axiom,
% 3.82/4.02 ! [N2: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 3.82/4.02 ( ( ? [X4: vEBT_VEBT] :
% 3.82/4.02 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N2 @ A ) ) )
% 3.82/4.02 & ( P @ X4 ) ) )
% 3.82/4.02 = ( ( P @ A )
% 3.82/4.02 & ( N2 != zero_zero_nat ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % Bex_set_replicate
% 3.82/4.02 thf(fact_1739_Ball__set__replicate,axiom,
% 3.82/4.02 ! [N2: nat,A: int,P: int > $o] :
% 3.82/4.02 ( ( ! [X4: int] :
% 3.82/4.02 ( ( member_int @ X4 @ ( set_int2 @ ( replicate_int @ N2 @ A ) ) )
% 3.82/4.02 => ( P @ X4 ) ) )
% 3.82/4.02 = ( ( P @ A )
% 3.82/4.02 | ( N2 = zero_zero_nat ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % Ball_set_replicate
% 3.82/4.02 thf(fact_1740_Ball__set__replicate,axiom,
% 3.82/4.02 ! [N2: nat,A: nat,P: nat > $o] :
% 3.82/4.02 ( ( ! [X4: nat] :
% 3.82/4.02 ( ( member_nat @ X4 @ ( set_nat2 @ ( replicate_nat @ N2 @ A ) ) )
% 3.82/4.02 => ( P @ X4 ) ) )
% 3.82/4.02 = ( ( P @ A )
% 3.82/4.02 | ( N2 = zero_zero_nat ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % Ball_set_replicate
% 3.82/4.02 thf(fact_1741_Ball__set__replicate,axiom,
% 3.82/4.02 ! [N2: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 3.82/4.02 ( ( ! [X4: vEBT_VEBT] :
% 3.82/4.02 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N2 @ A ) ) )
% 3.82/4.02 => ( P @ X4 ) ) )
% 3.82/4.02 = ( ( P @ A )
% 3.82/4.02 | ( N2 = zero_zero_nat ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % Ball_set_replicate
% 3.82/4.02 thf(fact_1742_nth__replicate,axiom,
% 3.82/4.02 ! [I: nat,N2: nat,X: nat] :
% 3.82/4.02 ( ( ord_less_nat @ I @ N2 )
% 3.82/4.02 => ( ( nth_nat @ ( replicate_nat @ N2 @ X ) @ I )
% 3.82/4.02 = X ) ) ).
% 3.82/4.02
% 3.82/4.02 % nth_replicate
% 3.82/4.02 thf(fact_1743_nth__replicate,axiom,
% 3.82/4.02 ! [I: nat,N2: nat,X: int] :
% 3.82/4.02 ( ( ord_less_nat @ I @ N2 )
% 3.82/4.02 => ( ( nth_int @ ( replicate_int @ N2 @ X ) @ I )
% 3.82/4.02 = X ) ) ).
% 3.82/4.02
% 3.82/4.02 % nth_replicate
% 3.82/4.02 thf(fact_1744_nth__replicate,axiom,
% 3.82/4.02 ! [I: nat,N2: nat,X: vEBT_VEBT] :
% 3.82/4.02 ( ( ord_less_nat @ I @ N2 )
% 3.82/4.02 => ( ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N2 @ X ) @ I )
% 3.82/4.02 = X ) ) ).
% 3.82/4.02
% 3.82/4.02 % nth_replicate
% 3.82/4.02 thf(fact_1745_highlowprop,axiom,
% 3.82/4.02 ( ( ord_less_nat @ ( vEBT_VEBT_high @ mi @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 3.82/4.02 & ( ord_less_nat @ ( vEBT_VEBT_low @ mi @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % highlowprop
% 3.82/4.02 thf(fact_1746_add__2__eq__Suc,axiom,
% 3.82/4.02 ! [N2: nat] :
% 3.82/4.02 ( ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 3.82/4.02 = ( suc @ ( suc @ N2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % add_2_eq_Suc
% 3.82/4.02 thf(fact_1747_add__2__eq__Suc_H,axiom,
% 3.82/4.02 ! [N2: nat] :
% 3.82/4.02 ( ( plus_plus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.02 = ( suc @ ( suc @ N2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % add_2_eq_Suc'
% 3.82/4.02 thf(fact_1748_numeral__Bit0,axiom,
% 3.82/4.02 ! [N2: num] :
% 3.82/4.02 ( ( numeral_numeral_nat @ ( bit0 @ N2 ) )
% 3.82/4.02 = ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % numeral_Bit0
% 3.82/4.02 thf(fact_1749_numeral__Bit0,axiom,
% 3.82/4.02 ! [N2: num] :
% 3.82/4.02 ( ( numera1916890842035813515d_enat @ ( bit0 @ N2 ) )
% 3.82/4.02 = ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ ( numera1916890842035813515d_enat @ N2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % numeral_Bit0
% 3.82/4.02 thf(fact_1750_numeral__Bit0,axiom,
% 3.82/4.02 ! [N2: num] :
% 3.82/4.02 ( ( numeral_numeral_int @ ( bit0 @ N2 ) )
% 3.82/4.02 = ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % numeral_Bit0
% 3.82/4.02 thf(fact_1751_numeral__Bit0,axiom,
% 3.82/4.02 ! [N2: num] :
% 3.82/4.02 ( ( numeral_numeral_real @ ( bit0 @ N2 ) )
% 3.82/4.02 = ( plus_plus_real @ ( numeral_numeral_real @ N2 ) @ ( numeral_numeral_real @ N2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % numeral_Bit0
% 3.82/4.02 thf(fact_1752_listrel1__eq__len,axiom,
% 3.82/4.02 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT,R2: set_Pr6192946355708809607T_VEBT] :
% 3.82/4.02 ( ( member4439316823752958928T_VEBT @ ( produc3897820843166775703T_VEBT @ Xs @ Ys ) @ ( listrel1_VEBT_VEBT @ R2 ) )
% 3.82/4.02 => ( ( size_s6755466524823107622T_VEBT @ Xs )
% 3.82/4.02 = ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % listrel1_eq_len
% 3.82/4.02 thf(fact_1753_listrel1__eq__len,axiom,
% 3.82/4.02 ! [Xs: list_int,Ys: list_int,R2: set_Pr958786334691620121nt_int] :
% 3.82/4.02 ( ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Xs @ Ys ) @ ( listrel1_int @ R2 ) )
% 3.82/4.02 => ( ( size_size_list_int @ Xs )
% 3.82/4.02 = ( size_size_list_int @ Ys ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % listrel1_eq_len
% 3.82/4.02 thf(fact_1754_listrel1__eq__len,axiom,
% 3.82/4.02 ! [Xs: list_nat,Ys: list_nat,R2: set_Pr1261947904930325089at_nat] :
% 3.82/4.02 ( ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Xs @ Ys ) @ ( listrel1_nat @ R2 ) )
% 3.82/4.02 => ( ( size_size_list_nat @ Xs )
% 3.82/4.02 = ( size_size_list_nat @ Ys ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % listrel1_eq_len
% 3.82/4.02 thf(fact_1755_numeral__2__eq__2,axiom,
% 3.82/4.02 ( ( numeral_numeral_nat @ ( bit0 @ one ) )
% 3.82/4.02 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % numeral_2_eq_2
% 3.82/4.02 thf(fact_1756_find__None__iff,axiom,
% 3.82/4.02 ! [P: extended_enat > $o,Xs: list_Extended_enat] :
% 3.82/4.02 ( ( ( find_Extended_enat @ P @ Xs )
% 3.82/4.02 = none_Extended_enat )
% 3.82/4.02 = ( ~ ? [X4: extended_enat] :
% 3.82/4.02 ( ( member_Extended_enat @ X4 @ ( set_Extended_enat2 @ Xs ) )
% 3.82/4.02 & ( P @ X4 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % find_None_iff
% 3.82/4.02 thf(fact_1757_find__None__iff,axiom,
% 3.82/4.02 ! [P: real > $o,Xs: list_real] :
% 3.82/4.02 ( ( ( find_real @ P @ Xs )
% 3.82/4.02 = none_real )
% 3.82/4.02 = ( ~ ? [X4: real] :
% 3.82/4.02 ( ( member_real @ X4 @ ( set_real2 @ Xs ) )
% 3.82/4.02 & ( P @ X4 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % find_None_iff
% 3.82/4.02 thf(fact_1758_find__None__iff,axiom,
% 3.82/4.02 ! [P: set_nat > $o,Xs: list_set_nat] :
% 3.82/4.02 ( ( ( find_set_nat @ P @ Xs )
% 3.82/4.02 = none_set_nat )
% 3.82/4.02 = ( ~ ? [X4: set_nat] :
% 3.82/4.02 ( ( member_set_nat @ X4 @ ( set_set_nat2 @ Xs ) )
% 3.82/4.02 & ( P @ X4 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % find_None_iff
% 3.82/4.02 thf(fact_1759_find__None__iff,axiom,
% 3.82/4.02 ! [P: vEBT_VEBT > $o,Xs: list_VEBT_VEBT] :
% 3.82/4.02 ( ( ( find_VEBT_VEBT @ P @ Xs )
% 3.82/4.02 = none_VEBT_VEBT )
% 3.82/4.02 = ( ~ ? [X4: vEBT_VEBT] :
% 3.82/4.02 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs ) )
% 3.82/4.02 & ( P @ X4 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % find_None_iff
% 3.82/4.02 thf(fact_1760_find__None__iff,axiom,
% 3.82/4.02 ! [P: int > $o,Xs: list_int] :
% 3.82/4.02 ( ( ( find_int @ P @ Xs )
% 3.82/4.02 = none_int )
% 3.82/4.02 = ( ~ ? [X4: int] :
% 3.82/4.02 ( ( member_int @ X4 @ ( set_int2 @ Xs ) )
% 3.82/4.02 & ( P @ X4 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % find_None_iff
% 3.82/4.02 thf(fact_1761_find__None__iff,axiom,
% 3.82/4.02 ! [P: nat > $o,Xs: list_nat] :
% 3.82/4.02 ( ( ( find_nat @ P @ Xs )
% 3.82/4.02 = none_nat )
% 3.82/4.02 = ( ~ ? [X4: nat] :
% 3.82/4.02 ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 3.82/4.02 & ( P @ X4 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % find_None_iff
% 3.82/4.02 thf(fact_1762_find__None__iff,axiom,
% 3.82/4.02 ! [P: product_prod_nat_nat > $o,Xs: list_P6011104703257516679at_nat] :
% 3.82/4.02 ( ( ( find_P8199882355184865565at_nat @ P @ Xs )
% 3.82/4.02 = none_P5556105721700978146at_nat )
% 3.82/4.02 = ( ~ ? [X4: product_prod_nat_nat] :
% 3.82/4.02 ( ( member8440522571783428010at_nat @ X4 @ ( set_Pr5648618587558075414at_nat @ Xs ) )
% 3.82/4.02 & ( P @ X4 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % find_None_iff
% 3.82/4.02 thf(fact_1763_find__None__iff,axiom,
% 3.82/4.02 ! [P: num > $o,Xs: list_num] :
% 3.82/4.02 ( ( ( find_num @ P @ Xs )
% 3.82/4.02 = none_num )
% 3.82/4.02 = ( ~ ? [X4: num] :
% 3.82/4.02 ( ( member_num @ X4 @ ( set_num2 @ Xs ) )
% 3.82/4.02 & ( P @ X4 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % find_None_iff
% 3.82/4.02 thf(fact_1764_find__None__iff2,axiom,
% 3.82/4.02 ! [P: extended_enat > $o,Xs: list_Extended_enat] :
% 3.82/4.02 ( ( none_Extended_enat
% 3.82/4.02 = ( find_Extended_enat @ P @ Xs ) )
% 3.82/4.02 = ( ~ ? [X4: extended_enat] :
% 3.82/4.02 ( ( member_Extended_enat @ X4 @ ( set_Extended_enat2 @ Xs ) )
% 3.82/4.02 & ( P @ X4 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % find_None_iff2
% 3.82/4.02 thf(fact_1765_find__None__iff2,axiom,
% 3.82/4.02 ! [P: real > $o,Xs: list_real] :
% 3.82/4.02 ( ( none_real
% 3.82/4.02 = ( find_real @ P @ Xs ) )
% 3.82/4.02 = ( ~ ? [X4: real] :
% 3.82/4.02 ( ( member_real @ X4 @ ( set_real2 @ Xs ) )
% 3.82/4.02 & ( P @ X4 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % find_None_iff2
% 3.82/4.02 thf(fact_1766_find__None__iff2,axiom,
% 3.82/4.02 ! [P: set_nat > $o,Xs: list_set_nat] :
% 3.82/4.02 ( ( none_set_nat
% 3.82/4.02 = ( find_set_nat @ P @ Xs ) )
% 3.82/4.02 = ( ~ ? [X4: set_nat] :
% 3.82/4.02 ( ( member_set_nat @ X4 @ ( set_set_nat2 @ Xs ) )
% 3.82/4.02 & ( P @ X4 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % find_None_iff2
% 3.82/4.02 thf(fact_1767_find__None__iff2,axiom,
% 3.82/4.02 ! [P: vEBT_VEBT > $o,Xs: list_VEBT_VEBT] :
% 3.82/4.02 ( ( none_VEBT_VEBT
% 3.82/4.02 = ( find_VEBT_VEBT @ P @ Xs ) )
% 3.82/4.02 = ( ~ ? [X4: vEBT_VEBT] :
% 3.82/4.02 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs ) )
% 3.82/4.02 & ( P @ X4 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % find_None_iff2
% 3.82/4.02 thf(fact_1768_find__None__iff2,axiom,
% 3.82/4.02 ! [P: int > $o,Xs: list_int] :
% 3.82/4.02 ( ( none_int
% 3.82/4.02 = ( find_int @ P @ Xs ) )
% 3.82/4.02 = ( ~ ? [X4: int] :
% 3.82/4.02 ( ( member_int @ X4 @ ( set_int2 @ Xs ) )
% 3.82/4.02 & ( P @ X4 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % find_None_iff2
% 3.82/4.02 thf(fact_1769_find__None__iff2,axiom,
% 3.82/4.02 ! [P: nat > $o,Xs: list_nat] :
% 3.82/4.02 ( ( none_nat
% 3.82/4.02 = ( find_nat @ P @ Xs ) )
% 3.82/4.02 = ( ~ ? [X4: nat] :
% 3.82/4.02 ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 3.82/4.02 & ( P @ X4 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % find_None_iff2
% 3.82/4.02 thf(fact_1770_find__None__iff2,axiom,
% 3.82/4.02 ! [P: product_prod_nat_nat > $o,Xs: list_P6011104703257516679at_nat] :
% 3.82/4.02 ( ( none_P5556105721700978146at_nat
% 3.82/4.02 = ( find_P8199882355184865565at_nat @ P @ Xs ) )
% 3.82/4.02 = ( ~ ? [X4: product_prod_nat_nat] :
% 3.82/4.02 ( ( member8440522571783428010at_nat @ X4 @ ( set_Pr5648618587558075414at_nat @ Xs ) )
% 3.82/4.02 & ( P @ X4 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % find_None_iff2
% 3.82/4.02 thf(fact_1771_find__None__iff2,axiom,
% 3.82/4.02 ! [P: num > $o,Xs: list_num] :
% 3.82/4.02 ( ( none_num
% 3.82/4.02 = ( find_num @ P @ Xs ) )
% 3.82/4.02 = ( ~ ? [X4: num] :
% 3.82/4.02 ( ( member_num @ X4 @ ( set_num2 @ Xs ) )
% 3.82/4.02 & ( P @ X4 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % find_None_iff2
% 3.82/4.02 thf(fact_1772_VEBT__internal_Oexp__split__high__low_I1_J,axiom,
% 3.82/4.02 ! [X: nat,N2: nat,M2: nat] :
% 3.82/4.02 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M2 ) ) )
% 3.82/4.02 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.02 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 3.82/4.02 => ( ord_less_nat @ ( vEBT_VEBT_high @ X @ N2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % VEBT_internal.exp_split_high_low(1)
% 3.82/4.02 thf(fact_1773_option_Osize__gen_I1_J,axiom,
% 3.82/4.02 ! [X: product_prod_nat_nat > nat] :
% 3.82/4.02 ( ( size_o8335143837870341156at_nat @ X @ none_P5556105721700978146at_nat )
% 3.82/4.02 = ( suc @ zero_zero_nat ) ) ).
% 3.82/4.02
% 3.82/4.02 % option.size_gen(1)
% 3.82/4.02 thf(fact_1774_option_Osize__gen_I1_J,axiom,
% 3.82/4.02 ! [X: num > nat] :
% 3.82/4.02 ( ( size_option_num @ X @ none_num )
% 3.82/4.02 = ( suc @ zero_zero_nat ) ) ).
% 3.82/4.02
% 3.82/4.02 % option.size_gen(1)
% 3.82/4.02 thf(fact_1775_VEBT__internal_Oexp__split__high__low_I2_J,axiom,
% 3.82/4.02 ! [X: nat,N2: nat,M2: nat] :
% 3.82/4.02 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M2 ) ) )
% 3.82/4.02 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.02 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 3.82/4.02 => ( ord_less_nat @ ( vEBT_VEBT_low @ X @ N2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % VEBT_internal.exp_split_high_low(2)
% 3.82/4.02 thf(fact_1776_less__2__cases__iff,axiom,
% 3.82/4.02 ! [N2: nat] :
% 3.82/4.02 ( ( ord_less_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.02 = ( ( N2 = zero_zero_nat )
% 3.82/4.02 | ( N2
% 3.82/4.02 = ( suc @ zero_zero_nat ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % less_2_cases_iff
% 3.82/4.02 thf(fact_1777_less__2__cases,axiom,
% 3.82/4.02 ! [N2: nat] :
% 3.82/4.02 ( ( ord_less_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.02 => ( ( N2 = zero_zero_nat )
% 3.82/4.02 | ( N2
% 3.82/4.02 = ( suc @ zero_zero_nat ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % less_2_cases
% 3.82/4.02 thf(fact_1778_invar__vebt_Ointros_I2_J,axiom,
% 3.82/4.02 ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary: vEBT_VEBT,M2: nat,Deg: nat] :
% 3.82/4.02 ( ! [X5: vEBT_VEBT] :
% 3.82/4.02 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 3.82/4.02 => ( vEBT_invar_vebt @ X5 @ N2 ) )
% 3.82/4.02 => ( ( vEBT_invar_vebt @ Summary @ M2 )
% 3.82/4.02 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 3.82/4.02 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 3.82/4.02 => ( ( M2 = N2 )
% 3.82/4.02 => ( ( Deg
% 3.82/4.02 = ( plus_plus_nat @ N2 @ M2 ) )
% 3.82/4.02 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_12 )
% 3.82/4.02 => ( ! [X5: vEBT_VEBT] :
% 3.82/4.02 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 3.82/4.02 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) )
% 3.82/4.02 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % invar_vebt.intros(2)
% 3.82/4.02 thf(fact_1779_numeral__1__eq__Suc__0,axiom,
% 3.82/4.02 ( ( numeral_numeral_nat @ one )
% 3.82/4.02 = ( suc @ zero_zero_nat ) ) ).
% 3.82/4.02
% 3.82/4.02 % numeral_1_eq_Suc_0
% 3.82/4.02 thf(fact_1780_Suc__nat__number__of__add,axiom,
% 3.82/4.02 ! [V: num,N2: nat] :
% 3.82/4.02 ( ( suc @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N2 ) )
% 3.82/4.02 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ one ) ) @ N2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % Suc_nat_number_of_add
% 3.82/4.02 thf(fact_1781_zero__neq__numeral,axiom,
% 3.82/4.02 ! [N2: num] :
% 3.82/4.02 ( zero_zero_complex
% 3.82/4.02 != ( numera6690914467698888265omplex @ N2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % zero_neq_numeral
% 3.82/4.02 thf(fact_1782_zero__neq__numeral,axiom,
% 3.82/4.02 ! [N2: num] :
% 3.82/4.02 ( zero_zero_nat
% 3.82/4.02 != ( numeral_numeral_nat @ N2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % zero_neq_numeral
% 3.82/4.02 thf(fact_1783_zero__neq__numeral,axiom,
% 3.82/4.02 ! [N2: num] :
% 3.82/4.02 ( zero_z5237406670263579293d_enat
% 3.82/4.02 != ( numera1916890842035813515d_enat @ N2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % zero_neq_numeral
% 3.82/4.02 thf(fact_1784_zero__neq__numeral,axiom,
% 3.82/4.02 ! [N2: num] :
% 3.82/4.02 ( zero_zero_int
% 3.82/4.02 != ( numeral_numeral_int @ N2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % zero_neq_numeral
% 3.82/4.02 thf(fact_1785_zero__neq__numeral,axiom,
% 3.82/4.02 ! [N2: num] :
% 3.82/4.02 ( zero_zero_real
% 3.82/4.02 != ( numeral_numeral_real @ N2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % zero_neq_numeral
% 3.82/4.02 thf(fact_1786_fold__atLeastAtMost__nat_Ocases,axiom,
% 3.82/4.02 ! [X: produc4471711990508489141at_nat] :
% 3.82/4.02 ~ ! [F2: nat > nat > nat,A4: nat,B4: nat,Acc: nat] :
% 3.82/4.02 ( X
% 3.82/4.02 != ( produc3209952032786966637at_nat @ F2 @ ( produc487386426758144856at_nat @ A4 @ ( product_Pair_nat_nat @ B4 @ Acc ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % fold_atLeastAtMost_nat.cases
% 3.82/4.02 thf(fact_1787_invar__vebt_Ointros_I3_J,axiom,
% 3.82/4.02 ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary: vEBT_VEBT,M2: nat,Deg: nat] :
% 3.82/4.02 ( ! [X5: vEBT_VEBT] :
% 3.82/4.02 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 3.82/4.02 => ( vEBT_invar_vebt @ X5 @ N2 ) )
% 3.82/4.02 => ( ( vEBT_invar_vebt @ Summary @ M2 )
% 3.82/4.02 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 3.82/4.02 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 3.82/4.02 => ( ( M2
% 3.82/4.02 = ( suc @ N2 ) )
% 3.82/4.02 => ( ( Deg
% 3.82/4.02 = ( plus_plus_nat @ N2 @ M2 ) )
% 3.82/4.02 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_12 )
% 3.82/4.02 => ( ! [X5: vEBT_VEBT] :
% 3.82/4.02 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 3.82/4.02 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) )
% 3.82/4.02 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % invar_vebt.intros(3)
% 3.82/4.02 thf(fact_1788_num_Osize_I4_J,axiom,
% 3.82/4.02 ( ( size_size_num @ one )
% 3.82/4.02 = zero_zero_nat ) ).
% 3.82/4.02
% 3.82/4.02 % num.size(4)
% 3.82/4.02 thf(fact_1789_option_Osize_I3_J,axiom,
% 3.82/4.02 ( ( size_s170228958280169651at_nat @ none_P5556105721700978146at_nat )
% 3.82/4.02 = ( suc @ zero_zero_nat ) ) ).
% 3.82/4.02
% 3.82/4.02 % option.size(3)
% 3.82/4.02 thf(fact_1790_option_Osize_I3_J,axiom,
% 3.82/4.02 ( ( size_size_option_num @ none_num )
% 3.82/4.02 = ( suc @ zero_zero_nat ) ) ).
% 3.82/4.02
% 3.82/4.02 % option.size(3)
% 3.82/4.02 thf(fact_1791_find__cong,axiom,
% 3.82/4.02 ! [Xs: list_Extended_enat,Ys: list_Extended_enat,P: extended_enat > $o,Q: extended_enat > $o] :
% 3.82/4.02 ( ( Xs = Ys )
% 3.82/4.02 => ( ! [X5: extended_enat] :
% 3.82/4.02 ( ( member_Extended_enat @ X5 @ ( set_Extended_enat2 @ Ys ) )
% 3.82/4.02 => ( ( P @ X5 )
% 3.82/4.02 = ( Q @ X5 ) ) )
% 3.82/4.02 => ( ( find_Extended_enat @ P @ Xs )
% 3.82/4.02 = ( find_Extended_enat @ Q @ Ys ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % find_cong
% 3.82/4.02 thf(fact_1792_find__cong,axiom,
% 3.82/4.02 ! [Xs: list_real,Ys: list_real,P: real > $o,Q: real > $o] :
% 3.82/4.02 ( ( Xs = Ys )
% 3.82/4.02 => ( ! [X5: real] :
% 3.82/4.02 ( ( member_real @ X5 @ ( set_real2 @ Ys ) )
% 3.82/4.02 => ( ( P @ X5 )
% 3.82/4.02 = ( Q @ X5 ) ) )
% 3.82/4.02 => ( ( find_real @ P @ Xs )
% 3.82/4.02 = ( find_real @ Q @ Ys ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % find_cong
% 3.82/4.02 thf(fact_1793_find__cong,axiom,
% 3.82/4.02 ! [Xs: list_set_nat,Ys: list_set_nat,P: set_nat > $o,Q: set_nat > $o] :
% 3.82/4.02 ( ( Xs = Ys )
% 3.82/4.02 => ( ! [X5: set_nat] :
% 3.82/4.02 ( ( member_set_nat @ X5 @ ( set_set_nat2 @ Ys ) )
% 3.82/4.02 => ( ( P @ X5 )
% 3.82/4.02 = ( Q @ X5 ) ) )
% 3.82/4.02 => ( ( find_set_nat @ P @ Xs )
% 3.82/4.02 = ( find_set_nat @ Q @ Ys ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % find_cong
% 3.82/4.02 thf(fact_1794_find__cong,axiom,
% 3.82/4.02 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT,P: vEBT_VEBT > $o,Q: vEBT_VEBT > $o] :
% 3.82/4.02 ( ( Xs = Ys )
% 3.82/4.02 => ( ! [X5: vEBT_VEBT] :
% 3.82/4.02 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ Ys ) )
% 3.82/4.02 => ( ( P @ X5 )
% 3.82/4.02 = ( Q @ X5 ) ) )
% 3.82/4.02 => ( ( find_VEBT_VEBT @ P @ Xs )
% 3.82/4.02 = ( find_VEBT_VEBT @ Q @ Ys ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % find_cong
% 3.82/4.02 thf(fact_1795_find__cong,axiom,
% 3.82/4.02 ! [Xs: list_int,Ys: list_int,P: int > $o,Q: int > $o] :
% 3.82/4.02 ( ( Xs = Ys )
% 3.82/4.02 => ( ! [X5: int] :
% 3.82/4.02 ( ( member_int @ X5 @ ( set_int2 @ Ys ) )
% 3.82/4.02 => ( ( P @ X5 )
% 3.82/4.02 = ( Q @ X5 ) ) )
% 3.82/4.02 => ( ( find_int @ P @ Xs )
% 3.82/4.02 = ( find_int @ Q @ Ys ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % find_cong
% 3.82/4.02 thf(fact_1796_find__cong,axiom,
% 3.82/4.02 ! [Xs: list_nat,Ys: list_nat,P: nat > $o,Q: nat > $o] :
% 3.82/4.02 ( ( Xs = Ys )
% 3.82/4.02 => ( ! [X5: nat] :
% 3.82/4.02 ( ( member_nat @ X5 @ ( set_nat2 @ Ys ) )
% 3.82/4.02 => ( ( P @ X5 )
% 3.82/4.02 = ( Q @ X5 ) ) )
% 3.82/4.02 => ( ( find_nat @ P @ Xs )
% 3.82/4.02 = ( find_nat @ Q @ Ys ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % find_cong
% 3.82/4.02 thf(fact_1797_not__numeral__le__zero,axiom,
% 3.82/4.02 ! [N2: num] :
% 3.82/4.02 ~ ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ zero_z5237406670263579293d_enat ) ).
% 3.82/4.02
% 3.82/4.02 % not_numeral_le_zero
% 3.82/4.02 thf(fact_1798_not__numeral__le__zero,axiom,
% 3.82/4.02 ! [N2: num] :
% 3.82/4.02 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ N2 ) @ zero_zero_real ) ).
% 3.82/4.02
% 3.82/4.02 % not_numeral_le_zero
% 3.82/4.02 thf(fact_1799_not__numeral__le__zero,axiom,
% 3.82/4.02 ! [N2: num] :
% 3.82/4.02 ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ N2 ) @ zero_zero_nat ) ).
% 3.82/4.02
% 3.82/4.02 % not_numeral_le_zero
% 3.82/4.02 thf(fact_1800_not__numeral__le__zero,axiom,
% 3.82/4.02 ! [N2: num] :
% 3.82/4.02 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ zero_zero_int ) ).
% 3.82/4.02
% 3.82/4.02 % not_numeral_le_zero
% 3.82/4.02 thf(fact_1801_zero__le__numeral,axiom,
% 3.82/4.02 ! [N2: num] : ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( numera1916890842035813515d_enat @ N2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % zero_le_numeral
% 3.82/4.02 thf(fact_1802_zero__le__numeral,axiom,
% 3.82/4.02 ! [N2: num] : ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ N2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % zero_le_numeral
% 3.82/4.02 thf(fact_1803_zero__le__numeral,axiom,
% 3.82/4.02 ! [N2: num] : ( ord_less_eq_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % zero_le_numeral
% 3.82/4.02 thf(fact_1804_zero__le__numeral,axiom,
% 3.82/4.02 ! [N2: num] : ( ord_less_eq_int @ zero_zero_int @ ( numeral_numeral_int @ N2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % zero_le_numeral
% 3.82/4.02 thf(fact_1805_not__numeral__less__zero,axiom,
% 3.82/4.02 ! [N2: num] :
% 3.82/4.02 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N2 ) @ zero_zero_nat ) ).
% 3.82/4.02
% 3.82/4.02 % not_numeral_less_zero
% 3.82/4.02 thf(fact_1806_not__numeral__less__zero,axiom,
% 3.82/4.02 ! [N2: num] :
% 3.82/4.02 ~ ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ zero_z5237406670263579293d_enat ) ).
% 3.82/4.02
% 3.82/4.02 % not_numeral_less_zero
% 3.82/4.02 thf(fact_1807_not__numeral__less__zero,axiom,
% 3.82/4.02 ! [N2: num] :
% 3.82/4.02 ~ ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ zero_zero_int ) ).
% 3.82/4.02
% 3.82/4.02 % not_numeral_less_zero
% 3.82/4.02 thf(fact_1808_not__numeral__less__zero,axiom,
% 3.82/4.02 ! [N2: num] :
% 3.82/4.02 ~ ( ord_less_real @ ( numeral_numeral_real @ N2 ) @ zero_zero_real ) ).
% 3.82/4.02
% 3.82/4.02 % not_numeral_less_zero
% 3.82/4.02 thf(fact_1809_zero__less__numeral,axiom,
% 3.82/4.02 ! [N2: num] : ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % zero_less_numeral
% 3.82/4.02 thf(fact_1810_zero__less__numeral,axiom,
% 3.82/4.02 ! [N2: num] : ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( numera1916890842035813515d_enat @ N2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % zero_less_numeral
% 3.82/4.02 thf(fact_1811_zero__less__numeral,axiom,
% 3.82/4.02 ! [N2: num] : ( ord_less_int @ zero_zero_int @ ( numeral_numeral_int @ N2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % zero_less_numeral
% 3.82/4.02 thf(fact_1812_zero__less__numeral,axiom,
% 3.82/4.02 ! [N2: num] : ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ N2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % zero_less_numeral
% 3.82/4.02 thf(fact_1813_replicate__eqI,axiom,
% 3.82/4.02 ! [Xs: list_Extended_enat,N2: nat,X: extended_enat] :
% 3.82/4.02 ( ( ( size_s3941691890525107288d_enat @ Xs )
% 3.82/4.02 = N2 )
% 3.82/4.02 => ( ! [Y3: extended_enat] :
% 3.82/4.02 ( ( member_Extended_enat @ Y3 @ ( set_Extended_enat2 @ Xs ) )
% 3.82/4.02 => ( Y3 = X ) )
% 3.82/4.02 => ( Xs
% 3.82/4.02 = ( replic7216382294607269926d_enat @ N2 @ X ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % replicate_eqI
% 3.82/4.02 thf(fact_1814_replicate__eqI,axiom,
% 3.82/4.02 ! [Xs: list_real,N2: nat,X: real] :
% 3.82/4.02 ( ( ( size_size_list_real @ Xs )
% 3.82/4.02 = N2 )
% 3.82/4.02 => ( ! [Y3: real] :
% 3.82/4.02 ( ( member_real @ Y3 @ ( set_real2 @ Xs ) )
% 3.82/4.02 => ( Y3 = X ) )
% 3.82/4.02 => ( Xs
% 3.82/4.02 = ( replicate_real @ N2 @ X ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % replicate_eqI
% 3.82/4.02 thf(fact_1815_replicate__eqI,axiom,
% 3.82/4.02 ! [Xs: list_set_nat,N2: nat,X: set_nat] :
% 3.82/4.02 ( ( ( size_s3254054031482475050et_nat @ Xs )
% 3.82/4.02 = N2 )
% 3.82/4.02 => ( ! [Y3: set_nat] :
% 3.82/4.02 ( ( member_set_nat @ Y3 @ ( set_set_nat2 @ Xs ) )
% 3.82/4.02 => ( Y3 = X ) )
% 3.82/4.02 => ( Xs
% 3.82/4.02 = ( replicate_set_nat @ N2 @ X ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % replicate_eqI
% 3.82/4.02 thf(fact_1816_replicate__eqI,axiom,
% 3.82/4.02 ! [Xs: list_VEBT_VEBT,N2: nat,X: vEBT_VEBT] :
% 3.82/4.02 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 3.82/4.02 = N2 )
% 3.82/4.02 => ( ! [Y3: vEBT_VEBT] :
% 3.82/4.02 ( ( member_VEBT_VEBT @ Y3 @ ( set_VEBT_VEBT2 @ Xs ) )
% 3.82/4.02 => ( Y3 = X ) )
% 3.82/4.02 => ( Xs
% 3.82/4.02 = ( replicate_VEBT_VEBT @ N2 @ X ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % replicate_eqI
% 3.82/4.02 thf(fact_1817_replicate__eqI,axiom,
% 3.82/4.02 ! [Xs: list_int,N2: nat,X: int] :
% 3.82/4.02 ( ( ( size_size_list_int @ Xs )
% 3.82/4.02 = N2 )
% 3.82/4.02 => ( ! [Y3: int] :
% 3.82/4.02 ( ( member_int @ Y3 @ ( set_int2 @ Xs ) )
% 3.82/4.02 => ( Y3 = X ) )
% 3.82/4.02 => ( Xs
% 3.82/4.02 = ( replicate_int @ N2 @ X ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % replicate_eqI
% 3.82/4.02 thf(fact_1818_replicate__eqI,axiom,
% 3.82/4.02 ! [Xs: list_nat,N2: nat,X: nat] :
% 3.82/4.02 ( ( ( size_size_list_nat @ Xs )
% 3.82/4.02 = N2 )
% 3.82/4.02 => ( ! [Y3: nat] :
% 3.82/4.02 ( ( member_nat @ Y3 @ ( set_nat2 @ Xs ) )
% 3.82/4.02 => ( Y3 = X ) )
% 3.82/4.02 => ( Xs
% 3.82/4.02 = ( replicate_nat @ N2 @ X ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % replicate_eqI
% 3.82/4.02 thf(fact_1819_replicate__length__same,axiom,
% 3.82/4.02 ! [Xs: list_VEBT_VEBT,X: vEBT_VEBT] :
% 3.82/4.02 ( ! [X5: vEBT_VEBT] :
% 3.82/4.02 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ Xs ) )
% 3.82/4.02 => ( X5 = X ) )
% 3.82/4.02 => ( ( replicate_VEBT_VEBT @ ( size_s6755466524823107622T_VEBT @ Xs ) @ X )
% 3.82/4.02 = Xs ) ) ).
% 3.82/4.02
% 3.82/4.02 % replicate_length_same
% 3.82/4.02 thf(fact_1820_replicate__length__same,axiom,
% 3.82/4.02 ! [Xs: list_int,X: int] :
% 3.82/4.02 ( ! [X5: int] :
% 3.82/4.02 ( ( member_int @ X5 @ ( set_int2 @ Xs ) )
% 3.82/4.02 => ( X5 = X ) )
% 3.82/4.02 => ( ( replicate_int @ ( size_size_list_int @ Xs ) @ X )
% 3.82/4.02 = Xs ) ) ).
% 3.82/4.02
% 3.82/4.02 % replicate_length_same
% 3.82/4.02 thf(fact_1821_replicate__length__same,axiom,
% 3.82/4.02 ! [Xs: list_nat,X: nat] :
% 3.82/4.02 ( ! [X5: nat] :
% 3.82/4.02 ( ( member_nat @ X5 @ ( set_nat2 @ Xs ) )
% 3.82/4.02 => ( X5 = X ) )
% 3.82/4.02 => ( ( replicate_nat @ ( size_size_list_nat @ Xs ) @ X )
% 3.82/4.02 = Xs ) ) ).
% 3.82/4.02
% 3.82/4.02 % replicate_length_same
% 3.82/4.02 thf(fact_1822_vebt__member_Osimps_I2_J,axiom,
% 3.82/4.02 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,X: nat] :
% 3.82/4.02 ~ ( vEBT_vebt_member @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ X ) ).
% 3.82/4.02
% 3.82/4.02 % vebt_member.simps(2)
% 3.82/4.02 thf(fact_1823_VEBT__internal_OminNull_Osimps_I4_J,axiom,
% 3.82/4.02 ! [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] : ( vEBT_VEBT_minNull @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) ) ).
% 3.82/4.02
% 3.82/4.02 % VEBT_internal.minNull.simps(4)
% 3.82/4.02 thf(fact_1824_invar__vebt_Ointros_I4_J,axiom,
% 3.82/4.02 ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary: vEBT_VEBT,M2: nat,Deg: nat,Mi: nat,Ma: nat] :
% 3.82/4.02 ( ! [X5: vEBT_VEBT] :
% 3.82/4.02 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 3.82/4.02 => ( vEBT_invar_vebt @ X5 @ N2 ) )
% 3.82/4.02 => ( ( vEBT_invar_vebt @ Summary @ M2 )
% 3.82/4.02 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 3.82/4.02 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 3.82/4.02 => ( ( M2 = N2 )
% 3.82/4.02 => ( ( Deg
% 3.82/4.02 = ( plus_plus_nat @ N2 @ M2 ) )
% 3.82/4.02 => ( ! [I4: nat] :
% 3.82/4.02 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 3.82/4.02 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X6 ) )
% 3.82/4.02 = ( vEBT_V8194947554948674370ptions @ Summary @ I4 ) ) )
% 3.82/4.02 => ( ( ( Mi = Ma )
% 3.82/4.02 => ! [X5: vEBT_VEBT] :
% 3.82/4.02 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 3.82/4.02 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) )
% 3.82/4.02 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 3.82/4.02 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 3.82/4.02 => ( ( ( Mi != Ma )
% 3.82/4.02 => ! [I4: nat] :
% 3.82/4.02 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 3.82/4.02 => ( ( ( ( vEBT_VEBT_high @ Ma @ N2 )
% 3.82/4.02 = I4 )
% 3.82/4.02 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ Ma @ N2 ) ) )
% 3.82/4.02 & ! [X5: nat] :
% 3.82/4.02 ( ( ( ( vEBT_VEBT_high @ X5 @ N2 )
% 3.82/4.02 = I4 )
% 3.82/4.02 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ X5 @ N2 ) ) )
% 3.82/4.02 => ( ( ord_less_nat @ Mi @ X5 )
% 3.82/4.02 & ( ord_less_eq_nat @ X5 @ Ma ) ) ) ) ) )
% 3.82/4.02 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % invar_vebt.intros(4)
% 3.82/4.02 thf(fact_1825_num_Osize_I5_J,axiom,
% 3.82/4.02 ! [X22: num] :
% 3.82/4.02 ( ( size_size_num @ ( bit0 @ X22 ) )
% 3.82/4.02 = ( plus_plus_nat @ ( size_size_num @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % num.size(5)
% 3.82/4.02 thf(fact_1826_VEBT__internal_Omembermima_Osimps_I2_J,axiom,
% 3.82/4.02 ! [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT,Uz: nat] :
% 3.82/4.02 ~ ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) @ Uz ) ).
% 3.82/4.02
% 3.82/4.02 % VEBT_internal.membermima.simps(2)
% 3.82/4.02 thf(fact_1827_invar__vebt_Ointros_I5_J,axiom,
% 3.82/4.02 ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary: vEBT_VEBT,M2: nat,Deg: nat,Mi: nat,Ma: nat] :
% 3.82/4.02 ( ! [X5: vEBT_VEBT] :
% 3.82/4.02 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 3.82/4.02 => ( vEBT_invar_vebt @ X5 @ N2 ) )
% 3.82/4.02 => ( ( vEBT_invar_vebt @ Summary @ M2 )
% 3.82/4.02 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 3.82/4.02 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 3.82/4.02 => ( ( M2
% 3.82/4.02 = ( suc @ N2 ) )
% 3.82/4.02 => ( ( Deg
% 3.82/4.02 = ( plus_plus_nat @ N2 @ M2 ) )
% 3.82/4.02 => ( ! [I4: nat] :
% 3.82/4.02 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 3.82/4.02 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X6 ) )
% 3.82/4.02 = ( vEBT_V8194947554948674370ptions @ Summary @ I4 ) ) )
% 3.82/4.02 => ( ( ( Mi = Ma )
% 3.82/4.02 => ! [X5: vEBT_VEBT] :
% 3.82/4.02 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 3.82/4.02 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) )
% 3.82/4.02 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 3.82/4.02 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 3.82/4.02 => ( ( ( Mi != Ma )
% 3.82/4.02 => ! [I4: nat] :
% 3.82/4.02 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 3.82/4.02 => ( ( ( ( vEBT_VEBT_high @ Ma @ N2 )
% 3.82/4.02 = I4 )
% 3.82/4.02 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ Ma @ N2 ) ) )
% 3.82/4.02 & ! [X5: nat] :
% 3.82/4.02 ( ( ( ( vEBT_VEBT_high @ X5 @ N2 )
% 3.82/4.02 = I4 )
% 3.82/4.02 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ X5 @ N2 ) ) )
% 3.82/4.02 => ( ( ord_less_nat @ Mi @ X5 )
% 3.82/4.02 & ( ord_less_eq_nat @ X5 @ Ma ) ) ) ) ) )
% 3.82/4.02 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % invar_vebt.intros(5)
% 3.82/4.02 thf(fact_1828_length__code,axiom,
% 3.82/4.02 ( size_s6755466524823107622T_VEBT
% 3.82/4.02 = ( gen_length_VEBT_VEBT @ zero_zero_nat ) ) ).
% 3.82/4.02
% 3.82/4.02 % length_code
% 3.82/4.02 thf(fact_1829_length__code,axiom,
% 3.82/4.02 ( size_size_list_int
% 3.82/4.02 = ( gen_length_int @ zero_zero_nat ) ) ).
% 3.82/4.02
% 3.82/4.02 % length_code
% 3.82/4.02 thf(fact_1830_length__code,axiom,
% 3.82/4.02 ( size_size_list_nat
% 3.82/4.02 = ( gen_length_nat @ zero_zero_nat ) ) ).
% 3.82/4.02
% 3.82/4.02 % length_code
% 3.82/4.02 thf(fact_1831_sum__power2__eq__zero__iff,axiom,
% 3.82/4.02 ! [X: real,Y: real] :
% 3.82/4.02 ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 3.82/4.02 = zero_zero_real )
% 3.82/4.02 = ( ( X = zero_zero_real )
% 3.82/4.02 & ( Y = zero_zero_real ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % sum_power2_eq_zero_iff
% 3.82/4.02 thf(fact_1832_sum__power2__eq__zero__iff,axiom,
% 3.82/4.02 ! [X: int,Y: int] :
% 3.82/4.02 ( ( ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 3.82/4.02 = zero_zero_int )
% 3.82/4.02 = ( ( X = zero_zero_int )
% 3.82/4.02 & ( Y = zero_zero_int ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % sum_power2_eq_zero_iff
% 3.82/4.02 thf(fact_1833_zero__less__power2,axiom,
% 3.82/4.02 ! [A: real] :
% 3.82/4.02 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 3.82/4.02 = ( A != zero_zero_real ) ) ).
% 3.82/4.02
% 3.82/4.02 % zero_less_power2
% 3.82/4.02 thf(fact_1834_zero__less__power2,axiom,
% 3.82/4.02 ! [A: int] :
% 3.82/4.02 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 3.82/4.02 = ( A != zero_zero_int ) ) ).
% 3.82/4.02
% 3.82/4.02 % zero_less_power2
% 3.82/4.02 thf(fact_1835_power2__eq__iff__nonneg,axiom,
% 3.82/4.02 ! [X: real,Y: real] :
% 3.82/4.02 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 3.82/4.02 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 3.82/4.02 => ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.02 = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 3.82/4.02 = ( X = Y ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % power2_eq_iff_nonneg
% 3.82/4.02 thf(fact_1836_power2__eq__iff__nonneg,axiom,
% 3.82/4.02 ! [X: nat,Y: nat] :
% 3.82/4.02 ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 3.82/4.02 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 3.82/4.02 => ( ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.02 = ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 3.82/4.02 = ( X = Y ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % power2_eq_iff_nonneg
% 3.82/4.02 thf(fact_1837_power2__eq__iff__nonneg,axiom,
% 3.82/4.02 ! [X: int,Y: int] :
% 3.82/4.02 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 3.82/4.02 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 3.82/4.02 => ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.02 = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 3.82/4.02 = ( X = Y ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % power2_eq_iff_nonneg
% 3.82/4.02 thf(fact_1838_power2__less__eq__zero__iff,axiom,
% 3.82/4.02 ! [A: real] :
% 3.82/4.02 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real )
% 3.82/4.02 = ( A = zero_zero_real ) ) ).
% 3.82/4.02
% 3.82/4.02 % power2_less_eq_zero_iff
% 3.82/4.02 thf(fact_1839_power2__less__eq__zero__iff,axiom,
% 3.82/4.02 ! [A: int] :
% 3.82/4.02 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 3.82/4.02 = ( A = zero_zero_int ) ) ).
% 3.82/4.02
% 3.82/4.02 % power2_less_eq_zero_iff
% 3.82/4.02 thf(fact_1840_zero__eq__power2,axiom,
% 3.82/4.02 ! [A: nat] :
% 3.82/4.02 ( ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.02 = zero_zero_nat )
% 3.82/4.02 = ( A = zero_zero_nat ) ) ).
% 3.82/4.02
% 3.82/4.02 % zero_eq_power2
% 3.82/4.02 thf(fact_1841_zero__eq__power2,axiom,
% 3.82/4.02 ! [A: real] :
% 3.82/4.02 ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.02 = zero_zero_real )
% 3.82/4.02 = ( A = zero_zero_real ) ) ).
% 3.82/4.02
% 3.82/4.02 % zero_eq_power2
% 3.82/4.02 thf(fact_1842_zero__eq__power2,axiom,
% 3.82/4.02 ! [A: complex] :
% 3.82/4.02 ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.02 = zero_zero_complex )
% 3.82/4.02 = ( A = zero_zero_complex ) ) ).
% 3.82/4.02
% 3.82/4.02 % zero_eq_power2
% 3.82/4.02 thf(fact_1843_zero__eq__power2,axiom,
% 3.82/4.02 ! [A: int] :
% 3.82/4.02 ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.02 = zero_zero_int )
% 3.82/4.02 = ( A = zero_zero_int ) ) ).
% 3.82/4.02
% 3.82/4.02 % zero_eq_power2
% 3.82/4.02 thf(fact_1844_power__mono__iff,axiom,
% 3.82/4.02 ! [A: real,B2: real,N2: nat] :
% 3.82/4.02 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 3.82/4.02 => ( ( ord_less_eq_real @ zero_zero_real @ B2 )
% 3.82/4.02 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.02 => ( ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B2 @ N2 ) )
% 3.82/4.02 = ( ord_less_eq_real @ A @ B2 ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % power_mono_iff
% 3.82/4.02 thf(fact_1845_power__mono__iff,axiom,
% 3.82/4.02 ! [A: nat,B2: nat,N2: nat] :
% 3.82/4.02 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 3.82/4.02 => ( ( ord_less_eq_nat @ zero_zero_nat @ B2 )
% 3.82/4.02 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.02 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B2 @ N2 ) )
% 3.82/4.02 = ( ord_less_eq_nat @ A @ B2 ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % power_mono_iff
% 3.82/4.02 thf(fact_1846_power__mono__iff,axiom,
% 3.82/4.02 ! [A: int,B2: int,N2: nat] :
% 3.82/4.02 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 3.82/4.02 => ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 3.82/4.02 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.02 => ( ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B2 @ N2 ) )
% 3.82/4.02 = ( ord_less_eq_int @ A @ B2 ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % power_mono_iff
% 3.82/4.02 thf(fact_1847_insert__simp__norm,axiom,
% 3.82/4.02 ! [X: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 3.82/4.02 ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 3.82/4.02 => ( ( ord_less_nat @ Mi @ X )
% 3.82/4.02 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 3.82/4.02 => ( ( X != Ma )
% 3.82/4.02 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 3.82/4.02 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( ord_max_nat @ X @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % insert_simp_norm
% 3.82/4.02 thf(fact_1848_insert__simp__excp,axiom,
% 3.82/4.02 ! [Mi: nat,Deg: nat,TreeList2: list_VEBT_VEBT,X: nat,Ma: nat,Summary: vEBT_VEBT] :
% 3.82/4.02 ( ( ord_less_nat @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 3.82/4.02 => ( ( ord_less_nat @ X @ Mi )
% 3.82/4.02 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 3.82/4.02 => ( ( X != Ma )
% 3.82/4.02 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 3.82/4.02 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X @ ( ord_max_nat @ Mi @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % insert_simp_excp
% 3.82/4.02 thf(fact_1849_power__eq__0__iff,axiom,
% 3.82/4.02 ! [A: nat,N2: nat] :
% 3.82/4.02 ( ( ( power_power_nat @ A @ N2 )
% 3.82/4.02 = zero_zero_nat )
% 3.82/4.02 = ( ( A = zero_zero_nat )
% 3.82/4.02 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % power_eq_0_iff
% 3.82/4.02 thf(fact_1850_power__eq__0__iff,axiom,
% 3.82/4.02 ! [A: real,N2: nat] :
% 3.82/4.02 ( ( ( power_power_real @ A @ N2 )
% 3.82/4.02 = zero_zero_real )
% 3.82/4.02 = ( ( A = zero_zero_real )
% 3.82/4.02 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % power_eq_0_iff
% 3.82/4.02 thf(fact_1851_power__eq__0__iff,axiom,
% 3.82/4.02 ! [A: complex,N2: nat] :
% 3.82/4.02 ( ( ( power_power_complex @ A @ N2 )
% 3.82/4.02 = zero_zero_complex )
% 3.82/4.02 = ( ( A = zero_zero_complex )
% 3.82/4.02 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % power_eq_0_iff
% 3.82/4.02 thf(fact_1852_power__eq__0__iff,axiom,
% 3.82/4.02 ! [A: int,N2: nat] :
% 3.82/4.02 ( ( ( power_power_int @ A @ N2 )
% 3.82/4.02 = zero_zero_int )
% 3.82/4.02 = ( ( A = zero_zero_int )
% 3.82/4.02 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % power_eq_0_iff
% 3.82/4.02 thf(fact_1853_member__inv,axiom,
% 3.82/4.02 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 3.82/4.02 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 3.82/4.02 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 3.82/4.02 & ( ( X = Mi )
% 3.82/4.02 | ( X = Ma )
% 3.82/4.02 | ( ( ord_less_nat @ X @ Ma )
% 3.82/4.02 & ( ord_less_nat @ Mi @ X )
% 3.82/4.02 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 3.82/4.02 & ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % member_inv
% 3.82/4.02 thf(fact_1854_pow__sum,axiom,
% 3.82/4.02 ! [A: nat,B2: nat] :
% 3.82/4.02 ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 3.82/4.02 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % pow_sum
% 3.82/4.02 thf(fact_1855_high__def,axiom,
% 3.82/4.02 ( vEBT_VEBT_high
% 3.82/4.02 = ( ^ [X4: nat,N: nat] : ( divide_divide_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % high_def
% 3.82/4.02 thf(fact_1856__C9_C,axiom,
% 3.82/4.02 ( ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.02 = na ) ).
% 3.82/4.02
% 3.82/4.02 % "9"
% 3.82/4.02 thf(fact_1857_division__ring__divide__zero,axiom,
% 3.82/4.02 ! [A: complex] :
% 3.82/4.02 ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 3.82/4.02 = zero_zero_complex ) ).
% 3.82/4.02
% 3.82/4.02 % division_ring_divide_zero
% 3.82/4.02 thf(fact_1858_division__ring__divide__zero,axiom,
% 3.82/4.02 ! [A: real] :
% 3.82/4.02 ( ( divide_divide_real @ A @ zero_zero_real )
% 3.82/4.02 = zero_zero_real ) ).
% 3.82/4.02
% 3.82/4.02 % division_ring_divide_zero
% 3.82/4.02 thf(fact_1859_divide__cancel__right,axiom,
% 3.82/4.02 ! [A: complex,C: complex,B2: complex] :
% 3.82/4.02 ( ( ( divide1717551699836669952omplex @ A @ C )
% 3.82/4.02 = ( divide1717551699836669952omplex @ B2 @ C ) )
% 3.82/4.02 = ( ( C = zero_zero_complex )
% 3.82/4.02 | ( A = B2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % divide_cancel_right
% 3.82/4.02 thf(fact_1860_divide__cancel__right,axiom,
% 3.82/4.02 ! [A: real,C: real,B2: real] :
% 3.82/4.02 ( ( ( divide_divide_real @ A @ C )
% 3.82/4.02 = ( divide_divide_real @ B2 @ C ) )
% 3.82/4.02 = ( ( C = zero_zero_real )
% 3.82/4.02 | ( A = B2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % divide_cancel_right
% 3.82/4.02 thf(fact_1861_divide__cancel__left,axiom,
% 3.82/4.02 ! [C: complex,A: complex,B2: complex] :
% 3.82/4.02 ( ( ( divide1717551699836669952omplex @ C @ A )
% 3.82/4.02 = ( divide1717551699836669952omplex @ C @ B2 ) )
% 3.82/4.02 = ( ( C = zero_zero_complex )
% 3.82/4.02 | ( A = B2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % divide_cancel_left
% 3.82/4.02 thf(fact_1862_divide__cancel__left,axiom,
% 3.82/4.02 ! [C: real,A: real,B2: real] :
% 3.82/4.02 ( ( ( divide_divide_real @ C @ A )
% 3.82/4.02 = ( divide_divide_real @ C @ B2 ) )
% 3.82/4.02 = ( ( C = zero_zero_real )
% 3.82/4.02 | ( A = B2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % divide_cancel_left
% 3.82/4.02 thf(fact_1863_div__by__0,axiom,
% 3.82/4.02 ! [A: complex] :
% 3.82/4.02 ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 3.82/4.02 = zero_zero_complex ) ).
% 3.82/4.02
% 3.82/4.02 % div_by_0
% 3.82/4.02 thf(fact_1864_div__by__0,axiom,
% 3.82/4.02 ! [A: nat] :
% 3.82/4.02 ( ( divide_divide_nat @ A @ zero_zero_nat )
% 3.82/4.02 = zero_zero_nat ) ).
% 3.82/4.02
% 3.82/4.02 % div_by_0
% 3.82/4.02 thf(fact_1865_div__by__0,axiom,
% 3.82/4.02 ! [A: int] :
% 3.82/4.02 ( ( divide_divide_int @ A @ zero_zero_int )
% 3.82/4.02 = zero_zero_int ) ).
% 3.82/4.02
% 3.82/4.02 % div_by_0
% 3.82/4.02 thf(fact_1866_div__by__0,axiom,
% 3.82/4.02 ! [A: real] :
% 3.82/4.02 ( ( divide_divide_real @ A @ zero_zero_real )
% 3.82/4.02 = zero_zero_real ) ).
% 3.82/4.02
% 3.82/4.02 % div_by_0
% 3.82/4.02 thf(fact_1867_divide__eq__0__iff,axiom,
% 3.82/4.02 ! [A: complex,B2: complex] :
% 3.82/4.02 ( ( ( divide1717551699836669952omplex @ A @ B2 )
% 3.82/4.02 = zero_zero_complex )
% 3.82/4.02 = ( ( A = zero_zero_complex )
% 3.82/4.02 | ( B2 = zero_zero_complex ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % divide_eq_0_iff
% 3.82/4.02 thf(fact_1868_divide__eq__0__iff,axiom,
% 3.82/4.02 ! [A: real,B2: real] :
% 3.82/4.02 ( ( ( divide_divide_real @ A @ B2 )
% 3.82/4.02 = zero_zero_real )
% 3.82/4.02 = ( ( A = zero_zero_real )
% 3.82/4.02 | ( B2 = zero_zero_real ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % divide_eq_0_iff
% 3.82/4.02 thf(fact_1869_div__0,axiom,
% 3.82/4.02 ! [A: complex] :
% 3.82/4.02 ( ( divide1717551699836669952omplex @ zero_zero_complex @ A )
% 3.82/4.02 = zero_zero_complex ) ).
% 3.82/4.02
% 3.82/4.02 % div_0
% 3.82/4.02 thf(fact_1870_div__0,axiom,
% 3.82/4.02 ! [A: nat] :
% 3.82/4.02 ( ( divide_divide_nat @ zero_zero_nat @ A )
% 3.82/4.02 = zero_zero_nat ) ).
% 3.82/4.02
% 3.82/4.02 % div_0
% 3.82/4.02 thf(fact_1871_div__0,axiom,
% 3.82/4.02 ! [A: int] :
% 3.82/4.02 ( ( divide_divide_int @ zero_zero_int @ A )
% 3.82/4.02 = zero_zero_int ) ).
% 3.82/4.02
% 3.82/4.02 % div_0
% 3.82/4.02 thf(fact_1872_div__0,axiom,
% 3.82/4.02 ! [A: real] :
% 3.82/4.02 ( ( divide_divide_real @ zero_zero_real @ A )
% 3.82/4.02 = zero_zero_real ) ).
% 3.82/4.02
% 3.82/4.02 % div_0
% 3.82/4.02 thf(fact_1873_power__0__Suc,axiom,
% 3.82/4.02 ! [N2: nat] :
% 3.82/4.02 ( ( power_8040749407984259932d_enat @ zero_z5237406670263579293d_enat @ ( suc @ N2 ) )
% 3.82/4.02 = zero_z5237406670263579293d_enat ) ).
% 3.82/4.02
% 3.82/4.02 % power_0_Suc
% 3.82/4.02 thf(fact_1874_power__0__Suc,axiom,
% 3.82/4.02 ! [N2: nat] :
% 3.82/4.02 ( ( power_power_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 3.82/4.02 = zero_zero_nat ) ).
% 3.82/4.02
% 3.82/4.02 % power_0_Suc
% 3.82/4.02 thf(fact_1875_power__0__Suc,axiom,
% 3.82/4.02 ! [N2: nat] :
% 3.82/4.02 ( ( power_power_real @ zero_zero_real @ ( suc @ N2 ) )
% 3.82/4.02 = zero_zero_real ) ).
% 3.82/4.02
% 3.82/4.02 % power_0_Suc
% 3.82/4.02 thf(fact_1876_power__0__Suc,axiom,
% 3.82/4.02 ! [N2: nat] :
% 3.82/4.02 ( ( power_power_complex @ zero_zero_complex @ ( suc @ N2 ) )
% 3.82/4.02 = zero_zero_complex ) ).
% 3.82/4.02
% 3.82/4.02 % power_0_Suc
% 3.82/4.02 thf(fact_1877_power__0__Suc,axiom,
% 3.82/4.02 ! [N2: nat] :
% 3.82/4.02 ( ( power_power_int @ zero_zero_int @ ( suc @ N2 ) )
% 3.82/4.02 = zero_zero_int ) ).
% 3.82/4.02
% 3.82/4.02 % power_0_Suc
% 3.82/4.02 thf(fact_1878_power__zero__numeral,axiom,
% 3.82/4.02 ! [K: num] :
% 3.82/4.02 ( ( power_8040749407984259932d_enat @ zero_z5237406670263579293d_enat @ ( numeral_numeral_nat @ K ) )
% 3.82/4.02 = zero_z5237406670263579293d_enat ) ).
% 3.82/4.02
% 3.82/4.02 % power_zero_numeral
% 3.82/4.02 thf(fact_1879_power__zero__numeral,axiom,
% 3.82/4.02 ! [K: num] :
% 3.82/4.02 ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ K ) )
% 3.82/4.02 = zero_zero_nat ) ).
% 3.82/4.02
% 3.82/4.02 % power_zero_numeral
% 3.82/4.02 thf(fact_1880_power__zero__numeral,axiom,
% 3.82/4.02 ! [K: num] :
% 3.82/4.02 ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ K ) )
% 3.82/4.02 = zero_zero_real ) ).
% 3.82/4.02
% 3.82/4.02 % power_zero_numeral
% 3.82/4.02 thf(fact_1881_power__zero__numeral,axiom,
% 3.82/4.02 ! [K: num] :
% 3.82/4.02 ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ K ) )
% 3.82/4.02 = zero_zero_complex ) ).
% 3.82/4.02
% 3.82/4.02 % power_zero_numeral
% 3.82/4.02 thf(fact_1882_power__zero__numeral,axiom,
% 3.82/4.02 ! [K: num] :
% 3.82/4.02 ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ K ) )
% 3.82/4.02 = zero_zero_int ) ).
% 3.82/4.02
% 3.82/4.02 % power_zero_numeral
% 3.82/4.02 thf(fact_1883_power__Suc0__right,axiom,
% 3.82/4.02 ! [A: nat] :
% 3.82/4.02 ( ( power_power_nat @ A @ ( suc @ zero_zero_nat ) )
% 3.82/4.02 = A ) ).
% 3.82/4.02
% 3.82/4.02 % power_Suc0_right
% 3.82/4.02 thf(fact_1884_power__Suc0__right,axiom,
% 3.82/4.02 ! [A: real] :
% 3.82/4.02 ( ( power_power_real @ A @ ( suc @ zero_zero_nat ) )
% 3.82/4.02 = A ) ).
% 3.82/4.02
% 3.82/4.02 % power_Suc0_right
% 3.82/4.02 thf(fact_1885_power__Suc0__right,axiom,
% 3.82/4.02 ! [A: complex] :
% 3.82/4.02 ( ( power_power_complex @ A @ ( suc @ zero_zero_nat ) )
% 3.82/4.02 = A ) ).
% 3.82/4.02
% 3.82/4.02 % power_Suc0_right
% 3.82/4.02 thf(fact_1886_power__Suc0__right,axiom,
% 3.82/4.02 ! [A: int] :
% 3.82/4.02 ( ( power_power_int @ A @ ( suc @ zero_zero_nat ) )
% 3.82/4.02 = A ) ).
% 3.82/4.02
% 3.82/4.02 % power_Suc0_right
% 3.82/4.02 thf(fact_1887_nat__power__eq__Suc__0__iff,axiom,
% 3.82/4.02 ! [X: nat,M2: nat] :
% 3.82/4.02 ( ( ( power_power_nat @ X @ M2 )
% 3.82/4.02 = ( suc @ zero_zero_nat ) )
% 3.82/4.02 = ( ( M2 = zero_zero_nat )
% 3.82/4.02 | ( X
% 3.82/4.02 = ( suc @ zero_zero_nat ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % nat_power_eq_Suc_0_iff
% 3.82/4.02 thf(fact_1888_power__Suc__0,axiom,
% 3.82/4.02 ! [N2: nat] :
% 3.82/4.02 ( ( power_power_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 3.82/4.02 = ( suc @ zero_zero_nat ) ) ).
% 3.82/4.02
% 3.82/4.02 % power_Suc_0
% 3.82/4.02 thf(fact_1889_nat__zero__less__power__iff,axiom,
% 3.82/4.02 ! [X: nat,N2: nat] :
% 3.82/4.02 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N2 ) )
% 3.82/4.02 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 3.82/4.02 | ( N2 = zero_zero_nat ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % nat_zero_less_power_iff
% 3.82/4.02 thf(fact_1890_both__member__options__ding,axiom,
% 3.82/4.02 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N2: nat,X: nat] :
% 3.82/4.02 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ N2 )
% 3.82/4.02 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 3.82/4.02 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 3.82/4.02 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ X ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % both_member_options_ding
% 3.82/4.02 thf(fact_1891_add__divide__distrib,axiom,
% 3.82/4.02 ! [A: real,B2: real,C: real] :
% 3.82/4.02 ( ( divide_divide_real @ ( plus_plus_real @ A @ B2 ) @ C )
% 3.82/4.02 = ( plus_plus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B2 @ C ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % add_divide_distrib
% 3.82/4.02 thf(fact_1892_divide__le__0__iff,axiom,
% 3.82/4.02 ! [A: real,B2: real] :
% 3.82/4.02 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ B2 ) @ zero_zero_real )
% 3.82/4.02 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 3.82/4.02 & ( ord_less_eq_real @ B2 @ zero_zero_real ) )
% 3.82/4.02 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 3.82/4.02 & ( ord_less_eq_real @ zero_zero_real @ B2 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % divide_le_0_iff
% 3.82/4.02 thf(fact_1893_divide__right__mono,axiom,
% 3.82/4.02 ! [A: real,B2: real,C: real] :
% 3.82/4.02 ( ( ord_less_eq_real @ A @ B2 )
% 3.82/4.02 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 3.82/4.02 => ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B2 @ C ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % divide_right_mono
% 3.82/4.02 thf(fact_1894_zero__le__divide__iff,axiom,
% 3.82/4.02 ! [A: real,B2: real] :
% 3.82/4.02 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ B2 ) )
% 3.82/4.02 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 3.82/4.02 & ( ord_less_eq_real @ zero_zero_real @ B2 ) )
% 3.82/4.02 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 3.82/4.02 & ( ord_less_eq_real @ B2 @ zero_zero_real ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % zero_le_divide_iff
% 3.82/4.02 thf(fact_1895_divide__nonneg__nonneg,axiom,
% 3.82/4.02 ! [X: real,Y: real] :
% 3.82/4.02 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 3.82/4.02 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 3.82/4.02 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % divide_nonneg_nonneg
% 3.82/4.02 thf(fact_1896_divide__nonneg__nonpos,axiom,
% 3.82/4.02 ! [X: real,Y: real] :
% 3.82/4.02 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 3.82/4.02 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 3.82/4.02 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % divide_nonneg_nonpos
% 3.82/4.02 thf(fact_1897_divide__nonpos__nonneg,axiom,
% 3.82/4.02 ! [X: real,Y: real] :
% 3.82/4.02 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 3.82/4.02 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 3.82/4.02 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % divide_nonpos_nonneg
% 3.82/4.02 thf(fact_1898_divide__nonpos__nonpos,axiom,
% 3.82/4.02 ! [X: real,Y: real] :
% 3.82/4.02 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 3.82/4.02 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 3.82/4.02 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % divide_nonpos_nonpos
% 3.82/4.02 thf(fact_1899_divide__right__mono__neg,axiom,
% 3.82/4.02 ! [A: real,B2: real,C: real] :
% 3.82/4.02 ( ( ord_less_eq_real @ A @ B2 )
% 3.82/4.02 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 3.82/4.02 => ( ord_less_eq_real @ ( divide_divide_real @ B2 @ C ) @ ( divide_divide_real @ A @ C ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % divide_right_mono_neg
% 3.82/4.02 thf(fact_1900_divide__neg__neg,axiom,
% 3.82/4.02 ! [X: real,Y: real] :
% 3.82/4.02 ( ( ord_less_real @ X @ zero_zero_real )
% 3.82/4.02 => ( ( ord_less_real @ Y @ zero_zero_real )
% 3.82/4.02 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % divide_neg_neg
% 3.82/4.02 thf(fact_1901_divide__neg__pos,axiom,
% 3.82/4.02 ! [X: real,Y: real] :
% 3.82/4.02 ( ( ord_less_real @ X @ zero_zero_real )
% 3.82/4.02 => ( ( ord_less_real @ zero_zero_real @ Y )
% 3.82/4.02 => ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % divide_neg_pos
% 3.82/4.02 thf(fact_1902_divide__pos__neg,axiom,
% 3.82/4.02 ! [X: real,Y: real] :
% 3.82/4.02 ( ( ord_less_real @ zero_zero_real @ X )
% 3.82/4.02 => ( ( ord_less_real @ Y @ zero_zero_real )
% 3.82/4.02 => ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % divide_pos_neg
% 3.82/4.02 thf(fact_1903_divide__pos__pos,axiom,
% 3.82/4.02 ! [X: real,Y: real] :
% 3.82/4.02 ( ( ord_less_real @ zero_zero_real @ X )
% 3.82/4.02 => ( ( ord_less_real @ zero_zero_real @ Y )
% 3.82/4.02 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % divide_pos_pos
% 3.82/4.02 thf(fact_1904_divide__less__0__iff,axiom,
% 3.82/4.02 ! [A: real,B2: real] :
% 3.82/4.02 ( ( ord_less_real @ ( divide_divide_real @ A @ B2 ) @ zero_zero_real )
% 3.82/4.02 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 3.82/4.02 & ( ord_less_real @ B2 @ zero_zero_real ) )
% 3.82/4.02 | ( ( ord_less_real @ A @ zero_zero_real )
% 3.82/4.02 & ( ord_less_real @ zero_zero_real @ B2 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % divide_less_0_iff
% 3.82/4.02 thf(fact_1905_divide__less__cancel,axiom,
% 3.82/4.02 ! [A: real,C: real,B2: real] :
% 3.82/4.02 ( ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B2 @ C ) )
% 3.82/4.02 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.02 => ( ord_less_real @ A @ B2 ) )
% 3.82/4.02 & ( ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.02 => ( ord_less_real @ B2 @ A ) )
% 3.82/4.02 & ( C != zero_zero_real ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % divide_less_cancel
% 3.82/4.02 thf(fact_1906_zero__less__divide__iff,axiom,
% 3.82/4.02 ! [A: real,B2: real] :
% 3.82/4.02 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ B2 ) )
% 3.82/4.02 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 3.82/4.02 & ( ord_less_real @ zero_zero_real @ B2 ) )
% 3.82/4.02 | ( ( ord_less_real @ A @ zero_zero_real )
% 3.82/4.02 & ( ord_less_real @ B2 @ zero_zero_real ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % zero_less_divide_iff
% 3.82/4.02 thf(fact_1907_divide__strict__right__mono,axiom,
% 3.82/4.02 ! [A: real,B2: real,C: real] :
% 3.82/4.02 ( ( ord_less_real @ A @ B2 )
% 3.82/4.02 => ( ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.02 => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B2 @ C ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % divide_strict_right_mono
% 3.82/4.02 thf(fact_1908_divide__strict__right__mono__neg,axiom,
% 3.82/4.02 ! [B2: real,A: real,C: real] :
% 3.82/4.02 ( ( ord_less_real @ B2 @ A )
% 3.82/4.02 => ( ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.02 => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B2 @ C ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % divide_strict_right_mono_neg
% 3.82/4.02 thf(fact_1909_divide__nonpos__pos,axiom,
% 3.82/4.02 ! [X: real,Y: real] :
% 3.82/4.02 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 3.82/4.02 => ( ( ord_less_real @ zero_zero_real @ Y )
% 3.82/4.02 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % divide_nonpos_pos
% 3.82/4.02 thf(fact_1910_divide__nonpos__neg,axiom,
% 3.82/4.02 ! [X: real,Y: real] :
% 3.82/4.02 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 3.82/4.02 => ( ( ord_less_real @ Y @ zero_zero_real )
% 3.82/4.02 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % divide_nonpos_neg
% 3.82/4.02 thf(fact_1911_divide__nonneg__pos,axiom,
% 3.82/4.02 ! [X: real,Y: real] :
% 3.82/4.02 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 3.82/4.02 => ( ( ord_less_real @ zero_zero_real @ Y )
% 3.82/4.02 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % divide_nonneg_pos
% 3.82/4.02 thf(fact_1912_divide__nonneg__neg,axiom,
% 3.82/4.02 ! [X: real,Y: real] :
% 3.82/4.02 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 3.82/4.02 => ( ( ord_less_real @ Y @ zero_zero_real )
% 3.82/4.02 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % divide_nonneg_neg
% 3.82/4.02 thf(fact_1913_divide__le__cancel,axiom,
% 3.82/4.02 ! [A: real,C: real,B2: real] :
% 3.82/4.02 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B2 @ C ) )
% 3.82/4.02 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.02 => ( ord_less_eq_real @ A @ B2 ) )
% 3.82/4.02 & ( ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.02 => ( ord_less_eq_real @ B2 @ A ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % divide_le_cancel
% 3.82/4.02 thf(fact_1914_frac__less2,axiom,
% 3.82/4.02 ! [X: real,Y: real,W2: real,Z3: real] :
% 3.82/4.02 ( ( ord_less_real @ zero_zero_real @ X )
% 3.82/4.02 => ( ( ord_less_eq_real @ X @ Y )
% 3.82/4.02 => ( ( ord_less_real @ zero_zero_real @ W2 )
% 3.82/4.02 => ( ( ord_less_real @ W2 @ Z3 )
% 3.82/4.02 => ( ord_less_real @ ( divide_divide_real @ X @ Z3 ) @ ( divide_divide_real @ Y @ W2 ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % frac_less2
% 3.82/4.02 thf(fact_1915_frac__less,axiom,
% 3.82/4.02 ! [X: real,Y: real,W2: real,Z3: real] :
% 3.82/4.02 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 3.82/4.02 => ( ( ord_less_real @ X @ Y )
% 3.82/4.02 => ( ( ord_less_real @ zero_zero_real @ W2 )
% 3.82/4.02 => ( ( ord_less_eq_real @ W2 @ Z3 )
% 3.82/4.02 => ( ord_less_real @ ( divide_divide_real @ X @ Z3 ) @ ( divide_divide_real @ Y @ W2 ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % frac_less
% 3.82/4.02 thf(fact_1916_frac__le,axiom,
% 3.82/4.02 ! [Y: real,X: real,W2: real,Z3: real] :
% 3.82/4.02 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 3.82/4.02 => ( ( ord_less_eq_real @ X @ Y )
% 3.82/4.02 => ( ( ord_less_real @ zero_zero_real @ W2 )
% 3.82/4.02 => ( ( ord_less_eq_real @ W2 @ Z3 )
% 3.82/4.02 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Z3 ) @ ( divide_divide_real @ Y @ W2 ) ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % frac_le
% 3.82/4.02 thf(fact_1917_field__sum__of__halves,axiom,
% 3.82/4.02 ! [X: real] :
% 3.82/4.02 ( ( plus_plus_real @ ( divide_divide_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 3.82/4.02 = X ) ).
% 3.82/4.02
% 3.82/4.02 % field_sum_of_halves
% 3.82/4.02 thf(fact_1918_half__gt__zero,axiom,
% 3.82/4.02 ! [A: real] :
% 3.82/4.02 ( ( ord_less_real @ zero_zero_real @ A )
% 3.82/4.02 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % half_gt_zero
% 3.82/4.02 thf(fact_1919_half__gt__zero__iff,axiom,
% 3.82/4.02 ! [A: real] :
% 3.82/4.02 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 3.82/4.02 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 3.82/4.02
% 3.82/4.02 % half_gt_zero_iff
% 3.82/4.02 thf(fact_1920_field__less__half__sum,axiom,
% 3.82/4.02 ! [X: real,Y: real] :
% 3.82/4.02 ( ( ord_less_real @ X @ Y )
% 3.82/4.02 => ( ord_less_real @ X @ ( divide_divide_real @ ( plus_plus_real @ X @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % field_less_half_sum
% 3.82/4.02 thf(fact_1921_power__not__zero,axiom,
% 3.82/4.02 ! [A: nat,N2: nat] :
% 3.82/4.02 ( ( A != zero_zero_nat )
% 3.82/4.02 => ( ( power_power_nat @ A @ N2 )
% 3.82/4.02 != zero_zero_nat ) ) ).
% 3.82/4.02
% 3.82/4.02 % power_not_zero
% 3.82/4.02 thf(fact_1922_power__not__zero,axiom,
% 3.82/4.02 ! [A: real,N2: nat] :
% 3.82/4.02 ( ( A != zero_zero_real )
% 3.82/4.02 => ( ( power_power_real @ A @ N2 )
% 3.82/4.02 != zero_zero_real ) ) ).
% 3.82/4.02
% 3.82/4.02 % power_not_zero
% 3.82/4.02 thf(fact_1923_power__not__zero,axiom,
% 3.82/4.02 ! [A: complex,N2: nat] :
% 3.82/4.02 ( ( A != zero_zero_complex )
% 3.82/4.02 => ( ( power_power_complex @ A @ N2 )
% 3.82/4.02 != zero_zero_complex ) ) ).
% 3.82/4.02
% 3.82/4.02 % power_not_zero
% 3.82/4.02 thf(fact_1924_power__not__zero,axiom,
% 3.82/4.02 ! [A: int,N2: nat] :
% 3.82/4.02 ( ( A != zero_zero_int )
% 3.82/4.02 => ( ( power_power_int @ A @ N2 )
% 3.82/4.02 != zero_zero_int ) ) ).
% 3.82/4.02
% 3.82/4.02 % power_not_zero
% 3.82/4.02 thf(fact_1925_power__mono,axiom,
% 3.82/4.02 ! [A: real,B2: real,N2: nat] :
% 3.82/4.02 ( ( ord_less_eq_real @ A @ B2 )
% 3.82/4.02 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 3.82/4.02 => ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B2 @ N2 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % power_mono
% 3.82/4.02 thf(fact_1926_power__mono,axiom,
% 3.82/4.02 ! [A: nat,B2: nat,N2: nat] :
% 3.82/4.02 ( ( ord_less_eq_nat @ A @ B2 )
% 3.82/4.02 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 3.82/4.02 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B2 @ N2 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % power_mono
% 3.82/4.02 thf(fact_1927_power__mono,axiom,
% 3.82/4.02 ! [A: int,B2: int,N2: nat] :
% 3.82/4.02 ( ( ord_less_eq_int @ A @ B2 )
% 3.82/4.02 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 3.82/4.02 => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B2 @ N2 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % power_mono
% 3.82/4.02 thf(fact_1928_zero__le__power,axiom,
% 3.82/4.02 ! [A: real,N2: nat] :
% 3.82/4.02 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 3.82/4.02 => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % zero_le_power
% 3.82/4.02 thf(fact_1929_zero__le__power,axiom,
% 3.82/4.02 ! [A: nat,N2: nat] :
% 3.82/4.02 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 3.82/4.02 => ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ A @ N2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % zero_le_power
% 3.82/4.02 thf(fact_1930_zero__le__power,axiom,
% 3.82/4.02 ! [A: int,N2: nat] :
% 3.82/4.02 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 3.82/4.02 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % zero_le_power
% 3.82/4.02 thf(fact_1931_zero__less__power,axiom,
% 3.82/4.02 ! [A: nat,N2: nat] :
% 3.82/4.02 ( ( ord_less_nat @ zero_zero_nat @ A )
% 3.82/4.02 => ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ N2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % zero_less_power
% 3.82/4.02 thf(fact_1932_zero__less__power,axiom,
% 3.82/4.02 ! [A: real,N2: nat] :
% 3.82/4.02 ( ( ord_less_real @ zero_zero_real @ A )
% 3.82/4.02 => ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % zero_less_power
% 3.82/4.02 thf(fact_1933_zero__less__power,axiom,
% 3.82/4.02 ! [A: int,N2: nat] :
% 3.82/4.02 ( ( ord_less_int @ zero_zero_int @ A )
% 3.82/4.02 => ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % zero_less_power
% 3.82/4.02 thf(fact_1934_nat__power__less__imp__less,axiom,
% 3.82/4.02 ! [I: nat,M2: nat,N2: nat] :
% 3.82/4.02 ( ( ord_less_nat @ zero_zero_nat @ I )
% 3.82/4.02 => ( ( ord_less_nat @ ( power_power_nat @ I @ M2 ) @ ( power_power_nat @ I @ N2 ) )
% 3.82/4.02 => ( ord_less_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % nat_power_less_imp_less
% 3.82/4.02 thf(fact_1935_power__less__imp__less__base,axiom,
% 3.82/4.02 ! [A: real,N2: nat,B2: real] :
% 3.82/4.02 ( ( ord_less_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B2 @ N2 ) )
% 3.82/4.02 => ( ( ord_less_eq_real @ zero_zero_real @ B2 )
% 3.82/4.02 => ( ord_less_real @ A @ B2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % power_less_imp_less_base
% 3.82/4.02 thf(fact_1936_power__less__imp__less__base,axiom,
% 3.82/4.02 ! [A: nat,N2: nat,B2: nat] :
% 3.82/4.02 ( ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B2 @ N2 ) )
% 3.82/4.02 => ( ( ord_less_eq_nat @ zero_zero_nat @ B2 )
% 3.82/4.02 => ( ord_less_nat @ A @ B2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % power_less_imp_less_base
% 3.82/4.02 thf(fact_1937_power__less__imp__less__base,axiom,
% 3.82/4.02 ! [A: int,N2: nat,B2: int] :
% 3.82/4.02 ( ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B2 @ N2 ) )
% 3.82/4.02 => ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 3.82/4.02 => ( ord_less_int @ A @ B2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % power_less_imp_less_base
% 3.82/4.02 thf(fact_1938_power__inject__base,axiom,
% 3.82/4.02 ! [A: real,N2: nat,B2: real] :
% 3.82/4.02 ( ( ( power_power_real @ A @ ( suc @ N2 ) )
% 3.82/4.02 = ( power_power_real @ B2 @ ( suc @ N2 ) ) )
% 3.82/4.02 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 3.82/4.02 => ( ( ord_less_eq_real @ zero_zero_real @ B2 )
% 3.82/4.02 => ( A = B2 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % power_inject_base
% 3.82/4.02 thf(fact_1939_power__inject__base,axiom,
% 3.82/4.02 ! [A: nat,N2: nat,B2: nat] :
% 3.82/4.02 ( ( ( power_power_nat @ A @ ( suc @ N2 ) )
% 3.82/4.02 = ( power_power_nat @ B2 @ ( suc @ N2 ) ) )
% 3.82/4.02 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 3.82/4.02 => ( ( ord_less_eq_nat @ zero_zero_nat @ B2 )
% 3.82/4.02 => ( A = B2 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % power_inject_base
% 3.82/4.02 thf(fact_1940_power__inject__base,axiom,
% 3.82/4.02 ! [A: int,N2: nat,B2: int] :
% 3.82/4.02 ( ( ( power_power_int @ A @ ( suc @ N2 ) )
% 3.82/4.02 = ( power_power_int @ B2 @ ( suc @ N2 ) ) )
% 3.82/4.02 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 3.82/4.02 => ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 3.82/4.02 => ( A = B2 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % power_inject_base
% 3.82/4.02 thf(fact_1941_power__le__imp__le__base,axiom,
% 3.82/4.02 ! [A: real,N2: nat,B2: real] :
% 3.82/4.02 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N2 ) ) @ ( power_power_real @ B2 @ ( suc @ N2 ) ) )
% 3.82/4.02 => ( ( ord_less_eq_real @ zero_zero_real @ B2 )
% 3.82/4.02 => ( ord_less_eq_real @ A @ B2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % power_le_imp_le_base
% 3.82/4.02 thf(fact_1942_power__le__imp__le__base,axiom,
% 3.82/4.02 ! [A: nat,N2: nat,B2: nat] :
% 3.82/4.02 ( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) @ ( power_power_nat @ B2 @ ( suc @ N2 ) ) )
% 3.82/4.02 => ( ( ord_less_eq_nat @ zero_zero_nat @ B2 )
% 3.82/4.02 => ( ord_less_eq_nat @ A @ B2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % power_le_imp_le_base
% 3.82/4.02 thf(fact_1943_power__le__imp__le__base,axiom,
% 3.82/4.02 ! [A: int,N2: nat,B2: int] :
% 3.82/4.02 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N2 ) ) @ ( power_power_int @ B2 @ ( suc @ N2 ) ) )
% 3.82/4.02 => ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 3.82/4.02 => ( ord_less_eq_int @ A @ B2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % power_le_imp_le_base
% 3.82/4.02 thf(fact_1944_zero__power,axiom,
% 3.82/4.02 ! [N2: nat] :
% 3.82/4.02 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.02 => ( ( power_8040749407984259932d_enat @ zero_z5237406670263579293d_enat @ N2 )
% 3.82/4.02 = zero_z5237406670263579293d_enat ) ) ).
% 3.82/4.02
% 3.82/4.02 % zero_power
% 3.82/4.02 thf(fact_1945_zero__power,axiom,
% 3.82/4.02 ! [N2: nat] :
% 3.82/4.02 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.02 => ( ( power_power_nat @ zero_zero_nat @ N2 )
% 3.82/4.02 = zero_zero_nat ) ) ).
% 3.82/4.02
% 3.82/4.02 % zero_power
% 3.82/4.02 thf(fact_1946_zero__power,axiom,
% 3.82/4.02 ! [N2: nat] :
% 3.82/4.02 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.02 => ( ( power_power_real @ zero_zero_real @ N2 )
% 3.82/4.02 = zero_zero_real ) ) ).
% 3.82/4.02
% 3.82/4.02 % zero_power
% 3.82/4.02 thf(fact_1947_zero__power,axiom,
% 3.82/4.02 ! [N2: nat] :
% 3.82/4.02 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.02 => ( ( power_power_complex @ zero_zero_complex @ N2 )
% 3.82/4.02 = zero_zero_complex ) ) ).
% 3.82/4.02
% 3.82/4.02 % zero_power
% 3.82/4.02 thf(fact_1948_zero__power,axiom,
% 3.82/4.02 ! [N2: nat] :
% 3.82/4.02 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.02 => ( ( power_power_int @ zero_zero_int @ N2 )
% 3.82/4.02 = zero_zero_int ) ) ).
% 3.82/4.02
% 3.82/4.02 % zero_power
% 3.82/4.02 thf(fact_1949_power__gt__expt,axiom,
% 3.82/4.02 ! [N2: nat,K: nat] :
% 3.82/4.02 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 3.82/4.02 => ( ord_less_nat @ K @ ( power_power_nat @ N2 @ K ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % power_gt_expt
% 3.82/4.02 thf(fact_1950_nat__one__le__power,axiom,
% 3.82/4.02 ! [I: nat,N2: nat] :
% 3.82/4.02 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ I )
% 3.82/4.02 => ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ I @ N2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % nat_one_le_power
% 3.82/4.02 thf(fact_1951_power__eq__imp__eq__base,axiom,
% 3.82/4.02 ! [A: real,N2: nat,B2: real] :
% 3.82/4.02 ( ( ( power_power_real @ A @ N2 )
% 3.82/4.02 = ( power_power_real @ B2 @ N2 ) )
% 3.82/4.02 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 3.82/4.02 => ( ( ord_less_eq_real @ zero_zero_real @ B2 )
% 3.82/4.02 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.02 => ( A = B2 ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % power_eq_imp_eq_base
% 3.82/4.02 thf(fact_1952_power__eq__imp__eq__base,axiom,
% 3.82/4.02 ! [A: nat,N2: nat,B2: nat] :
% 3.82/4.02 ( ( ( power_power_nat @ A @ N2 )
% 3.82/4.02 = ( power_power_nat @ B2 @ N2 ) )
% 3.82/4.02 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 3.82/4.02 => ( ( ord_less_eq_nat @ zero_zero_nat @ B2 )
% 3.82/4.02 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.02 => ( A = B2 ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % power_eq_imp_eq_base
% 3.82/4.02 thf(fact_1953_power__eq__imp__eq__base,axiom,
% 3.82/4.02 ! [A: int,N2: nat,B2: int] :
% 3.82/4.02 ( ( ( power_power_int @ A @ N2 )
% 3.82/4.02 = ( power_power_int @ B2 @ N2 ) )
% 3.82/4.02 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 3.82/4.02 => ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 3.82/4.02 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.02 => ( A = B2 ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % power_eq_imp_eq_base
% 3.82/4.02 thf(fact_1954_power__eq__iff__eq__base,axiom,
% 3.82/4.02 ! [N2: nat,A: real,B2: real] :
% 3.82/4.02 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.02 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 3.82/4.02 => ( ( ord_less_eq_real @ zero_zero_real @ B2 )
% 3.82/4.02 => ( ( ( power_power_real @ A @ N2 )
% 3.82/4.02 = ( power_power_real @ B2 @ N2 ) )
% 3.82/4.02 = ( A = B2 ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % power_eq_iff_eq_base
% 3.82/4.02 thf(fact_1955_power__eq__iff__eq__base,axiom,
% 3.82/4.02 ! [N2: nat,A: nat,B2: nat] :
% 3.82/4.02 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.02 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 3.82/4.02 => ( ( ord_less_eq_nat @ zero_zero_nat @ B2 )
% 3.82/4.02 => ( ( ( power_power_nat @ A @ N2 )
% 3.82/4.02 = ( power_power_nat @ B2 @ N2 ) )
% 3.82/4.02 = ( A = B2 ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % power_eq_iff_eq_base
% 3.82/4.02 thf(fact_1956_power__eq__iff__eq__base,axiom,
% 3.82/4.02 ! [N2: nat,A: int,B2: int] :
% 3.82/4.02 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.02 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 3.82/4.02 => ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 3.82/4.02 => ( ( ( power_power_int @ A @ N2 )
% 3.82/4.02 = ( power_power_int @ B2 @ N2 ) )
% 3.82/4.02 = ( A = B2 ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % power_eq_iff_eq_base
% 3.82/4.02 thf(fact_1957_zero__power2,axiom,
% 3.82/4.02 ( ( power_8040749407984259932d_enat @ zero_z5237406670263579293d_enat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.02 = zero_z5237406670263579293d_enat ) ).
% 3.82/4.02
% 3.82/4.02 % zero_power2
% 3.82/4.02 thf(fact_1958_zero__power2,axiom,
% 3.82/4.02 ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.02 = zero_zero_nat ) ).
% 3.82/4.02
% 3.82/4.02 % zero_power2
% 3.82/4.02 thf(fact_1959_zero__power2,axiom,
% 3.82/4.02 ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.02 = zero_zero_real ) ).
% 3.82/4.02
% 3.82/4.02 % zero_power2
% 3.82/4.02 thf(fact_1960_zero__power2,axiom,
% 3.82/4.02 ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.02 = zero_zero_complex ) ).
% 3.82/4.02
% 3.82/4.02 % zero_power2
% 3.82/4.02 thf(fact_1961_zero__power2,axiom,
% 3.82/4.02 ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.02 = zero_zero_int ) ).
% 3.82/4.02
% 3.82/4.02 % zero_power2
% 3.82/4.02 thf(fact_1962_less__exp,axiom,
% 3.82/4.02 ! [N2: nat] : ( ord_less_nat @ N2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % less_exp
% 3.82/4.02 thf(fact_1963_self__le__ge2__pow,axiom,
% 3.82/4.02 ! [K: nat,M2: nat] :
% 3.82/4.02 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 3.82/4.02 => ( ord_less_eq_nat @ M2 @ ( power_power_nat @ K @ M2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % self_le_ge2_pow
% 3.82/4.02 thf(fact_1964_power2__nat__le__eq__le,axiom,
% 3.82/4.02 ! [M2: nat,N2: nat] :
% 3.82/4.02 ( ( ord_less_eq_nat @ ( power_power_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 3.82/4.02 = ( ord_less_eq_nat @ M2 @ N2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % power2_nat_le_eq_le
% 3.82/4.02 thf(fact_1965_power2__nat__le__imp__le,axiom,
% 3.82/4.02 ! [M2: nat,N2: nat] :
% 3.82/4.02 ( ( ord_less_eq_nat @ ( power_power_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N2 )
% 3.82/4.02 => ( ord_less_eq_nat @ M2 @ N2 ) ) ).
% 3.82/4.02
% 3.82/4.02 % power2_nat_le_imp_le
% 3.82/4.02 thf(fact_1966_zero__le__power2,axiom,
% 3.82/4.02 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % zero_le_power2
% 3.82/4.02 thf(fact_1967_zero__le__power2,axiom,
% 3.82/4.02 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % zero_le_power2
% 3.82/4.02 thf(fact_1968_power2__eq__imp__eq,axiom,
% 3.82/4.02 ! [X: real,Y: real] :
% 3.82/4.02 ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.02 = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 3.82/4.02 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 3.82/4.02 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 3.82/4.02 => ( X = Y ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % power2_eq_imp_eq
% 3.82/4.02 thf(fact_1969_power2__eq__imp__eq,axiom,
% 3.82/4.02 ! [X: nat,Y: nat] :
% 3.82/4.02 ( ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.02 = ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 3.82/4.02 => ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 3.82/4.02 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 3.82/4.02 => ( X = Y ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % power2_eq_imp_eq
% 3.82/4.02 thf(fact_1970_power2__eq__imp__eq,axiom,
% 3.82/4.02 ! [X: int,Y: int] :
% 3.82/4.02 ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.02 = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 3.82/4.02 => ( ( ord_less_eq_int @ zero_zero_int @ X )
% 3.82/4.02 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 3.82/4.02 => ( X = Y ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % power2_eq_imp_eq
% 3.82/4.02 thf(fact_1971_power2__le__imp__le,axiom,
% 3.82/4.02 ! [X: real,Y: real] :
% 3.82/4.02 ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 3.82/4.02 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 3.82/4.02 => ( ord_less_eq_real @ X @ Y ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % power2_le_imp_le
% 3.82/4.02 thf(fact_1972_power2__le__imp__le,axiom,
% 3.82/4.02 ! [X: nat,Y: nat] :
% 3.82/4.02 ( ( ord_less_eq_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 3.82/4.02 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 3.82/4.02 => ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % power2_le_imp_le
% 3.82/4.02 thf(fact_1973_power2__le__imp__le,axiom,
% 3.82/4.02 ! [X: int,Y: int] :
% 3.82/4.02 ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 3.82/4.02 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 3.82/4.02 => ( ord_less_eq_int @ X @ Y ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % power2_le_imp_le
% 3.82/4.02 thf(fact_1974_power__strict__mono,axiom,
% 3.82/4.02 ! [A: real,B2: real,N2: nat] :
% 3.82/4.02 ( ( ord_less_real @ A @ B2 )
% 3.82/4.02 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 3.82/4.02 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.02 => ( ord_less_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B2 @ N2 ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % power_strict_mono
% 3.82/4.02 thf(fact_1975_power__strict__mono,axiom,
% 3.82/4.02 ! [A: nat,B2: nat,N2: nat] :
% 3.82/4.02 ( ( ord_less_nat @ A @ B2 )
% 3.82/4.02 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 3.82/4.02 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.02 => ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B2 @ N2 ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % power_strict_mono
% 3.82/4.02 thf(fact_1976_power__strict__mono,axiom,
% 3.82/4.02 ! [A: int,B2: int,N2: nat] :
% 3.82/4.02 ( ( ord_less_int @ A @ B2 )
% 3.82/4.02 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 3.82/4.02 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.02 => ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B2 @ N2 ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % power_strict_mono
% 3.82/4.02 thf(fact_1977_power2__less__0,axiom,
% 3.82/4.02 ! [A: real] :
% 3.82/4.02 ~ ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real ) ).
% 3.82/4.02
% 3.82/4.02 % power2_less_0
% 3.82/4.02 thf(fact_1978_power2__less__0,axiom,
% 3.82/4.02 ! [A: int] :
% 3.82/4.02 ~ ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int ) ).
% 3.82/4.02
% 3.82/4.02 % power2_less_0
% 3.82/4.02 thf(fact_1979_power2__less__imp__less,axiom,
% 3.82/4.02 ! [X: real,Y: real] :
% 3.82/4.02 ( ( ord_less_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 3.82/4.02 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 3.82/4.02 => ( ord_less_real @ X @ Y ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % power2_less_imp_less
% 3.82/4.02 thf(fact_1980_power2__less__imp__less,axiom,
% 3.82/4.02 ! [X: nat,Y: nat] :
% 3.82/4.02 ( ( ord_less_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 3.82/4.02 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 3.82/4.02 => ( ord_less_nat @ X @ Y ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % power2_less_imp_less
% 3.82/4.02 thf(fact_1981_power2__less__imp__less,axiom,
% 3.82/4.02 ! [X: int,Y: int] :
% 3.82/4.02 ( ( ord_less_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 3.82/4.02 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 3.82/4.02 => ( ord_less_int @ X @ Y ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % power2_less_imp_less
% 3.82/4.02 thf(fact_1982_sum__power2__ge__zero,axiom,
% 3.82/4.02 ! [X: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % sum_power2_ge_zero
% 3.82/4.02 thf(fact_1983_sum__power2__ge__zero,axiom,
% 3.82/4.02 ! [X: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % sum_power2_ge_zero
% 3.82/4.02 thf(fact_1984_sum__power2__le__zero__iff,axiom,
% 3.82/4.02 ! [X: real,Y: real] :
% 3.82/4.02 ( ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real )
% 3.82/4.02 = ( ( X = zero_zero_real )
% 3.82/4.02 & ( Y = zero_zero_real ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % sum_power2_le_zero_iff
% 3.82/4.02 thf(fact_1985_sum__power2__le__zero__iff,axiom,
% 3.82/4.02 ! [X: int,Y: int] :
% 3.82/4.02 ( ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int )
% 3.82/4.02 = ( ( X = zero_zero_int )
% 3.82/4.02 & ( Y = zero_zero_int ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % sum_power2_le_zero_iff
% 3.82/4.02 thf(fact_1986_not__sum__power2__lt__zero,axiom,
% 3.82/4.02 ! [X: real,Y: real] :
% 3.82/4.02 ~ ( ord_less_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real ) ).
% 3.82/4.02
% 3.82/4.02 % not_sum_power2_lt_zero
% 3.82/4.02 thf(fact_1987_not__sum__power2__lt__zero,axiom,
% 3.82/4.02 ! [X: int,Y: int] :
% 3.82/4.02 ~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int ) ).
% 3.82/4.02
% 3.82/4.02 % not_sum_power2_lt_zero
% 3.82/4.02 thf(fact_1988_sum__power2__gt__zero__iff,axiom,
% 3.82/4.02 ! [X: real,Y: real] :
% 3.82/4.02 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 3.82/4.02 = ( ( X != zero_zero_real )
% 3.82/4.02 | ( Y != zero_zero_real ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % sum_power2_gt_zero_iff
% 3.82/4.02 thf(fact_1989_sum__power2__gt__zero__iff,axiom,
% 3.82/4.02 ! [X: int,Y: int] :
% 3.82/4.02 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 3.82/4.02 = ( ( X != zero_zero_int )
% 3.82/4.02 | ( Y != zero_zero_int ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % sum_power2_gt_zero_iff
% 3.82/4.02 thf(fact_1990_both__member__options__from__chilf__to__complete__tree,axiom,
% 3.82/4.02 ! [X: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 3.82/4.02 ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 3.82/4.02 => ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 3.82/4.02 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 3.82/4.02 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % both_member_options_from_chilf_to_complete_tree
% 3.82/4.02 thf(fact_1991_add__self__div__2,axiom,
% 3.82/4.02 ! [M2: nat] :
% 3.82/4.02 ( ( divide_divide_nat @ ( plus_plus_nat @ M2 @ M2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.02 = M2 ) ).
% 3.82/4.02
% 3.82/4.02 % add_self_div_2
% 3.82/4.02 thf(fact_1992_div2__Suc__Suc,axiom,
% 3.82/4.02 ! [M2: nat] :
% 3.82/4.02 ( ( divide_divide_nat @ ( suc @ ( suc @ M2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.02 = ( suc @ ( divide_divide_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % div2_Suc_Suc
% 3.82/4.02 thf(fact_1993_both__member__options__from__complete__tree__to__child,axiom,
% 3.82/4.02 ! [Deg: nat,Mi: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 3.82/4.02 ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 3.82/4.02 => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 3.82/4.02 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 3.82/4.02 | ( X = Mi )
% 3.82/4.02 | ( X = Ma ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % both_member_options_from_complete_tree_to_child
% 3.82/4.02 thf(fact_1994_div__less,axiom,
% 3.82/4.02 ! [M2: nat,N2: nat] :
% 3.82/4.02 ( ( ord_less_nat @ M2 @ N2 )
% 3.82/4.02 => ( ( divide_divide_nat @ M2 @ N2 )
% 3.82/4.02 = zero_zero_nat ) ) ).
% 3.82/4.02
% 3.82/4.02 % div_less
% 3.82/4.02 thf(fact_1995_div__by__Suc__0,axiom,
% 3.82/4.02 ! [M2: nat] :
% 3.82/4.02 ( ( divide_divide_nat @ M2 @ ( suc @ zero_zero_nat ) )
% 3.82/4.02 = M2 ) ).
% 3.82/4.02
% 3.82/4.02 % div_by_Suc_0
% 3.82/4.02 thf(fact_1996_set__n__deg__not__0,axiom,
% 3.82/4.02 ! [TreeList2: list_VEBT_VEBT,N2: nat,M2: nat] :
% 3.82/4.02 ( ! [X5: vEBT_VEBT] :
% 3.82/4.02 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 3.82/4.02 => ( vEBT_invar_vebt @ X5 @ N2 ) )
% 3.82/4.02 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 3.82/4.02 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 3.82/4.02 => ( ord_less_eq_nat @ one_one_nat @ N2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % set_n_deg_not_0
% 3.82/4.02 thf(fact_1997_div__2__gt__zero,axiom,
% 3.82/4.02 ! [N2: nat] :
% 3.82/4.02 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 3.82/4.02 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % div_2_gt_zero
% 3.82/4.02 thf(fact_1998_Suc__n__div__2__gt__zero,axiom,
% 3.82/4.02 ! [N2: nat] :
% 3.82/4.02 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.02 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % Suc_n_div_2_gt_zero
% 3.82/4.02 thf(fact_1999_div__exp__eq,axiom,
% 3.82/4.02 ! [A: nat,M2: nat,N2: nat] :
% 3.82/4.02 ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 3.82/4.02 = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N2 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % div_exp_eq
% 3.82/4.02 thf(fact_2000_div__exp__eq,axiom,
% 3.82/4.02 ! [A: int,M2: nat,N2: nat] :
% 3.82/4.02 ( ( divide_divide_int @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 3.82/4.02 = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N2 ) ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % div_exp_eq
% 3.82/4.02 thf(fact_2001_bits__div__0,axiom,
% 3.82/4.02 ! [A: nat] :
% 3.82/4.02 ( ( divide_divide_nat @ zero_zero_nat @ A )
% 3.82/4.02 = zero_zero_nat ) ).
% 3.82/4.02
% 3.82/4.02 % bits_div_0
% 3.82/4.02 thf(fact_2002_bits__div__0,axiom,
% 3.82/4.02 ! [A: int] :
% 3.82/4.02 ( ( divide_divide_int @ zero_zero_int @ A )
% 3.82/4.02 = zero_zero_int ) ).
% 3.82/4.02
% 3.82/4.02 % bits_div_0
% 3.82/4.02 thf(fact_2003_bits__div__by__0,axiom,
% 3.82/4.02 ! [A: nat] :
% 3.82/4.02 ( ( divide_divide_nat @ A @ zero_zero_nat )
% 3.82/4.02 = zero_zero_nat ) ).
% 3.82/4.02
% 3.82/4.02 % bits_div_by_0
% 3.82/4.02 thf(fact_2004_bits__div__by__0,axiom,
% 3.82/4.02 ! [A: int] :
% 3.82/4.02 ( ( divide_divide_int @ A @ zero_zero_int )
% 3.82/4.02 = zero_zero_int ) ).
% 3.82/4.02
% 3.82/4.02 % bits_div_by_0
% 3.82/4.02 thf(fact_2005_div__by__1,axiom,
% 3.82/4.02 ! [A: complex] :
% 3.82/4.02 ( ( divide1717551699836669952omplex @ A @ one_one_complex )
% 3.82/4.02 = A ) ).
% 3.82/4.02
% 3.82/4.02 % div_by_1
% 3.82/4.02 thf(fact_2006_div__by__1,axiom,
% 3.82/4.02 ! [A: nat] :
% 3.82/4.02 ( ( divide_divide_nat @ A @ one_one_nat )
% 3.82/4.02 = A ) ).
% 3.82/4.02
% 3.82/4.02 % div_by_1
% 3.82/4.02 thf(fact_2007_div__by__1,axiom,
% 3.82/4.02 ! [A: int] :
% 3.82/4.02 ( ( divide_divide_int @ A @ one_one_int )
% 3.82/4.02 = A ) ).
% 3.82/4.02
% 3.82/4.02 % div_by_1
% 3.82/4.02 thf(fact_2008_div__by__1,axiom,
% 3.82/4.02 ! [A: real] :
% 3.82/4.02 ( ( divide_divide_real @ A @ one_one_real )
% 3.82/4.02 = A ) ).
% 3.82/4.02
% 3.82/4.02 % div_by_1
% 3.82/4.02 thf(fact_2009_divide__eq__1__iff,axiom,
% 3.82/4.02 ! [A: complex,B2: complex] :
% 3.82/4.02 ( ( ( divide1717551699836669952omplex @ A @ B2 )
% 3.82/4.02 = one_one_complex )
% 3.82/4.02 = ( ( B2 != zero_zero_complex )
% 3.82/4.02 & ( A = B2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % divide_eq_1_iff
% 3.82/4.02 thf(fact_2010_divide__eq__1__iff,axiom,
% 3.82/4.02 ! [A: real,B2: real] :
% 3.82/4.02 ( ( ( divide_divide_real @ A @ B2 )
% 3.82/4.02 = one_one_real )
% 3.82/4.02 = ( ( B2 != zero_zero_real )
% 3.82/4.02 & ( A = B2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % divide_eq_1_iff
% 3.82/4.02 thf(fact_2011_div__self,axiom,
% 3.82/4.02 ! [A: complex] :
% 3.82/4.02 ( ( A != zero_zero_complex )
% 3.82/4.02 => ( ( divide1717551699836669952omplex @ A @ A )
% 3.82/4.02 = one_one_complex ) ) ).
% 3.82/4.02
% 3.82/4.02 % div_self
% 3.82/4.02 thf(fact_2012_div__self,axiom,
% 3.82/4.02 ! [A: nat] :
% 3.82/4.02 ( ( A != zero_zero_nat )
% 3.82/4.02 => ( ( divide_divide_nat @ A @ A )
% 3.82/4.02 = one_one_nat ) ) ).
% 3.82/4.02
% 3.82/4.02 % div_self
% 3.82/4.02 thf(fact_2013_div__self,axiom,
% 3.82/4.02 ! [A: int] :
% 3.82/4.02 ( ( A != zero_zero_int )
% 3.82/4.02 => ( ( divide_divide_int @ A @ A )
% 3.82/4.02 = one_one_int ) ) ).
% 3.82/4.02
% 3.82/4.02 % div_self
% 3.82/4.02 thf(fact_2014_div__self,axiom,
% 3.82/4.02 ! [A: real] :
% 3.82/4.02 ( ( A != zero_zero_real )
% 3.82/4.02 => ( ( divide_divide_real @ A @ A )
% 3.82/4.02 = one_one_real ) ) ).
% 3.82/4.02
% 3.82/4.02 % div_self
% 3.82/4.02 thf(fact_2015_one__eq__divide__iff,axiom,
% 3.82/4.02 ! [A: complex,B2: complex] :
% 3.82/4.02 ( ( one_one_complex
% 3.82/4.02 = ( divide1717551699836669952omplex @ A @ B2 ) )
% 3.82/4.02 = ( ( B2 != zero_zero_complex )
% 3.82/4.02 & ( A = B2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % one_eq_divide_iff
% 3.82/4.02 thf(fact_2016_one__eq__divide__iff,axiom,
% 3.82/4.02 ! [A: real,B2: real] :
% 3.82/4.02 ( ( one_one_real
% 3.82/4.02 = ( divide_divide_real @ A @ B2 ) )
% 3.82/4.02 = ( ( B2 != zero_zero_real )
% 3.82/4.02 & ( A = B2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % one_eq_divide_iff
% 3.82/4.02 thf(fact_2017_divide__self,axiom,
% 3.82/4.02 ! [A: complex] :
% 3.82/4.02 ( ( A != zero_zero_complex )
% 3.82/4.02 => ( ( divide1717551699836669952omplex @ A @ A )
% 3.82/4.02 = one_one_complex ) ) ).
% 3.82/4.02
% 3.82/4.02 % divide_self
% 3.82/4.02 thf(fact_2018_divide__self,axiom,
% 3.82/4.02 ! [A: real] :
% 3.82/4.02 ( ( A != zero_zero_real )
% 3.82/4.02 => ( ( divide_divide_real @ A @ A )
% 3.82/4.02 = one_one_real ) ) ).
% 3.82/4.02
% 3.82/4.02 % divide_self
% 3.82/4.02 thf(fact_2019_divide__self__if,axiom,
% 3.82/4.02 ! [A: complex] :
% 3.82/4.02 ( ( ( A = zero_zero_complex )
% 3.82/4.02 => ( ( divide1717551699836669952omplex @ A @ A )
% 3.82/4.02 = zero_zero_complex ) )
% 3.82/4.02 & ( ( A != zero_zero_complex )
% 3.82/4.02 => ( ( divide1717551699836669952omplex @ A @ A )
% 3.82/4.02 = one_one_complex ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % divide_self_if
% 3.82/4.02 thf(fact_2020_divide__self__if,axiom,
% 3.82/4.02 ! [A: real] :
% 3.82/4.02 ( ( ( A = zero_zero_real )
% 3.82/4.02 => ( ( divide_divide_real @ A @ A )
% 3.82/4.02 = zero_zero_real ) )
% 3.82/4.02 & ( ( A != zero_zero_real )
% 3.82/4.02 => ( ( divide_divide_real @ A @ A )
% 3.82/4.02 = one_one_real ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % divide_self_if
% 3.82/4.02 thf(fact_2021_divide__eq__eq__1,axiom,
% 3.82/4.02 ! [B2: real,A: real] :
% 3.82/4.02 ( ( ( divide_divide_real @ B2 @ A )
% 3.82/4.02 = one_one_real )
% 3.82/4.02 = ( ( A != zero_zero_real )
% 3.82/4.02 & ( A = B2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % divide_eq_eq_1
% 3.82/4.02 thf(fact_2022_eq__divide__eq__1,axiom,
% 3.82/4.02 ! [B2: real,A: real] :
% 3.82/4.02 ( ( one_one_real
% 3.82/4.02 = ( divide_divide_real @ B2 @ A ) )
% 3.82/4.02 = ( ( A != zero_zero_real )
% 3.82/4.02 & ( A = B2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % eq_divide_eq_1
% 3.82/4.02 thf(fact_2023_one__divide__eq__0__iff,axiom,
% 3.82/4.02 ! [A: real] :
% 3.82/4.02 ( ( ( divide_divide_real @ one_one_real @ A )
% 3.82/4.02 = zero_zero_real )
% 3.82/4.02 = ( A = zero_zero_real ) ) ).
% 3.82/4.02
% 3.82/4.02 % one_divide_eq_0_iff
% 3.82/4.02 thf(fact_2024_zero__eq__1__divide__iff,axiom,
% 3.82/4.02 ! [A: real] :
% 3.82/4.02 ( ( zero_zero_real
% 3.82/4.02 = ( divide_divide_real @ one_one_real @ A ) )
% 3.82/4.02 = ( A = zero_zero_real ) ) ).
% 3.82/4.02
% 3.82/4.02 % zero_eq_1_divide_iff
% 3.82/4.02 thf(fact_2025_power__inject__exp,axiom,
% 3.82/4.02 ! [A: nat,M2: nat,N2: nat] :
% 3.82/4.02 ( ( ord_less_nat @ one_one_nat @ A )
% 3.82/4.02 => ( ( ( power_power_nat @ A @ M2 )
% 3.82/4.02 = ( power_power_nat @ A @ N2 ) )
% 3.82/4.02 = ( M2 = N2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % power_inject_exp
% 3.82/4.02 thf(fact_2026_power__inject__exp,axiom,
% 3.82/4.02 ! [A: real,M2: nat,N2: nat] :
% 3.82/4.02 ( ( ord_less_real @ one_one_real @ A )
% 3.82/4.02 => ( ( ( power_power_real @ A @ M2 )
% 3.82/4.02 = ( power_power_real @ A @ N2 ) )
% 3.82/4.02 = ( M2 = N2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % power_inject_exp
% 3.82/4.02 thf(fact_2027_power__inject__exp,axiom,
% 3.82/4.02 ! [A: int,M2: nat,N2: nat] :
% 3.82/4.02 ( ( ord_less_int @ one_one_int @ A )
% 3.82/4.02 => ( ( ( power_power_int @ A @ M2 )
% 3.82/4.02 = ( power_power_int @ A @ N2 ) )
% 3.82/4.02 = ( M2 = N2 ) ) ) ).
% 3.82/4.02
% 3.82/4.02 % power_inject_exp
% 3.82/4.02 thf(fact_2028_max__0__1_I2_J,axiom,
% 3.82/4.02 ( ( ord_max_real @ one_one_real @ zero_zero_real )
% 3.82/4.03 = one_one_real ) ).
% 3.82/4.03
% 3.82/4.03 % max_0_1(2)
% 3.82/4.03 thf(fact_2029_max__0__1_I2_J,axiom,
% 3.82/4.03 ( ( ord_ma741700101516333627d_enat @ one_on7984719198319812577d_enat @ zero_z5237406670263579293d_enat )
% 3.82/4.03 = one_on7984719198319812577d_enat ) ).
% 3.82/4.03
% 3.82/4.03 % max_0_1(2)
% 3.82/4.03 thf(fact_2030_max__0__1_I2_J,axiom,
% 3.82/4.03 ( ( ord_max_nat @ one_one_nat @ zero_zero_nat )
% 3.82/4.03 = one_one_nat ) ).
% 3.82/4.03
% 3.82/4.03 % max_0_1(2)
% 3.82/4.03 thf(fact_2031_max__0__1_I2_J,axiom,
% 3.82/4.03 ( ( ord_max_int @ one_one_int @ zero_zero_int )
% 3.82/4.03 = one_one_int ) ).
% 3.82/4.03
% 3.82/4.03 % max_0_1(2)
% 3.82/4.03 thf(fact_2032_max__0__1_I1_J,axiom,
% 3.82/4.03 ( ( ord_max_real @ zero_zero_real @ one_one_real )
% 3.82/4.03 = one_one_real ) ).
% 3.82/4.03
% 3.82/4.03 % max_0_1(1)
% 3.82/4.03 thf(fact_2033_max__0__1_I1_J,axiom,
% 3.82/4.03 ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ one_on7984719198319812577d_enat )
% 3.82/4.03 = one_on7984719198319812577d_enat ) ).
% 3.82/4.03
% 3.82/4.03 % max_0_1(1)
% 3.82/4.03 thf(fact_2034_max__0__1_I1_J,axiom,
% 3.82/4.03 ( ( ord_max_nat @ zero_zero_nat @ one_one_nat )
% 3.82/4.03 = one_one_nat ) ).
% 3.82/4.03
% 3.82/4.03 % max_0_1(1)
% 3.82/4.03 thf(fact_2035_max__0__1_I1_J,axiom,
% 3.82/4.03 ( ( ord_max_int @ zero_zero_int @ one_one_int )
% 3.82/4.03 = one_one_int ) ).
% 3.82/4.03
% 3.82/4.03 % max_0_1(1)
% 3.82/4.03 thf(fact_2036_less__one,axiom,
% 3.82/4.03 ! [N2: nat] :
% 3.82/4.03 ( ( ord_less_nat @ N2 @ one_one_nat )
% 3.82/4.03 = ( N2 = zero_zero_nat ) ) ).
% 3.82/4.03
% 3.82/4.03 % less_one
% 3.82/4.03 thf(fact_2037_zero__le__divide__1__iff,axiom,
% 3.82/4.03 ! [A: real] :
% 3.82/4.03 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 3.82/4.03 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 3.82/4.03
% 3.82/4.03 % zero_le_divide_1_iff
% 3.82/4.03 thf(fact_2038_divide__le__0__1__iff,axiom,
% 3.82/4.03 ! [A: real] :
% 3.82/4.03 ( ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 3.82/4.03 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 3.82/4.03
% 3.82/4.03 % divide_le_0_1_iff
% 3.82/4.03 thf(fact_2039_zero__less__divide__1__iff,axiom,
% 3.82/4.03 ! [A: real] :
% 3.82/4.03 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 3.82/4.03 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 3.82/4.03
% 3.82/4.03 % zero_less_divide_1_iff
% 3.82/4.03 thf(fact_2040_less__divide__eq__1__pos,axiom,
% 3.82/4.03 ! [A: real,B2: real] :
% 3.82/4.03 ( ( ord_less_real @ zero_zero_real @ A )
% 3.82/4.03 => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B2 @ A ) )
% 3.82/4.03 = ( ord_less_real @ A @ B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % less_divide_eq_1_pos
% 3.82/4.03 thf(fact_2041_less__divide__eq__1__neg,axiom,
% 3.82/4.03 ! [A: real,B2: real] :
% 3.82/4.03 ( ( ord_less_real @ A @ zero_zero_real )
% 3.82/4.03 => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B2 @ A ) )
% 3.82/4.03 = ( ord_less_real @ B2 @ A ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % less_divide_eq_1_neg
% 3.82/4.03 thf(fact_2042_divide__less__eq__1__pos,axiom,
% 3.82/4.03 ! [A: real,B2: real] :
% 3.82/4.03 ( ( ord_less_real @ zero_zero_real @ A )
% 3.82/4.03 => ( ( ord_less_real @ ( divide_divide_real @ B2 @ A ) @ one_one_real )
% 3.82/4.03 = ( ord_less_real @ B2 @ A ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % divide_less_eq_1_pos
% 3.82/4.03 thf(fact_2043_divide__less__eq__1__neg,axiom,
% 3.82/4.03 ! [A: real,B2: real] :
% 3.82/4.03 ( ( ord_less_real @ A @ zero_zero_real )
% 3.82/4.03 => ( ( ord_less_real @ ( divide_divide_real @ B2 @ A ) @ one_one_real )
% 3.82/4.03 = ( ord_less_real @ A @ B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % divide_less_eq_1_neg
% 3.82/4.03 thf(fact_2044_divide__less__0__1__iff,axiom,
% 3.82/4.03 ! [A: real] :
% 3.82/4.03 ( ( ord_less_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 3.82/4.03 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 3.82/4.03
% 3.82/4.03 % divide_less_0_1_iff
% 3.82/4.03 thf(fact_2045_power__strict__increasing__iff,axiom,
% 3.82/4.03 ! [B2: nat,X: nat,Y: nat] :
% 3.82/4.03 ( ( ord_less_nat @ one_one_nat @ B2 )
% 3.82/4.03 => ( ( ord_less_nat @ ( power_power_nat @ B2 @ X ) @ ( power_power_nat @ B2 @ Y ) )
% 3.82/4.03 = ( ord_less_nat @ X @ Y ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_strict_increasing_iff
% 3.82/4.03 thf(fact_2046_power__strict__increasing__iff,axiom,
% 3.82/4.03 ! [B2: real,X: nat,Y: nat] :
% 3.82/4.03 ( ( ord_less_real @ one_one_real @ B2 )
% 3.82/4.03 => ( ( ord_less_real @ ( power_power_real @ B2 @ X ) @ ( power_power_real @ B2 @ Y ) )
% 3.82/4.03 = ( ord_less_nat @ X @ Y ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_strict_increasing_iff
% 3.82/4.03 thf(fact_2047_power__strict__increasing__iff,axiom,
% 3.82/4.03 ! [B2: int,X: nat,Y: nat] :
% 3.82/4.03 ( ( ord_less_int @ one_one_int @ B2 )
% 3.82/4.03 => ( ( ord_less_int @ ( power_power_int @ B2 @ X ) @ ( power_power_int @ B2 @ Y ) )
% 3.82/4.03 = ( ord_less_nat @ X @ Y ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_strict_increasing_iff
% 3.82/4.03 thf(fact_2048_divide__le__eq__1__neg,axiom,
% 3.82/4.03 ! [A: real,B2: real] :
% 3.82/4.03 ( ( ord_less_real @ A @ zero_zero_real )
% 3.82/4.03 => ( ( ord_less_eq_real @ ( divide_divide_real @ B2 @ A ) @ one_one_real )
% 3.82/4.03 = ( ord_less_eq_real @ A @ B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % divide_le_eq_1_neg
% 3.82/4.03 thf(fact_2049_divide__le__eq__1__pos,axiom,
% 3.82/4.03 ! [A: real,B2: real] :
% 3.82/4.03 ( ( ord_less_real @ zero_zero_real @ A )
% 3.82/4.03 => ( ( ord_less_eq_real @ ( divide_divide_real @ B2 @ A ) @ one_one_real )
% 3.82/4.03 = ( ord_less_eq_real @ B2 @ A ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % divide_le_eq_1_pos
% 3.82/4.03 thf(fact_2050_le__divide__eq__1__neg,axiom,
% 3.82/4.03 ! [A: real,B2: real] :
% 3.82/4.03 ( ( ord_less_real @ A @ zero_zero_real )
% 3.82/4.03 => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B2 @ A ) )
% 3.82/4.03 = ( ord_less_eq_real @ B2 @ A ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % le_divide_eq_1_neg
% 3.82/4.03 thf(fact_2051_le__divide__eq__1__pos,axiom,
% 3.82/4.03 ! [A: real,B2: real] :
% 3.82/4.03 ( ( ord_less_real @ zero_zero_real @ A )
% 3.82/4.03 => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B2 @ A ) )
% 3.82/4.03 = ( ord_less_eq_real @ A @ B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % le_divide_eq_1_pos
% 3.82/4.03 thf(fact_2052_one__add__one,axiom,
% 3.82/4.03 ( ( plus_plus_complex @ one_one_complex @ one_one_complex )
% 3.82/4.03 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % one_add_one
% 3.82/4.03 thf(fact_2053_one__add__one,axiom,
% 3.82/4.03 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 3.82/4.03 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % one_add_one
% 3.82/4.03 thf(fact_2054_one__add__one,axiom,
% 3.82/4.03 ( ( plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ one_on7984719198319812577d_enat )
% 3.82/4.03 = ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % one_add_one
% 3.82/4.03 thf(fact_2055_one__add__one,axiom,
% 3.82/4.03 ( ( plus_plus_int @ one_one_int @ one_one_int )
% 3.82/4.03 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % one_add_one
% 3.82/4.03 thf(fact_2056_one__add__one,axiom,
% 3.82/4.03 ( ( plus_plus_real @ one_one_real @ one_one_real )
% 3.82/4.03 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % one_add_one
% 3.82/4.03 thf(fact_2057_power__strict__decreasing__iff,axiom,
% 3.82/4.03 ! [B2: nat,M2: nat,N2: nat] :
% 3.82/4.03 ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 3.82/4.03 => ( ( ord_less_nat @ B2 @ one_one_nat )
% 3.82/4.03 => ( ( ord_less_nat @ ( power_power_nat @ B2 @ M2 ) @ ( power_power_nat @ B2 @ N2 ) )
% 3.82/4.03 = ( ord_less_nat @ N2 @ M2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_strict_decreasing_iff
% 3.82/4.03 thf(fact_2058_power__strict__decreasing__iff,axiom,
% 3.82/4.03 ! [B2: real,M2: nat,N2: nat] :
% 3.82/4.03 ( ( ord_less_real @ zero_zero_real @ B2 )
% 3.82/4.03 => ( ( ord_less_real @ B2 @ one_one_real )
% 3.82/4.03 => ( ( ord_less_real @ ( power_power_real @ B2 @ M2 ) @ ( power_power_real @ B2 @ N2 ) )
% 3.82/4.03 = ( ord_less_nat @ N2 @ M2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_strict_decreasing_iff
% 3.82/4.03 thf(fact_2059_power__strict__decreasing__iff,axiom,
% 3.82/4.03 ! [B2: int,M2: nat,N2: nat] :
% 3.82/4.03 ( ( ord_less_int @ zero_zero_int @ B2 )
% 3.82/4.03 => ( ( ord_less_int @ B2 @ one_one_int )
% 3.82/4.03 => ( ( ord_less_int @ ( power_power_int @ B2 @ M2 ) @ ( power_power_int @ B2 @ N2 ) )
% 3.82/4.03 = ( ord_less_nat @ N2 @ M2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_strict_decreasing_iff
% 3.82/4.03 thf(fact_2060_power__increasing__iff,axiom,
% 3.82/4.03 ! [B2: real,X: nat,Y: nat] :
% 3.82/4.03 ( ( ord_less_real @ one_one_real @ B2 )
% 3.82/4.03 => ( ( ord_less_eq_real @ ( power_power_real @ B2 @ X ) @ ( power_power_real @ B2 @ Y ) )
% 3.82/4.03 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_increasing_iff
% 3.82/4.03 thf(fact_2061_power__increasing__iff,axiom,
% 3.82/4.03 ! [B2: nat,X: nat,Y: nat] :
% 3.82/4.03 ( ( ord_less_nat @ one_one_nat @ B2 )
% 3.82/4.03 => ( ( ord_less_eq_nat @ ( power_power_nat @ B2 @ X ) @ ( power_power_nat @ B2 @ Y ) )
% 3.82/4.03 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_increasing_iff
% 3.82/4.03 thf(fact_2062_power__increasing__iff,axiom,
% 3.82/4.03 ! [B2: int,X: nat,Y: nat] :
% 3.82/4.03 ( ( ord_less_int @ one_one_int @ B2 )
% 3.82/4.03 => ( ( ord_less_eq_int @ ( power_power_int @ B2 @ X ) @ ( power_power_int @ B2 @ Y ) )
% 3.82/4.03 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_increasing_iff
% 3.82/4.03 thf(fact_2063_Suc__1,axiom,
% 3.82/4.03 ( ( suc @ one_one_nat )
% 3.82/4.03 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % Suc_1
% 3.82/4.03 thf(fact_2064_one__plus__numeral,axiom,
% 3.82/4.03 ! [N2: num] :
% 3.82/4.03 ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ N2 ) )
% 3.82/4.03 = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % one_plus_numeral
% 3.82/4.03 thf(fact_2065_one__plus__numeral,axiom,
% 3.82/4.03 ! [N2: num] :
% 3.82/4.03 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) )
% 3.82/4.03 = ( numeral_numeral_nat @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % one_plus_numeral
% 3.82/4.03 thf(fact_2066_one__plus__numeral,axiom,
% 3.82/4.03 ! [N2: num] :
% 3.82/4.03 ( ( plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ N2 ) )
% 3.82/4.03 = ( numera1916890842035813515d_enat @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % one_plus_numeral
% 3.82/4.03 thf(fact_2067_one__plus__numeral,axiom,
% 3.82/4.03 ! [N2: num] :
% 3.82/4.03 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ N2 ) )
% 3.82/4.03 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % one_plus_numeral
% 3.82/4.03 thf(fact_2068_one__plus__numeral,axiom,
% 3.82/4.03 ! [N2: num] :
% 3.82/4.03 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ N2 ) )
% 3.82/4.03 = ( numeral_numeral_real @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % one_plus_numeral
% 3.82/4.03 thf(fact_2069_numeral__plus__one,axiom,
% 3.82/4.03 ! [N2: num] :
% 3.82/4.03 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ N2 ) @ one_one_complex )
% 3.82/4.03 = ( numera6690914467698888265omplex @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % numeral_plus_one
% 3.82/4.03 thf(fact_2070_numeral__plus__one,axiom,
% 3.82/4.03 ! [N2: num] :
% 3.82/4.03 ( ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ one_one_nat )
% 3.82/4.03 = ( numeral_numeral_nat @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % numeral_plus_one
% 3.82/4.03 thf(fact_2071_numeral__plus__one,axiom,
% 3.82/4.03 ! [N2: num] :
% 3.82/4.03 ( ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ one_on7984719198319812577d_enat )
% 3.82/4.03 = ( numera1916890842035813515d_enat @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % numeral_plus_one
% 3.82/4.03 thf(fact_2072_numeral__plus__one,axiom,
% 3.82/4.03 ! [N2: num] :
% 3.82/4.03 ( ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ one_one_int )
% 3.82/4.03 = ( numeral_numeral_int @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % numeral_plus_one
% 3.82/4.03 thf(fact_2073_numeral__plus__one,axiom,
% 3.82/4.03 ! [N2: num] :
% 3.82/4.03 ( ( plus_plus_real @ ( numeral_numeral_real @ N2 ) @ one_one_real )
% 3.82/4.03 = ( numeral_numeral_real @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % numeral_plus_one
% 3.82/4.03 thf(fact_2074_numeral__le__one__iff,axiom,
% 3.82/4.03 ! [N2: num] :
% 3.82/4.03 ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ one_on7984719198319812577d_enat )
% 3.82/4.03 = ( ord_less_eq_num @ N2 @ one ) ) ).
% 3.82/4.03
% 3.82/4.03 % numeral_le_one_iff
% 3.82/4.03 thf(fact_2075_numeral__le__one__iff,axiom,
% 3.82/4.03 ! [N2: num] :
% 3.82/4.03 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N2 ) @ one_one_real )
% 3.82/4.03 = ( ord_less_eq_num @ N2 @ one ) ) ).
% 3.82/4.03
% 3.82/4.03 % numeral_le_one_iff
% 3.82/4.03 thf(fact_2076_numeral__le__one__iff,axiom,
% 3.82/4.03 ! [N2: num] :
% 3.82/4.03 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ N2 ) @ one_one_nat )
% 3.82/4.03 = ( ord_less_eq_num @ N2 @ one ) ) ).
% 3.82/4.03
% 3.82/4.03 % numeral_le_one_iff
% 3.82/4.03 thf(fact_2077_numeral__le__one__iff,axiom,
% 3.82/4.03 ! [N2: num] :
% 3.82/4.03 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ one_one_int )
% 3.82/4.03 = ( ord_less_eq_num @ N2 @ one ) ) ).
% 3.82/4.03
% 3.82/4.03 % numeral_le_one_iff
% 3.82/4.03 thf(fact_2078_one__less__numeral__iff,axiom,
% 3.82/4.03 ! [N2: num] :
% 3.82/4.03 ( ( ord_less_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) )
% 3.82/4.03 = ( ord_less_num @ one @ N2 ) ) ).
% 3.82/4.03
% 3.82/4.03 % one_less_numeral_iff
% 3.82/4.03 thf(fact_2079_one__less__numeral__iff,axiom,
% 3.82/4.03 ! [N2: num] :
% 3.82/4.03 ( ( ord_le72135733267957522d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ N2 ) )
% 3.82/4.03 = ( ord_less_num @ one @ N2 ) ) ).
% 3.82/4.03
% 3.82/4.03 % one_less_numeral_iff
% 3.82/4.03 thf(fact_2080_one__less__numeral__iff,axiom,
% 3.82/4.03 ! [N2: num] :
% 3.82/4.03 ( ( ord_less_int @ one_one_int @ ( numeral_numeral_int @ N2 ) )
% 3.82/4.03 = ( ord_less_num @ one @ N2 ) ) ).
% 3.82/4.03
% 3.82/4.03 % one_less_numeral_iff
% 3.82/4.03 thf(fact_2081_one__less__numeral__iff,axiom,
% 3.82/4.03 ! [N2: num] :
% 3.82/4.03 ( ( ord_less_real @ one_one_real @ ( numeral_numeral_real @ N2 ) )
% 3.82/4.03 = ( ord_less_num @ one @ N2 ) ) ).
% 3.82/4.03
% 3.82/4.03 % one_less_numeral_iff
% 3.82/4.03 thf(fact_2082_bits__1__div__2,axiom,
% 3.82/4.03 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.03 = zero_zero_nat ) ).
% 3.82/4.03
% 3.82/4.03 % bits_1_div_2
% 3.82/4.03 thf(fact_2083_bits__1__div__2,axiom,
% 3.82/4.03 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 3.82/4.03 = zero_zero_int ) ).
% 3.82/4.03
% 3.82/4.03 % bits_1_div_2
% 3.82/4.03 thf(fact_2084_one__div__two__eq__zero,axiom,
% 3.82/4.03 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.03 = zero_zero_nat ) ).
% 3.82/4.03
% 3.82/4.03 % one_div_two_eq_zero
% 3.82/4.03 thf(fact_2085_one__div__two__eq__zero,axiom,
% 3.82/4.03 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 3.82/4.03 = zero_zero_int ) ).
% 3.82/4.03
% 3.82/4.03 % one_div_two_eq_zero
% 3.82/4.03 thf(fact_2086_power__decreasing__iff,axiom,
% 3.82/4.03 ! [B2: real,M2: nat,N2: nat] :
% 3.82/4.03 ( ( ord_less_real @ zero_zero_real @ B2 )
% 3.82/4.03 => ( ( ord_less_real @ B2 @ one_one_real )
% 3.82/4.03 => ( ( ord_less_eq_real @ ( power_power_real @ B2 @ M2 ) @ ( power_power_real @ B2 @ N2 ) )
% 3.82/4.03 = ( ord_less_eq_nat @ N2 @ M2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_decreasing_iff
% 3.82/4.03 thf(fact_2087_power__decreasing__iff,axiom,
% 3.82/4.03 ! [B2: nat,M2: nat,N2: nat] :
% 3.82/4.03 ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 3.82/4.03 => ( ( ord_less_nat @ B2 @ one_one_nat )
% 3.82/4.03 => ( ( ord_less_eq_nat @ ( power_power_nat @ B2 @ M2 ) @ ( power_power_nat @ B2 @ N2 ) )
% 3.82/4.03 = ( ord_less_eq_nat @ N2 @ M2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_decreasing_iff
% 3.82/4.03 thf(fact_2088_power__decreasing__iff,axiom,
% 3.82/4.03 ! [B2: int,M2: nat,N2: nat] :
% 3.82/4.03 ( ( ord_less_int @ zero_zero_int @ B2 )
% 3.82/4.03 => ( ( ord_less_int @ B2 @ one_one_int )
% 3.82/4.03 => ( ( ord_less_eq_int @ ( power_power_int @ B2 @ M2 ) @ ( power_power_int @ B2 @ N2 ) )
% 3.82/4.03 = ( ord_less_eq_nat @ N2 @ M2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_decreasing_iff
% 3.82/4.03 thf(fact_2089_one__reorient,axiom,
% 3.82/4.03 ! [X: nat] :
% 3.82/4.03 ( ( one_one_nat = X )
% 3.82/4.03 = ( X = one_one_nat ) ) ).
% 3.82/4.03
% 3.82/4.03 % one_reorient
% 3.82/4.03 thf(fact_2090_one__reorient,axiom,
% 3.82/4.03 ! [X: int] :
% 3.82/4.03 ( ( one_one_int = X )
% 3.82/4.03 = ( X = one_one_int ) ) ).
% 3.82/4.03
% 3.82/4.03 % one_reorient
% 3.82/4.03 thf(fact_2091_one__reorient,axiom,
% 3.82/4.03 ! [X: complex] :
% 3.82/4.03 ( ( one_one_complex = X )
% 3.82/4.03 = ( X = one_one_complex ) ) ).
% 3.82/4.03
% 3.82/4.03 % one_reorient
% 3.82/4.03 thf(fact_2092_one__reorient,axiom,
% 3.82/4.03 ! [X: real] :
% 3.82/4.03 ( ( one_one_real = X )
% 3.82/4.03 = ( X = one_one_real ) ) ).
% 3.82/4.03
% 3.82/4.03 % one_reorient
% 3.82/4.03 thf(fact_2093_le__numeral__extra_I4_J,axiom,
% 3.82/4.03 ord_less_eq_real @ one_one_real @ one_one_real ).
% 3.82/4.03
% 3.82/4.03 % le_numeral_extra(4)
% 3.82/4.03 thf(fact_2094_le__numeral__extra_I4_J,axiom,
% 3.82/4.03 ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 3.82/4.03
% 3.82/4.03 % le_numeral_extra(4)
% 3.82/4.03 thf(fact_2095_le__numeral__extra_I4_J,axiom,
% 3.82/4.03 ord_less_eq_int @ one_one_int @ one_one_int ).
% 3.82/4.03
% 3.82/4.03 % le_numeral_extra(4)
% 3.82/4.03 thf(fact_2096_zero__neq__one,axiom,
% 3.82/4.03 zero_zero_nat != one_one_nat ).
% 3.82/4.03
% 3.82/4.03 % zero_neq_one
% 3.82/4.03 thf(fact_2097_zero__neq__one,axiom,
% 3.82/4.03 zero_zero_real != one_one_real ).
% 3.82/4.03
% 3.82/4.03 % zero_neq_one
% 3.82/4.03 thf(fact_2098_zero__neq__one,axiom,
% 3.82/4.03 zero_zero_int != one_one_int ).
% 3.82/4.03
% 3.82/4.03 % zero_neq_one
% 3.82/4.03 thf(fact_2099_zero__neq__one,axiom,
% 3.82/4.03 zero_zero_complex != one_one_complex ).
% 3.82/4.03
% 3.82/4.03 % zero_neq_one
% 3.82/4.03 thf(fact_2100_zero__neq__one,axiom,
% 3.82/4.03 zero_z5237406670263579293d_enat != one_on7984719198319812577d_enat ).
% 3.82/4.03
% 3.82/4.03 % zero_neq_one
% 3.82/4.03 thf(fact_2101_less__numeral__extra_I4_J,axiom,
% 3.82/4.03 ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 3.82/4.03
% 3.82/4.03 % less_numeral_extra(4)
% 3.82/4.03 thf(fact_2102_less__numeral__extra_I4_J,axiom,
% 3.82/4.03 ~ ( ord_le72135733267957522d_enat @ one_on7984719198319812577d_enat @ one_on7984719198319812577d_enat ) ).
% 3.82/4.03
% 3.82/4.03 % less_numeral_extra(4)
% 3.82/4.03 thf(fact_2103_less__numeral__extra_I4_J,axiom,
% 3.82/4.03 ~ ( ord_less_real @ one_one_real @ one_one_real ) ).
% 3.82/4.03
% 3.82/4.03 % less_numeral_extra(4)
% 3.82/4.03 thf(fact_2104_less__numeral__extra_I4_J,axiom,
% 3.82/4.03 ~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% 3.82/4.03
% 3.82/4.03 % less_numeral_extra(4)
% 3.82/4.03 thf(fact_2105_div__add__self1,axiom,
% 3.82/4.03 ! [B2: nat,A: nat] :
% 3.82/4.03 ( ( B2 != zero_zero_nat )
% 3.82/4.03 => ( ( divide_divide_nat @ ( plus_plus_nat @ B2 @ A ) @ B2 )
% 3.82/4.03 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B2 ) @ one_one_nat ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % div_add_self1
% 3.82/4.03 thf(fact_2106_div__add__self1,axiom,
% 3.82/4.03 ! [B2: int,A: int] :
% 3.82/4.03 ( ( B2 != zero_zero_int )
% 3.82/4.03 => ( ( divide_divide_int @ ( plus_plus_int @ B2 @ A ) @ B2 )
% 3.82/4.03 = ( plus_plus_int @ ( divide_divide_int @ A @ B2 ) @ one_one_int ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % div_add_self1
% 3.82/4.03 thf(fact_2107_div__add__self2,axiom,
% 3.82/4.03 ! [B2: nat,A: nat] :
% 3.82/4.03 ( ( B2 != zero_zero_nat )
% 3.82/4.03 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B2 ) @ B2 )
% 3.82/4.03 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B2 ) @ one_one_nat ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % div_add_self2
% 3.82/4.03 thf(fact_2108_div__add__self2,axiom,
% 3.82/4.03 ! [B2: int,A: int] :
% 3.82/4.03 ( ( B2 != zero_zero_int )
% 3.82/4.03 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B2 ) @ B2 )
% 3.82/4.03 = ( plus_plus_int @ ( divide_divide_int @ A @ B2 ) @ one_one_int ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % div_add_self2
% 3.82/4.03 thf(fact_2109_not__one__le__zero,axiom,
% 3.82/4.03 ~ ( ord_le2932123472753598470d_enat @ one_on7984719198319812577d_enat @ zero_z5237406670263579293d_enat ) ).
% 3.82/4.03
% 3.82/4.03 % not_one_le_zero
% 3.82/4.03 thf(fact_2110_not__one__le__zero,axiom,
% 3.82/4.03 ~ ( ord_less_eq_real @ one_one_real @ zero_zero_real ) ).
% 3.82/4.03
% 3.82/4.03 % not_one_le_zero
% 3.82/4.03 thf(fact_2111_not__one__le__zero,axiom,
% 3.82/4.03 ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).
% 3.82/4.03
% 3.82/4.03 % not_one_le_zero
% 3.82/4.03 thf(fact_2112_not__one__le__zero,axiom,
% 3.82/4.03 ~ ( ord_less_eq_int @ one_one_int @ zero_zero_int ) ).
% 3.82/4.03
% 3.82/4.03 % not_one_le_zero
% 3.82/4.03 thf(fact_2113_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 3.82/4.03 ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ one_on7984719198319812577d_enat ).
% 3.82/4.03
% 3.82/4.03 % linordered_nonzero_semiring_class.zero_le_one
% 3.82/4.03 thf(fact_2114_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 3.82/4.03 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 3.82/4.03
% 3.82/4.03 % linordered_nonzero_semiring_class.zero_le_one
% 3.82/4.03 thf(fact_2115_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 3.82/4.03 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 3.82/4.03
% 3.82/4.03 % linordered_nonzero_semiring_class.zero_le_one
% 3.82/4.03 thf(fact_2116_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 3.82/4.03 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 3.82/4.03
% 3.82/4.03 % linordered_nonzero_semiring_class.zero_le_one
% 3.82/4.03 thf(fact_2117_zero__less__one__class_Ozero__le__one,axiom,
% 3.82/4.03 ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ one_on7984719198319812577d_enat ).
% 3.82/4.03
% 3.82/4.03 % zero_less_one_class.zero_le_one
% 3.82/4.03 thf(fact_2118_zero__less__one__class_Ozero__le__one,axiom,
% 3.82/4.03 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 3.82/4.03
% 3.82/4.03 % zero_less_one_class.zero_le_one
% 3.82/4.03 thf(fact_2119_zero__less__one__class_Ozero__le__one,axiom,
% 3.82/4.03 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 3.82/4.03
% 3.82/4.03 % zero_less_one_class.zero_le_one
% 3.82/4.03 thf(fact_2120_zero__less__one__class_Ozero__le__one,axiom,
% 3.82/4.03 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 3.82/4.03
% 3.82/4.03 % zero_less_one_class.zero_le_one
% 3.82/4.03 thf(fact_2121_not__one__less__zero,axiom,
% 3.82/4.03 ~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).
% 3.82/4.03
% 3.82/4.03 % not_one_less_zero
% 3.82/4.03 thf(fact_2122_not__one__less__zero,axiom,
% 3.82/4.03 ~ ( ord_le72135733267957522d_enat @ one_on7984719198319812577d_enat @ zero_z5237406670263579293d_enat ) ).
% 3.82/4.03
% 3.82/4.03 % not_one_less_zero
% 3.82/4.03 thf(fact_2123_not__one__less__zero,axiom,
% 3.82/4.03 ~ ( ord_less_real @ one_one_real @ zero_zero_real ) ).
% 3.82/4.03
% 3.82/4.03 % not_one_less_zero
% 3.82/4.03 thf(fact_2124_not__one__less__zero,axiom,
% 3.82/4.03 ~ ( ord_less_int @ one_one_int @ zero_zero_int ) ).
% 3.82/4.03
% 3.82/4.03 % not_one_less_zero
% 3.82/4.03 thf(fact_2125_zero__less__one,axiom,
% 3.82/4.03 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 3.82/4.03
% 3.82/4.03 % zero_less_one
% 3.82/4.03 thf(fact_2126_zero__less__one,axiom,
% 3.82/4.03 ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ one_on7984719198319812577d_enat ).
% 3.82/4.03
% 3.82/4.03 % zero_less_one
% 3.82/4.03 thf(fact_2127_zero__less__one,axiom,
% 3.82/4.03 ord_less_real @ zero_zero_real @ one_one_real ).
% 3.82/4.03
% 3.82/4.03 % zero_less_one
% 3.82/4.03 thf(fact_2128_zero__less__one,axiom,
% 3.82/4.03 ord_less_int @ zero_zero_int @ one_one_int ).
% 3.82/4.03
% 3.82/4.03 % zero_less_one
% 3.82/4.03 thf(fact_2129_less__numeral__extra_I1_J,axiom,
% 3.82/4.03 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 3.82/4.03
% 3.82/4.03 % less_numeral_extra(1)
% 3.82/4.03 thf(fact_2130_less__numeral__extra_I1_J,axiom,
% 3.82/4.03 ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ one_on7984719198319812577d_enat ).
% 3.82/4.03
% 3.82/4.03 % less_numeral_extra(1)
% 3.82/4.03 thf(fact_2131_less__numeral__extra_I1_J,axiom,
% 3.82/4.03 ord_less_real @ zero_zero_real @ one_one_real ).
% 3.82/4.03
% 3.82/4.03 % less_numeral_extra(1)
% 3.82/4.03 thf(fact_2132_less__numeral__extra_I1_J,axiom,
% 3.82/4.03 ord_less_int @ zero_zero_int @ one_one_int ).
% 3.82/4.03
% 3.82/4.03 % less_numeral_extra(1)
% 3.82/4.03 thf(fact_2133_one__le__numeral,axiom,
% 3.82/4.03 ! [N2: num] : ( ord_le2932123472753598470d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ N2 ) ) ).
% 3.82/4.03
% 3.82/4.03 % one_le_numeral
% 3.82/4.03 thf(fact_2134_one__le__numeral,axiom,
% 3.82/4.03 ! [N2: num] : ( ord_less_eq_real @ one_one_real @ ( numeral_numeral_real @ N2 ) ) ).
% 3.82/4.03
% 3.82/4.03 % one_le_numeral
% 3.82/4.03 thf(fact_2135_one__le__numeral,axiom,
% 3.82/4.03 ! [N2: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) ) ).
% 3.82/4.03
% 3.82/4.03 % one_le_numeral
% 3.82/4.03 thf(fact_2136_one__le__numeral,axiom,
% 3.82/4.03 ! [N2: num] : ( ord_less_eq_int @ one_one_int @ ( numeral_numeral_int @ N2 ) ) ).
% 3.82/4.03
% 3.82/4.03 % one_le_numeral
% 3.82/4.03 thf(fact_2137_not__numeral__less__one,axiom,
% 3.82/4.03 ! [N2: num] :
% 3.82/4.03 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N2 ) @ one_one_nat ) ).
% 3.82/4.03
% 3.82/4.03 % not_numeral_less_one
% 3.82/4.03 thf(fact_2138_not__numeral__less__one,axiom,
% 3.82/4.03 ! [N2: num] :
% 3.82/4.03 ~ ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ one_on7984719198319812577d_enat ) ).
% 3.82/4.03
% 3.82/4.03 % not_numeral_less_one
% 3.82/4.03 thf(fact_2139_not__numeral__less__one,axiom,
% 3.82/4.03 ! [N2: num] :
% 3.82/4.03 ~ ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ one_one_int ) ).
% 3.82/4.03
% 3.82/4.03 % not_numeral_less_one
% 3.82/4.03 thf(fact_2140_not__numeral__less__one,axiom,
% 3.82/4.03 ! [N2: num] :
% 3.82/4.03 ~ ( ord_less_real @ ( numeral_numeral_real @ N2 ) @ one_one_real ) ).
% 3.82/4.03
% 3.82/4.03 % not_numeral_less_one
% 3.82/4.03 thf(fact_2141_add__mono1,axiom,
% 3.82/4.03 ! [A: nat,B2: nat] :
% 3.82/4.03 ( ( ord_less_nat @ A @ B2 )
% 3.82/4.03 => ( ord_less_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( plus_plus_nat @ B2 @ one_one_nat ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % add_mono1
% 3.82/4.03 thf(fact_2142_add__mono1,axiom,
% 3.82/4.03 ! [A: extended_enat,B2: extended_enat] :
% 3.82/4.03 ( ( ord_le72135733267957522d_enat @ A @ B2 )
% 3.82/4.03 => ( ord_le72135733267957522d_enat @ ( plus_p3455044024723400733d_enat @ A @ one_on7984719198319812577d_enat ) @ ( plus_p3455044024723400733d_enat @ B2 @ one_on7984719198319812577d_enat ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % add_mono1
% 3.82/4.03 thf(fact_2143_add__mono1,axiom,
% 3.82/4.03 ! [A: real,B2: real] :
% 3.82/4.03 ( ( ord_less_real @ A @ B2 )
% 3.82/4.03 => ( ord_less_real @ ( plus_plus_real @ A @ one_one_real ) @ ( plus_plus_real @ B2 @ one_one_real ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % add_mono1
% 3.82/4.03 thf(fact_2144_add__mono1,axiom,
% 3.82/4.03 ! [A: int,B2: int] :
% 3.82/4.03 ( ( ord_less_int @ A @ B2 )
% 3.82/4.03 => ( ord_less_int @ ( plus_plus_int @ A @ one_one_int ) @ ( plus_plus_int @ B2 @ one_one_int ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % add_mono1
% 3.82/4.03 thf(fact_2145_less__add__one,axiom,
% 3.82/4.03 ! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ) ).
% 3.82/4.03
% 3.82/4.03 % less_add_one
% 3.82/4.03 thf(fact_2146_less__add__one,axiom,
% 3.82/4.03 ! [A: real] : ( ord_less_real @ A @ ( plus_plus_real @ A @ one_one_real ) ) ).
% 3.82/4.03
% 3.82/4.03 % less_add_one
% 3.82/4.03 thf(fact_2147_less__add__one,axiom,
% 3.82/4.03 ! [A: int] : ( ord_less_int @ A @ ( plus_plus_int @ A @ one_one_int ) ) ).
% 3.82/4.03
% 3.82/4.03 % less_add_one
% 3.82/4.03 thf(fact_2148_right__inverse__eq,axiom,
% 3.82/4.03 ! [B2: complex,A: complex] :
% 3.82/4.03 ( ( B2 != zero_zero_complex )
% 3.82/4.03 => ( ( ( divide1717551699836669952omplex @ A @ B2 )
% 3.82/4.03 = one_one_complex )
% 3.82/4.03 = ( A = B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % right_inverse_eq
% 3.82/4.03 thf(fact_2149_right__inverse__eq,axiom,
% 3.82/4.03 ! [B2: real,A: real] :
% 3.82/4.03 ( ( B2 != zero_zero_real )
% 3.82/4.03 => ( ( ( divide_divide_real @ A @ B2 )
% 3.82/4.03 = one_one_real )
% 3.82/4.03 = ( A = B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % right_inverse_eq
% 3.82/4.03 thf(fact_2150_one__plus__numeral__commute,axiom,
% 3.82/4.03 ! [X: num] :
% 3.82/4.03 ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ X ) )
% 3.82/4.03 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X ) @ one_one_complex ) ) ).
% 3.82/4.03
% 3.82/4.03 % one_plus_numeral_commute
% 3.82/4.03 thf(fact_2151_one__plus__numeral__commute,axiom,
% 3.82/4.03 ! [X: num] :
% 3.82/4.03 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ X ) )
% 3.82/4.03 = ( plus_plus_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat ) ) ).
% 3.82/4.03
% 3.82/4.03 % one_plus_numeral_commute
% 3.82/4.03 thf(fact_2152_one__plus__numeral__commute,axiom,
% 3.82/4.03 ! [X: num] :
% 3.82/4.03 ( ( plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ X ) )
% 3.82/4.03 = ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ X ) @ one_on7984719198319812577d_enat ) ) ).
% 3.82/4.03
% 3.82/4.03 % one_plus_numeral_commute
% 3.82/4.03 thf(fact_2153_one__plus__numeral__commute,axiom,
% 3.82/4.03 ! [X: num] :
% 3.82/4.03 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ X ) )
% 3.82/4.03 = ( plus_plus_int @ ( numeral_numeral_int @ X ) @ one_one_int ) ) ).
% 3.82/4.03
% 3.82/4.03 % one_plus_numeral_commute
% 3.82/4.03 thf(fact_2154_one__plus__numeral__commute,axiom,
% 3.82/4.03 ! [X: num] :
% 3.82/4.03 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ X ) )
% 3.82/4.03 = ( plus_plus_real @ ( numeral_numeral_real @ X ) @ one_one_real ) ) ).
% 3.82/4.03
% 3.82/4.03 % one_plus_numeral_commute
% 3.82/4.03 thf(fact_2155_one__le__power,axiom,
% 3.82/4.03 ! [A: real,N2: nat] :
% 3.82/4.03 ( ( ord_less_eq_real @ one_one_real @ A )
% 3.82/4.03 => ( ord_less_eq_real @ one_one_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % one_le_power
% 3.82/4.03 thf(fact_2156_one__le__power,axiom,
% 3.82/4.03 ! [A: nat,N2: nat] :
% 3.82/4.03 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 3.82/4.03 => ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A @ N2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % one_le_power
% 3.82/4.03 thf(fact_2157_one__le__power,axiom,
% 3.82/4.03 ! [A: int,N2: nat] :
% 3.82/4.03 ( ( ord_less_eq_int @ one_one_int @ A )
% 3.82/4.03 => ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % one_le_power
% 3.82/4.03 thf(fact_2158_div__eq__dividend__iff,axiom,
% 3.82/4.03 ! [M2: nat,N2: nat] :
% 3.82/4.03 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 3.82/4.03 => ( ( ( divide_divide_nat @ M2 @ N2 )
% 3.82/4.03 = M2 )
% 3.82/4.03 = ( N2 = one_one_nat ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % div_eq_dividend_iff
% 3.82/4.03 thf(fact_2159_div__less__dividend,axiom,
% 3.82/4.03 ! [N2: nat,M2: nat] :
% 3.82/4.03 ( ( ord_less_nat @ one_one_nat @ N2 )
% 3.82/4.03 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 3.82/4.03 => ( ord_less_nat @ ( divide_divide_nat @ M2 @ N2 ) @ M2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % div_less_dividend
% 3.82/4.03 thf(fact_2160_power__0,axiom,
% 3.82/4.03 ! [A: nat] :
% 3.82/4.03 ( ( power_power_nat @ A @ zero_zero_nat )
% 3.82/4.03 = one_one_nat ) ).
% 3.82/4.03
% 3.82/4.03 % power_0
% 3.82/4.03 thf(fact_2161_power__0,axiom,
% 3.82/4.03 ! [A: real] :
% 3.82/4.03 ( ( power_power_real @ A @ zero_zero_nat )
% 3.82/4.03 = one_one_real ) ).
% 3.82/4.03
% 3.82/4.03 % power_0
% 3.82/4.03 thf(fact_2162_power__0,axiom,
% 3.82/4.03 ! [A: complex] :
% 3.82/4.03 ( ( power_power_complex @ A @ zero_zero_nat )
% 3.82/4.03 = one_one_complex ) ).
% 3.82/4.03
% 3.82/4.03 % power_0
% 3.82/4.03 thf(fact_2163_power__0,axiom,
% 3.82/4.03 ! [A: int] :
% 3.82/4.03 ( ( power_power_int @ A @ zero_zero_nat )
% 3.82/4.03 = one_one_int ) ).
% 3.82/4.03
% 3.82/4.03 % power_0
% 3.82/4.03 thf(fact_2164_One__nat__def,axiom,
% 3.82/4.03 ( one_one_nat
% 3.82/4.03 = ( suc @ zero_zero_nat ) ) ).
% 3.82/4.03
% 3.82/4.03 % One_nat_def
% 3.82/4.03 thf(fact_2165_Suc__eq__plus1,axiom,
% 3.82/4.03 ( suc
% 3.82/4.03 = ( ^ [N: nat] : ( plus_plus_nat @ N @ one_one_nat ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % Suc_eq_plus1
% 3.82/4.03 thf(fact_2166_plus__1__eq__Suc,axiom,
% 3.82/4.03 ( ( plus_plus_nat @ one_one_nat )
% 3.82/4.03 = suc ) ).
% 3.82/4.03
% 3.82/4.03 % plus_1_eq_Suc
% 3.82/4.03 thf(fact_2167_Suc__eq__plus1__left,axiom,
% 3.82/4.03 ( suc
% 3.82/4.03 = ( plus_plus_nat @ one_one_nat ) ) ).
% 3.82/4.03
% 3.82/4.03 % Suc_eq_plus1_left
% 3.82/4.03 thf(fact_2168_zero__less__two,axiom,
% 3.82/4.03 ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ).
% 3.82/4.03
% 3.82/4.03 % zero_less_two
% 3.82/4.03 thf(fact_2169_zero__less__two,axiom,
% 3.82/4.03 ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ one_on7984719198319812577d_enat ) ).
% 3.82/4.03
% 3.82/4.03 % zero_less_two
% 3.82/4.03 thf(fact_2170_zero__less__two,axiom,
% 3.82/4.03 ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ one_one_real ) ).
% 3.82/4.03
% 3.82/4.03 % zero_less_two
% 3.82/4.03 thf(fact_2171_zero__less__two,axiom,
% 3.82/4.03 ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ) ).
% 3.82/4.03
% 3.82/4.03 % zero_less_two
% 3.82/4.03 thf(fact_2172_less__divide__eq__1,axiom,
% 3.82/4.03 ! [B2: real,A: real] :
% 3.82/4.03 ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B2 @ A ) )
% 3.82/4.03 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 3.82/4.03 & ( ord_less_real @ A @ B2 ) )
% 3.82/4.03 | ( ( ord_less_real @ A @ zero_zero_real )
% 3.82/4.03 & ( ord_less_real @ B2 @ A ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % less_divide_eq_1
% 3.82/4.03 thf(fact_2173_divide__less__eq__1,axiom,
% 3.82/4.03 ! [B2: real,A: real] :
% 3.82/4.03 ( ( ord_less_real @ ( divide_divide_real @ B2 @ A ) @ one_one_real )
% 3.82/4.03 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 3.82/4.03 & ( ord_less_real @ B2 @ A ) )
% 3.82/4.03 | ( ( ord_less_real @ A @ zero_zero_real )
% 3.82/4.03 & ( ord_less_real @ A @ B2 ) )
% 3.82/4.03 | ( A = zero_zero_real ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % divide_less_eq_1
% 3.82/4.03 thf(fact_2174_power__le__one,axiom,
% 3.82/4.03 ! [A: real,N2: nat] :
% 3.82/4.03 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 3.82/4.03 => ( ( ord_less_eq_real @ A @ one_one_real )
% 3.82/4.03 => ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ one_one_real ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_le_one
% 3.82/4.03 thf(fact_2175_power__le__one,axiom,
% 3.82/4.03 ! [A: nat,N2: nat] :
% 3.82/4.03 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 3.82/4.03 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 3.82/4.03 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ one_one_nat ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_le_one
% 3.82/4.03 thf(fact_2176_power__le__one,axiom,
% 3.82/4.03 ! [A: int,N2: nat] :
% 3.82/4.03 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 3.82/4.03 => ( ( ord_less_eq_int @ A @ one_one_int )
% 3.82/4.03 => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ one_one_int ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_le_one
% 3.82/4.03 thf(fact_2177_less__half__sum,axiom,
% 3.82/4.03 ! [A: real,B2: real] :
% 3.82/4.03 ( ( ord_less_real @ A @ B2 )
% 3.82/4.03 => ( ord_less_real @ A @ ( divide_divide_real @ ( plus_plus_real @ A @ B2 ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % less_half_sum
% 3.82/4.03 thf(fact_2178_gt__half__sum,axiom,
% 3.82/4.03 ! [A: real,B2: real] :
% 3.82/4.03 ( ( ord_less_real @ A @ B2 )
% 3.82/4.03 => ( ord_less_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B2 ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) @ B2 ) ) ).
% 3.82/4.03
% 3.82/4.03 % gt_half_sum
% 3.82/4.03 thf(fact_2179_power__0__left,axiom,
% 3.82/4.03 ! [N2: nat] :
% 3.82/4.03 ( ( ( N2 = zero_zero_nat )
% 3.82/4.03 => ( ( power_8040749407984259932d_enat @ zero_z5237406670263579293d_enat @ N2 )
% 3.82/4.03 = one_on7984719198319812577d_enat ) )
% 3.82/4.03 & ( ( N2 != zero_zero_nat )
% 3.82/4.03 => ( ( power_8040749407984259932d_enat @ zero_z5237406670263579293d_enat @ N2 )
% 3.82/4.03 = zero_z5237406670263579293d_enat ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_0_left
% 3.82/4.03 thf(fact_2180_power__0__left,axiom,
% 3.82/4.03 ! [N2: nat] :
% 3.82/4.03 ( ( ( N2 = zero_zero_nat )
% 3.82/4.03 => ( ( power_power_nat @ zero_zero_nat @ N2 )
% 3.82/4.03 = one_one_nat ) )
% 3.82/4.03 & ( ( N2 != zero_zero_nat )
% 3.82/4.03 => ( ( power_power_nat @ zero_zero_nat @ N2 )
% 3.82/4.03 = zero_zero_nat ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_0_left
% 3.82/4.03 thf(fact_2181_power__0__left,axiom,
% 3.82/4.03 ! [N2: nat] :
% 3.82/4.03 ( ( ( N2 = zero_zero_nat )
% 3.82/4.03 => ( ( power_power_real @ zero_zero_real @ N2 )
% 3.82/4.03 = one_one_real ) )
% 3.82/4.03 & ( ( N2 != zero_zero_nat )
% 3.82/4.03 => ( ( power_power_real @ zero_zero_real @ N2 )
% 3.82/4.03 = zero_zero_real ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_0_left
% 3.82/4.03 thf(fact_2182_power__0__left,axiom,
% 3.82/4.03 ! [N2: nat] :
% 3.82/4.03 ( ( ( N2 = zero_zero_nat )
% 3.82/4.03 => ( ( power_power_complex @ zero_zero_complex @ N2 )
% 3.82/4.03 = one_one_complex ) )
% 3.82/4.03 & ( ( N2 != zero_zero_nat )
% 3.82/4.03 => ( ( power_power_complex @ zero_zero_complex @ N2 )
% 3.82/4.03 = zero_zero_complex ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_0_left
% 3.82/4.03 thf(fact_2183_power__0__left,axiom,
% 3.82/4.03 ! [N2: nat] :
% 3.82/4.03 ( ( ( N2 = zero_zero_nat )
% 3.82/4.03 => ( ( power_power_int @ zero_zero_int @ N2 )
% 3.82/4.03 = one_one_int ) )
% 3.82/4.03 & ( ( N2 != zero_zero_nat )
% 3.82/4.03 => ( ( power_power_int @ zero_zero_int @ N2 )
% 3.82/4.03 = zero_zero_int ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_0_left
% 3.82/4.03 thf(fact_2184_power__gt1,axiom,
% 3.82/4.03 ! [A: nat,N2: nat] :
% 3.82/4.03 ( ( ord_less_nat @ one_one_nat @ A )
% 3.82/4.03 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_gt1
% 3.82/4.03 thf(fact_2185_power__gt1,axiom,
% 3.82/4.03 ! [A: real,N2: nat] :
% 3.82/4.03 ( ( ord_less_real @ one_one_real @ A )
% 3.82/4.03 => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ ( suc @ N2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_gt1
% 3.82/4.03 thf(fact_2186_power__gt1,axiom,
% 3.82/4.03 ! [A: int,N2: nat] :
% 3.82/4.03 ( ( ord_less_int @ one_one_int @ A )
% 3.82/4.03 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ ( suc @ N2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_gt1
% 3.82/4.03 thf(fact_2187_power__less__imp__less__exp,axiom,
% 3.82/4.03 ! [A: nat,M2: nat,N2: nat] :
% 3.82/4.03 ( ( ord_less_nat @ one_one_nat @ A )
% 3.82/4.03 => ( ( ord_less_nat @ ( power_power_nat @ A @ M2 ) @ ( power_power_nat @ A @ N2 ) )
% 3.82/4.03 => ( ord_less_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_less_imp_less_exp
% 3.82/4.03 thf(fact_2188_power__less__imp__less__exp,axiom,
% 3.82/4.03 ! [A: real,M2: nat,N2: nat] :
% 3.82/4.03 ( ( ord_less_real @ one_one_real @ A )
% 3.82/4.03 => ( ( ord_less_real @ ( power_power_real @ A @ M2 ) @ ( power_power_real @ A @ N2 ) )
% 3.82/4.03 => ( ord_less_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_less_imp_less_exp
% 3.82/4.03 thf(fact_2189_power__less__imp__less__exp,axiom,
% 3.82/4.03 ! [A: int,M2: nat,N2: nat] :
% 3.82/4.03 ( ( ord_less_int @ one_one_int @ A )
% 3.82/4.03 => ( ( ord_less_int @ ( power_power_int @ A @ M2 ) @ ( power_power_int @ A @ N2 ) )
% 3.82/4.03 => ( ord_less_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_less_imp_less_exp
% 3.82/4.03 thf(fact_2190_power__strict__increasing,axiom,
% 3.82/4.03 ! [N2: nat,N6: nat,A: nat] :
% 3.82/4.03 ( ( ord_less_nat @ N2 @ N6 )
% 3.82/4.03 => ( ( ord_less_nat @ one_one_nat @ A )
% 3.82/4.03 => ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ A @ N6 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_strict_increasing
% 3.82/4.03 thf(fact_2191_power__strict__increasing,axiom,
% 3.82/4.03 ! [N2: nat,N6: nat,A: real] :
% 3.82/4.03 ( ( ord_less_nat @ N2 @ N6 )
% 3.82/4.03 => ( ( ord_less_real @ one_one_real @ A )
% 3.82/4.03 => ( ord_less_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ A @ N6 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_strict_increasing
% 3.82/4.03 thf(fact_2192_power__strict__increasing,axiom,
% 3.82/4.03 ! [N2: nat,N6: nat,A: int] :
% 3.82/4.03 ( ( ord_less_nat @ N2 @ N6 )
% 3.82/4.03 => ( ( ord_less_int @ one_one_int @ A )
% 3.82/4.03 => ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ A @ N6 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_strict_increasing
% 3.82/4.03 thf(fact_2193_power__increasing,axiom,
% 3.82/4.03 ! [N2: nat,N6: nat,A: real] :
% 3.82/4.03 ( ( ord_less_eq_nat @ N2 @ N6 )
% 3.82/4.03 => ( ( ord_less_eq_real @ one_one_real @ A )
% 3.82/4.03 => ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ A @ N6 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_increasing
% 3.82/4.03 thf(fact_2194_power__increasing,axiom,
% 3.82/4.03 ! [N2: nat,N6: nat,A: nat] :
% 3.82/4.03 ( ( ord_less_eq_nat @ N2 @ N6 )
% 3.82/4.03 => ( ( ord_less_eq_nat @ one_one_nat @ A )
% 3.82/4.03 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ A @ N6 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_increasing
% 3.82/4.03 thf(fact_2195_power__increasing,axiom,
% 3.82/4.03 ! [N2: nat,N6: nat,A: int] :
% 3.82/4.03 ( ( ord_less_eq_nat @ N2 @ N6 )
% 3.82/4.03 => ( ( ord_less_eq_int @ one_one_int @ A )
% 3.82/4.03 => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ A @ N6 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_increasing
% 3.82/4.03 thf(fact_2196_nat__induct__non__zero,axiom,
% 3.82/4.03 ! [N2: nat,P: nat > $o] :
% 3.82/4.03 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.03 => ( ( P @ one_one_nat )
% 3.82/4.03 => ( ! [N3: nat] :
% 3.82/4.03 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 3.82/4.03 => ( ( P @ N3 )
% 3.82/4.03 => ( P @ ( suc @ N3 ) ) ) )
% 3.82/4.03 => ( P @ N2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % nat_induct_non_zero
% 3.82/4.03 thf(fact_2197_divide__le__eq__1,axiom,
% 3.82/4.03 ! [B2: real,A: real] :
% 3.82/4.03 ( ( ord_less_eq_real @ ( divide_divide_real @ B2 @ A ) @ one_one_real )
% 3.82/4.03 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 3.82/4.03 & ( ord_less_eq_real @ B2 @ A ) )
% 3.82/4.03 | ( ( ord_less_real @ A @ zero_zero_real )
% 3.82/4.03 & ( ord_less_eq_real @ A @ B2 ) )
% 3.82/4.03 | ( A = zero_zero_real ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % divide_le_eq_1
% 3.82/4.03 thf(fact_2198_le__divide__eq__1,axiom,
% 3.82/4.03 ! [B2: real,A: real] :
% 3.82/4.03 ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B2 @ A ) )
% 3.82/4.03 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 3.82/4.03 & ( ord_less_eq_real @ A @ B2 ) )
% 3.82/4.03 | ( ( ord_less_real @ A @ zero_zero_real )
% 3.82/4.03 & ( ord_less_eq_real @ B2 @ A ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % le_divide_eq_1
% 3.82/4.03 thf(fact_2199_power__Suc__le__self,axiom,
% 3.82/4.03 ! [A: real,N2: nat] :
% 3.82/4.03 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 3.82/4.03 => ( ( ord_less_eq_real @ A @ one_one_real )
% 3.82/4.03 => ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N2 ) ) @ A ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_Suc_le_self
% 3.82/4.03 thf(fact_2200_power__Suc__le__self,axiom,
% 3.82/4.03 ! [A: nat,N2: nat] :
% 3.82/4.03 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 3.82/4.03 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 3.82/4.03 => ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) @ A ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_Suc_le_self
% 3.82/4.03 thf(fact_2201_power__Suc__le__self,axiom,
% 3.82/4.03 ! [A: int,N2: nat] :
% 3.82/4.03 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 3.82/4.03 => ( ( ord_less_eq_int @ A @ one_one_int )
% 3.82/4.03 => ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N2 ) ) @ A ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_Suc_le_self
% 3.82/4.03 thf(fact_2202_power__Suc__less__one,axiom,
% 3.82/4.03 ! [A: nat,N2: nat] :
% 3.82/4.03 ( ( ord_less_nat @ zero_zero_nat @ A )
% 3.82/4.03 => ( ( ord_less_nat @ A @ one_one_nat )
% 3.82/4.03 => ( ord_less_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) @ one_one_nat ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_Suc_less_one
% 3.82/4.03 thf(fact_2203_power__Suc__less__one,axiom,
% 3.82/4.03 ! [A: real,N2: nat] :
% 3.82/4.03 ( ( ord_less_real @ zero_zero_real @ A )
% 3.82/4.03 => ( ( ord_less_real @ A @ one_one_real )
% 3.82/4.03 => ( ord_less_real @ ( power_power_real @ A @ ( suc @ N2 ) ) @ one_one_real ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_Suc_less_one
% 3.82/4.03 thf(fact_2204_power__Suc__less__one,axiom,
% 3.82/4.03 ! [A: int,N2: nat] :
% 3.82/4.03 ( ( ord_less_int @ zero_zero_int @ A )
% 3.82/4.03 => ( ( ord_less_int @ A @ one_one_int )
% 3.82/4.03 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ N2 ) ) @ one_one_int ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_Suc_less_one
% 3.82/4.03 thf(fact_2205_power__strict__decreasing,axiom,
% 3.82/4.03 ! [N2: nat,N6: nat,A: nat] :
% 3.82/4.03 ( ( ord_less_nat @ N2 @ N6 )
% 3.82/4.03 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 3.82/4.03 => ( ( ord_less_nat @ A @ one_one_nat )
% 3.82/4.03 => ( ord_less_nat @ ( power_power_nat @ A @ N6 ) @ ( power_power_nat @ A @ N2 ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_strict_decreasing
% 3.82/4.03 thf(fact_2206_power__strict__decreasing,axiom,
% 3.82/4.03 ! [N2: nat,N6: nat,A: real] :
% 3.82/4.03 ( ( ord_less_nat @ N2 @ N6 )
% 3.82/4.03 => ( ( ord_less_real @ zero_zero_real @ A )
% 3.82/4.03 => ( ( ord_less_real @ A @ one_one_real )
% 3.82/4.03 => ( ord_less_real @ ( power_power_real @ A @ N6 ) @ ( power_power_real @ A @ N2 ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_strict_decreasing
% 3.82/4.03 thf(fact_2207_power__strict__decreasing,axiom,
% 3.82/4.03 ! [N2: nat,N6: nat,A: int] :
% 3.82/4.03 ( ( ord_less_nat @ N2 @ N6 )
% 3.82/4.03 => ( ( ord_less_int @ zero_zero_int @ A )
% 3.82/4.03 => ( ( ord_less_int @ A @ one_one_int )
% 3.82/4.03 => ( ord_less_int @ ( power_power_int @ A @ N6 ) @ ( power_power_int @ A @ N2 ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_strict_decreasing
% 3.82/4.03 thf(fact_2208_power__decreasing,axiom,
% 3.82/4.03 ! [N2: nat,N6: nat,A: real] :
% 3.82/4.03 ( ( ord_less_eq_nat @ N2 @ N6 )
% 3.82/4.03 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 3.82/4.03 => ( ( ord_less_eq_real @ A @ one_one_real )
% 3.82/4.03 => ( ord_less_eq_real @ ( power_power_real @ A @ N6 ) @ ( power_power_real @ A @ N2 ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_decreasing
% 3.82/4.03 thf(fact_2209_power__decreasing,axiom,
% 3.82/4.03 ! [N2: nat,N6: nat,A: nat] :
% 3.82/4.03 ( ( ord_less_eq_nat @ N2 @ N6 )
% 3.82/4.03 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 3.82/4.03 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 3.82/4.03 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N6 ) @ ( power_power_nat @ A @ N2 ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_decreasing
% 3.82/4.03 thf(fact_2210_power__decreasing,axiom,
% 3.82/4.03 ! [N2: nat,N6: nat,A: int] :
% 3.82/4.03 ( ( ord_less_eq_nat @ N2 @ N6 )
% 3.82/4.03 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 3.82/4.03 => ( ( ord_less_eq_int @ A @ one_one_int )
% 3.82/4.03 => ( ord_less_eq_int @ ( power_power_int @ A @ N6 ) @ ( power_power_int @ A @ N2 ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_decreasing
% 3.82/4.03 thf(fact_2211_power__le__imp__le__exp,axiom,
% 3.82/4.03 ! [A: real,M2: nat,N2: nat] :
% 3.82/4.03 ( ( ord_less_real @ one_one_real @ A )
% 3.82/4.03 => ( ( ord_less_eq_real @ ( power_power_real @ A @ M2 ) @ ( power_power_real @ A @ N2 ) )
% 3.82/4.03 => ( ord_less_eq_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_le_imp_le_exp
% 3.82/4.03 thf(fact_2212_power__le__imp__le__exp,axiom,
% 3.82/4.03 ! [A: nat,M2: nat,N2: nat] :
% 3.82/4.03 ( ( ord_less_nat @ one_one_nat @ A )
% 3.82/4.03 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ M2 ) @ ( power_power_nat @ A @ N2 ) )
% 3.82/4.03 => ( ord_less_eq_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_le_imp_le_exp
% 3.82/4.03 thf(fact_2213_power__le__imp__le__exp,axiom,
% 3.82/4.03 ! [A: int,M2: nat,N2: nat] :
% 3.82/4.03 ( ( ord_less_int @ one_one_int @ A )
% 3.82/4.03 => ( ( ord_less_eq_int @ ( power_power_int @ A @ M2 ) @ ( power_power_int @ A @ N2 ) )
% 3.82/4.03 => ( ord_less_eq_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_le_imp_le_exp
% 3.82/4.03 thf(fact_2214_self__le__power,axiom,
% 3.82/4.03 ! [A: real,N2: nat] :
% 3.82/4.03 ( ( ord_less_eq_real @ one_one_real @ A )
% 3.82/4.03 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.03 => ( ord_less_eq_real @ A @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % self_le_power
% 3.82/4.03 thf(fact_2215_self__le__power,axiom,
% 3.82/4.03 ! [A: nat,N2: nat] :
% 3.82/4.03 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 3.82/4.03 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.03 => ( ord_less_eq_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % self_le_power
% 3.82/4.03 thf(fact_2216_self__le__power,axiom,
% 3.82/4.03 ! [A: int,N2: nat] :
% 3.82/4.03 ( ( ord_less_eq_int @ one_one_int @ A )
% 3.82/4.03 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.03 => ( ord_less_eq_int @ A @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % self_le_power
% 3.82/4.03 thf(fact_2217_one__less__power,axiom,
% 3.82/4.03 ! [A: nat,N2: nat] :
% 3.82/4.03 ( ( ord_less_nat @ one_one_nat @ A )
% 3.82/4.03 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.03 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % one_less_power
% 3.82/4.03 thf(fact_2218_one__less__power,axiom,
% 3.82/4.03 ! [A: real,N2: nat] :
% 3.82/4.03 ( ( ord_less_real @ one_one_real @ A )
% 3.82/4.03 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.03 => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % one_less_power
% 3.82/4.03 thf(fact_2219_one__less__power,axiom,
% 3.82/4.03 ! [A: int,N2: nat] :
% 3.82/4.03 ( ( ord_less_int @ one_one_int @ A )
% 3.82/4.03 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.03 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % one_less_power
% 3.82/4.03 thf(fact_2220_nat__1__add__1,axiom,
% 3.82/4.03 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 3.82/4.03 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % nat_1_add_1
% 3.82/4.03 thf(fact_2221_div__le__mono,axiom,
% 3.82/4.03 ! [M2: nat,N2: nat,K: nat] :
% 3.82/4.03 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.03 => ( ord_less_eq_nat @ ( divide_divide_nat @ M2 @ K ) @ ( divide_divide_nat @ N2 @ K ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % div_le_mono
% 3.82/4.03 thf(fact_2222_div__le__dividend,axiom,
% 3.82/4.03 ! [M2: nat,N2: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M2 @ N2 ) @ M2 ) ).
% 3.82/4.03
% 3.82/4.03 % div_le_dividend
% 3.82/4.03 thf(fact_2223_ex__power__ivl2,axiom,
% 3.82/4.03 ! [B2: nat,K: nat] :
% 3.82/4.03 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 )
% 3.82/4.03 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 3.82/4.03 => ? [N3: nat] :
% 3.82/4.03 ( ( ord_less_nat @ ( power_power_nat @ B2 @ N3 ) @ K )
% 3.82/4.03 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B2 @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % ex_power_ivl2
% 3.82/4.03 thf(fact_2224_ex__power__ivl1,axiom,
% 3.82/4.03 ! [B2: nat,K: nat] :
% 3.82/4.03 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 )
% 3.82/4.03 => ( ( ord_less_eq_nat @ one_one_nat @ K )
% 3.82/4.03 => ? [N3: nat] :
% 3.82/4.03 ( ( ord_less_eq_nat @ ( power_power_nat @ B2 @ N3 ) @ K )
% 3.82/4.03 & ( ord_less_nat @ K @ ( power_power_nat @ B2 @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % ex_power_ivl1
% 3.82/4.03 thf(fact_2225_Euclidean__Division_Odiv__eq__0__iff,axiom,
% 3.82/4.03 ! [M2: nat,N2: nat] :
% 3.82/4.03 ( ( ( divide_divide_nat @ M2 @ N2 )
% 3.82/4.03 = zero_zero_nat )
% 3.82/4.03 = ( ( ord_less_nat @ M2 @ N2 )
% 3.82/4.03 | ( N2 = zero_zero_nat ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % Euclidean_Division.div_eq_0_iff
% 3.82/4.03 thf(fact_2226_Suc__div__le__mono,axiom,
% 3.82/4.03 ! [M2: nat,N2: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M2 @ N2 ) @ ( divide_divide_nat @ ( suc @ M2 ) @ N2 ) ) ).
% 3.82/4.03
% 3.82/4.03 % Suc_div_le_mono
% 3.82/4.03 thf(fact_2227_div__le__mono2,axiom,
% 3.82/4.03 ! [M2: nat,N2: nat,K: nat] :
% 3.82/4.03 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 3.82/4.03 => ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.03 => ( ord_less_eq_nat @ ( divide_divide_nat @ K @ N2 ) @ ( divide_divide_nat @ K @ M2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % div_le_mono2
% 3.82/4.03 thf(fact_2228_div__greater__zero__iff,axiom,
% 3.82/4.03 ! [M2: nat,N2: nat] :
% 3.82/4.03 ( ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ M2 @ N2 ) )
% 3.82/4.03 = ( ( ord_less_eq_nat @ N2 @ M2 )
% 3.82/4.03 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % div_greater_zero_iff
% 3.82/4.03 thf(fact_2229_exp__add__not__zero__imp__left,axiom,
% 3.82/4.03 ! [M2: nat,N2: nat] :
% 3.82/4.03 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N2 ) )
% 3.82/4.03 != zero_zero_nat )
% 3.82/4.03 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 )
% 3.82/4.03 != zero_zero_nat ) ) ).
% 3.82/4.03
% 3.82/4.03 % exp_add_not_zero_imp_left
% 3.82/4.03 thf(fact_2230_exp__add__not__zero__imp__left,axiom,
% 3.82/4.03 ! [M2: nat,N2: nat] :
% 3.82/4.03 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N2 ) )
% 3.82/4.03 != zero_zero_int )
% 3.82/4.03 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 )
% 3.82/4.03 != zero_zero_int ) ) ).
% 3.82/4.03
% 3.82/4.03 % exp_add_not_zero_imp_left
% 3.82/4.03 thf(fact_2231_exp__add__not__zero__imp__right,axiom,
% 3.82/4.03 ! [M2: nat,N2: nat] :
% 3.82/4.03 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N2 ) )
% 3.82/4.03 != zero_zero_nat )
% 3.82/4.03 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 3.82/4.03 != zero_zero_nat ) ) ).
% 3.82/4.03
% 3.82/4.03 % exp_add_not_zero_imp_right
% 3.82/4.03 thf(fact_2232_exp__add__not__zero__imp__right,axiom,
% 3.82/4.03 ! [M2: nat,N2: nat] :
% 3.82/4.03 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N2 ) )
% 3.82/4.03 != zero_zero_int )
% 3.82/4.03 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 3.82/4.03 != zero_zero_int ) ) ).
% 3.82/4.03
% 3.82/4.03 % exp_add_not_zero_imp_right
% 3.82/4.03 thf(fact_2233_nat__induct2,axiom,
% 3.82/4.03 ! [P: nat > $o,N2: nat] :
% 3.82/4.03 ( ( P @ zero_zero_nat )
% 3.82/4.03 => ( ( P @ one_one_nat )
% 3.82/4.03 => ( ! [N3: nat] :
% 3.82/4.03 ( ( P @ N3 )
% 3.82/4.03 => ( P @ ( plus_plus_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 3.82/4.03 => ( P @ N2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % nat_induct2
% 3.82/4.03 thf(fact_2234_bit__concat__def,axiom,
% 3.82/4.03 ( vEBT_VEBT_bit_concat
% 3.82/4.03 = ( ^ [H: nat,L2: nat,D4: nat] : ( plus_plus_nat @ ( times_times_nat @ H @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ D4 ) ) @ L2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % bit_concat_def
% 3.82/4.03 thf(fact_2235_low__inv,axiom,
% 3.82/4.03 ! [X: nat,N2: nat,Y: nat] :
% 3.82/4.03 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 3.82/4.03 => ( ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ X ) @ N2 )
% 3.82/4.03 = X ) ) ).
% 3.82/4.03
% 3.82/4.03 % low_inv
% 3.82/4.03 thf(fact_2236_high__inv,axiom,
% 3.82/4.03 ! [X: nat,N2: nat,Y: nat] :
% 3.82/4.03 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 3.82/4.03 => ( ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ X ) @ N2 )
% 3.82/4.03 = Y ) ) ).
% 3.82/4.03
% 3.82/4.03 % high_inv
% 3.82/4.03 thf(fact_2237_invar__vebt_Ocases,axiom,
% 3.82/4.03 ! [A1: vEBT_VEBT,A22: nat] :
% 3.82/4.03 ( ( vEBT_invar_vebt @ A1 @ A22 )
% 3.82/4.03 => ( ( ? [A4: $o,B4: $o] :
% 3.82/4.03 ( A1
% 3.82/4.03 = ( vEBT_Leaf @ A4 @ B4 ) )
% 3.82/4.03 => ( A22
% 3.82/4.03 != ( suc @ zero_zero_nat ) ) )
% 3.82/4.03 => ( ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M3: nat,Deg2: nat] :
% 3.82/4.03 ( ( A1
% 3.82/4.03 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 3.82/4.03 => ( ( A22 = Deg2 )
% 3.82/4.03 => ( ! [X2: vEBT_VEBT] :
% 3.82/4.03 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 3.82/4.03 => ( vEBT_invar_vebt @ X2 @ N3 ) )
% 3.82/4.03 => ( ( vEBT_invar_vebt @ Summary2 @ M3 )
% 3.82/4.03 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 3.82/4.03 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 3.82/4.03 => ( ( M3 = N3 )
% 3.82/4.03 => ( ( Deg2
% 3.82/4.03 = ( plus_plus_nat @ N3 @ M3 ) )
% 3.82/4.03 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_1 )
% 3.82/4.03 => ~ ! [X2: vEBT_VEBT] :
% 3.82/4.03 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 3.82/4.03 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X_1 ) ) ) ) ) ) ) ) ) )
% 3.82/4.03 => ( ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M3: nat,Deg2: nat] :
% 3.82/4.03 ( ( A1
% 3.82/4.03 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 3.82/4.03 => ( ( A22 = Deg2 )
% 3.82/4.03 => ( ! [X2: vEBT_VEBT] :
% 3.82/4.03 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 3.82/4.03 => ( vEBT_invar_vebt @ X2 @ N3 ) )
% 3.82/4.03 => ( ( vEBT_invar_vebt @ Summary2 @ M3 )
% 3.82/4.03 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 3.82/4.03 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 3.82/4.03 => ( ( M3
% 3.82/4.03 = ( suc @ N3 ) )
% 3.82/4.03 => ( ( Deg2
% 3.82/4.03 = ( plus_plus_nat @ N3 @ M3 ) )
% 3.82/4.03 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_1 )
% 3.82/4.03 => ~ ! [X2: vEBT_VEBT] :
% 3.82/4.03 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 3.82/4.03 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X_1 ) ) ) ) ) ) ) ) ) )
% 3.82/4.03 => ( ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M3: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 3.82/4.03 ( ( A1
% 3.82/4.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList3 @ Summary2 ) )
% 3.82/4.03 => ( ( A22 = Deg2 )
% 3.82/4.03 => ( ! [X2: vEBT_VEBT] :
% 3.82/4.03 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 3.82/4.03 => ( vEBT_invar_vebt @ X2 @ N3 ) )
% 3.82/4.03 => ( ( vEBT_invar_vebt @ Summary2 @ M3 )
% 3.82/4.03 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 3.82/4.03 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 3.82/4.03 => ( ( M3 = N3 )
% 3.82/4.03 => ( ( Deg2
% 3.82/4.03 = ( plus_plus_nat @ N3 @ M3 ) )
% 3.82/4.03 => ( ! [I5: nat] :
% 3.82/4.03 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 3.82/4.03 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ X6 ) )
% 3.82/4.03 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 3.82/4.03 => ( ( ( Mi2 = Ma2 )
% 3.82/4.03 => ! [X2: vEBT_VEBT] :
% 3.82/4.03 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 3.82/4.03 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X_1 ) ) )
% 3.82/4.03 => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 3.82/4.03 => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 3.82/4.03 => ~ ( ( Mi2 != Ma2 )
% 3.82/4.03 => ! [I5: nat] :
% 3.82/4.03 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 3.82/4.03 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N3 )
% 3.82/4.03 = I5 )
% 3.82/4.03 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ ( vEBT_VEBT_low @ Ma2 @ N3 ) ) )
% 3.82/4.03 & ! [X2: nat] :
% 3.82/4.03 ( ( ( ( vEBT_VEBT_high @ X2 @ N3 )
% 3.82/4.03 = I5 )
% 3.82/4.03 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ ( vEBT_VEBT_low @ X2 @ N3 ) ) )
% 3.82/4.03 => ( ( ord_less_nat @ Mi2 @ X2 )
% 3.82/4.03 & ( ord_less_eq_nat @ X2 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 3.82/4.03 => ~ ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M3: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 3.82/4.03 ( ( A1
% 3.82/4.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList3 @ Summary2 ) )
% 3.82/4.03 => ( ( A22 = Deg2 )
% 3.82/4.03 => ( ! [X2: vEBT_VEBT] :
% 3.82/4.03 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 3.82/4.03 => ( vEBT_invar_vebt @ X2 @ N3 ) )
% 3.82/4.03 => ( ( vEBT_invar_vebt @ Summary2 @ M3 )
% 3.82/4.03 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 3.82/4.03 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 3.82/4.03 => ( ( M3
% 3.82/4.03 = ( suc @ N3 ) )
% 3.82/4.03 => ( ( Deg2
% 3.82/4.03 = ( plus_plus_nat @ N3 @ M3 ) )
% 3.82/4.03 => ( ! [I5: nat] :
% 3.82/4.03 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 3.82/4.03 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ X6 ) )
% 3.82/4.03 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 3.82/4.03 => ( ( ( Mi2 = Ma2 )
% 3.82/4.03 => ! [X2: vEBT_VEBT] :
% 3.82/4.03 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 3.82/4.03 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X_1 ) ) )
% 3.82/4.03 => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 3.82/4.03 => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 3.82/4.03 => ~ ( ( Mi2 != Ma2 )
% 3.82/4.03 => ! [I5: nat] :
% 3.82/4.03 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 3.82/4.03 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N3 )
% 3.82/4.03 = I5 )
% 3.82/4.03 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ ( vEBT_VEBT_low @ Ma2 @ N3 ) ) )
% 3.82/4.03 & ! [X2: nat] :
% 3.82/4.03 ( ( ( ( vEBT_VEBT_high @ X2 @ N3 )
% 3.82/4.03 = I5 )
% 3.82/4.03 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ ( vEBT_VEBT_low @ X2 @ N3 ) ) )
% 3.82/4.03 => ( ( ord_less_nat @ Mi2 @ X2 )
% 3.82/4.03 & ( ord_less_eq_nat @ X2 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % invar_vebt.cases
% 3.82/4.03 thf(fact_2238_invar__vebt_Osimps,axiom,
% 3.82/4.03 ( vEBT_invar_vebt
% 3.82/4.03 = ( ^ [A12: vEBT_VEBT,A23: nat] :
% 3.82/4.03 ( ( ? [A3: $o,B3: $o] :
% 3.82/4.03 ( A12
% 3.82/4.03 = ( vEBT_Leaf @ A3 @ B3 ) )
% 3.82/4.03 & ( A23
% 3.82/4.03 = ( suc @ zero_zero_nat ) ) )
% 3.82/4.03 | ? [TreeList: list_VEBT_VEBT,N: nat,Summary3: vEBT_VEBT] :
% 3.82/4.03 ( ( A12
% 3.82/4.03 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A23 @ TreeList @ Summary3 ) )
% 3.82/4.03 & ! [X4: vEBT_VEBT] :
% 3.82/4.03 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 3.82/4.03 => ( vEBT_invar_vebt @ X4 @ N ) )
% 3.82/4.03 & ( vEBT_invar_vebt @ Summary3 @ N )
% 3.82/4.03 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 3.82/4.03 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 3.82/4.03 & ( A23
% 3.82/4.03 = ( plus_plus_nat @ N @ N ) )
% 3.82/4.03 & ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X6 )
% 3.82/4.03 & ! [X4: vEBT_VEBT] :
% 3.82/4.03 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 3.82/4.03 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X6 ) ) )
% 3.82/4.03 | ? [TreeList: list_VEBT_VEBT,N: nat,Summary3: vEBT_VEBT] :
% 3.82/4.03 ( ( A12
% 3.82/4.03 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A23 @ TreeList @ Summary3 ) )
% 3.82/4.03 & ! [X4: vEBT_VEBT] :
% 3.82/4.03 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 3.82/4.03 => ( vEBT_invar_vebt @ X4 @ N ) )
% 3.82/4.03 & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N ) )
% 3.82/4.03 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 3.82/4.03 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) ) )
% 3.82/4.03 & ( A23
% 3.82/4.03 = ( plus_plus_nat @ N @ ( suc @ N ) ) )
% 3.82/4.03 & ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X6 )
% 3.82/4.03 & ! [X4: vEBT_VEBT] :
% 3.82/4.03 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 3.82/4.03 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X6 ) ) )
% 3.82/4.03 | ? [TreeList: list_VEBT_VEBT,N: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 3.82/4.03 ( ( A12
% 3.82/4.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A23 @ TreeList @ Summary3 ) )
% 3.82/4.03 & ! [X4: vEBT_VEBT] :
% 3.82/4.03 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 3.82/4.03 => ( vEBT_invar_vebt @ X4 @ N ) )
% 3.82/4.03 & ( vEBT_invar_vebt @ Summary3 @ N )
% 3.82/4.03 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 3.82/4.03 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 3.82/4.03 & ( A23
% 3.82/4.03 = ( plus_plus_nat @ N @ N ) )
% 3.82/4.03 & ! [I3: nat] :
% 3.82/4.03 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 3.82/4.03 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ X6 ) )
% 3.82/4.03 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I3 ) ) )
% 3.82/4.03 & ( ( Mi3 = Ma3 )
% 3.82/4.03 => ! [X4: vEBT_VEBT] :
% 3.82/4.03 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 3.82/4.03 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X6 ) ) )
% 3.82/4.03 & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 3.82/4.03 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A23 ) )
% 3.82/4.03 & ( ( Mi3 != Ma3 )
% 3.82/4.03 => ! [I3: nat] :
% 3.82/4.03 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 3.82/4.03 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N )
% 3.82/4.03 = I3 )
% 3.82/4.03 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ ( vEBT_VEBT_low @ Ma3 @ N ) ) )
% 3.82/4.03 & ! [X4: nat] :
% 3.82/4.03 ( ( ( ( vEBT_VEBT_high @ X4 @ N )
% 3.82/4.03 = I3 )
% 3.82/4.03 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ ( vEBT_VEBT_low @ X4 @ N ) ) )
% 3.82/4.03 => ( ( ord_less_nat @ Mi3 @ X4 )
% 3.82/4.03 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) )
% 3.82/4.03 | ? [TreeList: list_VEBT_VEBT,N: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 3.82/4.03 ( ( A12
% 3.82/4.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A23 @ TreeList @ Summary3 ) )
% 3.82/4.03 & ! [X4: vEBT_VEBT] :
% 3.82/4.03 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 3.82/4.03 => ( vEBT_invar_vebt @ X4 @ N ) )
% 3.82/4.03 & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N ) )
% 3.82/4.03 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 3.82/4.03 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) ) )
% 3.82/4.03 & ( A23
% 3.82/4.03 = ( plus_plus_nat @ N @ ( suc @ N ) ) )
% 3.82/4.03 & ! [I3: nat] :
% 3.82/4.03 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) ) )
% 3.82/4.03 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ X6 ) )
% 3.82/4.03 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I3 ) ) )
% 3.82/4.03 & ( ( Mi3 = Ma3 )
% 3.82/4.03 => ! [X4: vEBT_VEBT] :
% 3.82/4.03 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 3.82/4.03 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X6 ) ) )
% 3.82/4.03 & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 3.82/4.03 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A23 ) )
% 3.82/4.03 & ( ( Mi3 != Ma3 )
% 3.82/4.03 => ! [I3: nat] :
% 3.82/4.03 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) ) )
% 3.82/4.03 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N )
% 3.82/4.03 = I3 )
% 3.82/4.03 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ ( vEBT_VEBT_low @ Ma3 @ N ) ) )
% 3.82/4.03 & ! [X4: nat] :
% 3.82/4.03 ( ( ( ( vEBT_VEBT_high @ X4 @ N )
% 3.82/4.03 = I3 )
% 3.82/4.03 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ ( vEBT_VEBT_low @ X4 @ N ) ) )
% 3.82/4.03 => ( ( ord_less_nat @ Mi3 @ X4 )
% 3.82/4.03 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % invar_vebt.simps
% 3.82/4.03 thf(fact_2239_enat__ord__number_I1_J,axiom,
% 3.82/4.03 ! [M2: num,N2: num] :
% 3.82/4.03 ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M2 ) @ ( numera1916890842035813515d_enat @ N2 ) )
% 3.82/4.03 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % enat_ord_number(1)
% 3.82/4.03 thf(fact_2240_enat__ord__number_I2_J,axiom,
% 3.82/4.03 ! [M2: num,N2: num] :
% 3.82/4.03 ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M2 ) @ ( numera1916890842035813515d_enat @ N2 ) )
% 3.82/4.03 = ( ord_less_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % enat_ord_number(2)
% 3.82/4.03 thf(fact_2241_pos2,axiom,
% 3.82/4.03 ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ).
% 3.82/4.03
% 3.82/4.03 % pos2
% 3.82/4.03 thf(fact_2242_Leaf__0__not,axiom,
% 3.82/4.03 ! [A: $o,B2: $o] :
% 3.82/4.03 ~ ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B2 ) @ zero_zero_nat ) ).
% 3.82/4.03
% 3.82/4.03 % Leaf_0_not
% 3.82/4.03 thf(fact_2243_deg__1__Leafy,axiom,
% 3.82/4.03 ! [T: vEBT_VEBT,N2: nat] :
% 3.82/4.03 ( ( vEBT_invar_vebt @ T @ N2 )
% 3.82/4.03 => ( ( N2 = one_one_nat )
% 3.82/4.03 => ? [A4: $o,B4: $o] :
% 3.82/4.03 ( T
% 3.82/4.03 = ( vEBT_Leaf @ A4 @ B4 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % deg_1_Leafy
% 3.82/4.03 thf(fact_2244_deg__1__Leaf,axiom,
% 3.82/4.03 ! [T: vEBT_VEBT] :
% 3.82/4.03 ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 3.82/4.03 => ? [A4: $o,B4: $o] :
% 3.82/4.03 ( T
% 3.82/4.03 = ( vEBT_Leaf @ A4 @ B4 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % deg_1_Leaf
% 3.82/4.03 thf(fact_2245_deg1Leaf,axiom,
% 3.82/4.03 ! [T: vEBT_VEBT] :
% 3.82/4.03 ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 3.82/4.03 = ( ? [A3: $o,B3: $o] :
% 3.82/4.03 ( T
% 3.82/4.03 = ( vEBT_Leaf @ A3 @ B3 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % deg1Leaf
% 3.82/4.03 thf(fact_2246_mult__cancel__right,axiom,
% 3.82/4.03 ! [A: nat,C: nat,B2: nat] :
% 3.82/4.03 ( ( ( times_times_nat @ A @ C )
% 3.82/4.03 = ( times_times_nat @ B2 @ C ) )
% 3.82/4.03 = ( ( C = zero_zero_nat )
% 3.82/4.03 | ( A = B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_cancel_right
% 3.82/4.03 thf(fact_2247_mult__cancel__right,axiom,
% 3.82/4.03 ! [A: int,C: int,B2: int] :
% 3.82/4.03 ( ( ( times_times_int @ A @ C )
% 3.82/4.03 = ( times_times_int @ B2 @ C ) )
% 3.82/4.03 = ( ( C = zero_zero_int )
% 3.82/4.03 | ( A = B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_cancel_right
% 3.82/4.03 thf(fact_2248_mult__cancel__right,axiom,
% 3.82/4.03 ! [A: real,C: real,B2: real] :
% 3.82/4.03 ( ( ( times_times_real @ A @ C )
% 3.82/4.03 = ( times_times_real @ B2 @ C ) )
% 3.82/4.03 = ( ( C = zero_zero_real )
% 3.82/4.03 | ( A = B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_cancel_right
% 3.82/4.03 thf(fact_2249_mult__cancel__right,axiom,
% 3.82/4.03 ! [A: complex,C: complex,B2: complex] :
% 3.82/4.03 ( ( ( times_times_complex @ A @ C )
% 3.82/4.03 = ( times_times_complex @ B2 @ C ) )
% 3.82/4.03 = ( ( C = zero_zero_complex )
% 3.82/4.03 | ( A = B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_cancel_right
% 3.82/4.03 thf(fact_2250_mult__cancel__left,axiom,
% 3.82/4.03 ! [C: nat,A: nat,B2: nat] :
% 3.82/4.03 ( ( ( times_times_nat @ C @ A )
% 3.82/4.03 = ( times_times_nat @ C @ B2 ) )
% 3.82/4.03 = ( ( C = zero_zero_nat )
% 3.82/4.03 | ( A = B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_cancel_left
% 3.82/4.03 thf(fact_2251_mult__cancel__left,axiom,
% 3.82/4.03 ! [C: int,A: int,B2: int] :
% 3.82/4.03 ( ( ( times_times_int @ C @ A )
% 3.82/4.03 = ( times_times_int @ C @ B2 ) )
% 3.82/4.03 = ( ( C = zero_zero_int )
% 3.82/4.03 | ( A = B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_cancel_left
% 3.82/4.03 thf(fact_2252_mult__cancel__left,axiom,
% 3.82/4.03 ! [C: real,A: real,B2: real] :
% 3.82/4.03 ( ( ( times_times_real @ C @ A )
% 3.82/4.03 = ( times_times_real @ C @ B2 ) )
% 3.82/4.03 = ( ( C = zero_zero_real )
% 3.82/4.03 | ( A = B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_cancel_left
% 3.82/4.03 thf(fact_2253_mult__cancel__left,axiom,
% 3.82/4.03 ! [C: complex,A: complex,B2: complex] :
% 3.82/4.03 ( ( ( times_times_complex @ C @ A )
% 3.82/4.03 = ( times_times_complex @ C @ B2 ) )
% 3.82/4.03 = ( ( C = zero_zero_complex )
% 3.82/4.03 | ( A = B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_cancel_left
% 3.82/4.03 thf(fact_2254_mult__eq__0__iff,axiom,
% 3.82/4.03 ! [A: nat,B2: nat] :
% 3.82/4.03 ( ( ( times_times_nat @ A @ B2 )
% 3.82/4.03 = zero_zero_nat )
% 3.82/4.03 = ( ( A = zero_zero_nat )
% 3.82/4.03 | ( B2 = zero_zero_nat ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_eq_0_iff
% 3.82/4.03 thf(fact_2255_mult__eq__0__iff,axiom,
% 3.82/4.03 ! [A: int,B2: int] :
% 3.82/4.03 ( ( ( times_times_int @ A @ B2 )
% 3.82/4.03 = zero_zero_int )
% 3.82/4.03 = ( ( A = zero_zero_int )
% 3.82/4.03 | ( B2 = zero_zero_int ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_eq_0_iff
% 3.82/4.03 thf(fact_2256_mult__eq__0__iff,axiom,
% 3.82/4.03 ! [A: real,B2: real] :
% 3.82/4.03 ( ( ( times_times_real @ A @ B2 )
% 3.82/4.03 = zero_zero_real )
% 3.82/4.03 = ( ( A = zero_zero_real )
% 3.82/4.03 | ( B2 = zero_zero_real ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_eq_0_iff
% 3.82/4.03 thf(fact_2257_mult__eq__0__iff,axiom,
% 3.82/4.03 ! [A: complex,B2: complex] :
% 3.82/4.03 ( ( ( times_times_complex @ A @ B2 )
% 3.82/4.03 = zero_zero_complex )
% 3.82/4.03 = ( ( A = zero_zero_complex )
% 3.82/4.03 | ( B2 = zero_zero_complex ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_eq_0_iff
% 3.82/4.03 thf(fact_2258_mult__eq__0__iff,axiom,
% 3.82/4.03 ! [A: extended_enat,B2: extended_enat] :
% 3.82/4.03 ( ( ( times_7803423173614009249d_enat @ A @ B2 )
% 3.82/4.03 = zero_z5237406670263579293d_enat )
% 3.82/4.03 = ( ( A = zero_z5237406670263579293d_enat )
% 3.82/4.03 | ( B2 = zero_z5237406670263579293d_enat ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_eq_0_iff
% 3.82/4.03 thf(fact_2259_mult__zero__right,axiom,
% 3.82/4.03 ! [A: nat] :
% 3.82/4.03 ( ( times_times_nat @ A @ zero_zero_nat )
% 3.82/4.03 = zero_zero_nat ) ).
% 3.82/4.03
% 3.82/4.03 % mult_zero_right
% 3.82/4.03 thf(fact_2260_mult__zero__right,axiom,
% 3.82/4.03 ! [A: int] :
% 3.82/4.03 ( ( times_times_int @ A @ zero_zero_int )
% 3.82/4.03 = zero_zero_int ) ).
% 3.82/4.03
% 3.82/4.03 % mult_zero_right
% 3.82/4.03 thf(fact_2261_mult__zero__right,axiom,
% 3.82/4.03 ! [A: real] :
% 3.82/4.03 ( ( times_times_real @ A @ zero_zero_real )
% 3.82/4.03 = zero_zero_real ) ).
% 3.82/4.03
% 3.82/4.03 % mult_zero_right
% 3.82/4.03 thf(fact_2262_mult__zero__right,axiom,
% 3.82/4.03 ! [A: complex] :
% 3.82/4.03 ( ( times_times_complex @ A @ zero_zero_complex )
% 3.82/4.03 = zero_zero_complex ) ).
% 3.82/4.03
% 3.82/4.03 % mult_zero_right
% 3.82/4.03 thf(fact_2263_mult__zero__right,axiom,
% 3.82/4.03 ! [A: extended_enat] :
% 3.82/4.03 ( ( times_7803423173614009249d_enat @ A @ zero_z5237406670263579293d_enat )
% 3.82/4.03 = zero_z5237406670263579293d_enat ) ).
% 3.82/4.03
% 3.82/4.03 % mult_zero_right
% 3.82/4.03 thf(fact_2264_mult__zero__left,axiom,
% 3.82/4.03 ! [A: nat] :
% 3.82/4.03 ( ( times_times_nat @ zero_zero_nat @ A )
% 3.82/4.03 = zero_zero_nat ) ).
% 3.82/4.03
% 3.82/4.03 % mult_zero_left
% 3.82/4.03 thf(fact_2265_mult__zero__left,axiom,
% 3.82/4.03 ! [A: int] :
% 3.82/4.03 ( ( times_times_int @ zero_zero_int @ A )
% 3.82/4.03 = zero_zero_int ) ).
% 3.82/4.03
% 3.82/4.03 % mult_zero_left
% 3.82/4.03 thf(fact_2266_mult__zero__left,axiom,
% 3.82/4.03 ! [A: real] :
% 3.82/4.03 ( ( times_times_real @ zero_zero_real @ A )
% 3.82/4.03 = zero_zero_real ) ).
% 3.82/4.03
% 3.82/4.03 % mult_zero_left
% 3.82/4.03 thf(fact_2267_mult__zero__left,axiom,
% 3.82/4.03 ! [A: complex] :
% 3.82/4.03 ( ( times_times_complex @ zero_zero_complex @ A )
% 3.82/4.03 = zero_zero_complex ) ).
% 3.82/4.03
% 3.82/4.03 % mult_zero_left
% 3.82/4.03 thf(fact_2268_mult__zero__left,axiom,
% 3.82/4.03 ! [A: extended_enat] :
% 3.82/4.03 ( ( times_7803423173614009249d_enat @ zero_z5237406670263579293d_enat @ A )
% 3.82/4.03 = zero_z5237406670263579293d_enat ) ).
% 3.82/4.03
% 3.82/4.03 % mult_zero_left
% 3.82/4.03 thf(fact_2269_mult_Oright__neutral,axiom,
% 3.82/4.03 ! [A: nat] :
% 3.82/4.03 ( ( times_times_nat @ A @ one_one_nat )
% 3.82/4.03 = A ) ).
% 3.82/4.03
% 3.82/4.03 % mult.right_neutral
% 3.82/4.03 thf(fact_2270_mult_Oright__neutral,axiom,
% 3.82/4.03 ! [A: int] :
% 3.82/4.03 ( ( times_times_int @ A @ one_one_int )
% 3.82/4.03 = A ) ).
% 3.82/4.03
% 3.82/4.03 % mult.right_neutral
% 3.82/4.03 thf(fact_2271_mult_Oright__neutral,axiom,
% 3.82/4.03 ! [A: real] :
% 3.82/4.03 ( ( times_times_real @ A @ one_one_real )
% 3.82/4.03 = A ) ).
% 3.82/4.03
% 3.82/4.03 % mult.right_neutral
% 3.82/4.03 thf(fact_2272_mult_Oright__neutral,axiom,
% 3.82/4.03 ! [A: complex] :
% 3.82/4.03 ( ( times_times_complex @ A @ one_one_complex )
% 3.82/4.03 = A ) ).
% 3.82/4.03
% 3.82/4.03 % mult.right_neutral
% 3.82/4.03 thf(fact_2273_mult_Oright__neutral,axiom,
% 3.82/4.03 ! [A: extended_enat] :
% 3.82/4.03 ( ( times_7803423173614009249d_enat @ A @ one_on7984719198319812577d_enat )
% 3.82/4.03 = A ) ).
% 3.82/4.03
% 3.82/4.03 % mult.right_neutral
% 3.82/4.03 thf(fact_2274_mult__1,axiom,
% 3.82/4.03 ! [A: nat] :
% 3.82/4.03 ( ( times_times_nat @ one_one_nat @ A )
% 3.82/4.03 = A ) ).
% 3.82/4.03
% 3.82/4.03 % mult_1
% 3.82/4.03 thf(fact_2275_mult__1,axiom,
% 3.82/4.03 ! [A: int] :
% 3.82/4.03 ( ( times_times_int @ one_one_int @ A )
% 3.82/4.03 = A ) ).
% 3.82/4.03
% 3.82/4.03 % mult_1
% 3.82/4.03 thf(fact_2276_mult__1,axiom,
% 3.82/4.03 ! [A: real] :
% 3.82/4.03 ( ( times_times_real @ one_one_real @ A )
% 3.82/4.03 = A ) ).
% 3.82/4.03
% 3.82/4.03 % mult_1
% 3.82/4.03 thf(fact_2277_mult__1,axiom,
% 3.82/4.03 ! [A: complex] :
% 3.82/4.03 ( ( times_times_complex @ one_one_complex @ A )
% 3.82/4.03 = A ) ).
% 3.82/4.03
% 3.82/4.03 % mult_1
% 3.82/4.03 thf(fact_2278_mult__1,axiom,
% 3.82/4.03 ! [A: extended_enat] :
% 3.82/4.03 ( ( times_7803423173614009249d_enat @ one_on7984719198319812577d_enat @ A )
% 3.82/4.03 = A ) ).
% 3.82/4.03
% 3.82/4.03 % mult_1
% 3.82/4.03 thf(fact_2279_times__divide__eq__left,axiom,
% 3.82/4.03 ! [B2: complex,C: complex,A: complex] :
% 3.82/4.03 ( ( times_times_complex @ ( divide1717551699836669952omplex @ B2 @ C ) @ A )
% 3.82/4.03 = ( divide1717551699836669952omplex @ ( times_times_complex @ B2 @ A ) @ C ) ) ).
% 3.82/4.03
% 3.82/4.03 % times_divide_eq_left
% 3.82/4.03 thf(fact_2280_times__divide__eq__left,axiom,
% 3.82/4.03 ! [B2: real,C: real,A: real] :
% 3.82/4.03 ( ( times_times_real @ ( divide_divide_real @ B2 @ C ) @ A )
% 3.82/4.03 = ( divide_divide_real @ ( times_times_real @ B2 @ A ) @ C ) ) ).
% 3.82/4.03
% 3.82/4.03 % times_divide_eq_left
% 3.82/4.03 thf(fact_2281_divide__divide__eq__left,axiom,
% 3.82/4.03 ! [A: complex,B2: complex,C: complex] :
% 3.82/4.03 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B2 ) @ C )
% 3.82/4.03 = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ B2 @ C ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % divide_divide_eq_left
% 3.82/4.03 thf(fact_2282_divide__divide__eq__left,axiom,
% 3.82/4.03 ! [A: real,B2: real,C: real] :
% 3.82/4.03 ( ( divide_divide_real @ ( divide_divide_real @ A @ B2 ) @ C )
% 3.82/4.03 = ( divide_divide_real @ A @ ( times_times_real @ B2 @ C ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % divide_divide_eq_left
% 3.82/4.03 thf(fact_2283_divide__divide__eq__right,axiom,
% 3.82/4.03 ! [A: complex,B2: complex,C: complex] :
% 3.82/4.03 ( ( divide1717551699836669952omplex @ A @ ( divide1717551699836669952omplex @ B2 @ C ) )
% 3.82/4.03 = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ B2 ) ) ).
% 3.82/4.03
% 3.82/4.03 % divide_divide_eq_right
% 3.82/4.03 thf(fact_2284_divide__divide__eq__right,axiom,
% 3.82/4.03 ! [A: real,B2: real,C: real] :
% 3.82/4.03 ( ( divide_divide_real @ A @ ( divide_divide_real @ B2 @ C ) )
% 3.82/4.03 = ( divide_divide_real @ ( times_times_real @ A @ C ) @ B2 ) ) ).
% 3.82/4.03
% 3.82/4.03 % divide_divide_eq_right
% 3.82/4.03 thf(fact_2285_times__divide__eq__right,axiom,
% 3.82/4.03 ! [A: complex,B2: complex,C: complex] :
% 3.82/4.03 ( ( times_times_complex @ A @ ( divide1717551699836669952omplex @ B2 @ C ) )
% 3.82/4.03 = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B2 ) @ C ) ) ).
% 3.82/4.03
% 3.82/4.03 % times_divide_eq_right
% 3.82/4.03 thf(fact_2286_times__divide__eq__right,axiom,
% 3.82/4.03 ! [A: real,B2: real,C: real] :
% 3.82/4.03 ( ( times_times_real @ A @ ( divide_divide_real @ B2 @ C ) )
% 3.82/4.03 = ( divide_divide_real @ ( times_times_real @ A @ B2 ) @ C ) ) ).
% 3.82/4.03
% 3.82/4.03 % times_divide_eq_right
% 3.82/4.03 thf(fact_2287_mult__cancel2,axiom,
% 3.82/4.03 ! [M2: nat,K: nat,N2: nat] :
% 3.82/4.03 ( ( ( times_times_nat @ M2 @ K )
% 3.82/4.03 = ( times_times_nat @ N2 @ K ) )
% 3.82/4.03 = ( ( M2 = N2 )
% 3.82/4.03 | ( K = zero_zero_nat ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_cancel2
% 3.82/4.03 thf(fact_2288_mult__cancel1,axiom,
% 3.82/4.03 ! [K: nat,M2: nat,N2: nat] :
% 3.82/4.03 ( ( ( times_times_nat @ K @ M2 )
% 3.82/4.03 = ( times_times_nat @ K @ N2 ) )
% 3.82/4.03 = ( ( M2 = N2 )
% 3.82/4.03 | ( K = zero_zero_nat ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_cancel1
% 3.82/4.03 thf(fact_2289_mult__0__right,axiom,
% 3.82/4.03 ! [M2: nat] :
% 3.82/4.03 ( ( times_times_nat @ M2 @ zero_zero_nat )
% 3.82/4.03 = zero_zero_nat ) ).
% 3.82/4.03
% 3.82/4.03 % mult_0_right
% 3.82/4.03 thf(fact_2290_mult__is__0,axiom,
% 3.82/4.03 ! [M2: nat,N2: nat] :
% 3.82/4.03 ( ( ( times_times_nat @ M2 @ N2 )
% 3.82/4.03 = zero_zero_nat )
% 3.82/4.03 = ( ( M2 = zero_zero_nat )
% 3.82/4.03 | ( N2 = zero_zero_nat ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_is_0
% 3.82/4.03 thf(fact_2291_nat__1__eq__mult__iff,axiom,
% 3.82/4.03 ! [M2: nat,N2: nat] :
% 3.82/4.03 ( ( one_one_nat
% 3.82/4.03 = ( times_times_nat @ M2 @ N2 ) )
% 3.82/4.03 = ( ( M2 = one_one_nat )
% 3.82/4.03 & ( N2 = one_one_nat ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % nat_1_eq_mult_iff
% 3.82/4.03 thf(fact_2292_nat__mult__eq__1__iff,axiom,
% 3.82/4.03 ! [M2: nat,N2: nat] :
% 3.82/4.03 ( ( ( times_times_nat @ M2 @ N2 )
% 3.82/4.03 = one_one_nat )
% 3.82/4.03 = ( ( M2 = one_one_nat )
% 3.82/4.03 & ( N2 = one_one_nat ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % nat_mult_eq_1_iff
% 3.82/4.03 thf(fact_2293_mult__cancel__right2,axiom,
% 3.82/4.03 ! [A: int,C: int] :
% 3.82/4.03 ( ( ( times_times_int @ A @ C )
% 3.82/4.03 = C )
% 3.82/4.03 = ( ( C = zero_zero_int )
% 3.82/4.03 | ( A = one_one_int ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_cancel_right2
% 3.82/4.03 thf(fact_2294_mult__cancel__right2,axiom,
% 3.82/4.03 ! [A: real,C: real] :
% 3.82/4.03 ( ( ( times_times_real @ A @ C )
% 3.82/4.03 = C )
% 3.82/4.03 = ( ( C = zero_zero_real )
% 3.82/4.03 | ( A = one_one_real ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_cancel_right2
% 3.82/4.03 thf(fact_2295_mult__cancel__right2,axiom,
% 3.82/4.03 ! [A: complex,C: complex] :
% 3.82/4.03 ( ( ( times_times_complex @ A @ C )
% 3.82/4.03 = C )
% 3.82/4.03 = ( ( C = zero_zero_complex )
% 3.82/4.03 | ( A = one_one_complex ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_cancel_right2
% 3.82/4.03 thf(fact_2296_mult__cancel__right1,axiom,
% 3.82/4.03 ! [C: int,B2: int] :
% 3.82/4.03 ( ( C
% 3.82/4.03 = ( times_times_int @ B2 @ C ) )
% 3.82/4.03 = ( ( C = zero_zero_int )
% 3.82/4.03 | ( B2 = one_one_int ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_cancel_right1
% 3.82/4.03 thf(fact_2297_mult__cancel__right1,axiom,
% 3.82/4.03 ! [C: real,B2: real] :
% 3.82/4.03 ( ( C
% 3.82/4.03 = ( times_times_real @ B2 @ C ) )
% 3.82/4.03 = ( ( C = zero_zero_real )
% 3.82/4.03 | ( B2 = one_one_real ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_cancel_right1
% 3.82/4.03 thf(fact_2298_mult__cancel__right1,axiom,
% 3.82/4.03 ! [C: complex,B2: complex] :
% 3.82/4.03 ( ( C
% 3.82/4.03 = ( times_times_complex @ B2 @ C ) )
% 3.82/4.03 = ( ( C = zero_zero_complex )
% 3.82/4.03 | ( B2 = one_one_complex ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_cancel_right1
% 3.82/4.03 thf(fact_2299_mult__cancel__left2,axiom,
% 3.82/4.03 ! [C: int,A: int] :
% 3.82/4.03 ( ( ( times_times_int @ C @ A )
% 3.82/4.03 = C )
% 3.82/4.03 = ( ( C = zero_zero_int )
% 3.82/4.03 | ( A = one_one_int ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_cancel_left2
% 3.82/4.03 thf(fact_2300_mult__cancel__left2,axiom,
% 3.82/4.03 ! [C: real,A: real] :
% 3.82/4.03 ( ( ( times_times_real @ C @ A )
% 3.82/4.03 = C )
% 3.82/4.03 = ( ( C = zero_zero_real )
% 3.82/4.03 | ( A = one_one_real ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_cancel_left2
% 3.82/4.03 thf(fact_2301_mult__cancel__left2,axiom,
% 3.82/4.03 ! [C: complex,A: complex] :
% 3.82/4.03 ( ( ( times_times_complex @ C @ A )
% 3.82/4.03 = C )
% 3.82/4.03 = ( ( C = zero_zero_complex )
% 3.82/4.03 | ( A = one_one_complex ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_cancel_left2
% 3.82/4.03 thf(fact_2302_mult__cancel__left1,axiom,
% 3.82/4.03 ! [C: int,B2: int] :
% 3.82/4.03 ( ( C
% 3.82/4.03 = ( times_times_int @ C @ B2 ) )
% 3.82/4.03 = ( ( C = zero_zero_int )
% 3.82/4.03 | ( B2 = one_one_int ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_cancel_left1
% 3.82/4.03 thf(fact_2303_mult__cancel__left1,axiom,
% 3.82/4.03 ! [C: real,B2: real] :
% 3.82/4.03 ( ( C
% 3.82/4.03 = ( times_times_real @ C @ B2 ) )
% 3.82/4.03 = ( ( C = zero_zero_real )
% 3.82/4.03 | ( B2 = one_one_real ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_cancel_left1
% 3.82/4.03 thf(fact_2304_mult__cancel__left1,axiom,
% 3.82/4.03 ! [C: complex,B2: complex] :
% 3.82/4.03 ( ( C
% 3.82/4.03 = ( times_times_complex @ C @ B2 ) )
% 3.82/4.03 = ( ( C = zero_zero_complex )
% 3.82/4.03 | ( B2 = one_one_complex ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_cancel_left1
% 3.82/4.03 thf(fact_2305_sum__squares__eq__zero__iff,axiom,
% 3.82/4.03 ! [X: int,Y: int] :
% 3.82/4.03 ( ( ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) )
% 3.82/4.03 = zero_zero_int )
% 3.82/4.03 = ( ( X = zero_zero_int )
% 3.82/4.03 & ( Y = zero_zero_int ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % sum_squares_eq_zero_iff
% 3.82/4.03 thf(fact_2306_sum__squares__eq__zero__iff,axiom,
% 3.82/4.03 ! [X: real,Y: real] :
% 3.82/4.03 ( ( ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) )
% 3.82/4.03 = zero_zero_real )
% 3.82/4.03 = ( ( X = zero_zero_real )
% 3.82/4.03 & ( Y = zero_zero_real ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % sum_squares_eq_zero_iff
% 3.82/4.03 thf(fact_2307_nonzero__mult__divide__mult__cancel__right2,axiom,
% 3.82/4.03 ! [C: complex,A: complex,B2: complex] :
% 3.82/4.03 ( ( C != zero_zero_complex )
% 3.82/4.03 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ C @ B2 ) )
% 3.82/4.03 = ( divide1717551699836669952omplex @ A @ B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % nonzero_mult_divide_mult_cancel_right2
% 3.82/4.03 thf(fact_2308_nonzero__mult__divide__mult__cancel__right2,axiom,
% 3.82/4.03 ! [C: real,A: real,B2: real] :
% 3.82/4.03 ( ( C != zero_zero_real )
% 3.82/4.03 => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ C @ B2 ) )
% 3.82/4.03 = ( divide_divide_real @ A @ B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % nonzero_mult_divide_mult_cancel_right2
% 3.82/4.03 thf(fact_2309_nonzero__mult__div__cancel__right,axiom,
% 3.82/4.03 ! [B2: complex,A: complex] :
% 3.82/4.03 ( ( B2 != zero_zero_complex )
% 3.82/4.03 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B2 ) @ B2 )
% 3.82/4.03 = A ) ) ).
% 3.82/4.03
% 3.82/4.03 % nonzero_mult_div_cancel_right
% 3.82/4.03 thf(fact_2310_nonzero__mult__div__cancel__right,axiom,
% 3.82/4.03 ! [B2: nat,A: nat] :
% 3.82/4.03 ( ( B2 != zero_zero_nat )
% 3.82/4.03 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B2 ) @ B2 )
% 3.82/4.03 = A ) ) ).
% 3.82/4.03
% 3.82/4.03 % nonzero_mult_div_cancel_right
% 3.82/4.03 thf(fact_2311_nonzero__mult__div__cancel__right,axiom,
% 3.82/4.03 ! [B2: int,A: int] :
% 3.82/4.03 ( ( B2 != zero_zero_int )
% 3.82/4.03 => ( ( divide_divide_int @ ( times_times_int @ A @ B2 ) @ B2 )
% 3.82/4.03 = A ) ) ).
% 3.82/4.03
% 3.82/4.03 % nonzero_mult_div_cancel_right
% 3.82/4.03 thf(fact_2312_nonzero__mult__div__cancel__right,axiom,
% 3.82/4.03 ! [B2: real,A: real] :
% 3.82/4.03 ( ( B2 != zero_zero_real )
% 3.82/4.03 => ( ( divide_divide_real @ ( times_times_real @ A @ B2 ) @ B2 )
% 3.82/4.03 = A ) ) ).
% 3.82/4.03
% 3.82/4.03 % nonzero_mult_div_cancel_right
% 3.82/4.03 thf(fact_2313_nonzero__mult__divide__mult__cancel__right,axiom,
% 3.82/4.03 ! [C: complex,A: complex,B2: complex] :
% 3.82/4.03 ( ( C != zero_zero_complex )
% 3.82/4.03 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B2 @ C ) )
% 3.82/4.03 = ( divide1717551699836669952omplex @ A @ B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % nonzero_mult_divide_mult_cancel_right
% 3.82/4.03 thf(fact_2314_nonzero__mult__divide__mult__cancel__right,axiom,
% 3.82/4.03 ! [C: real,A: real,B2: real] :
% 3.82/4.03 ( ( C != zero_zero_real )
% 3.82/4.03 => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B2 @ C ) )
% 3.82/4.03 = ( divide_divide_real @ A @ B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % nonzero_mult_divide_mult_cancel_right
% 3.82/4.03 thf(fact_2315_nonzero__mult__divide__mult__cancel__left2,axiom,
% 3.82/4.03 ! [C: complex,A: complex,B2: complex] :
% 3.82/4.03 ( ( C != zero_zero_complex )
% 3.82/4.03 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ B2 @ C ) )
% 3.82/4.03 = ( divide1717551699836669952omplex @ A @ B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % nonzero_mult_divide_mult_cancel_left2
% 3.82/4.03 thf(fact_2316_nonzero__mult__divide__mult__cancel__left2,axiom,
% 3.82/4.03 ! [C: real,A: real,B2: real] :
% 3.82/4.03 ( ( C != zero_zero_real )
% 3.82/4.03 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ B2 @ C ) )
% 3.82/4.03 = ( divide_divide_real @ A @ B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % nonzero_mult_divide_mult_cancel_left2
% 3.82/4.03 thf(fact_2317_nonzero__mult__div__cancel__left,axiom,
% 3.82/4.03 ! [A: complex,B2: complex] :
% 3.82/4.03 ( ( A != zero_zero_complex )
% 3.82/4.03 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B2 ) @ A )
% 3.82/4.03 = B2 ) ) ).
% 3.82/4.03
% 3.82/4.03 % nonzero_mult_div_cancel_left
% 3.82/4.03 thf(fact_2318_nonzero__mult__div__cancel__left,axiom,
% 3.82/4.03 ! [A: nat,B2: nat] :
% 3.82/4.03 ( ( A != zero_zero_nat )
% 3.82/4.03 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B2 ) @ A )
% 3.82/4.03 = B2 ) ) ).
% 3.82/4.03
% 3.82/4.03 % nonzero_mult_div_cancel_left
% 3.82/4.03 thf(fact_2319_nonzero__mult__div__cancel__left,axiom,
% 3.82/4.03 ! [A: int,B2: int] :
% 3.82/4.03 ( ( A != zero_zero_int )
% 3.82/4.03 => ( ( divide_divide_int @ ( times_times_int @ A @ B2 ) @ A )
% 3.82/4.03 = B2 ) ) ).
% 3.82/4.03
% 3.82/4.03 % nonzero_mult_div_cancel_left
% 3.82/4.03 thf(fact_2320_nonzero__mult__div__cancel__left,axiom,
% 3.82/4.03 ! [A: real,B2: real] :
% 3.82/4.03 ( ( A != zero_zero_real )
% 3.82/4.03 => ( ( divide_divide_real @ ( times_times_real @ A @ B2 ) @ A )
% 3.82/4.03 = B2 ) ) ).
% 3.82/4.03
% 3.82/4.03 % nonzero_mult_div_cancel_left
% 3.82/4.03 thf(fact_2321_nonzero__mult__divide__mult__cancel__left,axiom,
% 3.82/4.03 ! [C: complex,A: complex,B2: complex] :
% 3.82/4.03 ( ( C != zero_zero_complex )
% 3.82/4.03 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B2 ) )
% 3.82/4.03 = ( divide1717551699836669952omplex @ A @ B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % nonzero_mult_divide_mult_cancel_left
% 3.82/4.03 thf(fact_2322_nonzero__mult__divide__mult__cancel__left,axiom,
% 3.82/4.03 ! [C: real,A: real,B2: real] :
% 3.82/4.03 ( ( C != zero_zero_real )
% 3.82/4.03 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B2 ) )
% 3.82/4.03 = ( divide_divide_real @ A @ B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % nonzero_mult_divide_mult_cancel_left
% 3.82/4.03 thf(fact_2323_mult__divide__mult__cancel__left__if,axiom,
% 3.82/4.03 ! [C: complex,A: complex,B2: complex] :
% 3.82/4.03 ( ( ( C = zero_zero_complex )
% 3.82/4.03 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B2 ) )
% 3.82/4.03 = zero_zero_complex ) )
% 3.82/4.03 & ( ( C != zero_zero_complex )
% 3.82/4.03 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B2 ) )
% 3.82/4.03 = ( divide1717551699836669952omplex @ A @ B2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_divide_mult_cancel_left_if
% 3.82/4.03 thf(fact_2324_mult__divide__mult__cancel__left__if,axiom,
% 3.82/4.03 ! [C: real,A: real,B2: real] :
% 3.82/4.03 ( ( ( C = zero_zero_real )
% 3.82/4.03 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B2 ) )
% 3.82/4.03 = zero_zero_real ) )
% 3.82/4.03 & ( ( C != zero_zero_real )
% 3.82/4.03 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B2 ) )
% 3.82/4.03 = ( divide_divide_real @ A @ B2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_divide_mult_cancel_left_if
% 3.82/4.03 thf(fact_2325_div__mult__mult1__if,axiom,
% 3.82/4.03 ! [C: nat,A: nat,B2: nat] :
% 3.82/4.03 ( ( ( C = zero_zero_nat )
% 3.82/4.03 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B2 ) )
% 3.82/4.03 = zero_zero_nat ) )
% 3.82/4.03 & ( ( C != zero_zero_nat )
% 3.82/4.03 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B2 ) )
% 3.82/4.03 = ( divide_divide_nat @ A @ B2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % div_mult_mult1_if
% 3.82/4.03 thf(fact_2326_div__mult__mult1__if,axiom,
% 3.82/4.03 ! [C: int,A: int,B2: int] :
% 3.82/4.03 ( ( ( C = zero_zero_int )
% 3.82/4.03 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B2 ) )
% 3.82/4.03 = zero_zero_int ) )
% 3.82/4.03 & ( ( C != zero_zero_int )
% 3.82/4.03 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B2 ) )
% 3.82/4.03 = ( divide_divide_int @ A @ B2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % div_mult_mult1_if
% 3.82/4.03 thf(fact_2327_div__mult__mult2,axiom,
% 3.82/4.03 ! [C: nat,A: nat,B2: nat] :
% 3.82/4.03 ( ( C != zero_zero_nat )
% 3.82/4.03 => ( ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B2 @ C ) )
% 3.82/4.03 = ( divide_divide_nat @ A @ B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % div_mult_mult2
% 3.82/4.03 thf(fact_2328_div__mult__mult2,axiom,
% 3.82/4.03 ! [C: int,A: int,B2: int] :
% 3.82/4.03 ( ( C != zero_zero_int )
% 3.82/4.03 => ( ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B2 @ C ) )
% 3.82/4.03 = ( divide_divide_int @ A @ B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % div_mult_mult2
% 3.82/4.03 thf(fact_2329_div__mult__mult1,axiom,
% 3.82/4.03 ! [C: nat,A: nat,B2: nat] :
% 3.82/4.03 ( ( C != zero_zero_nat )
% 3.82/4.03 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B2 ) )
% 3.82/4.03 = ( divide_divide_nat @ A @ B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % div_mult_mult1
% 3.82/4.03 thf(fact_2330_div__mult__mult1,axiom,
% 3.82/4.03 ! [C: int,A: int,B2: int] :
% 3.82/4.03 ( ( C != zero_zero_int )
% 3.82/4.03 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B2 ) )
% 3.82/4.03 = ( divide_divide_int @ A @ B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % div_mult_mult1
% 3.82/4.03 thf(fact_2331_distrib__right__numeral,axiom,
% 3.82/4.03 ! [A: complex,B2: complex,V: num] :
% 3.82/4.03 ( ( times_times_complex @ ( plus_plus_complex @ A @ B2 ) @ ( numera6690914467698888265omplex @ V ) )
% 3.82/4.03 = ( plus_plus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B2 @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % distrib_right_numeral
% 3.82/4.03 thf(fact_2332_distrib__right__numeral,axiom,
% 3.82/4.03 ! [A: nat,B2: nat,V: num] :
% 3.82/4.03 ( ( times_times_nat @ ( plus_plus_nat @ A @ B2 ) @ ( numeral_numeral_nat @ V ) )
% 3.82/4.03 = ( plus_plus_nat @ ( times_times_nat @ A @ ( numeral_numeral_nat @ V ) ) @ ( times_times_nat @ B2 @ ( numeral_numeral_nat @ V ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % distrib_right_numeral
% 3.82/4.03 thf(fact_2333_distrib__right__numeral,axiom,
% 3.82/4.03 ! [A: extended_enat,B2: extended_enat,V: num] :
% 3.82/4.03 ( ( times_7803423173614009249d_enat @ ( plus_p3455044024723400733d_enat @ A @ B2 ) @ ( numera1916890842035813515d_enat @ V ) )
% 3.82/4.03 = ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ A @ ( numera1916890842035813515d_enat @ V ) ) @ ( times_7803423173614009249d_enat @ B2 @ ( numera1916890842035813515d_enat @ V ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % distrib_right_numeral
% 3.82/4.03 thf(fact_2334_distrib__right__numeral,axiom,
% 3.82/4.03 ! [A: int,B2: int,V: num] :
% 3.82/4.03 ( ( times_times_int @ ( plus_plus_int @ A @ B2 ) @ ( numeral_numeral_int @ V ) )
% 3.82/4.03 = ( plus_plus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B2 @ ( numeral_numeral_int @ V ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % distrib_right_numeral
% 3.82/4.03 thf(fact_2335_distrib__right__numeral,axiom,
% 3.82/4.03 ! [A: real,B2: real,V: num] :
% 3.82/4.03 ( ( times_times_real @ ( plus_plus_real @ A @ B2 ) @ ( numeral_numeral_real @ V ) )
% 3.82/4.03 = ( plus_plus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B2 @ ( numeral_numeral_real @ V ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % distrib_right_numeral
% 3.82/4.03 thf(fact_2336_distrib__left__numeral,axiom,
% 3.82/4.03 ! [V: num,B2: complex,C: complex] :
% 3.82/4.03 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ B2 @ C ) )
% 3.82/4.03 = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B2 ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % distrib_left_numeral
% 3.82/4.03 thf(fact_2337_distrib__left__numeral,axiom,
% 3.82/4.03 ! [V: num,B2: nat,C: nat] :
% 3.82/4.03 ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ B2 @ C ) )
% 3.82/4.03 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ B2 ) @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ C ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % distrib_left_numeral
% 3.82/4.03 thf(fact_2338_distrib__left__numeral,axiom,
% 3.82/4.03 ! [V: num,B2: extended_enat,C: extended_enat] :
% 3.82/4.03 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ V ) @ ( plus_p3455044024723400733d_enat @ B2 @ C ) )
% 3.82/4.03 = ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ V ) @ B2 ) @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ V ) @ C ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % distrib_left_numeral
% 3.82/4.03 thf(fact_2339_distrib__left__numeral,axiom,
% 3.82/4.03 ! [V: num,B2: int,C: int] :
% 3.82/4.03 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ B2 @ C ) )
% 3.82/4.03 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B2 ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % distrib_left_numeral
% 3.82/4.03 thf(fact_2340_distrib__left__numeral,axiom,
% 3.82/4.03 ! [V: num,B2: real,C: real] :
% 3.82/4.03 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ B2 @ C ) )
% 3.82/4.03 = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B2 ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % distrib_left_numeral
% 3.82/4.03 thf(fact_2341_one__eq__mult__iff,axiom,
% 3.82/4.03 ! [M2: nat,N2: nat] :
% 3.82/4.03 ( ( ( suc @ zero_zero_nat )
% 3.82/4.03 = ( times_times_nat @ M2 @ N2 ) )
% 3.82/4.03 = ( ( M2
% 3.82/4.03 = ( suc @ zero_zero_nat ) )
% 3.82/4.03 & ( N2
% 3.82/4.03 = ( suc @ zero_zero_nat ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % one_eq_mult_iff
% 3.82/4.03 thf(fact_2342_mult__eq__1__iff,axiom,
% 3.82/4.03 ! [M2: nat,N2: nat] :
% 3.82/4.03 ( ( ( times_times_nat @ M2 @ N2 )
% 3.82/4.03 = ( suc @ zero_zero_nat ) )
% 3.82/4.03 = ( ( M2
% 3.82/4.03 = ( suc @ zero_zero_nat ) )
% 3.82/4.03 & ( N2
% 3.82/4.03 = ( suc @ zero_zero_nat ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_eq_1_iff
% 3.82/4.03 thf(fact_2343_mult__less__cancel2,axiom,
% 3.82/4.03 ! [M2: nat,K: nat,N2: nat] :
% 3.82/4.03 ( ( ord_less_nat @ ( times_times_nat @ M2 @ K ) @ ( times_times_nat @ N2 @ K ) )
% 3.82/4.03 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 3.82/4.03 & ( ord_less_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_less_cancel2
% 3.82/4.03 thf(fact_2344_nat__0__less__mult__iff,axiom,
% 3.82/4.03 ! [M2: nat,N2: nat] :
% 3.82/4.03 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M2 @ N2 ) )
% 3.82/4.03 = ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 3.82/4.03 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % nat_0_less_mult_iff
% 3.82/4.03 thf(fact_2345_mult__Suc__right,axiom,
% 3.82/4.03 ! [M2: nat,N2: nat] :
% 3.82/4.03 ( ( times_times_nat @ M2 @ ( suc @ N2 ) )
% 3.82/4.03 = ( plus_plus_nat @ M2 @ ( times_times_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_Suc_right
% 3.82/4.03 thf(fact_2346_le__divide__eq__numeral1_I1_J,axiom,
% 3.82/4.03 ! [A: real,B2: real,W2: num] :
% 3.82/4.03 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B2 @ ( numeral_numeral_real @ W2 ) ) )
% 3.82/4.03 = ( ord_less_eq_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) ) @ B2 ) ) ).
% 3.82/4.03
% 3.82/4.03 % le_divide_eq_numeral1(1)
% 3.82/4.03 thf(fact_2347_divide__le__eq__numeral1_I1_J,axiom,
% 3.82/4.03 ! [B2: real,W2: num,A: real] :
% 3.82/4.03 ( ( ord_less_eq_real @ ( divide_divide_real @ B2 @ ( numeral_numeral_real @ W2 ) ) @ A )
% 3.82/4.03 = ( ord_less_eq_real @ B2 @ ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % divide_le_eq_numeral1(1)
% 3.82/4.03 thf(fact_2348_divide__eq__eq__numeral1_I1_J,axiom,
% 3.82/4.03 ! [B2: complex,W2: num,A: complex] :
% 3.82/4.03 ( ( ( divide1717551699836669952omplex @ B2 @ ( numera6690914467698888265omplex @ W2 ) )
% 3.82/4.03 = A )
% 3.82/4.03 = ( ( ( ( numera6690914467698888265omplex @ W2 )
% 3.82/4.03 != zero_zero_complex )
% 3.82/4.03 => ( B2
% 3.82/4.03 = ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W2 ) ) ) )
% 3.82/4.03 & ( ( ( numera6690914467698888265omplex @ W2 )
% 3.82/4.03 = zero_zero_complex )
% 3.82/4.03 => ( A = zero_zero_complex ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % divide_eq_eq_numeral1(1)
% 3.82/4.03 thf(fact_2349_divide__eq__eq__numeral1_I1_J,axiom,
% 3.82/4.03 ! [B2: real,W2: num,A: real] :
% 3.82/4.03 ( ( ( divide_divide_real @ B2 @ ( numeral_numeral_real @ W2 ) )
% 3.82/4.03 = A )
% 3.82/4.03 = ( ( ( ( numeral_numeral_real @ W2 )
% 3.82/4.03 != zero_zero_real )
% 3.82/4.03 => ( B2
% 3.82/4.03 = ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) ) ) )
% 3.82/4.03 & ( ( ( numeral_numeral_real @ W2 )
% 3.82/4.03 = zero_zero_real )
% 3.82/4.03 => ( A = zero_zero_real ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % divide_eq_eq_numeral1(1)
% 3.82/4.03 thf(fact_2350_eq__divide__eq__numeral1_I1_J,axiom,
% 3.82/4.03 ! [A: complex,B2: complex,W2: num] :
% 3.82/4.03 ( ( A
% 3.82/4.03 = ( divide1717551699836669952omplex @ B2 @ ( numera6690914467698888265omplex @ W2 ) ) )
% 3.82/4.03 = ( ( ( ( numera6690914467698888265omplex @ W2 )
% 3.82/4.03 != zero_zero_complex )
% 3.82/4.03 => ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W2 ) )
% 3.82/4.03 = B2 ) )
% 3.82/4.03 & ( ( ( numera6690914467698888265omplex @ W2 )
% 3.82/4.03 = zero_zero_complex )
% 3.82/4.03 => ( A = zero_zero_complex ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % eq_divide_eq_numeral1(1)
% 3.82/4.03 thf(fact_2351_eq__divide__eq__numeral1_I1_J,axiom,
% 3.82/4.03 ! [A: real,B2: real,W2: num] :
% 3.82/4.03 ( ( A
% 3.82/4.03 = ( divide_divide_real @ B2 @ ( numeral_numeral_real @ W2 ) ) )
% 3.82/4.03 = ( ( ( ( numeral_numeral_real @ W2 )
% 3.82/4.03 != zero_zero_real )
% 3.82/4.03 => ( ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) )
% 3.82/4.03 = B2 ) )
% 3.82/4.03 & ( ( ( numeral_numeral_real @ W2 )
% 3.82/4.03 = zero_zero_real )
% 3.82/4.03 => ( A = zero_zero_real ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % eq_divide_eq_numeral1(1)
% 3.82/4.03 thf(fact_2352_less__divide__eq__numeral1_I1_J,axiom,
% 3.82/4.03 ! [A: real,B2: real,W2: num] :
% 3.82/4.03 ( ( ord_less_real @ A @ ( divide_divide_real @ B2 @ ( numeral_numeral_real @ W2 ) ) )
% 3.82/4.03 = ( ord_less_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) ) @ B2 ) ) ).
% 3.82/4.03
% 3.82/4.03 % less_divide_eq_numeral1(1)
% 3.82/4.03 thf(fact_2353_divide__less__eq__numeral1_I1_J,axiom,
% 3.82/4.03 ! [B2: real,W2: num,A: real] :
% 3.82/4.03 ( ( ord_less_real @ ( divide_divide_real @ B2 @ ( numeral_numeral_real @ W2 ) ) @ A )
% 3.82/4.03 = ( ord_less_real @ B2 @ ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % divide_less_eq_numeral1(1)
% 3.82/4.03 thf(fact_2354_nonzero__divide__mult__cancel__left,axiom,
% 3.82/4.03 ! [A: complex,B2: complex] :
% 3.82/4.03 ( ( A != zero_zero_complex )
% 3.82/4.03 => ( ( divide1717551699836669952omplex @ A @ ( times_times_complex @ A @ B2 ) )
% 3.82/4.03 = ( divide1717551699836669952omplex @ one_one_complex @ B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % nonzero_divide_mult_cancel_left
% 3.82/4.03 thf(fact_2355_nonzero__divide__mult__cancel__left,axiom,
% 3.82/4.03 ! [A: real,B2: real] :
% 3.82/4.03 ( ( A != zero_zero_real )
% 3.82/4.03 => ( ( divide_divide_real @ A @ ( times_times_real @ A @ B2 ) )
% 3.82/4.03 = ( divide_divide_real @ one_one_real @ B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % nonzero_divide_mult_cancel_left
% 3.82/4.03 thf(fact_2356_nonzero__divide__mult__cancel__right,axiom,
% 3.82/4.03 ! [B2: complex,A: complex] :
% 3.82/4.03 ( ( B2 != zero_zero_complex )
% 3.82/4.03 => ( ( divide1717551699836669952omplex @ B2 @ ( times_times_complex @ A @ B2 ) )
% 3.82/4.03 = ( divide1717551699836669952omplex @ one_one_complex @ A ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % nonzero_divide_mult_cancel_right
% 3.82/4.03 thf(fact_2357_nonzero__divide__mult__cancel__right,axiom,
% 3.82/4.03 ! [B2: real,A: real] :
% 3.82/4.03 ( ( B2 != zero_zero_real )
% 3.82/4.03 => ( ( divide_divide_real @ B2 @ ( times_times_real @ A @ B2 ) )
% 3.82/4.03 = ( divide_divide_real @ one_one_real @ A ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % nonzero_divide_mult_cancel_right
% 3.82/4.03 thf(fact_2358_div__mult__self4,axiom,
% 3.82/4.03 ! [B2: nat,C: nat,A: nat] :
% 3.82/4.03 ( ( B2 != zero_zero_nat )
% 3.82/4.03 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ B2 @ C ) @ A ) @ B2 )
% 3.82/4.03 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % div_mult_self4
% 3.82/4.03 thf(fact_2359_div__mult__self4,axiom,
% 3.82/4.03 ! [B2: int,C: int,A: int] :
% 3.82/4.03 ( ( B2 != zero_zero_int )
% 3.82/4.03 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ B2 @ C ) @ A ) @ B2 )
% 3.82/4.03 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % div_mult_self4
% 3.82/4.03 thf(fact_2360_div__mult__self3,axiom,
% 3.82/4.03 ! [B2: nat,C: nat,A: nat] :
% 3.82/4.03 ( ( B2 != zero_zero_nat )
% 3.82/4.03 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B2 ) @ A ) @ B2 )
% 3.82/4.03 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % div_mult_self3
% 3.82/4.03 thf(fact_2361_div__mult__self3,axiom,
% 3.82/4.03 ! [B2: int,C: int,A: int] :
% 3.82/4.03 ( ( B2 != zero_zero_int )
% 3.82/4.03 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ C @ B2 ) @ A ) @ B2 )
% 3.82/4.03 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % div_mult_self3
% 3.82/4.03 thf(fact_2362_div__mult__self2,axiom,
% 3.82/4.03 ! [B2: nat,A: nat,C: nat] :
% 3.82/4.03 ( ( B2 != zero_zero_nat )
% 3.82/4.03 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B2 @ C ) ) @ B2 )
% 3.82/4.03 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % div_mult_self2
% 3.82/4.03 thf(fact_2363_div__mult__self2,axiom,
% 3.82/4.03 ! [B2: int,A: int,C: int] :
% 3.82/4.03 ( ( B2 != zero_zero_int )
% 3.82/4.03 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ B2 @ C ) ) @ B2 )
% 3.82/4.03 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % div_mult_self2
% 3.82/4.03 thf(fact_2364_div__mult__self1,axiom,
% 3.82/4.03 ! [B2: nat,A: nat,C: nat] :
% 3.82/4.03 ( ( B2 != zero_zero_nat )
% 3.82/4.03 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B2 ) ) @ B2 )
% 3.82/4.03 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % div_mult_self1
% 3.82/4.03 thf(fact_2365_div__mult__self1,axiom,
% 3.82/4.03 ! [B2: int,A: int,C: int] :
% 3.82/4.03 ( ( B2 != zero_zero_int )
% 3.82/4.03 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B2 ) ) @ B2 )
% 3.82/4.03 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % div_mult_self1
% 3.82/4.03 thf(fact_2366_one__le__mult__iff,axiom,
% 3.82/4.03 ! [M2: nat,N2: nat] :
% 3.82/4.03 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M2 @ N2 ) )
% 3.82/4.03 = ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ M2 )
% 3.82/4.03 & ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % one_le_mult_iff
% 3.82/4.03 thf(fact_2367_mult__le__cancel2,axiom,
% 3.82/4.03 ! [M2: nat,K: nat,N2: nat] :
% 3.82/4.03 ( ( ord_less_eq_nat @ ( times_times_nat @ M2 @ K ) @ ( times_times_nat @ N2 @ K ) )
% 3.82/4.03 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 3.82/4.03 => ( ord_less_eq_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_le_cancel2
% 3.82/4.03 thf(fact_2368_div__mult__self__is__m,axiom,
% 3.82/4.03 ! [N2: nat,M2: nat] :
% 3.82/4.03 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.03 => ( ( divide_divide_nat @ ( times_times_nat @ M2 @ N2 ) @ N2 )
% 3.82/4.03 = M2 ) ) ).
% 3.82/4.03
% 3.82/4.03 % div_mult_self_is_m
% 3.82/4.03 thf(fact_2369_div__mult__self1__is__m,axiom,
% 3.82/4.03 ! [N2: nat,M2: nat] :
% 3.82/4.03 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.03 => ( ( divide_divide_nat @ ( times_times_nat @ N2 @ M2 ) @ N2 )
% 3.82/4.03 = M2 ) ) ).
% 3.82/4.03
% 3.82/4.03 % div_mult_self1_is_m
% 3.82/4.03 thf(fact_2370_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 3.82/4.03 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.03 ( ( times_times_nat @ ( times_times_nat @ A @ B2 ) @ C )
% 3.82/4.03 = ( times_times_nat @ A @ ( times_times_nat @ B2 @ C ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % ab_semigroup_mult_class.mult_ac(1)
% 3.82/4.03 thf(fact_2371_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 3.82/4.03 ! [A: int,B2: int,C: int] :
% 3.82/4.03 ( ( times_times_int @ ( times_times_int @ A @ B2 ) @ C )
% 3.82/4.03 = ( times_times_int @ A @ ( times_times_int @ B2 @ C ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % ab_semigroup_mult_class.mult_ac(1)
% 3.82/4.03 thf(fact_2372_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 3.82/4.03 ! [A: real,B2: real,C: real] :
% 3.82/4.03 ( ( times_times_real @ ( times_times_real @ A @ B2 ) @ C )
% 3.82/4.03 = ( times_times_real @ A @ ( times_times_real @ B2 @ C ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % ab_semigroup_mult_class.mult_ac(1)
% 3.82/4.03 thf(fact_2373_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 3.82/4.03 ! [A: complex,B2: complex,C: complex] :
% 3.82/4.03 ( ( times_times_complex @ ( times_times_complex @ A @ B2 ) @ C )
% 3.82/4.03 = ( times_times_complex @ A @ ( times_times_complex @ B2 @ C ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % ab_semigroup_mult_class.mult_ac(1)
% 3.82/4.03 thf(fact_2374_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 3.82/4.03 ! [A: extended_enat,B2: extended_enat,C: extended_enat] :
% 3.82/4.03 ( ( times_7803423173614009249d_enat @ ( times_7803423173614009249d_enat @ A @ B2 ) @ C )
% 3.82/4.03 = ( times_7803423173614009249d_enat @ A @ ( times_7803423173614009249d_enat @ B2 @ C ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % ab_semigroup_mult_class.mult_ac(1)
% 3.82/4.03 thf(fact_2375_mult_Oassoc,axiom,
% 3.82/4.03 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.03 ( ( times_times_nat @ ( times_times_nat @ A @ B2 ) @ C )
% 3.82/4.03 = ( times_times_nat @ A @ ( times_times_nat @ B2 @ C ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult.assoc
% 3.82/4.03 thf(fact_2376_mult_Oassoc,axiom,
% 3.82/4.03 ! [A: int,B2: int,C: int] :
% 3.82/4.03 ( ( times_times_int @ ( times_times_int @ A @ B2 ) @ C )
% 3.82/4.03 = ( times_times_int @ A @ ( times_times_int @ B2 @ C ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult.assoc
% 3.82/4.03 thf(fact_2377_mult_Oassoc,axiom,
% 3.82/4.03 ! [A: real,B2: real,C: real] :
% 3.82/4.03 ( ( times_times_real @ ( times_times_real @ A @ B2 ) @ C )
% 3.82/4.03 = ( times_times_real @ A @ ( times_times_real @ B2 @ C ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult.assoc
% 3.82/4.03 thf(fact_2378_mult_Oassoc,axiom,
% 3.82/4.03 ! [A: complex,B2: complex,C: complex] :
% 3.82/4.03 ( ( times_times_complex @ ( times_times_complex @ A @ B2 ) @ C )
% 3.82/4.03 = ( times_times_complex @ A @ ( times_times_complex @ B2 @ C ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult.assoc
% 3.82/4.03 thf(fact_2379_mult_Oassoc,axiom,
% 3.82/4.03 ! [A: extended_enat,B2: extended_enat,C: extended_enat] :
% 3.82/4.03 ( ( times_7803423173614009249d_enat @ ( times_7803423173614009249d_enat @ A @ B2 ) @ C )
% 3.82/4.03 = ( times_7803423173614009249d_enat @ A @ ( times_7803423173614009249d_enat @ B2 @ C ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult.assoc
% 3.82/4.03 thf(fact_2380_mult_Ocommute,axiom,
% 3.82/4.03 ( times_times_nat
% 3.82/4.03 = ( ^ [A3: nat,B3: nat] : ( times_times_nat @ B3 @ A3 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult.commute
% 3.82/4.03 thf(fact_2381_mult_Ocommute,axiom,
% 3.82/4.03 ( times_times_int
% 3.82/4.03 = ( ^ [A3: int,B3: int] : ( times_times_int @ B3 @ A3 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult.commute
% 3.82/4.03 thf(fact_2382_mult_Ocommute,axiom,
% 3.82/4.03 ( times_times_real
% 3.82/4.03 = ( ^ [A3: real,B3: real] : ( times_times_real @ B3 @ A3 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult.commute
% 3.82/4.03 thf(fact_2383_mult_Ocommute,axiom,
% 3.82/4.03 ( times_times_complex
% 3.82/4.03 = ( ^ [A3: complex,B3: complex] : ( times_times_complex @ B3 @ A3 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult.commute
% 3.82/4.03 thf(fact_2384_mult_Ocommute,axiom,
% 3.82/4.03 ( times_7803423173614009249d_enat
% 3.82/4.03 = ( ^ [A3: extended_enat,B3: extended_enat] : ( times_7803423173614009249d_enat @ B3 @ A3 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult.commute
% 3.82/4.03 thf(fact_2385_mult_Oleft__commute,axiom,
% 3.82/4.03 ! [B2: nat,A: nat,C: nat] :
% 3.82/4.03 ( ( times_times_nat @ B2 @ ( times_times_nat @ A @ C ) )
% 3.82/4.03 = ( times_times_nat @ A @ ( times_times_nat @ B2 @ C ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult.left_commute
% 3.82/4.03 thf(fact_2386_mult_Oleft__commute,axiom,
% 3.82/4.03 ! [B2: int,A: int,C: int] :
% 3.82/4.03 ( ( times_times_int @ B2 @ ( times_times_int @ A @ C ) )
% 3.82/4.03 = ( times_times_int @ A @ ( times_times_int @ B2 @ C ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult.left_commute
% 3.82/4.03 thf(fact_2387_mult_Oleft__commute,axiom,
% 3.82/4.03 ! [B2: real,A: real,C: real] :
% 3.82/4.03 ( ( times_times_real @ B2 @ ( times_times_real @ A @ C ) )
% 3.82/4.03 = ( times_times_real @ A @ ( times_times_real @ B2 @ C ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult.left_commute
% 3.82/4.03 thf(fact_2388_mult_Oleft__commute,axiom,
% 3.82/4.03 ! [B2: complex,A: complex,C: complex] :
% 3.82/4.03 ( ( times_times_complex @ B2 @ ( times_times_complex @ A @ C ) )
% 3.82/4.03 = ( times_times_complex @ A @ ( times_times_complex @ B2 @ C ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult.left_commute
% 3.82/4.03 thf(fact_2389_mult_Oleft__commute,axiom,
% 3.82/4.03 ! [B2: extended_enat,A: extended_enat,C: extended_enat] :
% 3.82/4.03 ( ( times_7803423173614009249d_enat @ B2 @ ( times_7803423173614009249d_enat @ A @ C ) )
% 3.82/4.03 = ( times_7803423173614009249d_enat @ A @ ( times_7803423173614009249d_enat @ B2 @ C ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult.left_commute
% 3.82/4.03 thf(fact_2390_VEBT_Osize_I4_J,axiom,
% 3.82/4.03 ! [X21: $o,X222: $o] :
% 3.82/4.03 ( ( size_size_VEBT_VEBT @ ( vEBT_Leaf @ X21 @ X222 ) )
% 3.82/4.03 = zero_zero_nat ) ).
% 3.82/4.03
% 3.82/4.03 % VEBT.size(4)
% 3.82/4.03 thf(fact_2391_mult__right__cancel,axiom,
% 3.82/4.03 ! [C: nat,A: nat,B2: nat] :
% 3.82/4.03 ( ( C != zero_zero_nat )
% 3.82/4.03 => ( ( ( times_times_nat @ A @ C )
% 3.82/4.03 = ( times_times_nat @ B2 @ C ) )
% 3.82/4.03 = ( A = B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_right_cancel
% 3.82/4.03 thf(fact_2392_mult__right__cancel,axiom,
% 3.82/4.03 ! [C: int,A: int,B2: int] :
% 3.82/4.03 ( ( C != zero_zero_int )
% 3.82/4.03 => ( ( ( times_times_int @ A @ C )
% 3.82/4.03 = ( times_times_int @ B2 @ C ) )
% 3.82/4.03 = ( A = B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_right_cancel
% 3.82/4.03 thf(fact_2393_mult__right__cancel,axiom,
% 3.82/4.03 ! [C: real,A: real,B2: real] :
% 3.82/4.03 ( ( C != zero_zero_real )
% 3.82/4.03 => ( ( ( times_times_real @ A @ C )
% 3.82/4.03 = ( times_times_real @ B2 @ C ) )
% 3.82/4.03 = ( A = B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_right_cancel
% 3.82/4.03 thf(fact_2394_mult__right__cancel,axiom,
% 3.82/4.03 ! [C: complex,A: complex,B2: complex] :
% 3.82/4.03 ( ( C != zero_zero_complex )
% 3.82/4.03 => ( ( ( times_times_complex @ A @ C )
% 3.82/4.03 = ( times_times_complex @ B2 @ C ) )
% 3.82/4.03 = ( A = B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_right_cancel
% 3.82/4.03 thf(fact_2395_mult__left__cancel,axiom,
% 3.82/4.03 ! [C: nat,A: nat,B2: nat] :
% 3.82/4.03 ( ( C != zero_zero_nat )
% 3.82/4.03 => ( ( ( times_times_nat @ C @ A )
% 3.82/4.03 = ( times_times_nat @ C @ B2 ) )
% 3.82/4.03 = ( A = B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_left_cancel
% 3.82/4.03 thf(fact_2396_mult__left__cancel,axiom,
% 3.82/4.03 ! [C: int,A: int,B2: int] :
% 3.82/4.03 ( ( C != zero_zero_int )
% 3.82/4.03 => ( ( ( times_times_int @ C @ A )
% 3.82/4.03 = ( times_times_int @ C @ B2 ) )
% 3.82/4.03 = ( A = B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_left_cancel
% 3.82/4.03 thf(fact_2397_mult__left__cancel,axiom,
% 3.82/4.03 ! [C: real,A: real,B2: real] :
% 3.82/4.03 ( ( C != zero_zero_real )
% 3.82/4.03 => ( ( ( times_times_real @ C @ A )
% 3.82/4.03 = ( times_times_real @ C @ B2 ) )
% 3.82/4.03 = ( A = B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_left_cancel
% 3.82/4.03 thf(fact_2398_mult__left__cancel,axiom,
% 3.82/4.03 ! [C: complex,A: complex,B2: complex] :
% 3.82/4.03 ( ( C != zero_zero_complex )
% 3.82/4.03 => ( ( ( times_times_complex @ C @ A )
% 3.82/4.03 = ( times_times_complex @ C @ B2 ) )
% 3.82/4.03 = ( A = B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_left_cancel
% 3.82/4.03 thf(fact_2399_no__zero__divisors,axiom,
% 3.82/4.03 ! [A: nat,B2: nat] :
% 3.82/4.03 ( ( A != zero_zero_nat )
% 3.82/4.03 => ( ( B2 != zero_zero_nat )
% 3.82/4.03 => ( ( times_times_nat @ A @ B2 )
% 3.82/4.03 != zero_zero_nat ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % no_zero_divisors
% 3.82/4.03 thf(fact_2400_no__zero__divisors,axiom,
% 3.82/4.03 ! [A: int,B2: int] :
% 3.82/4.03 ( ( A != zero_zero_int )
% 3.82/4.03 => ( ( B2 != zero_zero_int )
% 3.82/4.03 => ( ( times_times_int @ A @ B2 )
% 3.82/4.03 != zero_zero_int ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % no_zero_divisors
% 3.82/4.03 thf(fact_2401_no__zero__divisors,axiom,
% 3.82/4.03 ! [A: real,B2: real] :
% 3.82/4.03 ( ( A != zero_zero_real )
% 3.82/4.03 => ( ( B2 != zero_zero_real )
% 3.82/4.03 => ( ( times_times_real @ A @ B2 )
% 3.82/4.03 != zero_zero_real ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % no_zero_divisors
% 3.82/4.03 thf(fact_2402_no__zero__divisors,axiom,
% 3.82/4.03 ! [A: complex,B2: complex] :
% 3.82/4.03 ( ( A != zero_zero_complex )
% 3.82/4.03 => ( ( B2 != zero_zero_complex )
% 3.82/4.03 => ( ( times_times_complex @ A @ B2 )
% 3.82/4.03 != zero_zero_complex ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % no_zero_divisors
% 3.82/4.03 thf(fact_2403_no__zero__divisors,axiom,
% 3.82/4.03 ! [A: extended_enat,B2: extended_enat] :
% 3.82/4.03 ( ( A != zero_z5237406670263579293d_enat )
% 3.82/4.03 => ( ( B2 != zero_z5237406670263579293d_enat )
% 3.82/4.03 => ( ( times_7803423173614009249d_enat @ A @ B2 )
% 3.82/4.03 != zero_z5237406670263579293d_enat ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % no_zero_divisors
% 3.82/4.03 thf(fact_2404_divisors__zero,axiom,
% 3.82/4.03 ! [A: nat,B2: nat] :
% 3.82/4.03 ( ( ( times_times_nat @ A @ B2 )
% 3.82/4.03 = zero_zero_nat )
% 3.82/4.03 => ( ( A = zero_zero_nat )
% 3.82/4.03 | ( B2 = zero_zero_nat ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % divisors_zero
% 3.82/4.03 thf(fact_2405_divisors__zero,axiom,
% 3.82/4.03 ! [A: int,B2: int] :
% 3.82/4.03 ( ( ( times_times_int @ A @ B2 )
% 3.82/4.03 = zero_zero_int )
% 3.82/4.03 => ( ( A = zero_zero_int )
% 3.82/4.03 | ( B2 = zero_zero_int ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % divisors_zero
% 3.82/4.03 thf(fact_2406_divisors__zero,axiom,
% 3.82/4.03 ! [A: real,B2: real] :
% 3.82/4.03 ( ( ( times_times_real @ A @ B2 )
% 3.82/4.03 = zero_zero_real )
% 3.82/4.03 => ( ( A = zero_zero_real )
% 3.82/4.03 | ( B2 = zero_zero_real ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % divisors_zero
% 3.82/4.03 thf(fact_2407_divisors__zero,axiom,
% 3.82/4.03 ! [A: complex,B2: complex] :
% 3.82/4.03 ( ( ( times_times_complex @ A @ B2 )
% 3.82/4.03 = zero_zero_complex )
% 3.82/4.03 => ( ( A = zero_zero_complex )
% 3.82/4.03 | ( B2 = zero_zero_complex ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % divisors_zero
% 3.82/4.03 thf(fact_2408_divisors__zero,axiom,
% 3.82/4.03 ! [A: extended_enat,B2: extended_enat] :
% 3.82/4.03 ( ( ( times_7803423173614009249d_enat @ A @ B2 )
% 3.82/4.03 = zero_z5237406670263579293d_enat )
% 3.82/4.03 => ( ( A = zero_z5237406670263579293d_enat )
% 3.82/4.03 | ( B2 = zero_z5237406670263579293d_enat ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % divisors_zero
% 3.82/4.03 thf(fact_2409_mult__not__zero,axiom,
% 3.82/4.03 ! [A: nat,B2: nat] :
% 3.82/4.03 ( ( ( times_times_nat @ A @ B2 )
% 3.82/4.03 != zero_zero_nat )
% 3.82/4.03 => ( ( A != zero_zero_nat )
% 3.82/4.03 & ( B2 != zero_zero_nat ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_not_zero
% 3.82/4.03 thf(fact_2410_mult__not__zero,axiom,
% 3.82/4.03 ! [A: int,B2: int] :
% 3.82/4.03 ( ( ( times_times_int @ A @ B2 )
% 3.82/4.03 != zero_zero_int )
% 3.82/4.03 => ( ( A != zero_zero_int )
% 3.82/4.03 & ( B2 != zero_zero_int ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_not_zero
% 3.82/4.03 thf(fact_2411_mult__not__zero,axiom,
% 3.82/4.03 ! [A: real,B2: real] :
% 3.82/4.03 ( ( ( times_times_real @ A @ B2 )
% 3.82/4.03 != zero_zero_real )
% 3.82/4.03 => ( ( A != zero_zero_real )
% 3.82/4.03 & ( B2 != zero_zero_real ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_not_zero
% 3.82/4.03 thf(fact_2412_mult__not__zero,axiom,
% 3.82/4.03 ! [A: complex,B2: complex] :
% 3.82/4.03 ( ( ( times_times_complex @ A @ B2 )
% 3.82/4.03 != zero_zero_complex )
% 3.82/4.03 => ( ( A != zero_zero_complex )
% 3.82/4.03 & ( B2 != zero_zero_complex ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_not_zero
% 3.82/4.03 thf(fact_2413_mult__not__zero,axiom,
% 3.82/4.03 ! [A: extended_enat,B2: extended_enat] :
% 3.82/4.03 ( ( ( times_7803423173614009249d_enat @ A @ B2 )
% 3.82/4.03 != zero_z5237406670263579293d_enat )
% 3.82/4.03 => ( ( A != zero_z5237406670263579293d_enat )
% 3.82/4.03 & ( B2 != zero_z5237406670263579293d_enat ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_not_zero
% 3.82/4.03 thf(fact_2414_comm__monoid__mult__class_Omult__1,axiom,
% 3.82/4.03 ! [A: nat] :
% 3.82/4.03 ( ( times_times_nat @ one_one_nat @ A )
% 3.82/4.03 = A ) ).
% 3.82/4.03
% 3.82/4.03 % comm_monoid_mult_class.mult_1
% 3.82/4.03 thf(fact_2415_comm__monoid__mult__class_Omult__1,axiom,
% 3.82/4.03 ! [A: int] :
% 3.82/4.03 ( ( times_times_int @ one_one_int @ A )
% 3.82/4.03 = A ) ).
% 3.82/4.03
% 3.82/4.03 % comm_monoid_mult_class.mult_1
% 3.82/4.03 thf(fact_2416_comm__monoid__mult__class_Omult__1,axiom,
% 3.82/4.03 ! [A: real] :
% 3.82/4.03 ( ( times_times_real @ one_one_real @ A )
% 3.82/4.03 = A ) ).
% 3.82/4.03
% 3.82/4.03 % comm_monoid_mult_class.mult_1
% 3.82/4.03 thf(fact_2417_comm__monoid__mult__class_Omult__1,axiom,
% 3.82/4.03 ! [A: complex] :
% 3.82/4.03 ( ( times_times_complex @ one_one_complex @ A )
% 3.82/4.03 = A ) ).
% 3.82/4.03
% 3.82/4.03 % comm_monoid_mult_class.mult_1
% 3.82/4.03 thf(fact_2418_comm__monoid__mult__class_Omult__1,axiom,
% 3.82/4.03 ! [A: extended_enat] :
% 3.82/4.03 ( ( times_7803423173614009249d_enat @ one_on7984719198319812577d_enat @ A )
% 3.82/4.03 = A ) ).
% 3.82/4.03
% 3.82/4.03 % comm_monoid_mult_class.mult_1
% 3.82/4.03 thf(fact_2419_mult_Ocomm__neutral,axiom,
% 3.82/4.03 ! [A: nat] :
% 3.82/4.03 ( ( times_times_nat @ A @ one_one_nat )
% 3.82/4.03 = A ) ).
% 3.82/4.03
% 3.82/4.03 % mult.comm_neutral
% 3.82/4.03 thf(fact_2420_mult_Ocomm__neutral,axiom,
% 3.82/4.03 ! [A: int] :
% 3.82/4.03 ( ( times_times_int @ A @ one_one_int )
% 3.82/4.03 = A ) ).
% 3.82/4.03
% 3.82/4.03 % mult.comm_neutral
% 3.82/4.03 thf(fact_2421_mult_Ocomm__neutral,axiom,
% 3.82/4.03 ! [A: real] :
% 3.82/4.03 ( ( times_times_real @ A @ one_one_real )
% 3.82/4.03 = A ) ).
% 3.82/4.03
% 3.82/4.03 % mult.comm_neutral
% 3.82/4.03 thf(fact_2422_mult_Ocomm__neutral,axiom,
% 3.82/4.03 ! [A: complex] :
% 3.82/4.03 ( ( times_times_complex @ A @ one_one_complex )
% 3.82/4.03 = A ) ).
% 3.82/4.03
% 3.82/4.03 % mult.comm_neutral
% 3.82/4.03 thf(fact_2423_mult_Ocomm__neutral,axiom,
% 3.82/4.03 ! [A: extended_enat] :
% 3.82/4.03 ( ( times_7803423173614009249d_enat @ A @ one_on7984719198319812577d_enat )
% 3.82/4.03 = A ) ).
% 3.82/4.03
% 3.82/4.03 % mult.comm_neutral
% 3.82/4.03 thf(fact_2424_crossproduct__noteq,axiom,
% 3.82/4.03 ! [A: nat,B2: nat,C: nat,D: nat] :
% 3.82/4.03 ( ( ( A != B2 )
% 3.82/4.03 & ( C != D ) )
% 3.82/4.03 = ( ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B2 @ D ) )
% 3.82/4.03 != ( plus_plus_nat @ ( times_times_nat @ A @ D ) @ ( times_times_nat @ B2 @ C ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % crossproduct_noteq
% 3.82/4.03 thf(fact_2425_crossproduct__noteq,axiom,
% 3.82/4.03 ! [A: int,B2: int,C: int,D: int] :
% 3.82/4.03 ( ( ( A != B2 )
% 3.82/4.03 & ( C != D ) )
% 3.82/4.03 = ( ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B2 @ D ) )
% 3.82/4.03 != ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B2 @ C ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % crossproduct_noteq
% 3.82/4.03 thf(fact_2426_crossproduct__noteq,axiom,
% 3.82/4.03 ! [A: real,B2: real,C: real,D: real] :
% 3.82/4.03 ( ( ( A != B2 )
% 3.82/4.03 & ( C != D ) )
% 3.82/4.03 = ( ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B2 @ D ) )
% 3.82/4.03 != ( plus_plus_real @ ( times_times_real @ A @ D ) @ ( times_times_real @ B2 @ C ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % crossproduct_noteq
% 3.82/4.03 thf(fact_2427_crossproduct__noteq,axiom,
% 3.82/4.03 ! [A: complex,B2: complex,C: complex,D: complex] :
% 3.82/4.03 ( ( ( A != B2 )
% 3.82/4.03 & ( C != D ) )
% 3.82/4.03 = ( ( plus_plus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B2 @ D ) )
% 3.82/4.03 != ( plus_plus_complex @ ( times_times_complex @ A @ D ) @ ( times_times_complex @ B2 @ C ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % crossproduct_noteq
% 3.82/4.03 thf(fact_2428_crossproduct__eq,axiom,
% 3.82/4.03 ! [W2: nat,Y: nat,X: nat,Z3: nat] :
% 3.82/4.03 ( ( ( plus_plus_nat @ ( times_times_nat @ W2 @ Y ) @ ( times_times_nat @ X @ Z3 ) )
% 3.82/4.03 = ( plus_plus_nat @ ( times_times_nat @ W2 @ Z3 ) @ ( times_times_nat @ X @ Y ) ) )
% 3.82/4.03 = ( ( W2 = X )
% 3.82/4.03 | ( Y = Z3 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % crossproduct_eq
% 3.82/4.03 thf(fact_2429_crossproduct__eq,axiom,
% 3.82/4.03 ! [W2: int,Y: int,X: int,Z3: int] :
% 3.82/4.03 ( ( ( plus_plus_int @ ( times_times_int @ W2 @ Y ) @ ( times_times_int @ X @ Z3 ) )
% 3.82/4.03 = ( plus_plus_int @ ( times_times_int @ W2 @ Z3 ) @ ( times_times_int @ X @ Y ) ) )
% 3.82/4.03 = ( ( W2 = X )
% 3.82/4.03 | ( Y = Z3 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % crossproduct_eq
% 3.82/4.03 thf(fact_2430_crossproduct__eq,axiom,
% 3.82/4.03 ! [W2: real,Y: real,X: real,Z3: real] :
% 3.82/4.03 ( ( ( plus_plus_real @ ( times_times_real @ W2 @ Y ) @ ( times_times_real @ X @ Z3 ) )
% 3.82/4.03 = ( plus_plus_real @ ( times_times_real @ W2 @ Z3 ) @ ( times_times_real @ X @ Y ) ) )
% 3.82/4.03 = ( ( W2 = X )
% 3.82/4.03 | ( Y = Z3 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % crossproduct_eq
% 3.82/4.03 thf(fact_2431_crossproduct__eq,axiom,
% 3.82/4.03 ! [W2: complex,Y: complex,X: complex,Z3: complex] :
% 3.82/4.03 ( ( ( plus_plus_complex @ ( times_times_complex @ W2 @ Y ) @ ( times_times_complex @ X @ Z3 ) )
% 3.82/4.03 = ( plus_plus_complex @ ( times_times_complex @ W2 @ Z3 ) @ ( times_times_complex @ X @ Y ) ) )
% 3.82/4.03 = ( ( W2 = X )
% 3.82/4.03 | ( Y = Z3 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % crossproduct_eq
% 3.82/4.03 thf(fact_2432_combine__common__factor,axiom,
% 3.82/4.03 ! [A: nat,E2: nat,B2: nat,C: nat] :
% 3.82/4.03 ( ( plus_plus_nat @ ( times_times_nat @ A @ E2 ) @ ( plus_plus_nat @ ( times_times_nat @ B2 @ E2 ) @ C ) )
% 3.82/4.03 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B2 ) @ E2 ) @ C ) ) ).
% 3.82/4.03
% 3.82/4.03 % combine_common_factor
% 3.82/4.03 thf(fact_2433_combine__common__factor,axiom,
% 3.82/4.03 ! [A: int,E2: int,B2: int,C: int] :
% 3.82/4.03 ( ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ ( plus_plus_int @ ( times_times_int @ B2 @ E2 ) @ C ) )
% 3.82/4.03 = ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A @ B2 ) @ E2 ) @ C ) ) ).
% 3.82/4.03
% 3.82/4.03 % combine_common_factor
% 3.82/4.03 thf(fact_2434_combine__common__factor,axiom,
% 3.82/4.03 ! [A: real,E2: real,B2: real,C: real] :
% 3.82/4.03 ( ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ ( plus_plus_real @ ( times_times_real @ B2 @ E2 ) @ C ) )
% 3.82/4.03 = ( plus_plus_real @ ( times_times_real @ ( plus_plus_real @ A @ B2 ) @ E2 ) @ C ) ) ).
% 3.82/4.03
% 3.82/4.03 % combine_common_factor
% 3.82/4.03 thf(fact_2435_combine__common__factor,axiom,
% 3.82/4.03 ! [A: complex,E2: complex,B2: complex,C: complex] :
% 3.82/4.03 ( ( plus_plus_complex @ ( times_times_complex @ A @ E2 ) @ ( plus_plus_complex @ ( times_times_complex @ B2 @ E2 ) @ C ) )
% 3.82/4.03 = ( plus_plus_complex @ ( times_times_complex @ ( plus_plus_complex @ A @ B2 ) @ E2 ) @ C ) ) ).
% 3.82/4.03
% 3.82/4.03 % combine_common_factor
% 3.82/4.03 thf(fact_2436_combine__common__factor,axiom,
% 3.82/4.03 ! [A: extended_enat,E2: extended_enat,B2: extended_enat,C: extended_enat] :
% 3.82/4.03 ( ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ A @ E2 ) @ ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ B2 @ E2 ) @ C ) )
% 3.82/4.03 = ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ ( plus_p3455044024723400733d_enat @ A @ B2 ) @ E2 ) @ C ) ) ).
% 3.82/4.03
% 3.82/4.03 % combine_common_factor
% 3.82/4.03 thf(fact_2437_distrib__right,axiom,
% 3.82/4.03 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.03 ( ( times_times_nat @ ( plus_plus_nat @ A @ B2 ) @ C )
% 3.82/4.03 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B2 @ C ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % distrib_right
% 3.82/4.03 thf(fact_2438_distrib__right,axiom,
% 3.82/4.03 ! [A: int,B2: int,C: int] :
% 3.82/4.03 ( ( times_times_int @ ( plus_plus_int @ A @ B2 ) @ C )
% 3.82/4.03 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B2 @ C ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % distrib_right
% 3.82/4.03 thf(fact_2439_distrib__right,axiom,
% 3.82/4.03 ! [A: real,B2: real,C: real] :
% 3.82/4.03 ( ( times_times_real @ ( plus_plus_real @ A @ B2 ) @ C )
% 3.82/4.03 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B2 @ C ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % distrib_right
% 3.82/4.03 thf(fact_2440_distrib__right,axiom,
% 3.82/4.03 ! [A: complex,B2: complex,C: complex] :
% 3.82/4.03 ( ( times_times_complex @ ( plus_plus_complex @ A @ B2 ) @ C )
% 3.82/4.03 = ( plus_plus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B2 @ C ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % distrib_right
% 3.82/4.03 thf(fact_2441_distrib__right,axiom,
% 3.82/4.03 ! [A: extended_enat,B2: extended_enat,C: extended_enat] :
% 3.82/4.03 ( ( times_7803423173614009249d_enat @ ( plus_p3455044024723400733d_enat @ A @ B2 ) @ C )
% 3.82/4.03 = ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ A @ C ) @ ( times_7803423173614009249d_enat @ B2 @ C ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % distrib_right
% 3.82/4.03 thf(fact_2442_distrib__left,axiom,
% 3.82/4.03 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.03 ( ( times_times_nat @ A @ ( plus_plus_nat @ B2 @ C ) )
% 3.82/4.03 = ( plus_plus_nat @ ( times_times_nat @ A @ B2 ) @ ( times_times_nat @ A @ C ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % distrib_left
% 3.82/4.03 thf(fact_2443_distrib__left,axiom,
% 3.82/4.03 ! [A: int,B2: int,C: int] :
% 3.82/4.03 ( ( times_times_int @ A @ ( plus_plus_int @ B2 @ C ) )
% 3.82/4.03 = ( plus_plus_int @ ( times_times_int @ A @ B2 ) @ ( times_times_int @ A @ C ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % distrib_left
% 3.82/4.03 thf(fact_2444_distrib__left,axiom,
% 3.82/4.03 ! [A: real,B2: real,C: real] :
% 3.82/4.03 ( ( times_times_real @ A @ ( plus_plus_real @ B2 @ C ) )
% 3.82/4.03 = ( plus_plus_real @ ( times_times_real @ A @ B2 ) @ ( times_times_real @ A @ C ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % distrib_left
% 3.82/4.03 thf(fact_2445_distrib__left,axiom,
% 3.82/4.03 ! [A: complex,B2: complex,C: complex] :
% 3.82/4.03 ( ( times_times_complex @ A @ ( plus_plus_complex @ B2 @ C ) )
% 3.82/4.03 = ( plus_plus_complex @ ( times_times_complex @ A @ B2 ) @ ( times_times_complex @ A @ C ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % distrib_left
% 3.82/4.03 thf(fact_2446_distrib__left,axiom,
% 3.82/4.03 ! [A: extended_enat,B2: extended_enat,C: extended_enat] :
% 3.82/4.03 ( ( times_7803423173614009249d_enat @ A @ ( plus_p3455044024723400733d_enat @ B2 @ C ) )
% 3.82/4.03 = ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ A @ B2 ) @ ( times_7803423173614009249d_enat @ A @ C ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % distrib_left
% 3.82/4.03 thf(fact_2447_comm__semiring__class_Odistrib,axiom,
% 3.82/4.03 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.03 ( ( times_times_nat @ ( plus_plus_nat @ A @ B2 ) @ C )
% 3.82/4.03 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B2 @ C ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % comm_semiring_class.distrib
% 3.82/4.03 thf(fact_2448_comm__semiring__class_Odistrib,axiom,
% 3.82/4.03 ! [A: int,B2: int,C: int] :
% 3.82/4.03 ( ( times_times_int @ ( plus_plus_int @ A @ B2 ) @ C )
% 3.82/4.03 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B2 @ C ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % comm_semiring_class.distrib
% 3.82/4.03 thf(fact_2449_comm__semiring__class_Odistrib,axiom,
% 3.82/4.03 ! [A: real,B2: real,C: real] :
% 3.82/4.03 ( ( times_times_real @ ( plus_plus_real @ A @ B2 ) @ C )
% 3.82/4.03 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B2 @ C ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % comm_semiring_class.distrib
% 3.82/4.03 thf(fact_2450_comm__semiring__class_Odistrib,axiom,
% 3.82/4.03 ! [A: complex,B2: complex,C: complex] :
% 3.82/4.03 ( ( times_times_complex @ ( plus_plus_complex @ A @ B2 ) @ C )
% 3.82/4.03 = ( plus_plus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B2 @ C ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % comm_semiring_class.distrib
% 3.82/4.03 thf(fact_2451_comm__semiring__class_Odistrib,axiom,
% 3.82/4.03 ! [A: extended_enat,B2: extended_enat,C: extended_enat] :
% 3.82/4.03 ( ( times_7803423173614009249d_enat @ ( plus_p3455044024723400733d_enat @ A @ B2 ) @ C )
% 3.82/4.03 = ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ A @ C ) @ ( times_7803423173614009249d_enat @ B2 @ C ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % comm_semiring_class.distrib
% 3.82/4.03 thf(fact_2452_ring__class_Oring__distribs_I1_J,axiom,
% 3.82/4.03 ! [A: int,B2: int,C: int] :
% 3.82/4.03 ( ( times_times_int @ A @ ( plus_plus_int @ B2 @ C ) )
% 3.82/4.03 = ( plus_plus_int @ ( times_times_int @ A @ B2 ) @ ( times_times_int @ A @ C ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % ring_class.ring_distribs(1)
% 3.82/4.03 thf(fact_2453_ring__class_Oring__distribs_I1_J,axiom,
% 3.82/4.03 ! [A: real,B2: real,C: real] :
% 3.82/4.03 ( ( times_times_real @ A @ ( plus_plus_real @ B2 @ C ) )
% 3.82/4.03 = ( plus_plus_real @ ( times_times_real @ A @ B2 ) @ ( times_times_real @ A @ C ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % ring_class.ring_distribs(1)
% 3.82/4.03 thf(fact_2454_ring__class_Oring__distribs_I1_J,axiom,
% 3.82/4.03 ! [A: complex,B2: complex,C: complex] :
% 3.82/4.03 ( ( times_times_complex @ A @ ( plus_plus_complex @ B2 @ C ) )
% 3.82/4.03 = ( plus_plus_complex @ ( times_times_complex @ A @ B2 ) @ ( times_times_complex @ A @ C ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % ring_class.ring_distribs(1)
% 3.82/4.03 thf(fact_2455_ring__class_Oring__distribs_I2_J,axiom,
% 3.82/4.03 ! [A: int,B2: int,C: int] :
% 3.82/4.03 ( ( times_times_int @ ( plus_plus_int @ A @ B2 ) @ C )
% 3.82/4.03 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B2 @ C ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % ring_class.ring_distribs(2)
% 3.82/4.03 thf(fact_2456_ring__class_Oring__distribs_I2_J,axiom,
% 3.82/4.03 ! [A: real,B2: real,C: real] :
% 3.82/4.03 ( ( times_times_real @ ( plus_plus_real @ A @ B2 ) @ C )
% 3.82/4.03 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B2 @ C ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % ring_class.ring_distribs(2)
% 3.82/4.03 thf(fact_2457_ring__class_Oring__distribs_I2_J,axiom,
% 3.82/4.03 ! [A: complex,B2: complex,C: complex] :
% 3.82/4.03 ( ( times_times_complex @ ( plus_plus_complex @ A @ B2 ) @ C )
% 3.82/4.03 = ( plus_plus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B2 @ C ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % ring_class.ring_distribs(2)
% 3.82/4.03 thf(fact_2458_times__divide__times__eq,axiom,
% 3.82/4.03 ! [X: complex,Y: complex,Z3: complex,W2: complex] :
% 3.82/4.03 ( ( times_times_complex @ ( divide1717551699836669952omplex @ X @ Y ) @ ( divide1717551699836669952omplex @ Z3 @ W2 ) )
% 3.82/4.03 = ( divide1717551699836669952omplex @ ( times_times_complex @ X @ Z3 ) @ ( times_times_complex @ Y @ W2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % times_divide_times_eq
% 3.82/4.03 thf(fact_2459_times__divide__times__eq,axiom,
% 3.82/4.03 ! [X: real,Y: real,Z3: real,W2: real] :
% 3.82/4.03 ( ( times_times_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ Z3 @ W2 ) )
% 3.82/4.03 = ( divide_divide_real @ ( times_times_real @ X @ Z3 ) @ ( times_times_real @ Y @ W2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % times_divide_times_eq
% 3.82/4.03 thf(fact_2460_divide__divide__times__eq,axiom,
% 3.82/4.03 ! [X: complex,Y: complex,Z3: complex,W2: complex] :
% 3.82/4.03 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ X @ Y ) @ ( divide1717551699836669952omplex @ Z3 @ W2 ) )
% 3.82/4.03 = ( divide1717551699836669952omplex @ ( times_times_complex @ X @ W2 ) @ ( times_times_complex @ Y @ Z3 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % divide_divide_times_eq
% 3.82/4.03 thf(fact_2461_divide__divide__times__eq,axiom,
% 3.82/4.03 ! [X: real,Y: real,Z3: real,W2: real] :
% 3.82/4.03 ( ( divide_divide_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ Z3 @ W2 ) )
% 3.82/4.03 = ( divide_divide_real @ ( times_times_real @ X @ W2 ) @ ( times_times_real @ Y @ Z3 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % divide_divide_times_eq
% 3.82/4.03 thf(fact_2462_divide__divide__eq__left_H,axiom,
% 3.82/4.03 ! [A: complex,B2: complex,C: complex] :
% 3.82/4.03 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B2 ) @ C )
% 3.82/4.03 = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ C @ B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % divide_divide_eq_left'
% 3.82/4.03 thf(fact_2463_divide__divide__eq__left_H,axiom,
% 3.82/4.03 ! [A: real,B2: real,C: real] :
% 3.82/4.03 ( ( divide_divide_real @ ( divide_divide_real @ A @ B2 ) @ C )
% 3.82/4.03 = ( divide_divide_real @ A @ ( times_times_real @ C @ B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % divide_divide_eq_left'
% 3.82/4.03 thf(fact_2464_Suc__mult__cancel1,axiom,
% 3.82/4.03 ! [K: nat,M2: nat,N2: nat] :
% 3.82/4.03 ( ( ( times_times_nat @ ( suc @ K ) @ M2 )
% 3.82/4.03 = ( times_times_nat @ ( suc @ K ) @ N2 ) )
% 3.82/4.03 = ( M2 = N2 ) ) ).
% 3.82/4.03
% 3.82/4.03 % Suc_mult_cancel1
% 3.82/4.03 thf(fact_2465_mult__0,axiom,
% 3.82/4.03 ! [N2: nat] :
% 3.82/4.03 ( ( times_times_nat @ zero_zero_nat @ N2 )
% 3.82/4.03 = zero_zero_nat ) ).
% 3.82/4.03
% 3.82/4.03 % mult_0
% 3.82/4.03 thf(fact_2466_mult__le__mono2,axiom,
% 3.82/4.03 ! [I: nat,J: nat,K: nat] :
% 3.82/4.03 ( ( ord_less_eq_nat @ I @ J )
% 3.82/4.03 => ( ord_less_eq_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_le_mono2
% 3.82/4.03 thf(fact_2467_mult__le__mono1,axiom,
% 3.82/4.03 ! [I: nat,J: nat,K: nat] :
% 3.82/4.03 ( ( ord_less_eq_nat @ I @ J )
% 3.82/4.03 => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_le_mono1
% 3.82/4.03 thf(fact_2468_mult__le__mono,axiom,
% 3.82/4.03 ! [I: nat,J: nat,K: nat,L: nat] :
% 3.82/4.03 ( ( ord_less_eq_nat @ I @ J )
% 3.82/4.03 => ( ( ord_less_eq_nat @ K @ L )
% 3.82/4.03 => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ L ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_le_mono
% 3.82/4.03 thf(fact_2469_le__square,axiom,
% 3.82/4.03 ! [M2: nat] : ( ord_less_eq_nat @ M2 @ ( times_times_nat @ M2 @ M2 ) ) ).
% 3.82/4.03
% 3.82/4.03 % le_square
% 3.82/4.03 thf(fact_2470_le__cube,axiom,
% 3.82/4.03 ! [M2: nat] : ( ord_less_eq_nat @ M2 @ ( times_times_nat @ M2 @ ( times_times_nat @ M2 @ M2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % le_cube
% 3.82/4.03 thf(fact_2471_add__mult__distrib2,axiom,
% 3.82/4.03 ! [K: nat,M2: nat,N2: nat] :
% 3.82/4.03 ( ( times_times_nat @ K @ ( plus_plus_nat @ M2 @ N2 ) )
% 3.82/4.03 = ( plus_plus_nat @ ( times_times_nat @ K @ M2 ) @ ( times_times_nat @ K @ N2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % add_mult_distrib2
% 3.82/4.03 thf(fact_2472_add__mult__distrib,axiom,
% 3.82/4.03 ! [M2: nat,N2: nat,K: nat] :
% 3.82/4.03 ( ( times_times_nat @ ( plus_plus_nat @ M2 @ N2 ) @ K )
% 3.82/4.03 = ( plus_plus_nat @ ( times_times_nat @ M2 @ K ) @ ( times_times_nat @ N2 @ K ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % add_mult_distrib
% 3.82/4.03 thf(fact_2473_nat__mult__1,axiom,
% 3.82/4.03 ! [N2: nat] :
% 3.82/4.03 ( ( times_times_nat @ one_one_nat @ N2 )
% 3.82/4.03 = N2 ) ).
% 3.82/4.03
% 3.82/4.03 % nat_mult_1
% 3.82/4.03 thf(fact_2474_nat__mult__1__right,axiom,
% 3.82/4.03 ! [N2: nat] :
% 3.82/4.03 ( ( times_times_nat @ N2 @ one_one_nat )
% 3.82/4.03 = N2 ) ).
% 3.82/4.03
% 3.82/4.03 % nat_mult_1_right
% 3.82/4.03 thf(fact_2475_VEBT__internal_Omembermima_Osimps_I1_J,axiom,
% 3.82/4.03 ! [Uu: $o,Uv: $o,Uw: nat] :
% 3.82/4.03 ~ ( vEBT_VEBT_membermima @ ( vEBT_Leaf @ Uu @ Uv ) @ Uw ) ).
% 3.82/4.03
% 3.82/4.03 % VEBT_internal.membermima.simps(1)
% 3.82/4.03 thf(fact_2476_VEBT__internal_OminNull_Osimps_I1_J,axiom,
% 3.82/4.03 vEBT_VEBT_minNull @ ( vEBT_Leaf @ $false @ $false ) ).
% 3.82/4.03
% 3.82/4.03 % VEBT_internal.minNull.simps(1)
% 3.82/4.03 thf(fact_2477_VEBT__internal_OminNull_Osimps_I2_J,axiom,
% 3.82/4.03 ! [Uv: $o] :
% 3.82/4.03 ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ $true @ Uv ) ) ).
% 3.82/4.03
% 3.82/4.03 % VEBT_internal.minNull.simps(2)
% 3.82/4.03 thf(fact_2478_VEBT__internal_OminNull_Osimps_I3_J,axiom,
% 3.82/4.03 ! [Uu: $o] :
% 3.82/4.03 ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ Uu @ $true ) ) ).
% 3.82/4.03
% 3.82/4.03 % VEBT_internal.minNull.simps(3)
% 3.82/4.03 thf(fact_2479_nat__mult__max__left,axiom,
% 3.82/4.03 ! [M2: nat,N2: nat,Q3: nat] :
% 3.82/4.03 ( ( times_times_nat @ ( ord_max_nat @ M2 @ N2 ) @ Q3 )
% 3.82/4.03 = ( ord_max_nat @ ( times_times_nat @ M2 @ Q3 ) @ ( times_times_nat @ N2 @ Q3 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % nat_mult_max_left
% 3.82/4.03 thf(fact_2480_nat__mult__max__right,axiom,
% 3.82/4.03 ! [M2: nat,N2: nat,Q3: nat] :
% 3.82/4.03 ( ( times_times_nat @ M2 @ ( ord_max_nat @ N2 @ Q3 ) )
% 3.82/4.03 = ( ord_max_nat @ ( times_times_nat @ M2 @ N2 ) @ ( times_times_nat @ M2 @ Q3 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % nat_mult_max_right
% 3.82/4.03 thf(fact_2481_mult__mono,axiom,
% 3.82/4.03 ! [A: extended_enat,B2: extended_enat,C: extended_enat,D: extended_enat] :
% 3.82/4.03 ( ( ord_le2932123472753598470d_enat @ A @ B2 )
% 3.82/4.03 => ( ( ord_le2932123472753598470d_enat @ C @ D )
% 3.82/4.03 => ( ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ B2 )
% 3.82/4.03 => ( ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ C )
% 3.82/4.03 => ( ord_le2932123472753598470d_enat @ ( times_7803423173614009249d_enat @ A @ C ) @ ( times_7803423173614009249d_enat @ B2 @ D ) ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_mono
% 3.82/4.03 thf(fact_2482_mult__mono,axiom,
% 3.82/4.03 ! [A: real,B2: real,C: real,D: real] :
% 3.82/4.03 ( ( ord_less_eq_real @ A @ B2 )
% 3.82/4.03 => ( ( ord_less_eq_real @ C @ D )
% 3.82/4.03 => ( ( ord_less_eq_real @ zero_zero_real @ B2 )
% 3.82/4.03 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B2 @ D ) ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_mono
% 3.82/4.03 thf(fact_2483_mult__mono,axiom,
% 3.82/4.03 ! [A: nat,B2: nat,C: nat,D: nat] :
% 3.82/4.03 ( ( ord_less_eq_nat @ A @ B2 )
% 3.82/4.03 => ( ( ord_less_eq_nat @ C @ D )
% 3.82/4.03 => ( ( ord_less_eq_nat @ zero_zero_nat @ B2 )
% 3.82/4.03 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 3.82/4.03 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B2 @ D ) ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_mono
% 3.82/4.03 thf(fact_2484_mult__mono,axiom,
% 3.82/4.03 ! [A: int,B2: int,C: int,D: int] :
% 3.82/4.03 ( ( ord_less_eq_int @ A @ B2 )
% 3.82/4.03 => ( ( ord_less_eq_int @ C @ D )
% 3.82/4.03 => ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 3.82/4.03 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 3.82/4.03 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B2 @ D ) ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_mono
% 3.82/4.03 thf(fact_2485_mult__mono_H,axiom,
% 3.82/4.03 ! [A: extended_enat,B2: extended_enat,C: extended_enat,D: extended_enat] :
% 3.82/4.03 ( ( ord_le2932123472753598470d_enat @ A @ B2 )
% 3.82/4.03 => ( ( ord_le2932123472753598470d_enat @ C @ D )
% 3.82/4.03 => ( ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ A )
% 3.82/4.03 => ( ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ C )
% 3.82/4.03 => ( ord_le2932123472753598470d_enat @ ( times_7803423173614009249d_enat @ A @ C ) @ ( times_7803423173614009249d_enat @ B2 @ D ) ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_mono'
% 3.82/4.03 thf(fact_2486_mult__mono_H,axiom,
% 3.82/4.03 ! [A: real,B2: real,C: real,D: real] :
% 3.82/4.03 ( ( ord_less_eq_real @ A @ B2 )
% 3.82/4.03 => ( ( ord_less_eq_real @ C @ D )
% 3.82/4.03 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 3.82/4.03 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B2 @ D ) ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_mono'
% 3.82/4.03 thf(fact_2487_mult__mono_H,axiom,
% 3.82/4.03 ! [A: nat,B2: nat,C: nat,D: nat] :
% 3.82/4.03 ( ( ord_less_eq_nat @ A @ B2 )
% 3.82/4.03 => ( ( ord_less_eq_nat @ C @ D )
% 3.82/4.03 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 3.82/4.03 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 3.82/4.03 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B2 @ D ) ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_mono'
% 3.82/4.03 thf(fact_2488_mult__mono_H,axiom,
% 3.82/4.03 ! [A: int,B2: int,C: int,D: int] :
% 3.82/4.03 ( ( ord_less_eq_int @ A @ B2 )
% 3.82/4.03 => ( ( ord_less_eq_int @ C @ D )
% 3.82/4.03 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 3.82/4.03 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 3.82/4.03 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B2 @ D ) ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_mono'
% 3.82/4.03 thf(fact_2489_zero__le__square,axiom,
% 3.82/4.03 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ A ) ) ).
% 3.82/4.03
% 3.82/4.03 % zero_le_square
% 3.82/4.03 thf(fact_2490_zero__le__square,axiom,
% 3.82/4.03 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ A ) ) ).
% 3.82/4.03
% 3.82/4.03 % zero_le_square
% 3.82/4.03 thf(fact_2491_split__mult__pos__le,axiom,
% 3.82/4.03 ! [A: real,B2: real] :
% 3.82/4.03 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 3.82/4.03 & ( ord_less_eq_real @ zero_zero_real @ B2 ) )
% 3.82/4.03 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 3.82/4.03 & ( ord_less_eq_real @ B2 @ zero_zero_real ) ) )
% 3.82/4.03 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % split_mult_pos_le
% 3.82/4.03 thf(fact_2492_split__mult__pos__le,axiom,
% 3.82/4.03 ! [A: int,B2: int] :
% 3.82/4.03 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 3.82/4.03 & ( ord_less_eq_int @ zero_zero_int @ B2 ) )
% 3.82/4.03 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 3.82/4.03 & ( ord_less_eq_int @ B2 @ zero_zero_int ) ) )
% 3.82/4.03 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % split_mult_pos_le
% 3.82/4.03 thf(fact_2493_mult__left__mono__neg,axiom,
% 3.82/4.03 ! [B2: real,A: real,C: real] :
% 3.82/4.03 ( ( ord_less_eq_real @ B2 @ A )
% 3.82/4.03 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 3.82/4.03 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_left_mono_neg
% 3.82/4.03 thf(fact_2494_mult__left__mono__neg,axiom,
% 3.82/4.03 ! [B2: int,A: int,C: int] :
% 3.82/4.03 ( ( ord_less_eq_int @ B2 @ A )
% 3.82/4.03 => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 3.82/4.03 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_left_mono_neg
% 3.82/4.03 thf(fact_2495_mult__nonpos__nonpos,axiom,
% 3.82/4.03 ! [A: real,B2: real] :
% 3.82/4.03 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 3.82/4.03 => ( ( ord_less_eq_real @ B2 @ zero_zero_real )
% 3.82/4.03 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_nonpos_nonpos
% 3.82/4.03 thf(fact_2496_mult__nonpos__nonpos,axiom,
% 3.82/4.03 ! [A: int,B2: int] :
% 3.82/4.03 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 3.82/4.03 => ( ( ord_less_eq_int @ B2 @ zero_zero_int )
% 3.82/4.03 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_nonpos_nonpos
% 3.82/4.03 thf(fact_2497_mult__left__mono,axiom,
% 3.82/4.03 ! [A: extended_enat,B2: extended_enat,C: extended_enat] :
% 3.82/4.03 ( ( ord_le2932123472753598470d_enat @ A @ B2 )
% 3.82/4.03 => ( ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ C )
% 3.82/4.03 => ( ord_le2932123472753598470d_enat @ ( times_7803423173614009249d_enat @ C @ A ) @ ( times_7803423173614009249d_enat @ C @ B2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_left_mono
% 3.82/4.03 thf(fact_2498_mult__left__mono,axiom,
% 3.82/4.03 ! [A: real,B2: real,C: real] :
% 3.82/4.03 ( ( ord_less_eq_real @ A @ B2 )
% 3.82/4.03 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_left_mono
% 3.82/4.03 thf(fact_2499_mult__left__mono,axiom,
% 3.82/4.03 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.03 ( ( ord_less_eq_nat @ A @ B2 )
% 3.82/4.03 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 3.82/4.03 => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_left_mono
% 3.82/4.03 thf(fact_2500_mult__left__mono,axiom,
% 3.82/4.03 ! [A: int,B2: int,C: int] :
% 3.82/4.03 ( ( ord_less_eq_int @ A @ B2 )
% 3.82/4.03 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 3.82/4.03 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_left_mono
% 3.82/4.03 thf(fact_2501_mult__right__mono__neg,axiom,
% 3.82/4.03 ! [B2: real,A: real,C: real] :
% 3.82/4.03 ( ( ord_less_eq_real @ B2 @ A )
% 3.82/4.03 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 3.82/4.03 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B2 @ C ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_right_mono_neg
% 3.82/4.03 thf(fact_2502_mult__right__mono__neg,axiom,
% 3.82/4.03 ! [B2: int,A: int,C: int] :
% 3.82/4.03 ( ( ord_less_eq_int @ B2 @ A )
% 3.82/4.03 => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 3.82/4.03 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B2 @ C ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_right_mono_neg
% 3.82/4.03 thf(fact_2503_mult__right__mono,axiom,
% 3.82/4.03 ! [A: extended_enat,B2: extended_enat,C: extended_enat] :
% 3.82/4.03 ( ( ord_le2932123472753598470d_enat @ A @ B2 )
% 3.82/4.03 => ( ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ C )
% 3.82/4.03 => ( ord_le2932123472753598470d_enat @ ( times_7803423173614009249d_enat @ A @ C ) @ ( times_7803423173614009249d_enat @ B2 @ C ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_right_mono
% 3.82/4.03 thf(fact_2504_mult__right__mono,axiom,
% 3.82/4.03 ! [A: real,B2: real,C: real] :
% 3.82/4.03 ( ( ord_less_eq_real @ A @ B2 )
% 3.82/4.03 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B2 @ C ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_right_mono
% 3.82/4.03 thf(fact_2505_mult__right__mono,axiom,
% 3.82/4.03 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.03 ( ( ord_less_eq_nat @ A @ B2 )
% 3.82/4.03 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 3.82/4.03 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B2 @ C ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_right_mono
% 3.82/4.03 thf(fact_2506_mult__right__mono,axiom,
% 3.82/4.03 ! [A: int,B2: int,C: int] :
% 3.82/4.03 ( ( ord_less_eq_int @ A @ B2 )
% 3.82/4.03 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 3.82/4.03 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B2 @ C ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_right_mono
% 3.82/4.03 thf(fact_2507_mult__le__0__iff,axiom,
% 3.82/4.03 ! [A: real,B2: real] :
% 3.82/4.03 ( ( ord_less_eq_real @ ( times_times_real @ A @ B2 ) @ zero_zero_real )
% 3.82/4.03 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 3.82/4.03 & ( ord_less_eq_real @ B2 @ zero_zero_real ) )
% 3.82/4.03 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 3.82/4.03 & ( ord_less_eq_real @ zero_zero_real @ B2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_le_0_iff
% 3.82/4.03 thf(fact_2508_mult__le__0__iff,axiom,
% 3.82/4.03 ! [A: int,B2: int] :
% 3.82/4.03 ( ( ord_less_eq_int @ ( times_times_int @ A @ B2 ) @ zero_zero_int )
% 3.82/4.03 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 3.82/4.03 & ( ord_less_eq_int @ B2 @ zero_zero_int ) )
% 3.82/4.03 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 3.82/4.03 & ( ord_less_eq_int @ zero_zero_int @ B2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_le_0_iff
% 3.82/4.03 thf(fact_2509_split__mult__neg__le,axiom,
% 3.82/4.03 ! [A: real,B2: real] :
% 3.82/4.03 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 3.82/4.03 & ( ord_less_eq_real @ B2 @ zero_zero_real ) )
% 3.82/4.03 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 3.82/4.03 & ( ord_less_eq_real @ zero_zero_real @ B2 ) ) )
% 3.82/4.03 => ( ord_less_eq_real @ ( times_times_real @ A @ B2 ) @ zero_zero_real ) ) ).
% 3.82/4.03
% 3.82/4.03 % split_mult_neg_le
% 3.82/4.03 thf(fact_2510_split__mult__neg__le,axiom,
% 3.82/4.03 ! [A: nat,B2: nat] :
% 3.82/4.03 ( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 3.82/4.03 & ( ord_less_eq_nat @ B2 @ zero_zero_nat ) )
% 3.82/4.03 | ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 3.82/4.03 & ( ord_less_eq_nat @ zero_zero_nat @ B2 ) ) )
% 3.82/4.03 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B2 ) @ zero_zero_nat ) ) ).
% 3.82/4.03
% 3.82/4.03 % split_mult_neg_le
% 3.82/4.03 thf(fact_2511_split__mult__neg__le,axiom,
% 3.82/4.03 ! [A: int,B2: int] :
% 3.82/4.03 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 3.82/4.03 & ( ord_less_eq_int @ B2 @ zero_zero_int ) )
% 3.82/4.03 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 3.82/4.03 & ( ord_less_eq_int @ zero_zero_int @ B2 ) ) )
% 3.82/4.03 => ( ord_less_eq_int @ ( times_times_int @ A @ B2 ) @ zero_zero_int ) ) ).
% 3.82/4.03
% 3.82/4.03 % split_mult_neg_le
% 3.82/4.03 thf(fact_2512_mult__nonneg__nonneg,axiom,
% 3.82/4.03 ! [A: real,B2: real] :
% 3.82/4.03 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 3.82/4.03 => ( ( ord_less_eq_real @ zero_zero_real @ B2 )
% 3.82/4.03 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_nonneg_nonneg
% 3.82/4.03 thf(fact_2513_mult__nonneg__nonneg,axiom,
% 3.82/4.03 ! [A: nat,B2: nat] :
% 3.82/4.03 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 3.82/4.03 => ( ( ord_less_eq_nat @ zero_zero_nat @ B2 )
% 3.82/4.03 => ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A @ B2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_nonneg_nonneg
% 3.82/4.03 thf(fact_2514_mult__nonneg__nonneg,axiom,
% 3.82/4.03 ! [A: int,B2: int] :
% 3.82/4.03 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 3.82/4.03 => ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 3.82/4.03 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_nonneg_nonneg
% 3.82/4.03 thf(fact_2515_mult__nonneg__nonpos,axiom,
% 3.82/4.03 ! [A: real,B2: real] :
% 3.82/4.03 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 3.82/4.03 => ( ( ord_less_eq_real @ B2 @ zero_zero_real )
% 3.82/4.03 => ( ord_less_eq_real @ ( times_times_real @ A @ B2 ) @ zero_zero_real ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_nonneg_nonpos
% 3.82/4.03 thf(fact_2516_mult__nonneg__nonpos,axiom,
% 3.82/4.03 ! [A: nat,B2: nat] :
% 3.82/4.03 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 3.82/4.03 => ( ( ord_less_eq_nat @ B2 @ zero_zero_nat )
% 3.82/4.03 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B2 ) @ zero_zero_nat ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_nonneg_nonpos
% 3.82/4.03 thf(fact_2517_mult__nonneg__nonpos,axiom,
% 3.82/4.03 ! [A: int,B2: int] :
% 3.82/4.03 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 3.82/4.03 => ( ( ord_less_eq_int @ B2 @ zero_zero_int )
% 3.82/4.03 => ( ord_less_eq_int @ ( times_times_int @ A @ B2 ) @ zero_zero_int ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_nonneg_nonpos
% 3.82/4.03 thf(fact_2518_mult__nonpos__nonneg,axiom,
% 3.82/4.03 ! [A: real,B2: real] :
% 3.82/4.03 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 3.82/4.03 => ( ( ord_less_eq_real @ zero_zero_real @ B2 )
% 3.82/4.03 => ( ord_less_eq_real @ ( times_times_real @ A @ B2 ) @ zero_zero_real ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_nonpos_nonneg
% 3.82/4.03 thf(fact_2519_mult__nonpos__nonneg,axiom,
% 3.82/4.03 ! [A: nat,B2: nat] :
% 3.82/4.03 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 3.82/4.03 => ( ( ord_less_eq_nat @ zero_zero_nat @ B2 )
% 3.82/4.03 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B2 ) @ zero_zero_nat ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_nonpos_nonneg
% 3.82/4.03 thf(fact_2520_mult__nonpos__nonneg,axiom,
% 3.82/4.03 ! [A: int,B2: int] :
% 3.82/4.03 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 3.82/4.03 => ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 3.82/4.03 => ( ord_less_eq_int @ ( times_times_int @ A @ B2 ) @ zero_zero_int ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_nonpos_nonneg
% 3.82/4.03 thf(fact_2521_mult__nonneg__nonpos2,axiom,
% 3.82/4.03 ! [A: real,B2: real] :
% 3.82/4.03 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 3.82/4.03 => ( ( ord_less_eq_real @ B2 @ zero_zero_real )
% 3.82/4.03 => ( ord_less_eq_real @ ( times_times_real @ B2 @ A ) @ zero_zero_real ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_nonneg_nonpos2
% 3.82/4.03 thf(fact_2522_mult__nonneg__nonpos2,axiom,
% 3.82/4.03 ! [A: nat,B2: nat] :
% 3.82/4.03 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 3.82/4.03 => ( ( ord_less_eq_nat @ B2 @ zero_zero_nat )
% 3.82/4.03 => ( ord_less_eq_nat @ ( times_times_nat @ B2 @ A ) @ zero_zero_nat ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_nonneg_nonpos2
% 3.82/4.03 thf(fact_2523_mult__nonneg__nonpos2,axiom,
% 3.82/4.03 ! [A: int,B2: int] :
% 3.82/4.03 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 3.82/4.03 => ( ( ord_less_eq_int @ B2 @ zero_zero_int )
% 3.82/4.03 => ( ord_less_eq_int @ ( times_times_int @ B2 @ A ) @ zero_zero_int ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_nonneg_nonpos2
% 3.82/4.03 thf(fact_2524_zero__le__mult__iff,axiom,
% 3.82/4.03 ! [A: real,B2: real] :
% 3.82/4.03 ( ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B2 ) )
% 3.82/4.03 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 3.82/4.03 & ( ord_less_eq_real @ zero_zero_real @ B2 ) )
% 3.82/4.03 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 3.82/4.03 & ( ord_less_eq_real @ B2 @ zero_zero_real ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % zero_le_mult_iff
% 3.82/4.03 thf(fact_2525_zero__le__mult__iff,axiom,
% 3.82/4.03 ! [A: int,B2: int] :
% 3.82/4.03 ( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B2 ) )
% 3.82/4.03 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 3.82/4.03 & ( ord_less_eq_int @ zero_zero_int @ B2 ) )
% 3.82/4.03 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 3.82/4.03 & ( ord_less_eq_int @ B2 @ zero_zero_int ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % zero_le_mult_iff
% 3.82/4.03 thf(fact_2526_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 3.82/4.03 ! [A: extended_enat,B2: extended_enat,C: extended_enat] :
% 3.82/4.03 ( ( ord_le2932123472753598470d_enat @ A @ B2 )
% 3.82/4.03 => ( ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ C )
% 3.82/4.03 => ( ord_le2932123472753598470d_enat @ ( times_7803423173614009249d_enat @ C @ A ) @ ( times_7803423173614009249d_enat @ C @ B2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % ordered_comm_semiring_class.comm_mult_left_mono
% 3.82/4.03 thf(fact_2527_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 3.82/4.03 ! [A: real,B2: real,C: real] :
% 3.82/4.03 ( ( ord_less_eq_real @ A @ B2 )
% 3.82/4.03 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % ordered_comm_semiring_class.comm_mult_left_mono
% 3.82/4.03 thf(fact_2528_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 3.82/4.03 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.03 ( ( ord_less_eq_nat @ A @ B2 )
% 3.82/4.03 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 3.82/4.03 => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % ordered_comm_semiring_class.comm_mult_left_mono
% 3.82/4.03 thf(fact_2529_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 3.82/4.03 ! [A: int,B2: int,C: int] :
% 3.82/4.03 ( ( ord_less_eq_int @ A @ B2 )
% 3.82/4.03 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 3.82/4.03 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % ordered_comm_semiring_class.comm_mult_left_mono
% 3.82/4.03 thf(fact_2530_mult__neg__neg,axiom,
% 3.82/4.03 ! [A: real,B2: real] :
% 3.82/4.03 ( ( ord_less_real @ A @ zero_zero_real )
% 3.82/4.03 => ( ( ord_less_real @ B2 @ zero_zero_real )
% 3.82/4.03 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_neg_neg
% 3.82/4.03 thf(fact_2531_mult__neg__neg,axiom,
% 3.82/4.03 ! [A: int,B2: int] :
% 3.82/4.03 ( ( ord_less_int @ A @ zero_zero_int )
% 3.82/4.03 => ( ( ord_less_int @ B2 @ zero_zero_int )
% 3.82/4.03 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_neg_neg
% 3.82/4.03 thf(fact_2532_not__square__less__zero,axiom,
% 3.82/4.03 ! [A: real] :
% 3.82/4.03 ~ ( ord_less_real @ ( times_times_real @ A @ A ) @ zero_zero_real ) ).
% 3.82/4.03
% 3.82/4.03 % not_square_less_zero
% 3.82/4.03 thf(fact_2533_not__square__less__zero,axiom,
% 3.82/4.03 ! [A: int] :
% 3.82/4.03 ~ ( ord_less_int @ ( times_times_int @ A @ A ) @ zero_zero_int ) ).
% 3.82/4.03
% 3.82/4.03 % not_square_less_zero
% 3.82/4.03 thf(fact_2534_mult__less__0__iff,axiom,
% 3.82/4.03 ! [A: real,B2: real] :
% 3.82/4.03 ( ( ord_less_real @ ( times_times_real @ A @ B2 ) @ zero_zero_real )
% 3.82/4.03 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 3.82/4.03 & ( ord_less_real @ B2 @ zero_zero_real ) )
% 3.82/4.03 | ( ( ord_less_real @ A @ zero_zero_real )
% 3.82/4.03 & ( ord_less_real @ zero_zero_real @ B2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_less_0_iff
% 3.82/4.03 thf(fact_2535_mult__less__0__iff,axiom,
% 3.82/4.03 ! [A: int,B2: int] :
% 3.82/4.03 ( ( ord_less_int @ ( times_times_int @ A @ B2 ) @ zero_zero_int )
% 3.82/4.03 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 3.82/4.03 & ( ord_less_int @ B2 @ zero_zero_int ) )
% 3.82/4.03 | ( ( ord_less_int @ A @ zero_zero_int )
% 3.82/4.03 & ( ord_less_int @ zero_zero_int @ B2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_less_0_iff
% 3.82/4.03 thf(fact_2536_mult__neg__pos,axiom,
% 3.82/4.03 ! [A: nat,B2: nat] :
% 3.82/4.03 ( ( ord_less_nat @ A @ zero_zero_nat )
% 3.82/4.03 => ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 3.82/4.03 => ( ord_less_nat @ ( times_times_nat @ A @ B2 ) @ zero_zero_nat ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_neg_pos
% 3.82/4.03 thf(fact_2537_mult__neg__pos,axiom,
% 3.82/4.03 ! [A: real,B2: real] :
% 3.82/4.03 ( ( ord_less_real @ A @ zero_zero_real )
% 3.82/4.03 => ( ( ord_less_real @ zero_zero_real @ B2 )
% 3.82/4.03 => ( ord_less_real @ ( times_times_real @ A @ B2 ) @ zero_zero_real ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_neg_pos
% 3.82/4.03 thf(fact_2538_mult__neg__pos,axiom,
% 3.82/4.03 ! [A: int,B2: int] :
% 3.82/4.03 ( ( ord_less_int @ A @ zero_zero_int )
% 3.82/4.03 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 3.82/4.03 => ( ord_less_int @ ( times_times_int @ A @ B2 ) @ zero_zero_int ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_neg_pos
% 3.82/4.03 thf(fact_2539_mult__pos__neg,axiom,
% 3.82/4.03 ! [A: nat,B2: nat] :
% 3.82/4.03 ( ( ord_less_nat @ zero_zero_nat @ A )
% 3.82/4.03 => ( ( ord_less_nat @ B2 @ zero_zero_nat )
% 3.82/4.03 => ( ord_less_nat @ ( times_times_nat @ A @ B2 ) @ zero_zero_nat ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_pos_neg
% 3.82/4.03 thf(fact_2540_mult__pos__neg,axiom,
% 3.82/4.03 ! [A: real,B2: real] :
% 3.82/4.03 ( ( ord_less_real @ zero_zero_real @ A )
% 3.82/4.03 => ( ( ord_less_real @ B2 @ zero_zero_real )
% 3.82/4.03 => ( ord_less_real @ ( times_times_real @ A @ B2 ) @ zero_zero_real ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_pos_neg
% 3.82/4.03 thf(fact_2541_mult__pos__neg,axiom,
% 3.82/4.03 ! [A: int,B2: int] :
% 3.82/4.03 ( ( ord_less_int @ zero_zero_int @ A )
% 3.82/4.03 => ( ( ord_less_int @ B2 @ zero_zero_int )
% 3.82/4.03 => ( ord_less_int @ ( times_times_int @ A @ B2 ) @ zero_zero_int ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_pos_neg
% 3.82/4.03 thf(fact_2542_mult__pos__pos,axiom,
% 3.82/4.03 ! [A: nat,B2: nat] :
% 3.82/4.03 ( ( ord_less_nat @ zero_zero_nat @ A )
% 3.82/4.03 => ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 3.82/4.03 => ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_pos_pos
% 3.82/4.03 thf(fact_2543_mult__pos__pos,axiom,
% 3.82/4.03 ! [A: real,B2: real] :
% 3.82/4.03 ( ( ord_less_real @ zero_zero_real @ A )
% 3.82/4.03 => ( ( ord_less_real @ zero_zero_real @ B2 )
% 3.82/4.03 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_pos_pos
% 3.82/4.03 thf(fact_2544_mult__pos__pos,axiom,
% 3.82/4.03 ! [A: int,B2: int] :
% 3.82/4.03 ( ( ord_less_int @ zero_zero_int @ A )
% 3.82/4.03 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 3.82/4.03 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_pos_pos
% 3.82/4.03 thf(fact_2545_mult__pos__neg2,axiom,
% 3.82/4.03 ! [A: nat,B2: nat] :
% 3.82/4.03 ( ( ord_less_nat @ zero_zero_nat @ A )
% 3.82/4.03 => ( ( ord_less_nat @ B2 @ zero_zero_nat )
% 3.82/4.03 => ( ord_less_nat @ ( times_times_nat @ B2 @ A ) @ zero_zero_nat ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_pos_neg2
% 3.82/4.03 thf(fact_2546_mult__pos__neg2,axiom,
% 3.82/4.03 ! [A: real,B2: real] :
% 3.82/4.03 ( ( ord_less_real @ zero_zero_real @ A )
% 3.82/4.03 => ( ( ord_less_real @ B2 @ zero_zero_real )
% 3.82/4.03 => ( ord_less_real @ ( times_times_real @ B2 @ A ) @ zero_zero_real ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_pos_neg2
% 3.82/4.03 thf(fact_2547_mult__pos__neg2,axiom,
% 3.82/4.03 ! [A: int,B2: int] :
% 3.82/4.03 ( ( ord_less_int @ zero_zero_int @ A )
% 3.82/4.03 => ( ( ord_less_int @ B2 @ zero_zero_int )
% 3.82/4.03 => ( ord_less_int @ ( times_times_int @ B2 @ A ) @ zero_zero_int ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_pos_neg2
% 3.82/4.03 thf(fact_2548_zero__less__mult__iff,axiom,
% 3.82/4.03 ! [A: real,B2: real] :
% 3.82/4.03 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B2 ) )
% 3.82/4.03 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 3.82/4.03 & ( ord_less_real @ zero_zero_real @ B2 ) )
% 3.82/4.03 | ( ( ord_less_real @ A @ zero_zero_real )
% 3.82/4.03 & ( ord_less_real @ B2 @ zero_zero_real ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % zero_less_mult_iff
% 3.82/4.03 thf(fact_2549_zero__less__mult__iff,axiom,
% 3.82/4.03 ! [A: int,B2: int] :
% 3.82/4.03 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B2 ) )
% 3.82/4.03 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 3.82/4.03 & ( ord_less_int @ zero_zero_int @ B2 ) )
% 3.82/4.03 | ( ( ord_less_int @ A @ zero_zero_int )
% 3.82/4.03 & ( ord_less_int @ B2 @ zero_zero_int ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % zero_less_mult_iff
% 3.82/4.03 thf(fact_2550_zero__less__mult__pos,axiom,
% 3.82/4.03 ! [A: nat,B2: nat] :
% 3.82/4.03 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B2 ) )
% 3.82/4.03 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 3.82/4.03 => ( ord_less_nat @ zero_zero_nat @ B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % zero_less_mult_pos
% 3.82/4.03 thf(fact_2551_zero__less__mult__pos,axiom,
% 3.82/4.03 ! [A: real,B2: real] :
% 3.82/4.03 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B2 ) )
% 3.82/4.03 => ( ( ord_less_real @ zero_zero_real @ A )
% 3.82/4.03 => ( ord_less_real @ zero_zero_real @ B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % zero_less_mult_pos
% 3.82/4.03 thf(fact_2552_zero__less__mult__pos,axiom,
% 3.82/4.03 ! [A: int,B2: int] :
% 3.82/4.03 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B2 ) )
% 3.82/4.03 => ( ( ord_less_int @ zero_zero_int @ A )
% 3.82/4.03 => ( ord_less_int @ zero_zero_int @ B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % zero_less_mult_pos
% 3.82/4.03 thf(fact_2553_zero__less__mult__pos2,axiom,
% 3.82/4.03 ! [B2: nat,A: nat] :
% 3.82/4.03 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ B2 @ A ) )
% 3.82/4.03 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 3.82/4.03 => ( ord_less_nat @ zero_zero_nat @ B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % zero_less_mult_pos2
% 3.82/4.03 thf(fact_2554_zero__less__mult__pos2,axiom,
% 3.82/4.03 ! [B2: real,A: real] :
% 3.82/4.03 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ B2 @ A ) )
% 3.82/4.03 => ( ( ord_less_real @ zero_zero_real @ A )
% 3.82/4.03 => ( ord_less_real @ zero_zero_real @ B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % zero_less_mult_pos2
% 3.82/4.03 thf(fact_2555_zero__less__mult__pos2,axiom,
% 3.82/4.03 ! [B2: int,A: int] :
% 3.82/4.03 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B2 @ A ) )
% 3.82/4.03 => ( ( ord_less_int @ zero_zero_int @ A )
% 3.82/4.03 => ( ord_less_int @ zero_zero_int @ B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % zero_less_mult_pos2
% 3.82/4.03 thf(fact_2556_mult__less__cancel__left__neg,axiom,
% 3.82/4.03 ! [C: real,A: real,B2: real] :
% 3.82/4.03 ( ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.03 => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B2 ) )
% 3.82/4.03 = ( ord_less_real @ B2 @ A ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_less_cancel_left_neg
% 3.82/4.03 thf(fact_2557_mult__less__cancel__left__neg,axiom,
% 3.82/4.03 ! [C: int,A: int,B2: int] :
% 3.82/4.03 ( ( ord_less_int @ C @ zero_zero_int )
% 3.82/4.03 => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B2 ) )
% 3.82/4.03 = ( ord_less_int @ B2 @ A ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_less_cancel_left_neg
% 3.82/4.03 thf(fact_2558_mult__less__cancel__left__pos,axiom,
% 3.82/4.03 ! [C: real,A: real,B2: real] :
% 3.82/4.03 ( ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B2 ) )
% 3.82/4.03 = ( ord_less_real @ A @ B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_less_cancel_left_pos
% 3.82/4.03 thf(fact_2559_mult__less__cancel__left__pos,axiom,
% 3.82/4.03 ! [C: int,A: int,B2: int] :
% 3.82/4.03 ( ( ord_less_int @ zero_zero_int @ C )
% 3.82/4.03 => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B2 ) )
% 3.82/4.03 = ( ord_less_int @ A @ B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_less_cancel_left_pos
% 3.82/4.03 thf(fact_2560_mult__strict__left__mono__neg,axiom,
% 3.82/4.03 ! [B2: real,A: real,C: real] :
% 3.82/4.03 ( ( ord_less_real @ B2 @ A )
% 3.82/4.03 => ( ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.03 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_strict_left_mono_neg
% 3.82/4.03 thf(fact_2561_mult__strict__left__mono__neg,axiom,
% 3.82/4.03 ! [B2: int,A: int,C: int] :
% 3.82/4.03 ( ( ord_less_int @ B2 @ A )
% 3.82/4.03 => ( ( ord_less_int @ C @ zero_zero_int )
% 3.82/4.03 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_strict_left_mono_neg
% 3.82/4.03 thf(fact_2562_mult__strict__left__mono,axiom,
% 3.82/4.03 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.03 ( ( ord_less_nat @ A @ B2 )
% 3.82/4.03 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 3.82/4.03 => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_strict_left_mono
% 3.82/4.03 thf(fact_2563_mult__strict__left__mono,axiom,
% 3.82/4.03 ! [A: real,B2: real,C: real] :
% 3.82/4.03 ( ( ord_less_real @ A @ B2 )
% 3.82/4.03 => ( ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_strict_left_mono
% 3.82/4.03 thf(fact_2564_mult__strict__left__mono,axiom,
% 3.82/4.03 ! [A: int,B2: int,C: int] :
% 3.82/4.03 ( ( ord_less_int @ A @ B2 )
% 3.82/4.03 => ( ( ord_less_int @ zero_zero_int @ C )
% 3.82/4.03 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_strict_left_mono
% 3.82/4.03 thf(fact_2565_mult__less__cancel__left__disj,axiom,
% 3.82/4.03 ! [C: real,A: real,B2: real] :
% 3.82/4.03 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B2 ) )
% 3.82/4.03 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.03 & ( ord_less_real @ A @ B2 ) )
% 3.82/4.03 | ( ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.03 & ( ord_less_real @ B2 @ A ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_less_cancel_left_disj
% 3.82/4.03 thf(fact_2566_mult__less__cancel__left__disj,axiom,
% 3.82/4.03 ! [C: int,A: int,B2: int] :
% 3.82/4.03 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B2 ) )
% 3.82/4.03 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 3.82/4.03 & ( ord_less_int @ A @ B2 ) )
% 3.82/4.03 | ( ( ord_less_int @ C @ zero_zero_int )
% 3.82/4.03 & ( ord_less_int @ B2 @ A ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_less_cancel_left_disj
% 3.82/4.03 thf(fact_2567_mult__strict__right__mono__neg,axiom,
% 3.82/4.03 ! [B2: real,A: real,C: real] :
% 3.82/4.03 ( ( ord_less_real @ B2 @ A )
% 3.82/4.03 => ( ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.03 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B2 @ C ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_strict_right_mono_neg
% 3.82/4.03 thf(fact_2568_mult__strict__right__mono__neg,axiom,
% 3.82/4.03 ! [B2: int,A: int,C: int] :
% 3.82/4.03 ( ( ord_less_int @ B2 @ A )
% 3.82/4.03 => ( ( ord_less_int @ C @ zero_zero_int )
% 3.82/4.03 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B2 @ C ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_strict_right_mono_neg
% 3.82/4.03 thf(fact_2569_mult__strict__right__mono,axiom,
% 3.82/4.03 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.03 ( ( ord_less_nat @ A @ B2 )
% 3.82/4.03 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 3.82/4.03 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B2 @ C ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_strict_right_mono
% 3.82/4.03 thf(fact_2570_mult__strict__right__mono,axiom,
% 3.82/4.03 ! [A: real,B2: real,C: real] :
% 3.82/4.03 ( ( ord_less_real @ A @ B2 )
% 3.82/4.03 => ( ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B2 @ C ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_strict_right_mono
% 3.82/4.03 thf(fact_2571_mult__strict__right__mono,axiom,
% 3.82/4.03 ! [A: int,B2: int,C: int] :
% 3.82/4.03 ( ( ord_less_int @ A @ B2 )
% 3.82/4.03 => ( ( ord_less_int @ zero_zero_int @ C )
% 3.82/4.03 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B2 @ C ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_strict_right_mono
% 3.82/4.03 thf(fact_2572_mult__less__cancel__right__disj,axiom,
% 3.82/4.03 ! [A: real,C: real,B2: real] :
% 3.82/4.03 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B2 @ C ) )
% 3.82/4.03 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.03 & ( ord_less_real @ A @ B2 ) )
% 3.82/4.03 | ( ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.03 & ( ord_less_real @ B2 @ A ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_less_cancel_right_disj
% 3.82/4.03 thf(fact_2573_mult__less__cancel__right__disj,axiom,
% 3.82/4.03 ! [A: int,C: int,B2: int] :
% 3.82/4.03 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B2 @ C ) )
% 3.82/4.03 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 3.82/4.03 & ( ord_less_int @ A @ B2 ) )
% 3.82/4.03 | ( ( ord_less_int @ C @ zero_zero_int )
% 3.82/4.03 & ( ord_less_int @ B2 @ A ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_less_cancel_right_disj
% 3.82/4.03 thf(fact_2574_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 3.82/4.03 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.03 ( ( ord_less_nat @ A @ B2 )
% 3.82/4.03 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 3.82/4.03 => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 3.82/4.03 thf(fact_2575_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 3.82/4.03 ! [A: real,B2: real,C: real] :
% 3.82/4.03 ( ( ord_less_real @ A @ B2 )
% 3.82/4.03 => ( ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 3.82/4.03 thf(fact_2576_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 3.82/4.03 ! [A: int,B2: int,C: int] :
% 3.82/4.03 ( ( ord_less_int @ A @ B2 )
% 3.82/4.03 => ( ( ord_less_int @ zero_zero_int @ C )
% 3.82/4.03 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 3.82/4.03 thf(fact_2577_add__scale__eq__noteq,axiom,
% 3.82/4.03 ! [R2: nat,A: nat,B2: nat,C: nat,D: nat] :
% 3.82/4.03 ( ( R2 != zero_zero_nat )
% 3.82/4.03 => ( ( ( A = B2 )
% 3.82/4.03 & ( C != D ) )
% 3.82/4.03 => ( ( plus_plus_nat @ A @ ( times_times_nat @ R2 @ C ) )
% 3.82/4.03 != ( plus_plus_nat @ B2 @ ( times_times_nat @ R2 @ D ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % add_scale_eq_noteq
% 3.82/4.03 thf(fact_2578_add__scale__eq__noteq,axiom,
% 3.82/4.03 ! [R2: int,A: int,B2: int,C: int,D: int] :
% 3.82/4.03 ( ( R2 != zero_zero_int )
% 3.82/4.03 => ( ( ( A = B2 )
% 3.82/4.03 & ( C != D ) )
% 3.82/4.03 => ( ( plus_plus_int @ A @ ( times_times_int @ R2 @ C ) )
% 3.82/4.03 != ( plus_plus_int @ B2 @ ( times_times_int @ R2 @ D ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % add_scale_eq_noteq
% 3.82/4.03 thf(fact_2579_add__scale__eq__noteq,axiom,
% 3.82/4.03 ! [R2: real,A: real,B2: real,C: real,D: real] :
% 3.82/4.03 ( ( R2 != zero_zero_real )
% 3.82/4.03 => ( ( ( A = B2 )
% 3.82/4.03 & ( C != D ) )
% 3.82/4.03 => ( ( plus_plus_real @ A @ ( times_times_real @ R2 @ C ) )
% 3.82/4.03 != ( plus_plus_real @ B2 @ ( times_times_real @ R2 @ D ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % add_scale_eq_noteq
% 3.82/4.03 thf(fact_2580_add__scale__eq__noteq,axiom,
% 3.82/4.03 ! [R2: complex,A: complex,B2: complex,C: complex,D: complex] :
% 3.82/4.03 ( ( R2 != zero_zero_complex )
% 3.82/4.03 => ( ( ( A = B2 )
% 3.82/4.03 & ( C != D ) )
% 3.82/4.03 => ( ( plus_plus_complex @ A @ ( times_times_complex @ R2 @ C ) )
% 3.82/4.03 != ( plus_plus_complex @ B2 @ ( times_times_complex @ R2 @ D ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % add_scale_eq_noteq
% 3.82/4.03 thf(fact_2581_less__1__mult,axiom,
% 3.82/4.03 ! [M2: nat,N2: nat] :
% 3.82/4.03 ( ( ord_less_nat @ one_one_nat @ M2 )
% 3.82/4.03 => ( ( ord_less_nat @ one_one_nat @ N2 )
% 3.82/4.03 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ M2 @ N2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % less_1_mult
% 3.82/4.03 thf(fact_2582_less__1__mult,axiom,
% 3.82/4.03 ! [M2: real,N2: real] :
% 3.82/4.03 ( ( ord_less_real @ one_one_real @ M2 )
% 3.82/4.03 => ( ( ord_less_real @ one_one_real @ N2 )
% 3.82/4.03 => ( ord_less_real @ one_one_real @ ( times_times_real @ M2 @ N2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % less_1_mult
% 3.82/4.03 thf(fact_2583_less__1__mult,axiom,
% 3.82/4.03 ! [M2: int,N2: int] :
% 3.82/4.03 ( ( ord_less_int @ one_one_int @ M2 )
% 3.82/4.03 => ( ( ord_less_int @ one_one_int @ N2 )
% 3.82/4.03 => ( ord_less_int @ one_one_int @ ( times_times_int @ M2 @ N2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % less_1_mult
% 3.82/4.03 thf(fact_2584_frac__eq__eq,axiom,
% 3.82/4.03 ! [Y: complex,Z3: complex,X: complex,W2: complex] :
% 3.82/4.03 ( ( Y != zero_zero_complex )
% 3.82/4.03 => ( ( Z3 != zero_zero_complex )
% 3.82/4.03 => ( ( ( divide1717551699836669952omplex @ X @ Y )
% 3.82/4.03 = ( divide1717551699836669952omplex @ W2 @ Z3 ) )
% 3.82/4.03 = ( ( times_times_complex @ X @ Z3 )
% 3.82/4.03 = ( times_times_complex @ W2 @ Y ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % frac_eq_eq
% 3.82/4.03 thf(fact_2585_frac__eq__eq,axiom,
% 3.82/4.03 ! [Y: real,Z3: real,X: real,W2: real] :
% 3.82/4.03 ( ( Y != zero_zero_real )
% 3.82/4.03 => ( ( Z3 != zero_zero_real )
% 3.82/4.03 => ( ( ( divide_divide_real @ X @ Y )
% 3.82/4.03 = ( divide_divide_real @ W2 @ Z3 ) )
% 3.82/4.03 = ( ( times_times_real @ X @ Z3 )
% 3.82/4.03 = ( times_times_real @ W2 @ Y ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % frac_eq_eq
% 3.82/4.03 thf(fact_2586_divide__eq__eq,axiom,
% 3.82/4.03 ! [B2: complex,C: complex,A: complex] :
% 3.82/4.03 ( ( ( divide1717551699836669952omplex @ B2 @ C )
% 3.82/4.03 = A )
% 3.82/4.03 = ( ( ( C != zero_zero_complex )
% 3.82/4.03 => ( B2
% 3.82/4.03 = ( times_times_complex @ A @ C ) ) )
% 3.82/4.03 & ( ( C = zero_zero_complex )
% 3.82/4.03 => ( A = zero_zero_complex ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % divide_eq_eq
% 3.82/4.03 thf(fact_2587_divide__eq__eq,axiom,
% 3.82/4.03 ! [B2: real,C: real,A: real] :
% 3.82/4.03 ( ( ( divide_divide_real @ B2 @ C )
% 3.82/4.03 = A )
% 3.82/4.03 = ( ( ( C != zero_zero_real )
% 3.82/4.03 => ( B2
% 3.82/4.03 = ( times_times_real @ A @ C ) ) )
% 3.82/4.03 & ( ( C = zero_zero_real )
% 3.82/4.03 => ( A = zero_zero_real ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % divide_eq_eq
% 3.82/4.03 thf(fact_2588_eq__divide__eq,axiom,
% 3.82/4.03 ! [A: complex,B2: complex,C: complex] :
% 3.82/4.03 ( ( A
% 3.82/4.03 = ( divide1717551699836669952omplex @ B2 @ C ) )
% 3.82/4.03 = ( ( ( C != zero_zero_complex )
% 3.82/4.03 => ( ( times_times_complex @ A @ C )
% 3.82/4.03 = B2 ) )
% 3.82/4.03 & ( ( C = zero_zero_complex )
% 3.82/4.03 => ( A = zero_zero_complex ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % eq_divide_eq
% 3.82/4.03 thf(fact_2589_eq__divide__eq,axiom,
% 3.82/4.03 ! [A: real,B2: real,C: real] :
% 3.82/4.03 ( ( A
% 3.82/4.03 = ( divide_divide_real @ B2 @ C ) )
% 3.82/4.03 = ( ( ( C != zero_zero_real )
% 3.82/4.03 => ( ( times_times_real @ A @ C )
% 3.82/4.03 = B2 ) )
% 3.82/4.03 & ( ( C = zero_zero_real )
% 3.82/4.03 => ( A = zero_zero_real ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % eq_divide_eq
% 3.82/4.03 thf(fact_2590_divide__eq__imp,axiom,
% 3.82/4.03 ! [C: complex,B2: complex,A: complex] :
% 3.82/4.03 ( ( C != zero_zero_complex )
% 3.82/4.03 => ( ( B2
% 3.82/4.03 = ( times_times_complex @ A @ C ) )
% 3.82/4.03 => ( ( divide1717551699836669952omplex @ B2 @ C )
% 3.82/4.03 = A ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % divide_eq_imp
% 3.82/4.03 thf(fact_2591_divide__eq__imp,axiom,
% 3.82/4.03 ! [C: real,B2: real,A: real] :
% 3.82/4.03 ( ( C != zero_zero_real )
% 3.82/4.03 => ( ( B2
% 3.82/4.03 = ( times_times_real @ A @ C ) )
% 3.82/4.03 => ( ( divide_divide_real @ B2 @ C )
% 3.82/4.03 = A ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % divide_eq_imp
% 3.82/4.03 thf(fact_2592_eq__divide__imp,axiom,
% 3.82/4.03 ! [C: complex,A: complex,B2: complex] :
% 3.82/4.03 ( ( C != zero_zero_complex )
% 3.82/4.03 => ( ( ( times_times_complex @ A @ C )
% 3.82/4.03 = B2 )
% 3.82/4.03 => ( A
% 3.82/4.03 = ( divide1717551699836669952omplex @ B2 @ C ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % eq_divide_imp
% 3.82/4.03 thf(fact_2593_eq__divide__imp,axiom,
% 3.82/4.03 ! [C: real,A: real,B2: real] :
% 3.82/4.03 ( ( C != zero_zero_real )
% 3.82/4.03 => ( ( ( times_times_real @ A @ C )
% 3.82/4.03 = B2 )
% 3.82/4.03 => ( A
% 3.82/4.03 = ( divide_divide_real @ B2 @ C ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % eq_divide_imp
% 3.82/4.03 thf(fact_2594_nonzero__divide__eq__eq,axiom,
% 3.82/4.03 ! [C: complex,B2: complex,A: complex] :
% 3.82/4.03 ( ( C != zero_zero_complex )
% 3.82/4.03 => ( ( ( divide1717551699836669952omplex @ B2 @ C )
% 3.82/4.03 = A )
% 3.82/4.03 = ( B2
% 3.82/4.03 = ( times_times_complex @ A @ C ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % nonzero_divide_eq_eq
% 3.82/4.03 thf(fact_2595_nonzero__divide__eq__eq,axiom,
% 3.82/4.03 ! [C: real,B2: real,A: real] :
% 3.82/4.03 ( ( C != zero_zero_real )
% 3.82/4.03 => ( ( ( divide_divide_real @ B2 @ C )
% 3.82/4.03 = A )
% 3.82/4.03 = ( B2
% 3.82/4.03 = ( times_times_real @ A @ C ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % nonzero_divide_eq_eq
% 3.82/4.03 thf(fact_2596_nonzero__eq__divide__eq,axiom,
% 3.82/4.03 ! [C: complex,A: complex,B2: complex] :
% 3.82/4.03 ( ( C != zero_zero_complex )
% 3.82/4.03 => ( ( A
% 3.82/4.03 = ( divide1717551699836669952omplex @ B2 @ C ) )
% 3.82/4.03 = ( ( times_times_complex @ A @ C )
% 3.82/4.03 = B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % nonzero_eq_divide_eq
% 3.82/4.03 thf(fact_2597_nonzero__eq__divide__eq,axiom,
% 3.82/4.03 ! [C: real,A: real,B2: real] :
% 3.82/4.03 ( ( C != zero_zero_real )
% 3.82/4.03 => ( ( A
% 3.82/4.03 = ( divide_divide_real @ B2 @ C ) )
% 3.82/4.03 = ( ( times_times_real @ A @ C )
% 3.82/4.03 = B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % nonzero_eq_divide_eq
% 3.82/4.03 thf(fact_2598_power__Suc,axiom,
% 3.82/4.03 ! [A: nat,N2: nat] :
% 3.82/4.03 ( ( power_power_nat @ A @ ( suc @ N2 ) )
% 3.82/4.03 = ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_Suc
% 3.82/4.03 thf(fact_2599_power__Suc,axiom,
% 3.82/4.03 ! [A: int,N2: nat] :
% 3.82/4.03 ( ( power_power_int @ A @ ( suc @ N2 ) )
% 3.82/4.03 = ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_Suc
% 3.82/4.03 thf(fact_2600_power__Suc,axiom,
% 3.82/4.03 ! [A: real,N2: nat] :
% 3.82/4.03 ( ( power_power_real @ A @ ( suc @ N2 ) )
% 3.82/4.03 = ( times_times_real @ A @ ( power_power_real @ A @ N2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_Suc
% 3.82/4.03 thf(fact_2601_power__Suc,axiom,
% 3.82/4.03 ! [A: complex,N2: nat] :
% 3.82/4.03 ( ( power_power_complex @ A @ ( suc @ N2 ) )
% 3.82/4.03 = ( times_times_complex @ A @ ( power_power_complex @ A @ N2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_Suc
% 3.82/4.03 thf(fact_2602_power__Suc,axiom,
% 3.82/4.03 ! [A: extended_enat,N2: nat] :
% 3.82/4.03 ( ( power_8040749407984259932d_enat @ A @ ( suc @ N2 ) )
% 3.82/4.03 = ( times_7803423173614009249d_enat @ A @ ( power_8040749407984259932d_enat @ A @ N2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_Suc
% 3.82/4.03 thf(fact_2603_power__Suc2,axiom,
% 3.82/4.03 ! [A: nat,N2: nat] :
% 3.82/4.03 ( ( power_power_nat @ A @ ( suc @ N2 ) )
% 3.82/4.03 = ( times_times_nat @ ( power_power_nat @ A @ N2 ) @ A ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_Suc2
% 3.82/4.03 thf(fact_2604_power__Suc2,axiom,
% 3.82/4.03 ! [A: int,N2: nat] :
% 3.82/4.03 ( ( power_power_int @ A @ ( suc @ N2 ) )
% 3.82/4.03 = ( times_times_int @ ( power_power_int @ A @ N2 ) @ A ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_Suc2
% 3.82/4.03 thf(fact_2605_power__Suc2,axiom,
% 3.82/4.03 ! [A: real,N2: nat] :
% 3.82/4.03 ( ( power_power_real @ A @ ( suc @ N2 ) )
% 3.82/4.03 = ( times_times_real @ ( power_power_real @ A @ N2 ) @ A ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_Suc2
% 3.82/4.03 thf(fact_2606_power__Suc2,axiom,
% 3.82/4.03 ! [A: complex,N2: nat] :
% 3.82/4.03 ( ( power_power_complex @ A @ ( suc @ N2 ) )
% 3.82/4.03 = ( times_times_complex @ ( power_power_complex @ A @ N2 ) @ A ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_Suc2
% 3.82/4.03 thf(fact_2607_power__Suc2,axiom,
% 3.82/4.03 ! [A: extended_enat,N2: nat] :
% 3.82/4.03 ( ( power_8040749407984259932d_enat @ A @ ( suc @ N2 ) )
% 3.82/4.03 = ( times_7803423173614009249d_enat @ ( power_8040749407984259932d_enat @ A @ N2 ) @ A ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_Suc2
% 3.82/4.03 thf(fact_2608_Suc__mult__less__cancel1,axiom,
% 3.82/4.03 ! [K: nat,M2: nat,N2: nat] :
% 3.82/4.03 ( ( ord_less_nat @ ( times_times_nat @ ( suc @ K ) @ M2 ) @ ( times_times_nat @ ( suc @ K ) @ N2 ) )
% 3.82/4.03 = ( ord_less_nat @ M2 @ N2 ) ) ).
% 3.82/4.03
% 3.82/4.03 % Suc_mult_less_cancel1
% 3.82/4.03 thf(fact_2609_power__add,axiom,
% 3.82/4.03 ! [A: nat,M2: nat,N2: nat] :
% 3.82/4.03 ( ( power_power_nat @ A @ ( plus_plus_nat @ M2 @ N2 ) )
% 3.82/4.03 = ( times_times_nat @ ( power_power_nat @ A @ M2 ) @ ( power_power_nat @ A @ N2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_add
% 3.82/4.03 thf(fact_2610_power__add,axiom,
% 3.82/4.03 ! [A: int,M2: nat,N2: nat] :
% 3.82/4.03 ( ( power_power_int @ A @ ( plus_plus_nat @ M2 @ N2 ) )
% 3.82/4.03 = ( times_times_int @ ( power_power_int @ A @ M2 ) @ ( power_power_int @ A @ N2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_add
% 3.82/4.03 thf(fact_2611_power__add,axiom,
% 3.82/4.03 ! [A: real,M2: nat,N2: nat] :
% 3.82/4.03 ( ( power_power_real @ A @ ( plus_plus_nat @ M2 @ N2 ) )
% 3.82/4.03 = ( times_times_real @ ( power_power_real @ A @ M2 ) @ ( power_power_real @ A @ N2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_add
% 3.82/4.03 thf(fact_2612_power__add,axiom,
% 3.82/4.03 ! [A: complex,M2: nat,N2: nat] :
% 3.82/4.03 ( ( power_power_complex @ A @ ( plus_plus_nat @ M2 @ N2 ) )
% 3.82/4.03 = ( times_times_complex @ ( power_power_complex @ A @ M2 ) @ ( power_power_complex @ A @ N2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_add
% 3.82/4.03 thf(fact_2613_power__add,axiom,
% 3.82/4.03 ! [A: extended_enat,M2: nat,N2: nat] :
% 3.82/4.03 ( ( power_8040749407984259932d_enat @ A @ ( plus_plus_nat @ M2 @ N2 ) )
% 3.82/4.03 = ( times_7803423173614009249d_enat @ ( power_8040749407984259932d_enat @ A @ M2 ) @ ( power_8040749407984259932d_enat @ A @ N2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_add
% 3.82/4.03 thf(fact_2614_mult__less__mono1,axiom,
% 3.82/4.03 ! [I: nat,J: nat,K: nat] :
% 3.82/4.03 ( ( ord_less_nat @ I @ J )
% 3.82/4.03 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 3.82/4.03 => ( ord_less_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_less_mono1
% 3.82/4.03 thf(fact_2615_mult__less__mono2,axiom,
% 3.82/4.03 ! [I: nat,J: nat,K: nat] :
% 3.82/4.03 ( ( ord_less_nat @ I @ J )
% 3.82/4.03 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 3.82/4.03 => ( ord_less_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_less_mono2
% 3.82/4.03 thf(fact_2616_vebt__buildup_Osimps_I1_J,axiom,
% 3.82/4.03 ( ( vEBT_vebt_buildup @ zero_zero_nat )
% 3.82/4.03 = ( vEBT_Leaf @ $false @ $false ) ) ).
% 3.82/4.03
% 3.82/4.03 % vebt_buildup.simps(1)
% 3.82/4.03 thf(fact_2617_Suc__mult__le__cancel1,axiom,
% 3.82/4.03 ! [K: nat,M2: nat,N2: nat] :
% 3.82/4.03 ( ( ord_less_eq_nat @ ( times_times_nat @ ( suc @ K ) @ M2 ) @ ( times_times_nat @ ( suc @ K ) @ N2 ) )
% 3.82/4.03 = ( ord_less_eq_nat @ M2 @ N2 ) ) ).
% 3.82/4.03
% 3.82/4.03 % Suc_mult_le_cancel1
% 3.82/4.03 thf(fact_2618_mult__Suc,axiom,
% 3.82/4.03 ! [M2: nat,N2: nat] :
% 3.82/4.03 ( ( times_times_nat @ ( suc @ M2 ) @ N2 )
% 3.82/4.03 = ( plus_plus_nat @ N2 @ ( times_times_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_Suc
% 3.82/4.03 thf(fact_2619_VEBT__internal_Ovalid_H_Osimps_I1_J,axiom,
% 3.82/4.03 ! [Uu: $o,Uv: $o,D: nat] :
% 3.82/4.03 ( ( vEBT_VEBT_valid @ ( vEBT_Leaf @ Uu @ Uv ) @ D )
% 3.82/4.03 = ( D = one_one_nat ) ) ).
% 3.82/4.03
% 3.82/4.03 % VEBT_internal.valid'.simps(1)
% 3.82/4.03 thf(fact_2620_mult__eq__self__implies__10,axiom,
% 3.82/4.03 ! [M2: nat,N2: nat] :
% 3.82/4.03 ( ( M2
% 3.82/4.03 = ( times_times_nat @ M2 @ N2 ) )
% 3.82/4.03 => ( ( N2 = one_one_nat )
% 3.82/4.03 | ( M2 = zero_zero_nat ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_eq_self_implies_10
% 3.82/4.03 thf(fact_2621_less__mult__imp__div__less,axiom,
% 3.82/4.03 ! [M2: nat,I: nat,N2: nat] :
% 3.82/4.03 ( ( ord_less_nat @ M2 @ ( times_times_nat @ I @ N2 ) )
% 3.82/4.03 => ( ord_less_nat @ ( divide_divide_nat @ M2 @ N2 ) @ I ) ) ).
% 3.82/4.03
% 3.82/4.03 % less_mult_imp_div_less
% 3.82/4.03 thf(fact_2622_div__times__less__eq__dividend,axiom,
% 3.82/4.03 ! [M2: nat,N2: nat] : ( ord_less_eq_nat @ ( times_times_nat @ ( divide_divide_nat @ M2 @ N2 ) @ N2 ) @ M2 ) ).
% 3.82/4.03
% 3.82/4.03 % div_times_less_eq_dividend
% 3.82/4.03 thf(fact_2623_times__div__less__eq__dividend,axiom,
% 3.82/4.03 ! [N2: nat,M2: nat] : ( ord_less_eq_nat @ ( times_times_nat @ N2 @ ( divide_divide_nat @ M2 @ N2 ) ) @ M2 ) ).
% 3.82/4.03
% 3.82/4.03 % times_div_less_eq_dividend
% 3.82/4.03 thf(fact_2624_power__odd__eq,axiom,
% 3.82/4.03 ! [A: nat,N2: nat] :
% 3.82/4.03 ( ( power_power_nat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 3.82/4.03 = ( times_times_nat @ A @ ( power_power_nat @ ( power_power_nat @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_odd_eq
% 3.82/4.03 thf(fact_2625_power__odd__eq,axiom,
% 3.82/4.03 ! [A: int,N2: nat] :
% 3.82/4.03 ( ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 3.82/4.03 = ( times_times_int @ A @ ( power_power_int @ ( power_power_int @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_odd_eq
% 3.82/4.03 thf(fact_2626_power__odd__eq,axiom,
% 3.82/4.03 ! [A: real,N2: nat] :
% 3.82/4.03 ( ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 3.82/4.03 = ( times_times_real @ A @ ( power_power_real @ ( power_power_real @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_odd_eq
% 3.82/4.03 thf(fact_2627_power__odd__eq,axiom,
% 3.82/4.03 ! [A: complex,N2: nat] :
% 3.82/4.03 ( ( power_power_complex @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 3.82/4.03 = ( times_times_complex @ A @ ( power_power_complex @ ( power_power_complex @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_odd_eq
% 3.82/4.03 thf(fact_2628_power__odd__eq,axiom,
% 3.82/4.03 ! [A: extended_enat,N2: nat] :
% 3.82/4.03 ( ( power_8040749407984259932d_enat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 3.82/4.03 = ( times_7803423173614009249d_enat @ A @ ( power_8040749407984259932d_enat @ ( power_8040749407984259932d_enat @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_odd_eq
% 3.82/4.03 thf(fact_2629_Suc__double__not__eq__double,axiom,
% 3.82/4.03 ! [M2: nat,N2: nat] :
% 3.82/4.03 ( ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 3.82/4.03 != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 3.82/4.03
% 3.82/4.03 % Suc_double_not_eq_double
% 3.82/4.03 thf(fact_2630_double__not__eq__Suc__double,axiom,
% 3.82/4.03 ! [M2: nat,N2: nat] :
% 3.82/4.03 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 )
% 3.82/4.03 != ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % double_not_eq_Suc_double
% 3.82/4.03 thf(fact_2631_VEBT__internal_Onaive__member_Ocases,axiom,
% 3.82/4.03 ! [X: produc9072475918466114483BT_nat] :
% 3.82/4.03 ( ! [A4: $o,B4: $o,X5: nat] :
% 3.82/4.03 ( X
% 3.82/4.03 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B4 ) @ X5 ) )
% 3.82/4.03 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,Ux2: nat] :
% 3.82/4.03 ( X
% 3.82/4.03 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Ux2 ) )
% 3.82/4.03 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT,X5: nat] :
% 3.82/4.03 ( X
% 3.82/4.03 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) @ X5 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % VEBT_internal.naive_member.cases
% 3.82/4.03 thf(fact_2632_invar__vebt_Ointros_I1_J,axiom,
% 3.82/4.03 ! [A: $o,B2: $o] : ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B2 ) @ ( suc @ zero_zero_nat ) ) ).
% 3.82/4.03
% 3.82/4.03 % invar_vebt.intros(1)
% 3.82/4.03 thf(fact_2633_mult__less__le__imp__less,axiom,
% 3.82/4.03 ! [A: real,B2: real,C: real,D: real] :
% 3.82/4.03 ( ( ord_less_real @ A @ B2 )
% 3.82/4.03 => ( ( ord_less_eq_real @ C @ D )
% 3.82/4.03 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 3.82/4.03 => ( ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B2 @ D ) ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_less_le_imp_less
% 3.82/4.03 thf(fact_2634_mult__less__le__imp__less,axiom,
% 3.82/4.03 ! [A: nat,B2: nat,C: nat,D: nat] :
% 3.82/4.03 ( ( ord_less_nat @ A @ B2 )
% 3.82/4.03 => ( ( ord_less_eq_nat @ C @ D )
% 3.82/4.03 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 3.82/4.03 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 3.82/4.03 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B2 @ D ) ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_less_le_imp_less
% 3.82/4.03 thf(fact_2635_mult__less__le__imp__less,axiom,
% 3.82/4.03 ! [A: int,B2: int,C: int,D: int] :
% 3.82/4.03 ( ( ord_less_int @ A @ B2 )
% 3.82/4.03 => ( ( ord_less_eq_int @ C @ D )
% 3.82/4.03 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 3.82/4.03 => ( ( ord_less_int @ zero_zero_int @ C )
% 3.82/4.03 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B2 @ D ) ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_less_le_imp_less
% 3.82/4.03 thf(fact_2636_mult__le__less__imp__less,axiom,
% 3.82/4.03 ! [A: real,B2: real,C: real,D: real] :
% 3.82/4.03 ( ( ord_less_eq_real @ A @ B2 )
% 3.82/4.03 => ( ( ord_less_real @ C @ D )
% 3.82/4.03 => ( ( ord_less_real @ zero_zero_real @ A )
% 3.82/4.03 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B2 @ D ) ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_le_less_imp_less
% 3.82/4.03 thf(fact_2637_mult__le__less__imp__less,axiom,
% 3.82/4.03 ! [A: nat,B2: nat,C: nat,D: nat] :
% 3.82/4.03 ( ( ord_less_eq_nat @ A @ B2 )
% 3.82/4.03 => ( ( ord_less_nat @ C @ D )
% 3.82/4.03 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 3.82/4.03 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 3.82/4.03 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B2 @ D ) ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_le_less_imp_less
% 3.82/4.03 thf(fact_2638_mult__le__less__imp__less,axiom,
% 3.82/4.03 ! [A: int,B2: int,C: int,D: int] :
% 3.82/4.03 ( ( ord_less_eq_int @ A @ B2 )
% 3.82/4.03 => ( ( ord_less_int @ C @ D )
% 3.82/4.03 => ( ( ord_less_int @ zero_zero_int @ A )
% 3.82/4.03 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 3.82/4.03 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B2 @ D ) ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_le_less_imp_less
% 3.82/4.03 thf(fact_2639_mult__right__le__imp__le,axiom,
% 3.82/4.03 ! [A: real,C: real,B2: real] :
% 3.82/4.03 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B2 @ C ) )
% 3.82/4.03 => ( ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ord_less_eq_real @ A @ B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_right_le_imp_le
% 3.82/4.03 thf(fact_2640_mult__right__le__imp__le,axiom,
% 3.82/4.03 ! [A: nat,C: nat,B2: nat] :
% 3.82/4.03 ( ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B2 @ C ) )
% 3.82/4.03 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 3.82/4.03 => ( ord_less_eq_nat @ A @ B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_right_le_imp_le
% 3.82/4.03 thf(fact_2641_mult__right__le__imp__le,axiom,
% 3.82/4.03 ! [A: int,C: int,B2: int] :
% 3.82/4.03 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B2 @ C ) )
% 3.82/4.03 => ( ( ord_less_int @ zero_zero_int @ C )
% 3.82/4.03 => ( ord_less_eq_int @ A @ B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_right_le_imp_le
% 3.82/4.03 thf(fact_2642_mult__left__le__imp__le,axiom,
% 3.82/4.03 ! [C: real,A: real,B2: real] :
% 3.82/4.03 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B2 ) )
% 3.82/4.03 => ( ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ord_less_eq_real @ A @ B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_left_le_imp_le
% 3.82/4.03 thf(fact_2643_mult__left__le__imp__le,axiom,
% 3.82/4.03 ! [C: nat,A: nat,B2: nat] :
% 3.82/4.03 ( ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B2 ) )
% 3.82/4.03 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 3.82/4.03 => ( ord_less_eq_nat @ A @ B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_left_le_imp_le
% 3.82/4.03 thf(fact_2644_mult__left__le__imp__le,axiom,
% 3.82/4.03 ! [C: int,A: int,B2: int] :
% 3.82/4.03 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B2 ) )
% 3.82/4.03 => ( ( ord_less_int @ zero_zero_int @ C )
% 3.82/4.03 => ( ord_less_eq_int @ A @ B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_left_le_imp_le
% 3.82/4.03 thf(fact_2645_mult__le__cancel__left__pos,axiom,
% 3.82/4.03 ! [C: real,A: real,B2: real] :
% 3.82/4.03 ( ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B2 ) )
% 3.82/4.03 = ( ord_less_eq_real @ A @ B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_le_cancel_left_pos
% 3.82/4.03 thf(fact_2646_mult__le__cancel__left__pos,axiom,
% 3.82/4.03 ! [C: int,A: int,B2: int] :
% 3.82/4.03 ( ( ord_less_int @ zero_zero_int @ C )
% 3.82/4.03 => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B2 ) )
% 3.82/4.03 = ( ord_less_eq_int @ A @ B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_le_cancel_left_pos
% 3.82/4.03 thf(fact_2647_mult__le__cancel__left__neg,axiom,
% 3.82/4.03 ! [C: real,A: real,B2: real] :
% 3.82/4.03 ( ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.03 => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B2 ) )
% 3.82/4.03 = ( ord_less_eq_real @ B2 @ A ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_le_cancel_left_neg
% 3.82/4.03 thf(fact_2648_mult__le__cancel__left__neg,axiom,
% 3.82/4.03 ! [C: int,A: int,B2: int] :
% 3.82/4.03 ( ( ord_less_int @ C @ zero_zero_int )
% 3.82/4.03 => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B2 ) )
% 3.82/4.03 = ( ord_less_eq_int @ B2 @ A ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_le_cancel_left_neg
% 3.82/4.03 thf(fact_2649_mult__less__cancel__right,axiom,
% 3.82/4.03 ! [A: real,C: real,B2: real] :
% 3.82/4.03 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B2 @ C ) )
% 3.82/4.03 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ord_less_real @ A @ B2 ) )
% 3.82/4.03 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 3.82/4.03 => ( ord_less_real @ B2 @ A ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_less_cancel_right
% 3.82/4.03 thf(fact_2650_mult__less__cancel__right,axiom,
% 3.82/4.03 ! [A: int,C: int,B2: int] :
% 3.82/4.03 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B2 @ C ) )
% 3.82/4.03 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 3.82/4.03 => ( ord_less_int @ A @ B2 ) )
% 3.82/4.03 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 3.82/4.03 => ( ord_less_int @ B2 @ A ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_less_cancel_right
% 3.82/4.03 thf(fact_2651_mult__strict__mono_H,axiom,
% 3.82/4.03 ! [A: real,B2: real,C: real,D: real] :
% 3.82/4.03 ( ( ord_less_real @ A @ B2 )
% 3.82/4.03 => ( ( ord_less_real @ C @ D )
% 3.82/4.03 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 3.82/4.03 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B2 @ D ) ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_strict_mono'
% 3.82/4.03 thf(fact_2652_mult__strict__mono_H,axiom,
% 3.82/4.03 ! [A: nat,B2: nat,C: nat,D: nat] :
% 3.82/4.03 ( ( ord_less_nat @ A @ B2 )
% 3.82/4.03 => ( ( ord_less_nat @ C @ D )
% 3.82/4.03 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 3.82/4.03 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 3.82/4.03 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B2 @ D ) ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_strict_mono'
% 3.82/4.03 thf(fact_2653_mult__strict__mono_H,axiom,
% 3.82/4.03 ! [A: int,B2: int,C: int,D: int] :
% 3.82/4.03 ( ( ord_less_int @ A @ B2 )
% 3.82/4.03 => ( ( ord_less_int @ C @ D )
% 3.82/4.03 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 3.82/4.03 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 3.82/4.03 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B2 @ D ) ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_strict_mono'
% 3.82/4.03 thf(fact_2654_mult__right__less__imp__less,axiom,
% 3.82/4.03 ! [A: real,C: real,B2: real] :
% 3.82/4.03 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B2 @ C ) )
% 3.82/4.03 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ord_less_real @ A @ B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_right_less_imp_less
% 3.82/4.03 thf(fact_2655_mult__right__less__imp__less,axiom,
% 3.82/4.03 ! [A: nat,C: nat,B2: nat] :
% 3.82/4.03 ( ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B2 @ C ) )
% 3.82/4.03 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 3.82/4.03 => ( ord_less_nat @ A @ B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_right_less_imp_less
% 3.82/4.03 thf(fact_2656_mult__right__less__imp__less,axiom,
% 3.82/4.03 ! [A: int,C: int,B2: int] :
% 3.82/4.03 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B2 @ C ) )
% 3.82/4.03 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 3.82/4.03 => ( ord_less_int @ A @ B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_right_less_imp_less
% 3.82/4.03 thf(fact_2657_mult__less__cancel__left,axiom,
% 3.82/4.03 ! [C: real,A: real,B2: real] :
% 3.82/4.03 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B2 ) )
% 3.82/4.03 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ord_less_real @ A @ B2 ) )
% 3.82/4.03 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 3.82/4.03 => ( ord_less_real @ B2 @ A ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_less_cancel_left
% 3.82/4.03 thf(fact_2658_mult__less__cancel__left,axiom,
% 3.82/4.03 ! [C: int,A: int,B2: int] :
% 3.82/4.03 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B2 ) )
% 3.82/4.03 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 3.82/4.03 => ( ord_less_int @ A @ B2 ) )
% 3.82/4.03 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 3.82/4.03 => ( ord_less_int @ B2 @ A ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_less_cancel_left
% 3.82/4.03 thf(fact_2659_mult__strict__mono,axiom,
% 3.82/4.03 ! [A: real,B2: real,C: real,D: real] :
% 3.82/4.03 ( ( ord_less_real @ A @ B2 )
% 3.82/4.03 => ( ( ord_less_real @ C @ D )
% 3.82/4.03 => ( ( ord_less_real @ zero_zero_real @ B2 )
% 3.82/4.03 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B2 @ D ) ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_strict_mono
% 3.82/4.03 thf(fact_2660_mult__strict__mono,axiom,
% 3.82/4.03 ! [A: nat,B2: nat,C: nat,D: nat] :
% 3.82/4.03 ( ( ord_less_nat @ A @ B2 )
% 3.82/4.03 => ( ( ord_less_nat @ C @ D )
% 3.82/4.03 => ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 3.82/4.03 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 3.82/4.03 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B2 @ D ) ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_strict_mono
% 3.82/4.03 thf(fact_2661_mult__strict__mono,axiom,
% 3.82/4.03 ! [A: int,B2: int,C: int,D: int] :
% 3.82/4.03 ( ( ord_less_int @ A @ B2 )
% 3.82/4.03 => ( ( ord_less_int @ C @ D )
% 3.82/4.03 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 3.82/4.03 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 3.82/4.03 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B2 @ D ) ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_strict_mono
% 3.82/4.03 thf(fact_2662_mult__left__less__imp__less,axiom,
% 3.82/4.03 ! [C: real,A: real,B2: real] :
% 3.82/4.03 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B2 ) )
% 3.82/4.03 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ord_less_real @ A @ B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_left_less_imp_less
% 3.82/4.03 thf(fact_2663_mult__left__less__imp__less,axiom,
% 3.82/4.03 ! [C: nat,A: nat,B2: nat] :
% 3.82/4.03 ( ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B2 ) )
% 3.82/4.03 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 3.82/4.03 => ( ord_less_nat @ A @ B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_left_less_imp_less
% 3.82/4.03 thf(fact_2664_mult__left__less__imp__less,axiom,
% 3.82/4.03 ! [C: int,A: int,B2: int] :
% 3.82/4.03 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B2 ) )
% 3.82/4.03 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 3.82/4.03 => ( ord_less_int @ A @ B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_left_less_imp_less
% 3.82/4.03 thf(fact_2665_mult__le__cancel__right,axiom,
% 3.82/4.03 ! [A: real,C: real,B2: real] :
% 3.82/4.03 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B2 @ C ) )
% 3.82/4.03 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ord_less_eq_real @ A @ B2 ) )
% 3.82/4.03 & ( ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.03 => ( ord_less_eq_real @ B2 @ A ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_le_cancel_right
% 3.82/4.03 thf(fact_2666_mult__le__cancel__right,axiom,
% 3.82/4.03 ! [A: int,C: int,B2: int] :
% 3.82/4.03 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B2 @ C ) )
% 3.82/4.03 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 3.82/4.03 => ( ord_less_eq_int @ A @ B2 ) )
% 3.82/4.03 & ( ( ord_less_int @ C @ zero_zero_int )
% 3.82/4.03 => ( ord_less_eq_int @ B2 @ A ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_le_cancel_right
% 3.82/4.03 thf(fact_2667_mult__le__cancel__left,axiom,
% 3.82/4.03 ! [C: real,A: real,B2: real] :
% 3.82/4.03 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B2 ) )
% 3.82/4.03 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ord_less_eq_real @ A @ B2 ) )
% 3.82/4.03 & ( ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.03 => ( ord_less_eq_real @ B2 @ A ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_le_cancel_left
% 3.82/4.03 thf(fact_2668_mult__le__cancel__left,axiom,
% 3.82/4.03 ! [C: int,A: int,B2: int] :
% 3.82/4.03 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B2 ) )
% 3.82/4.03 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 3.82/4.03 => ( ord_less_eq_int @ A @ B2 ) )
% 3.82/4.03 & ( ( ord_less_int @ C @ zero_zero_int )
% 3.82/4.03 => ( ord_less_eq_int @ B2 @ A ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_le_cancel_left
% 3.82/4.03 thf(fact_2669_mult__left__le__one__le,axiom,
% 3.82/4.03 ! [X: real,Y: real] :
% 3.82/4.03 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 3.82/4.03 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 3.82/4.03 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 3.82/4.03 => ( ord_less_eq_real @ ( times_times_real @ Y @ X ) @ X ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_left_le_one_le
% 3.82/4.03 thf(fact_2670_mult__left__le__one__le,axiom,
% 3.82/4.03 ! [X: int,Y: int] :
% 3.82/4.03 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 3.82/4.03 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 3.82/4.03 => ( ( ord_less_eq_int @ Y @ one_one_int )
% 3.82/4.03 => ( ord_less_eq_int @ ( times_times_int @ Y @ X ) @ X ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_left_le_one_le
% 3.82/4.03 thf(fact_2671_mult__right__le__one__le,axiom,
% 3.82/4.03 ! [X: real,Y: real] :
% 3.82/4.03 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 3.82/4.03 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 3.82/4.03 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 3.82/4.03 => ( ord_less_eq_real @ ( times_times_real @ X @ Y ) @ X ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_right_le_one_le
% 3.82/4.03 thf(fact_2672_mult__right__le__one__le,axiom,
% 3.82/4.03 ! [X: int,Y: int] :
% 3.82/4.03 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 3.82/4.03 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 3.82/4.03 => ( ( ord_less_eq_int @ Y @ one_one_int )
% 3.82/4.03 => ( ord_less_eq_int @ ( times_times_int @ X @ Y ) @ X ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_right_le_one_le
% 3.82/4.03 thf(fact_2673_mult__le__one,axiom,
% 3.82/4.03 ! [A: extended_enat,B2: extended_enat] :
% 3.82/4.03 ( ( ord_le2932123472753598470d_enat @ A @ one_on7984719198319812577d_enat )
% 3.82/4.03 => ( ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ B2 )
% 3.82/4.03 => ( ( ord_le2932123472753598470d_enat @ B2 @ one_on7984719198319812577d_enat )
% 3.82/4.03 => ( ord_le2932123472753598470d_enat @ ( times_7803423173614009249d_enat @ A @ B2 ) @ one_on7984719198319812577d_enat ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_le_one
% 3.82/4.03 thf(fact_2674_mult__le__one,axiom,
% 3.82/4.03 ! [A: real,B2: real] :
% 3.82/4.03 ( ( ord_less_eq_real @ A @ one_one_real )
% 3.82/4.03 => ( ( ord_less_eq_real @ zero_zero_real @ B2 )
% 3.82/4.03 => ( ( ord_less_eq_real @ B2 @ one_one_real )
% 3.82/4.03 => ( ord_less_eq_real @ ( times_times_real @ A @ B2 ) @ one_one_real ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_le_one
% 3.82/4.03 thf(fact_2675_mult__le__one,axiom,
% 3.82/4.03 ! [A: nat,B2: nat] :
% 3.82/4.03 ( ( ord_less_eq_nat @ A @ one_one_nat )
% 3.82/4.03 => ( ( ord_less_eq_nat @ zero_zero_nat @ B2 )
% 3.82/4.03 => ( ( ord_less_eq_nat @ B2 @ one_one_nat )
% 3.82/4.03 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B2 ) @ one_one_nat ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_le_one
% 3.82/4.03 thf(fact_2676_mult__le__one,axiom,
% 3.82/4.03 ! [A: int,B2: int] :
% 3.82/4.03 ( ( ord_less_eq_int @ A @ one_one_int )
% 3.82/4.03 => ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 3.82/4.03 => ( ( ord_less_eq_int @ B2 @ one_one_int )
% 3.82/4.03 => ( ord_less_eq_int @ ( times_times_int @ A @ B2 ) @ one_one_int ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_le_one
% 3.82/4.03 thf(fact_2677_mult__left__le,axiom,
% 3.82/4.03 ! [C: extended_enat,A: extended_enat] :
% 3.82/4.03 ( ( ord_le2932123472753598470d_enat @ C @ one_on7984719198319812577d_enat )
% 3.82/4.03 => ( ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ A )
% 3.82/4.03 => ( ord_le2932123472753598470d_enat @ ( times_7803423173614009249d_enat @ A @ C ) @ A ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_left_le
% 3.82/4.03 thf(fact_2678_mult__left__le,axiom,
% 3.82/4.03 ! [C: real,A: real] :
% 3.82/4.03 ( ( ord_less_eq_real @ C @ one_one_real )
% 3.82/4.03 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 3.82/4.03 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ A ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_left_le
% 3.82/4.03 thf(fact_2679_mult__left__le,axiom,
% 3.82/4.03 ! [C: nat,A: nat] :
% 3.82/4.03 ( ( ord_less_eq_nat @ C @ one_one_nat )
% 3.82/4.03 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 3.82/4.03 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ A ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_left_le
% 3.82/4.03 thf(fact_2680_mult__left__le,axiom,
% 3.82/4.03 ! [C: int,A: int] :
% 3.82/4.03 ( ( ord_less_eq_int @ C @ one_one_int )
% 3.82/4.03 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 3.82/4.03 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ A ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_left_le
% 3.82/4.03 thf(fact_2681_sum__squares__le__zero__iff,axiom,
% 3.82/4.03 ! [X: real,Y: real] :
% 3.82/4.03 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) @ zero_zero_real )
% 3.82/4.03 = ( ( X = zero_zero_real )
% 3.82/4.03 & ( Y = zero_zero_real ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % sum_squares_le_zero_iff
% 3.82/4.03 thf(fact_2682_sum__squares__le__zero__iff,axiom,
% 3.82/4.03 ! [X: int,Y: int] :
% 3.82/4.03 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int )
% 3.82/4.03 = ( ( X = zero_zero_int )
% 3.82/4.03 & ( Y = zero_zero_int ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % sum_squares_le_zero_iff
% 3.82/4.03 thf(fact_2683_sum__squares__ge__zero,axiom,
% 3.82/4.03 ! [X: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % sum_squares_ge_zero
% 3.82/4.03 thf(fact_2684_sum__squares__ge__zero,axiom,
% 3.82/4.03 ! [X: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % sum_squares_ge_zero
% 3.82/4.03 thf(fact_2685_vebt__insert_Osimps_I1_J,axiom,
% 3.82/4.03 ! [X: nat,A: $o,B2: $o] :
% 3.82/4.03 ( ( ( X = zero_zero_nat )
% 3.82/4.03 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B2 ) @ X )
% 3.82/4.03 = ( vEBT_Leaf @ $true @ B2 ) ) )
% 3.82/4.03 & ( ( X != zero_zero_nat )
% 3.82/4.03 => ( ( ( X = one_one_nat )
% 3.82/4.03 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B2 ) @ X )
% 3.82/4.03 = ( vEBT_Leaf @ A @ $true ) ) )
% 3.82/4.03 & ( ( X != one_one_nat )
% 3.82/4.03 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B2 ) @ X )
% 3.82/4.03 = ( vEBT_Leaf @ A @ B2 ) ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % vebt_insert.simps(1)
% 3.82/4.03 thf(fact_2686_sum__squares__gt__zero__iff,axiom,
% 3.82/4.03 ! [X: real,Y: real] :
% 3.82/4.03 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) )
% 3.82/4.03 = ( ( X != zero_zero_real )
% 3.82/4.03 | ( Y != zero_zero_real ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % sum_squares_gt_zero_iff
% 3.82/4.03 thf(fact_2687_sum__squares__gt__zero__iff,axiom,
% 3.82/4.03 ! [X: int,Y: int] :
% 3.82/4.03 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) )
% 3.82/4.03 = ( ( X != zero_zero_int )
% 3.82/4.03 | ( Y != zero_zero_int ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % sum_squares_gt_zero_iff
% 3.82/4.03 thf(fact_2688_not__sum__squares__lt__zero,axiom,
% 3.82/4.03 ! [X: real,Y: real] :
% 3.82/4.03 ~ ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) @ zero_zero_real ) ).
% 3.82/4.03
% 3.82/4.03 % not_sum_squares_lt_zero
% 3.82/4.03 thf(fact_2689_not__sum__squares__lt__zero,axiom,
% 3.82/4.03 ! [X: int,Y: int] :
% 3.82/4.03 ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int ) ).
% 3.82/4.03
% 3.82/4.03 % not_sum_squares_lt_zero
% 3.82/4.03 thf(fact_2690_divide__less__eq,axiom,
% 3.82/4.03 ! [B2: real,C: real,A: real] :
% 3.82/4.03 ( ( ord_less_real @ ( divide_divide_real @ B2 @ C ) @ A )
% 3.82/4.03 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ord_less_real @ B2 @ ( times_times_real @ A @ C ) ) )
% 3.82/4.03 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.03 => ( ord_less_real @ ( times_times_real @ A @ C ) @ B2 ) )
% 3.82/4.03 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.03 => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % divide_less_eq
% 3.82/4.03 thf(fact_2691_less__divide__eq,axiom,
% 3.82/4.03 ! [A: real,B2: real,C: real] :
% 3.82/4.03 ( ( ord_less_real @ A @ ( divide_divide_real @ B2 @ C ) )
% 3.82/4.03 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ord_less_real @ ( times_times_real @ A @ C ) @ B2 ) )
% 3.82/4.03 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.03 => ( ord_less_real @ B2 @ ( times_times_real @ A @ C ) ) )
% 3.82/4.03 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.03 => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % less_divide_eq
% 3.82/4.03 thf(fact_2692_neg__divide__less__eq,axiom,
% 3.82/4.03 ! [C: real,B2: real,A: real] :
% 3.82/4.03 ( ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.03 => ( ( ord_less_real @ ( divide_divide_real @ B2 @ C ) @ A )
% 3.82/4.03 = ( ord_less_real @ ( times_times_real @ A @ C ) @ B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % neg_divide_less_eq
% 3.82/4.03 thf(fact_2693_neg__less__divide__eq,axiom,
% 3.82/4.03 ! [C: real,A: real,B2: real] :
% 3.82/4.03 ( ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.03 => ( ( ord_less_real @ A @ ( divide_divide_real @ B2 @ C ) )
% 3.82/4.03 = ( ord_less_real @ B2 @ ( times_times_real @ A @ C ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % neg_less_divide_eq
% 3.82/4.03 thf(fact_2694_pos__divide__less__eq,axiom,
% 3.82/4.03 ! [C: real,B2: real,A: real] :
% 3.82/4.03 ( ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ( ord_less_real @ ( divide_divide_real @ B2 @ C ) @ A )
% 3.82/4.03 = ( ord_less_real @ B2 @ ( times_times_real @ A @ C ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % pos_divide_less_eq
% 3.82/4.03 thf(fact_2695_pos__less__divide__eq,axiom,
% 3.82/4.03 ! [C: real,A: real,B2: real] :
% 3.82/4.03 ( ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ( ord_less_real @ A @ ( divide_divide_real @ B2 @ C ) )
% 3.82/4.03 = ( ord_less_real @ ( times_times_real @ A @ C ) @ B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % pos_less_divide_eq
% 3.82/4.03 thf(fact_2696_mult__imp__div__pos__less,axiom,
% 3.82/4.03 ! [Y: real,X: real,Z3: real] :
% 3.82/4.03 ( ( ord_less_real @ zero_zero_real @ Y )
% 3.82/4.03 => ( ( ord_less_real @ X @ ( times_times_real @ Z3 @ Y ) )
% 3.82/4.03 => ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ Z3 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_imp_div_pos_less
% 3.82/4.03 thf(fact_2697_mult__imp__less__div__pos,axiom,
% 3.82/4.03 ! [Y: real,Z3: real,X: real] :
% 3.82/4.03 ( ( ord_less_real @ zero_zero_real @ Y )
% 3.82/4.03 => ( ( ord_less_real @ ( times_times_real @ Z3 @ Y ) @ X )
% 3.82/4.03 => ( ord_less_real @ Z3 @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_imp_less_div_pos
% 3.82/4.03 thf(fact_2698_divide__strict__left__mono,axiom,
% 3.82/4.03 ! [B2: real,A: real,C: real] :
% 3.82/4.03 ( ( ord_less_real @ B2 @ A )
% 3.82/4.03 => ( ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B2 ) )
% 3.82/4.03 => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B2 ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % divide_strict_left_mono
% 3.82/4.03 thf(fact_2699_divide__strict__left__mono__neg,axiom,
% 3.82/4.03 ! [A: real,B2: real,C: real] :
% 3.82/4.03 ( ( ord_less_real @ A @ B2 )
% 3.82/4.03 => ( ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.03 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B2 ) )
% 3.82/4.03 => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B2 ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % divide_strict_left_mono_neg
% 3.82/4.03 thf(fact_2700_vebt__buildup_Osimps_I2_J,axiom,
% 3.82/4.03 ( ( vEBT_vebt_buildup @ ( suc @ zero_zero_nat ) )
% 3.82/4.03 = ( vEBT_Leaf @ $false @ $false ) ) ).
% 3.82/4.03
% 3.82/4.03 % vebt_buildup.simps(2)
% 3.82/4.03 thf(fact_2701_divide__eq__eq__numeral_I1_J,axiom,
% 3.82/4.03 ! [B2: complex,C: complex,W2: num] :
% 3.82/4.03 ( ( ( divide1717551699836669952omplex @ B2 @ C )
% 3.82/4.03 = ( numera6690914467698888265omplex @ W2 ) )
% 3.82/4.03 = ( ( ( C != zero_zero_complex )
% 3.82/4.03 => ( B2
% 3.82/4.03 = ( times_times_complex @ ( numera6690914467698888265omplex @ W2 ) @ C ) ) )
% 3.82/4.03 & ( ( C = zero_zero_complex )
% 3.82/4.03 => ( ( numera6690914467698888265omplex @ W2 )
% 3.82/4.03 = zero_zero_complex ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % divide_eq_eq_numeral(1)
% 3.82/4.03 thf(fact_2702_divide__eq__eq__numeral_I1_J,axiom,
% 3.82/4.03 ! [B2: real,C: real,W2: num] :
% 3.82/4.03 ( ( ( divide_divide_real @ B2 @ C )
% 3.82/4.03 = ( numeral_numeral_real @ W2 ) )
% 3.82/4.03 = ( ( ( C != zero_zero_real )
% 3.82/4.03 => ( B2
% 3.82/4.03 = ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) ) )
% 3.82/4.03 & ( ( C = zero_zero_real )
% 3.82/4.03 => ( ( numeral_numeral_real @ W2 )
% 3.82/4.03 = zero_zero_real ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % divide_eq_eq_numeral(1)
% 3.82/4.03 thf(fact_2703_eq__divide__eq__numeral_I1_J,axiom,
% 3.82/4.03 ! [W2: num,B2: complex,C: complex] :
% 3.82/4.03 ( ( ( numera6690914467698888265omplex @ W2 )
% 3.82/4.03 = ( divide1717551699836669952omplex @ B2 @ C ) )
% 3.82/4.03 = ( ( ( C != zero_zero_complex )
% 3.82/4.03 => ( ( times_times_complex @ ( numera6690914467698888265omplex @ W2 ) @ C )
% 3.82/4.03 = B2 ) )
% 3.82/4.03 & ( ( C = zero_zero_complex )
% 3.82/4.03 => ( ( numera6690914467698888265omplex @ W2 )
% 3.82/4.03 = zero_zero_complex ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % eq_divide_eq_numeral(1)
% 3.82/4.03 thf(fact_2704_eq__divide__eq__numeral_I1_J,axiom,
% 3.82/4.03 ! [W2: num,B2: real,C: real] :
% 3.82/4.03 ( ( ( numeral_numeral_real @ W2 )
% 3.82/4.03 = ( divide_divide_real @ B2 @ C ) )
% 3.82/4.03 = ( ( ( C != zero_zero_real )
% 3.82/4.03 => ( ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C )
% 3.82/4.03 = B2 ) )
% 3.82/4.03 & ( ( C = zero_zero_real )
% 3.82/4.03 => ( ( numeral_numeral_real @ W2 )
% 3.82/4.03 = zero_zero_real ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % eq_divide_eq_numeral(1)
% 3.82/4.03 thf(fact_2705_vebt__member_Osimps_I1_J,axiom,
% 3.82/4.03 ! [A: $o,B2: $o,X: nat] :
% 3.82/4.03 ( ( vEBT_vebt_member @ ( vEBT_Leaf @ A @ B2 ) @ X )
% 3.82/4.03 = ( ( ( X = zero_zero_nat )
% 3.82/4.03 => A )
% 3.82/4.03 & ( ( X != zero_zero_nat )
% 3.82/4.03 => ( ( ( X = one_one_nat )
% 3.82/4.03 => B2 )
% 3.82/4.03 & ( X = one_one_nat ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % vebt_member.simps(1)
% 3.82/4.03 thf(fact_2706_divide__add__eq__iff,axiom,
% 3.82/4.03 ! [Z3: complex,X: complex,Y: complex] :
% 3.82/4.03 ( ( Z3 != zero_zero_complex )
% 3.82/4.03 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X @ Z3 ) @ Y )
% 3.82/4.03 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X @ ( times_times_complex @ Y @ Z3 ) ) @ Z3 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % divide_add_eq_iff
% 3.82/4.03 thf(fact_2707_divide__add__eq__iff,axiom,
% 3.82/4.03 ! [Z3: real,X: real,Y: real] :
% 3.82/4.03 ( ( Z3 != zero_zero_real )
% 3.82/4.03 => ( ( plus_plus_real @ ( divide_divide_real @ X @ Z3 ) @ Y )
% 3.82/4.03 = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Y @ Z3 ) ) @ Z3 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % divide_add_eq_iff
% 3.82/4.03 thf(fact_2708_add__divide__eq__iff,axiom,
% 3.82/4.03 ! [Z3: complex,X: complex,Y: complex] :
% 3.82/4.03 ( ( Z3 != zero_zero_complex )
% 3.82/4.03 => ( ( plus_plus_complex @ X @ ( divide1717551699836669952omplex @ Y @ Z3 ) )
% 3.82/4.03 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X @ Z3 ) @ Y ) @ Z3 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % add_divide_eq_iff
% 3.82/4.03 thf(fact_2709_add__divide__eq__iff,axiom,
% 3.82/4.03 ! [Z3: real,X: real,Y: real] :
% 3.82/4.03 ( ( Z3 != zero_zero_real )
% 3.82/4.03 => ( ( plus_plus_real @ X @ ( divide_divide_real @ Y @ Z3 ) )
% 3.82/4.03 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X @ Z3 ) @ Y ) @ Z3 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % add_divide_eq_iff
% 3.82/4.03 thf(fact_2710_add__num__frac,axiom,
% 3.82/4.03 ! [Y: complex,Z3: complex,X: complex] :
% 3.82/4.03 ( ( Y != zero_zero_complex )
% 3.82/4.03 => ( ( plus_plus_complex @ Z3 @ ( divide1717551699836669952omplex @ X @ Y ) )
% 3.82/4.03 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X @ ( times_times_complex @ Z3 @ Y ) ) @ Y ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % add_num_frac
% 3.82/4.03 thf(fact_2711_add__num__frac,axiom,
% 3.82/4.03 ! [Y: real,Z3: real,X: real] :
% 3.82/4.03 ( ( Y != zero_zero_real )
% 3.82/4.03 => ( ( plus_plus_real @ Z3 @ ( divide_divide_real @ X @ Y ) )
% 3.82/4.03 = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Z3 @ Y ) ) @ Y ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % add_num_frac
% 3.82/4.03 thf(fact_2712_add__frac__num,axiom,
% 3.82/4.03 ! [Y: complex,X: complex,Z3: complex] :
% 3.82/4.03 ( ( Y != zero_zero_complex )
% 3.82/4.03 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X @ Y ) @ Z3 )
% 3.82/4.03 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X @ ( times_times_complex @ Z3 @ Y ) ) @ Y ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % add_frac_num
% 3.82/4.03 thf(fact_2713_add__frac__num,axiom,
% 3.82/4.03 ! [Y: real,X: real,Z3: real] :
% 3.82/4.03 ( ( Y != zero_zero_real )
% 3.82/4.03 => ( ( plus_plus_real @ ( divide_divide_real @ X @ Y ) @ Z3 )
% 3.82/4.03 = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Z3 @ Y ) ) @ Y ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % add_frac_num
% 3.82/4.03 thf(fact_2714_add__frac__eq,axiom,
% 3.82/4.03 ! [Y: complex,Z3: complex,X: complex,W2: complex] :
% 3.82/4.03 ( ( Y != zero_zero_complex )
% 3.82/4.03 => ( ( Z3 != zero_zero_complex )
% 3.82/4.03 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X @ Y ) @ ( divide1717551699836669952omplex @ W2 @ Z3 ) )
% 3.82/4.03 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X @ Z3 ) @ ( times_times_complex @ W2 @ Y ) ) @ ( times_times_complex @ Y @ Z3 ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % add_frac_eq
% 3.82/4.03 thf(fact_2715_add__frac__eq,axiom,
% 3.82/4.03 ! [Y: real,Z3: real,X: real,W2: real] :
% 3.82/4.03 ( ( Y != zero_zero_real )
% 3.82/4.03 => ( ( Z3 != zero_zero_real )
% 3.82/4.03 => ( ( plus_plus_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W2 @ Z3 ) )
% 3.82/4.03 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X @ Z3 ) @ ( times_times_real @ W2 @ Y ) ) @ ( times_times_real @ Y @ Z3 ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % add_frac_eq
% 3.82/4.03 thf(fact_2716_add__divide__eq__if__simps_I1_J,axiom,
% 3.82/4.03 ! [Z3: complex,A: complex,B2: complex] :
% 3.82/4.03 ( ( ( Z3 = zero_zero_complex )
% 3.82/4.03 => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B2 @ Z3 ) )
% 3.82/4.03 = A ) )
% 3.82/4.03 & ( ( Z3 != zero_zero_complex )
% 3.82/4.03 => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B2 @ Z3 ) )
% 3.82/4.03 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ A @ Z3 ) @ B2 ) @ Z3 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % add_divide_eq_if_simps(1)
% 3.82/4.03 thf(fact_2717_add__divide__eq__if__simps_I1_J,axiom,
% 3.82/4.03 ! [Z3: real,A: real,B2: real] :
% 3.82/4.03 ( ( ( Z3 = zero_zero_real )
% 3.82/4.03 => ( ( plus_plus_real @ A @ ( divide_divide_real @ B2 @ Z3 ) )
% 3.82/4.03 = A ) )
% 3.82/4.03 & ( ( Z3 != zero_zero_real )
% 3.82/4.03 => ( ( plus_plus_real @ A @ ( divide_divide_real @ B2 @ Z3 ) )
% 3.82/4.03 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ A @ Z3 ) @ B2 ) @ Z3 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % add_divide_eq_if_simps(1)
% 3.82/4.03 thf(fact_2718_add__divide__eq__if__simps_I2_J,axiom,
% 3.82/4.03 ! [Z3: complex,A: complex,B2: complex] :
% 3.82/4.03 ( ( ( Z3 = zero_zero_complex )
% 3.82/4.03 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z3 ) @ B2 )
% 3.82/4.03 = B2 ) )
% 3.82/4.03 & ( ( Z3 != zero_zero_complex )
% 3.82/4.03 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z3 ) @ B2 )
% 3.82/4.03 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ ( times_times_complex @ B2 @ Z3 ) ) @ Z3 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % add_divide_eq_if_simps(2)
% 3.82/4.03 thf(fact_2719_add__divide__eq__if__simps_I2_J,axiom,
% 3.82/4.03 ! [Z3: real,A: real,B2: real] :
% 3.82/4.03 ( ( ( Z3 = zero_zero_real )
% 3.82/4.03 => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z3 ) @ B2 )
% 3.82/4.03 = B2 ) )
% 3.82/4.03 & ( ( Z3 != zero_zero_real )
% 3.82/4.03 => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z3 ) @ B2 )
% 3.82/4.03 = ( divide_divide_real @ ( plus_plus_real @ A @ ( times_times_real @ B2 @ Z3 ) ) @ Z3 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % add_divide_eq_if_simps(2)
% 3.82/4.03 thf(fact_2720_power__gt1__lemma,axiom,
% 3.82/4.03 ! [A: nat,N2: nat] :
% 3.82/4.03 ( ( ord_less_nat @ one_one_nat @ A )
% 3.82/4.03 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_gt1_lemma
% 3.82/4.03 thf(fact_2721_power__gt1__lemma,axiom,
% 3.82/4.03 ! [A: real,N2: nat] :
% 3.82/4.03 ( ( ord_less_real @ one_one_real @ A )
% 3.82/4.03 => ( ord_less_real @ one_one_real @ ( times_times_real @ A @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_gt1_lemma
% 3.82/4.03 thf(fact_2722_power__gt1__lemma,axiom,
% 3.82/4.03 ! [A: int,N2: nat] :
% 3.82/4.03 ( ( ord_less_int @ one_one_int @ A )
% 3.82/4.03 => ( ord_less_int @ one_one_int @ ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_gt1_lemma
% 3.82/4.03 thf(fact_2723_power__less__power__Suc,axiom,
% 3.82/4.03 ! [A: nat,N2: nat] :
% 3.82/4.03 ( ( ord_less_nat @ one_one_nat @ A )
% 3.82/4.03 => ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_less_power_Suc
% 3.82/4.03 thf(fact_2724_power__less__power__Suc,axiom,
% 3.82/4.03 ! [A: real,N2: nat] :
% 3.82/4.03 ( ( ord_less_real @ one_one_real @ A )
% 3.82/4.03 => ( ord_less_real @ ( power_power_real @ A @ N2 ) @ ( times_times_real @ A @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_less_power_Suc
% 3.82/4.03 thf(fact_2725_power__less__power__Suc,axiom,
% 3.82/4.03 ! [A: int,N2: nat] :
% 3.82/4.03 ( ( ord_less_int @ one_one_int @ A )
% 3.82/4.03 => ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_less_power_Suc
% 3.82/4.03 thf(fact_2726_VEBT__internal_Onaive__member_Osimps_I1_J,axiom,
% 3.82/4.03 ! [A: $o,B2: $o,X: nat] :
% 3.82/4.03 ( ( vEBT_V5719532721284313246member @ ( vEBT_Leaf @ A @ B2 ) @ X )
% 3.82/4.03 = ( ( ( X = zero_zero_nat )
% 3.82/4.03 => A )
% 3.82/4.03 & ( ( X != zero_zero_nat )
% 3.82/4.03 => ( ( ( X = one_one_nat )
% 3.82/4.03 => B2 )
% 3.82/4.03 & ( X = one_one_nat ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % VEBT_internal.naive_member.simps(1)
% 3.82/4.03 thf(fact_2727_one__less__mult,axiom,
% 3.82/4.03 ! [N2: nat,M2: nat] :
% 3.82/4.03 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 3.82/4.03 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M2 )
% 3.82/4.03 => ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M2 @ N2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % one_less_mult
% 3.82/4.03 thf(fact_2728_n__less__m__mult__n,axiom,
% 3.82/4.03 ! [N2: nat,M2: nat] :
% 3.82/4.03 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.03 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M2 )
% 3.82/4.03 => ( ord_less_nat @ N2 @ ( times_times_nat @ M2 @ N2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % n_less_m_mult_n
% 3.82/4.03 thf(fact_2729_n__less__n__mult__m,axiom,
% 3.82/4.03 ! [N2: nat,M2: nat] :
% 3.82/4.03 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.03 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M2 )
% 3.82/4.03 => ( ord_less_nat @ N2 @ ( times_times_nat @ N2 @ M2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % n_less_n_mult_m
% 3.82/4.03 thf(fact_2730_VEBT__internal_OminNull_Oelims_I3_J,axiom,
% 3.82/4.03 ! [X: vEBT_VEBT] :
% 3.82/4.03 ( ~ ( vEBT_VEBT_minNull @ X )
% 3.82/4.03 => ( ! [Uv2: $o] :
% 3.82/4.03 ( X
% 3.82/4.03 != ( vEBT_Leaf @ $true @ Uv2 ) )
% 3.82/4.03 => ( ! [Uu2: $o] :
% 3.82/4.03 ( X
% 3.82/4.03 != ( vEBT_Leaf @ Uu2 @ $true ) )
% 3.82/4.03 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 3.82/4.03 ( X
% 3.82/4.03 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % VEBT_internal.minNull.elims(3)
% 3.82/4.03 thf(fact_2731_div__less__iff__less__mult,axiom,
% 3.82/4.03 ! [Q3: nat,M2: nat,N2: nat] :
% 3.82/4.03 ( ( ord_less_nat @ zero_zero_nat @ Q3 )
% 3.82/4.03 => ( ( ord_less_nat @ ( divide_divide_nat @ M2 @ Q3 ) @ N2 )
% 3.82/4.03 = ( ord_less_nat @ M2 @ ( times_times_nat @ N2 @ Q3 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % div_less_iff_less_mult
% 3.82/4.03 thf(fact_2732_VEBT__internal_OminNull_Oelims_I2_J,axiom,
% 3.82/4.03 ! [X: vEBT_VEBT] :
% 3.82/4.03 ( ( vEBT_VEBT_minNull @ X )
% 3.82/4.03 => ( ( X
% 3.82/4.03 != ( vEBT_Leaf @ $false @ $false ) )
% 3.82/4.03 => ~ ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 3.82/4.03 ( X
% 3.82/4.03 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % VEBT_internal.minNull.elims(2)
% 3.82/4.03 thf(fact_2733_realpow__pos__nth2,axiom,
% 3.82/4.03 ! [A: real,N2: nat] :
% 3.82/4.03 ( ( ord_less_real @ zero_zero_real @ A )
% 3.82/4.03 => ? [R3: real] :
% 3.82/4.03 ( ( ord_less_real @ zero_zero_real @ R3 )
% 3.82/4.03 & ( ( power_power_real @ R3 @ ( suc @ N2 ) )
% 3.82/4.03 = A ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % realpow_pos_nth2
% 3.82/4.03 thf(fact_2734_field__le__mult__one__interval,axiom,
% 3.82/4.03 ! [X: real,Y: real] :
% 3.82/4.03 ( ! [Z: real] :
% 3.82/4.03 ( ( ord_less_real @ zero_zero_real @ Z )
% 3.82/4.03 => ( ( ord_less_real @ Z @ one_one_real )
% 3.82/4.03 => ( ord_less_eq_real @ ( times_times_real @ Z @ X ) @ Y ) ) )
% 3.82/4.03 => ( ord_less_eq_real @ X @ Y ) ) ).
% 3.82/4.03
% 3.82/4.03 % field_le_mult_one_interval
% 3.82/4.03 thf(fact_2735_mult__less__cancel__right2,axiom,
% 3.82/4.03 ! [A: real,C: real] :
% 3.82/4.03 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ C )
% 3.82/4.03 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ord_less_real @ A @ one_one_real ) )
% 3.82/4.03 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 3.82/4.03 => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_less_cancel_right2
% 3.82/4.03 thf(fact_2736_mult__less__cancel__right2,axiom,
% 3.82/4.03 ! [A: int,C: int] :
% 3.82/4.03 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ C )
% 3.82/4.03 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 3.82/4.03 => ( ord_less_int @ A @ one_one_int ) )
% 3.82/4.03 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 3.82/4.03 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_less_cancel_right2
% 3.82/4.03 thf(fact_2737_mult__less__cancel__right1,axiom,
% 3.82/4.03 ! [C: real,B2: real] :
% 3.82/4.03 ( ( ord_less_real @ C @ ( times_times_real @ B2 @ C ) )
% 3.82/4.03 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ord_less_real @ one_one_real @ B2 ) )
% 3.82/4.03 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 3.82/4.03 => ( ord_less_real @ B2 @ one_one_real ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_less_cancel_right1
% 3.82/4.03 thf(fact_2738_mult__less__cancel__right1,axiom,
% 3.82/4.03 ! [C: int,B2: int] :
% 3.82/4.03 ( ( ord_less_int @ C @ ( times_times_int @ B2 @ C ) )
% 3.82/4.03 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 3.82/4.03 => ( ord_less_int @ one_one_int @ B2 ) )
% 3.82/4.03 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 3.82/4.03 => ( ord_less_int @ B2 @ one_one_int ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_less_cancel_right1
% 3.82/4.03 thf(fact_2739_mult__less__cancel__left2,axiom,
% 3.82/4.03 ! [C: real,A: real] :
% 3.82/4.03 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ C )
% 3.82/4.03 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ord_less_real @ A @ one_one_real ) )
% 3.82/4.03 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 3.82/4.03 => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_less_cancel_left2
% 3.82/4.03 thf(fact_2740_mult__less__cancel__left2,axiom,
% 3.82/4.03 ! [C: int,A: int] :
% 3.82/4.03 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ C )
% 3.82/4.03 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 3.82/4.03 => ( ord_less_int @ A @ one_one_int ) )
% 3.82/4.03 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 3.82/4.03 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_less_cancel_left2
% 3.82/4.03 thf(fact_2741_mult__less__cancel__left1,axiom,
% 3.82/4.03 ! [C: real,B2: real] :
% 3.82/4.03 ( ( ord_less_real @ C @ ( times_times_real @ C @ B2 ) )
% 3.82/4.03 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ord_less_real @ one_one_real @ B2 ) )
% 3.82/4.03 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 3.82/4.03 => ( ord_less_real @ B2 @ one_one_real ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_less_cancel_left1
% 3.82/4.03 thf(fact_2742_mult__less__cancel__left1,axiom,
% 3.82/4.03 ! [C: int,B2: int] :
% 3.82/4.03 ( ( ord_less_int @ C @ ( times_times_int @ C @ B2 ) )
% 3.82/4.03 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 3.82/4.03 => ( ord_less_int @ one_one_int @ B2 ) )
% 3.82/4.03 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 3.82/4.03 => ( ord_less_int @ B2 @ one_one_int ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_less_cancel_left1
% 3.82/4.03 thf(fact_2743_mult__le__cancel__right2,axiom,
% 3.82/4.03 ! [A: real,C: real] :
% 3.82/4.03 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ C )
% 3.82/4.03 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ord_less_eq_real @ A @ one_one_real ) )
% 3.82/4.03 & ( ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.03 => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_le_cancel_right2
% 3.82/4.03 thf(fact_2744_mult__le__cancel__right2,axiom,
% 3.82/4.03 ! [A: int,C: int] :
% 3.82/4.03 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ C )
% 3.82/4.03 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 3.82/4.03 => ( ord_less_eq_int @ A @ one_one_int ) )
% 3.82/4.03 & ( ( ord_less_int @ C @ zero_zero_int )
% 3.82/4.03 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_le_cancel_right2
% 3.82/4.03 thf(fact_2745_mult__le__cancel__right1,axiom,
% 3.82/4.03 ! [C: real,B2: real] :
% 3.82/4.03 ( ( ord_less_eq_real @ C @ ( times_times_real @ B2 @ C ) )
% 3.82/4.03 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ord_less_eq_real @ one_one_real @ B2 ) )
% 3.82/4.03 & ( ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.03 => ( ord_less_eq_real @ B2 @ one_one_real ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_le_cancel_right1
% 3.82/4.03 thf(fact_2746_mult__le__cancel__right1,axiom,
% 3.82/4.03 ! [C: int,B2: int] :
% 3.82/4.03 ( ( ord_less_eq_int @ C @ ( times_times_int @ B2 @ C ) )
% 3.82/4.03 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 3.82/4.03 => ( ord_less_eq_int @ one_one_int @ B2 ) )
% 3.82/4.03 & ( ( ord_less_int @ C @ zero_zero_int )
% 3.82/4.03 => ( ord_less_eq_int @ B2 @ one_one_int ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_le_cancel_right1
% 3.82/4.03 thf(fact_2747_mult__le__cancel__left2,axiom,
% 3.82/4.03 ! [C: real,A: real] :
% 3.82/4.03 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ C )
% 3.82/4.03 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ord_less_eq_real @ A @ one_one_real ) )
% 3.82/4.03 & ( ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.03 => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_le_cancel_left2
% 3.82/4.03 thf(fact_2748_mult__le__cancel__left2,axiom,
% 3.82/4.03 ! [C: int,A: int] :
% 3.82/4.03 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ C )
% 3.82/4.03 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 3.82/4.03 => ( ord_less_eq_int @ A @ one_one_int ) )
% 3.82/4.03 & ( ( ord_less_int @ C @ zero_zero_int )
% 3.82/4.03 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_le_cancel_left2
% 3.82/4.03 thf(fact_2749_mult__le__cancel__left1,axiom,
% 3.82/4.03 ! [C: real,B2: real] :
% 3.82/4.03 ( ( ord_less_eq_real @ C @ ( times_times_real @ C @ B2 ) )
% 3.82/4.03 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ord_less_eq_real @ one_one_real @ B2 ) )
% 3.82/4.03 & ( ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.03 => ( ord_less_eq_real @ B2 @ one_one_real ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_le_cancel_left1
% 3.82/4.03 thf(fact_2750_mult__le__cancel__left1,axiom,
% 3.82/4.03 ! [C: int,B2: int] :
% 3.82/4.03 ( ( ord_less_eq_int @ C @ ( times_times_int @ C @ B2 ) )
% 3.82/4.03 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 3.82/4.03 => ( ord_less_eq_int @ one_one_int @ B2 ) )
% 3.82/4.03 & ( ( ord_less_int @ C @ zero_zero_int )
% 3.82/4.03 => ( ord_less_eq_int @ B2 @ one_one_int ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_le_cancel_left1
% 3.82/4.03 thf(fact_2751_divide__left__mono__neg,axiom,
% 3.82/4.03 ! [A: real,B2: real,C: real] :
% 3.82/4.03 ( ( ord_less_eq_real @ A @ B2 )
% 3.82/4.03 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 3.82/4.03 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B2 ) )
% 3.82/4.03 => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B2 ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % divide_left_mono_neg
% 3.82/4.03 thf(fact_2752_mult__imp__le__div__pos,axiom,
% 3.82/4.03 ! [Y: real,Z3: real,X: real] :
% 3.82/4.03 ( ( ord_less_real @ zero_zero_real @ Y )
% 3.82/4.03 => ( ( ord_less_eq_real @ ( times_times_real @ Z3 @ Y ) @ X )
% 3.82/4.03 => ( ord_less_eq_real @ Z3 @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_imp_le_div_pos
% 3.82/4.03 thf(fact_2753_mult__imp__div__pos__le,axiom,
% 3.82/4.03 ! [Y: real,X: real,Z3: real] :
% 3.82/4.03 ( ( ord_less_real @ zero_zero_real @ Y )
% 3.82/4.03 => ( ( ord_less_eq_real @ X @ ( times_times_real @ Z3 @ Y ) )
% 3.82/4.03 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ Z3 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_imp_div_pos_le
% 3.82/4.03 thf(fact_2754_pos__le__divide__eq,axiom,
% 3.82/4.03 ! [C: real,A: real,B2: real] :
% 3.82/4.03 ( ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B2 @ C ) )
% 3.82/4.03 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % pos_le_divide_eq
% 3.82/4.03 thf(fact_2755_pos__divide__le__eq,axiom,
% 3.82/4.03 ! [C: real,B2: real,A: real] :
% 3.82/4.03 ( ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ( ord_less_eq_real @ ( divide_divide_real @ B2 @ C ) @ A )
% 3.82/4.03 = ( ord_less_eq_real @ B2 @ ( times_times_real @ A @ C ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % pos_divide_le_eq
% 3.82/4.03 thf(fact_2756_neg__le__divide__eq,axiom,
% 3.82/4.03 ! [C: real,A: real,B2: real] :
% 3.82/4.03 ( ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.03 => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B2 @ C ) )
% 3.82/4.03 = ( ord_less_eq_real @ B2 @ ( times_times_real @ A @ C ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % neg_le_divide_eq
% 3.82/4.03 thf(fact_2757_neg__divide__le__eq,axiom,
% 3.82/4.03 ! [C: real,B2: real,A: real] :
% 3.82/4.03 ( ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.03 => ( ( ord_less_eq_real @ ( divide_divide_real @ B2 @ C ) @ A )
% 3.82/4.03 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % neg_divide_le_eq
% 3.82/4.03 thf(fact_2758_divide__left__mono,axiom,
% 3.82/4.03 ! [B2: real,A: real,C: real] :
% 3.82/4.03 ( ( ord_less_eq_real @ B2 @ A )
% 3.82/4.03 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B2 ) )
% 3.82/4.03 => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B2 ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % divide_left_mono
% 3.82/4.03 thf(fact_2759_le__divide__eq,axiom,
% 3.82/4.03 ! [A: real,B2: real,C: real] :
% 3.82/4.03 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B2 @ C ) )
% 3.82/4.03 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B2 ) )
% 3.82/4.03 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.03 => ( ord_less_eq_real @ B2 @ ( times_times_real @ A @ C ) ) )
% 3.82/4.03 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.03 => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % le_divide_eq
% 3.82/4.03 thf(fact_2760_divide__le__eq,axiom,
% 3.82/4.03 ! [B2: real,C: real,A: real] :
% 3.82/4.03 ( ( ord_less_eq_real @ ( divide_divide_real @ B2 @ C ) @ A )
% 3.82/4.03 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ord_less_eq_real @ B2 @ ( times_times_real @ A @ C ) ) )
% 3.82/4.03 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.03 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B2 ) )
% 3.82/4.03 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.03 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % divide_le_eq
% 3.82/4.03 thf(fact_2761_convex__bound__le,axiom,
% 3.82/4.03 ! [X: real,A: real,Y: real,U: real,V: real] :
% 3.82/4.03 ( ( ord_less_eq_real @ X @ A )
% 3.82/4.03 => ( ( ord_less_eq_real @ Y @ A )
% 3.82/4.03 => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 3.82/4.03 => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 3.82/4.03 => ( ( ( plus_plus_real @ U @ V )
% 3.82/4.03 = one_one_real )
% 3.82/4.03 => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ U @ X ) @ ( times_times_real @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % convex_bound_le
% 3.82/4.03 thf(fact_2762_convex__bound__le,axiom,
% 3.82/4.03 ! [X: int,A: int,Y: int,U: int,V: int] :
% 3.82/4.03 ( ( ord_less_eq_int @ X @ A )
% 3.82/4.03 => ( ( ord_less_eq_int @ Y @ A )
% 3.82/4.03 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 3.82/4.03 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 3.82/4.03 => ( ( ( plus_plus_int @ U @ V )
% 3.82/4.03 = one_one_int )
% 3.82/4.03 => ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % convex_bound_le
% 3.82/4.03 thf(fact_2763_divide__less__eq__numeral_I1_J,axiom,
% 3.82/4.03 ! [B2: real,C: real,W2: num] :
% 3.82/4.03 ( ( ord_less_real @ ( divide_divide_real @ B2 @ C ) @ ( numeral_numeral_real @ W2 ) )
% 3.82/4.03 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ord_less_real @ B2 @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) ) )
% 3.82/4.03 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.03 => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) @ B2 ) )
% 3.82/4.03 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.03 => ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % divide_less_eq_numeral(1)
% 3.82/4.03 thf(fact_2764_less__divide__eq__numeral_I1_J,axiom,
% 3.82/4.03 ! [W2: num,B2: real,C: real] :
% 3.82/4.03 ( ( ord_less_real @ ( numeral_numeral_real @ W2 ) @ ( divide_divide_real @ B2 @ C ) )
% 3.82/4.03 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) @ B2 ) )
% 3.82/4.03 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.03 => ( ord_less_real @ B2 @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) ) )
% 3.82/4.03 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.03 => ( ord_less_real @ ( numeral_numeral_real @ W2 ) @ zero_zero_real ) ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % less_divide_eq_numeral(1)
% 3.82/4.03 thf(fact_2765_power__Suc__less,axiom,
% 3.82/4.03 ! [A: nat,N2: nat] :
% 3.82/4.03 ( ( ord_less_nat @ zero_zero_nat @ A )
% 3.82/4.03 => ( ( ord_less_nat @ A @ one_one_nat )
% 3.82/4.03 => ( ord_less_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_Suc_less
% 3.82/4.03 thf(fact_2766_power__Suc__less,axiom,
% 3.82/4.03 ! [A: real,N2: nat] :
% 3.82/4.03 ( ( ord_less_real @ zero_zero_real @ A )
% 3.82/4.03 => ( ( ord_less_real @ A @ one_one_real )
% 3.82/4.03 => ( ord_less_real @ ( times_times_real @ A @ ( power_power_real @ A @ N2 ) ) @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_Suc_less
% 3.82/4.03 thf(fact_2767_power__Suc__less,axiom,
% 3.82/4.03 ! [A: int,N2: nat] :
% 3.82/4.03 ( ( ord_less_int @ zero_zero_int @ A )
% 3.82/4.03 => ( ( ord_less_int @ A @ one_one_int )
% 3.82/4.03 => ( ord_less_int @ ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power_Suc_less
% 3.82/4.03 thf(fact_2768_mult__2,axiom,
% 3.82/4.03 ! [Z3: complex] :
% 3.82/4.03 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z3 )
% 3.82/4.03 = ( plus_plus_complex @ Z3 @ Z3 ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_2
% 3.82/4.03 thf(fact_2769_mult__2,axiom,
% 3.82/4.03 ! [Z3: nat] :
% 3.82/4.03 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Z3 )
% 3.82/4.03 = ( plus_plus_nat @ Z3 @ Z3 ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_2
% 3.82/4.03 thf(fact_2770_mult__2,axiom,
% 3.82/4.03 ! [Z3: extended_enat] :
% 3.82/4.03 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ Z3 )
% 3.82/4.03 = ( plus_p3455044024723400733d_enat @ Z3 @ Z3 ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_2
% 3.82/4.03 thf(fact_2771_mult__2,axiom,
% 3.82/4.03 ! [Z3: int] :
% 3.82/4.03 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Z3 )
% 3.82/4.03 = ( plus_plus_int @ Z3 @ Z3 ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_2
% 3.82/4.03 thf(fact_2772_mult__2,axiom,
% 3.82/4.03 ! [Z3: real] :
% 3.82/4.03 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z3 )
% 3.82/4.03 = ( plus_plus_real @ Z3 @ Z3 ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_2
% 3.82/4.03 thf(fact_2773_mult__2__right,axiom,
% 3.82/4.03 ! [Z3: complex] :
% 3.82/4.03 ( ( times_times_complex @ Z3 @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) )
% 3.82/4.03 = ( plus_plus_complex @ Z3 @ Z3 ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_2_right
% 3.82/4.03 thf(fact_2774_mult__2__right,axiom,
% 3.82/4.03 ! [Z3: nat] :
% 3.82/4.03 ( ( times_times_nat @ Z3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.03 = ( plus_plus_nat @ Z3 @ Z3 ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_2_right
% 3.82/4.03 thf(fact_2775_mult__2__right,axiom,
% 3.82/4.03 ! [Z3: extended_enat] :
% 3.82/4.03 ( ( times_7803423173614009249d_enat @ Z3 @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) )
% 3.82/4.03 = ( plus_p3455044024723400733d_enat @ Z3 @ Z3 ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_2_right
% 3.82/4.03 thf(fact_2776_mult__2__right,axiom,
% 3.82/4.03 ! [Z3: int] :
% 3.82/4.03 ( ( times_times_int @ Z3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 3.82/4.03 = ( plus_plus_int @ Z3 @ Z3 ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_2_right
% 3.82/4.03 thf(fact_2777_mult__2__right,axiom,
% 3.82/4.03 ! [Z3: real] :
% 3.82/4.03 ( ( times_times_real @ Z3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 3.82/4.03 = ( plus_plus_real @ Z3 @ Z3 ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_2_right
% 3.82/4.03 thf(fact_2778_left__add__twice,axiom,
% 3.82/4.03 ! [A: complex,B2: complex] :
% 3.82/4.03 ( ( plus_plus_complex @ A @ ( plus_plus_complex @ A @ B2 ) )
% 3.82/4.03 = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ A ) @ B2 ) ) ).
% 3.82/4.03
% 3.82/4.03 % left_add_twice
% 3.82/4.03 thf(fact_2779_left__add__twice,axiom,
% 3.82/4.03 ! [A: nat,B2: nat] :
% 3.82/4.03 ( ( plus_plus_nat @ A @ ( plus_plus_nat @ A @ B2 ) )
% 3.82/4.03 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ B2 ) ) ).
% 3.82/4.03
% 3.82/4.03 % left_add_twice
% 3.82/4.03 thf(fact_2780_left__add__twice,axiom,
% 3.82/4.03 ! [A: extended_enat,B2: extended_enat] :
% 3.82/4.03 ( ( plus_p3455044024723400733d_enat @ A @ ( plus_p3455044024723400733d_enat @ A @ B2 ) )
% 3.82/4.03 = ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ A ) @ B2 ) ) ).
% 3.82/4.03
% 3.82/4.03 % left_add_twice
% 3.82/4.03 thf(fact_2781_left__add__twice,axiom,
% 3.82/4.03 ! [A: int,B2: int] :
% 3.82/4.03 ( ( plus_plus_int @ A @ ( plus_plus_int @ A @ B2 ) )
% 3.82/4.03 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ B2 ) ) ).
% 3.82/4.03
% 3.82/4.03 % left_add_twice
% 3.82/4.03 thf(fact_2782_left__add__twice,axiom,
% 3.82/4.03 ! [A: real,B2: real] :
% 3.82/4.03 ( ( plus_plus_real @ A @ ( plus_plus_real @ A @ B2 ) )
% 3.82/4.03 = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ B2 ) ) ).
% 3.82/4.03
% 3.82/4.03 % left_add_twice
% 3.82/4.03 thf(fact_2783_div__nat__eqI,axiom,
% 3.82/4.03 ! [N2: nat,Q3: nat,M2: nat] :
% 3.82/4.03 ( ( ord_less_eq_nat @ ( times_times_nat @ N2 @ Q3 ) @ M2 )
% 3.82/4.03 => ( ( ord_less_nat @ M2 @ ( times_times_nat @ N2 @ ( suc @ Q3 ) ) )
% 3.82/4.03 => ( ( divide_divide_nat @ M2 @ N2 )
% 3.82/4.03 = Q3 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % div_nat_eqI
% 3.82/4.03 thf(fact_2784_less__eq__div__iff__mult__less__eq,axiom,
% 3.82/4.03 ! [Q3: nat,M2: nat,N2: nat] :
% 3.82/4.03 ( ( ord_less_nat @ zero_zero_nat @ Q3 )
% 3.82/4.03 => ( ( ord_less_eq_nat @ M2 @ ( divide_divide_nat @ N2 @ Q3 ) )
% 3.82/4.03 = ( ord_less_eq_nat @ ( times_times_nat @ M2 @ Q3 ) @ N2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % less_eq_div_iff_mult_less_eq
% 3.82/4.03 thf(fact_2785_split__div,axiom,
% 3.82/4.03 ! [P: nat > $o,M2: nat,N2: nat] :
% 3.82/4.03 ( ( P @ ( divide_divide_nat @ M2 @ N2 ) )
% 3.82/4.03 = ( ( ( N2 = zero_zero_nat )
% 3.82/4.03 => ( P @ zero_zero_nat ) )
% 3.82/4.03 & ( ( N2 != zero_zero_nat )
% 3.82/4.03 => ! [I3: nat,J2: nat] :
% 3.82/4.03 ( ( ord_less_nat @ J2 @ N2 )
% 3.82/4.03 => ( ( M2
% 3.82/4.03 = ( plus_plus_nat @ ( times_times_nat @ N2 @ I3 ) @ J2 ) )
% 3.82/4.03 => ( P @ I3 ) ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % split_div
% 3.82/4.03 thf(fact_2786_dividend__less__div__times,axiom,
% 3.82/4.03 ! [N2: nat,M2: nat] :
% 3.82/4.03 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.03 => ( ord_less_nat @ M2 @ ( plus_plus_nat @ N2 @ ( times_times_nat @ ( divide_divide_nat @ M2 @ N2 ) @ N2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % dividend_less_div_times
% 3.82/4.03 thf(fact_2787_dividend__less__times__div,axiom,
% 3.82/4.03 ! [N2: nat,M2: nat] :
% 3.82/4.03 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.03 => ( ord_less_nat @ M2 @ ( plus_plus_nat @ N2 @ ( times_times_nat @ N2 @ ( divide_divide_nat @ M2 @ N2 ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % dividend_less_times_div
% 3.82/4.03 thf(fact_2788_VEBT__internal_OminNull_Oelims_I1_J,axiom,
% 3.82/4.03 ! [X: vEBT_VEBT,Y: $o] :
% 3.82/4.03 ( ( ( vEBT_VEBT_minNull @ X )
% 3.82/4.03 = Y )
% 3.82/4.03 => ( ( ( X
% 3.82/4.03 = ( vEBT_Leaf @ $false @ $false ) )
% 3.82/4.03 => ~ Y )
% 3.82/4.03 => ( ( ? [Uv2: $o] :
% 3.82/4.03 ( X
% 3.82/4.03 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 3.82/4.03 => Y )
% 3.82/4.03 => ( ( ? [Uu2: $o] :
% 3.82/4.03 ( X
% 3.82/4.03 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 3.82/4.03 => Y )
% 3.82/4.03 => ( ( ? [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 3.82/4.03 ( X
% 3.82/4.03 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 3.82/4.03 => ~ Y )
% 3.82/4.03 => ~ ( ? [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 3.82/4.03 ( X
% 3.82/4.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 3.82/4.03 => Y ) ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % VEBT_internal.minNull.elims(1)
% 3.82/4.03 thf(fact_2789_convex__bound__lt,axiom,
% 3.82/4.03 ! [X: real,A: real,Y: real,U: real,V: real] :
% 3.82/4.03 ( ( ord_less_real @ X @ A )
% 3.82/4.03 => ( ( ord_less_real @ Y @ A )
% 3.82/4.03 => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 3.82/4.03 => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 3.82/4.03 => ( ( ( plus_plus_real @ U @ V )
% 3.82/4.03 = one_one_real )
% 3.82/4.03 => ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ U @ X ) @ ( times_times_real @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % convex_bound_lt
% 3.82/4.03 thf(fact_2790_convex__bound__lt,axiom,
% 3.82/4.03 ! [X: int,A: int,Y: int,U: int,V: int] :
% 3.82/4.03 ( ( ord_less_int @ X @ A )
% 3.82/4.03 => ( ( ord_less_int @ Y @ A )
% 3.82/4.03 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 3.82/4.03 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 3.82/4.03 => ( ( ( plus_plus_int @ U @ V )
% 3.82/4.03 = one_one_int )
% 3.82/4.03 => ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % convex_bound_lt
% 3.82/4.03 thf(fact_2791_divide__le__eq__numeral_I1_J,axiom,
% 3.82/4.03 ! [B2: real,C: real,W2: num] :
% 3.82/4.03 ( ( ord_less_eq_real @ ( divide_divide_real @ B2 @ C ) @ ( numeral_numeral_real @ W2 ) )
% 3.82/4.03 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ord_less_eq_real @ B2 @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) ) )
% 3.82/4.03 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.03 => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) @ B2 ) )
% 3.82/4.03 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.03 => ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % divide_le_eq_numeral(1)
% 3.82/4.03 thf(fact_2792_le__divide__eq__numeral_I1_J,axiom,
% 3.82/4.03 ! [W2: num,B2: real,C: real] :
% 3.82/4.03 ( ( ord_less_eq_real @ ( numeral_numeral_real @ W2 ) @ ( divide_divide_real @ B2 @ C ) )
% 3.82/4.03 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) @ B2 ) )
% 3.82/4.03 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.03 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.03 => ( ord_less_eq_real @ B2 @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) ) )
% 3.82/4.03 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.03 => ( ord_less_eq_real @ ( numeral_numeral_real @ W2 ) @ zero_zero_real ) ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % le_divide_eq_numeral(1)
% 3.82/4.03 thf(fact_2793_sum__squares__bound,axiom,
% 3.82/4.03 ! [X: real,Y: real] : ( ord_less_eq_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ Y ) @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % sum_squares_bound
% 3.82/4.03 thf(fact_2794_split__div_H,axiom,
% 3.82/4.03 ! [P: nat > $o,M2: nat,N2: nat] :
% 3.82/4.03 ( ( P @ ( divide_divide_nat @ M2 @ N2 ) )
% 3.82/4.03 = ( ( ( N2 = zero_zero_nat )
% 3.82/4.03 & ( P @ zero_zero_nat ) )
% 3.82/4.03 | ? [Q5: nat] :
% 3.82/4.03 ( ( ord_less_eq_nat @ ( times_times_nat @ N2 @ Q5 ) @ M2 )
% 3.82/4.03 & ( ord_less_nat @ M2 @ ( times_times_nat @ N2 @ ( suc @ Q5 ) ) )
% 3.82/4.03 & ( P @ Q5 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % split_div'
% 3.82/4.03 thf(fact_2795_vebt__member_Ocases,axiom,
% 3.82/4.03 ! [X: produc9072475918466114483BT_nat] :
% 3.82/4.03 ( ! [A4: $o,B4: $o,X5: nat] :
% 3.82/4.03 ( X
% 3.82/4.03 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B4 ) @ X5 ) )
% 3.82/4.03 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,X5: nat] :
% 3.82/4.03 ( X
% 3.82/4.03 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ X5 ) )
% 3.82/4.03 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT,X5: nat] :
% 3.82/4.03 ( X
% 3.82/4.03 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ X5 ) )
% 3.82/4.03 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT,X5: nat] :
% 3.82/4.03 ( X
% 3.82/4.03 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ X5 ) )
% 3.82/4.03 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X5: nat] :
% 3.82/4.03 ( X
% 3.82/4.03 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ X5 ) ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % vebt_member.cases
% 3.82/4.03 thf(fact_2796_vebt__insert_Ocases,axiom,
% 3.82/4.03 ! [X: produc9072475918466114483BT_nat] :
% 3.82/4.03 ( ! [A4: $o,B4: $o,X5: nat] :
% 3.82/4.03 ( X
% 3.82/4.03 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B4 ) @ X5 ) )
% 3.82/4.03 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT,X5: nat] :
% 3.82/4.03 ( X
% 3.82/4.03 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) @ X5 ) )
% 3.82/4.03 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT,X5: nat] :
% 3.82/4.03 ( X
% 3.82/4.03 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) @ X5 ) )
% 3.82/4.03 => ( ! [V2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X5: nat] :
% 3.82/4.03 ( X
% 3.82/4.03 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) @ X5 ) )
% 3.82/4.03 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X5: nat] :
% 3.82/4.03 ( X
% 3.82/4.03 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ X5 ) ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % vebt_insert.cases
% 3.82/4.03 thf(fact_2797_VEBT__internal_Omembermima_Ocases,axiom,
% 3.82/4.03 ! [X: produc9072475918466114483BT_nat] :
% 3.82/4.03 ( ! [Uu2: $o,Uv2: $o,Uw2: nat] :
% 3.82/4.03 ( X
% 3.82/4.03 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Uw2 ) )
% 3.82/4.03 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT,Uz2: nat] :
% 3.82/4.03 ( X
% 3.82/4.03 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Uz2 ) )
% 3.82/4.03 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT,X5: nat] :
% 3.82/4.03 ( X
% 3.82/4.03 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ X5 ) )
% 3.82/4.03 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT,X5: nat] :
% 3.82/4.03 ( X
% 3.82/4.03 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ X5 ) )
% 3.82/4.03 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd: vEBT_VEBT,X5: nat] :
% 3.82/4.03 ( X
% 3.82/4.03 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) @ X5 ) ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % VEBT_internal.membermima.cases
% 3.82/4.03 thf(fact_2798_power2__sum,axiom,
% 3.82/4.03 ! [X: complex,Y: complex] :
% 3.82/4.03 ( ( power_power_complex @ ( plus_plus_complex @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.03 = ( plus_plus_complex @ ( plus_plus_complex @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power2_sum
% 3.82/4.03 thf(fact_2799_power2__sum,axiom,
% 3.82/4.03 ! [X: nat,Y: nat] :
% 3.82/4.03 ( ( power_power_nat @ ( plus_plus_nat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.03 = ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power2_sum
% 3.82/4.03 thf(fact_2800_power2__sum,axiom,
% 3.82/4.03 ! [X: extended_enat,Y: extended_enat] :
% 3.82/4.03 ( ( power_8040749407984259932d_enat @ ( plus_p3455044024723400733d_enat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.03 = ( plus_p3455044024723400733d_enat @ ( plus_p3455044024723400733d_enat @ ( power_8040749407984259932d_enat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8040749407984259932d_enat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_7803423173614009249d_enat @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power2_sum
% 3.82/4.03 thf(fact_2801_power2__sum,axiom,
% 3.82/4.03 ! [X: int,Y: int] :
% 3.82/4.03 ( ( power_power_int @ ( plus_plus_int @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.03 = ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power2_sum
% 3.82/4.03 thf(fact_2802_power2__sum,axiom,
% 3.82/4.03 ! [X: real,Y: real] :
% 3.82/4.03 ( ( power_power_real @ ( plus_plus_real @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.03 = ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % power2_sum
% 3.82/4.03 thf(fact_2803_zero__le__even__power_H,axiom,
% 3.82/4.03 ! [A: real,N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % zero_le_even_power'
% 3.82/4.03 thf(fact_2804_zero__le__even__power_H,axiom,
% 3.82/4.03 ! [A: int,N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % zero_le_even_power'
% 3.82/4.03 thf(fact_2805_nat__bit__induct,axiom,
% 3.82/4.03 ! [P: nat > $o,N2: nat] :
% 3.82/4.03 ( ( P @ zero_zero_nat )
% 3.82/4.03 => ( ! [N3: nat] :
% 3.82/4.03 ( ( P @ N3 )
% 3.82/4.03 => ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 3.82/4.03 => ( P @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 3.82/4.03 => ( ! [N3: nat] :
% 3.82/4.03 ( ( P @ N3 )
% 3.82/4.03 => ( P @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 3.82/4.03 => ( P @ N2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % nat_bit_induct
% 3.82/4.03 thf(fact_2806_arith__geo__mean,axiom,
% 3.82/4.03 ! [U: real,X: real,Y: real] :
% 3.82/4.03 ( ( ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.03 = ( times_times_real @ X @ Y ) )
% 3.82/4.03 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 3.82/4.03 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 3.82/4.03 => ( ord_less_eq_real @ U @ ( divide_divide_real @ ( plus_plus_real @ X @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % arith_geo_mean
% 3.82/4.03 thf(fact_2807_triangle__def,axiom,
% 3.82/4.03 ( nat_triangle
% 3.82/4.03 = ( ^ [N: nat] : ( divide_divide_nat @ ( times_times_nat @ N @ ( suc @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % triangle_def
% 3.82/4.03 thf(fact_2808_realpow__pos__nth,axiom,
% 3.82/4.03 ! [N2: nat,A: real] :
% 3.82/4.03 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.03 => ( ( ord_less_real @ zero_zero_real @ A )
% 3.82/4.03 => ? [R3: real] :
% 3.82/4.03 ( ( ord_less_real @ zero_zero_real @ R3 )
% 3.82/4.03 & ( ( power_power_real @ R3 @ N2 )
% 3.82/4.03 = A ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % realpow_pos_nth
% 3.82/4.03 thf(fact_2809_realpow__pos__nth__unique,axiom,
% 3.82/4.03 ! [N2: nat,A: real] :
% 3.82/4.03 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.03 => ( ( ord_less_real @ zero_zero_real @ A )
% 3.82/4.03 => ? [X5: real] :
% 3.82/4.03 ( ( ord_less_real @ zero_zero_real @ X5 )
% 3.82/4.03 & ( ( power_power_real @ X5 @ N2 )
% 3.82/4.03 = A )
% 3.82/4.03 & ! [Y6: real] :
% 3.82/4.03 ( ( ( ord_less_real @ zero_zero_real @ Y6 )
% 3.82/4.03 & ( ( power_power_real @ Y6 @ N2 )
% 3.82/4.03 = A ) )
% 3.82/4.03 => ( Y6 = X5 ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % realpow_pos_nth_unique
% 3.82/4.03 thf(fact_2810_odd__0__le__power__imp__0__le,axiom,
% 3.82/4.03 ! [A: real,N2: nat] :
% 3.82/4.03 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 3.82/4.03 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 3.82/4.03
% 3.82/4.03 % odd_0_le_power_imp_0_le
% 3.82/4.03 thf(fact_2811_odd__0__le__power__imp__0__le,axiom,
% 3.82/4.03 ! [A: int,N2: nat] :
% 3.82/4.03 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 3.82/4.03 => ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 3.82/4.03
% 3.82/4.03 % odd_0_le_power_imp_0_le
% 3.82/4.03 thf(fact_2812_odd__power__less__zero,axiom,
% 3.82/4.03 ! [A: real,N2: nat] :
% 3.82/4.03 ( ( ord_less_real @ A @ zero_zero_real )
% 3.82/4.03 => ( ord_less_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ zero_zero_real ) ) ).
% 3.82/4.03
% 3.82/4.03 % odd_power_less_zero
% 3.82/4.03 thf(fact_2813_odd__power__less__zero,axiom,
% 3.82/4.03 ! [A: int,N2: nat] :
% 3.82/4.03 ( ( ord_less_int @ A @ zero_zero_int )
% 3.82/4.03 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ zero_zero_int ) ) ).
% 3.82/4.03
% 3.82/4.03 % odd_power_less_zero
% 3.82/4.03 thf(fact_2814_nat__mult__le__cancel__disj,axiom,
% 3.82/4.03 ! [K: nat,M2: nat,N2: nat] :
% 3.82/4.03 ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M2 ) @ ( times_times_nat @ K @ N2 ) )
% 3.82/4.03 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 3.82/4.03 => ( ord_less_eq_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % nat_mult_le_cancel_disj
% 3.82/4.03 thf(fact_2815_nat__mult__div__cancel__disj,axiom,
% 3.82/4.03 ! [K: nat,M2: nat,N2: nat] :
% 3.82/4.03 ( ( ( K = zero_zero_nat )
% 3.82/4.03 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M2 ) @ ( times_times_nat @ K @ N2 ) )
% 3.82/4.03 = zero_zero_nat ) )
% 3.82/4.03 & ( ( K != zero_zero_nat )
% 3.82/4.03 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M2 ) @ ( times_times_nat @ K @ N2 ) )
% 3.82/4.03 = ( divide_divide_nat @ M2 @ N2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % nat_mult_div_cancel_disj
% 3.82/4.03 thf(fact_2816_nat__mult__less__cancel__disj,axiom,
% 3.82/4.03 ! [K: nat,M2: nat,N2: nat] :
% 3.82/4.03 ( ( ord_less_nat @ ( times_times_nat @ K @ M2 ) @ ( times_times_nat @ K @ N2 ) )
% 3.82/4.03 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 3.82/4.03 & ( ord_less_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % nat_mult_less_cancel_disj
% 3.82/4.03 thf(fact_2817_set__bit__0,axiom,
% 3.82/4.03 ! [A: nat] :
% 3.82/4.03 ( ( bit_se7882103937844011126it_nat @ zero_zero_nat @ A )
% 3.82/4.03 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % set_bit_0
% 3.82/4.03 thf(fact_2818_set__bit__0,axiom,
% 3.82/4.03 ! [A: int] :
% 3.82/4.03 ( ( bit_se7879613467334960850it_int @ zero_zero_nat @ A )
% 3.82/4.03 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % set_bit_0
% 3.82/4.03 thf(fact_2819_unset__bit__0,axiom,
% 3.82/4.03 ! [A: nat] :
% 3.82/4.03 ( ( bit_se4205575877204974255it_nat @ zero_zero_nat @ A )
% 3.82/4.03 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % unset_bit_0
% 3.82/4.03 thf(fact_2820_unset__bit__0,axiom,
% 3.82/4.03 ! [A: int] :
% 3.82/4.03 ( ( bit_se4203085406695923979it_int @ zero_zero_nat @ A )
% 3.82/4.03 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % unset_bit_0
% 3.82/4.03 thf(fact_2821_nat__mult__div__cancel1,axiom,
% 3.82/4.03 ! [K: nat,M2: nat,N2: nat] :
% 3.82/4.03 ( ( ord_less_nat @ zero_zero_nat @ K )
% 3.82/4.03 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M2 ) @ ( times_times_nat @ K @ N2 ) )
% 3.82/4.03 = ( divide_divide_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % nat_mult_div_cancel1
% 3.82/4.03 thf(fact_2822_nat__mult__le__cancel1,axiom,
% 3.82/4.03 ! [K: nat,M2: nat,N2: nat] :
% 3.82/4.03 ( ( ord_less_nat @ zero_zero_nat @ K )
% 3.82/4.03 => ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M2 ) @ ( times_times_nat @ K @ N2 ) )
% 3.82/4.03 = ( ord_less_eq_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % nat_mult_le_cancel1
% 3.82/4.03 thf(fact_2823_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 3.82/4.03 ! [C: nat,A: nat,B2: nat] :
% 3.82/4.03 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 3.82/4.03 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B2 @ C ) )
% 3.82/4.03 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B2 ) @ C ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 3.82/4.03 thf(fact_2824_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 3.82/4.03 ! [C: int,A: int,B2: int] :
% 3.82/4.03 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 3.82/4.03 => ( ( divide_divide_int @ A @ ( times_times_int @ B2 @ C ) )
% 3.82/4.03 = ( divide_divide_int @ ( divide_divide_int @ A @ B2 ) @ C ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 3.82/4.03 thf(fact_2825_discrete,axiom,
% 3.82/4.03 ( ord_less_nat
% 3.82/4.03 = ( ^ [A3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A3 @ one_one_nat ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % discrete
% 3.82/4.03 thf(fact_2826_discrete,axiom,
% 3.82/4.03 ( ord_less_int
% 3.82/4.03 = ( ^ [A3: int] : ( ord_less_eq_int @ ( plus_plus_int @ A3 @ one_one_int ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % discrete
% 3.82/4.03 thf(fact_2827_nat__mult__eq__cancel__disj,axiom,
% 3.82/4.03 ! [K: nat,M2: nat,N2: nat] :
% 3.82/4.03 ( ( ( times_times_nat @ K @ M2 )
% 3.82/4.03 = ( times_times_nat @ K @ N2 ) )
% 3.82/4.03 = ( ( K = zero_zero_nat )
% 3.82/4.03 | ( M2 = N2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % nat_mult_eq_cancel_disj
% 3.82/4.03 thf(fact_2828_left__add__mult__distrib,axiom,
% 3.82/4.03 ! [I: nat,U: nat,J: nat,K: nat] :
% 3.82/4.03 ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ K ) )
% 3.82/4.03 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I @ J ) @ U ) @ K ) ) ).
% 3.82/4.03
% 3.82/4.03 % left_add_mult_distrib
% 3.82/4.03 thf(fact_2829_nat__mult__less__cancel1,axiom,
% 3.82/4.03 ! [K: nat,M2: nat,N2: nat] :
% 3.82/4.03 ( ( ord_less_nat @ zero_zero_nat @ K )
% 3.82/4.03 => ( ( ord_less_nat @ ( times_times_nat @ K @ M2 ) @ ( times_times_nat @ K @ N2 ) )
% 3.82/4.03 = ( ord_less_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % nat_mult_less_cancel1
% 3.82/4.03 thf(fact_2830_nat__mult__eq__cancel1,axiom,
% 3.82/4.03 ! [K: nat,M2: nat,N2: nat] :
% 3.82/4.03 ( ( ord_less_nat @ zero_zero_nat @ K )
% 3.82/4.03 => ( ( ( times_times_nat @ K @ M2 )
% 3.82/4.03 = ( times_times_nat @ K @ N2 ) )
% 3.82/4.03 = ( M2 = N2 ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % nat_mult_eq_cancel1
% 3.82/4.03 thf(fact_2831_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 3.82/4.03 ! [A: nat,B2: nat] :
% 3.82/4.03 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 3.82/4.03 => ( ( ord_less_nat @ A @ B2 )
% 3.82/4.03 => ( ( divide_divide_nat @ A @ B2 )
% 3.82/4.03 = zero_zero_nat ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % unique_euclidean_semiring_numeral_class.div_less
% 3.82/4.03 thf(fact_2832_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 3.82/4.03 ! [A: int,B2: int] :
% 3.82/4.03 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 3.82/4.03 => ( ( ord_less_int @ A @ B2 )
% 3.82/4.03 => ( ( divide_divide_int @ A @ B2 )
% 3.82/4.03 = zero_zero_int ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % unique_euclidean_semiring_numeral_class.div_less
% 3.82/4.03 thf(fact_2833_div__positive,axiom,
% 3.82/4.03 ! [B2: nat,A: nat] :
% 3.82/4.03 ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 3.82/4.03 => ( ( ord_less_eq_nat @ B2 @ A )
% 3.82/4.03 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ A @ B2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % div_positive
% 3.82/4.03 thf(fact_2834_div__positive,axiom,
% 3.82/4.03 ! [B2: int,A: int] :
% 3.82/4.03 ( ( ord_less_int @ zero_zero_int @ B2 )
% 3.82/4.03 => ( ( ord_less_eq_int @ B2 @ A )
% 3.82/4.03 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % div_positive
% 3.82/4.03 thf(fact_2835_mult__le__cancel__iff1,axiom,
% 3.82/4.03 ! [Z3: real,X: real,Y: real] :
% 3.82/4.03 ( ( ord_less_real @ zero_zero_real @ Z3 )
% 3.82/4.03 => ( ( ord_less_eq_real @ ( times_times_real @ X @ Z3 ) @ ( times_times_real @ Y @ Z3 ) )
% 3.82/4.03 = ( ord_less_eq_real @ X @ Y ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_le_cancel_iff1
% 3.82/4.03 thf(fact_2836_mult__le__cancel__iff1,axiom,
% 3.82/4.03 ! [Z3: int,X: int,Y: int] :
% 3.82/4.03 ( ( ord_less_int @ zero_zero_int @ Z3 )
% 3.82/4.03 => ( ( ord_less_eq_int @ ( times_times_int @ X @ Z3 ) @ ( times_times_int @ Y @ Z3 ) )
% 3.82/4.03 = ( ord_less_eq_int @ X @ Y ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_le_cancel_iff1
% 3.82/4.03 thf(fact_2837_mult__le__cancel__iff2,axiom,
% 3.82/4.03 ! [Z3: real,X: real,Y: real] :
% 3.82/4.03 ( ( ord_less_real @ zero_zero_real @ Z3 )
% 3.82/4.03 => ( ( ord_less_eq_real @ ( times_times_real @ Z3 @ X ) @ ( times_times_real @ Z3 @ Y ) )
% 3.82/4.03 = ( ord_less_eq_real @ X @ Y ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_le_cancel_iff2
% 3.82/4.03 thf(fact_2838_mult__le__cancel__iff2,axiom,
% 3.82/4.03 ! [Z3: int,X: int,Y: int] :
% 3.82/4.03 ( ( ord_less_int @ zero_zero_int @ Z3 )
% 3.82/4.03 => ( ( ord_less_eq_int @ ( times_times_int @ Z3 @ X ) @ ( times_times_int @ Z3 @ Y ) )
% 3.82/4.03 = ( ord_less_eq_int @ X @ Y ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_le_cancel_iff2
% 3.82/4.03 thf(fact_2839_divides__aux__eq,axiom,
% 3.82/4.03 ! [Q3: nat,R2: nat] :
% 3.82/4.03 ( ( unique6322359934112328802ux_nat @ ( product_Pair_nat_nat @ Q3 @ R2 ) )
% 3.82/4.03 = ( R2 = zero_zero_nat ) ) ).
% 3.82/4.03
% 3.82/4.03 % divides_aux_eq
% 3.82/4.03 thf(fact_2840_divides__aux__eq,axiom,
% 3.82/4.03 ! [Q3: int,R2: int] :
% 3.82/4.03 ( ( unique6319869463603278526ux_int @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 3.82/4.03 = ( R2 = zero_zero_int ) ) ).
% 3.82/4.03
% 3.82/4.03 % divides_aux_eq
% 3.82/4.03 thf(fact_2841_low__def,axiom,
% 3.82/4.03 ( vEBT_VEBT_low
% 3.82/4.03 = ( ^ [X4: nat,N: nat] : ( modulo_modulo_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % low_def
% 3.82/4.03 thf(fact_2842_even__succ__div__exp,axiom,
% 3.82/4.03 ! [A: nat,N2: nat] :
% 3.82/4.03 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 3.82/4.03 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.03 => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 3.82/4.03 = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % even_succ_div_exp
% 3.82/4.03 thf(fact_2843_even__succ__div__exp,axiom,
% 3.82/4.03 ! [A: int,N2: nat] :
% 3.82/4.03 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 3.82/4.03 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.03 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 3.82/4.03 = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % even_succ_div_exp
% 3.82/4.03 thf(fact_2844_set__decode__Suc,axiom,
% 3.82/4.03 ! [N2: nat,X: nat] :
% 3.82/4.03 ( ( member_nat @ ( suc @ N2 ) @ ( nat_set_decode @ X ) )
% 3.82/4.03 = ( member_nat @ N2 @ ( nat_set_decode @ ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % set_decode_Suc
% 3.82/4.03 thf(fact_2845_vebt__insert_Oelims,axiom,
% 3.82/4.03 ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 3.82/4.03 ( ( ( vEBT_vebt_insert @ X @ Xa2 )
% 3.82/4.03 = Y )
% 3.82/4.03 => ( ! [A4: $o,B4: $o] :
% 3.82/4.03 ( ( X
% 3.82/4.03 = ( vEBT_Leaf @ A4 @ B4 ) )
% 3.82/4.03 => ~ ( ( ( Xa2 = zero_zero_nat )
% 3.82/4.03 => ( Y
% 3.82/4.03 = ( vEBT_Leaf @ $true @ B4 ) ) )
% 3.82/4.03 & ( ( Xa2 != zero_zero_nat )
% 3.82/4.03 => ( ( ( Xa2 = one_one_nat )
% 3.82/4.03 => ( Y
% 3.82/4.03 = ( vEBT_Leaf @ A4 @ $true ) ) )
% 3.82/4.03 & ( ( Xa2 != one_one_nat )
% 3.82/4.03 => ( Y
% 3.82/4.03 = ( vEBT_Leaf @ A4 @ B4 ) ) ) ) ) ) )
% 3.82/4.03 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 3.82/4.03 ( ( X
% 3.82/4.03 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) )
% 3.82/4.03 => ( Y
% 3.82/4.03 != ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) ) )
% 3.82/4.03 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 3.82/4.03 ( ( X
% 3.82/4.03 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) )
% 3.82/4.03 => ( Y
% 3.82/4.03 != ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) ) )
% 3.82/4.03 => ( ! [V2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 3.82/4.03 ( ( X
% 3.82/4.03 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) )
% 3.82/4.03 => ( Y
% 3.82/4.03 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) ) )
% 3.82/4.03 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 3.82/4.03 ( ( X
% 3.82/4.03 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 3.82/4.03 => ( Y
% 3.82/4.03 != ( if_VEBT_VEBT
% 3.82/4.03 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 3.82/4.03 & ~ ( ( Xa2 = Mi2 )
% 3.82/4.03 | ( Xa2 = Ma2 ) ) )
% 3.82/4.03 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Xa2 @ Mi2 ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ Ma2 ) ) ) @ ( suc @ ( suc @ Va ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 3.82/4.03 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) ) ) ) ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % vebt_insert.elims
% 3.82/4.03 thf(fact_2846_length__product,axiom,
% 3.82/4.03 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 3.82/4.03 ( ( size_s7466405169056248089T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs @ Ys ) )
% 3.82/4.03 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % length_product
% 3.82/4.03 thf(fact_2847_length__product,axiom,
% 3.82/4.03 ! [Xs: list_VEBT_VEBT,Ys: list_int] :
% 3.82/4.03 ( ( size_s3661962791536183091BT_int @ ( produc7292646706713671643BT_int @ Xs @ Ys ) )
% 3.82/4.03 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_int @ Ys ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % length_product
% 3.82/4.03 thf(fact_2848_length__product,axiom,
% 3.82/4.03 ! [Xs: list_VEBT_VEBT,Ys: list_nat] :
% 3.82/4.03 ( ( size_s6152045936467909847BT_nat @ ( produc7295137177222721919BT_nat @ Xs @ Ys ) )
% 3.82/4.03 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % length_product
% 3.82/4.03 thf(fact_2849_length__product,axiom,
% 3.82/4.03 ! [Xs: list_int,Ys: list_VEBT_VEBT] :
% 3.82/4.03 ( ( size_s6639371672096860321T_VEBT @ ( produc662631939642741121T_VEBT @ Xs @ Ys ) )
% 3.82/4.03 = ( times_times_nat @ ( size_size_list_int @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % length_product
% 3.82/4.03 thf(fact_2850_length__product,axiom,
% 3.82/4.03 ! [Xs: list_int,Ys: list_int] :
% 3.82/4.03 ( ( size_s5157815400016825771nt_int @ ( product_int_int @ Xs @ Ys ) )
% 3.82/4.03 = ( times_times_nat @ ( size_size_list_int @ Xs ) @ ( size_size_list_int @ Ys ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % length_product
% 3.82/4.03 thf(fact_2851_length__product,axiom,
% 3.82/4.03 ! [Xs: list_int,Ys: list_nat] :
% 3.82/4.03 ( ( size_s7647898544948552527nt_nat @ ( product_int_nat @ Xs @ Ys ) )
% 3.82/4.03 = ( times_times_nat @ ( size_size_list_int @ Xs ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % length_product
% 3.82/4.03 thf(fact_2852_length__product,axiom,
% 3.82/4.03 ! [Xs: list_nat,Ys: list_VEBT_VEBT] :
% 3.82/4.03 ( ( size_s4762443039079500285T_VEBT @ ( produc7156399406898700509T_VEBT @ Xs @ Ys ) )
% 3.82/4.03 = ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % length_product
% 3.82/4.03 thf(fact_2853_length__product,axiom,
% 3.82/4.03 ! [Xs: list_nat,Ys: list_int] :
% 3.82/4.03 ( ( size_s2970893825323803983at_int @ ( product_nat_int @ Xs @ Ys ) )
% 3.82/4.03 = ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_size_list_int @ Ys ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % length_product
% 3.82/4.03 thf(fact_2854_length__product,axiom,
% 3.82/4.03 ! [Xs: list_nat,Ys: list_nat] :
% 3.82/4.03 ( ( size_s5460976970255530739at_nat @ ( product_nat_nat @ Xs @ Ys ) )
% 3.82/4.03 = ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % length_product
% 3.82/4.03 thf(fact_2855_mult__less__iff1,axiom,
% 3.82/4.03 ! [Z3: real,X: real,Y: real] :
% 3.82/4.03 ( ( ord_less_real @ zero_zero_real @ Z3 )
% 3.82/4.03 => ( ( ord_less_real @ ( times_times_real @ X @ Z3 ) @ ( times_times_real @ Y @ Z3 ) )
% 3.82/4.03 = ( ord_less_real @ X @ Y ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_less_iff1
% 3.82/4.03 thf(fact_2856_mult__less__iff1,axiom,
% 3.82/4.03 ! [Z3: int,X: int,Y: int] :
% 3.82/4.03 ( ( ord_less_int @ zero_zero_int @ Z3 )
% 3.82/4.03 => ( ( ord_less_int @ ( times_times_int @ X @ Z3 ) @ ( times_times_int @ Y @ Z3 ) )
% 3.82/4.03 = ( ord_less_int @ X @ Y ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % mult_less_iff1
% 3.82/4.03 thf(fact_2857_set__vebt_H__def,axiom,
% 3.82/4.03 ( vEBT_VEBT_set_vebt
% 3.82/4.03 = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_vebt_member @ T2 ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % set_vebt'_def
% 3.82/4.03 thf(fact_2858_nat__dvd__1__iff__1,axiom,
% 3.82/4.03 ! [M2: nat] :
% 3.82/4.03 ( ( dvd_dvd_nat @ M2 @ one_one_nat )
% 3.82/4.03 = ( M2 = one_one_nat ) ) ).
% 3.82/4.03
% 3.82/4.03 % nat_dvd_1_iff_1
% 3.82/4.03 thf(fact_2859_finite__Collect__disjI,axiom,
% 3.82/4.03 ! [P: real > $o,Q: real > $o] :
% 3.82/4.03 ( ( finite_finite_real
% 3.82/4.03 @ ( collect_real
% 3.82/4.03 @ ^ [X4: real] :
% 3.82/4.03 ( ( P @ X4 )
% 3.82/4.03 | ( Q @ X4 ) ) ) )
% 3.82/4.03 = ( ( finite_finite_real @ ( collect_real @ P ) )
% 3.82/4.03 & ( finite_finite_real @ ( collect_real @ Q ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % finite_Collect_disjI
% 3.82/4.03 thf(fact_2860_finite__Collect__disjI,axiom,
% 3.82/4.03 ! [P: list_nat > $o,Q: list_nat > $o] :
% 3.82/4.03 ( ( finite8100373058378681591st_nat
% 3.82/4.03 @ ( collect_list_nat
% 3.82/4.03 @ ^ [X4: list_nat] :
% 3.82/4.03 ( ( P @ X4 )
% 3.82/4.03 | ( Q @ X4 ) ) ) )
% 3.82/4.03 = ( ( finite8100373058378681591st_nat @ ( collect_list_nat @ P ) )
% 3.82/4.03 & ( finite8100373058378681591st_nat @ ( collect_list_nat @ Q ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % finite_Collect_disjI
% 3.82/4.03 thf(fact_2861_finite__Collect__disjI,axiom,
% 3.82/4.03 ! [P: set_nat > $o,Q: set_nat > $o] :
% 3.82/4.03 ( ( finite1152437895449049373et_nat
% 3.82/4.03 @ ( collect_set_nat
% 3.82/4.03 @ ^ [X4: set_nat] :
% 3.82/4.03 ( ( P @ X4 )
% 3.82/4.03 | ( Q @ X4 ) ) ) )
% 3.82/4.03 = ( ( finite1152437895449049373et_nat @ ( collect_set_nat @ P ) )
% 3.82/4.03 & ( finite1152437895449049373et_nat @ ( collect_set_nat @ Q ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % finite_Collect_disjI
% 3.82/4.03 thf(fact_2862_finite__Collect__disjI,axiom,
% 3.82/4.03 ! [P: nat > $o,Q: nat > $o] :
% 3.82/4.03 ( ( finite_finite_nat
% 3.82/4.03 @ ( collect_nat
% 3.82/4.03 @ ^ [X4: nat] :
% 3.82/4.03 ( ( P @ X4 )
% 3.82/4.03 | ( Q @ X4 ) ) ) )
% 3.82/4.03 = ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 3.82/4.03 & ( finite_finite_nat @ ( collect_nat @ Q ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % finite_Collect_disjI
% 3.82/4.03 thf(fact_2863_finite__Collect__disjI,axiom,
% 3.82/4.03 ! [P: complex > $o,Q: complex > $o] :
% 3.82/4.03 ( ( finite3207457112153483333omplex
% 3.82/4.03 @ ( collect_complex
% 3.82/4.03 @ ^ [X4: complex] :
% 3.82/4.03 ( ( P @ X4 )
% 3.82/4.03 | ( Q @ X4 ) ) ) )
% 3.82/4.03 = ( ( finite3207457112153483333omplex @ ( collect_complex @ P ) )
% 3.82/4.03 & ( finite3207457112153483333omplex @ ( collect_complex @ Q ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % finite_Collect_disjI
% 3.82/4.03 thf(fact_2864_finite__Collect__disjI,axiom,
% 3.82/4.03 ! [P: int > $o,Q: int > $o] :
% 3.82/4.03 ( ( finite_finite_int
% 3.82/4.03 @ ( collect_int
% 3.82/4.03 @ ^ [X4: int] :
% 3.82/4.03 ( ( P @ X4 )
% 3.82/4.03 | ( Q @ X4 ) ) ) )
% 3.82/4.03 = ( ( finite_finite_int @ ( collect_int @ P ) )
% 3.82/4.03 & ( finite_finite_int @ ( collect_int @ Q ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % finite_Collect_disjI
% 3.82/4.03 thf(fact_2865_finite__Collect__disjI,axiom,
% 3.82/4.03 ! [P: extended_enat > $o,Q: extended_enat > $o] :
% 3.82/4.03 ( ( finite4001608067531595151d_enat
% 3.82/4.03 @ ( collec4429806609662206161d_enat
% 3.82/4.03 @ ^ [X4: extended_enat] :
% 3.82/4.03 ( ( P @ X4 )
% 3.82/4.03 | ( Q @ X4 ) ) ) )
% 3.82/4.03 = ( ( finite4001608067531595151d_enat @ ( collec4429806609662206161d_enat @ P ) )
% 3.82/4.03 & ( finite4001608067531595151d_enat @ ( collec4429806609662206161d_enat @ Q ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % finite_Collect_disjI
% 3.82/4.03 thf(fact_2866_finite__Collect__conjI,axiom,
% 3.82/4.03 ! [P: real > $o,Q: real > $o] :
% 3.82/4.03 ( ( ( finite_finite_real @ ( collect_real @ P ) )
% 3.82/4.03 | ( finite_finite_real @ ( collect_real @ Q ) ) )
% 3.82/4.03 => ( finite_finite_real
% 3.82/4.03 @ ( collect_real
% 3.82/4.03 @ ^ [X4: real] :
% 3.82/4.03 ( ( P @ X4 )
% 3.82/4.03 & ( Q @ X4 ) ) ) ) ) ).
% 3.82/4.03
% 3.82/4.03 % finite_Collect_conjI
% 3.82/4.03 thf(fact_2867_finite__Collect__conjI,axiom,
% 3.82/4.03 ! [P: list_nat > $o,Q: list_nat > $o] :
% 3.82/4.03 ( ( ( finite8100373058378681591st_nat @ ( collect_list_nat @ P ) )
% 3.82/4.03 | ( finite8100373058378681591st_nat @ ( collect_list_nat @ Q ) ) )
% 3.82/4.03 => ( finite8100373058378681591st_nat
% 3.82/4.03 @ ( collect_list_nat
% 3.82/4.04 @ ^ [X4: list_nat] :
% 3.82/4.04 ( ( P @ X4 )
% 3.82/4.04 & ( Q @ X4 ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % finite_Collect_conjI
% 3.82/4.04 thf(fact_2868_finite__Collect__conjI,axiom,
% 3.82/4.04 ! [P: set_nat > $o,Q: set_nat > $o] :
% 3.82/4.04 ( ( ( finite1152437895449049373et_nat @ ( collect_set_nat @ P ) )
% 3.82/4.04 | ( finite1152437895449049373et_nat @ ( collect_set_nat @ Q ) ) )
% 3.82/4.04 => ( finite1152437895449049373et_nat
% 3.82/4.04 @ ( collect_set_nat
% 3.82/4.04 @ ^ [X4: set_nat] :
% 3.82/4.04 ( ( P @ X4 )
% 3.82/4.04 & ( Q @ X4 ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % finite_Collect_conjI
% 3.82/4.04 thf(fact_2869_finite__Collect__conjI,axiom,
% 3.82/4.04 ! [P: nat > $o,Q: nat > $o] :
% 3.82/4.04 ( ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 3.82/4.04 | ( finite_finite_nat @ ( collect_nat @ Q ) ) )
% 3.82/4.04 => ( finite_finite_nat
% 3.82/4.04 @ ( collect_nat
% 3.82/4.04 @ ^ [X4: nat] :
% 3.82/4.04 ( ( P @ X4 )
% 3.82/4.04 & ( Q @ X4 ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % finite_Collect_conjI
% 3.82/4.04 thf(fact_2870_finite__Collect__conjI,axiom,
% 3.82/4.04 ! [P: complex > $o,Q: complex > $o] :
% 3.82/4.04 ( ( ( finite3207457112153483333omplex @ ( collect_complex @ P ) )
% 3.82/4.04 | ( finite3207457112153483333omplex @ ( collect_complex @ Q ) ) )
% 3.82/4.04 => ( finite3207457112153483333omplex
% 3.82/4.04 @ ( collect_complex
% 3.82/4.04 @ ^ [X4: complex] :
% 3.82/4.04 ( ( P @ X4 )
% 3.82/4.04 & ( Q @ X4 ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % finite_Collect_conjI
% 3.82/4.04 thf(fact_2871_finite__Collect__conjI,axiom,
% 3.82/4.04 ! [P: int > $o,Q: int > $o] :
% 3.82/4.04 ( ( ( finite_finite_int @ ( collect_int @ P ) )
% 3.82/4.04 | ( finite_finite_int @ ( collect_int @ Q ) ) )
% 3.82/4.04 => ( finite_finite_int
% 3.82/4.04 @ ( collect_int
% 3.82/4.04 @ ^ [X4: int] :
% 3.82/4.04 ( ( P @ X4 )
% 3.82/4.04 & ( Q @ X4 ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % finite_Collect_conjI
% 3.82/4.04 thf(fact_2872_finite__Collect__conjI,axiom,
% 3.82/4.04 ! [P: extended_enat > $o,Q: extended_enat > $o] :
% 3.82/4.04 ( ( ( finite4001608067531595151d_enat @ ( collec4429806609662206161d_enat @ P ) )
% 3.82/4.04 | ( finite4001608067531595151d_enat @ ( collec4429806609662206161d_enat @ Q ) ) )
% 3.82/4.04 => ( finite4001608067531595151d_enat
% 3.82/4.04 @ ( collec4429806609662206161d_enat
% 3.82/4.04 @ ^ [X4: extended_enat] :
% 3.82/4.04 ( ( P @ X4 )
% 3.82/4.04 & ( Q @ X4 ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % finite_Collect_conjI
% 3.82/4.04 thf(fact_2873_dvd__0__left__iff,axiom,
% 3.82/4.04 ! [A: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 3.82/4.04 = ( A = zero_zero_nat ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_0_left_iff
% 3.82/4.04 thf(fact_2874_dvd__0__left__iff,axiom,
% 3.82/4.04 ! [A: real] :
% 3.82/4.04 ( ( dvd_dvd_real @ zero_zero_real @ A )
% 3.82/4.04 = ( A = zero_zero_real ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_0_left_iff
% 3.82/4.04 thf(fact_2875_dvd__0__left__iff,axiom,
% 3.82/4.04 ! [A: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ zero_zero_int @ A )
% 3.82/4.04 = ( A = zero_zero_int ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_0_left_iff
% 3.82/4.04 thf(fact_2876_dvd__0__left__iff,axiom,
% 3.82/4.04 ! [A: complex] :
% 3.82/4.04 ( ( dvd_dvd_complex @ zero_zero_complex @ A )
% 3.82/4.04 = ( A = zero_zero_complex ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_0_left_iff
% 3.82/4.04 thf(fact_2877_dvd__0__left__iff,axiom,
% 3.82/4.04 ! [A: extended_enat] :
% 3.82/4.04 ( ( dvd_dv3785147216227455552d_enat @ zero_z5237406670263579293d_enat @ A )
% 3.82/4.04 = ( A = zero_z5237406670263579293d_enat ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_0_left_iff
% 3.82/4.04 thf(fact_2878_dvd__0__right,axiom,
% 3.82/4.04 ! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_0_right
% 3.82/4.04 thf(fact_2879_dvd__0__right,axiom,
% 3.82/4.04 ! [A: real] : ( dvd_dvd_real @ A @ zero_zero_real ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_0_right
% 3.82/4.04 thf(fact_2880_dvd__0__right,axiom,
% 3.82/4.04 ! [A: int] : ( dvd_dvd_int @ A @ zero_zero_int ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_0_right
% 3.82/4.04 thf(fact_2881_dvd__0__right,axiom,
% 3.82/4.04 ! [A: complex] : ( dvd_dvd_complex @ A @ zero_zero_complex ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_0_right
% 3.82/4.04 thf(fact_2882_dvd__0__right,axiom,
% 3.82/4.04 ! [A: extended_enat] : ( dvd_dv3785147216227455552d_enat @ A @ zero_z5237406670263579293d_enat ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_0_right
% 3.82/4.04 thf(fact_2883_dvd__add__triv__right__iff,axiom,
% 3.82/4.04 ! [A: nat,B2: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B2 @ A ) )
% 3.82/4.04 = ( dvd_dvd_nat @ A @ B2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_add_triv_right_iff
% 3.82/4.04 thf(fact_2884_dvd__add__triv__right__iff,axiom,
% 3.82/4.04 ! [A: int,B2: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B2 @ A ) )
% 3.82/4.04 = ( dvd_dvd_int @ A @ B2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_add_triv_right_iff
% 3.82/4.04 thf(fact_2885_dvd__add__triv__right__iff,axiom,
% 3.82/4.04 ! [A: real,B2: real] :
% 3.82/4.04 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B2 @ A ) )
% 3.82/4.04 = ( dvd_dvd_real @ A @ B2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_add_triv_right_iff
% 3.82/4.04 thf(fact_2886_dvd__add__triv__left__iff,axiom,
% 3.82/4.04 ! [A: nat,B2: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ A @ B2 ) )
% 3.82/4.04 = ( dvd_dvd_nat @ A @ B2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_add_triv_left_iff
% 3.82/4.04 thf(fact_2887_dvd__add__triv__left__iff,axiom,
% 3.82/4.04 ! [A: int,B2: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ A @ B2 ) )
% 3.82/4.04 = ( dvd_dvd_int @ A @ B2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_add_triv_left_iff
% 3.82/4.04 thf(fact_2888_dvd__add__triv__left__iff,axiom,
% 3.82/4.04 ! [A: real,B2: real] :
% 3.82/4.04 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ A @ B2 ) )
% 3.82/4.04 = ( dvd_dvd_real @ A @ B2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_add_triv_left_iff
% 3.82/4.04 thf(fact_2889_dvd__1__iff__1,axiom,
% 3.82/4.04 ! [M2: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ M2 @ ( suc @ zero_zero_nat ) )
% 3.82/4.04 = ( M2
% 3.82/4.04 = ( suc @ zero_zero_nat ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_1_iff_1
% 3.82/4.04 thf(fact_2890_dvd__1__left,axiom,
% 3.82/4.04 ! [K: nat] : ( dvd_dvd_nat @ ( suc @ zero_zero_nat ) @ K ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_1_left
% 3.82/4.04 thf(fact_2891_mod__self,axiom,
% 3.82/4.04 ! [A: nat] :
% 3.82/4.04 ( ( modulo_modulo_nat @ A @ A )
% 3.82/4.04 = zero_zero_nat ) ).
% 3.82/4.04
% 3.82/4.04 % mod_self
% 3.82/4.04 thf(fact_2892_mod__self,axiom,
% 3.82/4.04 ! [A: int] :
% 3.82/4.04 ( ( modulo_modulo_int @ A @ A )
% 3.82/4.04 = zero_zero_int ) ).
% 3.82/4.04
% 3.82/4.04 % mod_self
% 3.82/4.04 thf(fact_2893_mod__by__0,axiom,
% 3.82/4.04 ! [A: nat] :
% 3.82/4.04 ( ( modulo_modulo_nat @ A @ zero_zero_nat )
% 3.82/4.04 = A ) ).
% 3.82/4.04
% 3.82/4.04 % mod_by_0
% 3.82/4.04 thf(fact_2894_mod__by__0,axiom,
% 3.82/4.04 ! [A: int] :
% 3.82/4.04 ( ( modulo_modulo_int @ A @ zero_zero_int )
% 3.82/4.04 = A ) ).
% 3.82/4.04
% 3.82/4.04 % mod_by_0
% 3.82/4.04 thf(fact_2895_mod__0,axiom,
% 3.82/4.04 ! [A: nat] :
% 3.82/4.04 ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 3.82/4.04 = zero_zero_nat ) ).
% 3.82/4.04
% 3.82/4.04 % mod_0
% 3.82/4.04 thf(fact_2896_mod__0,axiom,
% 3.82/4.04 ! [A: int] :
% 3.82/4.04 ( ( modulo_modulo_int @ zero_zero_int @ A )
% 3.82/4.04 = zero_zero_int ) ).
% 3.82/4.04
% 3.82/4.04 % mod_0
% 3.82/4.04 thf(fact_2897_bits__mod__0,axiom,
% 3.82/4.04 ! [A: nat] :
% 3.82/4.04 ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 3.82/4.04 = zero_zero_nat ) ).
% 3.82/4.04
% 3.82/4.04 % bits_mod_0
% 3.82/4.04 thf(fact_2898_bits__mod__0,axiom,
% 3.82/4.04 ! [A: int] :
% 3.82/4.04 ( ( modulo_modulo_int @ zero_zero_int @ A )
% 3.82/4.04 = zero_zero_int ) ).
% 3.82/4.04
% 3.82/4.04 % bits_mod_0
% 3.82/4.04 thf(fact_2899_div__dvd__div,axiom,
% 3.82/4.04 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ A @ B2 )
% 3.82/4.04 => ( ( dvd_dvd_nat @ A @ C )
% 3.82/4.04 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ B2 @ A ) @ ( divide_divide_nat @ C @ A ) )
% 3.82/4.04 = ( dvd_dvd_nat @ B2 @ C ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % div_dvd_div
% 3.82/4.04 thf(fact_2900_div__dvd__div,axiom,
% 3.82/4.04 ! [A: int,B2: int,C: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ A @ B2 )
% 3.82/4.04 => ( ( dvd_dvd_int @ A @ C )
% 3.82/4.04 => ( ( dvd_dvd_int @ ( divide_divide_int @ B2 @ A ) @ ( divide_divide_int @ C @ A ) )
% 3.82/4.04 = ( dvd_dvd_int @ B2 @ C ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % div_dvd_div
% 3.82/4.04 thf(fact_2901_mod__add__self2,axiom,
% 3.82/4.04 ! [A: nat,B2: nat] :
% 3.82/4.04 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B2 ) @ B2 )
% 3.82/4.04 = ( modulo_modulo_nat @ A @ B2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % mod_add_self2
% 3.82/4.04 thf(fact_2902_mod__add__self2,axiom,
% 3.82/4.04 ! [A: int,B2: int] :
% 3.82/4.04 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B2 ) @ B2 )
% 3.82/4.04 = ( modulo_modulo_int @ A @ B2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % mod_add_self2
% 3.82/4.04 thf(fact_2903_mod__add__self1,axiom,
% 3.82/4.04 ! [B2: nat,A: nat] :
% 3.82/4.04 ( ( modulo_modulo_nat @ ( plus_plus_nat @ B2 @ A ) @ B2 )
% 3.82/4.04 = ( modulo_modulo_nat @ A @ B2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % mod_add_self1
% 3.82/4.04 thf(fact_2904_mod__add__self1,axiom,
% 3.82/4.04 ! [B2: int,A: int] :
% 3.82/4.04 ( ( modulo_modulo_int @ ( plus_plus_int @ B2 @ A ) @ B2 )
% 3.82/4.04 = ( modulo_modulo_int @ A @ B2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % mod_add_self1
% 3.82/4.04 thf(fact_2905_nat__mult__dvd__cancel__disj,axiom,
% 3.82/4.04 ! [K: nat,M2: nat,N2: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M2 ) @ ( times_times_nat @ K @ N2 ) )
% 3.82/4.04 = ( ( K = zero_zero_nat )
% 3.82/4.04 | ( dvd_dvd_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % nat_mult_dvd_cancel_disj
% 3.82/4.04 thf(fact_2906_mod__less,axiom,
% 3.82/4.04 ! [M2: nat,N2: nat] :
% 3.82/4.04 ( ( ord_less_nat @ M2 @ N2 )
% 3.82/4.04 => ( ( modulo_modulo_nat @ M2 @ N2 )
% 3.82/4.04 = M2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % mod_less
% 3.82/4.04 thf(fact_2907_finite__Collect__subsets,axiom,
% 3.82/4.04 ! [A2: set_complex] :
% 3.82/4.04 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.04 => ( finite6551019134538273531omplex
% 3.82/4.04 @ ( collect_set_complex
% 3.82/4.04 @ ^ [B5: set_complex] : ( ord_le211207098394363844omplex @ B5 @ A2 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % finite_Collect_subsets
% 3.82/4.04 thf(fact_2908_finite__Collect__subsets,axiom,
% 3.82/4.04 ! [A2: set_Extended_enat] :
% 3.82/4.04 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.04 => ( finite5468666774076196335d_enat
% 3.82/4.04 @ ( collec2260605976452661553d_enat
% 3.82/4.04 @ ^ [B5: set_Extended_enat] : ( ord_le7203529160286727270d_enat @ B5 @ A2 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % finite_Collect_subsets
% 3.82/4.04 thf(fact_2909_finite__Collect__subsets,axiom,
% 3.82/4.04 ! [A2: set_nat] :
% 3.82/4.04 ( ( finite_finite_nat @ A2 )
% 3.82/4.04 => ( finite1152437895449049373et_nat
% 3.82/4.04 @ ( collect_set_nat
% 3.82/4.04 @ ^ [B5: set_nat] : ( ord_less_eq_set_nat @ B5 @ A2 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % finite_Collect_subsets
% 3.82/4.04 thf(fact_2910_finite__Collect__subsets,axiom,
% 3.82/4.04 ! [A2: set_int] :
% 3.82/4.04 ( ( finite_finite_int @ A2 )
% 3.82/4.04 => ( finite6197958912794628473et_int
% 3.82/4.04 @ ( collect_set_int
% 3.82/4.04 @ ^ [B5: set_int] : ( ord_less_eq_set_int @ B5 @ A2 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % finite_Collect_subsets
% 3.82/4.04 thf(fact_2911_finite__Collect__less__nat,axiom,
% 3.82/4.04 ! [K: nat] :
% 3.82/4.04 ( finite_finite_nat
% 3.82/4.04 @ ( collect_nat
% 3.82/4.04 @ ^ [N: nat] : ( ord_less_nat @ N @ K ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % finite_Collect_less_nat
% 3.82/4.04 thf(fact_2912_finite__Collect__le__nat,axiom,
% 3.82/4.04 ! [K: nat] :
% 3.82/4.04 ( finite_finite_nat
% 3.82/4.04 @ ( collect_nat
% 3.82/4.04 @ ^ [N: nat] : ( ord_less_eq_nat @ N @ K ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % finite_Collect_le_nat
% 3.82/4.04 thf(fact_2913_dvd__times__right__cancel__iff,axiom,
% 3.82/4.04 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.04 ( ( A != zero_zero_nat )
% 3.82/4.04 => ( ( dvd_dvd_nat @ ( times_times_nat @ B2 @ A ) @ ( times_times_nat @ C @ A ) )
% 3.82/4.04 = ( dvd_dvd_nat @ B2 @ C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_times_right_cancel_iff
% 3.82/4.04 thf(fact_2914_dvd__times__right__cancel__iff,axiom,
% 3.82/4.04 ! [A: int,B2: int,C: int] :
% 3.82/4.04 ( ( A != zero_zero_int )
% 3.82/4.04 => ( ( dvd_dvd_int @ ( times_times_int @ B2 @ A ) @ ( times_times_int @ C @ A ) )
% 3.82/4.04 = ( dvd_dvd_int @ B2 @ C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_times_right_cancel_iff
% 3.82/4.04 thf(fact_2915_dvd__times__left__cancel__iff,axiom,
% 3.82/4.04 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.04 ( ( A != zero_zero_nat )
% 3.82/4.04 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B2 ) @ ( times_times_nat @ A @ C ) )
% 3.82/4.04 = ( dvd_dvd_nat @ B2 @ C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_times_left_cancel_iff
% 3.82/4.04 thf(fact_2916_dvd__times__left__cancel__iff,axiom,
% 3.82/4.04 ! [A: int,B2: int,C: int] :
% 3.82/4.04 ( ( A != zero_zero_int )
% 3.82/4.04 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B2 ) @ ( times_times_int @ A @ C ) )
% 3.82/4.04 = ( dvd_dvd_int @ B2 @ C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_times_left_cancel_iff
% 3.82/4.04 thf(fact_2917_dvd__mult__cancel__right,axiom,
% 3.82/4.04 ! [A: int,C: int,B2: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B2 @ C ) )
% 3.82/4.04 = ( ( C = zero_zero_int )
% 3.82/4.04 | ( dvd_dvd_int @ A @ B2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_mult_cancel_right
% 3.82/4.04 thf(fact_2918_dvd__mult__cancel__right,axiom,
% 3.82/4.04 ! [A: real,C: real,B2: real] :
% 3.82/4.04 ( ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B2 @ C ) )
% 3.82/4.04 = ( ( C = zero_zero_real )
% 3.82/4.04 | ( dvd_dvd_real @ A @ B2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_mult_cancel_right
% 3.82/4.04 thf(fact_2919_dvd__mult__cancel__right,axiom,
% 3.82/4.04 ! [A: complex,C: complex,B2: complex] :
% 3.82/4.04 ( ( dvd_dvd_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B2 @ C ) )
% 3.82/4.04 = ( ( C = zero_zero_complex )
% 3.82/4.04 | ( dvd_dvd_complex @ A @ B2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_mult_cancel_right
% 3.82/4.04 thf(fact_2920_dvd__mult__cancel__left,axiom,
% 3.82/4.04 ! [C: int,A: int,B2: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B2 ) )
% 3.82/4.04 = ( ( C = zero_zero_int )
% 3.82/4.04 | ( dvd_dvd_int @ A @ B2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_mult_cancel_left
% 3.82/4.04 thf(fact_2921_dvd__mult__cancel__left,axiom,
% 3.82/4.04 ! [C: real,A: real,B2: real] :
% 3.82/4.04 ( ( dvd_dvd_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B2 ) )
% 3.82/4.04 = ( ( C = zero_zero_real )
% 3.82/4.04 | ( dvd_dvd_real @ A @ B2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_mult_cancel_left
% 3.82/4.04 thf(fact_2922_dvd__mult__cancel__left,axiom,
% 3.82/4.04 ! [C: complex,A: complex,B2: complex] :
% 3.82/4.04 ( ( dvd_dvd_complex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B2 ) )
% 3.82/4.04 = ( ( C = zero_zero_complex )
% 3.82/4.04 | ( dvd_dvd_complex @ A @ B2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_mult_cancel_left
% 3.82/4.04 thf(fact_2923_unit__prod,axiom,
% 3.82/4.04 ! [A: nat,B2: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 3.82/4.04 => ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 3.82/4.04 => ( dvd_dvd_nat @ ( times_times_nat @ A @ B2 ) @ one_one_nat ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % unit_prod
% 3.82/4.04 thf(fact_2924_unit__prod,axiom,
% 3.82/4.04 ! [A: int,B2: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ A @ one_one_int )
% 3.82/4.04 => ( ( dvd_dvd_int @ B2 @ one_one_int )
% 3.82/4.04 => ( dvd_dvd_int @ ( times_times_int @ A @ B2 ) @ one_one_int ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % unit_prod
% 3.82/4.04 thf(fact_2925_dvd__add__times__triv__right__iff,axiom,
% 3.82/4.04 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B2 @ ( times_times_nat @ C @ A ) ) )
% 3.82/4.04 = ( dvd_dvd_nat @ A @ B2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_add_times_triv_right_iff
% 3.82/4.04 thf(fact_2926_dvd__add__times__triv__right__iff,axiom,
% 3.82/4.04 ! [A: int,B2: int,C: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B2 @ ( times_times_int @ C @ A ) ) )
% 3.82/4.04 = ( dvd_dvd_int @ A @ B2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_add_times_triv_right_iff
% 3.82/4.04 thf(fact_2927_dvd__add__times__triv__right__iff,axiom,
% 3.82/4.04 ! [A: real,B2: real,C: real] :
% 3.82/4.04 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B2 @ ( times_times_real @ C @ A ) ) )
% 3.82/4.04 = ( dvd_dvd_real @ A @ B2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_add_times_triv_right_iff
% 3.82/4.04 thf(fact_2928_dvd__add__times__triv__right__iff,axiom,
% 3.82/4.04 ! [A: complex,B2: complex,C: complex] :
% 3.82/4.04 ( ( dvd_dvd_complex @ A @ ( plus_plus_complex @ B2 @ ( times_times_complex @ C @ A ) ) )
% 3.82/4.04 = ( dvd_dvd_complex @ A @ B2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_add_times_triv_right_iff
% 3.82/4.04 thf(fact_2929_dvd__add__times__triv__left__iff,axiom,
% 3.82/4.04 ! [A: nat,C: nat,B2: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ ( times_times_nat @ C @ A ) @ B2 ) )
% 3.82/4.04 = ( dvd_dvd_nat @ A @ B2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_add_times_triv_left_iff
% 3.82/4.04 thf(fact_2930_dvd__add__times__triv__left__iff,axiom,
% 3.82/4.04 ! [A: int,C: int,B2: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ ( times_times_int @ C @ A ) @ B2 ) )
% 3.82/4.04 = ( dvd_dvd_int @ A @ B2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_add_times_triv_left_iff
% 3.82/4.04 thf(fact_2931_dvd__add__times__triv__left__iff,axiom,
% 3.82/4.04 ! [A: real,C: real,B2: real] :
% 3.82/4.04 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ ( times_times_real @ C @ A ) @ B2 ) )
% 3.82/4.04 = ( dvd_dvd_real @ A @ B2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_add_times_triv_left_iff
% 3.82/4.04 thf(fact_2932_dvd__add__times__triv__left__iff,axiom,
% 3.82/4.04 ! [A: complex,C: complex,B2: complex] :
% 3.82/4.04 ( ( dvd_dvd_complex @ A @ ( plus_plus_complex @ ( times_times_complex @ C @ A ) @ B2 ) )
% 3.82/4.04 = ( dvd_dvd_complex @ A @ B2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_add_times_triv_left_iff
% 3.82/4.04 thf(fact_2933_mod__mult__self1__is__0,axiom,
% 3.82/4.04 ! [B2: nat,A: nat] :
% 3.82/4.04 ( ( modulo_modulo_nat @ ( times_times_nat @ B2 @ A ) @ B2 )
% 3.82/4.04 = zero_zero_nat ) ).
% 3.82/4.04
% 3.82/4.04 % mod_mult_self1_is_0
% 3.82/4.04 thf(fact_2934_mod__mult__self1__is__0,axiom,
% 3.82/4.04 ! [B2: int,A: int] :
% 3.82/4.04 ( ( modulo_modulo_int @ ( times_times_int @ B2 @ A ) @ B2 )
% 3.82/4.04 = zero_zero_int ) ).
% 3.82/4.04
% 3.82/4.04 % mod_mult_self1_is_0
% 3.82/4.04 thf(fact_2935_mod__mult__self2__is__0,axiom,
% 3.82/4.04 ! [A: nat,B2: nat] :
% 3.82/4.04 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B2 ) @ B2 )
% 3.82/4.04 = zero_zero_nat ) ).
% 3.82/4.04
% 3.82/4.04 % mod_mult_self2_is_0
% 3.82/4.04 thf(fact_2936_mod__mult__self2__is__0,axiom,
% 3.82/4.04 ! [A: int,B2: int] :
% 3.82/4.04 ( ( modulo_modulo_int @ ( times_times_int @ A @ B2 ) @ B2 )
% 3.82/4.04 = zero_zero_int ) ).
% 3.82/4.04
% 3.82/4.04 % mod_mult_self2_is_0
% 3.82/4.04 thf(fact_2937_mod__by__1,axiom,
% 3.82/4.04 ! [A: nat] :
% 3.82/4.04 ( ( modulo_modulo_nat @ A @ one_one_nat )
% 3.82/4.04 = zero_zero_nat ) ).
% 3.82/4.04
% 3.82/4.04 % mod_by_1
% 3.82/4.04 thf(fact_2938_mod__by__1,axiom,
% 3.82/4.04 ! [A: int] :
% 3.82/4.04 ( ( modulo_modulo_int @ A @ one_one_int )
% 3.82/4.04 = zero_zero_int ) ).
% 3.82/4.04
% 3.82/4.04 % mod_by_1
% 3.82/4.04 thf(fact_2939_bits__mod__by__1,axiom,
% 3.82/4.04 ! [A: nat] :
% 3.82/4.04 ( ( modulo_modulo_nat @ A @ one_one_nat )
% 3.82/4.04 = zero_zero_nat ) ).
% 3.82/4.04
% 3.82/4.04 % bits_mod_by_1
% 3.82/4.04 thf(fact_2940_bits__mod__by__1,axiom,
% 3.82/4.04 ! [A: int] :
% 3.82/4.04 ( ( modulo_modulo_int @ A @ one_one_int )
% 3.82/4.04 = zero_zero_int ) ).
% 3.82/4.04
% 3.82/4.04 % bits_mod_by_1
% 3.82/4.04 thf(fact_2941_dvd__div__mult__self,axiom,
% 3.82/4.04 ! [A: nat,B2: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ A @ B2 )
% 3.82/4.04 => ( ( times_times_nat @ ( divide_divide_nat @ B2 @ A ) @ A )
% 3.82/4.04 = B2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_div_mult_self
% 3.82/4.04 thf(fact_2942_dvd__div__mult__self,axiom,
% 3.82/4.04 ! [A: int,B2: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ A @ B2 )
% 3.82/4.04 => ( ( times_times_int @ ( divide_divide_int @ B2 @ A ) @ A )
% 3.82/4.04 = B2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_div_mult_self
% 3.82/4.04 thf(fact_2943_dvd__mult__div__cancel,axiom,
% 3.82/4.04 ! [A: nat,B2: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ A @ B2 )
% 3.82/4.04 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B2 @ A ) )
% 3.82/4.04 = B2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_mult_div_cancel
% 3.82/4.04 thf(fact_2944_dvd__mult__div__cancel,axiom,
% 3.82/4.04 ! [A: int,B2: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ A @ B2 )
% 3.82/4.04 => ( ( times_times_int @ A @ ( divide_divide_int @ B2 @ A ) )
% 3.82/4.04 = B2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_mult_div_cancel
% 3.82/4.04 thf(fact_2945_unit__div,axiom,
% 3.82/4.04 ! [A: nat,B2: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 3.82/4.04 => ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 3.82/4.04 => ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B2 ) @ one_one_nat ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % unit_div
% 3.82/4.04 thf(fact_2946_unit__div,axiom,
% 3.82/4.04 ! [A: int,B2: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ A @ one_one_int )
% 3.82/4.04 => ( ( dvd_dvd_int @ B2 @ one_one_int )
% 3.82/4.04 => ( dvd_dvd_int @ ( divide_divide_int @ A @ B2 ) @ one_one_int ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % unit_div
% 3.82/4.04 thf(fact_2947_unit__div__1__unit,axiom,
% 3.82/4.04 ! [A: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 3.82/4.04 => ( dvd_dvd_nat @ ( divide_divide_nat @ one_one_nat @ A ) @ one_one_nat ) ) ).
% 3.82/4.04
% 3.82/4.04 % unit_div_1_unit
% 3.82/4.04 thf(fact_2948_unit__div__1__unit,axiom,
% 3.82/4.04 ! [A: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ A @ one_one_int )
% 3.82/4.04 => ( dvd_dvd_int @ ( divide_divide_int @ one_one_int @ A ) @ one_one_int ) ) ).
% 3.82/4.04
% 3.82/4.04 % unit_div_1_unit
% 3.82/4.04 thf(fact_2949_unit__div__1__div__1,axiom,
% 3.82/4.04 ! [A: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 3.82/4.04 => ( ( divide_divide_nat @ one_one_nat @ ( divide_divide_nat @ one_one_nat @ A ) )
% 3.82/4.04 = A ) ) ).
% 3.82/4.04
% 3.82/4.04 % unit_div_1_div_1
% 3.82/4.04 thf(fact_2950_unit__div__1__div__1,axiom,
% 3.82/4.04 ! [A: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ A @ one_one_int )
% 3.82/4.04 => ( ( divide_divide_int @ one_one_int @ ( divide_divide_int @ one_one_int @ A ) )
% 3.82/4.04 = A ) ) ).
% 3.82/4.04
% 3.82/4.04 % unit_div_1_div_1
% 3.82/4.04 thf(fact_2951_div__add,axiom,
% 3.82/4.04 ! [C: nat,A: nat,B2: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ C @ A )
% 3.82/4.04 => ( ( dvd_dvd_nat @ C @ B2 )
% 3.82/4.04 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B2 ) @ C )
% 3.82/4.04 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B2 @ C ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % div_add
% 3.82/4.04 thf(fact_2952_div__add,axiom,
% 3.82/4.04 ! [C: int,A: int,B2: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ C @ A )
% 3.82/4.04 => ( ( dvd_dvd_int @ C @ B2 )
% 3.82/4.04 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B2 ) @ C )
% 3.82/4.04 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B2 @ C ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % div_add
% 3.82/4.04 thf(fact_2953_mod__div__trivial,axiom,
% 3.82/4.04 ! [A: nat,B2: nat] :
% 3.82/4.04 ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B2 ) @ B2 )
% 3.82/4.04 = zero_zero_nat ) ).
% 3.82/4.04
% 3.82/4.04 % mod_div_trivial
% 3.82/4.04 thf(fact_2954_mod__div__trivial,axiom,
% 3.82/4.04 ! [A: int,B2: int] :
% 3.82/4.04 ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B2 ) @ B2 )
% 3.82/4.04 = zero_zero_int ) ).
% 3.82/4.04
% 3.82/4.04 % mod_div_trivial
% 3.82/4.04 thf(fact_2955_bits__mod__div__trivial,axiom,
% 3.82/4.04 ! [A: nat,B2: nat] :
% 3.82/4.04 ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B2 ) @ B2 )
% 3.82/4.04 = zero_zero_nat ) ).
% 3.82/4.04
% 3.82/4.04 % bits_mod_div_trivial
% 3.82/4.04 thf(fact_2956_bits__mod__div__trivial,axiom,
% 3.82/4.04 ! [A: int,B2: int] :
% 3.82/4.04 ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B2 ) @ B2 )
% 3.82/4.04 = zero_zero_int ) ).
% 3.82/4.04
% 3.82/4.04 % bits_mod_div_trivial
% 3.82/4.04 thf(fact_2957_mod__mult__self4,axiom,
% 3.82/4.04 ! [B2: nat,C: nat,A: nat] :
% 3.82/4.04 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ B2 @ C ) @ A ) @ B2 )
% 3.82/4.04 = ( modulo_modulo_nat @ A @ B2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % mod_mult_self4
% 3.82/4.04 thf(fact_2958_mod__mult__self4,axiom,
% 3.82/4.04 ! [B2: int,C: int,A: int] :
% 3.82/4.04 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ B2 @ C ) @ A ) @ B2 )
% 3.82/4.04 = ( modulo_modulo_int @ A @ B2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % mod_mult_self4
% 3.82/4.04 thf(fact_2959_mod__mult__self3,axiom,
% 3.82/4.04 ! [C: nat,B2: nat,A: nat] :
% 3.82/4.04 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B2 ) @ A ) @ B2 )
% 3.82/4.04 = ( modulo_modulo_nat @ A @ B2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % mod_mult_self3
% 3.82/4.04 thf(fact_2960_mod__mult__self3,axiom,
% 3.82/4.04 ! [C: int,B2: int,A: int] :
% 3.82/4.04 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ C @ B2 ) @ A ) @ B2 )
% 3.82/4.04 = ( modulo_modulo_int @ A @ B2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % mod_mult_self3
% 3.82/4.04 thf(fact_2961_mod__mult__self2,axiom,
% 3.82/4.04 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.04 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B2 @ C ) ) @ B2 )
% 3.82/4.04 = ( modulo_modulo_nat @ A @ B2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % mod_mult_self2
% 3.82/4.04 thf(fact_2962_mod__mult__self2,axiom,
% 3.82/4.04 ! [A: int,B2: int,C: int] :
% 3.82/4.04 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ B2 @ C ) ) @ B2 )
% 3.82/4.04 = ( modulo_modulo_int @ A @ B2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % mod_mult_self2
% 3.82/4.04 thf(fact_2963_mod__mult__self1,axiom,
% 3.82/4.04 ! [A: nat,C: nat,B2: nat] :
% 3.82/4.04 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B2 ) ) @ B2 )
% 3.82/4.04 = ( modulo_modulo_nat @ A @ B2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % mod_mult_self1
% 3.82/4.04 thf(fact_2964_mod__mult__self1,axiom,
% 3.82/4.04 ! [A: int,C: int,B2: int] :
% 3.82/4.04 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B2 ) ) @ B2 )
% 3.82/4.04 = ( modulo_modulo_int @ A @ B2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % mod_mult_self1
% 3.82/4.04 thf(fact_2965_dvd__imp__mod__0,axiom,
% 3.82/4.04 ! [A: nat,B2: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ A @ B2 )
% 3.82/4.04 => ( ( modulo_modulo_nat @ B2 @ A )
% 3.82/4.04 = zero_zero_nat ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_imp_mod_0
% 3.82/4.04 thf(fact_2966_dvd__imp__mod__0,axiom,
% 3.82/4.04 ! [A: int,B2: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ A @ B2 )
% 3.82/4.04 => ( ( modulo_modulo_int @ B2 @ A )
% 3.82/4.04 = zero_zero_int ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_imp_mod_0
% 3.82/4.04 thf(fact_2967_mod__by__Suc__0,axiom,
% 3.82/4.04 ! [M2: nat] :
% 3.82/4.04 ( ( modulo_modulo_nat @ M2 @ ( suc @ zero_zero_nat ) )
% 3.82/4.04 = zero_zero_nat ) ).
% 3.82/4.04
% 3.82/4.04 % mod_by_Suc_0
% 3.82/4.04 thf(fact_2968_set__decode__zero,axiom,
% 3.82/4.04 ( ( nat_set_decode @ zero_zero_nat )
% 3.82/4.04 = bot_bot_set_nat ) ).
% 3.82/4.04
% 3.82/4.04 % set_decode_zero
% 3.82/4.04 thf(fact_2969_unit__div__mult__self,axiom,
% 3.82/4.04 ! [A: nat,B2: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 3.82/4.04 => ( ( times_times_nat @ ( divide_divide_nat @ B2 @ A ) @ A )
% 3.82/4.04 = B2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % unit_div_mult_self
% 3.82/4.04 thf(fact_2970_unit__div__mult__self,axiom,
% 3.82/4.04 ! [A: int,B2: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ A @ one_one_int )
% 3.82/4.04 => ( ( times_times_int @ ( divide_divide_int @ B2 @ A ) @ A )
% 3.82/4.04 = B2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % unit_div_mult_self
% 3.82/4.04 thf(fact_2971_unit__mult__div__div,axiom,
% 3.82/4.04 ! [A: nat,B2: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 3.82/4.04 => ( ( times_times_nat @ B2 @ ( divide_divide_nat @ one_one_nat @ A ) )
% 3.82/4.04 = ( divide_divide_nat @ B2 @ A ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % unit_mult_div_div
% 3.82/4.04 thf(fact_2972_unit__mult__div__div,axiom,
% 3.82/4.04 ! [A: int,B2: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ A @ one_one_int )
% 3.82/4.04 => ( ( times_times_int @ B2 @ ( divide_divide_int @ one_one_int @ A ) )
% 3.82/4.04 = ( divide_divide_int @ B2 @ A ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % unit_mult_div_div
% 3.82/4.04 thf(fact_2973_even__Suc,axiom,
% 3.82/4.04 ! [N2: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) )
% 3.82/4.04 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % even_Suc
% 3.82/4.04 thf(fact_2974_even__Suc__Suc__iff,axiom,
% 3.82/4.04 ! [N2: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ N2 ) ) )
% 3.82/4.04 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % even_Suc_Suc_iff
% 3.82/4.04 thf(fact_2975_pow__divides__pow__iff,axiom,
% 3.82/4.04 ! [N2: nat,A: nat,B2: nat] :
% 3.82/4.04 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.04 => ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B2 @ N2 ) )
% 3.82/4.04 = ( dvd_dvd_nat @ A @ B2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % pow_divides_pow_iff
% 3.82/4.04 thf(fact_2976_pow__divides__pow__iff,axiom,
% 3.82/4.04 ! [N2: nat,A: int,B2: int] :
% 3.82/4.04 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.04 => ( ( dvd_dvd_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B2 @ N2 ) )
% 3.82/4.04 = ( dvd_dvd_int @ A @ B2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % pow_divides_pow_iff
% 3.82/4.04 thf(fact_2977_Suc__mod__mult__self4,axiom,
% 3.82/4.04 ! [N2: nat,K: nat,M2: nat] :
% 3.82/4.04 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ N2 @ K ) @ M2 ) ) @ N2 )
% 3.82/4.04 = ( modulo_modulo_nat @ ( suc @ M2 ) @ N2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % Suc_mod_mult_self4
% 3.82/4.04 thf(fact_2978_Suc__mod__mult__self3,axiom,
% 3.82/4.04 ! [K: nat,N2: nat,M2: nat] :
% 3.82/4.04 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ K @ N2 ) @ M2 ) ) @ N2 )
% 3.82/4.04 = ( modulo_modulo_nat @ ( suc @ M2 ) @ N2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % Suc_mod_mult_self3
% 3.82/4.04 thf(fact_2979_Suc__mod__mult__self2,axiom,
% 3.82/4.04 ! [M2: nat,N2: nat,K: nat] :
% 3.82/4.04 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M2 @ ( times_times_nat @ N2 @ K ) ) ) @ N2 )
% 3.82/4.04 = ( modulo_modulo_nat @ ( suc @ M2 ) @ N2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % Suc_mod_mult_self2
% 3.82/4.04 thf(fact_2980_Suc__mod__mult__self1,axiom,
% 3.82/4.04 ! [M2: nat,K: nat,N2: nat] :
% 3.82/4.04 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M2 @ ( times_times_nat @ K @ N2 ) ) ) @ N2 )
% 3.82/4.04 = ( modulo_modulo_nat @ ( suc @ M2 ) @ N2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % Suc_mod_mult_self1
% 3.82/4.04 thf(fact_2981_even__add,axiom,
% 3.82/4.04 ! [A: nat,B2: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B2 ) )
% 3.82/4.04 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 3.82/4.04 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % even_add
% 3.82/4.04 thf(fact_2982_even__add,axiom,
% 3.82/4.04 ! [A: int,B2: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B2 ) )
% 3.82/4.04 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 3.82/4.04 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % even_add
% 3.82/4.04 thf(fact_2983_odd__add,axiom,
% 3.82/4.04 ! [A: nat,B2: nat] :
% 3.82/4.04 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B2 ) ) )
% 3.82/4.04 = ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 3.82/4.04 != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % odd_add
% 3.82/4.04 thf(fact_2984_odd__add,axiom,
% 3.82/4.04 ! [A: int,B2: int] :
% 3.82/4.04 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B2 ) ) )
% 3.82/4.04 = ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 3.82/4.04 != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % odd_add
% 3.82/4.04 thf(fact_2985_odd__Suc__div__two,axiom,
% 3.82/4.04 ! [N2: nat] :
% 3.82/4.04 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 3.82/4.04 => ( ( divide_divide_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.04 = ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % odd_Suc_div_two
% 3.82/4.04 thf(fact_2986_even__Suc__div__two,axiom,
% 3.82/4.04 ! [N2: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 3.82/4.04 => ( ( divide_divide_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.04 = ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % even_Suc_div_two
% 3.82/4.04 thf(fact_2987_mod2__Suc__Suc,axiom,
% 3.82/4.04 ! [M2: nat] :
% 3.82/4.04 ( ( modulo_modulo_nat @ ( suc @ ( suc @ M2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.04 = ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % mod2_Suc_Suc
% 3.82/4.04 thf(fact_2988_Suc__times__numeral__mod__eq,axiom,
% 3.82/4.04 ! [K: num,N2: nat] :
% 3.82/4.04 ( ( ( numeral_numeral_nat @ K )
% 3.82/4.04 != one_one_nat )
% 3.82/4.04 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ K ) @ N2 ) ) @ ( numeral_numeral_nat @ K ) )
% 3.82/4.04 = one_one_nat ) ) ).
% 3.82/4.04
% 3.82/4.04 % Suc_times_numeral_mod_eq
% 3.82/4.04 thf(fact_2989_set__decode__0,axiom,
% 3.82/4.04 ! [X: nat] :
% 3.82/4.04 ( ( member_nat @ zero_zero_nat @ ( nat_set_decode @ X ) )
% 3.82/4.04 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % set_decode_0
% 3.82/4.04 thf(fact_2990_zero__le__power__eq__numeral,axiom,
% 3.82/4.04 ! [A: real,W2: num] :
% 3.82/4.04 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 3.82/4.04 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 3.82/4.04 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 3.82/4.04 & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % zero_le_power_eq_numeral
% 3.82/4.04 thf(fact_2991_zero__le__power__eq__numeral,axiom,
% 3.82/4.04 ! [A: int,W2: num] :
% 3.82/4.04 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 3.82/4.04 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 3.82/4.04 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 3.82/4.04 & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % zero_le_power_eq_numeral
% 3.82/4.04 thf(fact_2992_power__less__zero__eq__numeral,axiom,
% 3.82/4.04 ! [A: real,W2: num] :
% 3.82/4.04 ( ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_zero_real )
% 3.82/4.04 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 3.82/4.04 & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % power_less_zero_eq_numeral
% 3.82/4.04 thf(fact_2993_power__less__zero__eq__numeral,axiom,
% 3.82/4.04 ! [A: int,W2: num] :
% 3.82/4.04 ( ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_zero_int )
% 3.82/4.04 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 3.82/4.04 & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % power_less_zero_eq_numeral
% 3.82/4.04 thf(fact_2994_power__less__zero__eq,axiom,
% 3.82/4.04 ! [A: real,N2: nat] :
% 3.82/4.04 ( ( ord_less_real @ ( power_power_real @ A @ N2 ) @ zero_zero_real )
% 3.82/4.04 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 3.82/4.04 & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % power_less_zero_eq
% 3.82/4.04 thf(fact_2995_power__less__zero__eq,axiom,
% 3.82/4.04 ! [A: int,N2: nat] :
% 3.82/4.04 ( ( ord_less_int @ ( power_power_int @ A @ N2 ) @ zero_zero_int )
% 3.82/4.04 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 3.82/4.04 & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % power_less_zero_eq
% 3.82/4.04 thf(fact_2996_even__plus__one__iff,axiom,
% 3.82/4.04 ! [A: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ one_one_nat ) )
% 3.82/4.04 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % even_plus_one_iff
% 3.82/4.04 thf(fact_2997_even__plus__one__iff,axiom,
% 3.82/4.04 ! [A: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ one_one_int ) )
% 3.82/4.04 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % even_plus_one_iff
% 3.82/4.04 thf(fact_2998_not__mod__2__eq__1__eq__0,axiom,
% 3.82/4.04 ! [A: nat] :
% 3.82/4.04 ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.04 != one_one_nat )
% 3.82/4.04 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.04 = zero_zero_nat ) ) ).
% 3.82/4.04
% 3.82/4.04 % not_mod_2_eq_1_eq_0
% 3.82/4.04 thf(fact_2999_not__mod__2__eq__1__eq__0,axiom,
% 3.82/4.04 ! [A: int] :
% 3.82/4.04 ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 3.82/4.04 != one_one_int )
% 3.82/4.04 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 3.82/4.04 = zero_zero_int ) ) ).
% 3.82/4.04
% 3.82/4.04 % not_mod_2_eq_1_eq_0
% 3.82/4.04 thf(fact_3000_not__mod__2__eq__0__eq__1,axiom,
% 3.82/4.04 ! [A: nat] :
% 3.82/4.04 ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.04 != zero_zero_nat )
% 3.82/4.04 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.04 = one_one_nat ) ) ).
% 3.82/4.04
% 3.82/4.04 % not_mod_2_eq_0_eq_1
% 3.82/4.04 thf(fact_3001_not__mod__2__eq__0__eq__1,axiom,
% 3.82/4.04 ! [A: int] :
% 3.82/4.04 ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 3.82/4.04 != zero_zero_int )
% 3.82/4.04 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 3.82/4.04 = one_one_int ) ) ).
% 3.82/4.04
% 3.82/4.04 % not_mod_2_eq_0_eq_1
% 3.82/4.04 thf(fact_3002_not__mod2__eq__Suc__0__eq__0,axiom,
% 3.82/4.04 ! [N2: nat] :
% 3.82/4.04 ( ( ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.04 != ( suc @ zero_zero_nat ) )
% 3.82/4.04 = ( ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.04 = zero_zero_nat ) ) ).
% 3.82/4.04
% 3.82/4.04 % not_mod2_eq_Suc_0_eq_0
% 3.82/4.04 thf(fact_3003_add__self__mod__2,axiom,
% 3.82/4.04 ! [M2: nat] :
% 3.82/4.04 ( ( modulo_modulo_nat @ ( plus_plus_nat @ M2 @ M2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.04 = zero_zero_nat ) ).
% 3.82/4.04
% 3.82/4.04 % add_self_mod_2
% 3.82/4.04 thf(fact_3004_zero__less__power__eq__numeral,axiom,
% 3.82/4.04 ! [A: real,W2: num] :
% 3.82/4.04 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 3.82/4.04 = ( ( ( numeral_numeral_nat @ W2 )
% 3.82/4.04 = zero_zero_nat )
% 3.82/4.04 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 3.82/4.04 & ( A != zero_zero_real ) )
% 3.82/4.04 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 3.82/4.04 & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % zero_less_power_eq_numeral
% 3.82/4.04 thf(fact_3005_zero__less__power__eq__numeral,axiom,
% 3.82/4.04 ! [A: int,W2: num] :
% 3.82/4.04 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 3.82/4.04 = ( ( ( numeral_numeral_nat @ W2 )
% 3.82/4.04 = zero_zero_nat )
% 3.82/4.04 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 3.82/4.04 & ( A != zero_zero_int ) )
% 3.82/4.04 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 3.82/4.04 & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % zero_less_power_eq_numeral
% 3.82/4.04 thf(fact_3006_even__succ__div__two,axiom,
% 3.82/4.04 ! [A: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 3.82/4.04 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.04 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % even_succ_div_two
% 3.82/4.04 thf(fact_3007_even__succ__div__two,axiom,
% 3.82/4.04 ! [A: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 3.82/4.04 => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 3.82/4.04 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % even_succ_div_two
% 3.82/4.04 thf(fact_3008_odd__succ__div__two,axiom,
% 3.82/4.04 ! [A: nat] :
% 3.82/4.04 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 3.82/4.04 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.04 = ( plus_plus_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % odd_succ_div_two
% 3.82/4.04 thf(fact_3009_odd__succ__div__two,axiom,
% 3.82/4.04 ! [A: int] :
% 3.82/4.04 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 3.82/4.04 => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 3.82/4.04 = ( plus_plus_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % odd_succ_div_two
% 3.82/4.04 thf(fact_3010_even__succ__div__2,axiom,
% 3.82/4.04 ! [A: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 3.82/4.04 => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.04 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % even_succ_div_2
% 3.82/4.04 thf(fact_3011_even__succ__div__2,axiom,
% 3.82/4.04 ! [A: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 3.82/4.04 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 3.82/4.04 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % even_succ_div_2
% 3.82/4.04 thf(fact_3012_even__power,axiom,
% 3.82/4.04 ! [A: nat,N2: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ A @ N2 ) )
% 3.82/4.04 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 3.82/4.04 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % even_power
% 3.82/4.04 thf(fact_3013_even__power,axiom,
% 3.82/4.04 ! [A: int,N2: nat] :
% 3.82/4.04 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( power_power_int @ A @ N2 ) )
% 3.82/4.04 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 3.82/4.04 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % even_power
% 3.82/4.04 thf(fact_3014_mod2__gr__0,axiom,
% 3.82/4.04 ! [M2: nat] :
% 3.82/4.04 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 3.82/4.04 = ( ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.04 = one_one_nat ) ) ).
% 3.82/4.04
% 3.82/4.04 % mod2_gr_0
% 3.82/4.04 thf(fact_3015_odd__two__times__div__two__succ,axiom,
% 3.82/4.04 ! [A: nat] :
% 3.82/4.04 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 3.82/4.04 => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 3.82/4.04 = A ) ) ).
% 3.82/4.04
% 3.82/4.04 % odd_two_times_div_two_succ
% 3.82/4.04 thf(fact_3016_odd__two__times__div__two__succ,axiom,
% 3.82/4.04 ! [A: int] :
% 3.82/4.04 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 3.82/4.04 => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ one_one_int )
% 3.82/4.04 = A ) ) ).
% 3.82/4.04
% 3.82/4.04 % odd_two_times_div_two_succ
% 3.82/4.04 thf(fact_3017_power__le__zero__eq__numeral,axiom,
% 3.82/4.04 ! [A: real,W2: num] :
% 3.82/4.04 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_zero_real )
% 3.82/4.04 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W2 ) )
% 3.82/4.04 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 3.82/4.04 & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 3.82/4.04 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 3.82/4.04 & ( A = zero_zero_real ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % power_le_zero_eq_numeral
% 3.82/4.04 thf(fact_3018_power__le__zero__eq__numeral,axiom,
% 3.82/4.04 ! [A: int,W2: num] :
% 3.82/4.04 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_zero_int )
% 3.82/4.04 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W2 ) )
% 3.82/4.04 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 3.82/4.04 & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 3.82/4.04 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 3.82/4.04 & ( A = zero_zero_int ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % power_le_zero_eq_numeral
% 3.82/4.04 thf(fact_3019_even__succ__mod__exp,axiom,
% 3.82/4.04 ! [A: nat,N2: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 3.82/4.04 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.04 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 3.82/4.04 = ( plus_plus_nat @ one_one_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % even_succ_mod_exp
% 3.82/4.04 thf(fact_3020_even__succ__mod__exp,axiom,
% 3.82/4.04 ! [A: int,N2: nat] :
% 3.82/4.04 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 3.82/4.04 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.04 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 3.82/4.04 = ( plus_plus_int @ one_one_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % even_succ_mod_exp
% 3.82/4.04 thf(fact_3021_strict__subset__divisors__dvd,axiom,
% 3.82/4.04 ! [A: real,B2: real] :
% 3.82/4.04 ( ( ord_less_set_real
% 3.82/4.04 @ ( collect_real
% 3.82/4.04 @ ^ [C3: real] : ( dvd_dvd_real @ C3 @ A ) )
% 3.82/4.04 @ ( collect_real
% 3.82/4.04 @ ^ [C3: real] : ( dvd_dvd_real @ C3 @ B2 ) ) )
% 3.82/4.04 = ( ( dvd_dvd_real @ A @ B2 )
% 3.82/4.04 & ~ ( dvd_dvd_real @ B2 @ A ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % strict_subset_divisors_dvd
% 3.82/4.04 thf(fact_3022_strict__subset__divisors__dvd,axiom,
% 3.82/4.04 ! [A: nat,B2: nat] :
% 3.82/4.04 ( ( ord_less_set_nat
% 3.82/4.04 @ ( collect_nat
% 3.82/4.04 @ ^ [C3: nat] : ( dvd_dvd_nat @ C3 @ A ) )
% 3.82/4.04 @ ( collect_nat
% 3.82/4.04 @ ^ [C3: nat] : ( dvd_dvd_nat @ C3 @ B2 ) ) )
% 3.82/4.04 = ( ( dvd_dvd_nat @ A @ B2 )
% 3.82/4.04 & ~ ( dvd_dvd_nat @ B2 @ A ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % strict_subset_divisors_dvd
% 3.82/4.04 thf(fact_3023_strict__subset__divisors__dvd,axiom,
% 3.82/4.04 ! [A: int,B2: int] :
% 3.82/4.04 ( ( ord_less_set_int
% 3.82/4.04 @ ( collect_int
% 3.82/4.04 @ ^ [C3: int] : ( dvd_dvd_int @ C3 @ A ) )
% 3.82/4.04 @ ( collect_int
% 3.82/4.04 @ ^ [C3: int] : ( dvd_dvd_int @ C3 @ B2 ) ) )
% 3.82/4.04 = ( ( dvd_dvd_int @ A @ B2 )
% 3.82/4.04 & ~ ( dvd_dvd_int @ B2 @ A ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % strict_subset_divisors_dvd
% 3.82/4.04 thf(fact_3024_less__set__def,axiom,
% 3.82/4.04 ( ord_le2529575680413868914d_enat
% 3.82/4.04 = ( ^ [A5: set_Extended_enat,B5: set_Extended_enat] :
% 3.82/4.04 ( ord_le8499522857272258027enat_o
% 3.82/4.04 @ ^ [X4: extended_enat] : ( member_Extended_enat @ X4 @ A5 )
% 3.82/4.04 @ ^ [X4: extended_enat] : ( member_Extended_enat @ X4 @ B5 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % less_set_def
% 3.82/4.04 thf(fact_3025_less__set__def,axiom,
% 3.82/4.04 ( ord_less_set_real
% 3.82/4.04 = ( ^ [A5: set_real,B5: set_real] :
% 3.82/4.04 ( ord_less_real_o
% 3.82/4.04 @ ^ [X4: real] : ( member_real @ X4 @ A5 )
% 3.82/4.04 @ ^ [X4: real] : ( member_real @ X4 @ B5 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % less_set_def
% 3.82/4.04 thf(fact_3026_less__set__def,axiom,
% 3.82/4.04 ( ord_less_set_set_nat
% 3.82/4.04 = ( ^ [A5: set_set_nat,B5: set_set_nat] :
% 3.82/4.04 ( ord_less_set_nat_o
% 3.82/4.04 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ A5 )
% 3.82/4.04 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ B5 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % less_set_def
% 3.82/4.04 thf(fact_3027_less__set__def,axiom,
% 3.82/4.04 ( ord_less_set_nat
% 3.82/4.04 = ( ^ [A5: set_nat,B5: set_nat] :
% 3.82/4.04 ( ord_less_nat_o
% 3.82/4.04 @ ^ [X4: nat] : ( member_nat @ X4 @ A5 )
% 3.82/4.04 @ ^ [X4: nat] : ( member_nat @ X4 @ B5 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % less_set_def
% 3.82/4.04 thf(fact_3028_less__set__def,axiom,
% 3.82/4.04 ( ord_less_set_int
% 3.82/4.04 = ( ^ [A5: set_int,B5: set_int] :
% 3.82/4.04 ( ord_less_int_o
% 3.82/4.04 @ ^ [X4: int] : ( member_int @ X4 @ A5 )
% 3.82/4.04 @ ^ [X4: int] : ( member_int @ X4 @ B5 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % less_set_def
% 3.82/4.04 thf(fact_3029_mod__eq__0__iff__dvd,axiom,
% 3.82/4.04 ! [A: nat,B2: nat] :
% 3.82/4.04 ( ( ( modulo_modulo_nat @ A @ B2 )
% 3.82/4.04 = zero_zero_nat )
% 3.82/4.04 = ( dvd_dvd_nat @ B2 @ A ) ) ).
% 3.82/4.04
% 3.82/4.04 % mod_eq_0_iff_dvd
% 3.82/4.04 thf(fact_3030_mod__eq__0__iff__dvd,axiom,
% 3.82/4.04 ! [A: int,B2: int] :
% 3.82/4.04 ( ( ( modulo_modulo_int @ A @ B2 )
% 3.82/4.04 = zero_zero_int )
% 3.82/4.04 = ( dvd_dvd_int @ B2 @ A ) ) ).
% 3.82/4.04
% 3.82/4.04 % mod_eq_0_iff_dvd
% 3.82/4.04 thf(fact_3031_dvd__eq__mod__eq__0,axiom,
% 3.82/4.04 ( dvd_dvd_nat
% 3.82/4.04 = ( ^ [A3: nat,B3: nat] :
% 3.82/4.04 ( ( modulo_modulo_nat @ B3 @ A3 )
% 3.82/4.04 = zero_zero_nat ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_eq_mod_eq_0
% 3.82/4.04 thf(fact_3032_dvd__eq__mod__eq__0,axiom,
% 3.82/4.04 ( dvd_dvd_int
% 3.82/4.04 = ( ^ [A3: int,B3: int] :
% 3.82/4.04 ( ( modulo_modulo_int @ B3 @ A3 )
% 3.82/4.04 = zero_zero_int ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_eq_mod_eq_0
% 3.82/4.04 thf(fact_3033_mod__0__imp__dvd,axiom,
% 3.82/4.04 ! [A: nat,B2: nat] :
% 3.82/4.04 ( ( ( modulo_modulo_nat @ A @ B2 )
% 3.82/4.04 = zero_zero_nat )
% 3.82/4.04 => ( dvd_dvd_nat @ B2 @ A ) ) ).
% 3.82/4.04
% 3.82/4.04 % mod_0_imp_dvd
% 3.82/4.04 thf(fact_3034_mod__0__imp__dvd,axiom,
% 3.82/4.04 ! [A: int,B2: int] :
% 3.82/4.04 ( ( ( modulo_modulo_int @ A @ B2 )
% 3.82/4.04 = zero_zero_int )
% 3.82/4.04 => ( dvd_dvd_int @ B2 @ A ) ) ).
% 3.82/4.04
% 3.82/4.04 % mod_0_imp_dvd
% 3.82/4.04 thf(fact_3035_empty__def,axiom,
% 3.82/4.04 ( bot_bot_set_list_nat
% 3.82/4.04 = ( collect_list_nat
% 3.82/4.04 @ ^ [X4: list_nat] : $false ) ) ).
% 3.82/4.04
% 3.82/4.04 % empty_def
% 3.82/4.04 thf(fact_3036_empty__def,axiom,
% 3.82/4.04 ( bot_bot_set_set_nat
% 3.82/4.04 = ( collect_set_nat
% 3.82/4.04 @ ^ [X4: set_nat] : $false ) ) ).
% 3.82/4.04
% 3.82/4.04 % empty_def
% 3.82/4.04 thf(fact_3037_empty__def,axiom,
% 3.82/4.04 ( bot_bo7653980558646680370d_enat
% 3.82/4.04 = ( collec4429806609662206161d_enat
% 3.82/4.04 @ ^ [X4: extended_enat] : $false ) ) ).
% 3.82/4.04
% 3.82/4.04 % empty_def
% 3.82/4.04 thf(fact_3038_empty__def,axiom,
% 3.82/4.04 ( bot_bot_set_real
% 3.82/4.04 = ( collect_real
% 3.82/4.04 @ ^ [X4: real] : $false ) ) ).
% 3.82/4.04
% 3.82/4.04 % empty_def
% 3.82/4.04 thf(fact_3039_empty__def,axiom,
% 3.82/4.04 ( bot_bot_set_nat
% 3.82/4.04 = ( collect_nat
% 3.82/4.04 @ ^ [X4: nat] : $false ) ) ).
% 3.82/4.04
% 3.82/4.04 % empty_def
% 3.82/4.04 thf(fact_3040_empty__def,axiom,
% 3.82/4.04 ( bot_bot_set_int
% 3.82/4.04 = ( collect_int
% 3.82/4.04 @ ^ [X4: int] : $false ) ) ).
% 3.82/4.04
% 3.82/4.04 % empty_def
% 3.82/4.04 thf(fact_3041_dvd__refl,axiom,
% 3.82/4.04 ! [A: nat] : ( dvd_dvd_nat @ A @ A ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_refl
% 3.82/4.04 thf(fact_3042_dvd__refl,axiom,
% 3.82/4.04 ! [A: int] : ( dvd_dvd_int @ A @ A ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_refl
% 3.82/4.04 thf(fact_3043_dvd__trans,axiom,
% 3.82/4.04 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ A @ B2 )
% 3.82/4.04 => ( ( dvd_dvd_nat @ B2 @ C )
% 3.82/4.04 => ( dvd_dvd_nat @ A @ C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_trans
% 3.82/4.04 thf(fact_3044_dvd__trans,axiom,
% 3.82/4.04 ! [A: int,B2: int,C: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ A @ B2 )
% 3.82/4.04 => ( ( dvd_dvd_int @ B2 @ C )
% 3.82/4.04 => ( dvd_dvd_int @ A @ C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_trans
% 3.82/4.04 thf(fact_3045_dvd__mod__iff,axiom,
% 3.82/4.04 ! [C: nat,B2: nat,A: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ C @ B2 )
% 3.82/4.04 => ( ( dvd_dvd_nat @ C @ ( modulo_modulo_nat @ A @ B2 ) )
% 3.82/4.04 = ( dvd_dvd_nat @ C @ A ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_mod_iff
% 3.82/4.04 thf(fact_3046_dvd__mod__iff,axiom,
% 3.82/4.04 ! [C: int,B2: int,A: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ C @ B2 )
% 3.82/4.04 => ( ( dvd_dvd_int @ C @ ( modulo_modulo_int @ A @ B2 ) )
% 3.82/4.04 = ( dvd_dvd_int @ C @ A ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_mod_iff
% 3.82/4.04 thf(fact_3047_dvd__mod__imp__dvd,axiom,
% 3.82/4.04 ! [C: nat,A: nat,B2: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ C @ ( modulo_modulo_nat @ A @ B2 ) )
% 3.82/4.04 => ( ( dvd_dvd_nat @ C @ B2 )
% 3.82/4.04 => ( dvd_dvd_nat @ C @ A ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_mod_imp_dvd
% 3.82/4.04 thf(fact_3048_dvd__mod__imp__dvd,axiom,
% 3.82/4.04 ! [C: int,A: int,B2: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ C @ ( modulo_modulo_int @ A @ B2 ) )
% 3.82/4.04 => ( ( dvd_dvd_int @ C @ B2 )
% 3.82/4.04 => ( dvd_dvd_int @ C @ A ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_mod_imp_dvd
% 3.82/4.04 thf(fact_3049_not__finite__existsD,axiom,
% 3.82/4.04 ! [P: real > $o] :
% 3.82/4.04 ( ~ ( finite_finite_real @ ( collect_real @ P ) )
% 3.82/4.04 => ? [X_12: real] : ( P @ X_12 ) ) ).
% 3.82/4.04
% 3.82/4.04 % not_finite_existsD
% 3.82/4.04 thf(fact_3050_not__finite__existsD,axiom,
% 3.82/4.04 ! [P: list_nat > $o] :
% 3.82/4.04 ( ~ ( finite8100373058378681591st_nat @ ( collect_list_nat @ P ) )
% 3.82/4.04 => ? [X_12: list_nat] : ( P @ X_12 ) ) ).
% 3.82/4.04
% 3.82/4.04 % not_finite_existsD
% 3.82/4.04 thf(fact_3051_not__finite__existsD,axiom,
% 3.82/4.04 ! [P: set_nat > $o] :
% 3.82/4.04 ( ~ ( finite1152437895449049373et_nat @ ( collect_set_nat @ P ) )
% 3.82/4.04 => ? [X_12: set_nat] : ( P @ X_12 ) ) ).
% 3.82/4.04
% 3.82/4.04 % not_finite_existsD
% 3.82/4.04 thf(fact_3052_not__finite__existsD,axiom,
% 3.82/4.04 ! [P: nat > $o] :
% 3.82/4.04 ( ~ ( finite_finite_nat @ ( collect_nat @ P ) )
% 3.82/4.04 => ? [X_12: nat] : ( P @ X_12 ) ) ).
% 3.82/4.04
% 3.82/4.04 % not_finite_existsD
% 3.82/4.04 thf(fact_3053_not__finite__existsD,axiom,
% 3.82/4.04 ! [P: complex > $o] :
% 3.82/4.04 ( ~ ( finite3207457112153483333omplex @ ( collect_complex @ P ) )
% 3.82/4.04 => ? [X_12: complex] : ( P @ X_12 ) ) ).
% 3.82/4.04
% 3.82/4.04 % not_finite_existsD
% 3.82/4.04 thf(fact_3054_not__finite__existsD,axiom,
% 3.82/4.04 ! [P: int > $o] :
% 3.82/4.04 ( ~ ( finite_finite_int @ ( collect_int @ P ) )
% 3.82/4.04 => ? [X_12: int] : ( P @ X_12 ) ) ).
% 3.82/4.04
% 3.82/4.04 % not_finite_existsD
% 3.82/4.04 thf(fact_3055_not__finite__existsD,axiom,
% 3.82/4.04 ! [P: extended_enat > $o] :
% 3.82/4.04 ( ~ ( finite4001608067531595151d_enat @ ( collec4429806609662206161d_enat @ P ) )
% 3.82/4.04 => ? [X_12: extended_enat] : ( P @ X_12 ) ) ).
% 3.82/4.04
% 3.82/4.04 % not_finite_existsD
% 3.82/4.04 thf(fact_3056_pigeonhole__infinite__rel,axiom,
% 3.82/4.04 ! [A2: set_real,B: set_nat,R: real > nat > $o] :
% 3.82/4.04 ( ~ ( finite_finite_real @ A2 )
% 3.82/4.04 => ( ( finite_finite_nat @ B )
% 3.82/4.04 => ( ! [X5: real] :
% 3.82/4.04 ( ( member_real @ X5 @ A2 )
% 3.82/4.04 => ? [Xa: nat] :
% 3.82/4.04 ( ( member_nat @ Xa @ B )
% 3.82/4.04 & ( R @ X5 @ Xa ) ) )
% 3.82/4.04 => ? [X5: nat] :
% 3.82/4.04 ( ( member_nat @ X5 @ B )
% 3.82/4.04 & ~ ( finite_finite_real
% 3.82/4.04 @ ( collect_real
% 3.82/4.04 @ ^ [A3: real] :
% 3.82/4.04 ( ( member_real @ A3 @ A2 )
% 3.82/4.04 & ( R @ A3 @ X5 ) ) ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % pigeonhole_infinite_rel
% 3.82/4.04 thf(fact_3057_pigeonhole__infinite__rel,axiom,
% 3.82/4.04 ! [A2: set_real,B: set_complex,R: real > complex > $o] :
% 3.82/4.04 ( ~ ( finite_finite_real @ A2 )
% 3.82/4.04 => ( ( finite3207457112153483333omplex @ B )
% 3.82/4.04 => ( ! [X5: real] :
% 3.82/4.04 ( ( member_real @ X5 @ A2 )
% 3.82/4.04 => ? [Xa: complex] :
% 3.82/4.04 ( ( member_complex @ Xa @ B )
% 3.82/4.04 & ( R @ X5 @ Xa ) ) )
% 3.82/4.04 => ? [X5: complex] :
% 3.82/4.04 ( ( member_complex @ X5 @ B )
% 3.82/4.04 & ~ ( finite_finite_real
% 3.82/4.04 @ ( collect_real
% 3.82/4.04 @ ^ [A3: real] :
% 3.82/4.04 ( ( member_real @ A3 @ A2 )
% 3.82/4.04 & ( R @ A3 @ X5 ) ) ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % pigeonhole_infinite_rel
% 3.82/4.04 thf(fact_3058_pigeonhole__infinite__rel,axiom,
% 3.82/4.04 ! [A2: set_real,B: set_int,R: real > int > $o] :
% 3.82/4.04 ( ~ ( finite_finite_real @ A2 )
% 3.82/4.04 => ( ( finite_finite_int @ B )
% 3.82/4.04 => ( ! [X5: real] :
% 3.82/4.04 ( ( member_real @ X5 @ A2 )
% 3.82/4.04 => ? [Xa: int] :
% 3.82/4.04 ( ( member_int @ Xa @ B )
% 3.82/4.04 & ( R @ X5 @ Xa ) ) )
% 3.82/4.04 => ? [X5: int] :
% 3.82/4.04 ( ( member_int @ X5 @ B )
% 3.82/4.04 & ~ ( finite_finite_real
% 3.82/4.04 @ ( collect_real
% 3.82/4.04 @ ^ [A3: real] :
% 3.82/4.04 ( ( member_real @ A3 @ A2 )
% 3.82/4.04 & ( R @ A3 @ X5 ) ) ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % pigeonhole_infinite_rel
% 3.82/4.04 thf(fact_3059_pigeonhole__infinite__rel,axiom,
% 3.82/4.04 ! [A2: set_real,B: set_Extended_enat,R: real > extended_enat > $o] :
% 3.82/4.04 ( ~ ( finite_finite_real @ A2 )
% 3.82/4.04 => ( ( finite4001608067531595151d_enat @ B )
% 3.82/4.04 => ( ! [X5: real] :
% 3.82/4.04 ( ( member_real @ X5 @ A2 )
% 3.82/4.04 => ? [Xa: extended_enat] :
% 3.82/4.04 ( ( member_Extended_enat @ Xa @ B )
% 3.82/4.04 & ( R @ X5 @ Xa ) ) )
% 3.82/4.04 => ? [X5: extended_enat] :
% 3.82/4.04 ( ( member_Extended_enat @ X5 @ B )
% 3.82/4.04 & ~ ( finite_finite_real
% 3.82/4.04 @ ( collect_real
% 3.82/4.04 @ ^ [A3: real] :
% 3.82/4.04 ( ( member_real @ A3 @ A2 )
% 3.82/4.04 & ( R @ A3 @ X5 ) ) ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % pigeonhole_infinite_rel
% 3.82/4.04 thf(fact_3060_pigeonhole__infinite__rel,axiom,
% 3.82/4.04 ! [A2: set_nat,B: set_nat,R: nat > nat > $o] :
% 3.82/4.04 ( ~ ( finite_finite_nat @ A2 )
% 3.82/4.04 => ( ( finite_finite_nat @ B )
% 3.82/4.04 => ( ! [X5: nat] :
% 3.82/4.04 ( ( member_nat @ X5 @ A2 )
% 3.82/4.04 => ? [Xa: nat] :
% 3.82/4.04 ( ( member_nat @ Xa @ B )
% 3.82/4.04 & ( R @ X5 @ Xa ) ) )
% 3.82/4.04 => ? [X5: nat] :
% 3.82/4.04 ( ( member_nat @ X5 @ B )
% 3.82/4.04 & ~ ( finite_finite_nat
% 3.82/4.04 @ ( collect_nat
% 3.82/4.04 @ ^ [A3: nat] :
% 3.82/4.04 ( ( member_nat @ A3 @ A2 )
% 3.82/4.04 & ( R @ A3 @ X5 ) ) ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % pigeonhole_infinite_rel
% 3.82/4.04 thf(fact_3061_pigeonhole__infinite__rel,axiom,
% 3.82/4.04 ! [A2: set_nat,B: set_complex,R: nat > complex > $o] :
% 3.82/4.04 ( ~ ( finite_finite_nat @ A2 )
% 3.82/4.04 => ( ( finite3207457112153483333omplex @ B )
% 3.82/4.04 => ( ! [X5: nat] :
% 3.82/4.04 ( ( member_nat @ X5 @ A2 )
% 3.82/4.04 => ? [Xa: complex] :
% 3.82/4.04 ( ( member_complex @ Xa @ B )
% 3.82/4.04 & ( R @ X5 @ Xa ) ) )
% 3.82/4.04 => ? [X5: complex] :
% 3.82/4.04 ( ( member_complex @ X5 @ B )
% 3.82/4.04 & ~ ( finite_finite_nat
% 3.82/4.04 @ ( collect_nat
% 3.82/4.04 @ ^ [A3: nat] :
% 3.82/4.04 ( ( member_nat @ A3 @ A2 )
% 3.82/4.04 & ( R @ A3 @ X5 ) ) ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % pigeonhole_infinite_rel
% 3.82/4.04 thf(fact_3062_pigeonhole__infinite__rel,axiom,
% 3.82/4.04 ! [A2: set_nat,B: set_int,R: nat > int > $o] :
% 3.82/4.04 ( ~ ( finite_finite_nat @ A2 )
% 3.82/4.04 => ( ( finite_finite_int @ B )
% 3.82/4.04 => ( ! [X5: nat] :
% 3.82/4.04 ( ( member_nat @ X5 @ A2 )
% 3.82/4.04 => ? [Xa: int] :
% 3.82/4.04 ( ( member_int @ Xa @ B )
% 3.82/4.04 & ( R @ X5 @ Xa ) ) )
% 3.82/4.04 => ? [X5: int] :
% 3.82/4.04 ( ( member_int @ X5 @ B )
% 3.82/4.04 & ~ ( finite_finite_nat
% 3.82/4.04 @ ( collect_nat
% 3.82/4.04 @ ^ [A3: nat] :
% 3.82/4.04 ( ( member_nat @ A3 @ A2 )
% 3.82/4.04 & ( R @ A3 @ X5 ) ) ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % pigeonhole_infinite_rel
% 3.82/4.04 thf(fact_3063_pigeonhole__infinite__rel,axiom,
% 3.82/4.04 ! [A2: set_nat,B: set_Extended_enat,R: nat > extended_enat > $o] :
% 3.82/4.04 ( ~ ( finite_finite_nat @ A2 )
% 3.82/4.04 => ( ( finite4001608067531595151d_enat @ B )
% 3.82/4.04 => ( ! [X5: nat] :
% 3.82/4.04 ( ( member_nat @ X5 @ A2 )
% 3.82/4.04 => ? [Xa: extended_enat] :
% 3.82/4.04 ( ( member_Extended_enat @ Xa @ B )
% 3.82/4.04 & ( R @ X5 @ Xa ) ) )
% 3.82/4.04 => ? [X5: extended_enat] :
% 3.82/4.04 ( ( member_Extended_enat @ X5 @ B )
% 3.82/4.04 & ~ ( finite_finite_nat
% 3.82/4.04 @ ( collect_nat
% 3.82/4.04 @ ^ [A3: nat] :
% 3.82/4.04 ( ( member_nat @ A3 @ A2 )
% 3.82/4.04 & ( R @ A3 @ X5 ) ) ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % pigeonhole_infinite_rel
% 3.82/4.04 thf(fact_3064_pigeonhole__infinite__rel,axiom,
% 3.82/4.04 ! [A2: set_complex,B: set_nat,R: complex > nat > $o] :
% 3.82/4.04 ( ~ ( finite3207457112153483333omplex @ A2 )
% 3.82/4.04 => ( ( finite_finite_nat @ B )
% 3.82/4.04 => ( ! [X5: complex] :
% 3.82/4.04 ( ( member_complex @ X5 @ A2 )
% 3.82/4.04 => ? [Xa: nat] :
% 3.82/4.04 ( ( member_nat @ Xa @ B )
% 3.82/4.04 & ( R @ X5 @ Xa ) ) )
% 3.82/4.04 => ? [X5: nat] :
% 3.82/4.04 ( ( member_nat @ X5 @ B )
% 3.82/4.04 & ~ ( finite3207457112153483333omplex
% 3.82/4.04 @ ( collect_complex
% 3.82/4.04 @ ^ [A3: complex] :
% 3.82/4.04 ( ( member_complex @ A3 @ A2 )
% 3.82/4.04 & ( R @ A3 @ X5 ) ) ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % pigeonhole_infinite_rel
% 3.82/4.04 thf(fact_3065_pigeonhole__infinite__rel,axiom,
% 3.82/4.04 ! [A2: set_complex,B: set_complex,R: complex > complex > $o] :
% 3.82/4.04 ( ~ ( finite3207457112153483333omplex @ A2 )
% 3.82/4.04 => ( ( finite3207457112153483333omplex @ B )
% 3.82/4.04 => ( ! [X5: complex] :
% 3.82/4.04 ( ( member_complex @ X5 @ A2 )
% 3.82/4.04 => ? [Xa: complex] :
% 3.82/4.04 ( ( member_complex @ Xa @ B )
% 3.82/4.04 & ( R @ X5 @ Xa ) ) )
% 3.82/4.04 => ? [X5: complex] :
% 3.82/4.04 ( ( member_complex @ X5 @ B )
% 3.82/4.04 & ~ ( finite3207457112153483333omplex
% 3.82/4.04 @ ( collect_complex
% 3.82/4.04 @ ^ [A3: complex] :
% 3.82/4.04 ( ( member_complex @ A3 @ A2 )
% 3.82/4.04 & ( R @ A3 @ X5 ) ) ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % pigeonhole_infinite_rel
% 3.82/4.04 thf(fact_3066_pred__subset__eq,axiom,
% 3.82/4.04 ! [R: set_Extended_enat,S2: set_Extended_enat] :
% 3.82/4.04 ( ( ord_le100613205991271927enat_o
% 3.82/4.04 @ ^ [X4: extended_enat] : ( member_Extended_enat @ X4 @ R )
% 3.82/4.04 @ ^ [X4: extended_enat] : ( member_Extended_enat @ X4 @ S2 ) )
% 3.82/4.04 = ( ord_le7203529160286727270d_enat @ R @ S2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % pred_subset_eq
% 3.82/4.04 thf(fact_3067_pred__subset__eq,axiom,
% 3.82/4.04 ! [R: set_real,S2: set_real] :
% 3.82/4.04 ( ( ord_less_eq_real_o
% 3.82/4.04 @ ^ [X4: real] : ( member_real @ X4 @ R )
% 3.82/4.04 @ ^ [X4: real] : ( member_real @ X4 @ S2 ) )
% 3.82/4.04 = ( ord_less_eq_set_real @ R @ S2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % pred_subset_eq
% 3.82/4.04 thf(fact_3068_pred__subset__eq,axiom,
% 3.82/4.04 ! [R: set_set_nat,S2: set_set_nat] :
% 3.82/4.04 ( ( ord_le3964352015994296041_nat_o
% 3.82/4.04 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ R )
% 3.82/4.04 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ S2 ) )
% 3.82/4.04 = ( ord_le6893508408891458716et_nat @ R @ S2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % pred_subset_eq
% 3.82/4.04 thf(fact_3069_pred__subset__eq,axiom,
% 3.82/4.04 ! [R: set_nat,S2: set_nat] :
% 3.82/4.04 ( ( ord_less_eq_nat_o
% 3.82/4.04 @ ^ [X4: nat] : ( member_nat @ X4 @ R )
% 3.82/4.04 @ ^ [X4: nat] : ( member_nat @ X4 @ S2 ) )
% 3.82/4.04 = ( ord_less_eq_set_nat @ R @ S2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % pred_subset_eq
% 3.82/4.04 thf(fact_3070_pred__subset__eq,axiom,
% 3.82/4.04 ! [R: set_int,S2: set_int] :
% 3.82/4.04 ( ( ord_less_eq_int_o
% 3.82/4.04 @ ^ [X4: int] : ( member_int @ X4 @ R )
% 3.82/4.04 @ ^ [X4: int] : ( member_int @ X4 @ S2 ) )
% 3.82/4.04 = ( ord_less_eq_set_int @ R @ S2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % pred_subset_eq
% 3.82/4.04 thf(fact_3071_less__eq__set__def,axiom,
% 3.82/4.04 ( ord_le7203529160286727270d_enat
% 3.82/4.04 = ( ^ [A5: set_Extended_enat,B5: set_Extended_enat] :
% 3.82/4.04 ( ord_le100613205991271927enat_o
% 3.82/4.04 @ ^ [X4: extended_enat] : ( member_Extended_enat @ X4 @ A5 )
% 3.82/4.04 @ ^ [X4: extended_enat] : ( member_Extended_enat @ X4 @ B5 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % less_eq_set_def
% 3.82/4.04 thf(fact_3072_less__eq__set__def,axiom,
% 3.82/4.04 ( ord_less_eq_set_real
% 3.82/4.04 = ( ^ [A5: set_real,B5: set_real] :
% 3.82/4.04 ( ord_less_eq_real_o
% 3.82/4.04 @ ^ [X4: real] : ( member_real @ X4 @ A5 )
% 3.82/4.04 @ ^ [X4: real] : ( member_real @ X4 @ B5 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % less_eq_set_def
% 3.82/4.04 thf(fact_3073_less__eq__set__def,axiom,
% 3.82/4.04 ( ord_le6893508408891458716et_nat
% 3.82/4.04 = ( ^ [A5: set_set_nat,B5: set_set_nat] :
% 3.82/4.04 ( ord_le3964352015994296041_nat_o
% 3.82/4.04 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ A5 )
% 3.82/4.04 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ B5 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % less_eq_set_def
% 3.82/4.04 thf(fact_3074_less__eq__set__def,axiom,
% 3.82/4.04 ( ord_less_eq_set_nat
% 3.82/4.04 = ( ^ [A5: set_nat,B5: set_nat] :
% 3.82/4.04 ( ord_less_eq_nat_o
% 3.82/4.04 @ ^ [X4: nat] : ( member_nat @ X4 @ A5 )
% 3.82/4.04 @ ^ [X4: nat] : ( member_nat @ X4 @ B5 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % less_eq_set_def
% 3.82/4.04 thf(fact_3075_less__eq__set__def,axiom,
% 3.82/4.04 ( ord_less_eq_set_int
% 3.82/4.04 = ( ^ [A5: set_int,B5: set_int] :
% 3.82/4.04 ( ord_less_eq_int_o
% 3.82/4.04 @ ^ [X4: int] : ( member_int @ X4 @ A5 )
% 3.82/4.04 @ ^ [X4: int] : ( member_int @ X4 @ B5 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % less_eq_set_def
% 3.82/4.04 thf(fact_3076_Collect__subset,axiom,
% 3.82/4.04 ! [A2: set_Extended_enat,P: extended_enat > $o] :
% 3.82/4.04 ( ord_le7203529160286727270d_enat
% 3.82/4.04 @ ( collec4429806609662206161d_enat
% 3.82/4.04 @ ^ [X4: extended_enat] :
% 3.82/4.04 ( ( member_Extended_enat @ X4 @ A2 )
% 3.82/4.04 & ( P @ X4 ) ) )
% 3.82/4.04 @ A2 ) ).
% 3.82/4.04
% 3.82/4.04 % Collect_subset
% 3.82/4.04 thf(fact_3077_Collect__subset,axiom,
% 3.82/4.04 ! [A2: set_real,P: real > $o] :
% 3.82/4.04 ( ord_less_eq_set_real
% 3.82/4.04 @ ( collect_real
% 3.82/4.04 @ ^ [X4: real] :
% 3.82/4.04 ( ( member_real @ X4 @ A2 )
% 3.82/4.04 & ( P @ X4 ) ) )
% 3.82/4.04 @ A2 ) ).
% 3.82/4.04
% 3.82/4.04 % Collect_subset
% 3.82/4.04 thf(fact_3078_Collect__subset,axiom,
% 3.82/4.04 ! [A2: set_list_nat,P: list_nat > $o] :
% 3.82/4.04 ( ord_le6045566169113846134st_nat
% 3.82/4.04 @ ( collect_list_nat
% 3.82/4.04 @ ^ [X4: list_nat] :
% 3.82/4.04 ( ( member_list_nat @ X4 @ A2 )
% 3.82/4.04 & ( P @ X4 ) ) )
% 3.82/4.04 @ A2 ) ).
% 3.82/4.04
% 3.82/4.04 % Collect_subset
% 3.82/4.04 thf(fact_3079_Collect__subset,axiom,
% 3.82/4.04 ! [A2: set_set_nat,P: set_nat > $o] :
% 3.82/4.04 ( ord_le6893508408891458716et_nat
% 3.82/4.04 @ ( collect_set_nat
% 3.82/4.04 @ ^ [X4: set_nat] :
% 3.82/4.04 ( ( member_set_nat @ X4 @ A2 )
% 3.82/4.04 & ( P @ X4 ) ) )
% 3.82/4.04 @ A2 ) ).
% 3.82/4.04
% 3.82/4.04 % Collect_subset
% 3.82/4.04 thf(fact_3080_Collect__subset,axiom,
% 3.82/4.04 ! [A2: set_nat,P: nat > $o] :
% 3.82/4.04 ( ord_less_eq_set_nat
% 3.82/4.04 @ ( collect_nat
% 3.82/4.04 @ ^ [X4: nat] :
% 3.82/4.04 ( ( member_nat @ X4 @ A2 )
% 3.82/4.04 & ( P @ X4 ) ) )
% 3.82/4.04 @ A2 ) ).
% 3.82/4.04
% 3.82/4.04 % Collect_subset
% 3.82/4.04 thf(fact_3081_Collect__subset,axiom,
% 3.82/4.04 ! [A2: set_int,P: int > $o] :
% 3.82/4.04 ( ord_less_eq_set_int
% 3.82/4.04 @ ( collect_int
% 3.82/4.04 @ ^ [X4: int] :
% 3.82/4.04 ( ( member_int @ X4 @ A2 )
% 3.82/4.04 & ( P @ X4 ) ) )
% 3.82/4.04 @ A2 ) ).
% 3.82/4.04
% 3.82/4.04 % Collect_subset
% 3.82/4.04 thf(fact_3082_subset__divisors__dvd,axiom,
% 3.82/4.04 ! [A: real,B2: real] :
% 3.82/4.04 ( ( ord_less_eq_set_real
% 3.82/4.04 @ ( collect_real
% 3.82/4.04 @ ^ [C3: real] : ( dvd_dvd_real @ C3 @ A ) )
% 3.82/4.04 @ ( collect_real
% 3.82/4.04 @ ^ [C3: real] : ( dvd_dvd_real @ C3 @ B2 ) ) )
% 3.82/4.04 = ( dvd_dvd_real @ A @ B2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % subset_divisors_dvd
% 3.82/4.04 thf(fact_3083_subset__divisors__dvd,axiom,
% 3.82/4.04 ! [A: nat,B2: nat] :
% 3.82/4.04 ( ( ord_less_eq_set_nat
% 3.82/4.04 @ ( collect_nat
% 3.82/4.04 @ ^ [C3: nat] : ( dvd_dvd_nat @ C3 @ A ) )
% 3.82/4.04 @ ( collect_nat
% 3.82/4.04 @ ^ [C3: nat] : ( dvd_dvd_nat @ C3 @ B2 ) ) )
% 3.82/4.04 = ( dvd_dvd_nat @ A @ B2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % subset_divisors_dvd
% 3.82/4.04 thf(fact_3084_subset__divisors__dvd,axiom,
% 3.82/4.04 ! [A: int,B2: int] :
% 3.82/4.04 ( ( ord_less_eq_set_int
% 3.82/4.04 @ ( collect_int
% 3.82/4.04 @ ^ [C3: int] : ( dvd_dvd_int @ C3 @ A ) )
% 3.82/4.04 @ ( collect_int
% 3.82/4.04 @ ^ [C3: int] : ( dvd_dvd_int @ C3 @ B2 ) ) )
% 3.82/4.04 = ( dvd_dvd_int @ A @ B2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % subset_divisors_dvd
% 3.82/4.04 thf(fact_3085_Collect__restrict,axiom,
% 3.82/4.04 ! [X8: set_Extended_enat,P: extended_enat > $o] :
% 3.82/4.04 ( ord_le7203529160286727270d_enat
% 3.82/4.04 @ ( collec4429806609662206161d_enat
% 3.82/4.04 @ ^ [X4: extended_enat] :
% 3.82/4.04 ( ( member_Extended_enat @ X4 @ X8 )
% 3.82/4.04 & ( P @ X4 ) ) )
% 3.82/4.04 @ X8 ) ).
% 3.82/4.04
% 3.82/4.04 % Collect_restrict
% 3.82/4.04 thf(fact_3086_Collect__restrict,axiom,
% 3.82/4.04 ! [X8: set_real,P: real > $o] :
% 3.82/4.04 ( ord_less_eq_set_real
% 3.82/4.04 @ ( collect_real
% 3.82/4.04 @ ^ [X4: real] :
% 3.82/4.04 ( ( member_real @ X4 @ X8 )
% 3.82/4.04 & ( P @ X4 ) ) )
% 3.82/4.04 @ X8 ) ).
% 3.82/4.04
% 3.82/4.04 % Collect_restrict
% 3.82/4.04 thf(fact_3087_Collect__restrict,axiom,
% 3.82/4.04 ! [X8: set_list_nat,P: list_nat > $o] :
% 3.82/4.04 ( ord_le6045566169113846134st_nat
% 3.82/4.04 @ ( collect_list_nat
% 3.82/4.04 @ ^ [X4: list_nat] :
% 3.82/4.04 ( ( member_list_nat @ X4 @ X8 )
% 3.82/4.04 & ( P @ X4 ) ) )
% 3.82/4.04 @ X8 ) ).
% 3.82/4.04
% 3.82/4.04 % Collect_restrict
% 3.82/4.04 thf(fact_3088_Collect__restrict,axiom,
% 3.82/4.04 ! [X8: set_set_nat,P: set_nat > $o] :
% 3.82/4.04 ( ord_le6893508408891458716et_nat
% 3.82/4.04 @ ( collect_set_nat
% 3.82/4.04 @ ^ [X4: set_nat] :
% 3.82/4.04 ( ( member_set_nat @ X4 @ X8 )
% 3.82/4.04 & ( P @ X4 ) ) )
% 3.82/4.04 @ X8 ) ).
% 3.82/4.04
% 3.82/4.04 % Collect_restrict
% 3.82/4.04 thf(fact_3089_Collect__restrict,axiom,
% 3.82/4.04 ! [X8: set_nat,P: nat > $o] :
% 3.82/4.04 ( ord_less_eq_set_nat
% 3.82/4.04 @ ( collect_nat
% 3.82/4.04 @ ^ [X4: nat] :
% 3.82/4.04 ( ( member_nat @ X4 @ X8 )
% 3.82/4.04 & ( P @ X4 ) ) )
% 3.82/4.04 @ X8 ) ).
% 3.82/4.04
% 3.82/4.04 % Collect_restrict
% 3.82/4.04 thf(fact_3090_Collect__restrict,axiom,
% 3.82/4.04 ! [X8: set_int,P: int > $o] :
% 3.82/4.04 ( ord_less_eq_set_int
% 3.82/4.04 @ ( collect_int
% 3.82/4.04 @ ^ [X4: int] :
% 3.82/4.04 ( ( member_int @ X4 @ X8 )
% 3.82/4.04 & ( P @ X4 ) ) )
% 3.82/4.04 @ X8 ) ).
% 3.82/4.04
% 3.82/4.04 % Collect_restrict
% 3.82/4.04 thf(fact_3091_prop__restrict,axiom,
% 3.82/4.04 ! [X: extended_enat,Z5: set_Extended_enat,X8: set_Extended_enat,P: extended_enat > $o] :
% 3.82/4.04 ( ( member_Extended_enat @ X @ Z5 )
% 3.82/4.04 => ( ( ord_le7203529160286727270d_enat @ Z5
% 3.82/4.04 @ ( collec4429806609662206161d_enat
% 3.82/4.04 @ ^ [X4: extended_enat] :
% 3.82/4.04 ( ( member_Extended_enat @ X4 @ X8 )
% 3.82/4.04 & ( P @ X4 ) ) ) )
% 3.82/4.04 => ( P @ X ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % prop_restrict
% 3.82/4.04 thf(fact_3092_prop__restrict,axiom,
% 3.82/4.04 ! [X: real,Z5: set_real,X8: set_real,P: real > $o] :
% 3.82/4.04 ( ( member_real @ X @ Z5 )
% 3.82/4.04 => ( ( ord_less_eq_set_real @ Z5
% 3.82/4.04 @ ( collect_real
% 3.82/4.04 @ ^ [X4: real] :
% 3.82/4.04 ( ( member_real @ X4 @ X8 )
% 3.82/4.04 & ( P @ X4 ) ) ) )
% 3.82/4.04 => ( P @ X ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % prop_restrict
% 3.82/4.04 thf(fact_3093_prop__restrict,axiom,
% 3.82/4.04 ! [X: list_nat,Z5: set_list_nat,X8: set_list_nat,P: list_nat > $o] :
% 3.82/4.04 ( ( member_list_nat @ X @ Z5 )
% 3.82/4.04 => ( ( ord_le6045566169113846134st_nat @ Z5
% 3.82/4.04 @ ( collect_list_nat
% 3.82/4.04 @ ^ [X4: list_nat] :
% 3.82/4.04 ( ( member_list_nat @ X4 @ X8 )
% 3.82/4.04 & ( P @ X4 ) ) ) )
% 3.82/4.04 => ( P @ X ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % prop_restrict
% 3.82/4.04 thf(fact_3094_prop__restrict,axiom,
% 3.82/4.04 ! [X: set_nat,Z5: set_set_nat,X8: set_set_nat,P: set_nat > $o] :
% 3.82/4.04 ( ( member_set_nat @ X @ Z5 )
% 3.82/4.04 => ( ( ord_le6893508408891458716et_nat @ Z5
% 3.82/4.04 @ ( collect_set_nat
% 3.82/4.04 @ ^ [X4: set_nat] :
% 3.82/4.04 ( ( member_set_nat @ X4 @ X8 )
% 3.82/4.04 & ( P @ X4 ) ) ) )
% 3.82/4.04 => ( P @ X ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % prop_restrict
% 3.82/4.04 thf(fact_3095_prop__restrict,axiom,
% 3.82/4.04 ! [X: nat,Z5: set_nat,X8: set_nat,P: nat > $o] :
% 3.82/4.04 ( ( member_nat @ X @ Z5 )
% 3.82/4.04 => ( ( ord_less_eq_set_nat @ Z5
% 3.82/4.04 @ ( collect_nat
% 3.82/4.04 @ ^ [X4: nat] :
% 3.82/4.04 ( ( member_nat @ X4 @ X8 )
% 3.82/4.04 & ( P @ X4 ) ) ) )
% 3.82/4.04 => ( P @ X ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % prop_restrict
% 3.82/4.04 thf(fact_3096_prop__restrict,axiom,
% 3.82/4.04 ! [X: int,Z5: set_int,X8: set_int,P: int > $o] :
% 3.82/4.04 ( ( member_int @ X @ Z5 )
% 3.82/4.04 => ( ( ord_less_eq_set_int @ Z5
% 3.82/4.04 @ ( collect_int
% 3.82/4.04 @ ^ [X4: int] :
% 3.82/4.04 ( ( member_int @ X4 @ X8 )
% 3.82/4.04 & ( P @ X4 ) ) ) )
% 3.82/4.04 => ( P @ X ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % prop_restrict
% 3.82/4.04 thf(fact_3097_lambda__zero,axiom,
% 3.82/4.04 ( ( ^ [H: nat] : zero_zero_nat )
% 3.82/4.04 = ( times_times_nat @ zero_zero_nat ) ) ).
% 3.82/4.04
% 3.82/4.04 % lambda_zero
% 3.82/4.04 thf(fact_3098_lambda__zero,axiom,
% 3.82/4.04 ( ( ^ [H: int] : zero_zero_int )
% 3.82/4.04 = ( times_times_int @ zero_zero_int ) ) ).
% 3.82/4.04
% 3.82/4.04 % lambda_zero
% 3.82/4.04 thf(fact_3099_lambda__zero,axiom,
% 3.82/4.04 ( ( ^ [H: real] : zero_zero_real )
% 3.82/4.04 = ( times_times_real @ zero_zero_real ) ) ).
% 3.82/4.04
% 3.82/4.04 % lambda_zero
% 3.82/4.04 thf(fact_3100_lambda__zero,axiom,
% 3.82/4.04 ( ( ^ [H: complex] : zero_zero_complex )
% 3.82/4.04 = ( times_times_complex @ zero_zero_complex ) ) ).
% 3.82/4.04
% 3.82/4.04 % lambda_zero
% 3.82/4.04 thf(fact_3101_lambda__zero,axiom,
% 3.82/4.04 ( ( ^ [H: extended_enat] : zero_z5237406670263579293d_enat )
% 3.82/4.04 = ( times_7803423173614009249d_enat @ zero_z5237406670263579293d_enat ) ) ).
% 3.82/4.04
% 3.82/4.04 % lambda_zero
% 3.82/4.04 thf(fact_3102_lambda__one,axiom,
% 3.82/4.04 ( ( ^ [X4: nat] : X4 )
% 3.82/4.04 = ( times_times_nat @ one_one_nat ) ) ).
% 3.82/4.04
% 3.82/4.04 % lambda_one
% 3.82/4.04 thf(fact_3103_lambda__one,axiom,
% 3.82/4.04 ( ( ^ [X4: int] : X4 )
% 3.82/4.04 = ( times_times_int @ one_one_int ) ) ).
% 3.82/4.04
% 3.82/4.04 % lambda_one
% 3.82/4.04 thf(fact_3104_lambda__one,axiom,
% 3.82/4.04 ( ( ^ [X4: real] : X4 )
% 3.82/4.04 = ( times_times_real @ one_one_real ) ) ).
% 3.82/4.04
% 3.82/4.04 % lambda_one
% 3.82/4.04 thf(fact_3105_lambda__one,axiom,
% 3.82/4.04 ( ( ^ [X4: complex] : X4 )
% 3.82/4.04 = ( times_times_complex @ one_one_complex ) ) ).
% 3.82/4.04
% 3.82/4.04 % lambda_one
% 3.82/4.04 thf(fact_3106_lambda__one,axiom,
% 3.82/4.04 ( ( ^ [X4: extended_enat] : X4 )
% 3.82/4.04 = ( times_7803423173614009249d_enat @ one_on7984719198319812577d_enat ) ) ).
% 3.82/4.04
% 3.82/4.04 % lambda_one
% 3.82/4.04 thf(fact_3107_max__def__raw,axiom,
% 3.82/4.04 ( ord_max_real
% 3.82/4.04 = ( ^ [A3: real,B3: real] : ( if_real @ ( ord_less_eq_real @ A3 @ B3 ) @ B3 @ A3 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % max_def_raw
% 3.82/4.04 thf(fact_3108_max__def__raw,axiom,
% 3.82/4.04 ( ord_max_set_nat
% 3.82/4.04 = ( ^ [A3: set_nat,B3: set_nat] : ( if_set_nat @ ( ord_less_eq_set_nat @ A3 @ B3 ) @ B3 @ A3 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % max_def_raw
% 3.82/4.04 thf(fact_3109_max__def__raw,axiom,
% 3.82/4.04 ( ord_max_set_int
% 3.82/4.04 = ( ^ [A3: set_int,B3: set_int] : ( if_set_int @ ( ord_less_eq_set_int @ A3 @ B3 ) @ B3 @ A3 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % max_def_raw
% 3.82/4.04 thf(fact_3110_max__def__raw,axiom,
% 3.82/4.04 ( ord_max_nat
% 3.82/4.04 = ( ^ [A3: nat,B3: nat] : ( if_nat @ ( ord_less_eq_nat @ A3 @ B3 ) @ B3 @ A3 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % max_def_raw
% 3.82/4.04 thf(fact_3111_max__def__raw,axiom,
% 3.82/4.04 ( ord_max_int
% 3.82/4.04 = ( ^ [A3: int,B3: int] : ( if_int @ ( ord_less_eq_int @ A3 @ B3 ) @ B3 @ A3 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % max_def_raw
% 3.82/4.04 thf(fact_3112_finite__divisors__nat,axiom,
% 3.82/4.04 ! [M2: nat] :
% 3.82/4.04 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 3.82/4.04 => ( finite_finite_nat
% 3.82/4.04 @ ( collect_nat
% 3.82/4.04 @ ^ [D4: nat] : ( dvd_dvd_nat @ D4 @ M2 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % finite_divisors_nat
% 3.82/4.04 thf(fact_3113_unit__imp__mod__eq__0,axiom,
% 3.82/4.04 ! [B2: nat,A: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 3.82/4.04 => ( ( modulo_modulo_nat @ A @ B2 )
% 3.82/4.04 = zero_zero_nat ) ) ).
% 3.82/4.04
% 3.82/4.04 % unit_imp_mod_eq_0
% 3.82/4.04 thf(fact_3114_unit__imp__mod__eq__0,axiom,
% 3.82/4.04 ! [B2: int,A: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ B2 @ one_one_int )
% 3.82/4.04 => ( ( modulo_modulo_int @ A @ B2 )
% 3.82/4.04 = zero_zero_int ) ) ).
% 3.82/4.04
% 3.82/4.04 % unit_imp_mod_eq_0
% 3.82/4.04 thf(fact_3115_bot__empty__eq2,axiom,
% 3.82/4.04 ( bot_bot_nat_nat_o
% 3.82/4.04 = ( ^ [X4: nat,Y5: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y5 ) @ bot_bo2099793752762293965at_nat ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % bot_empty_eq2
% 3.82/4.04 thf(fact_3116_bot__empty__eq2,axiom,
% 3.82/4.04 ( bot_bo1565574316222977092_nat_o
% 3.82/4.04 = ( ^ [X4: vEBT_VEBT,Y5: nat] : ( member373505688050248522BT_nat @ ( produc738532404422230701BT_nat @ X4 @ Y5 ) @ bot_bo1642239108664514429BT_nat ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % bot_empty_eq2
% 3.82/4.04 thf(fact_3117_bot__empty__eq2,axiom,
% 3.82/4.04 ( bot_bot_int_int_o
% 3.82/4.04 = ( ^ [X4: int,Y5: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y5 ) @ bot_bo1796632182523588997nt_int ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % bot_empty_eq2
% 3.82/4.04 thf(fact_3118_bot__empty__eq2,axiom,
% 3.82/4.04 ( bot_bo4898103413517107610_nat_o
% 3.82/4.04 = ( ^ [X4: product_prod_nat_nat,Y5: product_prod_nat_nat] : ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X4 @ Y5 ) @ bot_bo5327735625951526323at_nat ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % bot_empty_eq2
% 3.82/4.04 thf(fact_3119_finite__M__bounded__by__nat,axiom,
% 3.82/4.04 ! [P: nat > $o,I: nat] :
% 3.82/4.04 ( finite_finite_nat
% 3.82/4.04 @ ( collect_nat
% 3.82/4.04 @ ^ [K2: nat] :
% 3.82/4.04 ( ( P @ K2 )
% 3.82/4.04 & ( ord_less_nat @ K2 @ I ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % finite_M_bounded_by_nat
% 3.82/4.04 thf(fact_3120_finite__less__ub,axiom,
% 3.82/4.04 ! [F: nat > nat,U: nat] :
% 3.82/4.04 ( ! [N3: nat] : ( ord_less_eq_nat @ N3 @ ( F @ N3 ) )
% 3.82/4.04 => ( finite_finite_nat
% 3.82/4.04 @ ( collect_nat
% 3.82/4.04 @ ^ [N: nat] : ( ord_less_eq_nat @ ( F @ N ) @ U ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % finite_less_ub
% 3.82/4.04 thf(fact_3121_mod__greater__zero__iff__not__dvd,axiom,
% 3.82/4.04 ! [M2: nat,N2: nat] :
% 3.82/4.04 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M2 @ N2 ) )
% 3.82/4.04 = ( ~ ( dvd_dvd_nat @ N2 @ M2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % mod_greater_zero_iff_not_dvd
% 3.82/4.04 thf(fact_3122_mod__add__right__eq,axiom,
% 3.82/4.04 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.04 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( modulo_modulo_nat @ B2 @ C ) ) @ C )
% 3.82/4.04 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B2 ) @ C ) ) ).
% 3.82/4.04
% 3.82/4.04 % mod_add_right_eq
% 3.82/4.04 thf(fact_3123_mod__add__right__eq,axiom,
% 3.82/4.04 ! [A: int,B2: int,C: int] :
% 3.82/4.04 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( modulo_modulo_int @ B2 @ C ) ) @ C )
% 3.82/4.04 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B2 ) @ C ) ) ).
% 3.82/4.04
% 3.82/4.04 % mod_add_right_eq
% 3.82/4.04 thf(fact_3124_mod__add__left__eq,axiom,
% 3.82/4.04 ! [A: nat,C: nat,B2: nat] :
% 3.82/4.04 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ B2 ) @ C )
% 3.82/4.04 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B2 ) @ C ) ) ).
% 3.82/4.04
% 3.82/4.04 % mod_add_left_eq
% 3.82/4.04 thf(fact_3125_mod__add__left__eq,axiom,
% 3.82/4.04 ! [A: int,C: int,B2: int] :
% 3.82/4.04 ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ B2 ) @ C )
% 3.82/4.04 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B2 ) @ C ) ) ).
% 3.82/4.04
% 3.82/4.04 % mod_add_left_eq
% 3.82/4.04 thf(fact_3126_mod__add__cong,axiom,
% 3.82/4.04 ! [A: nat,C: nat,A7: nat,B2: nat,B7: nat] :
% 3.82/4.04 ( ( ( modulo_modulo_nat @ A @ C )
% 3.82/4.04 = ( modulo_modulo_nat @ A7 @ C ) )
% 3.82/4.04 => ( ( ( modulo_modulo_nat @ B2 @ C )
% 3.82/4.04 = ( modulo_modulo_nat @ B7 @ C ) )
% 3.82/4.04 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B2 ) @ C )
% 3.82/4.04 = ( modulo_modulo_nat @ ( plus_plus_nat @ A7 @ B7 ) @ C ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % mod_add_cong
% 3.82/4.04 thf(fact_3127_mod__add__cong,axiom,
% 3.82/4.04 ! [A: int,C: int,A7: int,B2: int,B7: int] :
% 3.82/4.04 ( ( ( modulo_modulo_int @ A @ C )
% 3.82/4.04 = ( modulo_modulo_int @ A7 @ C ) )
% 3.82/4.04 => ( ( ( modulo_modulo_int @ B2 @ C )
% 3.82/4.04 = ( modulo_modulo_int @ B7 @ C ) )
% 3.82/4.04 => ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B2 ) @ C )
% 3.82/4.04 = ( modulo_modulo_int @ ( plus_plus_int @ A7 @ B7 ) @ C ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % mod_add_cong
% 3.82/4.04 thf(fact_3128_mod__add__eq,axiom,
% 3.82/4.04 ! [A: nat,C: nat,B2: nat] :
% 3.82/4.04 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B2 @ C ) ) @ C )
% 3.82/4.04 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B2 ) @ C ) ) ).
% 3.82/4.04
% 3.82/4.04 % mod_add_eq
% 3.82/4.04 thf(fact_3129_mod__add__eq,axiom,
% 3.82/4.04 ! [A: int,C: int,B2: int] :
% 3.82/4.04 ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B2 @ C ) ) @ C )
% 3.82/4.04 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B2 ) @ C ) ) ).
% 3.82/4.04
% 3.82/4.04 % mod_add_eq
% 3.82/4.04 thf(fact_3130_dvd__0__left,axiom,
% 3.82/4.04 ! [A: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 3.82/4.04 => ( A = zero_zero_nat ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_0_left
% 3.82/4.04 thf(fact_3131_dvd__0__left,axiom,
% 3.82/4.04 ! [A: real] :
% 3.82/4.04 ( ( dvd_dvd_real @ zero_zero_real @ A )
% 3.82/4.04 => ( A = zero_zero_real ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_0_left
% 3.82/4.04 thf(fact_3132_dvd__0__left,axiom,
% 3.82/4.04 ! [A: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ zero_zero_int @ A )
% 3.82/4.04 => ( A = zero_zero_int ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_0_left
% 3.82/4.04 thf(fact_3133_dvd__0__left,axiom,
% 3.82/4.04 ! [A: complex] :
% 3.82/4.04 ( ( dvd_dvd_complex @ zero_zero_complex @ A )
% 3.82/4.04 => ( A = zero_zero_complex ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_0_left
% 3.82/4.04 thf(fact_3134_dvd__0__left,axiom,
% 3.82/4.04 ! [A: extended_enat] :
% 3.82/4.04 ( ( dvd_dv3785147216227455552d_enat @ zero_z5237406670263579293d_enat @ A )
% 3.82/4.04 => ( A = zero_z5237406670263579293d_enat ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_0_left
% 3.82/4.04 thf(fact_3135_dvd__field__iff,axiom,
% 3.82/4.04 ( dvd_dvd_real
% 3.82/4.04 = ( ^ [A3: real,B3: real] :
% 3.82/4.04 ( ( A3 = zero_zero_real )
% 3.82/4.04 => ( B3 = zero_zero_real ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_field_iff
% 3.82/4.04 thf(fact_3136_dvd__field__iff,axiom,
% 3.82/4.04 ( dvd_dvd_complex
% 3.82/4.04 = ( ^ [A3: complex,B3: complex] :
% 3.82/4.04 ( ( A3 = zero_zero_complex )
% 3.82/4.04 => ( B3 = zero_zero_complex ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_field_iff
% 3.82/4.04 thf(fact_3137_mod__Suc__Suc__eq,axiom,
% 3.82/4.04 ! [M2: nat,N2: nat] :
% 3.82/4.04 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( modulo_modulo_nat @ M2 @ N2 ) ) ) @ N2 )
% 3.82/4.04 = ( modulo_modulo_nat @ ( suc @ ( suc @ M2 ) ) @ N2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % mod_Suc_Suc_eq
% 3.82/4.04 thf(fact_3138_mod__Suc__eq,axiom,
% 3.82/4.04 ! [M2: nat,N2: nat] :
% 3.82/4.04 ( ( modulo_modulo_nat @ ( suc @ ( modulo_modulo_nat @ M2 @ N2 ) ) @ N2 )
% 3.82/4.04 = ( modulo_modulo_nat @ ( suc @ M2 ) @ N2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % mod_Suc_eq
% 3.82/4.04 thf(fact_3139_dvdE,axiom,
% 3.82/4.04 ! [B2: nat,A: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ B2 @ A )
% 3.82/4.04 => ~ ! [K3: nat] :
% 3.82/4.04 ( A
% 3.82/4.04 != ( times_times_nat @ B2 @ K3 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvdE
% 3.82/4.04 thf(fact_3140_dvdE,axiom,
% 3.82/4.04 ! [B2: int,A: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ B2 @ A )
% 3.82/4.04 => ~ ! [K3: int] :
% 3.82/4.04 ( A
% 3.82/4.04 != ( times_times_int @ B2 @ K3 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvdE
% 3.82/4.04 thf(fact_3141_dvdE,axiom,
% 3.82/4.04 ! [B2: real,A: real] :
% 3.82/4.04 ( ( dvd_dvd_real @ B2 @ A )
% 3.82/4.04 => ~ ! [K3: real] :
% 3.82/4.04 ( A
% 3.82/4.04 != ( times_times_real @ B2 @ K3 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvdE
% 3.82/4.04 thf(fact_3142_dvdE,axiom,
% 3.82/4.04 ! [B2: complex,A: complex] :
% 3.82/4.04 ( ( dvd_dvd_complex @ B2 @ A )
% 3.82/4.04 => ~ ! [K3: complex] :
% 3.82/4.04 ( A
% 3.82/4.04 != ( times_times_complex @ B2 @ K3 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvdE
% 3.82/4.04 thf(fact_3143_dvdE,axiom,
% 3.82/4.04 ! [B2: extended_enat,A: extended_enat] :
% 3.82/4.04 ( ( dvd_dv3785147216227455552d_enat @ B2 @ A )
% 3.82/4.04 => ~ ! [K3: extended_enat] :
% 3.82/4.04 ( A
% 3.82/4.04 != ( times_7803423173614009249d_enat @ B2 @ K3 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvdE
% 3.82/4.04 thf(fact_3144_dvdI,axiom,
% 3.82/4.04 ! [A: nat,B2: nat,K: nat] :
% 3.82/4.04 ( ( A
% 3.82/4.04 = ( times_times_nat @ B2 @ K ) )
% 3.82/4.04 => ( dvd_dvd_nat @ B2 @ A ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvdI
% 3.82/4.04 thf(fact_3145_dvdI,axiom,
% 3.82/4.04 ! [A: int,B2: int,K: int] :
% 3.82/4.04 ( ( A
% 3.82/4.04 = ( times_times_int @ B2 @ K ) )
% 3.82/4.04 => ( dvd_dvd_int @ B2 @ A ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvdI
% 3.82/4.04 thf(fact_3146_dvdI,axiom,
% 3.82/4.04 ! [A: real,B2: real,K: real] :
% 3.82/4.04 ( ( A
% 3.82/4.04 = ( times_times_real @ B2 @ K ) )
% 3.82/4.04 => ( dvd_dvd_real @ B2 @ A ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvdI
% 3.82/4.04 thf(fact_3147_dvdI,axiom,
% 3.82/4.04 ! [A: complex,B2: complex,K: complex] :
% 3.82/4.04 ( ( A
% 3.82/4.04 = ( times_times_complex @ B2 @ K ) )
% 3.82/4.04 => ( dvd_dvd_complex @ B2 @ A ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvdI
% 3.82/4.04 thf(fact_3148_dvdI,axiom,
% 3.82/4.04 ! [A: extended_enat,B2: extended_enat,K: extended_enat] :
% 3.82/4.04 ( ( A
% 3.82/4.04 = ( times_7803423173614009249d_enat @ B2 @ K ) )
% 3.82/4.04 => ( dvd_dv3785147216227455552d_enat @ B2 @ A ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvdI
% 3.82/4.04 thf(fact_3149_dvd__def,axiom,
% 3.82/4.04 ( dvd_dvd_nat
% 3.82/4.04 = ( ^ [B3: nat,A3: nat] :
% 3.82/4.04 ? [K2: nat] :
% 3.82/4.04 ( A3
% 3.82/4.04 = ( times_times_nat @ B3 @ K2 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_def
% 3.82/4.04 thf(fact_3150_dvd__def,axiom,
% 3.82/4.04 ( dvd_dvd_int
% 3.82/4.04 = ( ^ [B3: int,A3: int] :
% 3.82/4.04 ? [K2: int] :
% 3.82/4.04 ( A3
% 3.82/4.04 = ( times_times_int @ B3 @ K2 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_def
% 3.82/4.04 thf(fact_3151_dvd__def,axiom,
% 3.82/4.04 ( dvd_dvd_real
% 3.82/4.04 = ( ^ [B3: real,A3: real] :
% 3.82/4.04 ? [K2: real] :
% 3.82/4.04 ( A3
% 3.82/4.04 = ( times_times_real @ B3 @ K2 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_def
% 3.82/4.04 thf(fact_3152_dvd__def,axiom,
% 3.82/4.04 ( dvd_dvd_complex
% 3.82/4.04 = ( ^ [B3: complex,A3: complex] :
% 3.82/4.04 ? [K2: complex] :
% 3.82/4.04 ( A3
% 3.82/4.04 = ( times_times_complex @ B3 @ K2 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_def
% 3.82/4.04 thf(fact_3153_dvd__def,axiom,
% 3.82/4.04 ( dvd_dv3785147216227455552d_enat
% 3.82/4.04 = ( ^ [B3: extended_enat,A3: extended_enat] :
% 3.82/4.04 ? [K2: extended_enat] :
% 3.82/4.04 ( A3
% 3.82/4.04 = ( times_7803423173614009249d_enat @ B3 @ K2 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_def
% 3.82/4.04 thf(fact_3154_dvd__mult,axiom,
% 3.82/4.04 ! [A: nat,C: nat,B2: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ A @ C )
% 3.82/4.04 => ( dvd_dvd_nat @ A @ ( times_times_nat @ B2 @ C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_mult
% 3.82/4.04 thf(fact_3155_dvd__mult,axiom,
% 3.82/4.04 ! [A: int,C: int,B2: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ A @ C )
% 3.82/4.04 => ( dvd_dvd_int @ A @ ( times_times_int @ B2 @ C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_mult
% 3.82/4.04 thf(fact_3156_dvd__mult,axiom,
% 3.82/4.04 ! [A: real,C: real,B2: real] :
% 3.82/4.04 ( ( dvd_dvd_real @ A @ C )
% 3.82/4.04 => ( dvd_dvd_real @ A @ ( times_times_real @ B2 @ C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_mult
% 3.82/4.04 thf(fact_3157_dvd__mult,axiom,
% 3.82/4.04 ! [A: complex,C: complex,B2: complex] :
% 3.82/4.04 ( ( dvd_dvd_complex @ A @ C )
% 3.82/4.04 => ( dvd_dvd_complex @ A @ ( times_times_complex @ B2 @ C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_mult
% 3.82/4.04 thf(fact_3158_dvd__mult,axiom,
% 3.82/4.04 ! [A: extended_enat,C: extended_enat,B2: extended_enat] :
% 3.82/4.04 ( ( dvd_dv3785147216227455552d_enat @ A @ C )
% 3.82/4.04 => ( dvd_dv3785147216227455552d_enat @ A @ ( times_7803423173614009249d_enat @ B2 @ C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_mult
% 3.82/4.04 thf(fact_3159_dvd__mult2,axiom,
% 3.82/4.04 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ A @ B2 )
% 3.82/4.04 => ( dvd_dvd_nat @ A @ ( times_times_nat @ B2 @ C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_mult2
% 3.82/4.04 thf(fact_3160_dvd__mult2,axiom,
% 3.82/4.04 ! [A: int,B2: int,C: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ A @ B2 )
% 3.82/4.04 => ( dvd_dvd_int @ A @ ( times_times_int @ B2 @ C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_mult2
% 3.82/4.04 thf(fact_3161_dvd__mult2,axiom,
% 3.82/4.04 ! [A: real,B2: real,C: real] :
% 3.82/4.04 ( ( dvd_dvd_real @ A @ B2 )
% 3.82/4.04 => ( dvd_dvd_real @ A @ ( times_times_real @ B2 @ C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_mult2
% 3.82/4.04 thf(fact_3162_dvd__mult2,axiom,
% 3.82/4.04 ! [A: complex,B2: complex,C: complex] :
% 3.82/4.04 ( ( dvd_dvd_complex @ A @ B2 )
% 3.82/4.04 => ( dvd_dvd_complex @ A @ ( times_times_complex @ B2 @ C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_mult2
% 3.82/4.04 thf(fact_3163_dvd__mult2,axiom,
% 3.82/4.04 ! [A: extended_enat,B2: extended_enat,C: extended_enat] :
% 3.82/4.04 ( ( dvd_dv3785147216227455552d_enat @ A @ B2 )
% 3.82/4.04 => ( dvd_dv3785147216227455552d_enat @ A @ ( times_7803423173614009249d_enat @ B2 @ C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_mult2
% 3.82/4.04 thf(fact_3164_dvd__mult__left,axiom,
% 3.82/4.04 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B2 ) @ C )
% 3.82/4.04 => ( dvd_dvd_nat @ A @ C ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_mult_left
% 3.82/4.04 thf(fact_3165_dvd__mult__left,axiom,
% 3.82/4.04 ! [A: int,B2: int,C: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ ( times_times_int @ A @ B2 ) @ C )
% 3.82/4.04 => ( dvd_dvd_int @ A @ C ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_mult_left
% 3.82/4.04 thf(fact_3166_dvd__mult__left,axiom,
% 3.82/4.04 ! [A: real,B2: real,C: real] :
% 3.82/4.04 ( ( dvd_dvd_real @ ( times_times_real @ A @ B2 ) @ C )
% 3.82/4.04 => ( dvd_dvd_real @ A @ C ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_mult_left
% 3.82/4.04 thf(fact_3167_dvd__mult__left,axiom,
% 3.82/4.04 ! [A: complex,B2: complex,C: complex] :
% 3.82/4.04 ( ( dvd_dvd_complex @ ( times_times_complex @ A @ B2 ) @ C )
% 3.82/4.04 => ( dvd_dvd_complex @ A @ C ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_mult_left
% 3.82/4.04 thf(fact_3168_dvd__mult__left,axiom,
% 3.82/4.04 ! [A: extended_enat,B2: extended_enat,C: extended_enat] :
% 3.82/4.04 ( ( dvd_dv3785147216227455552d_enat @ ( times_7803423173614009249d_enat @ A @ B2 ) @ C )
% 3.82/4.04 => ( dvd_dv3785147216227455552d_enat @ A @ C ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_mult_left
% 3.82/4.04 thf(fact_3169_dvd__triv__left,axiom,
% 3.82/4.04 ! [A: nat,B2: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ A @ B2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_triv_left
% 3.82/4.04 thf(fact_3170_dvd__triv__left,axiom,
% 3.82/4.04 ! [A: int,B2: int] : ( dvd_dvd_int @ A @ ( times_times_int @ A @ B2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_triv_left
% 3.82/4.04 thf(fact_3171_dvd__triv__left,axiom,
% 3.82/4.04 ! [A: real,B2: real] : ( dvd_dvd_real @ A @ ( times_times_real @ A @ B2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_triv_left
% 3.82/4.04 thf(fact_3172_dvd__triv__left,axiom,
% 3.82/4.04 ! [A: complex,B2: complex] : ( dvd_dvd_complex @ A @ ( times_times_complex @ A @ B2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_triv_left
% 3.82/4.04 thf(fact_3173_dvd__triv__left,axiom,
% 3.82/4.04 ! [A: extended_enat,B2: extended_enat] : ( dvd_dv3785147216227455552d_enat @ A @ ( times_7803423173614009249d_enat @ A @ B2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_triv_left
% 3.82/4.04 thf(fact_3174_mult__dvd__mono,axiom,
% 3.82/4.04 ! [A: nat,B2: nat,C: nat,D: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ A @ B2 )
% 3.82/4.04 => ( ( dvd_dvd_nat @ C @ D )
% 3.82/4.04 => ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B2 @ D ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % mult_dvd_mono
% 3.82/4.04 thf(fact_3175_mult__dvd__mono,axiom,
% 3.82/4.04 ! [A: int,B2: int,C: int,D: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ A @ B2 )
% 3.82/4.04 => ( ( dvd_dvd_int @ C @ D )
% 3.82/4.04 => ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B2 @ D ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % mult_dvd_mono
% 3.82/4.04 thf(fact_3176_mult__dvd__mono,axiom,
% 3.82/4.04 ! [A: real,B2: real,C: real,D: real] :
% 3.82/4.04 ( ( dvd_dvd_real @ A @ B2 )
% 3.82/4.04 => ( ( dvd_dvd_real @ C @ D )
% 3.82/4.04 => ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B2 @ D ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % mult_dvd_mono
% 3.82/4.04 thf(fact_3177_mult__dvd__mono,axiom,
% 3.82/4.04 ! [A: complex,B2: complex,C: complex,D: complex] :
% 3.82/4.04 ( ( dvd_dvd_complex @ A @ B2 )
% 3.82/4.04 => ( ( dvd_dvd_complex @ C @ D )
% 3.82/4.04 => ( dvd_dvd_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B2 @ D ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % mult_dvd_mono
% 3.82/4.04 thf(fact_3178_mult__dvd__mono,axiom,
% 3.82/4.04 ! [A: extended_enat,B2: extended_enat,C: extended_enat,D: extended_enat] :
% 3.82/4.04 ( ( dvd_dv3785147216227455552d_enat @ A @ B2 )
% 3.82/4.04 => ( ( dvd_dv3785147216227455552d_enat @ C @ D )
% 3.82/4.04 => ( dvd_dv3785147216227455552d_enat @ ( times_7803423173614009249d_enat @ A @ C ) @ ( times_7803423173614009249d_enat @ B2 @ D ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % mult_dvd_mono
% 3.82/4.04 thf(fact_3179_dvd__mult__right,axiom,
% 3.82/4.04 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B2 ) @ C )
% 3.82/4.04 => ( dvd_dvd_nat @ B2 @ C ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_mult_right
% 3.82/4.04 thf(fact_3180_dvd__mult__right,axiom,
% 3.82/4.04 ! [A: int,B2: int,C: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ ( times_times_int @ A @ B2 ) @ C )
% 3.82/4.04 => ( dvd_dvd_int @ B2 @ C ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_mult_right
% 3.82/4.04 thf(fact_3181_dvd__mult__right,axiom,
% 3.82/4.04 ! [A: real,B2: real,C: real] :
% 3.82/4.04 ( ( dvd_dvd_real @ ( times_times_real @ A @ B2 ) @ C )
% 3.82/4.04 => ( dvd_dvd_real @ B2 @ C ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_mult_right
% 3.82/4.04 thf(fact_3182_dvd__mult__right,axiom,
% 3.82/4.04 ! [A: complex,B2: complex,C: complex] :
% 3.82/4.04 ( ( dvd_dvd_complex @ ( times_times_complex @ A @ B2 ) @ C )
% 3.82/4.04 => ( dvd_dvd_complex @ B2 @ C ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_mult_right
% 3.82/4.04 thf(fact_3183_dvd__mult__right,axiom,
% 3.82/4.04 ! [A: extended_enat,B2: extended_enat,C: extended_enat] :
% 3.82/4.04 ( ( dvd_dv3785147216227455552d_enat @ ( times_7803423173614009249d_enat @ A @ B2 ) @ C )
% 3.82/4.04 => ( dvd_dv3785147216227455552d_enat @ B2 @ C ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_mult_right
% 3.82/4.04 thf(fact_3184_dvd__triv__right,axiom,
% 3.82/4.04 ! [A: nat,B2: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ B2 @ A ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_triv_right
% 3.82/4.04 thf(fact_3185_dvd__triv__right,axiom,
% 3.82/4.04 ! [A: int,B2: int] : ( dvd_dvd_int @ A @ ( times_times_int @ B2 @ A ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_triv_right
% 3.82/4.04 thf(fact_3186_dvd__triv__right,axiom,
% 3.82/4.04 ! [A: real,B2: real] : ( dvd_dvd_real @ A @ ( times_times_real @ B2 @ A ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_triv_right
% 3.82/4.04 thf(fact_3187_dvd__triv__right,axiom,
% 3.82/4.04 ! [A: complex,B2: complex] : ( dvd_dvd_complex @ A @ ( times_times_complex @ B2 @ A ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_triv_right
% 3.82/4.04 thf(fact_3188_dvd__triv__right,axiom,
% 3.82/4.04 ! [A: extended_enat,B2: extended_enat] : ( dvd_dv3785147216227455552d_enat @ A @ ( times_7803423173614009249d_enat @ B2 @ A ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_triv_right
% 3.82/4.04 thf(fact_3189_one__dvd,axiom,
% 3.82/4.04 ! [A: nat] : ( dvd_dvd_nat @ one_one_nat @ A ) ).
% 3.82/4.04
% 3.82/4.04 % one_dvd
% 3.82/4.04 thf(fact_3190_one__dvd,axiom,
% 3.82/4.04 ! [A: int] : ( dvd_dvd_int @ one_one_int @ A ) ).
% 3.82/4.04
% 3.82/4.04 % one_dvd
% 3.82/4.04 thf(fact_3191_one__dvd,axiom,
% 3.82/4.04 ! [A: complex] : ( dvd_dvd_complex @ one_one_complex @ A ) ).
% 3.82/4.04
% 3.82/4.04 % one_dvd
% 3.82/4.04 thf(fact_3192_one__dvd,axiom,
% 3.82/4.04 ! [A: real] : ( dvd_dvd_real @ one_one_real @ A ) ).
% 3.82/4.04
% 3.82/4.04 % one_dvd
% 3.82/4.04 thf(fact_3193_unit__imp__dvd,axiom,
% 3.82/4.04 ! [B2: nat,A: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 3.82/4.04 => ( dvd_dvd_nat @ B2 @ A ) ) ).
% 3.82/4.04
% 3.82/4.04 % unit_imp_dvd
% 3.82/4.04 thf(fact_3194_unit__imp__dvd,axiom,
% 3.82/4.04 ! [B2: int,A: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ B2 @ one_one_int )
% 3.82/4.04 => ( dvd_dvd_int @ B2 @ A ) ) ).
% 3.82/4.04
% 3.82/4.04 % unit_imp_dvd
% 3.82/4.04 thf(fact_3195_dvd__unit__imp__unit,axiom,
% 3.82/4.04 ! [A: nat,B2: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ A @ B2 )
% 3.82/4.04 => ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 3.82/4.04 => ( dvd_dvd_nat @ A @ one_one_nat ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_unit_imp_unit
% 3.82/4.04 thf(fact_3196_dvd__unit__imp__unit,axiom,
% 3.82/4.04 ! [A: int,B2: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ A @ B2 )
% 3.82/4.04 => ( ( dvd_dvd_int @ B2 @ one_one_int )
% 3.82/4.04 => ( dvd_dvd_int @ A @ one_one_int ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_unit_imp_unit
% 3.82/4.04 thf(fact_3197_dvd__add__right__iff,axiom,
% 3.82/4.04 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ A @ B2 )
% 3.82/4.04 => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B2 @ C ) )
% 3.82/4.04 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_add_right_iff
% 3.82/4.04 thf(fact_3198_dvd__add__right__iff,axiom,
% 3.82/4.04 ! [A: int,B2: int,C: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ A @ B2 )
% 3.82/4.04 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B2 @ C ) )
% 3.82/4.04 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_add_right_iff
% 3.82/4.04 thf(fact_3199_dvd__add__right__iff,axiom,
% 3.82/4.04 ! [A: real,B2: real,C: real] :
% 3.82/4.04 ( ( dvd_dvd_real @ A @ B2 )
% 3.82/4.04 => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B2 @ C ) )
% 3.82/4.04 = ( dvd_dvd_real @ A @ C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_add_right_iff
% 3.82/4.04 thf(fact_3200_dvd__add__left__iff,axiom,
% 3.82/4.04 ! [A: nat,C: nat,B2: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ A @ C )
% 3.82/4.04 => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B2 @ C ) )
% 3.82/4.04 = ( dvd_dvd_nat @ A @ B2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_add_left_iff
% 3.82/4.04 thf(fact_3201_dvd__add__left__iff,axiom,
% 3.82/4.04 ! [A: int,C: int,B2: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ A @ C )
% 3.82/4.04 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B2 @ C ) )
% 3.82/4.04 = ( dvd_dvd_int @ A @ B2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_add_left_iff
% 3.82/4.04 thf(fact_3202_dvd__add__left__iff,axiom,
% 3.82/4.04 ! [A: real,C: real,B2: real] :
% 3.82/4.04 ( ( dvd_dvd_real @ A @ C )
% 3.82/4.04 => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B2 @ C ) )
% 3.82/4.04 = ( dvd_dvd_real @ A @ B2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_add_left_iff
% 3.82/4.04 thf(fact_3203_dvd__add,axiom,
% 3.82/4.04 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ A @ B2 )
% 3.82/4.04 => ( ( dvd_dvd_nat @ A @ C )
% 3.82/4.04 => ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B2 @ C ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_add
% 3.82/4.04 thf(fact_3204_dvd__add,axiom,
% 3.82/4.04 ! [A: int,B2: int,C: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ A @ B2 )
% 3.82/4.04 => ( ( dvd_dvd_int @ A @ C )
% 3.82/4.04 => ( dvd_dvd_int @ A @ ( plus_plus_int @ B2 @ C ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_add
% 3.82/4.04 thf(fact_3205_dvd__add,axiom,
% 3.82/4.04 ! [A: real,B2: real,C: real] :
% 3.82/4.04 ( ( dvd_dvd_real @ A @ B2 )
% 3.82/4.04 => ( ( dvd_dvd_real @ A @ C )
% 3.82/4.04 => ( dvd_dvd_real @ A @ ( plus_plus_real @ B2 @ C ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_add
% 3.82/4.04 thf(fact_3206_dvd__add,axiom,
% 3.82/4.04 ! [A: extended_enat,B2: extended_enat,C: extended_enat] :
% 3.82/4.04 ( ( dvd_dv3785147216227455552d_enat @ A @ B2 )
% 3.82/4.04 => ( ( dvd_dv3785147216227455552d_enat @ A @ C )
% 3.82/4.04 => ( dvd_dv3785147216227455552d_enat @ A @ ( plus_p3455044024723400733d_enat @ B2 @ C ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_add
% 3.82/4.04 thf(fact_3207_dvd__div__eq__iff,axiom,
% 3.82/4.04 ! [C: nat,A: nat,B2: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ C @ A )
% 3.82/4.04 => ( ( dvd_dvd_nat @ C @ B2 )
% 3.82/4.04 => ( ( ( divide_divide_nat @ A @ C )
% 3.82/4.04 = ( divide_divide_nat @ B2 @ C ) )
% 3.82/4.04 = ( A = B2 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_div_eq_iff
% 3.82/4.04 thf(fact_3208_dvd__div__eq__iff,axiom,
% 3.82/4.04 ! [C: int,A: int,B2: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ C @ A )
% 3.82/4.04 => ( ( dvd_dvd_int @ C @ B2 )
% 3.82/4.04 => ( ( ( divide_divide_int @ A @ C )
% 3.82/4.04 = ( divide_divide_int @ B2 @ C ) )
% 3.82/4.04 = ( A = B2 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_div_eq_iff
% 3.82/4.04 thf(fact_3209_dvd__div__eq__iff,axiom,
% 3.82/4.04 ! [C: real,A: real,B2: real] :
% 3.82/4.04 ( ( dvd_dvd_real @ C @ A )
% 3.82/4.04 => ( ( dvd_dvd_real @ C @ B2 )
% 3.82/4.04 => ( ( ( divide_divide_real @ A @ C )
% 3.82/4.04 = ( divide_divide_real @ B2 @ C ) )
% 3.82/4.04 = ( A = B2 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_div_eq_iff
% 3.82/4.04 thf(fact_3210_dvd__div__eq__cancel,axiom,
% 3.82/4.04 ! [A: nat,C: nat,B2: nat] :
% 3.82/4.04 ( ( ( divide_divide_nat @ A @ C )
% 3.82/4.04 = ( divide_divide_nat @ B2 @ C ) )
% 3.82/4.04 => ( ( dvd_dvd_nat @ C @ A )
% 3.82/4.04 => ( ( dvd_dvd_nat @ C @ B2 )
% 3.82/4.04 => ( A = B2 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_div_eq_cancel
% 3.82/4.04 thf(fact_3211_dvd__div__eq__cancel,axiom,
% 3.82/4.04 ! [A: int,C: int,B2: int] :
% 3.82/4.04 ( ( ( divide_divide_int @ A @ C )
% 3.82/4.04 = ( divide_divide_int @ B2 @ C ) )
% 3.82/4.04 => ( ( dvd_dvd_int @ C @ A )
% 3.82/4.04 => ( ( dvd_dvd_int @ C @ B2 )
% 3.82/4.04 => ( A = B2 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_div_eq_cancel
% 3.82/4.04 thf(fact_3212_dvd__div__eq__cancel,axiom,
% 3.82/4.04 ! [A: real,C: real,B2: real] :
% 3.82/4.04 ( ( ( divide_divide_real @ A @ C )
% 3.82/4.04 = ( divide_divide_real @ B2 @ C ) )
% 3.82/4.04 => ( ( dvd_dvd_real @ C @ A )
% 3.82/4.04 => ( ( dvd_dvd_real @ C @ B2 )
% 3.82/4.04 => ( A = B2 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_div_eq_cancel
% 3.82/4.04 thf(fact_3213_div__div__div__same,axiom,
% 3.82/4.04 ! [D: nat,B2: nat,A: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ D @ B2 )
% 3.82/4.04 => ( ( dvd_dvd_nat @ B2 @ A )
% 3.82/4.04 => ( ( divide_divide_nat @ ( divide_divide_nat @ A @ D ) @ ( divide_divide_nat @ B2 @ D ) )
% 3.82/4.04 = ( divide_divide_nat @ A @ B2 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % div_div_div_same
% 3.82/4.04 thf(fact_3214_div__div__div__same,axiom,
% 3.82/4.04 ! [D: int,B2: int,A: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ D @ B2 )
% 3.82/4.04 => ( ( dvd_dvd_int @ B2 @ A )
% 3.82/4.04 => ( ( divide_divide_int @ ( divide_divide_int @ A @ D ) @ ( divide_divide_int @ B2 @ D ) )
% 3.82/4.04 = ( divide_divide_int @ A @ B2 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % div_div_div_same
% 3.82/4.04 thf(fact_3215_mod__less__eq__dividend,axiom,
% 3.82/4.04 ! [M2: nat,N2: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M2 @ N2 ) @ M2 ) ).
% 3.82/4.04
% 3.82/4.04 % mod_less_eq_dividend
% 3.82/4.04 thf(fact_3216_gcd__nat_Oextremum__uniqueI,axiom,
% 3.82/4.04 ! [A: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 3.82/4.04 => ( A = zero_zero_nat ) ) ).
% 3.82/4.04
% 3.82/4.04 % gcd_nat.extremum_uniqueI
% 3.82/4.04 thf(fact_3217_gcd__nat_Onot__eq__extremum,axiom,
% 3.82/4.04 ! [A: nat] :
% 3.82/4.04 ( ( A != zero_zero_nat )
% 3.82/4.04 = ( ( dvd_dvd_nat @ A @ zero_zero_nat )
% 3.82/4.04 & ( A != zero_zero_nat ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % gcd_nat.not_eq_extremum
% 3.82/4.04 thf(fact_3218_gcd__nat_Oextremum__unique,axiom,
% 3.82/4.04 ! [A: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 3.82/4.04 = ( A = zero_zero_nat ) ) ).
% 3.82/4.04
% 3.82/4.04 % gcd_nat.extremum_unique
% 3.82/4.04 thf(fact_3219_gcd__nat_Oextremum__strict,axiom,
% 3.82/4.04 ! [A: nat] :
% 3.82/4.04 ~ ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 3.82/4.04 & ( zero_zero_nat != A ) ) ).
% 3.82/4.04
% 3.82/4.04 % gcd_nat.extremum_strict
% 3.82/4.04 thf(fact_3220_gcd__nat_Oextremum,axiom,
% 3.82/4.04 ! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ) ).
% 3.82/4.04
% 3.82/4.04 % gcd_nat.extremum
% 3.82/4.04 thf(fact_3221_numeral__code_I2_J,axiom,
% 3.82/4.04 ! [N2: num] :
% 3.82/4.04 ( ( numeral_numeral_nat @ ( bit0 @ N2 ) )
% 3.82/4.04 = ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % numeral_code(2)
% 3.82/4.04 thf(fact_3222_numeral__code_I2_J,axiom,
% 3.82/4.04 ! [N2: num] :
% 3.82/4.04 ( ( numera1916890842035813515d_enat @ ( bit0 @ N2 ) )
% 3.82/4.04 = ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ ( numera1916890842035813515d_enat @ N2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % numeral_code(2)
% 3.82/4.04 thf(fact_3223_numeral__code_I2_J,axiom,
% 3.82/4.04 ! [N2: num] :
% 3.82/4.04 ( ( numeral_numeral_int @ ( bit0 @ N2 ) )
% 3.82/4.04 = ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % numeral_code(2)
% 3.82/4.04 thf(fact_3224_numeral__code_I2_J,axiom,
% 3.82/4.04 ! [N2: num] :
% 3.82/4.04 ( ( numeral_numeral_real @ ( bit0 @ N2 ) )
% 3.82/4.04 = ( plus_plus_real @ ( numeral_numeral_real @ N2 ) @ ( numeral_numeral_real @ N2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % numeral_code(2)
% 3.82/4.04 thf(fact_3225_set__vebt__def,axiom,
% 3.82/4.04 ( vEBT_set_vebt
% 3.82/4.04 = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_V8194947554948674370ptions @ T2 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % set_vebt_def
% 3.82/4.04 thf(fact_3226_even__iff__mod__2__eq__zero,axiom,
% 3.82/4.04 ! [A: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 3.82/4.04 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.04 = zero_zero_nat ) ) ).
% 3.82/4.04
% 3.82/4.04 % even_iff_mod_2_eq_zero
% 3.82/4.04 thf(fact_3227_even__iff__mod__2__eq__zero,axiom,
% 3.82/4.04 ! [A: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 3.82/4.04 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 3.82/4.04 = zero_zero_int ) ) ).
% 3.82/4.04
% 3.82/4.04 % even_iff_mod_2_eq_zero
% 3.82/4.04 thf(fact_3228_subset__decode__imp__le,axiom,
% 3.82/4.04 ! [M2: nat,N2: nat] :
% 3.82/4.04 ( ( ord_less_eq_set_nat @ ( nat_set_decode @ M2 ) @ ( nat_set_decode @ N2 ) )
% 3.82/4.04 => ( ord_less_eq_nat @ M2 @ N2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % subset_decode_imp_le
% 3.82/4.04 thf(fact_3229_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 3.82/4.04 ! [A: nat,B2: nat] :
% 3.82/4.04 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 3.82/4.04 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ A @ B2 ) @ A ) ) ).
% 3.82/4.04
% 3.82/4.04 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 3.82/4.04 thf(fact_3230_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 3.82/4.04 ! [A: int,B2: int] :
% 3.82/4.04 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 3.82/4.04 => ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B2 ) @ A ) ) ).
% 3.82/4.04
% 3.82/4.04 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 3.82/4.04 thf(fact_3231_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 3.82/4.04 ! [B2: nat,A: nat] :
% 3.82/4.04 ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 3.82/4.04 => ( ord_less_nat @ ( modulo_modulo_nat @ A @ B2 ) @ B2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 3.82/4.04 thf(fact_3232_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 3.82/4.04 ! [B2: int,A: int] :
% 3.82/4.04 ( ( ord_less_int @ zero_zero_int @ B2 )
% 3.82/4.04 => ( ord_less_int @ ( modulo_modulo_int @ A @ B2 ) @ B2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 3.82/4.04 thf(fact_3233_mod__eq__self__iff__div__eq__0,axiom,
% 3.82/4.04 ! [A: nat,B2: nat] :
% 3.82/4.04 ( ( ( modulo_modulo_nat @ A @ B2 )
% 3.82/4.04 = A )
% 3.82/4.04 = ( ( divide_divide_nat @ A @ B2 )
% 3.82/4.04 = zero_zero_nat ) ) ).
% 3.82/4.04
% 3.82/4.04 % mod_eq_self_iff_div_eq_0
% 3.82/4.04 thf(fact_3234_mod__eq__self__iff__div__eq__0,axiom,
% 3.82/4.04 ! [A: int,B2: int] :
% 3.82/4.04 ( ( ( modulo_modulo_int @ A @ B2 )
% 3.82/4.04 = A )
% 3.82/4.04 = ( ( divide_divide_int @ A @ B2 )
% 3.82/4.04 = zero_zero_int ) ) ).
% 3.82/4.04
% 3.82/4.04 % mod_eq_self_iff_div_eq_0
% 3.82/4.04 thf(fact_3235_mod__eqE,axiom,
% 3.82/4.04 ! [A: int,C: int,B2: int] :
% 3.82/4.04 ( ( ( modulo_modulo_int @ A @ C )
% 3.82/4.04 = ( modulo_modulo_int @ B2 @ C ) )
% 3.82/4.04 => ~ ! [D5: int] :
% 3.82/4.04 ( B2
% 3.82/4.04 != ( plus_plus_int @ A @ ( times_times_int @ C @ D5 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % mod_eqE
% 3.82/4.04 thf(fact_3236_div__add1__eq,axiom,
% 3.82/4.04 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.04 ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B2 ) @ C )
% 3.82/4.04 = ( plus_plus_nat @ ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B2 @ C ) ) @ ( divide_divide_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B2 @ C ) ) @ C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % div_add1_eq
% 3.82/4.04 thf(fact_3237_div__add1__eq,axiom,
% 3.82/4.04 ! [A: int,B2: int,C: int] :
% 3.82/4.04 ( ( divide_divide_int @ ( plus_plus_int @ A @ B2 ) @ C )
% 3.82/4.04 = ( plus_plus_int @ ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B2 @ C ) ) @ ( divide_divide_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B2 @ C ) ) @ C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % div_add1_eq
% 3.82/4.04 thf(fact_3238_not__is__unit__0,axiom,
% 3.82/4.04 ~ ( dvd_dvd_nat @ zero_zero_nat @ one_one_nat ) ).
% 3.82/4.04
% 3.82/4.04 % not_is_unit_0
% 3.82/4.04 thf(fact_3239_not__is__unit__0,axiom,
% 3.82/4.04 ~ ( dvd_dvd_int @ zero_zero_int @ one_one_int ) ).
% 3.82/4.04
% 3.82/4.04 % not_is_unit_0
% 3.82/4.04 thf(fact_3240_minf_I10_J,axiom,
% 3.82/4.04 ! [D: nat,S: nat] :
% 3.82/4.04 ? [Z: nat] :
% 3.82/4.04 ! [X2: nat] :
% 3.82/4.04 ( ( ord_less_nat @ X2 @ Z )
% 3.82/4.04 => ( ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X2 @ S ) ) )
% 3.82/4.04 = ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X2 @ S ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % minf(10)
% 3.82/4.04 thf(fact_3241_minf_I10_J,axiom,
% 3.82/4.04 ! [D: extended_enat,S: extended_enat] :
% 3.82/4.04 ? [Z: extended_enat] :
% 3.82/4.04 ! [X2: extended_enat] :
% 3.82/4.04 ( ( ord_le72135733267957522d_enat @ X2 @ Z )
% 3.82/4.04 => ( ( ~ ( dvd_dv3785147216227455552d_enat @ D @ ( plus_p3455044024723400733d_enat @ X2 @ S ) ) )
% 3.82/4.04 = ( ~ ( dvd_dv3785147216227455552d_enat @ D @ ( plus_p3455044024723400733d_enat @ X2 @ S ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % minf(10)
% 3.82/4.04 thf(fact_3242_minf_I10_J,axiom,
% 3.82/4.04 ! [D: real,S: real] :
% 3.82/4.04 ? [Z: real] :
% 3.82/4.04 ! [X2: real] :
% 3.82/4.04 ( ( ord_less_real @ X2 @ Z )
% 3.82/4.04 => ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X2 @ S ) ) )
% 3.82/4.04 = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X2 @ S ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % minf(10)
% 3.82/4.04 thf(fact_3243_minf_I10_J,axiom,
% 3.82/4.04 ! [D: int,S: int] :
% 3.82/4.04 ? [Z: int] :
% 3.82/4.04 ! [X2: int] :
% 3.82/4.04 ( ( ord_less_int @ X2 @ Z )
% 3.82/4.04 => ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X2 @ S ) ) )
% 3.82/4.04 = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X2 @ S ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % minf(10)
% 3.82/4.04 thf(fact_3244_minf_I9_J,axiom,
% 3.82/4.04 ! [D: nat,S: nat] :
% 3.82/4.04 ? [Z: nat] :
% 3.82/4.04 ! [X2: nat] :
% 3.82/4.04 ( ( ord_less_nat @ X2 @ Z )
% 3.82/4.04 => ( ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X2 @ S ) )
% 3.82/4.04 = ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X2 @ S ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % minf(9)
% 3.82/4.04 thf(fact_3245_minf_I9_J,axiom,
% 3.82/4.04 ! [D: extended_enat,S: extended_enat] :
% 3.82/4.04 ? [Z: extended_enat] :
% 3.82/4.04 ! [X2: extended_enat] :
% 3.82/4.04 ( ( ord_le72135733267957522d_enat @ X2 @ Z )
% 3.82/4.04 => ( ( dvd_dv3785147216227455552d_enat @ D @ ( plus_p3455044024723400733d_enat @ X2 @ S ) )
% 3.82/4.04 = ( dvd_dv3785147216227455552d_enat @ D @ ( plus_p3455044024723400733d_enat @ X2 @ S ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % minf(9)
% 3.82/4.04 thf(fact_3246_minf_I9_J,axiom,
% 3.82/4.04 ! [D: real,S: real] :
% 3.82/4.04 ? [Z: real] :
% 3.82/4.04 ! [X2: real] :
% 3.82/4.04 ( ( ord_less_real @ X2 @ Z )
% 3.82/4.04 => ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X2 @ S ) )
% 3.82/4.04 = ( dvd_dvd_real @ D @ ( plus_plus_real @ X2 @ S ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % minf(9)
% 3.82/4.04 thf(fact_3247_minf_I9_J,axiom,
% 3.82/4.04 ! [D: int,S: int] :
% 3.82/4.04 ? [Z: int] :
% 3.82/4.04 ! [X2: int] :
% 3.82/4.04 ( ( ord_less_int @ X2 @ Z )
% 3.82/4.04 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X2 @ S ) )
% 3.82/4.04 = ( dvd_dvd_int @ D @ ( plus_plus_int @ X2 @ S ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % minf(9)
% 3.82/4.04 thf(fact_3248_pinf_I10_J,axiom,
% 3.82/4.04 ! [D: nat,S: nat] :
% 3.82/4.04 ? [Z: nat] :
% 3.82/4.04 ! [X2: nat] :
% 3.82/4.04 ( ( ord_less_nat @ Z @ X2 )
% 3.82/4.04 => ( ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X2 @ S ) ) )
% 3.82/4.04 = ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X2 @ S ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % pinf(10)
% 3.82/4.04 thf(fact_3249_pinf_I10_J,axiom,
% 3.82/4.04 ! [D: extended_enat,S: extended_enat] :
% 3.82/4.04 ? [Z: extended_enat] :
% 3.82/4.04 ! [X2: extended_enat] :
% 3.82/4.04 ( ( ord_le72135733267957522d_enat @ Z @ X2 )
% 3.82/4.04 => ( ( ~ ( dvd_dv3785147216227455552d_enat @ D @ ( plus_p3455044024723400733d_enat @ X2 @ S ) ) )
% 3.82/4.04 = ( ~ ( dvd_dv3785147216227455552d_enat @ D @ ( plus_p3455044024723400733d_enat @ X2 @ S ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % pinf(10)
% 3.82/4.04 thf(fact_3250_pinf_I10_J,axiom,
% 3.82/4.04 ! [D: real,S: real] :
% 3.82/4.04 ? [Z: real] :
% 3.82/4.04 ! [X2: real] :
% 3.82/4.04 ( ( ord_less_real @ Z @ X2 )
% 3.82/4.04 => ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X2 @ S ) ) )
% 3.82/4.04 = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X2 @ S ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % pinf(10)
% 3.82/4.04 thf(fact_3251_pinf_I10_J,axiom,
% 3.82/4.04 ! [D: int,S: int] :
% 3.82/4.04 ? [Z: int] :
% 3.82/4.04 ! [X2: int] :
% 3.82/4.04 ( ( ord_less_int @ Z @ X2 )
% 3.82/4.04 => ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X2 @ S ) ) )
% 3.82/4.04 = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X2 @ S ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % pinf(10)
% 3.82/4.04 thf(fact_3252_pinf_I9_J,axiom,
% 3.82/4.04 ! [D: nat,S: nat] :
% 3.82/4.04 ? [Z: nat] :
% 3.82/4.04 ! [X2: nat] :
% 3.82/4.04 ( ( ord_less_nat @ Z @ X2 )
% 3.82/4.04 => ( ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X2 @ S ) )
% 3.82/4.04 = ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X2 @ S ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % pinf(9)
% 3.82/4.04 thf(fact_3253_pinf_I9_J,axiom,
% 3.82/4.04 ! [D: extended_enat,S: extended_enat] :
% 3.82/4.04 ? [Z: extended_enat] :
% 3.82/4.04 ! [X2: extended_enat] :
% 3.82/4.04 ( ( ord_le72135733267957522d_enat @ Z @ X2 )
% 3.82/4.04 => ( ( dvd_dv3785147216227455552d_enat @ D @ ( plus_p3455044024723400733d_enat @ X2 @ S ) )
% 3.82/4.04 = ( dvd_dv3785147216227455552d_enat @ D @ ( plus_p3455044024723400733d_enat @ X2 @ S ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % pinf(9)
% 3.82/4.04 thf(fact_3254_pinf_I9_J,axiom,
% 3.82/4.04 ! [D: real,S: real] :
% 3.82/4.04 ? [Z: real] :
% 3.82/4.04 ! [X2: real] :
% 3.82/4.04 ( ( ord_less_real @ Z @ X2 )
% 3.82/4.04 => ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X2 @ S ) )
% 3.82/4.04 = ( dvd_dvd_real @ D @ ( plus_plus_real @ X2 @ S ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % pinf(9)
% 3.82/4.04 thf(fact_3255_pinf_I9_J,axiom,
% 3.82/4.04 ! [D: int,S: int] :
% 3.82/4.04 ? [Z: int] :
% 3.82/4.04 ! [X2: int] :
% 3.82/4.04 ( ( ord_less_int @ Z @ X2 )
% 3.82/4.04 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X2 @ S ) )
% 3.82/4.04 = ( dvd_dvd_int @ D @ ( plus_plus_int @ X2 @ S ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % pinf(9)
% 3.82/4.04 thf(fact_3256_dvd__div__eq__0__iff,axiom,
% 3.82/4.04 ! [B2: complex,A: complex] :
% 3.82/4.04 ( ( dvd_dvd_complex @ B2 @ A )
% 3.82/4.04 => ( ( ( divide1717551699836669952omplex @ A @ B2 )
% 3.82/4.04 = zero_zero_complex )
% 3.82/4.04 = ( A = zero_zero_complex ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_div_eq_0_iff
% 3.82/4.04 thf(fact_3257_dvd__div__eq__0__iff,axiom,
% 3.82/4.04 ! [B2: nat,A: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ B2 @ A )
% 3.82/4.04 => ( ( ( divide_divide_nat @ A @ B2 )
% 3.82/4.04 = zero_zero_nat )
% 3.82/4.04 = ( A = zero_zero_nat ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_div_eq_0_iff
% 3.82/4.04 thf(fact_3258_dvd__div__eq__0__iff,axiom,
% 3.82/4.04 ! [B2: int,A: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ B2 @ A )
% 3.82/4.04 => ( ( ( divide_divide_int @ A @ B2 )
% 3.82/4.04 = zero_zero_int )
% 3.82/4.04 = ( A = zero_zero_int ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_div_eq_0_iff
% 3.82/4.04 thf(fact_3259_dvd__div__eq__0__iff,axiom,
% 3.82/4.04 ! [B2: real,A: real] :
% 3.82/4.04 ( ( dvd_dvd_real @ B2 @ A )
% 3.82/4.04 => ( ( ( divide_divide_real @ A @ B2 )
% 3.82/4.04 = zero_zero_real )
% 3.82/4.04 = ( A = zero_zero_real ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_div_eq_0_iff
% 3.82/4.04 thf(fact_3260_unit__mult__right__cancel,axiom,
% 3.82/4.04 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 3.82/4.04 => ( ( ( times_times_nat @ B2 @ A )
% 3.82/4.04 = ( times_times_nat @ C @ A ) )
% 3.82/4.04 = ( B2 = C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % unit_mult_right_cancel
% 3.82/4.04 thf(fact_3261_unit__mult__right__cancel,axiom,
% 3.82/4.04 ! [A: int,B2: int,C: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ A @ one_one_int )
% 3.82/4.04 => ( ( ( times_times_int @ B2 @ A )
% 3.82/4.04 = ( times_times_int @ C @ A ) )
% 3.82/4.04 = ( B2 = C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % unit_mult_right_cancel
% 3.82/4.04 thf(fact_3262_unit__mult__left__cancel,axiom,
% 3.82/4.04 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 3.82/4.04 => ( ( ( times_times_nat @ A @ B2 )
% 3.82/4.04 = ( times_times_nat @ A @ C ) )
% 3.82/4.04 = ( B2 = C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % unit_mult_left_cancel
% 3.82/4.04 thf(fact_3263_unit__mult__left__cancel,axiom,
% 3.82/4.04 ! [A: int,B2: int,C: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ A @ one_one_int )
% 3.82/4.04 => ( ( ( times_times_int @ A @ B2 )
% 3.82/4.04 = ( times_times_int @ A @ C ) )
% 3.82/4.04 = ( B2 = C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % unit_mult_left_cancel
% 3.82/4.04 thf(fact_3264_mult__unit__dvd__iff_H,axiom,
% 3.82/4.04 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 3.82/4.04 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B2 ) @ C )
% 3.82/4.04 = ( dvd_dvd_nat @ B2 @ C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % mult_unit_dvd_iff'
% 3.82/4.04 thf(fact_3265_mult__unit__dvd__iff_H,axiom,
% 3.82/4.04 ! [A: int,B2: int,C: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ A @ one_one_int )
% 3.82/4.04 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B2 ) @ C )
% 3.82/4.04 = ( dvd_dvd_int @ B2 @ C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % mult_unit_dvd_iff'
% 3.82/4.04 thf(fact_3266_dvd__mult__unit__iff_H,axiom,
% 3.82/4.04 ! [B2: nat,A: nat,C: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 3.82/4.04 => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B2 @ C ) )
% 3.82/4.04 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_mult_unit_iff'
% 3.82/4.04 thf(fact_3267_dvd__mult__unit__iff_H,axiom,
% 3.82/4.04 ! [B2: int,A: int,C: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ B2 @ one_one_int )
% 3.82/4.04 => ( ( dvd_dvd_int @ A @ ( times_times_int @ B2 @ C ) )
% 3.82/4.04 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_mult_unit_iff'
% 3.82/4.04 thf(fact_3268_mult__unit__dvd__iff,axiom,
% 3.82/4.04 ! [B2: nat,A: nat,C: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 3.82/4.04 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B2 ) @ C )
% 3.82/4.04 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % mult_unit_dvd_iff
% 3.82/4.04 thf(fact_3269_mult__unit__dvd__iff,axiom,
% 3.82/4.04 ! [B2: int,A: int,C: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ B2 @ one_one_int )
% 3.82/4.04 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B2 ) @ C )
% 3.82/4.04 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % mult_unit_dvd_iff
% 3.82/4.04 thf(fact_3270_dvd__mult__unit__iff,axiom,
% 3.82/4.04 ! [B2: nat,A: nat,C: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 3.82/4.04 => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B2 ) )
% 3.82/4.04 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_mult_unit_iff
% 3.82/4.04 thf(fact_3271_dvd__mult__unit__iff,axiom,
% 3.82/4.04 ! [B2: int,A: int,C: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ B2 @ one_one_int )
% 3.82/4.04 => ( ( dvd_dvd_int @ A @ ( times_times_int @ C @ B2 ) )
% 3.82/4.04 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_mult_unit_iff
% 3.82/4.04 thf(fact_3272_is__unit__mult__iff,axiom,
% 3.82/4.04 ! [A: nat,B2: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B2 ) @ one_one_nat )
% 3.82/4.04 = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 3.82/4.04 & ( dvd_dvd_nat @ B2 @ one_one_nat ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % is_unit_mult_iff
% 3.82/4.04 thf(fact_3273_is__unit__mult__iff,axiom,
% 3.82/4.04 ! [A: int,B2: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ ( times_times_int @ A @ B2 ) @ one_one_int )
% 3.82/4.04 = ( ( dvd_dvd_int @ A @ one_one_int )
% 3.82/4.04 & ( dvd_dvd_int @ B2 @ one_one_int ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % is_unit_mult_iff
% 3.82/4.04 thf(fact_3274_mod__Suc,axiom,
% 3.82/4.04 ! [M2: nat,N2: nat] :
% 3.82/4.04 ( ( ( ( suc @ ( modulo_modulo_nat @ M2 @ N2 ) )
% 3.82/4.04 = N2 )
% 3.82/4.04 => ( ( modulo_modulo_nat @ ( suc @ M2 ) @ N2 )
% 3.82/4.04 = zero_zero_nat ) )
% 3.82/4.04 & ( ( ( suc @ ( modulo_modulo_nat @ M2 @ N2 ) )
% 3.82/4.04 != N2 )
% 3.82/4.04 => ( ( modulo_modulo_nat @ ( suc @ M2 ) @ N2 )
% 3.82/4.04 = ( suc @ ( modulo_modulo_nat @ M2 @ N2 ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % mod_Suc
% 3.82/4.04 thf(fact_3275_finite__set__decode,axiom,
% 3.82/4.04 ! [N2: nat] : ( finite_finite_nat @ ( nat_set_decode @ N2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % finite_set_decode
% 3.82/4.04 thf(fact_3276_mod__induct,axiom,
% 3.82/4.04 ! [P: nat > $o,N2: nat,P5: nat,M2: nat] :
% 3.82/4.04 ( ( P @ N2 )
% 3.82/4.04 => ( ( ord_less_nat @ N2 @ P5 )
% 3.82/4.04 => ( ( ord_less_nat @ M2 @ P5 )
% 3.82/4.04 => ( ! [N3: nat] :
% 3.82/4.04 ( ( ord_less_nat @ N3 @ P5 )
% 3.82/4.04 => ( ( P @ N3 )
% 3.82/4.04 => ( P @ ( modulo_modulo_nat @ ( suc @ N3 ) @ P5 ) ) ) )
% 3.82/4.04 => ( P @ M2 ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % mod_induct
% 3.82/4.04 thf(fact_3277_dvd__div__mult,axiom,
% 3.82/4.04 ! [C: nat,B2: nat,A: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ C @ B2 )
% 3.82/4.04 => ( ( times_times_nat @ ( divide_divide_nat @ B2 @ C ) @ A )
% 3.82/4.04 = ( divide_divide_nat @ ( times_times_nat @ B2 @ A ) @ C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_div_mult
% 3.82/4.04 thf(fact_3278_dvd__div__mult,axiom,
% 3.82/4.04 ! [C: int,B2: int,A: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ C @ B2 )
% 3.82/4.04 => ( ( times_times_int @ ( divide_divide_int @ B2 @ C ) @ A )
% 3.82/4.04 = ( divide_divide_int @ ( times_times_int @ B2 @ A ) @ C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_div_mult
% 3.82/4.04 thf(fact_3279_div__mult__swap,axiom,
% 3.82/4.04 ! [C: nat,B2: nat,A: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ C @ B2 )
% 3.82/4.04 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B2 @ C ) )
% 3.82/4.04 = ( divide_divide_nat @ ( times_times_nat @ A @ B2 ) @ C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % div_mult_swap
% 3.82/4.04 thf(fact_3280_div__mult__swap,axiom,
% 3.82/4.04 ! [C: int,B2: int,A: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ C @ B2 )
% 3.82/4.04 => ( ( times_times_int @ A @ ( divide_divide_int @ B2 @ C ) )
% 3.82/4.04 = ( divide_divide_int @ ( times_times_int @ A @ B2 ) @ C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % div_mult_swap
% 3.82/4.04 thf(fact_3281_div__div__eq__right,axiom,
% 3.82/4.04 ! [C: nat,B2: nat,A: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ C @ B2 )
% 3.82/4.04 => ( ( dvd_dvd_nat @ B2 @ A )
% 3.82/4.04 => ( ( divide_divide_nat @ A @ ( divide_divide_nat @ B2 @ C ) )
% 3.82/4.04 = ( times_times_nat @ ( divide_divide_nat @ A @ B2 ) @ C ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % div_div_eq_right
% 3.82/4.04 thf(fact_3282_div__div__eq__right,axiom,
% 3.82/4.04 ! [C: int,B2: int,A: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ C @ B2 )
% 3.82/4.04 => ( ( dvd_dvd_int @ B2 @ A )
% 3.82/4.04 => ( ( divide_divide_int @ A @ ( divide_divide_int @ B2 @ C ) )
% 3.82/4.04 = ( times_times_int @ ( divide_divide_int @ A @ B2 ) @ C ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % div_div_eq_right
% 3.82/4.04 thf(fact_3283_dvd__div__mult2__eq,axiom,
% 3.82/4.04 ! [B2: nat,C: nat,A: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ ( times_times_nat @ B2 @ C ) @ A )
% 3.82/4.04 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B2 @ C ) )
% 3.82/4.04 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B2 ) @ C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_div_mult2_eq
% 3.82/4.04 thf(fact_3284_dvd__div__mult2__eq,axiom,
% 3.82/4.04 ! [B2: int,C: int,A: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ ( times_times_int @ B2 @ C ) @ A )
% 3.82/4.04 => ( ( divide_divide_int @ A @ ( times_times_int @ B2 @ C ) )
% 3.82/4.04 = ( divide_divide_int @ ( divide_divide_int @ A @ B2 ) @ C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_div_mult2_eq
% 3.82/4.04 thf(fact_3285_dvd__mult__imp__div,axiom,
% 3.82/4.04 ! [A: nat,C: nat,B2: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B2 )
% 3.82/4.04 => ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B2 @ C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_mult_imp_div
% 3.82/4.04 thf(fact_3286_dvd__mult__imp__div,axiom,
% 3.82/4.04 ! [A: int,C: int,B2: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B2 )
% 3.82/4.04 => ( dvd_dvd_int @ A @ ( divide_divide_int @ B2 @ C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_mult_imp_div
% 3.82/4.04 thf(fact_3287_div__mult__div__if__dvd,axiom,
% 3.82/4.04 ! [B2: nat,A: nat,D: nat,C: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ B2 @ A )
% 3.82/4.04 => ( ( dvd_dvd_nat @ D @ C )
% 3.82/4.04 => ( ( times_times_nat @ ( divide_divide_nat @ A @ B2 ) @ ( divide_divide_nat @ C @ D ) )
% 3.82/4.04 = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B2 @ D ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % div_mult_div_if_dvd
% 3.82/4.04 thf(fact_3288_div__mult__div__if__dvd,axiom,
% 3.82/4.04 ! [B2: int,A: int,D: int,C: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ B2 @ A )
% 3.82/4.04 => ( ( dvd_dvd_int @ D @ C )
% 3.82/4.04 => ( ( times_times_int @ ( divide_divide_int @ A @ B2 ) @ ( divide_divide_int @ C @ D ) )
% 3.82/4.04 = ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B2 @ D ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % div_mult_div_if_dvd
% 3.82/4.04 thf(fact_3289_gcd__nat__induct,axiom,
% 3.82/4.04 ! [P: nat > nat > $o,M2: nat,N2: nat] :
% 3.82/4.04 ( ! [M3: nat] : ( P @ M3 @ zero_zero_nat )
% 3.82/4.04 => ( ! [M3: nat,N3: nat] :
% 3.82/4.04 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 3.82/4.04 => ( ( P @ N3 @ ( modulo_modulo_nat @ M3 @ N3 ) )
% 3.82/4.04 => ( P @ M3 @ N3 ) ) )
% 3.82/4.04 => ( P @ M2 @ N2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % gcd_nat_induct
% 3.82/4.04 thf(fact_3290_mod__less__divisor,axiom,
% 3.82/4.04 ! [N2: nat,M2: nat] :
% 3.82/4.04 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.04 => ( ord_less_nat @ ( modulo_modulo_nat @ M2 @ N2 ) @ N2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % mod_less_divisor
% 3.82/4.04 thf(fact_3291_dvd__div__unit__iff,axiom,
% 3.82/4.04 ! [B2: nat,A: nat,C: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 3.82/4.04 => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ C @ B2 ) )
% 3.82/4.04 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_div_unit_iff
% 3.82/4.04 thf(fact_3292_dvd__div__unit__iff,axiom,
% 3.82/4.04 ! [B2: int,A: int,C: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ B2 @ one_one_int )
% 3.82/4.04 => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ C @ B2 ) )
% 3.82/4.04 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_div_unit_iff
% 3.82/4.04 thf(fact_3293_div__unit__dvd__iff,axiom,
% 3.82/4.04 ! [B2: nat,A: nat,C: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 3.82/4.04 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B2 ) @ C )
% 3.82/4.04 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % div_unit_dvd_iff
% 3.82/4.04 thf(fact_3294_div__unit__dvd__iff,axiom,
% 3.82/4.04 ! [B2: int,A: int,C: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ B2 @ one_one_int )
% 3.82/4.04 => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B2 ) @ C )
% 3.82/4.04 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % div_unit_dvd_iff
% 3.82/4.04 thf(fact_3295_unit__div__cancel,axiom,
% 3.82/4.04 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 3.82/4.04 => ( ( ( divide_divide_nat @ B2 @ A )
% 3.82/4.04 = ( divide_divide_nat @ C @ A ) )
% 3.82/4.04 = ( B2 = C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % unit_div_cancel
% 3.82/4.04 thf(fact_3296_unit__div__cancel,axiom,
% 3.82/4.04 ! [A: int,B2: int,C: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ A @ one_one_int )
% 3.82/4.04 => ( ( ( divide_divide_int @ B2 @ A )
% 3.82/4.04 = ( divide_divide_int @ C @ A ) )
% 3.82/4.04 = ( B2 = C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % unit_div_cancel
% 3.82/4.04 thf(fact_3297_div__plus__div__distrib__dvd__right,axiom,
% 3.82/4.04 ! [C: nat,B2: nat,A: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ C @ B2 )
% 3.82/4.04 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B2 ) @ C )
% 3.82/4.04 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B2 @ C ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % div_plus_div_distrib_dvd_right
% 3.82/4.04 thf(fact_3298_div__plus__div__distrib__dvd__right,axiom,
% 3.82/4.04 ! [C: int,B2: int,A: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ C @ B2 )
% 3.82/4.04 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B2 ) @ C )
% 3.82/4.04 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B2 @ C ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % div_plus_div_distrib_dvd_right
% 3.82/4.04 thf(fact_3299_div__plus__div__distrib__dvd__left,axiom,
% 3.82/4.04 ! [C: nat,A: nat,B2: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ C @ A )
% 3.82/4.04 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B2 ) @ C )
% 3.82/4.04 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B2 @ C ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % div_plus_div_distrib_dvd_left
% 3.82/4.04 thf(fact_3300_div__plus__div__distrib__dvd__left,axiom,
% 3.82/4.04 ! [C: int,A: int,B2: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ C @ A )
% 3.82/4.04 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B2 ) @ C )
% 3.82/4.04 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B2 @ C ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % div_plus_div_distrib_dvd_left
% 3.82/4.04 thf(fact_3301_mod__Suc__le__divisor,axiom,
% 3.82/4.04 ! [M2: nat,N2: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M2 @ ( suc @ N2 ) ) @ N2 ) ).
% 3.82/4.04
% 3.82/4.04 % mod_Suc_le_divisor
% 3.82/4.04 thf(fact_3302_mod__eq__0D,axiom,
% 3.82/4.04 ! [M2: nat,D: nat] :
% 3.82/4.04 ( ( ( modulo_modulo_nat @ M2 @ D )
% 3.82/4.04 = zero_zero_nat )
% 3.82/4.04 => ? [Q2: nat] :
% 3.82/4.04 ( M2
% 3.82/4.04 = ( times_times_nat @ D @ Q2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % mod_eq_0D
% 3.82/4.04 thf(fact_3303_dvd__power__le,axiom,
% 3.82/4.04 ! [X: nat,Y: nat,N2: nat,M2: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ X @ Y )
% 3.82/4.04 => ( ( ord_less_eq_nat @ N2 @ M2 )
% 3.82/4.04 => ( dvd_dvd_nat @ ( power_power_nat @ X @ N2 ) @ ( power_power_nat @ Y @ M2 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_power_le
% 3.82/4.04 thf(fact_3304_dvd__power__le,axiom,
% 3.82/4.04 ! [X: real,Y: real,N2: nat,M2: nat] :
% 3.82/4.04 ( ( dvd_dvd_real @ X @ Y )
% 3.82/4.04 => ( ( ord_less_eq_nat @ N2 @ M2 )
% 3.82/4.04 => ( dvd_dvd_real @ ( power_power_real @ X @ N2 ) @ ( power_power_real @ Y @ M2 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_power_le
% 3.82/4.04 thf(fact_3305_dvd__power__le,axiom,
% 3.82/4.04 ! [X: complex,Y: complex,N2: nat,M2: nat] :
% 3.82/4.04 ( ( dvd_dvd_complex @ X @ Y )
% 3.82/4.04 => ( ( ord_less_eq_nat @ N2 @ M2 )
% 3.82/4.04 => ( dvd_dvd_complex @ ( power_power_complex @ X @ N2 ) @ ( power_power_complex @ Y @ M2 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_power_le
% 3.82/4.04 thf(fact_3306_dvd__power__le,axiom,
% 3.82/4.04 ! [X: int,Y: int,N2: nat,M2: nat] :
% 3.82/4.04 ( ( dvd_dvd_int @ X @ Y )
% 3.82/4.04 => ( ( ord_less_eq_nat @ N2 @ M2 )
% 3.82/4.04 => ( dvd_dvd_int @ ( power_power_int @ X @ N2 ) @ ( power_power_int @ Y @ M2 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_power_le
% 3.82/4.04 thf(fact_3307_power__le__dvd,axiom,
% 3.82/4.04 ! [A: nat,N2: nat,B2: nat,M2: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N2 ) @ B2 )
% 3.82/4.04 => ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.04 => ( dvd_dvd_nat @ ( power_power_nat @ A @ M2 ) @ B2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % power_le_dvd
% 3.82/4.04 thf(fact_3308_power__le__dvd,axiom,
% 3.82/4.04 ! [A: real,N2: nat,B2: real,M2: nat] :
% 3.82/4.04 ( ( dvd_dvd_real @ ( power_power_real @ A @ N2 ) @ B2 )
% 3.82/4.04 => ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.04 => ( dvd_dvd_real @ ( power_power_real @ A @ M2 ) @ B2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % power_le_dvd
% 3.82/4.04 thf(fact_3309_power__le__dvd,axiom,
% 3.82/4.04 ! [A: complex,N2: nat,B2: complex,M2: nat] :
% 3.82/4.04 ( ( dvd_dvd_complex @ ( power_power_complex @ A @ N2 ) @ B2 )
% 3.82/4.04 => ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.04 => ( dvd_dvd_complex @ ( power_power_complex @ A @ M2 ) @ B2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % power_le_dvd
% 3.82/4.04 thf(fact_3310_power__le__dvd,axiom,
% 3.82/4.04 ! [A: int,N2: nat,B2: int,M2: nat] :
% 3.82/4.04 ( ( dvd_dvd_int @ ( power_power_int @ A @ N2 ) @ B2 )
% 3.82/4.04 => ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.04 => ( dvd_dvd_int @ ( power_power_int @ A @ M2 ) @ B2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % power_le_dvd
% 3.82/4.04 thf(fact_3311_le__imp__power__dvd,axiom,
% 3.82/4.04 ! [M2: nat,N2: nat,A: nat] :
% 3.82/4.04 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.04 => ( dvd_dvd_nat @ ( power_power_nat @ A @ M2 ) @ ( power_power_nat @ A @ N2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % le_imp_power_dvd
% 3.82/4.04 thf(fact_3312_le__imp__power__dvd,axiom,
% 3.82/4.04 ! [M2: nat,N2: nat,A: real] :
% 3.82/4.04 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.04 => ( dvd_dvd_real @ ( power_power_real @ A @ M2 ) @ ( power_power_real @ A @ N2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % le_imp_power_dvd
% 3.82/4.04 thf(fact_3313_le__imp__power__dvd,axiom,
% 3.82/4.04 ! [M2: nat,N2: nat,A: complex] :
% 3.82/4.04 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.04 => ( dvd_dvd_complex @ ( power_power_complex @ A @ M2 ) @ ( power_power_complex @ A @ N2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % le_imp_power_dvd
% 3.82/4.04 thf(fact_3314_le__imp__power__dvd,axiom,
% 3.82/4.04 ! [M2: nat,N2: nat,A: int] :
% 3.82/4.04 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.04 => ( dvd_dvd_int @ ( power_power_int @ A @ M2 ) @ ( power_power_int @ A @ N2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % le_imp_power_dvd
% 3.82/4.04 thf(fact_3315_nat__mod__eq__iff,axiom,
% 3.82/4.04 ! [X: nat,N2: nat,Y: nat] :
% 3.82/4.04 ( ( ( modulo_modulo_nat @ X @ N2 )
% 3.82/4.04 = ( modulo_modulo_nat @ Y @ N2 ) )
% 3.82/4.04 = ( ? [Q1: nat,Q22: nat] :
% 3.82/4.04 ( ( plus_plus_nat @ X @ ( times_times_nat @ N2 @ Q1 ) )
% 3.82/4.04 = ( plus_plus_nat @ Y @ ( times_times_nat @ N2 @ Q22 ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % nat_mod_eq_iff
% 3.82/4.04 thf(fact_3316_dvd__pos__nat,axiom,
% 3.82/4.04 ! [N2: nat,M2: nat] :
% 3.82/4.04 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.04 => ( ( dvd_dvd_nat @ M2 @ N2 )
% 3.82/4.04 => ( ord_less_nat @ zero_zero_nat @ M2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_pos_nat
% 3.82/4.04 thf(fact_3317_nat__dvd__not__less,axiom,
% 3.82/4.04 ! [M2: nat,N2: nat] :
% 3.82/4.04 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 3.82/4.04 => ( ( ord_less_nat @ M2 @ N2 )
% 3.82/4.04 => ~ ( dvd_dvd_nat @ N2 @ M2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % nat_dvd_not_less
% 3.82/4.04 thf(fact_3318_bezout__add__nat,axiom,
% 3.82/4.04 ! [A: nat,B2: nat] :
% 3.82/4.04 ? [D5: nat,X5: nat,Y3: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ D5 @ A )
% 3.82/4.04 & ( dvd_dvd_nat @ D5 @ B2 )
% 3.82/4.04 & ( ( ( times_times_nat @ A @ X5 )
% 3.82/4.04 = ( plus_plus_nat @ ( times_times_nat @ B2 @ Y3 ) @ D5 ) )
% 3.82/4.04 | ( ( times_times_nat @ B2 @ X5 )
% 3.82/4.04 = ( plus_plus_nat @ ( times_times_nat @ A @ Y3 ) @ D5 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % bezout_add_nat
% 3.82/4.04 thf(fact_3319_bezout__lemma__nat,axiom,
% 3.82/4.04 ! [D: nat,A: nat,B2: nat,X: nat,Y: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ D @ A )
% 3.82/4.04 => ( ( dvd_dvd_nat @ D @ B2 )
% 3.82/4.04 => ( ( ( ( times_times_nat @ A @ X )
% 3.82/4.04 = ( plus_plus_nat @ ( times_times_nat @ B2 @ Y ) @ D ) )
% 3.82/4.04 | ( ( times_times_nat @ B2 @ X )
% 3.82/4.04 = ( plus_plus_nat @ ( times_times_nat @ A @ Y ) @ D ) ) )
% 3.82/4.04 => ? [X5: nat,Y3: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ D @ A )
% 3.82/4.04 & ( dvd_dvd_nat @ D @ ( plus_plus_nat @ A @ B2 ) )
% 3.82/4.04 & ( ( ( times_times_nat @ A @ X5 )
% 3.82/4.04 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B2 ) @ Y3 ) @ D ) )
% 3.82/4.04 | ( ( times_times_nat @ ( plus_plus_nat @ A @ B2 ) @ X5 )
% 3.82/4.04 = ( plus_plus_nat @ ( times_times_nat @ A @ Y3 ) @ D ) ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % bezout_lemma_nat
% 3.82/4.04 thf(fact_3320_parity__cases,axiom,
% 3.82/4.04 ! [A: nat] :
% 3.82/4.04 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 3.82/4.04 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.04 != zero_zero_nat ) )
% 3.82/4.04 => ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 3.82/4.04 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.04 != one_one_nat ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % parity_cases
% 3.82/4.04 thf(fact_3321_parity__cases,axiom,
% 3.82/4.04 ! [A: int] :
% 3.82/4.04 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 3.82/4.04 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 3.82/4.04 != zero_zero_int ) )
% 3.82/4.04 => ~ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 3.82/4.04 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 3.82/4.04 != one_one_int ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % parity_cases
% 3.82/4.04 thf(fact_3322_mod2__eq__if,axiom,
% 3.82/4.04 ! [A: nat] :
% 3.82/4.04 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 3.82/4.04 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.04 = zero_zero_nat ) )
% 3.82/4.04 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 3.82/4.04 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.04 = one_one_nat ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % mod2_eq_if
% 3.82/4.04 thf(fact_3323_mod2__eq__if,axiom,
% 3.82/4.04 ! [A: int] :
% 3.82/4.04 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 3.82/4.04 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 3.82/4.04 = zero_zero_int ) )
% 3.82/4.04 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 3.82/4.04 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 3.82/4.04 = one_one_int ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % mod2_eq_if
% 3.82/4.04 thf(fact_3324_finite__lists__length__eq,axiom,
% 3.82/4.04 ! [A2: set_complex,N2: nat] :
% 3.82/4.04 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.04 => ( finite8712137658972009173omplex
% 3.82/4.04 @ ( collect_list_complex
% 3.82/4.04 @ ^ [Xs3: list_complex] :
% 3.82/4.04 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs3 ) @ A2 )
% 3.82/4.04 & ( ( size_s3451745648224563538omplex @ Xs3 )
% 3.82/4.04 = N2 ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % finite_lists_length_eq
% 3.82/4.04 thf(fact_3325_finite__lists__length__eq,axiom,
% 3.82/4.04 ! [A2: set_Extended_enat,N2: nat] :
% 3.82/4.04 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.04 => ( finite1862508098717546133d_enat
% 3.82/4.04 @ ( collec8433460942617342167d_enat
% 3.82/4.04 @ ^ [Xs3: list_Extended_enat] :
% 3.82/4.04 ( ( ord_le7203529160286727270d_enat @ ( set_Extended_enat2 @ Xs3 ) @ A2 )
% 3.82/4.04 & ( ( size_s3941691890525107288d_enat @ Xs3 )
% 3.82/4.04 = N2 ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % finite_lists_length_eq
% 3.82/4.04 thf(fact_3326_finite__lists__length__eq,axiom,
% 3.82/4.04 ! [A2: set_VEBT_VEBT,N2: nat] :
% 3.82/4.04 ( ( finite5795047828879050333T_VEBT @ A2 )
% 3.82/4.04 => ( finite3004134309566078307T_VEBT
% 3.82/4.04 @ ( collec5608196760682091941T_VEBT
% 3.82/4.04 @ ^ [Xs3: list_VEBT_VEBT] :
% 3.82/4.04 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs3 ) @ A2 )
% 3.82/4.04 & ( ( size_s6755466524823107622T_VEBT @ Xs3 )
% 3.82/4.04 = N2 ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % finite_lists_length_eq
% 3.82/4.04 thf(fact_3327_finite__lists__length__eq,axiom,
% 3.82/4.04 ! [A2: set_nat,N2: nat] :
% 3.82/4.04 ( ( finite_finite_nat @ A2 )
% 3.82/4.04 => ( finite8100373058378681591st_nat
% 3.82/4.04 @ ( collect_list_nat
% 3.82/4.04 @ ^ [Xs3: list_nat] :
% 3.82/4.04 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs3 ) @ A2 )
% 3.82/4.04 & ( ( size_size_list_nat @ Xs3 )
% 3.82/4.04 = N2 ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % finite_lists_length_eq
% 3.82/4.04 thf(fact_3328_finite__lists__length__eq,axiom,
% 3.82/4.04 ! [A2: set_int,N2: nat] :
% 3.82/4.04 ( ( finite_finite_int @ A2 )
% 3.82/4.04 => ( finite3922522038869484883st_int
% 3.82/4.04 @ ( collect_list_int
% 3.82/4.04 @ ^ [Xs3: list_int] :
% 3.82/4.04 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs3 ) @ A2 )
% 3.82/4.04 & ( ( size_size_list_int @ Xs3 )
% 3.82/4.04 = N2 ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % finite_lists_length_eq
% 3.82/4.04 thf(fact_3329_vebt__buildup_Osimps_I3_J,axiom,
% 3.82/4.04 ! [Va2: nat] :
% 3.82/4.04 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 3.82/4.04 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va2 ) ) )
% 3.82/4.04 = ( 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 ) ) ) ) ) ) )
% 3.82/4.04 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 3.82/4.04 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va2 ) ) )
% 3.82/4.04 = ( 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 ) ) ) ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % vebt_buildup.simps(3)
% 3.82/4.04 thf(fact_3330_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 3.82/4.04 ! [B2: nat,A: nat] :
% 3.82/4.04 ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 3.82/4.04 => ( ord_less_eq_nat @ zero_zero_nat @ ( modulo_modulo_nat @ A @ B2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 3.82/4.04 thf(fact_3331_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 3.82/4.04 ! [B2: int,A: int] :
% 3.82/4.04 ( ( ord_less_int @ zero_zero_int @ B2 )
% 3.82/4.04 => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 3.82/4.04 thf(fact_3332_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 3.82/4.04 ! [A: nat,B2: nat] :
% 3.82/4.04 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 3.82/4.04 => ( ( ord_less_nat @ A @ B2 )
% 3.82/4.04 => ( ( modulo_modulo_nat @ A @ B2 )
% 3.82/4.04 = A ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % unique_euclidean_semiring_numeral_class.mod_less
% 3.82/4.04 thf(fact_3333_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 3.82/4.04 ! [A: int,B2: int] :
% 3.82/4.04 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 3.82/4.04 => ( ( ord_less_int @ A @ B2 )
% 3.82/4.04 => ( ( modulo_modulo_int @ A @ B2 )
% 3.82/4.04 = A ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % unique_euclidean_semiring_numeral_class.mod_less
% 3.82/4.04 thf(fact_3334_cong__exp__iff__simps_I2_J,axiom,
% 3.82/4.04 ! [N2: num,Q3: num] :
% 3.82/4.04 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 3.82/4.04 = zero_zero_nat )
% 3.82/4.04 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ Q3 ) )
% 3.82/4.04 = zero_zero_nat ) ) ).
% 3.82/4.04
% 3.82/4.04 % cong_exp_iff_simps(2)
% 3.82/4.04 thf(fact_3335_cong__exp__iff__simps_I2_J,axiom,
% 3.82/4.04 ! [N2: num,Q3: num] :
% 3.82/4.04 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 3.82/4.04 = zero_zero_int )
% 3.82/4.04 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ Q3 ) )
% 3.82/4.04 = zero_zero_int ) ) ).
% 3.82/4.04
% 3.82/4.04 % cong_exp_iff_simps(2)
% 3.82/4.04 thf(fact_3336_cong__exp__iff__simps_I1_J,axiom,
% 3.82/4.04 ! [N2: num] :
% 3.82/4.04 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ one ) )
% 3.82/4.04 = zero_zero_nat ) ).
% 3.82/4.04
% 3.82/4.04 % cong_exp_iff_simps(1)
% 3.82/4.04 thf(fact_3337_cong__exp__iff__simps_I1_J,axiom,
% 3.82/4.04 ! [N2: num] :
% 3.82/4.04 ( ( modulo_modulo_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ one ) )
% 3.82/4.04 = zero_zero_int ) ).
% 3.82/4.04
% 3.82/4.04 % cong_exp_iff_simps(1)
% 3.82/4.04 thf(fact_3338_finite__lists__length__le,axiom,
% 3.82/4.04 ! [A2: set_complex,N2: nat] :
% 3.82/4.04 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.04 => ( finite8712137658972009173omplex
% 3.82/4.04 @ ( collect_list_complex
% 3.82/4.04 @ ^ [Xs3: list_complex] :
% 3.82/4.04 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs3 ) @ A2 )
% 3.82/4.04 & ( ord_less_eq_nat @ ( size_s3451745648224563538omplex @ Xs3 ) @ N2 ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % finite_lists_length_le
% 3.82/4.04 thf(fact_3339_finite__lists__length__le,axiom,
% 3.82/4.04 ! [A2: set_Extended_enat,N2: nat] :
% 3.82/4.04 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.04 => ( finite1862508098717546133d_enat
% 3.82/4.04 @ ( collec8433460942617342167d_enat
% 3.82/4.04 @ ^ [Xs3: list_Extended_enat] :
% 3.82/4.04 ( ( ord_le7203529160286727270d_enat @ ( set_Extended_enat2 @ Xs3 ) @ A2 )
% 3.82/4.04 & ( ord_less_eq_nat @ ( size_s3941691890525107288d_enat @ Xs3 ) @ N2 ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % finite_lists_length_le
% 3.82/4.04 thf(fact_3340_finite__lists__length__le,axiom,
% 3.82/4.04 ! [A2: set_VEBT_VEBT,N2: nat] :
% 3.82/4.04 ( ( finite5795047828879050333T_VEBT @ A2 )
% 3.82/4.04 => ( finite3004134309566078307T_VEBT
% 3.82/4.04 @ ( collec5608196760682091941T_VEBT
% 3.82/4.04 @ ^ [Xs3: list_VEBT_VEBT] :
% 3.82/4.04 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs3 ) @ A2 )
% 3.82/4.04 & ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs3 ) @ N2 ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % finite_lists_length_le
% 3.82/4.04 thf(fact_3341_finite__lists__length__le,axiom,
% 3.82/4.04 ! [A2: set_nat,N2: nat] :
% 3.82/4.04 ( ( finite_finite_nat @ A2 )
% 3.82/4.04 => ( finite8100373058378681591st_nat
% 3.82/4.04 @ ( collect_list_nat
% 3.82/4.04 @ ^ [Xs3: list_nat] :
% 3.82/4.04 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs3 ) @ A2 )
% 3.82/4.04 & ( ord_less_eq_nat @ ( size_size_list_nat @ Xs3 ) @ N2 ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % finite_lists_length_le
% 3.82/4.04 thf(fact_3342_finite__lists__length__le,axiom,
% 3.82/4.04 ! [A2: set_int,N2: nat] :
% 3.82/4.04 ( ( finite_finite_int @ A2 )
% 3.82/4.04 => ( finite3922522038869484883st_int
% 3.82/4.04 @ ( collect_list_int
% 3.82/4.04 @ ^ [Xs3: list_int] :
% 3.82/4.04 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs3 ) @ A2 )
% 3.82/4.04 & ( ord_less_eq_nat @ ( size_size_list_int @ Xs3 ) @ N2 ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % finite_lists_length_le
% 3.82/4.04 thf(fact_3343_cancel__div__mod__rules_I2_J,axiom,
% 3.82/4.04 ! [B2: nat,A: nat,C: nat] :
% 3.82/4.04 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ B2 @ ( divide_divide_nat @ A @ B2 ) ) @ ( modulo_modulo_nat @ A @ B2 ) ) @ C )
% 3.82/4.04 = ( plus_plus_nat @ A @ C ) ) ).
% 3.82/4.04
% 3.82/4.04 % cancel_div_mod_rules(2)
% 3.82/4.04 thf(fact_3344_cancel__div__mod__rules_I2_J,axiom,
% 3.82/4.04 ! [B2: int,A: int,C: int] :
% 3.82/4.04 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ B2 @ ( divide_divide_int @ A @ B2 ) ) @ ( modulo_modulo_int @ A @ B2 ) ) @ C )
% 3.82/4.04 = ( plus_plus_int @ A @ C ) ) ).
% 3.82/4.04
% 3.82/4.04 % cancel_div_mod_rules(2)
% 3.82/4.04 thf(fact_3345_cancel__div__mod__rules_I1_J,axiom,
% 3.82/4.04 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.04 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B2 ) @ B2 ) @ ( modulo_modulo_nat @ A @ B2 ) ) @ C )
% 3.82/4.04 = ( plus_plus_nat @ A @ C ) ) ).
% 3.82/4.04
% 3.82/4.04 % cancel_div_mod_rules(1)
% 3.82/4.04 thf(fact_3346_cancel__div__mod__rules_I1_J,axiom,
% 3.82/4.04 ! [A: int,B2: int,C: int] :
% 3.82/4.04 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B2 ) @ B2 ) @ ( modulo_modulo_int @ A @ B2 ) ) @ C )
% 3.82/4.04 = ( plus_plus_int @ A @ C ) ) ).
% 3.82/4.04
% 3.82/4.04 % cancel_div_mod_rules(1)
% 3.82/4.04 thf(fact_3347_mod__div__decomp,axiom,
% 3.82/4.04 ! [A: nat,B2: nat] :
% 3.82/4.04 ( A
% 3.82/4.04 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B2 ) @ B2 ) @ ( modulo_modulo_nat @ A @ B2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % mod_div_decomp
% 3.82/4.04 thf(fact_3348_mod__div__decomp,axiom,
% 3.82/4.04 ! [A: int,B2: int] :
% 3.82/4.04 ( A
% 3.82/4.04 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B2 ) @ B2 ) @ ( modulo_modulo_int @ A @ B2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % mod_div_decomp
% 3.82/4.04 thf(fact_3349_div__mult__mod__eq,axiom,
% 3.82/4.04 ! [A: nat,B2: nat] :
% 3.82/4.04 ( ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B2 ) @ B2 ) @ ( modulo_modulo_nat @ A @ B2 ) )
% 3.82/4.04 = A ) ).
% 3.82/4.04
% 3.82/4.04 % div_mult_mod_eq
% 3.82/4.04 thf(fact_3350_div__mult__mod__eq,axiom,
% 3.82/4.04 ! [A: int,B2: int] :
% 3.82/4.04 ( ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B2 ) @ B2 ) @ ( modulo_modulo_int @ A @ B2 ) )
% 3.82/4.04 = A ) ).
% 3.82/4.04
% 3.82/4.04 % div_mult_mod_eq
% 3.82/4.04 thf(fact_3351_mod__div__mult__eq,axiom,
% 3.82/4.04 ! [A: nat,B2: nat] :
% 3.82/4.04 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B2 ) @ ( times_times_nat @ ( divide_divide_nat @ A @ B2 ) @ B2 ) )
% 3.82/4.04 = A ) ).
% 3.82/4.04
% 3.82/4.04 % mod_div_mult_eq
% 3.82/4.04 thf(fact_3352_mod__div__mult__eq,axiom,
% 3.82/4.04 ! [A: int,B2: int] :
% 3.82/4.04 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B2 ) @ ( times_times_int @ ( divide_divide_int @ A @ B2 ) @ B2 ) )
% 3.82/4.04 = A ) ).
% 3.82/4.04
% 3.82/4.04 % mod_div_mult_eq
% 3.82/4.04 thf(fact_3353_mod__mult__div__eq,axiom,
% 3.82/4.04 ! [A: nat,B2: nat] :
% 3.82/4.04 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B2 ) @ ( times_times_nat @ B2 @ ( divide_divide_nat @ A @ B2 ) ) )
% 3.82/4.04 = A ) ).
% 3.82/4.04
% 3.82/4.04 % mod_mult_div_eq
% 3.82/4.04 thf(fact_3354_mod__mult__div__eq,axiom,
% 3.82/4.04 ! [A: int,B2: int] :
% 3.82/4.04 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B2 ) @ ( times_times_int @ B2 @ ( divide_divide_int @ A @ B2 ) ) )
% 3.82/4.04 = A ) ).
% 3.82/4.04
% 3.82/4.04 % mod_mult_div_eq
% 3.82/4.04 thf(fact_3355_mult__div__mod__eq,axiom,
% 3.82/4.04 ! [B2: nat,A: nat] :
% 3.82/4.04 ( ( plus_plus_nat @ ( times_times_nat @ B2 @ ( divide_divide_nat @ A @ B2 ) ) @ ( modulo_modulo_nat @ A @ B2 ) )
% 3.82/4.04 = A ) ).
% 3.82/4.04
% 3.82/4.04 % mult_div_mod_eq
% 3.82/4.04 thf(fact_3356_mult__div__mod__eq,axiom,
% 3.82/4.04 ! [B2: int,A: int] :
% 3.82/4.04 ( ( plus_plus_int @ ( times_times_int @ B2 @ ( divide_divide_int @ A @ B2 ) ) @ ( modulo_modulo_int @ A @ B2 ) )
% 3.82/4.04 = A ) ).
% 3.82/4.04
% 3.82/4.04 % mult_div_mod_eq
% 3.82/4.04 thf(fact_3357_div__mult1__eq,axiom,
% 3.82/4.04 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.04 ( ( divide_divide_nat @ ( times_times_nat @ A @ B2 ) @ C )
% 3.82/4.04 = ( plus_plus_nat @ ( times_times_nat @ A @ ( divide_divide_nat @ B2 @ C ) ) @ ( divide_divide_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B2 @ C ) ) @ C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % div_mult1_eq
% 3.82/4.04 thf(fact_3358_div__mult1__eq,axiom,
% 3.82/4.04 ! [A: int,B2: int,C: int] :
% 3.82/4.04 ( ( divide_divide_int @ ( times_times_int @ A @ B2 ) @ C )
% 3.82/4.04 = ( plus_plus_int @ ( times_times_int @ A @ ( divide_divide_int @ B2 @ C ) ) @ ( divide_divide_int @ ( times_times_int @ A @ ( modulo_modulo_int @ B2 @ C ) ) @ C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % div_mult1_eq
% 3.82/4.04 thf(fact_3359_unit__dvdE,axiom,
% 3.82/4.04 ! [A: nat,B2: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 3.82/4.04 => ~ ( ( A != zero_zero_nat )
% 3.82/4.04 => ! [C2: nat] :
% 3.82/4.04 ( B2
% 3.82/4.04 != ( times_times_nat @ A @ C2 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % unit_dvdE
% 3.82/4.04 thf(fact_3360_unit__dvdE,axiom,
% 3.82/4.04 ! [A: int,B2: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ A @ one_one_int )
% 3.82/4.04 => ~ ( ( A != zero_zero_int )
% 3.82/4.04 => ! [C2: int] :
% 3.82/4.04 ( B2
% 3.82/4.04 != ( times_times_int @ A @ C2 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % unit_dvdE
% 3.82/4.04 thf(fact_3361_unity__coeff__ex,axiom,
% 3.82/4.04 ! [P: nat > $o,L: nat] :
% 3.82/4.04 ( ( ? [X4: nat] : ( P @ ( times_times_nat @ L @ X4 ) ) )
% 3.82/4.04 = ( ? [X4: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ L @ ( plus_plus_nat @ X4 @ zero_zero_nat ) )
% 3.82/4.04 & ( P @ X4 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % unity_coeff_ex
% 3.82/4.04 thf(fact_3362_unity__coeff__ex,axiom,
% 3.82/4.04 ! [P: int > $o,L: int] :
% 3.82/4.04 ( ( ? [X4: int] : ( P @ ( times_times_int @ L @ X4 ) ) )
% 3.82/4.04 = ( ? [X4: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ L @ ( plus_plus_int @ X4 @ zero_zero_int ) )
% 3.82/4.04 & ( P @ X4 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % unity_coeff_ex
% 3.82/4.04 thf(fact_3363_unity__coeff__ex,axiom,
% 3.82/4.04 ! [P: real > $o,L: real] :
% 3.82/4.04 ( ( ? [X4: real] : ( P @ ( times_times_real @ L @ X4 ) ) )
% 3.82/4.04 = ( ? [X4: real] :
% 3.82/4.04 ( ( dvd_dvd_real @ L @ ( plus_plus_real @ X4 @ zero_zero_real ) )
% 3.82/4.04 & ( P @ X4 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % unity_coeff_ex
% 3.82/4.04 thf(fact_3364_unity__coeff__ex,axiom,
% 3.82/4.04 ! [P: complex > $o,L: complex] :
% 3.82/4.04 ( ( ? [X4: complex] : ( P @ ( times_times_complex @ L @ X4 ) ) )
% 3.82/4.04 = ( ? [X4: complex] :
% 3.82/4.04 ( ( dvd_dvd_complex @ L @ ( plus_plus_complex @ X4 @ zero_zero_complex ) )
% 3.82/4.04 & ( P @ X4 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % unity_coeff_ex
% 3.82/4.04 thf(fact_3365_unity__coeff__ex,axiom,
% 3.82/4.04 ! [P: extended_enat > $o,L: extended_enat] :
% 3.82/4.04 ( ( ? [X4: extended_enat] : ( P @ ( times_7803423173614009249d_enat @ L @ X4 ) ) )
% 3.82/4.04 = ( ? [X4: extended_enat] :
% 3.82/4.04 ( ( dvd_dv3785147216227455552d_enat @ L @ ( plus_p3455044024723400733d_enat @ X4 @ zero_z5237406670263579293d_enat ) )
% 3.82/4.04 & ( P @ X4 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % unity_coeff_ex
% 3.82/4.04 thf(fact_3366_dvd__div__eq__mult,axiom,
% 3.82/4.04 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.04 ( ( A != zero_zero_nat )
% 3.82/4.04 => ( ( dvd_dvd_nat @ A @ B2 )
% 3.82/4.04 => ( ( ( divide_divide_nat @ B2 @ A )
% 3.82/4.04 = C )
% 3.82/4.04 = ( B2
% 3.82/4.04 = ( times_times_nat @ C @ A ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_div_eq_mult
% 3.82/4.04 thf(fact_3367_dvd__div__eq__mult,axiom,
% 3.82/4.04 ! [A: int,B2: int,C: int] :
% 3.82/4.04 ( ( A != zero_zero_int )
% 3.82/4.04 => ( ( dvd_dvd_int @ A @ B2 )
% 3.82/4.04 => ( ( ( divide_divide_int @ B2 @ A )
% 3.82/4.04 = C )
% 3.82/4.04 = ( B2
% 3.82/4.04 = ( times_times_int @ C @ A ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_div_eq_mult
% 3.82/4.04 thf(fact_3368_div__dvd__iff__mult,axiom,
% 3.82/4.04 ! [B2: nat,A: nat,C: nat] :
% 3.82/4.04 ( ( B2 != zero_zero_nat )
% 3.82/4.04 => ( ( dvd_dvd_nat @ B2 @ A )
% 3.82/4.04 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B2 ) @ C )
% 3.82/4.04 = ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B2 ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % div_dvd_iff_mult
% 3.82/4.04 thf(fact_3369_div__dvd__iff__mult,axiom,
% 3.82/4.04 ! [B2: int,A: int,C: int] :
% 3.82/4.04 ( ( B2 != zero_zero_int )
% 3.82/4.04 => ( ( dvd_dvd_int @ B2 @ A )
% 3.82/4.04 => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B2 ) @ C )
% 3.82/4.04 = ( dvd_dvd_int @ A @ ( times_times_int @ C @ B2 ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % div_dvd_iff_mult
% 3.82/4.04 thf(fact_3370_dvd__div__iff__mult,axiom,
% 3.82/4.04 ! [C: nat,B2: nat,A: nat] :
% 3.82/4.04 ( ( C != zero_zero_nat )
% 3.82/4.04 => ( ( dvd_dvd_nat @ C @ B2 )
% 3.82/4.04 => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B2 @ C ) )
% 3.82/4.04 = ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B2 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_div_iff_mult
% 3.82/4.04 thf(fact_3371_dvd__div__iff__mult,axiom,
% 3.82/4.04 ! [C: int,B2: int,A: int] :
% 3.82/4.04 ( ( C != zero_zero_int )
% 3.82/4.04 => ( ( dvd_dvd_int @ C @ B2 )
% 3.82/4.04 => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ B2 @ C ) )
% 3.82/4.04 = ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B2 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_div_iff_mult
% 3.82/4.04 thf(fact_3372_dvd__div__div__eq__mult,axiom,
% 3.82/4.04 ! [A: nat,C: nat,B2: nat,D: nat] :
% 3.82/4.04 ( ( A != zero_zero_nat )
% 3.82/4.04 => ( ( C != zero_zero_nat )
% 3.82/4.04 => ( ( dvd_dvd_nat @ A @ B2 )
% 3.82/4.04 => ( ( dvd_dvd_nat @ C @ D )
% 3.82/4.04 => ( ( ( divide_divide_nat @ B2 @ A )
% 3.82/4.04 = ( divide_divide_nat @ D @ C ) )
% 3.82/4.04 = ( ( times_times_nat @ B2 @ C )
% 3.82/4.04 = ( times_times_nat @ A @ D ) ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_div_div_eq_mult
% 3.82/4.04 thf(fact_3373_dvd__div__div__eq__mult,axiom,
% 3.82/4.04 ! [A: int,C: int,B2: int,D: int] :
% 3.82/4.04 ( ( A != zero_zero_int )
% 3.82/4.04 => ( ( C != zero_zero_int )
% 3.82/4.04 => ( ( dvd_dvd_int @ A @ B2 )
% 3.82/4.04 => ( ( dvd_dvd_int @ C @ D )
% 3.82/4.04 => ( ( ( divide_divide_int @ B2 @ A )
% 3.82/4.04 = ( divide_divide_int @ D @ C ) )
% 3.82/4.04 = ( ( times_times_int @ B2 @ C )
% 3.82/4.04 = ( times_times_int @ A @ D ) ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_div_div_eq_mult
% 3.82/4.04 thf(fact_3374_unit__div__eq__0__iff,axiom,
% 3.82/4.04 ! [B2: nat,A: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 3.82/4.04 => ( ( ( divide_divide_nat @ A @ B2 )
% 3.82/4.04 = zero_zero_nat )
% 3.82/4.04 = ( A = zero_zero_nat ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % unit_div_eq_0_iff
% 3.82/4.04 thf(fact_3375_unit__div__eq__0__iff,axiom,
% 3.82/4.04 ! [B2: int,A: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ B2 @ one_one_int )
% 3.82/4.04 => ( ( ( divide_divide_int @ A @ B2 )
% 3.82/4.04 = zero_zero_int )
% 3.82/4.04 = ( A = zero_zero_int ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % unit_div_eq_0_iff
% 3.82/4.04 thf(fact_3376_is__unit__div__mult2__eq,axiom,
% 3.82/4.04 ! [B2: nat,C: nat,A: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 3.82/4.04 => ( ( dvd_dvd_nat @ C @ one_one_nat )
% 3.82/4.04 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B2 @ C ) )
% 3.82/4.04 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B2 ) @ C ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % is_unit_div_mult2_eq
% 3.82/4.04 thf(fact_3377_is__unit__div__mult2__eq,axiom,
% 3.82/4.04 ! [B2: int,C: int,A: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ B2 @ one_one_int )
% 3.82/4.04 => ( ( dvd_dvd_int @ C @ one_one_int )
% 3.82/4.04 => ( ( divide_divide_int @ A @ ( times_times_int @ B2 @ C ) )
% 3.82/4.04 = ( divide_divide_int @ ( divide_divide_int @ A @ B2 ) @ C ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % is_unit_div_mult2_eq
% 3.82/4.04 thf(fact_3378_unit__div__mult__swap,axiom,
% 3.82/4.04 ! [C: nat,A: nat,B2: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ C @ one_one_nat )
% 3.82/4.04 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B2 @ C ) )
% 3.82/4.04 = ( divide_divide_nat @ ( times_times_nat @ A @ B2 ) @ C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % unit_div_mult_swap
% 3.82/4.04 thf(fact_3379_unit__div__mult__swap,axiom,
% 3.82/4.04 ! [C: int,A: int,B2: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ C @ one_one_int )
% 3.82/4.04 => ( ( times_times_int @ A @ ( divide_divide_int @ B2 @ C ) )
% 3.82/4.04 = ( divide_divide_int @ ( times_times_int @ A @ B2 ) @ C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % unit_div_mult_swap
% 3.82/4.04 thf(fact_3380_unit__div__commute,axiom,
% 3.82/4.04 ! [B2: nat,A: nat,C: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 3.82/4.04 => ( ( times_times_nat @ ( divide_divide_nat @ A @ B2 ) @ C )
% 3.82/4.04 = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ B2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % unit_div_commute
% 3.82/4.04 thf(fact_3381_unit__div__commute,axiom,
% 3.82/4.04 ! [B2: int,A: int,C: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ B2 @ one_one_int )
% 3.82/4.04 => ( ( times_times_int @ ( divide_divide_int @ A @ B2 ) @ C )
% 3.82/4.04 = ( divide_divide_int @ ( times_times_int @ A @ C ) @ B2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % unit_div_commute
% 3.82/4.04 thf(fact_3382_div__mult__unit2,axiom,
% 3.82/4.04 ! [C: nat,B2: nat,A: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ C @ one_one_nat )
% 3.82/4.04 => ( ( dvd_dvd_nat @ B2 @ A )
% 3.82/4.04 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B2 @ C ) )
% 3.82/4.04 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B2 ) @ C ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % div_mult_unit2
% 3.82/4.04 thf(fact_3383_div__mult__unit2,axiom,
% 3.82/4.04 ! [C: int,B2: int,A: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ C @ one_one_int )
% 3.82/4.04 => ( ( dvd_dvd_int @ B2 @ A )
% 3.82/4.04 => ( ( divide_divide_int @ A @ ( times_times_int @ B2 @ C ) )
% 3.82/4.04 = ( divide_divide_int @ ( divide_divide_int @ A @ B2 ) @ C ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % div_mult_unit2
% 3.82/4.04 thf(fact_3384_unit__eq__div2,axiom,
% 3.82/4.04 ! [B2: nat,A: nat,C: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 3.82/4.04 => ( ( A
% 3.82/4.04 = ( divide_divide_nat @ C @ B2 ) )
% 3.82/4.04 = ( ( times_times_nat @ A @ B2 )
% 3.82/4.04 = C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % unit_eq_div2
% 3.82/4.04 thf(fact_3385_unit__eq__div2,axiom,
% 3.82/4.04 ! [B2: int,A: int,C: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ B2 @ one_one_int )
% 3.82/4.04 => ( ( A
% 3.82/4.04 = ( divide_divide_int @ C @ B2 ) )
% 3.82/4.04 = ( ( times_times_int @ A @ B2 )
% 3.82/4.04 = C ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % unit_eq_div2
% 3.82/4.04 thf(fact_3386_unit__eq__div1,axiom,
% 3.82/4.04 ! [B2: nat,A: nat,C: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 3.82/4.04 => ( ( ( divide_divide_nat @ A @ B2 )
% 3.82/4.04 = C )
% 3.82/4.04 = ( A
% 3.82/4.04 = ( times_times_nat @ C @ B2 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % unit_eq_div1
% 3.82/4.04 thf(fact_3387_unit__eq__div1,axiom,
% 3.82/4.04 ! [B2: int,A: int,C: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ B2 @ one_one_int )
% 3.82/4.04 => ( ( ( divide_divide_int @ A @ B2 )
% 3.82/4.04 = C )
% 3.82/4.04 = ( A
% 3.82/4.04 = ( times_times_int @ C @ B2 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % unit_eq_div1
% 3.82/4.04 thf(fact_3388_mod__le__divisor,axiom,
% 3.82/4.04 ! [N2: nat,M2: nat] :
% 3.82/4.04 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.04 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ M2 @ N2 ) @ N2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % mod_le_divisor
% 3.82/4.04 thf(fact_3389_is__unit__power__iff,axiom,
% 3.82/4.04 ! [A: nat,N2: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N2 ) @ one_one_nat )
% 3.82/4.04 = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 3.82/4.04 | ( N2 = zero_zero_nat ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % is_unit_power_iff
% 3.82/4.04 thf(fact_3390_is__unit__power__iff,axiom,
% 3.82/4.04 ! [A: int,N2: nat] :
% 3.82/4.04 ( ( dvd_dvd_int @ ( power_power_int @ A @ N2 ) @ one_one_int )
% 3.82/4.04 = ( ( dvd_dvd_int @ A @ one_one_int )
% 3.82/4.04 | ( N2 = zero_zero_nat ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % is_unit_power_iff
% 3.82/4.04 thf(fact_3391_div__less__mono,axiom,
% 3.82/4.04 ! [A2: nat,B: nat,N2: nat] :
% 3.82/4.04 ( ( ord_less_nat @ A2 @ B )
% 3.82/4.04 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.04 => ( ( ( modulo_modulo_nat @ A2 @ N2 )
% 3.82/4.04 = zero_zero_nat )
% 3.82/4.04 => ( ( ( modulo_modulo_nat @ B @ N2 )
% 3.82/4.04 = zero_zero_nat )
% 3.82/4.04 => ( ord_less_nat @ ( divide_divide_nat @ A2 @ N2 ) @ ( divide_divide_nat @ B @ N2 ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % div_less_mono
% 3.82/4.04 thf(fact_3392_mod__eq__nat1E,axiom,
% 3.82/4.04 ! [M2: nat,Q3: nat,N2: nat] :
% 3.82/4.04 ( ( ( modulo_modulo_nat @ M2 @ Q3 )
% 3.82/4.04 = ( modulo_modulo_nat @ N2 @ Q3 ) )
% 3.82/4.04 => ( ( ord_less_eq_nat @ N2 @ M2 )
% 3.82/4.04 => ~ ! [S3: nat] :
% 3.82/4.04 ( M2
% 3.82/4.04 != ( plus_plus_nat @ N2 @ ( times_times_nat @ Q3 @ S3 ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % mod_eq_nat1E
% 3.82/4.04 thf(fact_3393_mod__eq__nat2E,axiom,
% 3.82/4.04 ! [M2: nat,Q3: nat,N2: nat] :
% 3.82/4.04 ( ( ( modulo_modulo_nat @ M2 @ Q3 )
% 3.82/4.04 = ( modulo_modulo_nat @ N2 @ Q3 ) )
% 3.82/4.04 => ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.04 => ~ ! [S3: nat] :
% 3.82/4.04 ( N2
% 3.82/4.04 != ( plus_plus_nat @ M2 @ ( times_times_nat @ Q3 @ S3 ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % mod_eq_nat2E
% 3.82/4.04 thf(fact_3394_nat__mod__eq__lemma,axiom,
% 3.82/4.04 ! [X: nat,N2: nat,Y: nat] :
% 3.82/4.04 ( ( ( modulo_modulo_nat @ X @ N2 )
% 3.82/4.04 = ( modulo_modulo_nat @ Y @ N2 ) )
% 3.82/4.04 => ( ( ord_less_eq_nat @ Y @ X )
% 3.82/4.04 => ? [Q2: nat] :
% 3.82/4.04 ( X
% 3.82/4.04 = ( plus_plus_nat @ Y @ ( times_times_nat @ N2 @ Q2 ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % nat_mod_eq_lemma
% 3.82/4.04 thf(fact_3395_dvd__imp__le,axiom,
% 3.82/4.04 ! [K: nat,N2: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ K @ N2 )
% 3.82/4.04 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.04 => ( ord_less_eq_nat @ K @ N2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_imp_le
% 3.82/4.04 thf(fact_3396_div__mod__decomp,axiom,
% 3.82/4.04 ! [A2: nat,N2: nat] :
% 3.82/4.04 ( A2
% 3.82/4.04 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A2 @ N2 ) @ N2 ) @ ( modulo_modulo_nat @ A2 @ N2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % div_mod_decomp
% 3.82/4.04 thf(fact_3397_mod__mult2__eq,axiom,
% 3.82/4.04 ! [M2: nat,N2: nat,Q3: nat] :
% 3.82/4.04 ( ( modulo_modulo_nat @ M2 @ ( times_times_nat @ N2 @ Q3 ) )
% 3.82/4.04 = ( plus_plus_nat @ ( times_times_nat @ N2 @ ( modulo_modulo_nat @ ( divide_divide_nat @ M2 @ N2 ) @ Q3 ) ) @ ( modulo_modulo_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % mod_mult2_eq
% 3.82/4.04 thf(fact_3398_dvd__mult__cancel,axiom,
% 3.82/4.04 ! [K: nat,M2: nat,N2: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M2 ) @ ( times_times_nat @ K @ N2 ) )
% 3.82/4.04 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 3.82/4.04 => ( dvd_dvd_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_mult_cancel
% 3.82/4.04 thf(fact_3399_nat__mult__dvd__cancel1,axiom,
% 3.82/4.04 ! [K: nat,M2: nat,N2: nat] :
% 3.82/4.04 ( ( ord_less_nat @ zero_zero_nat @ K )
% 3.82/4.04 => ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M2 ) @ ( times_times_nat @ K @ N2 ) )
% 3.82/4.04 = ( dvd_dvd_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % nat_mult_dvd_cancel1
% 3.82/4.04 thf(fact_3400_bezout__add__strong__nat,axiom,
% 3.82/4.04 ! [A: nat,B2: nat] :
% 3.82/4.04 ( ( A != zero_zero_nat )
% 3.82/4.04 => ? [D5: nat,X5: nat,Y3: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ D5 @ A )
% 3.82/4.04 & ( dvd_dvd_nat @ D5 @ B2 )
% 3.82/4.04 & ( ( times_times_nat @ A @ X5 )
% 3.82/4.04 = ( plus_plus_nat @ ( times_times_nat @ B2 @ Y3 ) @ D5 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % bezout_add_strong_nat
% 3.82/4.04 thf(fact_3401_vebt__buildup_Oelims,axiom,
% 3.82/4.04 ! [X: nat,Y: vEBT_VEBT] :
% 3.82/4.04 ( ( ( vEBT_vebt_buildup @ X )
% 3.82/4.04 = Y )
% 3.82/4.04 => ( ( ( X = zero_zero_nat )
% 3.82/4.04 => ( Y
% 3.82/4.04 != ( vEBT_Leaf @ $false @ $false ) ) )
% 3.82/4.04 => ( ( ( X
% 3.82/4.04 = ( suc @ zero_zero_nat ) )
% 3.82/4.04 => ( Y
% 3.82/4.04 != ( vEBT_Leaf @ $false @ $false ) ) )
% 3.82/4.04 => ~ ! [Va: nat] :
% 3.82/4.04 ( ( X
% 3.82/4.04 = ( suc @ ( suc @ Va ) ) )
% 3.82/4.04 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 3.82/4.04 => ( Y
% 3.82/4.04 = ( 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 ) ) ) ) ) ) )
% 3.82/4.04 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 3.82/4.04 => ( Y
% 3.82/4.04 = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % vebt_buildup.elims
% 3.82/4.04 thf(fact_3402_even__zero,axiom,
% 3.82/4.04 dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ zero_zero_nat ).
% 3.82/4.04
% 3.82/4.04 % even_zero
% 3.82/4.04 thf(fact_3403_even__zero,axiom,
% 3.82/4.04 dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ zero_zero_int ).
% 3.82/4.04
% 3.82/4.04 % even_zero
% 3.82/4.04 thf(fact_3404_is__unitE,axiom,
% 3.82/4.04 ! [A: nat,C: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 3.82/4.04 => ~ ( ( A != zero_zero_nat )
% 3.82/4.04 => ! [B4: nat] :
% 3.82/4.04 ( ( B4 != zero_zero_nat )
% 3.82/4.04 => ( ( dvd_dvd_nat @ B4 @ one_one_nat )
% 3.82/4.04 => ( ( ( divide_divide_nat @ one_one_nat @ A )
% 3.82/4.04 = B4 )
% 3.82/4.04 => ( ( ( divide_divide_nat @ one_one_nat @ B4 )
% 3.82/4.04 = A )
% 3.82/4.04 => ( ( ( times_times_nat @ A @ B4 )
% 3.82/4.04 = one_one_nat )
% 3.82/4.04 => ( ( divide_divide_nat @ C @ A )
% 3.82/4.04 != ( times_times_nat @ C @ B4 ) ) ) ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % is_unitE
% 3.82/4.04 thf(fact_3405_is__unitE,axiom,
% 3.82/4.04 ! [A: int,C: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ A @ one_one_int )
% 3.82/4.04 => ~ ( ( A != zero_zero_int )
% 3.82/4.04 => ! [B4: int] :
% 3.82/4.04 ( ( B4 != zero_zero_int )
% 3.82/4.04 => ( ( dvd_dvd_int @ B4 @ one_one_int )
% 3.82/4.04 => ( ( ( divide_divide_int @ one_one_int @ A )
% 3.82/4.04 = B4 )
% 3.82/4.04 => ( ( ( divide_divide_int @ one_one_int @ B4 )
% 3.82/4.04 = A )
% 3.82/4.04 => ( ( ( times_times_int @ A @ B4 )
% 3.82/4.04 = one_one_int )
% 3.82/4.04 => ( ( divide_divide_int @ C @ A )
% 3.82/4.04 != ( times_times_int @ C @ B4 ) ) ) ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % is_unitE
% 3.82/4.04 thf(fact_3406_is__unit__div__mult__cancel__left,axiom,
% 3.82/4.04 ! [A: nat,B2: nat] :
% 3.82/4.04 ( ( A != zero_zero_nat )
% 3.82/4.04 => ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 3.82/4.04 => ( ( divide_divide_nat @ A @ ( times_times_nat @ A @ B2 ) )
% 3.82/4.04 = ( divide_divide_nat @ one_one_nat @ B2 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % is_unit_div_mult_cancel_left
% 3.82/4.04 thf(fact_3407_is__unit__div__mult__cancel__left,axiom,
% 3.82/4.04 ! [A: int,B2: int] :
% 3.82/4.04 ( ( A != zero_zero_int )
% 3.82/4.04 => ( ( dvd_dvd_int @ B2 @ one_one_int )
% 3.82/4.04 => ( ( divide_divide_int @ A @ ( times_times_int @ A @ B2 ) )
% 3.82/4.04 = ( divide_divide_int @ one_one_int @ B2 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % is_unit_div_mult_cancel_left
% 3.82/4.04 thf(fact_3408_is__unit__div__mult__cancel__right,axiom,
% 3.82/4.04 ! [A: nat,B2: nat] :
% 3.82/4.04 ( ( A != zero_zero_nat )
% 3.82/4.04 => ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 3.82/4.04 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B2 @ A ) )
% 3.82/4.04 = ( divide_divide_nat @ one_one_nat @ B2 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % is_unit_div_mult_cancel_right
% 3.82/4.04 thf(fact_3409_is__unit__div__mult__cancel__right,axiom,
% 3.82/4.04 ! [A: int,B2: int] :
% 3.82/4.04 ( ( A != zero_zero_int )
% 3.82/4.04 => ( ( dvd_dvd_int @ B2 @ one_one_int )
% 3.82/4.04 => ( ( divide_divide_int @ A @ ( times_times_int @ B2 @ A ) )
% 3.82/4.04 = ( divide_divide_int @ one_one_int @ B2 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % is_unit_div_mult_cancel_right
% 3.82/4.04 thf(fact_3410_odd__even__add,axiom,
% 3.82/4.04 ! [A: nat,B2: nat] :
% 3.82/4.04 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 3.82/4.04 => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 )
% 3.82/4.04 => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B2 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % odd_even_add
% 3.82/4.04 thf(fact_3411_odd__even__add,axiom,
% 3.82/4.04 ! [A: int,B2: int] :
% 3.82/4.04 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 3.82/4.04 => ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 )
% 3.82/4.04 => ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B2 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % odd_even_add
% 3.82/4.04 thf(fact_3412_dvd__power__iff,axiom,
% 3.82/4.04 ! [X: nat,M2: nat,N2: nat] :
% 3.82/4.04 ( ( X != zero_zero_nat )
% 3.82/4.04 => ( ( dvd_dvd_nat @ ( power_power_nat @ X @ M2 ) @ ( power_power_nat @ X @ N2 ) )
% 3.82/4.04 = ( ( dvd_dvd_nat @ X @ one_one_nat )
% 3.82/4.04 | ( ord_less_eq_nat @ M2 @ N2 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_power_iff
% 3.82/4.04 thf(fact_3413_dvd__power__iff,axiom,
% 3.82/4.04 ! [X: int,M2: nat,N2: nat] :
% 3.82/4.04 ( ( X != zero_zero_int )
% 3.82/4.04 => ( ( dvd_dvd_int @ ( power_power_int @ X @ M2 ) @ ( power_power_int @ X @ N2 ) )
% 3.82/4.04 = ( ( dvd_dvd_int @ X @ one_one_int )
% 3.82/4.04 | ( ord_less_eq_nat @ M2 @ N2 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_power_iff
% 3.82/4.04 thf(fact_3414_dvd__power,axiom,
% 3.82/4.04 ! [N2: nat,X: nat] :
% 3.82/4.04 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.04 | ( X = one_one_nat ) )
% 3.82/4.04 => ( dvd_dvd_nat @ X @ ( power_power_nat @ X @ N2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_power
% 3.82/4.04 thf(fact_3415_dvd__power,axiom,
% 3.82/4.04 ! [N2: nat,X: real] :
% 3.82/4.04 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.04 | ( X = one_one_real ) )
% 3.82/4.04 => ( dvd_dvd_real @ X @ ( power_power_real @ X @ N2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_power
% 3.82/4.04 thf(fact_3416_dvd__power,axiom,
% 3.82/4.04 ! [N2: nat,X: complex] :
% 3.82/4.04 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.04 | ( X = one_one_complex ) )
% 3.82/4.04 => ( dvd_dvd_complex @ X @ ( power_power_complex @ X @ N2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_power
% 3.82/4.04 thf(fact_3417_dvd__power,axiom,
% 3.82/4.04 ! [N2: nat,X: int] :
% 3.82/4.04 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.04 | ( X = one_one_int ) )
% 3.82/4.04 => ( dvd_dvd_int @ X @ ( power_power_int @ X @ N2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_power
% 3.82/4.04 thf(fact_3418_split__mod,axiom,
% 3.82/4.04 ! [P: nat > $o,M2: nat,N2: nat] :
% 3.82/4.04 ( ( P @ ( modulo_modulo_nat @ M2 @ N2 ) )
% 3.82/4.04 = ( ( ( N2 = zero_zero_nat )
% 3.82/4.04 => ( P @ M2 ) )
% 3.82/4.04 & ( ( N2 != zero_zero_nat )
% 3.82/4.04 => ! [I3: nat,J2: nat] :
% 3.82/4.04 ( ( ord_less_nat @ J2 @ N2 )
% 3.82/4.04 => ( ( M2
% 3.82/4.04 = ( plus_plus_nat @ ( times_times_nat @ N2 @ I3 ) @ J2 ) )
% 3.82/4.04 => ( P @ J2 ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % split_mod
% 3.82/4.04 thf(fact_3419_dvd__mult__cancel1,axiom,
% 3.82/4.04 ! [M2: nat,N2: nat] :
% 3.82/4.04 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 3.82/4.04 => ( ( dvd_dvd_nat @ ( times_times_nat @ M2 @ N2 ) @ M2 )
% 3.82/4.04 = ( N2 = one_one_nat ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_mult_cancel1
% 3.82/4.04 thf(fact_3420_dvd__mult__cancel2,axiom,
% 3.82/4.04 ! [M2: nat,N2: nat] :
% 3.82/4.04 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 3.82/4.04 => ( ( dvd_dvd_nat @ ( times_times_nat @ N2 @ M2 ) @ M2 )
% 3.82/4.04 = ( N2 = one_one_nat ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_mult_cancel2
% 3.82/4.04 thf(fact_3421_power__dvd__imp__le,axiom,
% 3.82/4.04 ! [I: nat,M2: nat,N2: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ ( power_power_nat @ I @ M2 ) @ ( power_power_nat @ I @ N2 ) )
% 3.82/4.04 => ( ( ord_less_nat @ one_one_nat @ I )
% 3.82/4.04 => ( ord_less_eq_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % power_dvd_imp_le
% 3.82/4.04 thf(fact_3422_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 3.82/4.04 ! [C: nat,A: nat,B2: nat] :
% 3.82/4.04 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 3.82/4.04 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ B2 @ C ) )
% 3.82/4.04 = ( plus_plus_nat @ ( times_times_nat @ B2 @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ B2 ) @ C ) ) @ ( modulo_modulo_nat @ A @ B2 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 3.82/4.04 thf(fact_3423_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 3.82/4.04 ! [C: int,A: int,B2: int] :
% 3.82/4.04 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 3.82/4.04 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B2 @ C ) )
% 3.82/4.04 = ( plus_plus_int @ ( times_times_int @ B2 @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B2 ) @ C ) ) @ ( modulo_modulo_int @ A @ B2 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 3.82/4.04 thf(fact_3424_product__nth,axiom,
% 3.82/4.04 ! [N2: nat,Xs: list_P6011104703257516679at_nat,Ys: list_P6011104703257516679at_nat] :
% 3.82/4.04 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_s5460976970255530739at_nat @ Xs ) @ ( size_s5460976970255530739at_nat @ Ys ) ) )
% 3.82/4.04 => ( ( nth_Pr6744343527793145070at_nat @ ( produc3544356994491977349at_nat @ Xs @ Ys ) @ N2 )
% 3.82/4.04 = ( produc6161850002892822231at_nat @ ( nth_Pr7617993195940197384at_nat @ Xs @ ( divide_divide_nat @ N2 @ ( size_s5460976970255530739at_nat @ Ys ) ) ) @ ( nth_Pr7617993195940197384at_nat @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_s5460976970255530739at_nat @ Ys ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % product_nth
% 3.82/4.04 thf(fact_3425_product__nth,axiom,
% 3.82/4.04 ! [N2: nat,Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 3.82/4.04 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 3.82/4.04 => ( ( nth_Pr4953567300277697838T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs @ Ys ) @ N2 )
% 3.82/4.04 = ( 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 ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % product_nth
% 3.82/4.04 thf(fact_3426_product__nth,axiom,
% 3.82/4.04 ! [N2: nat,Xs: list_VEBT_VEBT,Ys: list_int] :
% 3.82/4.04 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_int @ Ys ) ) )
% 3.82/4.04 => ( ( nth_Pr6837108013167703752BT_int @ ( produc7292646706713671643BT_int @ Xs @ Ys ) @ N2 )
% 3.82/4.04 = ( 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 ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % product_nth
% 3.82/4.04 thf(fact_3427_product__nth,axiom,
% 3.82/4.04 ! [N2: nat,Xs: list_VEBT_VEBT,Ys: list_nat] :
% 3.82/4.04 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_nat @ Ys ) ) )
% 3.82/4.04 => ( ( nth_Pr1791586995822124652BT_nat @ ( produc7295137177222721919BT_nat @ Xs @ Ys ) @ N2 )
% 3.82/4.04 = ( 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 ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % product_nth
% 3.82/4.04 thf(fact_3428_product__nth,axiom,
% 3.82/4.04 ! [N2: nat,Xs: list_int,Ys: list_VEBT_VEBT] :
% 3.82/4.04 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_int @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 3.82/4.04 => ( ( nth_Pr3474266648193625910T_VEBT @ ( produc662631939642741121T_VEBT @ Xs @ Ys ) @ N2 )
% 3.82/4.04 = ( produc3329399203697025711T_VEBT @ ( nth_int @ Xs @ ( divide_divide_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % product_nth
% 3.82/4.04 thf(fact_3429_product__nth,axiom,
% 3.82/4.04 ! [N2: nat,Xs: list_int,Ys: list_int] :
% 3.82/4.04 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_int @ Xs ) @ ( size_size_list_int @ Ys ) ) )
% 3.82/4.04 => ( ( nth_Pr4439495888332055232nt_int @ ( product_int_int @ Xs @ Ys ) @ N2 )
% 3.82/4.04 = ( product_Pair_int_int @ ( nth_int @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_int @ Ys ) ) ) @ ( nth_int @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_int @ Ys ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % product_nth
% 3.82/4.04 thf(fact_3430_product__nth,axiom,
% 3.82/4.04 ! [N2: nat,Xs: list_int,Ys: list_nat] :
% 3.82/4.04 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_int @ Xs ) @ ( size_size_list_nat @ Ys ) ) )
% 3.82/4.04 => ( ( nth_Pr8617346907841251940nt_nat @ ( product_int_nat @ Xs @ Ys ) @ N2 )
% 3.82/4.04 = ( product_Pair_int_nat @ ( nth_int @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % product_nth
% 3.82/4.04 thf(fact_3431_product__nth,axiom,
% 3.82/4.04 ! [N2: nat,Xs: list_nat,Ys: list_VEBT_VEBT] :
% 3.82/4.04 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 3.82/4.04 => ( ( nth_Pr744662078594809490T_VEBT @ ( produc7156399406898700509T_VEBT @ Xs @ Ys ) @ N2 )
% 3.82/4.04 = ( produc599794634098209291T_VEBT @ ( nth_nat @ Xs @ ( divide_divide_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % product_nth
% 3.82/4.04 thf(fact_3432_product__nth,axiom,
% 3.82/4.04 ! [N2: nat,Xs: list_nat,Ys: list_int] :
% 3.82/4.04 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_size_list_int @ Ys ) ) )
% 3.82/4.04 => ( ( nth_Pr3440142176431000676at_int @ ( product_nat_int @ Xs @ Ys ) @ N2 )
% 3.82/4.04 = ( product_Pair_nat_int @ ( nth_nat @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_int @ Ys ) ) ) @ ( nth_int @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_int @ Ys ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % product_nth
% 3.82/4.04 thf(fact_3433_product__nth,axiom,
% 3.82/4.04 ! [N2: nat,Xs: list_nat,Ys: list_nat] :
% 3.82/4.04 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_size_list_nat @ Ys ) ) )
% 3.82/4.04 => ( ( nth_Pr7617993195940197384at_nat @ ( product_nat_nat @ Xs @ Ys ) @ N2 )
% 3.82/4.04 = ( product_Pair_nat_nat @ ( nth_nat @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % product_nth
% 3.82/4.04 thf(fact_3434_power__mono__odd,axiom,
% 3.82/4.04 ! [N2: nat,A: real,B2: real] :
% 3.82/4.04 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 3.82/4.04 => ( ( ord_less_eq_real @ A @ B2 )
% 3.82/4.04 => ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B2 @ N2 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % power_mono_odd
% 3.82/4.04 thf(fact_3435_power__mono__odd,axiom,
% 3.82/4.04 ! [N2: nat,A: int,B2: int] :
% 3.82/4.04 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 3.82/4.04 => ( ( ord_less_eq_int @ A @ B2 )
% 3.82/4.04 => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B2 @ N2 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % power_mono_odd
% 3.82/4.04 thf(fact_3436_Suc__times__mod__eq,axiom,
% 3.82/4.04 ! [M2: nat,N2: nat] :
% 3.82/4.04 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M2 )
% 3.82/4.04 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ M2 @ N2 ) ) @ M2 )
% 3.82/4.04 = one_one_nat ) ) ).
% 3.82/4.04
% 3.82/4.04 % Suc_times_mod_eq
% 3.82/4.04 thf(fact_3437_odd__pos,axiom,
% 3.82/4.04 ! [N2: nat] :
% 3.82/4.04 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 3.82/4.04 => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % odd_pos
% 3.82/4.04 thf(fact_3438_dvd__power__iff__le,axiom,
% 3.82/4.04 ! [K: nat,M2: nat,N2: nat] :
% 3.82/4.04 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 3.82/4.04 => ( ( dvd_dvd_nat @ ( power_power_nat @ K @ M2 ) @ ( power_power_nat @ K @ N2 ) )
% 3.82/4.04 = ( ord_less_eq_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_power_iff_le
% 3.82/4.04 thf(fact_3439_even__unset__bit__iff,axiom,
% 3.82/4.04 ! [M2: nat,A: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ M2 @ A ) )
% 3.82/4.04 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 3.82/4.04 | ( M2 = zero_zero_nat ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % even_unset_bit_iff
% 3.82/4.04 thf(fact_3440_even__unset__bit__iff,axiom,
% 3.82/4.04 ! [M2: nat,A: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ M2 @ A ) )
% 3.82/4.04 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 3.82/4.04 | ( M2 = zero_zero_nat ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % even_unset_bit_iff
% 3.82/4.04 thf(fact_3441_even__set__bit__iff,axiom,
% 3.82/4.04 ! [M2: nat,A: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ M2 @ A ) )
% 3.82/4.04 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 3.82/4.04 & ( M2 != zero_zero_nat ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % even_set_bit_iff
% 3.82/4.04 thf(fact_3442_even__set__bit__iff,axiom,
% 3.82/4.04 ! [M2: nat,A: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ M2 @ A ) )
% 3.82/4.04 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 3.82/4.04 & ( M2 != zero_zero_nat ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % even_set_bit_iff
% 3.82/4.04 thf(fact_3443_divmod__digit__0_I2_J,axiom,
% 3.82/4.04 ! [B2: nat,A: nat] :
% 3.82/4.04 ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 3.82/4.04 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) ) @ B2 )
% 3.82/4.04 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) )
% 3.82/4.04 = ( modulo_modulo_nat @ A @ B2 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % divmod_digit_0(2)
% 3.82/4.04 thf(fact_3444_divmod__digit__0_I2_J,axiom,
% 3.82/4.04 ! [B2: int,A: int] :
% 3.82/4.04 ( ( ord_less_int @ zero_zero_int @ B2 )
% 3.82/4.04 => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) ) @ B2 )
% 3.82/4.04 => ( ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) )
% 3.82/4.04 = ( modulo_modulo_int @ A @ B2 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % divmod_digit_0(2)
% 3.82/4.04 thf(fact_3445_bits__stable__imp__add__self,axiom,
% 3.82/4.04 ! [A: nat] :
% 3.82/4.04 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.04 = A )
% 3.82/4.04 => ( ( plus_plus_nat @ A @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 3.82/4.04 = zero_zero_nat ) ) ).
% 3.82/4.04
% 3.82/4.04 % bits_stable_imp_add_self
% 3.82/4.04 thf(fact_3446_bits__stable__imp__add__self,axiom,
% 3.82/4.04 ! [A: int] :
% 3.82/4.04 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 3.82/4.04 = A )
% 3.82/4.04 => ( ( plus_plus_int @ A @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 3.82/4.04 = zero_zero_int ) ) ).
% 3.82/4.04
% 3.82/4.04 % bits_stable_imp_add_self
% 3.82/4.04 thf(fact_3447_VEBT__internal_Onaive__member_Osimps_I3_J,axiom,
% 3.82/4.04 ! [Uy: option4927543243414619207at_nat,V: nat,TreeList2: list_VEBT_VEBT,S: vEBT_VEBT,X: nat] :
% 3.82/4.04 ( ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList2 @ S ) @ X )
% 3.82/4.04 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 3.82/4.04 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 3.82/4.04 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % VEBT_internal.naive_member.simps(3)
% 3.82/4.04 thf(fact_3448_div__exp__mod__exp__eq,axiom,
% 3.82/4.04 ! [A: nat,N2: nat,M2: nat] :
% 3.82/4.04 ( ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 3.82/4.04 = ( divide_divide_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M2 ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % div_exp_mod_exp_eq
% 3.82/4.04 thf(fact_3449_div__exp__mod__exp__eq,axiom,
% 3.82/4.04 ! [A: int,N2: nat,M2: nat] :
% 3.82/4.04 ( ( modulo_modulo_int @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) )
% 3.82/4.04 = ( divide_divide_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M2 ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % div_exp_mod_exp_eq
% 3.82/4.04 thf(fact_3450_oddE,axiom,
% 3.82/4.04 ! [A: nat] :
% 3.82/4.04 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 3.82/4.04 => ~ ! [B4: nat] :
% 3.82/4.04 ( A
% 3.82/4.04 != ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B4 ) @ one_one_nat ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % oddE
% 3.82/4.04 thf(fact_3451_oddE,axiom,
% 3.82/4.04 ! [A: int] :
% 3.82/4.04 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 3.82/4.04 => ~ ! [B4: int] :
% 3.82/4.04 ( A
% 3.82/4.04 != ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B4 ) @ one_one_int ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % oddE
% 3.82/4.04 thf(fact_3452_zero__le__power__eq,axiom,
% 3.82/4.04 ! [A: real,N2: nat] :
% 3.82/4.04 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) )
% 3.82/4.04 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 3.82/4.04 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 3.82/4.04 & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % zero_le_power_eq
% 3.82/4.04 thf(fact_3453_zero__le__power__eq,axiom,
% 3.82/4.04 ! [A: int,N2: nat] :
% 3.82/4.04 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) )
% 3.82/4.04 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 3.82/4.04 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 3.82/4.04 & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % zero_le_power_eq
% 3.82/4.04 thf(fact_3454_zero__le__odd__power,axiom,
% 3.82/4.04 ! [N2: nat,A: real] :
% 3.82/4.04 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 3.82/4.04 => ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) )
% 3.82/4.04 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % zero_le_odd_power
% 3.82/4.04 thf(fact_3455_zero__le__odd__power,axiom,
% 3.82/4.04 ! [N2: nat,A: int] :
% 3.82/4.04 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 3.82/4.04 => ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) )
% 3.82/4.04 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % zero_le_odd_power
% 3.82/4.04 thf(fact_3456_zero__le__even__power,axiom,
% 3.82/4.04 ! [N2: nat,A: real] :
% 3.82/4.04 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 3.82/4.04 => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % zero_le_even_power
% 3.82/4.04 thf(fact_3457_zero__le__even__power,axiom,
% 3.82/4.04 ! [N2: nat,A: int] :
% 3.82/4.04 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 3.82/4.04 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % zero_le_even_power
% 3.82/4.04 thf(fact_3458_verit__le__mono__div,axiom,
% 3.82/4.04 ! [A2: nat,B: nat,N2: nat] :
% 3.82/4.04 ( ( ord_less_nat @ A2 @ B )
% 3.82/4.04 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.04 => ( ord_less_eq_nat
% 3.82/4.04 @ ( plus_plus_nat @ ( divide_divide_nat @ A2 @ N2 )
% 3.82/4.04 @ ( if_nat
% 3.82/4.04 @ ( ( modulo_modulo_nat @ B @ N2 )
% 3.82/4.04 = zero_zero_nat )
% 3.82/4.04 @ one_one_nat
% 3.82/4.04 @ zero_zero_nat ) )
% 3.82/4.04 @ ( divide_divide_nat @ B @ N2 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % verit_le_mono_div
% 3.82/4.04 thf(fact_3459_VEBT__internal_Omembermima_Osimps_I5_J,axiom,
% 3.82/4.04 ! [V: nat,TreeList2: list_VEBT_VEBT,Vd2: vEBT_VEBT,X: nat] :
% 3.82/4.04 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList2 @ Vd2 ) @ X )
% 3.82/4.04 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 3.82/4.04 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 3.82/4.04 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % VEBT_internal.membermima.simps(5)
% 3.82/4.04 thf(fact_3460_divmod__digit__0_I1_J,axiom,
% 3.82/4.04 ! [B2: nat,A: nat] :
% 3.82/4.04 ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 3.82/4.04 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) ) @ B2 )
% 3.82/4.04 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) ) )
% 3.82/4.04 = ( divide_divide_nat @ A @ B2 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % divmod_digit_0(1)
% 3.82/4.04 thf(fact_3461_divmod__digit__0_I1_J,axiom,
% 3.82/4.04 ! [B2: int,A: int] :
% 3.82/4.04 ( ( ord_less_int @ zero_zero_int @ B2 )
% 3.82/4.04 => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) ) @ B2 )
% 3.82/4.04 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) ) )
% 3.82/4.04 = ( divide_divide_int @ A @ B2 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % divmod_digit_0(1)
% 3.82/4.04 thf(fact_3462_vebt__member_Osimps_I5_J,axiom,
% 3.82/4.04 ! [Mi: nat,Ma: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 3.82/4.04 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) @ X )
% 3.82/4.04 = ( ( X != Mi )
% 3.82/4.04 => ( ( X != Ma )
% 3.82/4.04 => ( ~ ( ord_less_nat @ X @ Mi )
% 3.82/4.04 & ( ~ ( ord_less_nat @ X @ Mi )
% 3.82/4.04 => ( ~ ( ord_less_nat @ Ma @ X )
% 3.82/4.04 & ( ~ ( ord_less_nat @ Ma @ X )
% 3.82/4.04 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 3.82/4.04 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 3.82/4.04 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % vebt_member.simps(5)
% 3.82/4.04 thf(fact_3463_VEBT__internal_Omembermima_Osimps_I4_J,axiom,
% 3.82/4.04 ! [Mi: nat,Ma: nat,V: nat,TreeList2: list_VEBT_VEBT,Vc: vEBT_VEBT,X: nat] :
% 3.82/4.04 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ V ) @ TreeList2 @ Vc ) @ X )
% 3.82/4.04 = ( ( X = Mi )
% 3.82/4.04 | ( X = Ma )
% 3.82/4.04 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 3.82/4.04 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 3.82/4.04 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % VEBT_internal.membermima.simps(4)
% 3.82/4.04 thf(fact_3464_zero__less__power__eq,axiom,
% 3.82/4.04 ! [A: real,N2: nat] :
% 3.82/4.04 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) )
% 3.82/4.04 = ( ( N2 = zero_zero_nat )
% 3.82/4.04 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 3.82/4.04 & ( A != zero_zero_real ) )
% 3.82/4.04 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 3.82/4.04 & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % zero_less_power_eq
% 3.82/4.04 thf(fact_3465_zero__less__power__eq,axiom,
% 3.82/4.04 ! [A: int,N2: nat] :
% 3.82/4.04 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) )
% 3.82/4.04 = ( ( N2 = zero_zero_nat )
% 3.82/4.04 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 3.82/4.04 & ( A != zero_zero_int ) )
% 3.82/4.04 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 3.82/4.04 & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % zero_less_power_eq
% 3.82/4.04 thf(fact_3466_VEBT__internal_Onaive__member_Oelims_I1_J,axiom,
% 3.82/4.04 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 3.82/4.04 ( ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 3.82/4.04 = Y )
% 3.82/4.04 => ( ! [A4: $o,B4: $o] :
% 3.82/4.04 ( ( X
% 3.82/4.04 = ( vEBT_Leaf @ A4 @ B4 ) )
% 3.82/4.04 => ( Y
% 3.82/4.04 = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 3.82/4.04 => A4 )
% 3.82/4.04 & ( ( Xa2 != zero_zero_nat )
% 3.82/4.04 => ( ( ( Xa2 = one_one_nat )
% 3.82/4.04 => B4 )
% 3.82/4.04 & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 3.82/4.04 => ( ( ? [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 3.82/4.04 ( X
% 3.82/4.04 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 3.82/4.04 => Y )
% 3.82/4.04 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 3.82/4.04 ( ? [S3: vEBT_VEBT] :
% 3.82/4.04 ( X
% 3.82/4.04 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 3.82/4.04 => ( Y
% 3.82/4.04 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 3.82/4.04 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 3.82/4.04 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % VEBT_internal.naive_member.elims(1)
% 3.82/4.04 thf(fact_3467_VEBT__internal_Onaive__member_Oelims_I2_J,axiom,
% 3.82/4.04 ! [X: vEBT_VEBT,Xa2: nat] :
% 3.82/4.04 ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 3.82/4.04 => ( ! [A4: $o,B4: $o] :
% 3.82/4.04 ( ( X
% 3.82/4.04 = ( vEBT_Leaf @ A4 @ B4 ) )
% 3.82/4.04 => ~ ( ( ( Xa2 = zero_zero_nat )
% 3.82/4.04 => A4 )
% 3.82/4.04 & ( ( Xa2 != zero_zero_nat )
% 3.82/4.04 => ( ( ( Xa2 = one_one_nat )
% 3.82/4.04 => B4 )
% 3.82/4.04 & ( Xa2 = one_one_nat ) ) ) ) )
% 3.82/4.04 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 3.82/4.04 ( ? [S3: vEBT_VEBT] :
% 3.82/4.04 ( X
% 3.82/4.04 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 3.82/4.04 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 3.82/4.04 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 3.82/4.04 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % VEBT_internal.naive_member.elims(2)
% 3.82/4.04 thf(fact_3468_VEBT__internal_Onaive__member_Oelims_I3_J,axiom,
% 3.82/4.04 ! [X: vEBT_VEBT,Xa2: nat] :
% 3.82/4.04 ( ~ ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 3.82/4.04 => ( ! [A4: $o,B4: $o] :
% 3.82/4.04 ( ( X
% 3.82/4.04 = ( vEBT_Leaf @ A4 @ B4 ) )
% 3.82/4.04 => ( ( ( Xa2 = zero_zero_nat )
% 3.82/4.04 => A4 )
% 3.82/4.04 & ( ( Xa2 != zero_zero_nat )
% 3.82/4.04 => ( ( ( Xa2 = one_one_nat )
% 3.82/4.04 => B4 )
% 3.82/4.04 & ( Xa2 = one_one_nat ) ) ) ) )
% 3.82/4.04 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 3.82/4.04 ( X
% 3.82/4.04 != ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 3.82/4.04 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 3.82/4.04 ( ? [S3: vEBT_VEBT] :
% 3.82/4.04 ( X
% 3.82/4.04 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 3.82/4.04 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 3.82/4.04 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 3.82/4.04 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % VEBT_internal.naive_member.elims(3)
% 3.82/4.04 thf(fact_3469_mod__double__modulus,axiom,
% 3.82/4.04 ! [M2: nat,X: nat] :
% 3.82/4.04 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 3.82/4.04 => ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 3.82/4.04 => ( ( ( modulo_modulo_nat @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 3.82/4.04 = ( modulo_modulo_nat @ X @ M2 ) )
% 3.82/4.04 | ( ( modulo_modulo_nat @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 3.82/4.04 = ( plus_plus_nat @ ( modulo_modulo_nat @ X @ M2 ) @ M2 ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % mod_double_modulus
% 3.82/4.04 thf(fact_3470_mod__double__modulus,axiom,
% 3.82/4.04 ! [M2: int,X: int] :
% 3.82/4.04 ( ( ord_less_int @ zero_zero_int @ M2 )
% 3.82/4.04 => ( ( ord_less_eq_int @ zero_zero_int @ X )
% 3.82/4.04 => ( ( ( modulo_modulo_int @ X @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) )
% 3.82/4.04 = ( modulo_modulo_int @ X @ M2 ) )
% 3.82/4.04 | ( ( modulo_modulo_int @ X @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) )
% 3.82/4.04 = ( plus_plus_int @ ( modulo_modulo_int @ X @ M2 ) @ M2 ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % mod_double_modulus
% 3.82/4.04 thf(fact_3471_VEBT__internal_Omembermima_Oelims_I2_J,axiom,
% 3.82/4.04 ! [X: vEBT_VEBT,Xa2: nat] :
% 3.82/4.04 ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 3.82/4.04 => ( ! [Mi2: nat,Ma2: nat] :
% 3.82/4.04 ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 3.82/4.04 ( X
% 3.82/4.04 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 3.82/4.04 => ~ ( ( Xa2 = Mi2 )
% 3.82/4.04 | ( Xa2 = Ma2 ) ) )
% 3.82/4.04 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 3.82/4.04 ( ? [Vc2: vEBT_VEBT] :
% 3.82/4.04 ( X
% 3.82/4.04 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 3.82/4.04 => ~ ( ( Xa2 = Mi2 )
% 3.82/4.04 | ( Xa2 = Ma2 )
% 3.82/4.04 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 3.82/4.04 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 3.82/4.04 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 3.82/4.04 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT] :
% 3.82/4.04 ( ? [Vd: vEBT_VEBT] :
% 3.82/4.04 ( X
% 3.82/4.04 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 3.82/4.04 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 3.82/4.04 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 3.82/4.04 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % VEBT_internal.membermima.elims(2)
% 3.82/4.04 thf(fact_3472_unset__bit__Suc,axiom,
% 3.82/4.04 ! [N2: nat,A: nat] :
% 3.82/4.04 ( ( bit_se4205575877204974255it_nat @ ( suc @ N2 ) @ A )
% 3.82/4.04 = ( 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 ) ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % unset_bit_Suc
% 3.82/4.04 thf(fact_3473_unset__bit__Suc,axiom,
% 3.82/4.04 ! [N2: nat,A: int] :
% 3.82/4.04 ( ( bit_se4203085406695923979it_int @ ( suc @ N2 ) @ A )
% 3.82/4.04 = ( 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 ) ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % unset_bit_Suc
% 3.82/4.04 thf(fact_3474_set__bit__Suc,axiom,
% 3.82/4.04 ! [N2: nat,A: nat] :
% 3.82/4.04 ( ( bit_se7882103937844011126it_nat @ ( suc @ N2 ) @ A )
% 3.82/4.04 = ( 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 ) ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % set_bit_Suc
% 3.82/4.04 thf(fact_3475_set__bit__Suc,axiom,
% 3.82/4.04 ! [N2: nat,A: int] :
% 3.82/4.04 ( ( bit_se7879613467334960850it_int @ ( suc @ N2 ) @ A )
% 3.82/4.04 = ( 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 ) ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % set_bit_Suc
% 3.82/4.04 thf(fact_3476_power__le__zero__eq,axiom,
% 3.82/4.04 ! [A: real,N2: nat] :
% 3.82/4.04 ( ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ zero_zero_real )
% 3.82/4.04 = ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.04 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 3.82/4.04 & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 3.82/4.04 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 3.82/4.04 & ( A = zero_zero_real ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % power_le_zero_eq
% 3.82/4.04 thf(fact_3477_power__le__zero__eq,axiom,
% 3.82/4.04 ! [A: int,N2: nat] :
% 3.82/4.04 ( ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ zero_zero_int )
% 3.82/4.04 = ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.04 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 3.82/4.04 & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 3.82/4.04 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 3.82/4.04 & ( A = zero_zero_int ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % power_le_zero_eq
% 3.82/4.04 thf(fact_3478_vebt__member_Oelims_I2_J,axiom,
% 3.82/4.04 ! [X: vEBT_VEBT,Xa2: nat] :
% 3.82/4.04 ( ( vEBT_vebt_member @ X @ Xa2 )
% 3.82/4.04 => ( ! [A4: $o,B4: $o] :
% 3.82/4.04 ( ( X
% 3.82/4.04 = ( vEBT_Leaf @ A4 @ B4 ) )
% 3.82/4.04 => ~ ( ( ( Xa2 = zero_zero_nat )
% 3.82/4.04 => A4 )
% 3.82/4.04 & ( ( Xa2 != zero_zero_nat )
% 3.82/4.04 => ( ( ( Xa2 = one_one_nat )
% 3.82/4.04 => B4 )
% 3.82/4.04 & ( Xa2 = one_one_nat ) ) ) ) )
% 3.82/4.04 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT] :
% 3.82/4.04 ( ? [Summary2: vEBT_VEBT] :
% 3.82/4.04 ( X
% 3.82/4.04 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 3.82/4.04 => ~ ( ( Xa2 != Mi2 )
% 3.82/4.04 => ( ( Xa2 != Ma2 )
% 3.82/4.04 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 3.82/4.04 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 3.82/4.04 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 3.82/4.04 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 3.82/4.04 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 3.82/4.04 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 3.82/4.04 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % vebt_member.elims(2)
% 3.82/4.04 thf(fact_3479_VEBT__internal_Omembermima_Oelims_I1_J,axiom,
% 3.82/4.04 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 3.82/4.04 ( ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 3.82/4.04 = Y )
% 3.82/4.04 => ( ( ? [Uu2: $o,Uv2: $o] :
% 3.82/4.04 ( X
% 3.82/4.04 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 3.82/4.04 => Y )
% 3.82/4.04 => ( ( ? [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 3.82/4.04 ( X
% 3.82/4.04 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 3.82/4.04 => Y )
% 3.82/4.04 => ( ! [Mi2: nat,Ma2: nat] :
% 3.82/4.04 ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 3.82/4.04 ( X
% 3.82/4.04 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 3.82/4.04 => ( Y
% 3.82/4.04 = ( ~ ( ( Xa2 = Mi2 )
% 3.82/4.04 | ( Xa2 = Ma2 ) ) ) ) )
% 3.82/4.04 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 3.82/4.04 ( ? [Vc2: vEBT_VEBT] :
% 3.82/4.04 ( X
% 3.82/4.04 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 3.82/4.04 => ( Y
% 3.82/4.04 = ( ~ ( ( Xa2 = Mi2 )
% 3.82/4.04 | ( Xa2 = Ma2 )
% 3.82/4.04 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 3.82/4.04 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 3.82/4.04 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) )
% 3.82/4.04 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT] :
% 3.82/4.04 ( ? [Vd: vEBT_VEBT] :
% 3.82/4.04 ( X
% 3.82/4.04 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 3.82/4.04 => ( Y
% 3.82/4.04 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 3.82/4.04 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 3.82/4.04 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % VEBT_internal.membermima.elims(1)
% 3.82/4.04 thf(fact_3480_VEBT__internal_Omembermima_Oelims_I3_J,axiom,
% 3.82/4.04 ! [X: vEBT_VEBT,Xa2: nat] :
% 3.82/4.04 ( ~ ( vEBT_VEBT_membermima @ X @ Xa2 )
% 3.82/4.04 => ( ! [Uu2: $o,Uv2: $o] :
% 3.82/4.04 ( X
% 3.82/4.04 != ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 3.82/4.04 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 3.82/4.04 ( X
% 3.82/4.04 != ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 3.82/4.04 => ( ! [Mi2: nat,Ma2: nat] :
% 3.82/4.04 ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 3.82/4.04 ( X
% 3.82/4.04 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 3.82/4.04 => ( ( Xa2 = Mi2 )
% 3.82/4.04 | ( Xa2 = Ma2 ) ) )
% 3.82/4.04 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 3.82/4.04 ( ? [Vc2: vEBT_VEBT] :
% 3.82/4.04 ( X
% 3.82/4.04 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 3.82/4.04 => ( ( Xa2 = Mi2 )
% 3.82/4.04 | ( Xa2 = Ma2 )
% 3.82/4.04 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 3.82/4.04 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 3.82/4.04 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 3.82/4.04 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT] :
% 3.82/4.04 ( ? [Vd: vEBT_VEBT] :
% 3.82/4.04 ( X
% 3.82/4.04 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 3.82/4.04 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 3.82/4.04 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 3.82/4.04 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % VEBT_internal.membermima.elims(3)
% 3.82/4.04 thf(fact_3481_vebt__insert_Osimps_I5_J,axiom,
% 3.82/4.04 ! [Mi: nat,Ma: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 3.82/4.04 ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) @ X )
% 3.82/4.04 = ( if_VEBT_VEBT
% 3.82/4.04 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 3.82/4.04 & ~ ( ( X = Mi )
% 3.82/4.04 | ( X = Ma ) ) )
% 3.82/4.04 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ X @ Mi ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ Ma ) ) ) @ ( suc @ ( suc @ Va2 ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) )
% 3.82/4.04 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % vebt_insert.simps(5)
% 3.82/4.04 thf(fact_3482_vebt__member_Oelims_I3_J,axiom,
% 3.82/4.04 ! [X: vEBT_VEBT,Xa2: nat] :
% 3.82/4.04 ( ~ ( vEBT_vebt_member @ X @ Xa2 )
% 3.82/4.04 => ( ! [A4: $o,B4: $o] :
% 3.82/4.04 ( ( X
% 3.82/4.04 = ( vEBT_Leaf @ A4 @ B4 ) )
% 3.82/4.04 => ( ( ( Xa2 = zero_zero_nat )
% 3.82/4.04 => A4 )
% 3.82/4.04 & ( ( Xa2 != zero_zero_nat )
% 3.82/4.04 => ( ( ( Xa2 = one_one_nat )
% 3.82/4.04 => B4 )
% 3.82/4.04 & ( Xa2 = one_one_nat ) ) ) ) )
% 3.82/4.04 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 3.82/4.04 ( X
% 3.82/4.04 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 3.82/4.04 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 3.82/4.04 ( X
% 3.82/4.04 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 3.82/4.04 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 3.82/4.04 ( X
% 3.82/4.04 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 3.82/4.04 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT] :
% 3.82/4.04 ( ? [Summary2: vEBT_VEBT] :
% 3.82/4.04 ( X
% 3.82/4.04 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 3.82/4.04 => ( ( Xa2 != Mi2 )
% 3.82/4.04 => ( ( Xa2 != Ma2 )
% 3.82/4.04 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 3.82/4.04 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 3.82/4.04 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 3.82/4.04 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 3.82/4.04 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 3.82/4.04 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 3.82/4.04 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % vebt_member.elims(3)
% 3.82/4.04 thf(fact_3483_vebt__member_Oelims_I1_J,axiom,
% 3.82/4.04 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 3.82/4.04 ( ( ( vEBT_vebt_member @ X @ Xa2 )
% 3.82/4.04 = Y )
% 3.82/4.04 => ( ! [A4: $o,B4: $o] :
% 3.82/4.04 ( ( X
% 3.82/4.04 = ( vEBT_Leaf @ A4 @ B4 ) )
% 3.82/4.04 => ( Y
% 3.82/4.04 = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 3.82/4.04 => A4 )
% 3.82/4.04 & ( ( Xa2 != zero_zero_nat )
% 3.82/4.04 => ( ( ( Xa2 = one_one_nat )
% 3.82/4.04 => B4 )
% 3.82/4.04 & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 3.82/4.04 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 3.82/4.04 ( X
% 3.82/4.04 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 3.82/4.04 => Y )
% 3.82/4.04 => ( ( ? [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 3.82/4.04 ( X
% 3.82/4.04 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 3.82/4.04 => Y )
% 3.82/4.04 => ( ( ? [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 3.82/4.04 ( X
% 3.82/4.04 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 3.82/4.04 => Y )
% 3.82/4.04 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT] :
% 3.82/4.04 ( ? [Summary2: vEBT_VEBT] :
% 3.82/4.04 ( X
% 3.82/4.04 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 3.82/4.04 => ( Y
% 3.82/4.04 = ( ~ ( ( Xa2 != Mi2 )
% 3.82/4.04 => ( ( Xa2 != Ma2 )
% 3.82/4.04 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 3.82/4.04 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 3.82/4.04 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 3.82/4.04 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 3.82/4.04 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 3.82/4.04 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 3.82/4.04 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % vebt_member.elims(1)
% 3.82/4.04 thf(fact_3484_divmod__digit__1_I1_J,axiom,
% 3.82/4.04 ! [A: nat,B2: nat] :
% 3.82/4.04 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 3.82/4.04 => ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 3.82/4.04 => ( ( ord_less_eq_nat @ B2 @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) ) )
% 3.82/4.04 => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) ) ) @ one_one_nat )
% 3.82/4.04 = ( divide_divide_nat @ A @ B2 ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % divmod_digit_1(1)
% 3.82/4.04 thf(fact_3485_divmod__digit__1_I1_J,axiom,
% 3.82/4.04 ! [A: int,B2: int] :
% 3.82/4.04 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 3.82/4.04 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 3.82/4.04 => ( ( ord_less_eq_int @ B2 @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) ) )
% 3.82/4.04 => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) ) ) @ one_one_int )
% 3.82/4.04 = ( divide_divide_int @ A @ B2 ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % divmod_digit_1(1)
% 3.82/4.04 thf(fact_3486_finite__nth__roots,axiom,
% 3.82/4.04 ! [N2: nat,C: complex] :
% 3.82/4.04 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.04 => ( finite3207457112153483333omplex
% 3.82/4.04 @ ( collect_complex
% 3.82/4.04 @ ^ [Z6: complex] :
% 3.82/4.04 ( ( power_power_complex @ Z6 @ N2 )
% 3.82/4.04 = C ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % finite_nth_roots
% 3.82/4.04 thf(fact_3487_finite__roots__unity,axiom,
% 3.82/4.04 ! [N2: nat] :
% 3.82/4.04 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 3.82/4.04 => ( finite_finite_real
% 3.82/4.04 @ ( collect_real
% 3.82/4.04 @ ^ [Z6: real] :
% 3.82/4.04 ( ( power_power_real @ Z6 @ N2 )
% 3.82/4.04 = one_one_real ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % finite_roots_unity
% 3.82/4.04 thf(fact_3488_finite__roots__unity,axiom,
% 3.82/4.04 ! [N2: nat] :
% 3.82/4.04 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 3.82/4.04 => ( finite3207457112153483333omplex
% 3.82/4.04 @ ( collect_complex
% 3.82/4.04 @ ^ [Z6: complex] :
% 3.82/4.04 ( ( power_power_complex @ Z6 @ N2 )
% 3.82/4.04 = one_one_complex ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % finite_roots_unity
% 3.82/4.04 thf(fact_3489_vebt__insert_Opelims,axiom,
% 3.82/4.04 ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 3.82/4.04 ( ( ( vEBT_vebt_insert @ X @ Xa2 )
% 3.82/4.04 = Y )
% 3.82/4.04 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 3.82/4.04 => ( ! [A4: $o,B4: $o] :
% 3.82/4.04 ( ( X
% 3.82/4.04 = ( vEBT_Leaf @ A4 @ B4 ) )
% 3.82/4.04 => ( ( ( ( Xa2 = zero_zero_nat )
% 3.82/4.04 => ( Y
% 3.82/4.04 = ( vEBT_Leaf @ $true @ B4 ) ) )
% 3.82/4.04 & ( ( Xa2 != zero_zero_nat )
% 3.82/4.04 => ( ( ( Xa2 = one_one_nat )
% 3.82/4.04 => ( Y
% 3.82/4.04 = ( vEBT_Leaf @ A4 @ $true ) ) )
% 3.82/4.04 & ( ( Xa2 != one_one_nat )
% 3.82/4.04 => ( Y
% 3.82/4.04 = ( vEBT_Leaf @ A4 @ B4 ) ) ) ) ) )
% 3.82/4.04 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B4 ) @ Xa2 ) ) ) )
% 3.82/4.04 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 3.82/4.04 ( ( X
% 3.82/4.04 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) )
% 3.82/4.04 => ( ( Y
% 3.82/4.04 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) )
% 3.82/4.04 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) @ Xa2 ) ) ) )
% 3.82/4.04 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 3.82/4.04 ( ( X
% 3.82/4.04 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) )
% 3.82/4.04 => ( ( Y
% 3.82/4.04 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) )
% 3.82/4.04 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) @ Xa2 ) ) ) )
% 3.82/4.04 => ( ! [V2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 3.82/4.04 ( ( X
% 3.82/4.04 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) )
% 3.82/4.04 => ( ( Y
% 3.82/4.04 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) )
% 3.82/4.04 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) )
% 3.82/4.04 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 3.82/4.04 ( ( X
% 3.82/4.04 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 3.82/4.04 => ( ( Y
% 3.82/4.04 = ( if_VEBT_VEBT
% 3.82/4.04 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 3.82/4.04 & ~ ( ( Xa2 = Mi2 )
% 3.82/4.04 | ( Xa2 = Ma2 ) ) )
% 3.82/4.04 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Xa2 @ Mi2 ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ Ma2 ) ) ) @ ( suc @ ( suc @ Va ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 3.82/4.04 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) ) )
% 3.82/4.04 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % vebt_insert.pelims
% 3.82/4.04 thf(fact_3490_flip__bit__Suc,axiom,
% 3.82/4.04 ! [N2: nat,A: nat] :
% 3.82/4.04 ( ( bit_se2161824704523386999it_nat @ ( suc @ N2 ) @ A )
% 3.82/4.04 = ( 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 ) ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % flip_bit_Suc
% 3.82/4.04 thf(fact_3491_flip__bit__Suc,axiom,
% 3.82/4.04 ! [N2: nat,A: int] :
% 3.82/4.04 ( ( bit_se2159334234014336723it_int @ ( suc @ N2 ) @ A )
% 3.82/4.04 = ( 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 ) ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % flip_bit_Suc
% 3.82/4.04 thf(fact_3492_prod_Ofinite__Collect__op,axiom,
% 3.82/4.04 ! [I6: set_real,X: real > nat,Y: real > nat] :
% 3.82/4.04 ( ( finite_finite_real
% 3.82/4.04 @ ( collect_real
% 3.82/4.04 @ ^ [I3: real] :
% 3.82/4.04 ( ( member_real @ I3 @ I6 )
% 3.82/4.04 & ( ( X @ I3 )
% 3.82/4.04 != one_one_nat ) ) ) )
% 3.82/4.04 => ( ( finite_finite_real
% 3.82/4.04 @ ( collect_real
% 3.82/4.04 @ ^ [I3: real] :
% 3.82/4.04 ( ( member_real @ I3 @ I6 )
% 3.82/4.04 & ( ( Y @ I3 )
% 3.82/4.04 != one_one_nat ) ) ) )
% 3.82/4.04 => ( finite_finite_real
% 3.82/4.04 @ ( collect_real
% 3.82/4.04 @ ^ [I3: real] :
% 3.82/4.04 ( ( member_real @ I3 @ I6 )
% 3.82/4.04 & ( ( times_times_nat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 3.82/4.04 != one_one_nat ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % prod.finite_Collect_op
% 3.82/4.04 thf(fact_3493_prod_Ofinite__Collect__op,axiom,
% 3.82/4.04 ! [I6: set_nat,X: nat > nat,Y: nat > nat] :
% 3.82/4.04 ( ( finite_finite_nat
% 3.82/4.04 @ ( collect_nat
% 3.82/4.04 @ ^ [I3: nat] :
% 3.82/4.04 ( ( member_nat @ I3 @ I6 )
% 3.82/4.04 & ( ( X @ I3 )
% 3.82/4.04 != one_one_nat ) ) ) )
% 3.82/4.04 => ( ( finite_finite_nat
% 3.82/4.04 @ ( collect_nat
% 3.82/4.04 @ ^ [I3: nat] :
% 3.82/4.04 ( ( member_nat @ I3 @ I6 )
% 3.82/4.04 & ( ( Y @ I3 )
% 3.82/4.04 != one_one_nat ) ) ) )
% 3.82/4.04 => ( finite_finite_nat
% 3.82/4.04 @ ( collect_nat
% 3.82/4.04 @ ^ [I3: nat] :
% 3.82/4.04 ( ( member_nat @ I3 @ I6 )
% 3.82/4.04 & ( ( times_times_nat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 3.82/4.04 != one_one_nat ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % prod.finite_Collect_op
% 3.82/4.04 thf(fact_3494_prod_Ofinite__Collect__op,axiom,
% 3.82/4.04 ! [I6: set_complex,X: complex > nat,Y: complex > nat] :
% 3.82/4.04 ( ( finite3207457112153483333omplex
% 3.82/4.04 @ ( collect_complex
% 3.82/4.04 @ ^ [I3: complex] :
% 3.82/4.04 ( ( member_complex @ I3 @ I6 )
% 3.82/4.04 & ( ( X @ I3 )
% 3.82/4.04 != one_one_nat ) ) ) )
% 3.82/4.04 => ( ( finite3207457112153483333omplex
% 3.82/4.04 @ ( collect_complex
% 3.82/4.04 @ ^ [I3: complex] :
% 3.82/4.04 ( ( member_complex @ I3 @ I6 )
% 3.82/4.04 & ( ( Y @ I3 )
% 3.82/4.04 != one_one_nat ) ) ) )
% 3.82/4.04 => ( finite3207457112153483333omplex
% 3.82/4.04 @ ( collect_complex
% 3.82/4.04 @ ^ [I3: complex] :
% 3.82/4.04 ( ( member_complex @ I3 @ I6 )
% 3.82/4.04 & ( ( times_times_nat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 3.82/4.04 != one_one_nat ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % prod.finite_Collect_op
% 3.82/4.04 thf(fact_3495_prod_Ofinite__Collect__op,axiom,
% 3.82/4.04 ! [I6: set_int,X: int > nat,Y: int > nat] :
% 3.82/4.04 ( ( finite_finite_int
% 3.82/4.04 @ ( collect_int
% 3.82/4.04 @ ^ [I3: int] :
% 3.82/4.04 ( ( member_int @ I3 @ I6 )
% 3.82/4.04 & ( ( X @ I3 )
% 3.82/4.04 != one_one_nat ) ) ) )
% 3.82/4.04 => ( ( finite_finite_int
% 3.82/4.04 @ ( collect_int
% 3.82/4.04 @ ^ [I3: int] :
% 3.82/4.04 ( ( member_int @ I3 @ I6 )
% 3.82/4.04 & ( ( Y @ I3 )
% 3.82/4.04 != one_one_nat ) ) ) )
% 3.82/4.04 => ( finite_finite_int
% 3.82/4.04 @ ( collect_int
% 3.82/4.04 @ ^ [I3: int] :
% 3.82/4.04 ( ( member_int @ I3 @ I6 )
% 3.82/4.04 & ( ( times_times_nat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 3.82/4.04 != one_one_nat ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % prod.finite_Collect_op
% 3.82/4.04 thf(fact_3496_prod_Ofinite__Collect__op,axiom,
% 3.82/4.04 ! [I6: set_Extended_enat,X: extended_enat > nat,Y: extended_enat > nat] :
% 3.82/4.04 ( ( finite4001608067531595151d_enat
% 3.82/4.04 @ ( collec4429806609662206161d_enat
% 3.82/4.04 @ ^ [I3: extended_enat] :
% 3.82/4.04 ( ( member_Extended_enat @ I3 @ I6 )
% 3.82/4.04 & ( ( X @ I3 )
% 3.82/4.04 != one_one_nat ) ) ) )
% 3.82/4.04 => ( ( finite4001608067531595151d_enat
% 3.82/4.04 @ ( collec4429806609662206161d_enat
% 3.82/4.04 @ ^ [I3: extended_enat] :
% 3.82/4.04 ( ( member_Extended_enat @ I3 @ I6 )
% 3.82/4.04 & ( ( Y @ I3 )
% 3.82/4.04 != one_one_nat ) ) ) )
% 3.82/4.04 => ( finite4001608067531595151d_enat
% 3.82/4.04 @ ( collec4429806609662206161d_enat
% 3.82/4.04 @ ^ [I3: extended_enat] :
% 3.82/4.04 ( ( member_Extended_enat @ I3 @ I6 )
% 3.82/4.04 & ( ( times_times_nat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 3.82/4.04 != one_one_nat ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % prod.finite_Collect_op
% 3.82/4.04 thf(fact_3497_prod_Ofinite__Collect__op,axiom,
% 3.82/4.04 ! [I6: set_real,X: real > int,Y: real > int] :
% 3.82/4.04 ( ( finite_finite_real
% 3.82/4.04 @ ( collect_real
% 3.82/4.04 @ ^ [I3: real] :
% 3.82/4.04 ( ( member_real @ I3 @ I6 )
% 3.82/4.04 & ( ( X @ I3 )
% 3.82/4.04 != one_one_int ) ) ) )
% 3.82/4.04 => ( ( finite_finite_real
% 3.82/4.04 @ ( collect_real
% 3.82/4.04 @ ^ [I3: real] :
% 3.82/4.04 ( ( member_real @ I3 @ I6 )
% 3.82/4.04 & ( ( Y @ I3 )
% 3.82/4.04 != one_one_int ) ) ) )
% 3.82/4.04 => ( finite_finite_real
% 3.82/4.04 @ ( collect_real
% 3.82/4.04 @ ^ [I3: real] :
% 3.82/4.04 ( ( member_real @ I3 @ I6 )
% 3.82/4.04 & ( ( times_times_int @ ( X @ I3 ) @ ( Y @ I3 ) )
% 3.82/4.04 != one_one_int ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % prod.finite_Collect_op
% 3.82/4.04 thf(fact_3498_prod_Ofinite__Collect__op,axiom,
% 3.82/4.04 ! [I6: set_nat,X: nat > int,Y: nat > int] :
% 3.82/4.04 ( ( finite_finite_nat
% 3.82/4.04 @ ( collect_nat
% 3.82/4.04 @ ^ [I3: nat] :
% 3.82/4.04 ( ( member_nat @ I3 @ I6 )
% 3.82/4.04 & ( ( X @ I3 )
% 3.82/4.04 != one_one_int ) ) ) )
% 3.82/4.04 => ( ( finite_finite_nat
% 3.82/4.04 @ ( collect_nat
% 3.82/4.04 @ ^ [I3: nat] :
% 3.82/4.04 ( ( member_nat @ I3 @ I6 )
% 3.82/4.04 & ( ( Y @ I3 )
% 3.82/4.04 != one_one_int ) ) ) )
% 3.82/4.04 => ( finite_finite_nat
% 3.82/4.04 @ ( collect_nat
% 3.82/4.04 @ ^ [I3: nat] :
% 3.82/4.04 ( ( member_nat @ I3 @ I6 )
% 3.82/4.04 & ( ( times_times_int @ ( X @ I3 ) @ ( Y @ I3 ) )
% 3.82/4.04 != one_one_int ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % prod.finite_Collect_op
% 3.82/4.04 thf(fact_3499_prod_Ofinite__Collect__op,axiom,
% 3.82/4.04 ! [I6: set_complex,X: complex > int,Y: complex > int] :
% 3.82/4.04 ( ( finite3207457112153483333omplex
% 3.82/4.04 @ ( collect_complex
% 3.82/4.04 @ ^ [I3: complex] :
% 3.82/4.04 ( ( member_complex @ I3 @ I6 )
% 3.82/4.04 & ( ( X @ I3 )
% 3.82/4.04 != one_one_int ) ) ) )
% 3.82/4.04 => ( ( finite3207457112153483333omplex
% 3.82/4.04 @ ( collect_complex
% 3.82/4.04 @ ^ [I3: complex] :
% 3.82/4.04 ( ( member_complex @ I3 @ I6 )
% 3.82/4.04 & ( ( Y @ I3 )
% 3.82/4.04 != one_one_int ) ) ) )
% 3.82/4.04 => ( finite3207457112153483333omplex
% 3.82/4.04 @ ( collect_complex
% 3.82/4.04 @ ^ [I3: complex] :
% 3.82/4.04 ( ( member_complex @ I3 @ I6 )
% 3.82/4.04 & ( ( times_times_int @ ( X @ I3 ) @ ( Y @ I3 ) )
% 3.82/4.04 != one_one_int ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % prod.finite_Collect_op
% 3.82/4.04 thf(fact_3500_prod_Ofinite__Collect__op,axiom,
% 3.82/4.04 ! [I6: set_int,X: int > int,Y: int > int] :
% 3.82/4.04 ( ( finite_finite_int
% 3.82/4.04 @ ( collect_int
% 3.82/4.04 @ ^ [I3: int] :
% 3.82/4.04 ( ( member_int @ I3 @ I6 )
% 3.82/4.04 & ( ( X @ I3 )
% 3.82/4.04 != one_one_int ) ) ) )
% 3.82/4.04 => ( ( finite_finite_int
% 3.82/4.04 @ ( collect_int
% 3.82/4.04 @ ^ [I3: int] :
% 3.82/4.04 ( ( member_int @ I3 @ I6 )
% 3.82/4.04 & ( ( Y @ I3 )
% 3.82/4.04 != one_one_int ) ) ) )
% 3.82/4.04 => ( finite_finite_int
% 3.82/4.04 @ ( collect_int
% 3.82/4.04 @ ^ [I3: int] :
% 3.82/4.04 ( ( member_int @ I3 @ I6 )
% 3.82/4.04 & ( ( times_times_int @ ( X @ I3 ) @ ( Y @ I3 ) )
% 3.82/4.04 != one_one_int ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % prod.finite_Collect_op
% 3.82/4.04 thf(fact_3501_prod_Ofinite__Collect__op,axiom,
% 3.82/4.04 ! [I6: set_Extended_enat,X: extended_enat > int,Y: extended_enat > int] :
% 3.82/4.04 ( ( finite4001608067531595151d_enat
% 3.82/4.04 @ ( collec4429806609662206161d_enat
% 3.82/4.04 @ ^ [I3: extended_enat] :
% 3.82/4.04 ( ( member_Extended_enat @ I3 @ I6 )
% 3.82/4.04 & ( ( X @ I3 )
% 3.82/4.04 != one_one_int ) ) ) )
% 3.82/4.04 => ( ( finite4001608067531595151d_enat
% 3.82/4.04 @ ( collec4429806609662206161d_enat
% 3.82/4.04 @ ^ [I3: extended_enat] :
% 3.82/4.04 ( ( member_Extended_enat @ I3 @ I6 )
% 3.82/4.04 & ( ( Y @ I3 )
% 3.82/4.04 != one_one_int ) ) ) )
% 3.82/4.04 => ( finite4001608067531595151d_enat
% 3.82/4.04 @ ( collec4429806609662206161d_enat
% 3.82/4.04 @ ^ [I3: extended_enat] :
% 3.82/4.04 ( ( member_Extended_enat @ I3 @ I6 )
% 3.82/4.04 & ( ( times_times_int @ ( X @ I3 ) @ ( Y @ I3 ) )
% 3.82/4.04 != one_one_int ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % prod.finite_Collect_op
% 3.82/4.04 thf(fact_3502_sum_Ofinite__Collect__op,axiom,
% 3.82/4.04 ! [I6: set_real,X: real > nat,Y: real > nat] :
% 3.82/4.04 ( ( finite_finite_real
% 3.82/4.04 @ ( collect_real
% 3.82/4.04 @ ^ [I3: real] :
% 3.82/4.04 ( ( member_real @ I3 @ I6 )
% 3.82/4.04 & ( ( X @ I3 )
% 3.82/4.04 != zero_zero_nat ) ) ) )
% 3.82/4.04 => ( ( finite_finite_real
% 3.82/4.04 @ ( collect_real
% 3.82/4.04 @ ^ [I3: real] :
% 3.82/4.04 ( ( member_real @ I3 @ I6 )
% 3.82/4.04 & ( ( Y @ I3 )
% 3.82/4.04 != zero_zero_nat ) ) ) )
% 3.82/4.04 => ( finite_finite_real
% 3.82/4.04 @ ( collect_real
% 3.82/4.04 @ ^ [I3: real] :
% 3.82/4.04 ( ( member_real @ I3 @ I6 )
% 3.82/4.04 & ( ( plus_plus_nat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 3.82/4.04 != zero_zero_nat ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % sum.finite_Collect_op
% 3.82/4.04 thf(fact_3503_sum_Ofinite__Collect__op,axiom,
% 3.82/4.04 ! [I6: set_nat,X: nat > nat,Y: nat > nat] :
% 3.82/4.04 ( ( finite_finite_nat
% 3.82/4.04 @ ( collect_nat
% 3.82/4.04 @ ^ [I3: nat] :
% 3.82/4.04 ( ( member_nat @ I3 @ I6 )
% 3.82/4.04 & ( ( X @ I3 )
% 3.82/4.04 != zero_zero_nat ) ) ) )
% 3.82/4.04 => ( ( finite_finite_nat
% 3.82/4.04 @ ( collect_nat
% 3.82/4.04 @ ^ [I3: nat] :
% 3.82/4.04 ( ( member_nat @ I3 @ I6 )
% 3.82/4.04 & ( ( Y @ I3 )
% 3.82/4.04 != zero_zero_nat ) ) ) )
% 3.82/4.04 => ( finite_finite_nat
% 3.82/4.04 @ ( collect_nat
% 3.82/4.04 @ ^ [I3: nat] :
% 3.82/4.04 ( ( member_nat @ I3 @ I6 )
% 3.82/4.04 & ( ( plus_plus_nat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 3.82/4.04 != zero_zero_nat ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % sum.finite_Collect_op
% 3.82/4.04 thf(fact_3504_sum_Ofinite__Collect__op,axiom,
% 3.82/4.04 ! [I6: set_complex,X: complex > nat,Y: complex > nat] :
% 3.82/4.04 ( ( finite3207457112153483333omplex
% 3.82/4.04 @ ( collect_complex
% 3.82/4.04 @ ^ [I3: complex] :
% 3.82/4.04 ( ( member_complex @ I3 @ I6 )
% 3.82/4.04 & ( ( X @ I3 )
% 3.82/4.04 != zero_zero_nat ) ) ) )
% 3.82/4.04 => ( ( finite3207457112153483333omplex
% 3.82/4.04 @ ( collect_complex
% 3.82/4.04 @ ^ [I3: complex] :
% 3.82/4.04 ( ( member_complex @ I3 @ I6 )
% 3.82/4.04 & ( ( Y @ I3 )
% 3.82/4.04 != zero_zero_nat ) ) ) )
% 3.82/4.04 => ( finite3207457112153483333omplex
% 3.82/4.04 @ ( collect_complex
% 3.82/4.04 @ ^ [I3: complex] :
% 3.82/4.04 ( ( member_complex @ I3 @ I6 )
% 3.82/4.04 & ( ( plus_plus_nat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 3.82/4.04 != zero_zero_nat ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % sum.finite_Collect_op
% 3.82/4.04 thf(fact_3505_sum_Ofinite__Collect__op,axiom,
% 3.82/4.04 ! [I6: set_int,X: int > nat,Y: int > nat] :
% 3.82/4.04 ( ( finite_finite_int
% 3.82/4.04 @ ( collect_int
% 3.82/4.04 @ ^ [I3: int] :
% 3.82/4.04 ( ( member_int @ I3 @ I6 )
% 3.82/4.04 & ( ( X @ I3 )
% 3.82/4.04 != zero_zero_nat ) ) ) )
% 3.82/4.04 => ( ( finite_finite_int
% 3.82/4.04 @ ( collect_int
% 3.82/4.04 @ ^ [I3: int] :
% 3.82/4.04 ( ( member_int @ I3 @ I6 )
% 3.82/4.04 & ( ( Y @ I3 )
% 3.82/4.04 != zero_zero_nat ) ) ) )
% 3.82/4.04 => ( finite_finite_int
% 3.82/4.04 @ ( collect_int
% 3.82/4.04 @ ^ [I3: int] :
% 3.82/4.04 ( ( member_int @ I3 @ I6 )
% 3.82/4.04 & ( ( plus_plus_nat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 3.82/4.04 != zero_zero_nat ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % sum.finite_Collect_op
% 3.82/4.04 thf(fact_3506_sum_Ofinite__Collect__op,axiom,
% 3.82/4.04 ! [I6: set_Extended_enat,X: extended_enat > nat,Y: extended_enat > nat] :
% 3.82/4.04 ( ( finite4001608067531595151d_enat
% 3.82/4.04 @ ( collec4429806609662206161d_enat
% 3.82/4.04 @ ^ [I3: extended_enat] :
% 3.82/4.04 ( ( member_Extended_enat @ I3 @ I6 )
% 3.82/4.04 & ( ( X @ I3 )
% 3.82/4.04 != zero_zero_nat ) ) ) )
% 3.82/4.04 => ( ( finite4001608067531595151d_enat
% 3.82/4.04 @ ( collec4429806609662206161d_enat
% 3.82/4.04 @ ^ [I3: extended_enat] :
% 3.82/4.04 ( ( member_Extended_enat @ I3 @ I6 )
% 3.82/4.04 & ( ( Y @ I3 )
% 3.82/4.04 != zero_zero_nat ) ) ) )
% 3.82/4.04 => ( finite4001608067531595151d_enat
% 3.82/4.04 @ ( collec4429806609662206161d_enat
% 3.82/4.04 @ ^ [I3: extended_enat] :
% 3.82/4.04 ( ( member_Extended_enat @ I3 @ I6 )
% 3.82/4.04 & ( ( plus_plus_nat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 3.82/4.04 != zero_zero_nat ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % sum.finite_Collect_op
% 3.82/4.04 thf(fact_3507_sum_Ofinite__Collect__op,axiom,
% 3.82/4.04 ! [I6: set_real,X: real > real,Y: real > real] :
% 3.82/4.04 ( ( finite_finite_real
% 3.82/4.04 @ ( collect_real
% 3.82/4.04 @ ^ [I3: real] :
% 3.82/4.04 ( ( member_real @ I3 @ I6 )
% 3.82/4.04 & ( ( X @ I3 )
% 3.82/4.04 != zero_zero_real ) ) ) )
% 3.82/4.04 => ( ( finite_finite_real
% 3.82/4.04 @ ( collect_real
% 3.82/4.04 @ ^ [I3: real] :
% 3.82/4.04 ( ( member_real @ I3 @ I6 )
% 3.82/4.04 & ( ( Y @ I3 )
% 3.82/4.04 != zero_zero_real ) ) ) )
% 3.82/4.04 => ( finite_finite_real
% 3.82/4.04 @ ( collect_real
% 3.82/4.04 @ ^ [I3: real] :
% 3.82/4.04 ( ( member_real @ I3 @ I6 )
% 3.82/4.04 & ( ( plus_plus_real @ ( X @ I3 ) @ ( Y @ I3 ) )
% 3.82/4.04 != zero_zero_real ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % sum.finite_Collect_op
% 3.82/4.04 thf(fact_3508_sum_Ofinite__Collect__op,axiom,
% 3.82/4.04 ! [I6: set_nat,X: nat > real,Y: nat > real] :
% 3.82/4.04 ( ( finite_finite_nat
% 3.82/4.04 @ ( collect_nat
% 3.82/4.04 @ ^ [I3: nat] :
% 3.82/4.04 ( ( member_nat @ I3 @ I6 )
% 3.82/4.04 & ( ( X @ I3 )
% 3.82/4.04 != zero_zero_real ) ) ) )
% 3.82/4.04 => ( ( finite_finite_nat
% 3.82/4.04 @ ( collect_nat
% 3.82/4.04 @ ^ [I3: nat] :
% 3.82/4.04 ( ( member_nat @ I3 @ I6 )
% 3.82/4.04 & ( ( Y @ I3 )
% 3.82/4.04 != zero_zero_real ) ) ) )
% 3.82/4.04 => ( finite_finite_nat
% 3.82/4.04 @ ( collect_nat
% 3.82/4.04 @ ^ [I3: nat] :
% 3.82/4.04 ( ( member_nat @ I3 @ I6 )
% 3.82/4.04 & ( ( plus_plus_real @ ( X @ I3 ) @ ( Y @ I3 ) )
% 3.82/4.04 != zero_zero_real ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % sum.finite_Collect_op
% 3.82/4.04 thf(fact_3509_sum_Ofinite__Collect__op,axiom,
% 3.82/4.04 ! [I6: set_complex,X: complex > real,Y: complex > real] :
% 3.82/4.04 ( ( finite3207457112153483333omplex
% 3.82/4.04 @ ( collect_complex
% 3.82/4.04 @ ^ [I3: complex] :
% 3.82/4.04 ( ( member_complex @ I3 @ I6 )
% 3.82/4.04 & ( ( X @ I3 )
% 3.82/4.04 != zero_zero_real ) ) ) )
% 3.82/4.04 => ( ( finite3207457112153483333omplex
% 3.82/4.04 @ ( collect_complex
% 3.82/4.04 @ ^ [I3: complex] :
% 3.82/4.04 ( ( member_complex @ I3 @ I6 )
% 3.82/4.04 & ( ( Y @ I3 )
% 3.82/4.04 != zero_zero_real ) ) ) )
% 3.82/4.04 => ( finite3207457112153483333omplex
% 3.82/4.04 @ ( collect_complex
% 3.82/4.04 @ ^ [I3: complex] :
% 3.82/4.04 ( ( member_complex @ I3 @ I6 )
% 3.82/4.04 & ( ( plus_plus_real @ ( X @ I3 ) @ ( Y @ I3 ) )
% 3.82/4.04 != zero_zero_real ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % sum.finite_Collect_op
% 3.82/4.04 thf(fact_3510_sum_Ofinite__Collect__op,axiom,
% 3.82/4.04 ! [I6: set_int,X: int > real,Y: int > real] :
% 3.82/4.04 ( ( finite_finite_int
% 3.82/4.04 @ ( collect_int
% 3.82/4.04 @ ^ [I3: int] :
% 3.82/4.04 ( ( member_int @ I3 @ I6 )
% 3.82/4.04 & ( ( X @ I3 )
% 3.82/4.04 != zero_zero_real ) ) ) )
% 3.82/4.04 => ( ( finite_finite_int
% 3.82/4.04 @ ( collect_int
% 3.82/4.04 @ ^ [I3: int] :
% 3.82/4.04 ( ( member_int @ I3 @ I6 )
% 3.82/4.04 & ( ( Y @ I3 )
% 3.82/4.04 != zero_zero_real ) ) ) )
% 3.82/4.04 => ( finite_finite_int
% 3.82/4.04 @ ( collect_int
% 3.82/4.04 @ ^ [I3: int] :
% 3.82/4.04 ( ( member_int @ I3 @ I6 )
% 3.82/4.04 & ( ( plus_plus_real @ ( X @ I3 ) @ ( Y @ I3 ) )
% 3.82/4.04 != zero_zero_real ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % sum.finite_Collect_op
% 3.82/4.04 thf(fact_3511_sum_Ofinite__Collect__op,axiom,
% 3.82/4.04 ! [I6: set_Extended_enat,X: extended_enat > real,Y: extended_enat > real] :
% 3.82/4.04 ( ( finite4001608067531595151d_enat
% 3.82/4.04 @ ( collec4429806609662206161d_enat
% 3.82/4.04 @ ^ [I3: extended_enat] :
% 3.82/4.04 ( ( member_Extended_enat @ I3 @ I6 )
% 3.82/4.04 & ( ( X @ I3 )
% 3.82/4.04 != zero_zero_real ) ) ) )
% 3.82/4.04 => ( ( finite4001608067531595151d_enat
% 3.82/4.04 @ ( collec4429806609662206161d_enat
% 3.82/4.04 @ ^ [I3: extended_enat] :
% 3.82/4.04 ( ( member_Extended_enat @ I3 @ I6 )
% 3.82/4.04 & ( ( Y @ I3 )
% 3.82/4.04 != zero_zero_real ) ) ) )
% 3.82/4.04 => ( finite4001608067531595151d_enat
% 3.82/4.04 @ ( collec4429806609662206161d_enat
% 3.82/4.04 @ ^ [I3: extended_enat] :
% 3.82/4.04 ( ( member_Extended_enat @ I3 @ I6 )
% 3.82/4.04 & ( ( plus_plus_real @ ( X @ I3 ) @ ( Y @ I3 ) )
% 3.82/4.04 != zero_zero_real ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % sum.finite_Collect_op
% 3.82/4.04 thf(fact_3512_vebt__member_Opelims_I1_J,axiom,
% 3.82/4.04 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 3.82/4.04 ( ( ( vEBT_vebt_member @ X @ Xa2 )
% 3.82/4.04 = Y )
% 3.82/4.04 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 3.82/4.04 => ( ! [A4: $o,B4: $o] :
% 3.82/4.04 ( ( X
% 3.82/4.04 = ( vEBT_Leaf @ A4 @ B4 ) )
% 3.82/4.04 => ( ( Y
% 3.82/4.04 = ( ( ( Xa2 = zero_zero_nat )
% 3.82/4.04 => A4 )
% 3.82/4.04 & ( ( Xa2 != zero_zero_nat )
% 3.82/4.04 => ( ( ( Xa2 = one_one_nat )
% 3.82/4.04 => B4 )
% 3.82/4.04 & ( Xa2 = one_one_nat ) ) ) ) )
% 3.82/4.04 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B4 ) @ Xa2 ) ) ) )
% 3.82/4.04 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 3.82/4.04 ( ( X
% 3.82/4.04 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 3.82/4.04 => ( ~ Y
% 3.82/4.04 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa2 ) ) ) )
% 3.82/4.04 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 3.82/4.04 ( ( X
% 3.82/4.04 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 3.82/4.04 => ( ~ Y
% 3.82/4.04 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 3.82/4.04 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 3.82/4.04 ( ( X
% 3.82/4.04 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 3.82/4.04 => ( ~ Y
% 3.82/4.04 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) ) )
% 3.82/4.04 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 3.82/4.04 ( ( X
% 3.82/4.04 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 3.82/4.04 => ( ( Y
% 3.82/4.04 = ( ( Xa2 != Mi2 )
% 3.82/4.04 => ( ( Xa2 != Ma2 )
% 3.82/4.04 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 3.82/4.04 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 3.82/4.04 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 3.82/4.04 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 3.82/4.04 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 3.82/4.04 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 3.82/4.04 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) )
% 3.82/4.04 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % vebt_member.pelims(1)
% 3.82/4.04 thf(fact_3513_vebt__member_Opelims_I3_J,axiom,
% 3.82/4.04 ! [X: vEBT_VEBT,Xa2: nat] :
% 3.82/4.04 ( ~ ( vEBT_vebt_member @ X @ Xa2 )
% 3.82/4.04 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 3.82/4.04 => ( ! [A4: $o,B4: $o] :
% 3.82/4.04 ( ( X
% 3.82/4.04 = ( vEBT_Leaf @ A4 @ B4 ) )
% 3.82/4.04 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B4 ) @ Xa2 ) )
% 3.82/4.04 => ( ( ( Xa2 = zero_zero_nat )
% 3.82/4.04 => A4 )
% 3.82/4.04 & ( ( Xa2 != zero_zero_nat )
% 3.82/4.04 => ( ( ( Xa2 = one_one_nat )
% 3.82/4.04 => B4 )
% 3.82/4.04 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 3.82/4.04 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 3.82/4.04 ( ( X
% 3.82/4.04 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 3.82/4.04 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa2 ) ) )
% 3.82/4.04 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 3.82/4.04 ( ( X
% 3.82/4.04 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 3.82/4.04 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) )
% 3.82/4.04 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 3.82/4.04 ( ( X
% 3.82/4.04 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 3.82/4.04 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) )
% 3.82/4.04 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 3.82/4.04 ( ( X
% 3.82/4.04 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 3.82/4.04 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) )
% 3.82/4.04 => ( ( Xa2 != Mi2 )
% 3.82/4.04 => ( ( Xa2 != Ma2 )
% 3.82/4.04 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 3.82/4.04 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 3.82/4.04 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 3.82/4.04 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 3.82/4.04 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 3.82/4.04 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 3.82/4.04 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % vebt_member.pelims(3)
% 3.82/4.04 thf(fact_3514_vebt__member_Opelims_I2_J,axiom,
% 3.82/4.04 ! [X: vEBT_VEBT,Xa2: nat] :
% 3.82/4.04 ( ( vEBT_vebt_member @ X @ Xa2 )
% 3.82/4.04 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 3.82/4.04 => ( ! [A4: $o,B4: $o] :
% 3.82/4.04 ( ( X
% 3.82/4.04 = ( vEBT_Leaf @ A4 @ B4 ) )
% 3.82/4.04 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B4 ) @ Xa2 ) )
% 3.82/4.04 => ~ ( ( ( Xa2 = zero_zero_nat )
% 3.82/4.04 => A4 )
% 3.82/4.04 & ( ( Xa2 != zero_zero_nat )
% 3.82/4.04 => ( ( ( Xa2 = one_one_nat )
% 3.82/4.04 => B4 )
% 3.82/4.04 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 3.82/4.04 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 3.82/4.04 ( ( X
% 3.82/4.04 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 3.82/4.04 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) )
% 3.82/4.04 => ~ ( ( Xa2 != Mi2 )
% 3.82/4.04 => ( ( Xa2 != Ma2 )
% 3.82/4.04 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 3.82/4.04 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 3.82/4.04 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 3.82/4.04 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 3.82/4.04 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 3.82/4.04 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 3.82/4.04 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % vebt_member.pelims(2)
% 3.82/4.04 thf(fact_3515_dvd__antisym,axiom,
% 3.82/4.04 ! [M2: nat,N2: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ M2 @ N2 )
% 3.82/4.04 => ( ( dvd_dvd_nat @ N2 @ M2 )
% 3.82/4.04 => ( M2 = N2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % dvd_antisym
% 3.82/4.04 thf(fact_3516_even__flip__bit__iff,axiom,
% 3.82/4.04 ! [M2: nat,A: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ M2 @ A ) )
% 3.82/4.04 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 3.82/4.04 != ( M2 = zero_zero_nat ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % even_flip_bit_iff
% 3.82/4.04 thf(fact_3517_even__flip__bit__iff,axiom,
% 3.82/4.04 ! [M2: nat,A: int] :
% 3.82/4.04 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ M2 @ A ) )
% 3.82/4.04 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 3.82/4.04 != ( M2 = zero_zero_nat ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % even_flip_bit_iff
% 3.82/4.04 thf(fact_3518_VEBT__internal_Onaive__member_Opelims_I1_J,axiom,
% 3.82/4.04 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 3.82/4.04 ( ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 3.82/4.04 = Y )
% 3.82/4.04 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 3.82/4.04 => ( ! [A4: $o,B4: $o] :
% 3.82/4.04 ( ( X
% 3.82/4.04 = ( vEBT_Leaf @ A4 @ B4 ) )
% 3.82/4.04 => ( ( Y
% 3.82/4.04 = ( ( ( Xa2 = zero_zero_nat )
% 3.82/4.04 => A4 )
% 3.82/4.04 & ( ( Xa2 != zero_zero_nat )
% 3.82/4.04 => ( ( ( Xa2 = one_one_nat )
% 3.82/4.04 => B4 )
% 3.82/4.04 & ( Xa2 = one_one_nat ) ) ) ) )
% 3.82/4.04 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B4 ) @ Xa2 ) ) ) )
% 3.82/4.04 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 3.82/4.04 ( ( X
% 3.82/4.04 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 3.82/4.04 => ( ~ Y
% 3.82/4.04 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Xa2 ) ) ) )
% 3.82/4.04 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 3.82/4.04 ( ( X
% 3.82/4.04 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 3.82/4.04 => ( ( Y
% 3.82/4.04 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 3.82/4.04 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 3.82/4.04 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) )
% 3.82/4.04 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) @ Xa2 ) ) ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % VEBT_internal.naive_member.pelims(1)
% 3.82/4.04 thf(fact_3519_VEBT__internal_Onaive__member_Opelims_I2_J,axiom,
% 3.82/4.04 ! [X: vEBT_VEBT,Xa2: nat] :
% 3.82/4.04 ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 3.82/4.04 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 3.82/4.04 => ( ! [A4: $o,B4: $o] :
% 3.82/4.04 ( ( X
% 3.82/4.04 = ( vEBT_Leaf @ A4 @ B4 ) )
% 3.82/4.04 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B4 ) @ Xa2 ) )
% 3.82/4.04 => ~ ( ( ( Xa2 = zero_zero_nat )
% 3.82/4.04 => A4 )
% 3.82/4.04 & ( ( Xa2 != zero_zero_nat )
% 3.82/4.04 => ( ( ( Xa2 = one_one_nat )
% 3.82/4.04 => B4 )
% 3.82/4.04 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 3.82/4.04 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 3.82/4.04 ( ( X
% 3.82/4.04 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 3.82/4.04 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) @ Xa2 ) )
% 3.82/4.04 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 3.82/4.04 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 3.82/4.04 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % VEBT_internal.naive_member.pelims(2)
% 3.82/4.04 thf(fact_3520_VEBT__internal_Onaive__member_Opelims_I3_J,axiom,
% 3.82/4.04 ! [X: vEBT_VEBT,Xa2: nat] :
% 3.82/4.04 ( ~ ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 3.82/4.04 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 3.82/4.04 => ( ! [A4: $o,B4: $o] :
% 3.82/4.04 ( ( X
% 3.82/4.04 = ( vEBT_Leaf @ A4 @ B4 ) )
% 3.82/4.04 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B4 ) @ Xa2 ) )
% 3.82/4.04 => ( ( ( Xa2 = zero_zero_nat )
% 3.82/4.04 => A4 )
% 3.82/4.04 & ( ( Xa2 != zero_zero_nat )
% 3.82/4.04 => ( ( ( Xa2 = one_one_nat )
% 3.82/4.04 => B4 )
% 3.82/4.04 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 3.82/4.04 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 3.82/4.04 ( ( X
% 3.82/4.04 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 3.82/4.04 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Xa2 ) ) )
% 3.82/4.04 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 3.82/4.04 ( ( X
% 3.82/4.04 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 3.82/4.04 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) @ Xa2 ) )
% 3.82/4.04 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 3.82/4.04 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 3.82/4.04 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % VEBT_internal.naive_member.pelims(3)
% 3.82/4.04 thf(fact_3521_VEBT__internal_Omembermima_Opelims_I1_J,axiom,
% 3.82/4.04 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 3.82/4.04 ( ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 3.82/4.04 = Y )
% 3.82/4.04 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 3.82/4.04 => ( ! [Uu2: $o,Uv2: $o] :
% 3.82/4.04 ( ( X
% 3.82/4.04 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 3.82/4.04 => ( ~ Y
% 3.82/4.04 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) ) )
% 3.82/4.04 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 3.82/4.04 ( ( X
% 3.82/4.04 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 3.82/4.04 => ( ~ Y
% 3.82/4.04 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa2 ) ) ) )
% 3.82/4.04 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 3.82/4.04 ( ( X
% 3.82/4.04 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 3.82/4.04 => ( ( Y
% 3.82/4.04 = ( ( Xa2 = Mi2 )
% 3.82/4.04 | ( Xa2 = Ma2 ) ) )
% 3.82/4.04 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa2 ) ) ) )
% 3.82/4.04 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 3.82/4.04 ( ( X
% 3.82/4.04 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 3.82/4.04 => ( ( Y
% 3.82/4.04 = ( ( Xa2 = Mi2 )
% 3.82/4.04 | ( Xa2 = Ma2 )
% 3.82/4.04 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 3.82/4.04 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 3.82/4.04 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 3.82/4.04 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ Xa2 ) ) ) )
% 3.82/4.04 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 3.82/4.04 ( ( X
% 3.82/4.04 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 3.82/4.04 => ( ( Y
% 3.82/4.04 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 3.82/4.04 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 3.82/4.04 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) )
% 3.82/4.04 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % VEBT_internal.membermima.pelims(1)
% 3.82/4.04 thf(fact_3522_VEBT__internal_Omembermima_Opelims_I3_J,axiom,
% 3.82/4.04 ! [X: vEBT_VEBT,Xa2: nat] :
% 3.82/4.04 ( ~ ( vEBT_VEBT_membermima @ X @ Xa2 )
% 3.82/4.04 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 3.82/4.04 => ( ! [Uu2: $o,Uv2: $o] :
% 3.82/4.04 ( ( X
% 3.82/4.04 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 3.82/4.04 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) )
% 3.82/4.04 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 3.82/4.04 ( ( X
% 3.82/4.04 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 3.82/4.04 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa2 ) ) )
% 3.82/4.04 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 3.82/4.04 ( ( X
% 3.82/4.04 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 3.82/4.04 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa2 ) )
% 3.82/4.04 => ( ( Xa2 = Mi2 )
% 3.82/4.04 | ( Xa2 = Ma2 ) ) ) )
% 3.82/4.04 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 3.82/4.04 ( ( X
% 3.82/4.04 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 3.82/4.04 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ Xa2 ) )
% 3.82/4.04 => ( ( Xa2 = Mi2 )
% 3.82/4.04 | ( Xa2 = Ma2 )
% 3.82/4.04 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 3.82/4.04 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 3.82/4.04 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) )
% 3.82/4.04 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 3.82/4.04 ( ( X
% 3.82/4.04 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 3.82/4.04 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) @ Xa2 ) )
% 3.82/4.04 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 3.82/4.04 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 3.82/4.04 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % VEBT_internal.membermima.pelims(3)
% 3.82/4.04 thf(fact_3523_VEBT__internal_Omembermima_Opelims_I2_J,axiom,
% 3.82/4.04 ! [X: vEBT_VEBT,Xa2: nat] :
% 3.82/4.04 ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 3.82/4.04 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 3.82/4.04 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 3.82/4.04 ( ( X
% 3.82/4.04 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 3.82/4.04 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa2 ) )
% 3.82/4.04 => ~ ( ( Xa2 = Mi2 )
% 3.82/4.04 | ( Xa2 = Ma2 ) ) ) )
% 3.82/4.04 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 3.82/4.04 ( ( X
% 3.82/4.04 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 3.82/4.04 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ Xa2 ) )
% 3.82/4.04 => ~ ( ( Xa2 = Mi2 )
% 3.82/4.04 | ( Xa2 = Ma2 )
% 3.82/4.04 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 3.82/4.04 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 3.82/4.04 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) )
% 3.82/4.04 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 3.82/4.04 ( ( X
% 3.82/4.04 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 3.82/4.04 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) @ Xa2 ) )
% 3.82/4.04 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 3.82/4.04 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 3.82/4.04 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % VEBT_internal.membermima.pelims(2)
% 3.82/4.04 thf(fact_3524_arcosh__1,axiom,
% 3.82/4.04 ( ( arcosh_real @ one_one_real )
% 3.82/4.04 = zero_zero_real ) ).
% 3.82/4.04
% 3.82/4.04 % arcosh_1
% 3.82/4.04 thf(fact_3525_arsinh__0,axiom,
% 3.82/4.04 ( ( arsinh_real @ zero_zero_real )
% 3.82/4.04 = zero_zero_real ) ).
% 3.82/4.04
% 3.82/4.04 % arsinh_0
% 3.82/4.04 thf(fact_3526_artanh__0,axiom,
% 3.82/4.04 ( ( artanh_real @ zero_zero_real )
% 3.82/4.04 = zero_zero_real ) ).
% 3.82/4.04
% 3.82/4.04 % artanh_0
% 3.82/4.04 thf(fact_3527_vebt__buildup_Opelims,axiom,
% 3.82/4.04 ! [X: nat,Y: vEBT_VEBT] :
% 3.82/4.04 ( ( ( vEBT_vebt_buildup @ X )
% 3.82/4.04 = Y )
% 3.82/4.04 => ( ( accp_nat @ vEBT_v4011308405150292612up_rel @ X )
% 3.82/4.04 => ( ( ( X = zero_zero_nat )
% 3.82/4.04 => ( ( Y
% 3.82/4.04 = ( vEBT_Leaf @ $false @ $false ) )
% 3.82/4.04 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ zero_zero_nat ) ) )
% 3.82/4.04 => ( ( ( X
% 3.82/4.04 = ( suc @ zero_zero_nat ) )
% 3.82/4.04 => ( ( Y
% 3.82/4.04 = ( vEBT_Leaf @ $false @ $false ) )
% 3.82/4.04 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ zero_zero_nat ) ) ) )
% 3.82/4.04 => ~ ! [Va: nat] :
% 3.82/4.04 ( ( X
% 3.82/4.04 = ( suc @ ( suc @ Va ) ) )
% 3.82/4.04 => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 3.82/4.04 => ( Y
% 3.82/4.04 = ( 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 ) ) ) ) ) ) )
% 3.82/4.04 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 3.82/4.04 => ( Y
% 3.82/4.04 = ( 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 ) ) ) ) ) ) ) ) )
% 3.82/4.04 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ ( suc @ Va ) ) ) ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % vebt_buildup.pelims
% 3.82/4.04 thf(fact_3528_flip__bit__0,axiom,
% 3.82/4.04 ! [A: nat] :
% 3.82/4.04 ( ( bit_se2161824704523386999it_nat @ zero_zero_nat @ A )
% 3.82/4.04 = ( 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 ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % flip_bit_0
% 3.82/4.04 thf(fact_3529_flip__bit__0,axiom,
% 3.82/4.04 ! [A: int] :
% 3.82/4.04 ( ( bit_se2159334234014336723it_int @ zero_zero_nat @ A )
% 3.82/4.04 = ( 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 ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % flip_bit_0
% 3.82/4.04 thf(fact_3530_signed__take__bit__Suc,axiom,
% 3.82/4.04 ! [N2: nat,A: int] :
% 3.82/4.04 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ A )
% 3.82/4.04 = ( 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 ) ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % signed_take_bit_Suc
% 3.82/4.04 thf(fact_3531_even__mult__exp__div__exp__iff,axiom,
% 3.82/4.04 ! [A: nat,M2: nat,N2: nat] :
% 3.82/4.04 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 3.82/4.04 = ( ( ord_less_nat @ N2 @ M2 )
% 3.82/4.04 | ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 3.82/4.04 = zero_zero_nat )
% 3.82/4.04 | ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.04 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % even_mult_exp_div_exp_iff
% 3.82/4.04 thf(fact_3532_even__mult__exp__div__exp__iff,axiom,
% 3.82/4.04 ! [A: int,M2: nat,N2: nat] :
% 3.82/4.04 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) )
% 3.82/4.04 = ( ( ord_less_nat @ N2 @ M2 )
% 3.82/4.04 | ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 3.82/4.04 = zero_zero_int )
% 3.82/4.04 | ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.04 & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % even_mult_exp_div_exp_iff
% 3.82/4.04 thf(fact_3533_even__set__encode__iff,axiom,
% 3.82/4.04 ! [A2: set_nat] :
% 3.82/4.04 ( ( finite_finite_nat @ A2 )
% 3.82/4.04 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat_set_encode @ A2 ) )
% 3.82/4.04 = ( ~ ( member_nat @ zero_zero_nat @ A2 ) ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % even_set_encode_iff
% 3.82/4.04 thf(fact_3534_num_Osize__gen_I2_J,axiom,
% 3.82/4.04 ! [X22: num] :
% 3.82/4.04 ( ( size_num @ ( bit0 @ X22 ) )
% 3.82/4.04 = ( plus_plus_nat @ ( size_num @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % num.size_gen(2)
% 3.82/4.04 thf(fact_3535_one__mod__2__pow__eq,axiom,
% 3.82/4.04 ! [N2: nat] :
% 3.82/4.04 ( ( modulo_modulo_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 3.82/4.04 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % one_mod_2_pow_eq
% 3.82/4.04 thf(fact_3536_one__mod__2__pow__eq,axiom,
% 3.82/4.04 ! [N2: nat] :
% 3.82/4.04 ( ( modulo_modulo_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 3.82/4.04 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % one_mod_2_pow_eq
% 3.82/4.04 thf(fact_3537_diff__self,axiom,
% 3.82/4.04 ! [A: complex] :
% 3.82/4.04 ( ( minus_minus_complex @ A @ A )
% 3.82/4.04 = zero_zero_complex ) ).
% 3.82/4.04
% 3.82/4.04 % diff_self
% 3.82/4.04 thf(fact_3538_diff__self,axiom,
% 3.82/4.04 ! [A: int] :
% 3.82/4.04 ( ( minus_minus_int @ A @ A )
% 3.82/4.04 = zero_zero_int ) ).
% 3.82/4.04
% 3.82/4.04 % diff_self
% 3.82/4.04 thf(fact_3539_diff__self,axiom,
% 3.82/4.04 ! [A: real] :
% 3.82/4.04 ( ( minus_minus_real @ A @ A )
% 3.82/4.04 = zero_zero_real ) ).
% 3.82/4.04
% 3.82/4.04 % diff_self
% 3.82/4.04 thf(fact_3540_diff__0__right,axiom,
% 3.82/4.04 ! [A: complex] :
% 3.82/4.04 ( ( minus_minus_complex @ A @ zero_zero_complex )
% 3.82/4.04 = A ) ).
% 3.82/4.04
% 3.82/4.04 % diff_0_right
% 3.82/4.04 thf(fact_3541_diff__0__right,axiom,
% 3.82/4.04 ! [A: int] :
% 3.82/4.04 ( ( minus_minus_int @ A @ zero_zero_int )
% 3.82/4.04 = A ) ).
% 3.82/4.04
% 3.82/4.04 % diff_0_right
% 3.82/4.04 thf(fact_3542_diff__0__right,axiom,
% 3.82/4.04 ! [A: real] :
% 3.82/4.04 ( ( minus_minus_real @ A @ zero_zero_real )
% 3.82/4.04 = A ) ).
% 3.82/4.04
% 3.82/4.04 % diff_0_right
% 3.82/4.04 thf(fact_3543_zero__diff,axiom,
% 3.82/4.04 ! [A: nat] :
% 3.82/4.04 ( ( minus_minus_nat @ zero_zero_nat @ A )
% 3.82/4.04 = zero_zero_nat ) ).
% 3.82/4.04
% 3.82/4.04 % zero_diff
% 3.82/4.04 thf(fact_3544_diff__zero,axiom,
% 3.82/4.04 ! [A: complex] :
% 3.82/4.04 ( ( minus_minus_complex @ A @ zero_zero_complex )
% 3.82/4.04 = A ) ).
% 3.82/4.04
% 3.82/4.04 % diff_zero
% 3.82/4.04 thf(fact_3545_diff__zero,axiom,
% 3.82/4.04 ! [A: nat] :
% 3.82/4.04 ( ( minus_minus_nat @ A @ zero_zero_nat )
% 3.82/4.04 = A ) ).
% 3.82/4.04
% 3.82/4.04 % diff_zero
% 3.82/4.04 thf(fact_3546_diff__zero,axiom,
% 3.82/4.04 ! [A: int] :
% 3.82/4.04 ( ( minus_minus_int @ A @ zero_zero_int )
% 3.82/4.04 = A ) ).
% 3.82/4.04
% 3.82/4.04 % diff_zero
% 3.82/4.04 thf(fact_3547_diff__zero,axiom,
% 3.82/4.04 ! [A: real] :
% 3.82/4.04 ( ( minus_minus_real @ A @ zero_zero_real )
% 3.82/4.04 = A ) ).
% 3.82/4.04
% 3.82/4.04 % diff_zero
% 3.82/4.04 thf(fact_3548_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 3.82/4.04 ! [A: complex] :
% 3.82/4.04 ( ( minus_minus_complex @ A @ A )
% 3.82/4.04 = zero_zero_complex ) ).
% 3.82/4.04
% 3.82/4.04 % cancel_comm_monoid_add_class.diff_cancel
% 3.82/4.04 thf(fact_3549_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 3.82/4.04 ! [A: nat] :
% 3.82/4.04 ( ( minus_minus_nat @ A @ A )
% 3.82/4.04 = zero_zero_nat ) ).
% 3.82/4.04
% 3.82/4.04 % cancel_comm_monoid_add_class.diff_cancel
% 3.82/4.04 thf(fact_3550_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 3.82/4.04 ! [A: int] :
% 3.82/4.04 ( ( minus_minus_int @ A @ A )
% 3.82/4.04 = zero_zero_int ) ).
% 3.82/4.04
% 3.82/4.04 % cancel_comm_monoid_add_class.diff_cancel
% 3.82/4.04 thf(fact_3551_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 3.82/4.04 ! [A: real] :
% 3.82/4.04 ( ( minus_minus_real @ A @ A )
% 3.82/4.04 = zero_zero_real ) ).
% 3.82/4.04
% 3.82/4.04 % cancel_comm_monoid_add_class.diff_cancel
% 3.82/4.04 thf(fact_3552_add__diff__cancel,axiom,
% 3.82/4.04 ! [A: int,B2: int] :
% 3.82/4.04 ( ( minus_minus_int @ ( plus_plus_int @ A @ B2 ) @ B2 )
% 3.82/4.04 = A ) ).
% 3.82/4.04
% 3.82/4.04 % add_diff_cancel
% 3.82/4.04 thf(fact_3553_add__diff__cancel,axiom,
% 3.82/4.04 ! [A: real,B2: real] :
% 3.82/4.04 ( ( minus_minus_real @ ( plus_plus_real @ A @ B2 ) @ B2 )
% 3.82/4.04 = A ) ).
% 3.82/4.04
% 3.82/4.04 % add_diff_cancel
% 3.82/4.04 thf(fact_3554_diff__add__cancel,axiom,
% 3.82/4.04 ! [A: int,B2: int] :
% 3.82/4.04 ( ( plus_plus_int @ ( minus_minus_int @ A @ B2 ) @ B2 )
% 3.82/4.04 = A ) ).
% 3.82/4.04
% 3.82/4.04 % diff_add_cancel
% 3.82/4.04 thf(fact_3555_diff__add__cancel,axiom,
% 3.82/4.04 ! [A: real,B2: real] :
% 3.82/4.04 ( ( plus_plus_real @ ( minus_minus_real @ A @ B2 ) @ B2 )
% 3.82/4.04 = A ) ).
% 3.82/4.04
% 3.82/4.04 % diff_add_cancel
% 3.82/4.04 thf(fact_3556_add__diff__cancel__left,axiom,
% 3.82/4.04 ! [C: nat,A: nat,B2: nat] :
% 3.82/4.04 ( ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B2 ) )
% 3.82/4.04 = ( minus_minus_nat @ A @ B2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % add_diff_cancel_left
% 3.82/4.04 thf(fact_3557_add__diff__cancel__left,axiom,
% 3.82/4.04 ! [C: int,A: int,B2: int] :
% 3.82/4.04 ( ( minus_minus_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B2 ) )
% 3.82/4.04 = ( minus_minus_int @ A @ B2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % add_diff_cancel_left
% 3.82/4.04 thf(fact_3558_add__diff__cancel__left,axiom,
% 3.82/4.04 ! [C: real,A: real,B2: real] :
% 3.82/4.04 ( ( minus_minus_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B2 ) )
% 3.82/4.04 = ( minus_minus_real @ A @ B2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % add_diff_cancel_left
% 3.82/4.04 thf(fact_3559_add__diff__cancel__left_H,axiom,
% 3.82/4.04 ! [A: nat,B2: nat] :
% 3.82/4.04 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B2 ) @ A )
% 3.82/4.04 = B2 ) ).
% 3.82/4.04
% 3.82/4.04 % add_diff_cancel_left'
% 3.82/4.04 thf(fact_3560_add__diff__cancel__left_H,axiom,
% 3.82/4.04 ! [A: int,B2: int] :
% 3.82/4.04 ( ( minus_minus_int @ ( plus_plus_int @ A @ B2 ) @ A )
% 3.82/4.04 = B2 ) ).
% 3.82/4.04
% 3.82/4.04 % add_diff_cancel_left'
% 3.82/4.04 thf(fact_3561_add__diff__cancel__left_H,axiom,
% 3.82/4.04 ! [A: real,B2: real] :
% 3.82/4.04 ( ( minus_minus_real @ ( plus_plus_real @ A @ B2 ) @ A )
% 3.82/4.04 = B2 ) ).
% 3.82/4.04
% 3.82/4.04 % add_diff_cancel_left'
% 3.82/4.04 thf(fact_3562_add__diff__cancel__right,axiom,
% 3.82/4.04 ! [A: nat,C: nat,B2: nat] :
% 3.82/4.04 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B2 @ C ) )
% 3.82/4.04 = ( minus_minus_nat @ A @ B2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % add_diff_cancel_right
% 3.82/4.04 thf(fact_3563_add__diff__cancel__right,axiom,
% 3.82/4.04 ! [A: int,C: int,B2: int] :
% 3.82/4.04 ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B2 @ C ) )
% 3.82/4.04 = ( minus_minus_int @ A @ B2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % add_diff_cancel_right
% 3.82/4.04 thf(fact_3564_add__diff__cancel__right,axiom,
% 3.82/4.04 ! [A: real,C: real,B2: real] :
% 3.82/4.04 ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B2 @ C ) )
% 3.82/4.04 = ( minus_minus_real @ A @ B2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % add_diff_cancel_right
% 3.82/4.04 thf(fact_3565_add__diff__cancel__right_H,axiom,
% 3.82/4.04 ! [A: nat,B2: nat] :
% 3.82/4.04 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B2 ) @ B2 )
% 3.82/4.04 = A ) ).
% 3.82/4.04
% 3.82/4.04 % add_diff_cancel_right'
% 3.82/4.04 thf(fact_3566_add__diff__cancel__right_H,axiom,
% 3.82/4.04 ! [A: int,B2: int] :
% 3.82/4.04 ( ( minus_minus_int @ ( plus_plus_int @ A @ B2 ) @ B2 )
% 3.82/4.04 = A ) ).
% 3.82/4.04
% 3.82/4.04 % add_diff_cancel_right'
% 3.82/4.04 thf(fact_3567_add__diff__cancel__right_H,axiom,
% 3.82/4.04 ! [A: real,B2: real] :
% 3.82/4.04 ( ( minus_minus_real @ ( plus_plus_real @ A @ B2 ) @ B2 )
% 3.82/4.04 = A ) ).
% 3.82/4.04
% 3.82/4.04 % add_diff_cancel_right'
% 3.82/4.04 thf(fact_3568_diff__Suc__Suc,axiom,
% 3.82/4.04 ! [M2: nat,N2: nat] :
% 3.82/4.04 ( ( minus_minus_nat @ ( suc @ M2 ) @ ( suc @ N2 ) )
% 3.82/4.04 = ( minus_minus_nat @ M2 @ N2 ) ) ).
% 3.82/4.04
% 3.82/4.04 % diff_Suc_Suc
% 3.82/4.04 thf(fact_3569_Suc__diff__diff,axiom,
% 3.82/4.04 ! [M2: nat,N2: nat,K: nat] :
% 3.82/4.04 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M2 ) @ N2 ) @ ( suc @ K ) )
% 3.82/4.04 = ( minus_minus_nat @ ( minus_minus_nat @ M2 @ N2 ) @ K ) ) ).
% 3.82/4.04
% 3.82/4.04 % Suc_diff_diff
% 3.82/4.04 thf(fact_3570_diff__0__eq__0,axiom,
% 3.82/4.04 ! [N2: nat] :
% 3.82/4.04 ( ( minus_minus_nat @ zero_zero_nat @ N2 )
% 3.82/4.04 = zero_zero_nat ) ).
% 3.82/4.04
% 3.82/4.04 % diff_0_eq_0
% 3.82/4.04 thf(fact_3571_diff__self__eq__0,axiom,
% 3.82/4.04 ! [M2: nat] :
% 3.82/4.04 ( ( minus_minus_nat @ M2 @ M2 )
% 3.82/4.04 = zero_zero_nat ) ).
% 3.82/4.04
% 3.82/4.04 % diff_self_eq_0
% 3.82/4.04 thf(fact_3572_diff__diff__cancel,axiom,
% 3.82/4.04 ! [I: nat,N2: nat] :
% 3.82/4.04 ( ( ord_less_eq_nat @ I @ N2 )
% 3.82/4.04 => ( ( minus_minus_nat @ N2 @ ( minus_minus_nat @ N2 @ I ) )
% 3.82/4.04 = I ) ) ).
% 3.82/4.04
% 3.82/4.04 % diff_diff_cancel
% 3.82/4.04 thf(fact_3573_diff__diff__left,axiom,
% 3.82/4.04 ! [I: nat,J: nat,K: nat] :
% 3.82/4.04 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 3.82/4.04 = ( minus_minus_nat @ I @ ( plus_plus_nat @ J @ K ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % diff_diff_left
% 3.82/4.04 thf(fact_3574_of__bool__less__eq__iff,axiom,
% 3.82/4.04 ! [P: $o,Q: $o] :
% 3.82/4.04 ( ( ord_less_eq_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) )
% 3.82/4.04 = ( P
% 3.82/4.04 => Q ) ) ).
% 3.82/4.04
% 3.82/4.04 % of_bool_less_eq_iff
% 3.82/4.04 thf(fact_3575_of__bool__less__eq__iff,axiom,
% 3.82/4.04 ! [P: $o,Q: $o] :
% 3.82/4.04 ( ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 3.82/4.04 = ( P
% 3.82/4.04 => Q ) ) ).
% 3.82/4.04
% 3.82/4.04 % of_bool_less_eq_iff
% 3.82/4.04 thf(fact_3576_of__bool__less__eq__iff,axiom,
% 3.82/4.04 ! [P: $o,Q: $o] :
% 3.82/4.04 ( ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 3.82/4.04 = ( P
% 3.82/4.04 => Q ) ) ).
% 3.82/4.04
% 3.82/4.04 % of_bool_less_eq_iff
% 3.82/4.04 thf(fact_3577_of__bool__eq_I1_J,axiom,
% 3.82/4.04 ( ( zero_n3304061248610475627l_real @ $false )
% 3.82/4.04 = zero_zero_real ) ).
% 3.82/4.04
% 3.82/4.04 % of_bool_eq(1)
% 3.82/4.04 thf(fact_3578_of__bool__eq_I1_J,axiom,
% 3.82/4.04 ( ( zero_n1201886186963655149omplex @ $false )
% 3.82/4.04 = zero_zero_complex ) ).
% 3.82/4.04
% 3.82/4.04 % of_bool_eq(1)
% 3.82/4.04 thf(fact_3579_of__bool__eq_I1_J,axiom,
% 3.82/4.04 ( ( zero_n1046097342994218471d_enat @ $false )
% 3.82/4.04 = zero_z5237406670263579293d_enat ) ).
% 3.82/4.04
% 3.82/4.04 % of_bool_eq(1)
% 3.82/4.04 thf(fact_3580_of__bool__eq_I1_J,axiom,
% 3.82/4.04 ( ( zero_n2687167440665602831ol_nat @ $false )
% 3.82/4.04 = zero_zero_nat ) ).
% 3.82/4.04
% 3.82/4.04 % of_bool_eq(1)
% 3.82/4.04 thf(fact_3581_of__bool__eq_I1_J,axiom,
% 3.82/4.04 ( ( zero_n2684676970156552555ol_int @ $false )
% 3.82/4.04 = zero_zero_int ) ).
% 3.82/4.04
% 3.82/4.04 % of_bool_eq(1)
% 3.82/4.04 thf(fact_3582_of__bool__eq__0__iff,axiom,
% 3.82/4.04 ! [P: $o] :
% 3.82/4.04 ( ( ( zero_n3304061248610475627l_real @ P )
% 3.82/4.04 = zero_zero_real )
% 3.82/4.04 = ~ P ) ).
% 3.82/4.04
% 3.82/4.04 % of_bool_eq_0_iff
% 3.82/4.04 thf(fact_3583_of__bool__eq__0__iff,axiom,
% 3.82/4.04 ! [P: $o] :
% 3.82/4.04 ( ( ( zero_n1201886186963655149omplex @ P )
% 3.82/4.04 = zero_zero_complex )
% 3.82/4.04 = ~ P ) ).
% 3.82/4.04
% 3.82/4.04 % of_bool_eq_0_iff
% 3.82/4.04 thf(fact_3584_of__bool__eq__0__iff,axiom,
% 3.82/4.04 ! [P: $o] :
% 3.82/4.04 ( ( ( zero_n1046097342994218471d_enat @ P )
% 3.82/4.04 = zero_z5237406670263579293d_enat )
% 3.82/4.04 = ~ P ) ).
% 3.82/4.04
% 3.82/4.04 % of_bool_eq_0_iff
% 3.82/4.04 thf(fact_3585_of__bool__eq__0__iff,axiom,
% 3.82/4.04 ! [P: $o] :
% 3.82/4.04 ( ( ( zero_n2687167440665602831ol_nat @ P )
% 3.82/4.04 = zero_zero_nat )
% 3.82/4.04 = ~ P ) ).
% 3.82/4.04
% 3.82/4.04 % of_bool_eq_0_iff
% 3.82/4.04 thf(fact_3586_of__bool__eq__0__iff,axiom,
% 3.82/4.04 ! [P: $o] :
% 3.82/4.04 ( ( ( zero_n2684676970156552555ol_int @ P )
% 3.82/4.04 = zero_zero_int )
% 3.82/4.04 = ~ P ) ).
% 3.82/4.04
% 3.82/4.04 % of_bool_eq_0_iff
% 3.82/4.04 thf(fact_3587_of__bool__less__iff,axiom,
% 3.82/4.04 ! [P: $o,Q: $o] :
% 3.82/4.04 ( ( ord_le72135733267957522d_enat @ ( zero_n1046097342994218471d_enat @ P ) @ ( zero_n1046097342994218471d_enat @ Q ) )
% 3.82/4.04 = ( ~ P
% 3.82/4.04 & Q ) ) ).
% 3.82/4.04
% 3.82/4.04 % of_bool_less_iff
% 3.82/4.04 thf(fact_3588_of__bool__less__iff,axiom,
% 3.82/4.04 ! [P: $o,Q: $o] :
% 3.82/4.04 ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) )
% 3.82/4.04 = ( ~ P
% 3.82/4.04 & Q ) ) ).
% 3.82/4.04
% 3.82/4.04 % of_bool_less_iff
% 3.82/4.04 thf(fact_3589_of__bool__less__iff,axiom,
% 3.82/4.04 ! [P: $o,Q: $o] :
% 3.82/4.04 ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 3.82/4.04 = ( ~ P
% 3.82/4.04 & Q ) ) ).
% 3.82/4.04
% 3.82/4.04 % of_bool_less_iff
% 3.82/4.04 thf(fact_3590_of__bool__less__iff,axiom,
% 3.82/4.04 ! [P: $o,Q: $o] :
% 3.82/4.04 ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 3.82/4.04 = ( ~ P
% 3.82/4.04 & Q ) ) ).
% 3.82/4.04
% 3.82/4.04 % of_bool_less_iff
% 3.82/4.04 thf(fact_3591_of__bool__eq__1__iff,axiom,
% 3.82/4.04 ! [P: $o] :
% 3.82/4.04 ( ( ( zero_n1201886186963655149omplex @ P )
% 3.82/4.04 = one_one_complex )
% 3.82/4.04 = P ) ).
% 3.82/4.04
% 3.82/4.04 % of_bool_eq_1_iff
% 3.82/4.04 thf(fact_3592_of__bool__eq__1__iff,axiom,
% 3.82/4.04 ! [P: $o] :
% 3.82/4.04 ( ( ( zero_n3304061248610475627l_real @ P )
% 3.82/4.04 = one_one_real )
% 3.82/4.04 = P ) ).
% 3.82/4.04
% 3.82/4.04 % of_bool_eq_1_iff
% 3.82/4.04 thf(fact_3593_of__bool__eq__1__iff,axiom,
% 3.82/4.04 ! [P: $o] :
% 3.82/4.04 ( ( ( zero_n2687167440665602831ol_nat @ P )
% 3.82/4.04 = one_one_nat )
% 3.82/4.04 = P ) ).
% 3.82/4.04
% 3.82/4.04 % of_bool_eq_1_iff
% 3.82/4.04 thf(fact_3594_of__bool__eq__1__iff,axiom,
% 3.82/4.04 ! [P: $o] :
% 3.82/4.04 ( ( ( zero_n2684676970156552555ol_int @ P )
% 3.82/4.04 = one_one_int )
% 3.82/4.04 = P ) ).
% 3.82/4.04
% 3.82/4.04 % of_bool_eq_1_iff
% 3.82/4.04 thf(fact_3595_of__bool__eq_I2_J,axiom,
% 3.82/4.04 ( ( zero_n1201886186963655149omplex @ $true )
% 3.82/4.04 = one_one_complex ) ).
% 3.82/4.04
% 3.82/4.04 % of_bool_eq(2)
% 3.82/4.04 thf(fact_3596_of__bool__eq_I2_J,axiom,
% 3.82/4.04 ( ( zero_n3304061248610475627l_real @ $true )
% 3.82/4.04 = one_one_real ) ).
% 3.82/4.04
% 3.82/4.04 % of_bool_eq(2)
% 3.82/4.04 thf(fact_3597_of__bool__eq_I2_J,axiom,
% 3.82/4.04 ( ( zero_n2687167440665602831ol_nat @ $true )
% 3.82/4.04 = one_one_nat ) ).
% 3.82/4.04
% 3.82/4.04 % of_bool_eq(2)
% 3.82/4.04 thf(fact_3598_of__bool__eq_I2_J,axiom,
% 3.82/4.04 ( ( zero_n2684676970156552555ol_int @ $true )
% 3.82/4.04 = one_one_int ) ).
% 3.82/4.04
% 3.82/4.04 % of_bool_eq(2)
% 3.82/4.04 thf(fact_3599_signed__take__bit__of__0,axiom,
% 3.82/4.04 ! [N2: nat] :
% 3.82/4.04 ( ( bit_ri631733984087533419it_int @ N2 @ zero_zero_int )
% 3.82/4.04 = zero_zero_int ) ).
% 3.82/4.04
% 3.82/4.04 % signed_take_bit_of_0
% 3.82/4.04 thf(fact_3600_of__bool__or__iff,axiom,
% 3.82/4.04 ! [P: $o,Q: $o] :
% 3.82/4.04 ( ( zero_n2687167440665602831ol_nat
% 3.82/4.04 @ ( P
% 3.82/4.04 | Q ) )
% 3.82/4.04 = ( ord_max_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) ) ) ).
% 3.82/4.04
% 3.82/4.04 % of_bool_or_iff
% 3.82/4.04 thf(fact_3601_of__bool__or__iff,axiom,
% 3.82/4.04 ! [P: $o,Q: $o] :
% 3.82/4.04 ( ( zero_n2684676970156552555ol_int
% 3.82/4.04 @ ( P
% 3.82/4.04 | Q ) )
% 3.82/4.04 = ( ord_max_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % of_bool_or_iff
% 3.82/4.05 thf(fact_3602_diff__ge__0__iff__ge,axiom,
% 3.82/4.05 ! [A: real,B2: real] :
% 3.82/4.05 ( ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ A @ B2 ) )
% 3.82/4.05 = ( ord_less_eq_real @ B2 @ A ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_ge_0_iff_ge
% 3.82/4.05 thf(fact_3603_diff__ge__0__iff__ge,axiom,
% 3.82/4.05 ! [A: int,B2: int] :
% 3.82/4.05 ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B2 ) )
% 3.82/4.05 = ( ord_less_eq_int @ B2 @ A ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_ge_0_iff_ge
% 3.82/4.05 thf(fact_3604_diff__gt__0__iff__gt,axiom,
% 3.82/4.05 ! [A: real,B2: real] :
% 3.82/4.05 ( ( ord_less_real @ zero_zero_real @ ( minus_minus_real @ A @ B2 ) )
% 3.82/4.05 = ( ord_less_real @ B2 @ A ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_gt_0_iff_gt
% 3.82/4.05 thf(fact_3605_diff__gt__0__iff__gt,axiom,
% 3.82/4.05 ! [A: int,B2: int] :
% 3.82/4.05 ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B2 ) )
% 3.82/4.05 = ( ord_less_int @ B2 @ A ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_gt_0_iff_gt
% 3.82/4.05 thf(fact_3606_le__add__diff__inverse2,axiom,
% 3.82/4.05 ! [B2: real,A: real] :
% 3.82/4.05 ( ( ord_less_eq_real @ B2 @ A )
% 3.82/4.05 => ( ( plus_plus_real @ ( minus_minus_real @ A @ B2 ) @ B2 )
% 3.82/4.05 = A ) ) ).
% 3.82/4.05
% 3.82/4.05 % le_add_diff_inverse2
% 3.82/4.05 thf(fact_3607_le__add__diff__inverse2,axiom,
% 3.82/4.05 ! [B2: nat,A: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ B2 @ A )
% 3.82/4.05 => ( ( plus_plus_nat @ ( minus_minus_nat @ A @ B2 ) @ B2 )
% 3.82/4.05 = A ) ) ).
% 3.82/4.05
% 3.82/4.05 % le_add_diff_inverse2
% 3.82/4.05 thf(fact_3608_le__add__diff__inverse2,axiom,
% 3.82/4.05 ! [B2: int,A: int] :
% 3.82/4.05 ( ( ord_less_eq_int @ B2 @ A )
% 3.82/4.05 => ( ( plus_plus_int @ ( minus_minus_int @ A @ B2 ) @ B2 )
% 3.82/4.05 = A ) ) ).
% 3.82/4.05
% 3.82/4.05 % le_add_diff_inverse2
% 3.82/4.05 thf(fact_3609_le__add__diff__inverse,axiom,
% 3.82/4.05 ! [B2: real,A: real] :
% 3.82/4.05 ( ( ord_less_eq_real @ B2 @ A )
% 3.82/4.05 => ( ( plus_plus_real @ B2 @ ( minus_minus_real @ A @ B2 ) )
% 3.82/4.05 = A ) ) ).
% 3.82/4.05
% 3.82/4.05 % le_add_diff_inverse
% 3.82/4.05 thf(fact_3610_le__add__diff__inverse,axiom,
% 3.82/4.05 ! [B2: nat,A: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ B2 @ A )
% 3.82/4.05 => ( ( plus_plus_nat @ B2 @ ( minus_minus_nat @ A @ B2 ) )
% 3.82/4.05 = A ) ) ).
% 3.82/4.05
% 3.82/4.05 % le_add_diff_inverse
% 3.82/4.05 thf(fact_3611_le__add__diff__inverse,axiom,
% 3.82/4.05 ! [B2: int,A: int] :
% 3.82/4.05 ( ( ord_less_eq_int @ B2 @ A )
% 3.82/4.05 => ( ( plus_plus_int @ B2 @ ( minus_minus_int @ A @ B2 ) )
% 3.82/4.05 = A ) ) ).
% 3.82/4.05
% 3.82/4.05 % le_add_diff_inverse
% 3.82/4.05 thf(fact_3612_diff__numeral__special_I9_J,axiom,
% 3.82/4.05 ( ( minus_minus_complex @ one_one_complex @ one_one_complex )
% 3.82/4.05 = zero_zero_complex ) ).
% 3.82/4.05
% 3.82/4.05 % diff_numeral_special(9)
% 3.82/4.05 thf(fact_3613_diff__numeral__special_I9_J,axiom,
% 3.82/4.05 ( ( minus_minus_int @ one_one_int @ one_one_int )
% 3.82/4.05 = zero_zero_int ) ).
% 3.82/4.05
% 3.82/4.05 % diff_numeral_special(9)
% 3.82/4.05 thf(fact_3614_diff__numeral__special_I9_J,axiom,
% 3.82/4.05 ( ( minus_minus_real @ one_one_real @ one_one_real )
% 3.82/4.05 = zero_zero_real ) ).
% 3.82/4.05
% 3.82/4.05 % diff_numeral_special(9)
% 3.82/4.05 thf(fact_3615_diff__add__zero,axiom,
% 3.82/4.05 ! [A: nat,B2: nat] :
% 3.82/4.05 ( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B2 ) )
% 3.82/4.05 = zero_zero_nat ) ).
% 3.82/4.05
% 3.82/4.05 % diff_add_zero
% 3.82/4.05 thf(fact_3616_signed__take__bit__Suc__bit0,axiom,
% 3.82/4.05 ! [N2: nat,K: num] :
% 3.82/4.05 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 3.82/4.05 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N2 @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % signed_take_bit_Suc_bit0
% 3.82/4.05 thf(fact_3617_div__diff,axiom,
% 3.82/4.05 ! [C: int,A: int,B2: int] :
% 3.82/4.05 ( ( dvd_dvd_int @ C @ A )
% 3.82/4.05 => ( ( dvd_dvd_int @ C @ B2 )
% 3.82/4.05 => ( ( divide_divide_int @ ( minus_minus_int @ A @ B2 ) @ C )
% 3.82/4.05 = ( minus_minus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B2 @ C ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % div_diff
% 3.82/4.05 thf(fact_3618_zero__less__of__bool__iff,axiom,
% 3.82/4.05 ! [P: $o] :
% 3.82/4.05 ( ( ord_less_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) )
% 3.82/4.05 = P ) ).
% 3.82/4.05
% 3.82/4.05 % zero_less_of_bool_iff
% 3.82/4.05 thf(fact_3619_zero__less__of__bool__iff,axiom,
% 3.82/4.05 ! [P: $o] :
% 3.82/4.05 ( ( ord_less_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 3.82/4.05 = P ) ).
% 3.82/4.05
% 3.82/4.05 % zero_less_of_bool_iff
% 3.82/4.05 thf(fact_3620_zero__less__of__bool__iff,axiom,
% 3.82/4.05 ! [P: $o] :
% 3.82/4.05 ( ( ord_less_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 3.82/4.05 = P ) ).
% 3.82/4.05
% 3.82/4.05 % zero_less_of_bool_iff
% 3.82/4.05 thf(fact_3621_zero__less__diff,axiom,
% 3.82/4.05 ! [N2: nat,M2: nat] :
% 3.82/4.05 ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N2 @ M2 ) )
% 3.82/4.05 = ( ord_less_nat @ M2 @ N2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % zero_less_diff
% 3.82/4.05 thf(fact_3622_diff__is__0__eq_H,axiom,
% 3.82/4.05 ! [M2: nat,N2: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.05 => ( ( minus_minus_nat @ M2 @ N2 )
% 3.82/4.05 = zero_zero_nat ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_is_0_eq'
% 3.82/4.05 thf(fact_3623_diff__is__0__eq,axiom,
% 3.82/4.05 ! [M2: nat,N2: nat] :
% 3.82/4.05 ( ( ( minus_minus_nat @ M2 @ N2 )
% 3.82/4.05 = zero_zero_nat )
% 3.82/4.05 = ( ord_less_eq_nat @ M2 @ N2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_is_0_eq
% 3.82/4.05 thf(fact_3624_of__bool__less__one__iff,axiom,
% 3.82/4.05 ! [P: $o] :
% 3.82/4.05 ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real )
% 3.82/4.05 = ~ P ) ).
% 3.82/4.05
% 3.82/4.05 % of_bool_less_one_iff
% 3.82/4.05 thf(fact_3625_of__bool__less__one__iff,axiom,
% 3.82/4.05 ! [P: $o] :
% 3.82/4.05 ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat )
% 3.82/4.05 = ~ P ) ).
% 3.82/4.05
% 3.82/4.05 % of_bool_less_one_iff
% 3.82/4.05 thf(fact_3626_of__bool__less__one__iff,axiom,
% 3.82/4.05 ! [P: $o] :
% 3.82/4.05 ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int )
% 3.82/4.05 = ~ P ) ).
% 3.82/4.05
% 3.82/4.05 % of_bool_less_one_iff
% 3.82/4.05 thf(fact_3627_of__bool__not__iff,axiom,
% 3.82/4.05 ! [P: $o] :
% 3.82/4.05 ( ( zero_n1201886186963655149omplex @ ~ P )
% 3.82/4.05 = ( minus_minus_complex @ one_one_complex @ ( zero_n1201886186963655149omplex @ P ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % of_bool_not_iff
% 3.82/4.05 thf(fact_3628_of__bool__not__iff,axiom,
% 3.82/4.05 ! [P: $o] :
% 3.82/4.05 ( ( zero_n3304061248610475627l_real @ ~ P )
% 3.82/4.05 = ( minus_minus_real @ one_one_real @ ( zero_n3304061248610475627l_real @ P ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % of_bool_not_iff
% 3.82/4.05 thf(fact_3629_of__bool__not__iff,axiom,
% 3.82/4.05 ! [P: $o] :
% 3.82/4.05 ( ( zero_n2684676970156552555ol_int @ ~ P )
% 3.82/4.05 = ( minus_minus_int @ one_one_int @ ( zero_n2684676970156552555ol_int @ P ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % of_bool_not_iff
% 3.82/4.05 thf(fact_3630_Nat_Odiff__diff__right,axiom,
% 3.82/4.05 ! [K: nat,J: nat,I: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ K @ J )
% 3.82/4.05 => ( ( minus_minus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 3.82/4.05 = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % Nat.diff_diff_right
% 3.82/4.05 thf(fact_3631_Nat_Oadd__diff__assoc2,axiom,
% 3.82/4.05 ! [K: nat,J: nat,I: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ K @ J )
% 3.82/4.05 => ( ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 3.82/4.05 = ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % Nat.add_diff_assoc2
% 3.82/4.05 thf(fact_3632_Nat_Oadd__diff__assoc,axiom,
% 3.82/4.05 ! [K: nat,J: nat,I: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ K @ J )
% 3.82/4.05 => ( ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 3.82/4.05 = ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % Nat.add_diff_assoc
% 3.82/4.05 thf(fact_3633_diff__Suc__1,axiom,
% 3.82/4.05 ! [N2: nat] :
% 3.82/4.05 ( ( minus_minus_nat @ ( suc @ N2 ) @ one_one_nat )
% 3.82/4.05 = N2 ) ).
% 3.82/4.05
% 3.82/4.05 % diff_Suc_1
% 3.82/4.05 thf(fact_3634_Suc__0__mod__eq,axiom,
% 3.82/4.05 ! [N2: nat] :
% 3.82/4.05 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 3.82/4.05 = ( zero_n2687167440665602831ol_nat
% 3.82/4.05 @ ( N2
% 3.82/4.05 != ( suc @ zero_zero_nat ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % Suc_0_mod_eq
% 3.82/4.05 thf(fact_3635_signed__take__bit__Suc__1,axiom,
% 3.82/4.05 ! [N2: nat] :
% 3.82/4.05 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ one_one_int )
% 3.82/4.05 = one_one_int ) ).
% 3.82/4.05
% 3.82/4.05 % signed_take_bit_Suc_1
% 3.82/4.05 thf(fact_3636_set__encode__empty,axiom,
% 3.82/4.05 ( ( nat_set_encode @ bot_bot_set_nat )
% 3.82/4.05 = zero_zero_nat ) ).
% 3.82/4.05
% 3.82/4.05 % set_encode_empty
% 3.82/4.05 thf(fact_3637_set__encode__inverse,axiom,
% 3.82/4.05 ! [A2: set_nat] :
% 3.82/4.05 ( ( finite_finite_nat @ A2 )
% 3.82/4.05 => ( ( nat_set_decode @ ( nat_set_encode @ A2 ) )
% 3.82/4.05 = A2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % set_encode_inverse
% 3.82/4.05 thf(fact_3638_Suc__pred,axiom,
% 3.82/4.05 ! [N2: nat] :
% 3.82/4.05 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.05 => ( ( suc @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) )
% 3.82/4.05 = N2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % Suc_pred
% 3.82/4.05 thf(fact_3639_diff__Suc__diff__eq2,axiom,
% 3.82/4.05 ! [K: nat,J: nat,I: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ K @ J )
% 3.82/4.05 => ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J @ K ) ) @ I )
% 3.82/4.05 = ( minus_minus_nat @ ( suc @ J ) @ ( plus_plus_nat @ K @ I ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_Suc_diff_eq2
% 3.82/4.05 thf(fact_3640_diff__Suc__diff__eq1,axiom,
% 3.82/4.05 ! [K: nat,J: nat,I: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ K @ J )
% 3.82/4.05 => ( ( minus_minus_nat @ I @ ( suc @ ( minus_minus_nat @ J @ K ) ) )
% 3.82/4.05 = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ ( suc @ J ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_Suc_diff_eq1
% 3.82/4.05 thf(fact_3641_Suc__diff__1,axiom,
% 3.82/4.05 ! [N2: nat] :
% 3.82/4.05 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.05 => ( ( suc @ ( minus_minus_nat @ N2 @ one_one_nat ) )
% 3.82/4.05 = N2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % Suc_diff_1
% 3.82/4.05 thf(fact_3642_even__diff,axiom,
% 3.82/4.05 ! [A: int,B2: int] :
% 3.82/4.05 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ A @ B2 ) )
% 3.82/4.05 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % even_diff
% 3.82/4.05 thf(fact_3643_of__bool__half__eq__0,axiom,
% 3.82/4.05 ! [B2: $o] :
% 3.82/4.05 ( ( divide_divide_nat @ ( zero_n2687167440665602831ol_nat @ B2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.05 = zero_zero_nat ) ).
% 3.82/4.05
% 3.82/4.05 % of_bool_half_eq_0
% 3.82/4.05 thf(fact_3644_of__bool__half__eq__0,axiom,
% 3.82/4.05 ! [B2: $o] :
% 3.82/4.05 ( ( divide_divide_int @ ( zero_n2684676970156552555ol_int @ B2 ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 3.82/4.05 = zero_zero_int ) ).
% 3.82/4.05
% 3.82/4.05 % of_bool_half_eq_0
% 3.82/4.05 thf(fact_3645_odd__Suc__minus__one,axiom,
% 3.82/4.05 ! [N2: nat] :
% 3.82/4.05 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 3.82/4.05 => ( ( suc @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) )
% 3.82/4.05 = N2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % odd_Suc_minus_one
% 3.82/4.05 thf(fact_3646_even__diff__nat,axiom,
% 3.82/4.05 ! [M2: nat,N2: nat] :
% 3.82/4.05 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M2 @ N2 ) )
% 3.82/4.05 = ( ( ord_less_nat @ M2 @ N2 )
% 3.82/4.05 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % even_diff_nat
% 3.82/4.05 thf(fact_3647_semiring__parity__class_Oeven__mask__iff,axiom,
% 3.82/4.05 ! [N2: nat] :
% 3.82/4.05 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) )
% 3.82/4.05 = ( N2 = zero_zero_nat ) ) ).
% 3.82/4.05
% 3.82/4.05 % semiring_parity_class.even_mask_iff
% 3.82/4.05 thf(fact_3648_semiring__parity__class_Oeven__mask__iff,axiom,
% 3.82/4.05 ! [N2: nat] :
% 3.82/4.05 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) )
% 3.82/4.05 = ( N2 = zero_zero_nat ) ) ).
% 3.82/4.05
% 3.82/4.05 % semiring_parity_class.even_mask_iff
% 3.82/4.05 thf(fact_3649_bits__1__div__exp,axiom,
% 3.82/4.05 ! [N2: nat] :
% 3.82/4.05 ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 3.82/4.05 = ( zero_n2687167440665602831ol_nat @ ( N2 = zero_zero_nat ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % bits_1_div_exp
% 3.82/4.05 thf(fact_3650_bits__1__div__exp,axiom,
% 3.82/4.05 ! [N2: nat] :
% 3.82/4.05 ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 3.82/4.05 = ( zero_n2684676970156552555ol_int @ ( N2 = zero_zero_nat ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % bits_1_div_exp
% 3.82/4.05 thf(fact_3651_one__div__2__pow__eq,axiom,
% 3.82/4.05 ! [N2: nat] :
% 3.82/4.05 ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 3.82/4.05 = ( zero_n2687167440665602831ol_nat @ ( N2 = zero_zero_nat ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % one_div_2_pow_eq
% 3.82/4.05 thf(fact_3652_one__div__2__pow__eq,axiom,
% 3.82/4.05 ! [N2: nat] :
% 3.82/4.05 ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 3.82/4.05 = ( zero_n2684676970156552555ol_int @ ( N2 = zero_zero_nat ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % one_div_2_pow_eq
% 3.82/4.05 thf(fact_3653_of__bool__eq__iff,axiom,
% 3.82/4.05 ! [P5: $o,Q3: $o] :
% 3.82/4.05 ( ( ( zero_n2687167440665602831ol_nat @ P5 )
% 3.82/4.05 = ( zero_n2687167440665602831ol_nat @ Q3 ) )
% 3.82/4.05 = ( P5 = Q3 ) ) ).
% 3.82/4.05
% 3.82/4.05 % of_bool_eq_iff
% 3.82/4.05 thf(fact_3654_of__bool__eq__iff,axiom,
% 3.82/4.05 ! [P5: $o,Q3: $o] :
% 3.82/4.05 ( ( ( zero_n2684676970156552555ol_int @ P5 )
% 3.82/4.05 = ( zero_n2684676970156552555ol_int @ Q3 ) )
% 3.82/4.05 = ( P5 = Q3 ) ) ).
% 3.82/4.05
% 3.82/4.05 % of_bool_eq_iff
% 3.82/4.05 thf(fact_3655_diff__commute,axiom,
% 3.82/4.05 ! [I: nat,J: nat,K: nat] :
% 3.82/4.05 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 3.82/4.05 = ( minus_minus_nat @ ( minus_minus_nat @ I @ K ) @ J ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_commute
% 3.82/4.05 thf(fact_3656_diff__right__commute,axiom,
% 3.82/4.05 ! [A: nat,C: nat,B2: nat] :
% 3.82/4.05 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B2 )
% 3.82/4.05 = ( minus_minus_nat @ ( minus_minus_nat @ A @ B2 ) @ C ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_right_commute
% 3.82/4.05 thf(fact_3657_diff__right__commute,axiom,
% 3.82/4.05 ! [A: int,C: int,B2: int] :
% 3.82/4.05 ( ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B2 )
% 3.82/4.05 = ( minus_minus_int @ ( minus_minus_int @ A @ B2 ) @ C ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_right_commute
% 3.82/4.05 thf(fact_3658_diff__right__commute,axiom,
% 3.82/4.05 ! [A: real,C: real,B2: real] :
% 3.82/4.05 ( ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B2 )
% 3.82/4.05 = ( minus_minus_real @ ( minus_minus_real @ A @ B2 ) @ C ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_right_commute
% 3.82/4.05 thf(fact_3659_diff__eq__diff__eq,axiom,
% 3.82/4.05 ! [A: int,B2: int,C: int,D: int] :
% 3.82/4.05 ( ( ( minus_minus_int @ A @ B2 )
% 3.82/4.05 = ( minus_minus_int @ C @ D ) )
% 3.82/4.05 => ( ( A = B2 )
% 3.82/4.05 = ( C = D ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_eq_diff_eq
% 3.82/4.05 thf(fact_3660_diff__eq__diff__eq,axiom,
% 3.82/4.05 ! [A: real,B2: real,C: real,D: real] :
% 3.82/4.05 ( ( ( minus_minus_real @ A @ B2 )
% 3.82/4.05 = ( minus_minus_real @ C @ D ) )
% 3.82/4.05 => ( ( A = B2 )
% 3.82/4.05 = ( C = D ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_eq_diff_eq
% 3.82/4.05 thf(fact_3661_of__bool__conj,axiom,
% 3.82/4.05 ! [P: $o,Q: $o] :
% 3.82/4.05 ( ( zero_n3304061248610475627l_real
% 3.82/4.05 @ ( P
% 3.82/4.05 & Q ) )
% 3.82/4.05 = ( times_times_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % of_bool_conj
% 3.82/4.05 thf(fact_3662_of__bool__conj,axiom,
% 3.82/4.05 ! [P: $o,Q: $o] :
% 3.82/4.05 ( ( zero_n1201886186963655149omplex
% 3.82/4.05 @ ( P
% 3.82/4.05 & Q ) )
% 3.82/4.05 = ( times_times_complex @ ( zero_n1201886186963655149omplex @ P ) @ ( zero_n1201886186963655149omplex @ Q ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % of_bool_conj
% 3.82/4.05 thf(fact_3663_of__bool__conj,axiom,
% 3.82/4.05 ! [P: $o,Q: $o] :
% 3.82/4.05 ( ( zero_n1046097342994218471d_enat
% 3.82/4.05 @ ( P
% 3.82/4.05 & Q ) )
% 3.82/4.05 = ( times_7803423173614009249d_enat @ ( zero_n1046097342994218471d_enat @ P ) @ ( zero_n1046097342994218471d_enat @ Q ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % of_bool_conj
% 3.82/4.05 thf(fact_3664_of__bool__conj,axiom,
% 3.82/4.05 ! [P: $o,Q: $o] :
% 3.82/4.05 ( ( zero_n2687167440665602831ol_nat
% 3.82/4.05 @ ( P
% 3.82/4.05 & Q ) )
% 3.82/4.05 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % of_bool_conj
% 3.82/4.05 thf(fact_3665_of__bool__conj,axiom,
% 3.82/4.05 ! [P: $o,Q: $o] :
% 3.82/4.05 ( ( zero_n2684676970156552555ol_int
% 3.82/4.05 @ ( P
% 3.82/4.05 & Q ) )
% 3.82/4.05 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % of_bool_conj
% 3.82/4.05 thf(fact_3666_diff__mono,axiom,
% 3.82/4.05 ! [A: real,B2: real,D: real,C: real] :
% 3.82/4.05 ( ( ord_less_eq_real @ A @ B2 )
% 3.82/4.05 => ( ( ord_less_eq_real @ D @ C )
% 3.82/4.05 => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B2 @ D ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_mono
% 3.82/4.05 thf(fact_3667_diff__mono,axiom,
% 3.82/4.05 ! [A: int,B2: int,D: int,C: int] :
% 3.82/4.05 ( ( ord_less_eq_int @ A @ B2 )
% 3.82/4.05 => ( ( ord_less_eq_int @ D @ C )
% 3.82/4.05 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B2 @ D ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_mono
% 3.82/4.05 thf(fact_3668_diff__left__mono,axiom,
% 3.82/4.05 ! [B2: real,A: real,C: real] :
% 3.82/4.05 ( ( ord_less_eq_real @ B2 @ A )
% 3.82/4.05 => ( ord_less_eq_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_left_mono
% 3.82/4.05 thf(fact_3669_diff__left__mono,axiom,
% 3.82/4.05 ! [B2: int,A: int,C: int] :
% 3.82/4.05 ( ( ord_less_eq_int @ B2 @ A )
% 3.82/4.05 => ( ord_less_eq_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_left_mono
% 3.82/4.05 thf(fact_3670_diff__right__mono,axiom,
% 3.82/4.05 ! [A: real,B2: real,C: real] :
% 3.82/4.05 ( ( ord_less_eq_real @ A @ B2 )
% 3.82/4.05 => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B2 @ C ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_right_mono
% 3.82/4.05 thf(fact_3671_diff__right__mono,axiom,
% 3.82/4.05 ! [A: int,B2: int,C: int] :
% 3.82/4.05 ( ( ord_less_eq_int @ A @ B2 )
% 3.82/4.05 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B2 @ C ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_right_mono
% 3.82/4.05 thf(fact_3672_diff__eq__diff__less__eq,axiom,
% 3.82/4.05 ! [A: real,B2: real,C: real,D: real] :
% 3.82/4.05 ( ( ( minus_minus_real @ A @ B2 )
% 3.82/4.05 = ( minus_minus_real @ C @ D ) )
% 3.82/4.05 => ( ( ord_less_eq_real @ A @ B2 )
% 3.82/4.05 = ( ord_less_eq_real @ C @ D ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_eq_diff_less_eq
% 3.82/4.05 thf(fact_3673_diff__eq__diff__less__eq,axiom,
% 3.82/4.05 ! [A: int,B2: int,C: int,D: int] :
% 3.82/4.05 ( ( ( minus_minus_int @ A @ B2 )
% 3.82/4.05 = ( minus_minus_int @ C @ D ) )
% 3.82/4.05 => ( ( ord_less_eq_int @ A @ B2 )
% 3.82/4.05 = ( ord_less_eq_int @ C @ D ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_eq_diff_less_eq
% 3.82/4.05 thf(fact_3674_eq__iff__diff__eq__0,axiom,
% 3.82/4.05 ( ( ^ [Y4: complex,Z2: complex] : ( Y4 = Z2 ) )
% 3.82/4.05 = ( ^ [A3: complex,B3: complex] :
% 3.82/4.05 ( ( minus_minus_complex @ A3 @ B3 )
% 3.82/4.05 = zero_zero_complex ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % eq_iff_diff_eq_0
% 3.82/4.05 thf(fact_3675_eq__iff__diff__eq__0,axiom,
% 3.82/4.05 ( ( ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 3.82/4.05 = ( ^ [A3: int,B3: int] :
% 3.82/4.05 ( ( minus_minus_int @ A3 @ B3 )
% 3.82/4.05 = zero_zero_int ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % eq_iff_diff_eq_0
% 3.82/4.05 thf(fact_3676_eq__iff__diff__eq__0,axiom,
% 3.82/4.05 ( ( ^ [Y4: real,Z2: real] : ( Y4 = Z2 ) )
% 3.82/4.05 = ( ^ [A3: real,B3: real] :
% 3.82/4.05 ( ( minus_minus_real @ A3 @ B3 )
% 3.82/4.05 = zero_zero_real ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % eq_iff_diff_eq_0
% 3.82/4.05 thf(fact_3677_diff__strict__mono,axiom,
% 3.82/4.05 ! [A: real,B2: real,D: real,C: real] :
% 3.82/4.05 ( ( ord_less_real @ A @ B2 )
% 3.82/4.05 => ( ( ord_less_real @ D @ C )
% 3.82/4.05 => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B2 @ D ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_strict_mono
% 3.82/4.05 thf(fact_3678_diff__strict__mono,axiom,
% 3.82/4.05 ! [A: int,B2: int,D: int,C: int] :
% 3.82/4.05 ( ( ord_less_int @ A @ B2 )
% 3.82/4.05 => ( ( ord_less_int @ D @ C )
% 3.82/4.05 => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B2 @ D ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_strict_mono
% 3.82/4.05 thf(fact_3679_diff__eq__diff__less,axiom,
% 3.82/4.05 ! [A: real,B2: real,C: real,D: real] :
% 3.82/4.05 ( ( ( minus_minus_real @ A @ B2 )
% 3.82/4.05 = ( minus_minus_real @ C @ D ) )
% 3.82/4.05 => ( ( ord_less_real @ A @ B2 )
% 3.82/4.05 = ( ord_less_real @ C @ D ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_eq_diff_less
% 3.82/4.05 thf(fact_3680_diff__eq__diff__less,axiom,
% 3.82/4.05 ! [A: int,B2: int,C: int,D: int] :
% 3.82/4.05 ( ( ( minus_minus_int @ A @ B2 )
% 3.82/4.05 = ( minus_minus_int @ C @ D ) )
% 3.82/4.05 => ( ( ord_less_int @ A @ B2 )
% 3.82/4.05 = ( ord_less_int @ C @ D ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_eq_diff_less
% 3.82/4.05 thf(fact_3681_diff__strict__left__mono,axiom,
% 3.82/4.05 ! [B2: real,A: real,C: real] :
% 3.82/4.05 ( ( ord_less_real @ B2 @ A )
% 3.82/4.05 => ( ord_less_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_strict_left_mono
% 3.82/4.05 thf(fact_3682_diff__strict__left__mono,axiom,
% 3.82/4.05 ! [B2: int,A: int,C: int] :
% 3.82/4.05 ( ( ord_less_int @ B2 @ A )
% 3.82/4.05 => ( ord_less_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_strict_left_mono
% 3.82/4.05 thf(fact_3683_diff__strict__right__mono,axiom,
% 3.82/4.05 ! [A: real,B2: real,C: real] :
% 3.82/4.05 ( ( ord_less_real @ A @ B2 )
% 3.82/4.05 => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B2 @ C ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_strict_right_mono
% 3.82/4.05 thf(fact_3684_diff__strict__right__mono,axiom,
% 3.82/4.05 ! [A: int,B2: int,C: int] :
% 3.82/4.05 ( ( ord_less_int @ A @ B2 )
% 3.82/4.05 => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B2 @ C ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_strict_right_mono
% 3.82/4.05 thf(fact_3685_right__diff__distrib_H,axiom,
% 3.82/4.05 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.05 ( ( times_times_nat @ A @ ( minus_minus_nat @ B2 @ C ) )
% 3.82/4.05 = ( minus_minus_nat @ ( times_times_nat @ A @ B2 ) @ ( times_times_nat @ A @ C ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % right_diff_distrib'
% 3.82/4.05 thf(fact_3686_right__diff__distrib_H,axiom,
% 3.82/4.05 ! [A: int,B2: int,C: int] :
% 3.82/4.05 ( ( times_times_int @ A @ ( minus_minus_int @ B2 @ C ) )
% 3.82/4.05 = ( minus_minus_int @ ( times_times_int @ A @ B2 ) @ ( times_times_int @ A @ C ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % right_diff_distrib'
% 3.82/4.05 thf(fact_3687_right__diff__distrib_H,axiom,
% 3.82/4.05 ! [A: real,B2: real,C: real] :
% 3.82/4.05 ( ( times_times_real @ A @ ( minus_minus_real @ B2 @ C ) )
% 3.82/4.05 = ( minus_minus_real @ ( times_times_real @ A @ B2 ) @ ( times_times_real @ A @ C ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % right_diff_distrib'
% 3.82/4.05 thf(fact_3688_right__diff__distrib_H,axiom,
% 3.82/4.05 ! [A: complex,B2: complex,C: complex] :
% 3.82/4.05 ( ( times_times_complex @ A @ ( minus_minus_complex @ B2 @ C ) )
% 3.82/4.05 = ( minus_minus_complex @ ( times_times_complex @ A @ B2 ) @ ( times_times_complex @ A @ C ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % right_diff_distrib'
% 3.82/4.05 thf(fact_3689_left__diff__distrib_H,axiom,
% 3.82/4.05 ! [B2: nat,C: nat,A: nat] :
% 3.82/4.05 ( ( times_times_nat @ ( minus_minus_nat @ B2 @ C ) @ A )
% 3.82/4.05 = ( minus_minus_nat @ ( times_times_nat @ B2 @ A ) @ ( times_times_nat @ C @ A ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % left_diff_distrib'
% 3.82/4.05 thf(fact_3690_left__diff__distrib_H,axiom,
% 3.82/4.05 ! [B2: int,C: int,A: int] :
% 3.82/4.05 ( ( times_times_int @ ( minus_minus_int @ B2 @ C ) @ A )
% 3.82/4.05 = ( minus_minus_int @ ( times_times_int @ B2 @ A ) @ ( times_times_int @ C @ A ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % left_diff_distrib'
% 3.82/4.05 thf(fact_3691_left__diff__distrib_H,axiom,
% 3.82/4.05 ! [B2: real,C: real,A: real] :
% 3.82/4.05 ( ( times_times_real @ ( minus_minus_real @ B2 @ C ) @ A )
% 3.82/4.05 = ( minus_minus_real @ ( times_times_real @ B2 @ A ) @ ( times_times_real @ C @ A ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % left_diff_distrib'
% 3.82/4.05 thf(fact_3692_left__diff__distrib_H,axiom,
% 3.82/4.05 ! [B2: complex,C: complex,A: complex] :
% 3.82/4.05 ( ( times_times_complex @ ( minus_minus_complex @ B2 @ C ) @ A )
% 3.82/4.05 = ( minus_minus_complex @ ( times_times_complex @ B2 @ A ) @ ( times_times_complex @ C @ A ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % left_diff_distrib'
% 3.82/4.05 thf(fact_3693_right__diff__distrib,axiom,
% 3.82/4.05 ! [A: int,B2: int,C: int] :
% 3.82/4.05 ( ( times_times_int @ A @ ( minus_minus_int @ B2 @ C ) )
% 3.82/4.05 = ( minus_minus_int @ ( times_times_int @ A @ B2 ) @ ( times_times_int @ A @ C ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % right_diff_distrib
% 3.82/4.05 thf(fact_3694_right__diff__distrib,axiom,
% 3.82/4.05 ! [A: real,B2: real,C: real] :
% 3.82/4.05 ( ( times_times_real @ A @ ( minus_minus_real @ B2 @ C ) )
% 3.82/4.05 = ( minus_minus_real @ ( times_times_real @ A @ B2 ) @ ( times_times_real @ A @ C ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % right_diff_distrib
% 3.82/4.05 thf(fact_3695_right__diff__distrib,axiom,
% 3.82/4.05 ! [A: complex,B2: complex,C: complex] :
% 3.82/4.05 ( ( times_times_complex @ A @ ( minus_minus_complex @ B2 @ C ) )
% 3.82/4.05 = ( minus_minus_complex @ ( times_times_complex @ A @ B2 ) @ ( times_times_complex @ A @ C ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % right_diff_distrib
% 3.82/4.05 thf(fact_3696_left__diff__distrib,axiom,
% 3.82/4.05 ! [A: int,B2: int,C: int] :
% 3.82/4.05 ( ( times_times_int @ ( minus_minus_int @ A @ B2 ) @ C )
% 3.82/4.05 = ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B2 @ C ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % left_diff_distrib
% 3.82/4.05 thf(fact_3697_left__diff__distrib,axiom,
% 3.82/4.05 ! [A: real,B2: real,C: real] :
% 3.82/4.05 ( ( times_times_real @ ( minus_minus_real @ A @ B2 ) @ C )
% 3.82/4.05 = ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B2 @ C ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % left_diff_distrib
% 3.82/4.05 thf(fact_3698_left__diff__distrib,axiom,
% 3.82/4.05 ! [A: complex,B2: complex,C: complex] :
% 3.82/4.05 ( ( times_times_complex @ ( minus_minus_complex @ A @ B2 ) @ C )
% 3.82/4.05 = ( minus_minus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B2 @ C ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % left_diff_distrib
% 3.82/4.05 thf(fact_3699_group__cancel_Osub1,axiom,
% 3.82/4.05 ! [A2: int,K: int,A: int,B2: int] :
% 3.82/4.05 ( ( A2
% 3.82/4.05 = ( plus_plus_int @ K @ A ) )
% 3.82/4.05 => ( ( minus_minus_int @ A2 @ B2 )
% 3.82/4.05 = ( plus_plus_int @ K @ ( minus_minus_int @ A @ B2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % group_cancel.sub1
% 3.82/4.05 thf(fact_3700_group__cancel_Osub1,axiom,
% 3.82/4.05 ! [A2: real,K: real,A: real,B2: real] :
% 3.82/4.05 ( ( A2
% 3.82/4.05 = ( plus_plus_real @ K @ A ) )
% 3.82/4.05 => ( ( minus_minus_real @ A2 @ B2 )
% 3.82/4.05 = ( plus_plus_real @ K @ ( minus_minus_real @ A @ B2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % group_cancel.sub1
% 3.82/4.05 thf(fact_3701_diff__eq__eq,axiom,
% 3.82/4.05 ! [A: int,B2: int,C: int] :
% 3.82/4.05 ( ( ( minus_minus_int @ A @ B2 )
% 3.82/4.05 = C )
% 3.82/4.05 = ( A
% 3.82/4.05 = ( plus_plus_int @ C @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_eq_eq
% 3.82/4.05 thf(fact_3702_diff__eq__eq,axiom,
% 3.82/4.05 ! [A: real,B2: real,C: real] :
% 3.82/4.05 ( ( ( minus_minus_real @ A @ B2 )
% 3.82/4.05 = C )
% 3.82/4.05 = ( A
% 3.82/4.05 = ( plus_plus_real @ C @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_eq_eq
% 3.82/4.05 thf(fact_3703_eq__diff__eq,axiom,
% 3.82/4.05 ! [A: int,C: int,B2: int] :
% 3.82/4.05 ( ( A
% 3.82/4.05 = ( minus_minus_int @ C @ B2 ) )
% 3.82/4.05 = ( ( plus_plus_int @ A @ B2 )
% 3.82/4.05 = C ) ) ).
% 3.82/4.05
% 3.82/4.05 % eq_diff_eq
% 3.82/4.05 thf(fact_3704_eq__diff__eq,axiom,
% 3.82/4.05 ! [A: real,C: real,B2: real] :
% 3.82/4.05 ( ( A
% 3.82/4.05 = ( minus_minus_real @ C @ B2 ) )
% 3.82/4.05 = ( ( plus_plus_real @ A @ B2 )
% 3.82/4.05 = C ) ) ).
% 3.82/4.05
% 3.82/4.05 % eq_diff_eq
% 3.82/4.05 thf(fact_3705_add__diff__eq,axiom,
% 3.82/4.05 ! [A: int,B2: int,C: int] :
% 3.82/4.05 ( ( plus_plus_int @ A @ ( minus_minus_int @ B2 @ C ) )
% 3.82/4.05 = ( minus_minus_int @ ( plus_plus_int @ A @ B2 ) @ C ) ) ).
% 3.82/4.05
% 3.82/4.05 % add_diff_eq
% 3.82/4.05 thf(fact_3706_add__diff__eq,axiom,
% 3.82/4.05 ! [A: real,B2: real,C: real] :
% 3.82/4.05 ( ( plus_plus_real @ A @ ( minus_minus_real @ B2 @ C ) )
% 3.82/4.05 = ( minus_minus_real @ ( plus_plus_real @ A @ B2 ) @ C ) ) ).
% 3.82/4.05
% 3.82/4.05 % add_diff_eq
% 3.82/4.05 thf(fact_3707_diff__diff__eq2,axiom,
% 3.82/4.05 ! [A: int,B2: int,C: int] :
% 3.82/4.05 ( ( minus_minus_int @ A @ ( minus_minus_int @ B2 @ C ) )
% 3.82/4.05 = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_diff_eq2
% 3.82/4.05 thf(fact_3708_diff__diff__eq2,axiom,
% 3.82/4.05 ! [A: real,B2: real,C: real] :
% 3.82/4.05 ( ( minus_minus_real @ A @ ( minus_minus_real @ B2 @ C ) )
% 3.82/4.05 = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_diff_eq2
% 3.82/4.05 thf(fact_3709_diff__add__eq,axiom,
% 3.82/4.05 ! [A: int,B2: int,C: int] :
% 3.82/4.05 ( ( plus_plus_int @ ( minus_minus_int @ A @ B2 ) @ C )
% 3.82/4.05 = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_add_eq
% 3.82/4.05 thf(fact_3710_diff__add__eq,axiom,
% 3.82/4.05 ! [A: real,B2: real,C: real] :
% 3.82/4.05 ( ( plus_plus_real @ ( minus_minus_real @ A @ B2 ) @ C )
% 3.82/4.05 = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_add_eq
% 3.82/4.05 thf(fact_3711_diff__add__eq__diff__diff__swap,axiom,
% 3.82/4.05 ! [A: int,B2: int,C: int] :
% 3.82/4.05 ( ( minus_minus_int @ A @ ( plus_plus_int @ B2 @ C ) )
% 3.82/4.05 = ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_add_eq_diff_diff_swap
% 3.82/4.05 thf(fact_3712_diff__add__eq__diff__diff__swap,axiom,
% 3.82/4.05 ! [A: real,B2: real,C: real] :
% 3.82/4.05 ( ( minus_minus_real @ A @ ( plus_plus_real @ B2 @ C ) )
% 3.82/4.05 = ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_add_eq_diff_diff_swap
% 3.82/4.05 thf(fact_3713_add__implies__diff,axiom,
% 3.82/4.05 ! [C: nat,B2: nat,A: nat] :
% 3.82/4.05 ( ( ( plus_plus_nat @ C @ B2 )
% 3.82/4.05 = A )
% 3.82/4.05 => ( C
% 3.82/4.05 = ( minus_minus_nat @ A @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % add_implies_diff
% 3.82/4.05 thf(fact_3714_add__implies__diff,axiom,
% 3.82/4.05 ! [C: int,B2: int,A: int] :
% 3.82/4.05 ( ( ( plus_plus_int @ C @ B2 )
% 3.82/4.05 = A )
% 3.82/4.05 => ( C
% 3.82/4.05 = ( minus_minus_int @ A @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % add_implies_diff
% 3.82/4.05 thf(fact_3715_add__implies__diff,axiom,
% 3.82/4.05 ! [C: real,B2: real,A: real] :
% 3.82/4.05 ( ( ( plus_plus_real @ C @ B2 )
% 3.82/4.05 = A )
% 3.82/4.05 => ( C
% 3.82/4.05 = ( minus_minus_real @ A @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % add_implies_diff
% 3.82/4.05 thf(fact_3716_diff__diff__eq,axiom,
% 3.82/4.05 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.05 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B2 ) @ C )
% 3.82/4.05 = ( minus_minus_nat @ A @ ( plus_plus_nat @ B2 @ C ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_diff_eq
% 3.82/4.05 thf(fact_3717_diff__diff__eq,axiom,
% 3.82/4.05 ! [A: int,B2: int,C: int] :
% 3.82/4.05 ( ( minus_minus_int @ ( minus_minus_int @ A @ B2 ) @ C )
% 3.82/4.05 = ( minus_minus_int @ A @ ( plus_plus_int @ B2 @ C ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_diff_eq
% 3.82/4.05 thf(fact_3718_diff__diff__eq,axiom,
% 3.82/4.05 ! [A: real,B2: real,C: real] :
% 3.82/4.05 ( ( minus_minus_real @ ( minus_minus_real @ A @ B2 ) @ C )
% 3.82/4.05 = ( minus_minus_real @ A @ ( plus_plus_real @ B2 @ C ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_diff_eq
% 3.82/4.05 thf(fact_3719_add__diff__add,axiom,
% 3.82/4.05 ! [A: int,C: int,B2: int,D: int] :
% 3.82/4.05 ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B2 @ D ) )
% 3.82/4.05 = ( plus_plus_int @ ( minus_minus_int @ A @ B2 ) @ ( minus_minus_int @ C @ D ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % add_diff_add
% 3.82/4.05 thf(fact_3720_add__diff__add,axiom,
% 3.82/4.05 ! [A: real,C: real,B2: real,D: real] :
% 3.82/4.05 ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B2 @ D ) )
% 3.82/4.05 = ( plus_plus_real @ ( minus_minus_real @ A @ B2 ) @ ( minus_minus_real @ C @ D ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % add_diff_add
% 3.82/4.05 thf(fact_3721_diff__divide__distrib,axiom,
% 3.82/4.05 ! [A: real,B2: real,C: real] :
% 3.82/4.05 ( ( divide_divide_real @ ( minus_minus_real @ A @ B2 ) @ C )
% 3.82/4.05 = ( minus_minus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B2 @ C ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_divide_distrib
% 3.82/4.05 thf(fact_3722_dvd__diff,axiom,
% 3.82/4.05 ! [X: int,Y: int,Z3: int] :
% 3.82/4.05 ( ( dvd_dvd_int @ X @ Y )
% 3.82/4.05 => ( ( dvd_dvd_int @ X @ Z3 )
% 3.82/4.05 => ( dvd_dvd_int @ X @ ( minus_minus_int @ Y @ Z3 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % dvd_diff
% 3.82/4.05 thf(fact_3723_dvd__diff,axiom,
% 3.82/4.05 ! [X: real,Y: real,Z3: real] :
% 3.82/4.05 ( ( dvd_dvd_real @ X @ Y )
% 3.82/4.05 => ( ( dvd_dvd_real @ X @ Z3 )
% 3.82/4.05 => ( dvd_dvd_real @ X @ ( minus_minus_real @ Y @ Z3 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % dvd_diff
% 3.82/4.05 thf(fact_3724_zero__induct__lemma,axiom,
% 3.82/4.05 ! [P: nat > $o,K: nat,I: nat] :
% 3.82/4.05 ( ( P @ K )
% 3.82/4.05 => ( ! [N3: nat] :
% 3.82/4.05 ( ( P @ ( suc @ N3 ) )
% 3.82/4.05 => ( P @ N3 ) )
% 3.82/4.05 => ( P @ ( minus_minus_nat @ K @ I ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % zero_induct_lemma
% 3.82/4.05 thf(fact_3725_minus__nat_Odiff__0,axiom,
% 3.82/4.05 ! [M2: nat] :
% 3.82/4.05 ( ( minus_minus_nat @ M2 @ zero_zero_nat )
% 3.82/4.05 = M2 ) ).
% 3.82/4.05
% 3.82/4.05 % minus_nat.diff_0
% 3.82/4.05 thf(fact_3726_diffs0__imp__equal,axiom,
% 3.82/4.05 ! [M2: nat,N2: nat] :
% 3.82/4.05 ( ( ( minus_minus_nat @ M2 @ N2 )
% 3.82/4.05 = zero_zero_nat )
% 3.82/4.05 => ( ( ( minus_minus_nat @ N2 @ M2 )
% 3.82/4.05 = zero_zero_nat )
% 3.82/4.05 => ( M2 = N2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % diffs0_imp_equal
% 3.82/4.05 thf(fact_3727_diff__less__mono2,axiom,
% 3.82/4.05 ! [M2: nat,N2: nat,L: nat] :
% 3.82/4.05 ( ( ord_less_nat @ M2 @ N2 )
% 3.82/4.05 => ( ( ord_less_nat @ M2 @ L )
% 3.82/4.05 => ( ord_less_nat @ ( minus_minus_nat @ L @ N2 ) @ ( minus_minus_nat @ L @ M2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_less_mono2
% 3.82/4.05 thf(fact_3728_less__imp__diff__less,axiom,
% 3.82/4.05 ! [J: nat,K: nat,N2: nat] :
% 3.82/4.05 ( ( ord_less_nat @ J @ K )
% 3.82/4.05 => ( ord_less_nat @ ( minus_minus_nat @ J @ N2 ) @ K ) ) ).
% 3.82/4.05
% 3.82/4.05 % less_imp_diff_less
% 3.82/4.05 thf(fact_3729_eq__diff__iff,axiom,
% 3.82/4.05 ! [K: nat,M2: nat,N2: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ K @ M2 )
% 3.82/4.05 => ( ( ord_less_eq_nat @ K @ N2 )
% 3.82/4.05 => ( ( ( minus_minus_nat @ M2 @ K )
% 3.82/4.05 = ( minus_minus_nat @ N2 @ K ) )
% 3.82/4.05 = ( M2 = N2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % eq_diff_iff
% 3.82/4.05 thf(fact_3730_le__diff__iff,axiom,
% 3.82/4.05 ! [K: nat,M2: nat,N2: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ K @ M2 )
% 3.82/4.05 => ( ( ord_less_eq_nat @ K @ N2 )
% 3.82/4.05 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M2 @ K ) @ ( minus_minus_nat @ N2 @ K ) )
% 3.82/4.05 = ( ord_less_eq_nat @ M2 @ N2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % le_diff_iff
% 3.82/4.05 thf(fact_3731_Nat_Odiff__diff__eq,axiom,
% 3.82/4.05 ! [K: nat,M2: nat,N2: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ K @ M2 )
% 3.82/4.05 => ( ( ord_less_eq_nat @ K @ N2 )
% 3.82/4.05 => ( ( minus_minus_nat @ ( minus_minus_nat @ M2 @ K ) @ ( minus_minus_nat @ N2 @ K ) )
% 3.82/4.05 = ( minus_minus_nat @ M2 @ N2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % Nat.diff_diff_eq
% 3.82/4.05 thf(fact_3732_diff__le__mono,axiom,
% 3.82/4.05 ! [M2: nat,N2: nat,L: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.05 => ( ord_less_eq_nat @ ( minus_minus_nat @ M2 @ L ) @ ( minus_minus_nat @ N2 @ L ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_le_mono
% 3.82/4.05 thf(fact_3733_diff__le__self,axiom,
% 3.82/4.05 ! [M2: nat,N2: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M2 @ N2 ) @ M2 ) ).
% 3.82/4.05
% 3.82/4.05 % diff_le_self
% 3.82/4.05 thf(fact_3734_le__diff__iff_H,axiom,
% 3.82/4.05 ! [A: nat,C: nat,B2: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ A @ C )
% 3.82/4.05 => ( ( ord_less_eq_nat @ B2 @ C )
% 3.82/4.05 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B2 ) )
% 3.82/4.05 = ( ord_less_eq_nat @ B2 @ A ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % le_diff_iff'
% 3.82/4.05 thf(fact_3735_diff__le__mono2,axiom,
% 3.82/4.05 ! [M2: nat,N2: nat,L: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.05 => ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N2 ) @ ( minus_minus_nat @ L @ M2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_le_mono2
% 3.82/4.05 thf(fact_3736_Nat_Odiff__cancel,axiom,
% 3.82/4.05 ! [K: nat,M2: nat,N2: nat] :
% 3.82/4.05 ( ( minus_minus_nat @ ( plus_plus_nat @ K @ M2 ) @ ( plus_plus_nat @ K @ N2 ) )
% 3.82/4.05 = ( minus_minus_nat @ M2 @ N2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % Nat.diff_cancel
% 3.82/4.05 thf(fact_3737_diff__cancel2,axiom,
% 3.82/4.05 ! [M2: nat,K: nat,N2: nat] :
% 3.82/4.05 ( ( minus_minus_nat @ ( plus_plus_nat @ M2 @ K ) @ ( plus_plus_nat @ N2 @ K ) )
% 3.82/4.05 = ( minus_minus_nat @ M2 @ N2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_cancel2
% 3.82/4.05 thf(fact_3738_diff__add__inverse,axiom,
% 3.82/4.05 ! [N2: nat,M2: nat] :
% 3.82/4.05 ( ( minus_minus_nat @ ( plus_plus_nat @ N2 @ M2 ) @ N2 )
% 3.82/4.05 = M2 ) ).
% 3.82/4.05
% 3.82/4.05 % diff_add_inverse
% 3.82/4.05 thf(fact_3739_diff__add__inverse2,axiom,
% 3.82/4.05 ! [M2: nat,N2: nat] :
% 3.82/4.05 ( ( minus_minus_nat @ ( plus_plus_nat @ M2 @ N2 ) @ N2 )
% 3.82/4.05 = M2 ) ).
% 3.82/4.05
% 3.82/4.05 % diff_add_inverse2
% 3.82/4.05 thf(fact_3740_diff__mult__distrib2,axiom,
% 3.82/4.05 ! [K: nat,M2: nat,N2: nat] :
% 3.82/4.05 ( ( times_times_nat @ K @ ( minus_minus_nat @ M2 @ N2 ) )
% 3.82/4.05 = ( minus_minus_nat @ ( times_times_nat @ K @ M2 ) @ ( times_times_nat @ K @ N2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_mult_distrib2
% 3.82/4.05 thf(fact_3741_diff__mult__distrib,axiom,
% 3.82/4.05 ! [M2: nat,N2: nat,K: nat] :
% 3.82/4.05 ( ( times_times_nat @ ( minus_minus_nat @ M2 @ N2 ) @ K )
% 3.82/4.05 = ( minus_minus_nat @ ( times_times_nat @ M2 @ K ) @ ( times_times_nat @ N2 @ K ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_mult_distrib
% 3.82/4.05 thf(fact_3742_max__diff__distrib__left,axiom,
% 3.82/4.05 ! [X: int,Y: int,Z3: int] :
% 3.82/4.05 ( ( minus_minus_int @ ( ord_max_int @ X @ Y ) @ Z3 )
% 3.82/4.05 = ( ord_max_int @ ( minus_minus_int @ X @ Z3 ) @ ( minus_minus_int @ Y @ Z3 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % max_diff_distrib_left
% 3.82/4.05 thf(fact_3743_max__diff__distrib__left,axiom,
% 3.82/4.05 ! [X: real,Y: real,Z3: real] :
% 3.82/4.05 ( ( minus_minus_real @ ( ord_max_real @ X @ Y ) @ Z3 )
% 3.82/4.05 = ( ord_max_real @ ( minus_minus_real @ X @ Z3 ) @ ( minus_minus_real @ Y @ Z3 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % max_diff_distrib_left
% 3.82/4.05 thf(fact_3744_dvd__diff__nat,axiom,
% 3.82/4.05 ! [K: nat,M2: nat,N2: nat] :
% 3.82/4.05 ( ( dvd_dvd_nat @ K @ M2 )
% 3.82/4.05 => ( ( dvd_dvd_nat @ K @ N2 )
% 3.82/4.05 => ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M2 @ N2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % dvd_diff_nat
% 3.82/4.05 thf(fact_3745_zero__less__eq__of__bool,axiom,
% 3.82/4.05 ! [P: $o] : ( ord_less_eq_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) ) ).
% 3.82/4.05
% 3.82/4.05 % zero_less_eq_of_bool
% 3.82/4.05 thf(fact_3746_zero__less__eq__of__bool,axiom,
% 3.82/4.05 ! [P: $o] : ( ord_less_eq_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 3.82/4.05
% 3.82/4.05 % zero_less_eq_of_bool
% 3.82/4.05 thf(fact_3747_zero__less__eq__of__bool,axiom,
% 3.82/4.05 ! [P: $o] : ( ord_less_eq_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) ) ).
% 3.82/4.05
% 3.82/4.05 % zero_less_eq_of_bool
% 3.82/4.05 thf(fact_3748_of__bool__less__eq__one,axiom,
% 3.82/4.05 ! [P: $o] : ( ord_less_eq_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real ) ).
% 3.82/4.05
% 3.82/4.05 % of_bool_less_eq_one
% 3.82/4.05 thf(fact_3749_of__bool__less__eq__one,axiom,
% 3.82/4.05 ! [P: $o] : ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat ) ).
% 3.82/4.05
% 3.82/4.05 % of_bool_less_eq_one
% 3.82/4.05 thf(fact_3750_of__bool__less__eq__one,axiom,
% 3.82/4.05 ! [P: $o] : ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int ) ).
% 3.82/4.05
% 3.82/4.05 % of_bool_less_eq_one
% 3.82/4.05 thf(fact_3751_split__of__bool__asm,axiom,
% 3.82/4.05 ! [P: real > $o,P5: $o] :
% 3.82/4.05 ( ( P @ ( zero_n3304061248610475627l_real @ P5 ) )
% 3.82/4.05 = ( ~ ( ( P5
% 3.82/4.05 & ~ ( P @ one_one_real ) )
% 3.82/4.05 | ( ~ P5
% 3.82/4.05 & ~ ( P @ zero_zero_real ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % split_of_bool_asm
% 3.82/4.05 thf(fact_3752_split__of__bool__asm,axiom,
% 3.82/4.05 ! [P: complex > $o,P5: $o] :
% 3.82/4.05 ( ( P @ ( zero_n1201886186963655149omplex @ P5 ) )
% 3.82/4.05 = ( ~ ( ( P5
% 3.82/4.05 & ~ ( P @ one_one_complex ) )
% 3.82/4.05 | ( ~ P5
% 3.82/4.05 & ~ ( P @ zero_zero_complex ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % split_of_bool_asm
% 3.82/4.05 thf(fact_3753_split__of__bool__asm,axiom,
% 3.82/4.05 ! [P: extended_enat > $o,P5: $o] :
% 3.82/4.05 ( ( P @ ( zero_n1046097342994218471d_enat @ P5 ) )
% 3.82/4.05 = ( ~ ( ( P5
% 3.82/4.05 & ~ ( P @ one_on7984719198319812577d_enat ) )
% 3.82/4.05 | ( ~ P5
% 3.82/4.05 & ~ ( P @ zero_z5237406670263579293d_enat ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % split_of_bool_asm
% 3.82/4.05 thf(fact_3754_split__of__bool__asm,axiom,
% 3.82/4.05 ! [P: nat > $o,P5: $o] :
% 3.82/4.05 ( ( P @ ( zero_n2687167440665602831ol_nat @ P5 ) )
% 3.82/4.05 = ( ~ ( ( P5
% 3.82/4.05 & ~ ( P @ one_one_nat ) )
% 3.82/4.05 | ( ~ P5
% 3.82/4.05 & ~ ( P @ zero_zero_nat ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % split_of_bool_asm
% 3.82/4.05 thf(fact_3755_split__of__bool__asm,axiom,
% 3.82/4.05 ! [P: int > $o,P5: $o] :
% 3.82/4.05 ( ( P @ ( zero_n2684676970156552555ol_int @ P5 ) )
% 3.82/4.05 = ( ~ ( ( P5
% 3.82/4.05 & ~ ( P @ one_one_int ) )
% 3.82/4.05 | ( ~ P5
% 3.82/4.05 & ~ ( P @ zero_zero_int ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % split_of_bool_asm
% 3.82/4.05 thf(fact_3756_split__of__bool,axiom,
% 3.82/4.05 ! [P: real > $o,P5: $o] :
% 3.82/4.05 ( ( P @ ( zero_n3304061248610475627l_real @ P5 ) )
% 3.82/4.05 = ( ( P5
% 3.82/4.05 => ( P @ one_one_real ) )
% 3.82/4.05 & ( ~ P5
% 3.82/4.05 => ( P @ zero_zero_real ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % split_of_bool
% 3.82/4.05 thf(fact_3757_split__of__bool,axiom,
% 3.82/4.05 ! [P: complex > $o,P5: $o] :
% 3.82/4.05 ( ( P @ ( zero_n1201886186963655149omplex @ P5 ) )
% 3.82/4.05 = ( ( P5
% 3.82/4.05 => ( P @ one_one_complex ) )
% 3.82/4.05 & ( ~ P5
% 3.82/4.05 => ( P @ zero_zero_complex ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % split_of_bool
% 3.82/4.05 thf(fact_3758_split__of__bool,axiom,
% 3.82/4.05 ! [P: extended_enat > $o,P5: $o] :
% 3.82/4.05 ( ( P @ ( zero_n1046097342994218471d_enat @ P5 ) )
% 3.82/4.05 = ( ( P5
% 3.82/4.05 => ( P @ one_on7984719198319812577d_enat ) )
% 3.82/4.05 & ( ~ P5
% 3.82/4.05 => ( P @ zero_z5237406670263579293d_enat ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % split_of_bool
% 3.82/4.05 thf(fact_3759_split__of__bool,axiom,
% 3.82/4.05 ! [P: nat > $o,P5: $o] :
% 3.82/4.05 ( ( P @ ( zero_n2687167440665602831ol_nat @ P5 ) )
% 3.82/4.05 = ( ( P5
% 3.82/4.05 => ( P @ one_one_nat ) )
% 3.82/4.05 & ( ~ P5
% 3.82/4.05 => ( P @ zero_zero_nat ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % split_of_bool
% 3.82/4.05 thf(fact_3760_split__of__bool,axiom,
% 3.82/4.05 ! [P: int > $o,P5: $o] :
% 3.82/4.05 ( ( P @ ( zero_n2684676970156552555ol_int @ P5 ) )
% 3.82/4.05 = ( ( P5
% 3.82/4.05 => ( P @ one_one_int ) )
% 3.82/4.05 & ( ~ P5
% 3.82/4.05 => ( P @ zero_zero_int ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % split_of_bool
% 3.82/4.05 thf(fact_3761_of__bool__def,axiom,
% 3.82/4.05 ( zero_n3304061248610475627l_real
% 3.82/4.05 = ( ^ [P6: $o] : ( if_real @ P6 @ one_one_real @ zero_zero_real ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % of_bool_def
% 3.82/4.05 thf(fact_3762_of__bool__def,axiom,
% 3.82/4.05 ( zero_n1201886186963655149omplex
% 3.82/4.05 = ( ^ [P6: $o] : ( if_complex @ P6 @ one_one_complex @ zero_zero_complex ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % of_bool_def
% 3.82/4.05 thf(fact_3763_of__bool__def,axiom,
% 3.82/4.05 ( zero_n1046097342994218471d_enat
% 3.82/4.05 = ( ^ [P6: $o] : ( if_Extended_enat @ P6 @ one_on7984719198319812577d_enat @ zero_z5237406670263579293d_enat ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % of_bool_def
% 3.82/4.05 thf(fact_3764_of__bool__def,axiom,
% 3.82/4.05 ( zero_n2687167440665602831ol_nat
% 3.82/4.05 = ( ^ [P6: $o] : ( if_nat @ P6 @ one_one_nat @ zero_zero_nat ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % of_bool_def
% 3.82/4.05 thf(fact_3765_of__bool__def,axiom,
% 3.82/4.05 ( zero_n2684676970156552555ol_int
% 3.82/4.05 = ( ^ [P6: $o] : ( if_int @ P6 @ one_one_int @ zero_zero_int ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % of_bool_def
% 3.82/4.05 thf(fact_3766_le__iff__diff__le__0,axiom,
% 3.82/4.05 ( ord_less_eq_real
% 3.82/4.05 = ( ^ [A3: real,B3: real] : ( ord_less_eq_real @ ( minus_minus_real @ A3 @ B3 ) @ zero_zero_real ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % le_iff_diff_le_0
% 3.82/4.05 thf(fact_3767_le__iff__diff__le__0,axiom,
% 3.82/4.05 ( ord_less_eq_int
% 3.82/4.05 = ( ^ [A3: int,B3: int] : ( ord_less_eq_int @ ( minus_minus_int @ A3 @ B3 ) @ zero_zero_int ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % le_iff_diff_le_0
% 3.82/4.05 thf(fact_3768_less__iff__diff__less__0,axiom,
% 3.82/4.05 ( ord_less_real
% 3.82/4.05 = ( ^ [A3: real,B3: real] : ( ord_less_real @ ( minus_minus_real @ A3 @ B3 ) @ zero_zero_real ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % less_iff_diff_less_0
% 3.82/4.05 thf(fact_3769_less__iff__diff__less__0,axiom,
% 3.82/4.05 ( ord_less_int
% 3.82/4.05 = ( ^ [A3: int,B3: int] : ( ord_less_int @ ( minus_minus_int @ A3 @ B3 ) @ zero_zero_int ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % less_iff_diff_less_0
% 3.82/4.05 thf(fact_3770_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 3.82/4.05 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ A @ B2 )
% 3.82/4.05 => ( ( ord_less_eq_nat @ A @ B2 )
% 3.82/4.05 => ( ( ( minus_minus_nat @ B2 @ A )
% 3.82/4.05 = C )
% 3.82/4.05 = ( B2
% 3.82/4.05 = ( plus_plus_nat @ C @ A ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % ordered_cancel_comm_monoid_diff_class.le_imp_diff_is_add
% 3.82/4.05 thf(fact_3771_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 3.82/4.05 ! [A: nat,B2: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ A @ B2 )
% 3.82/4.05 => ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B2 @ A ) )
% 3.82/4.05 = B2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % ordered_cancel_comm_monoid_diff_class.add_diff_inverse
% 3.82/4.05 thf(fact_3772_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 3.82/4.05 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ A @ B2 )
% 3.82/4.05 => ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B2 @ A ) )
% 3.82/4.05 = ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % ordered_cancel_comm_monoid_diff_class.diff_diff_right
% 3.82/4.05 thf(fact_3773_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 3.82/4.05 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ A @ B2 )
% 3.82/4.05 => ( ( minus_minus_nat @ ( plus_plus_nat @ B2 @ C ) @ A )
% 3.82/4.05 = ( plus_plus_nat @ ( minus_minus_nat @ B2 @ A ) @ C ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc2
% 3.82/4.05 thf(fact_3774_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 3.82/4.05 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ A @ B2 )
% 3.82/4.05 => ( ( plus_plus_nat @ ( minus_minus_nat @ B2 @ A ) @ C )
% 3.82/4.05 = ( minus_minus_nat @ ( plus_plus_nat @ B2 @ C ) @ A ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc2
% 3.82/4.05 thf(fact_3775_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 3.82/4.05 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ A @ B2 )
% 3.82/4.05 => ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B2 ) @ A )
% 3.82/4.05 = ( plus_plus_nat @ C @ ( minus_minus_nat @ B2 @ A ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc
% 3.82/4.05 thf(fact_3776_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 3.82/4.05 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ A @ B2 )
% 3.82/4.05 => ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B2 @ A ) )
% 3.82/4.05 = ( minus_minus_nat @ ( plus_plus_nat @ C @ B2 ) @ A ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc
% 3.82/4.05 thf(fact_3777_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 3.82/4.05 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ A @ B2 )
% 3.82/4.05 => ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B2 @ A ) )
% 3.82/4.05 = ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % ordered_cancel_comm_monoid_diff_class.le_diff_conv2
% 3.82/4.05 thf(fact_3778_le__add__diff,axiom,
% 3.82/4.05 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ A @ B2 )
% 3.82/4.05 => ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B2 @ C ) @ A ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % le_add_diff
% 3.82/4.05 thf(fact_3779_diff__add,axiom,
% 3.82/4.05 ! [A: nat,B2: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ A @ B2 )
% 3.82/4.05 => ( ( plus_plus_nat @ ( minus_minus_nat @ B2 @ A ) @ A )
% 3.82/4.05 = B2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_add
% 3.82/4.05 thf(fact_3780_le__diff__eq,axiom,
% 3.82/4.05 ! [A: real,C: real,B2: real] :
% 3.82/4.05 ( ( ord_less_eq_real @ A @ ( minus_minus_real @ C @ B2 ) )
% 3.82/4.05 = ( ord_less_eq_real @ ( plus_plus_real @ A @ B2 ) @ C ) ) ).
% 3.82/4.05
% 3.82/4.05 % le_diff_eq
% 3.82/4.05 thf(fact_3781_le__diff__eq,axiom,
% 3.82/4.05 ! [A: int,C: int,B2: int] :
% 3.82/4.05 ( ( ord_less_eq_int @ A @ ( minus_minus_int @ C @ B2 ) )
% 3.82/4.05 = ( ord_less_eq_int @ ( plus_plus_int @ A @ B2 ) @ C ) ) ).
% 3.82/4.05
% 3.82/4.05 % le_diff_eq
% 3.82/4.05 thf(fact_3782_diff__le__eq,axiom,
% 3.82/4.05 ! [A: real,B2: real,C: real] :
% 3.82/4.05 ( ( ord_less_eq_real @ ( minus_minus_real @ A @ B2 ) @ C )
% 3.82/4.05 = ( ord_less_eq_real @ A @ ( plus_plus_real @ C @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_le_eq
% 3.82/4.05 thf(fact_3783_diff__le__eq,axiom,
% 3.82/4.05 ! [A: int,B2: int,C: int] :
% 3.82/4.05 ( ( ord_less_eq_int @ ( minus_minus_int @ A @ B2 ) @ C )
% 3.82/4.05 = ( ord_less_eq_int @ A @ ( plus_plus_int @ C @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_le_eq
% 3.82/4.05 thf(fact_3784_add__le__add__imp__diff__le,axiom,
% 3.82/4.05 ! [I: real,K: real,N2: real,J: real] :
% 3.82/4.05 ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N2 )
% 3.82/4.05 => ( ( ord_less_eq_real @ N2 @ ( plus_plus_real @ J @ K ) )
% 3.82/4.05 => ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N2 )
% 3.82/4.05 => ( ( ord_less_eq_real @ N2 @ ( plus_plus_real @ J @ K ) )
% 3.82/4.05 => ( ord_less_eq_real @ ( minus_minus_real @ N2 @ K ) @ J ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % add_le_add_imp_diff_le
% 3.82/4.05 thf(fact_3785_add__le__add__imp__diff__le,axiom,
% 3.82/4.05 ! [I: nat,K: nat,N2: nat,J: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N2 )
% 3.82/4.05 => ( ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ J @ K ) )
% 3.82/4.05 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N2 )
% 3.82/4.05 => ( ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ J @ K ) )
% 3.82/4.05 => ( ord_less_eq_nat @ ( minus_minus_nat @ N2 @ K ) @ J ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % add_le_add_imp_diff_le
% 3.82/4.05 thf(fact_3786_add__le__add__imp__diff__le,axiom,
% 3.82/4.05 ! [I: int,K: int,N2: int,J: int] :
% 3.82/4.05 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N2 )
% 3.82/4.05 => ( ( ord_less_eq_int @ N2 @ ( plus_plus_int @ J @ K ) )
% 3.82/4.05 => ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N2 )
% 3.82/4.05 => ( ( ord_less_eq_int @ N2 @ ( plus_plus_int @ J @ K ) )
% 3.82/4.05 => ( ord_less_eq_int @ ( minus_minus_int @ N2 @ K ) @ J ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % add_le_add_imp_diff_le
% 3.82/4.05 thf(fact_3787_add__le__imp__le__diff,axiom,
% 3.82/4.05 ! [I: real,K: real,N2: real] :
% 3.82/4.05 ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N2 )
% 3.82/4.05 => ( ord_less_eq_real @ I @ ( minus_minus_real @ N2 @ K ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % add_le_imp_le_diff
% 3.82/4.05 thf(fact_3788_add__le__imp__le__diff,axiom,
% 3.82/4.05 ! [I: nat,K: nat,N2: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N2 )
% 3.82/4.05 => ( ord_less_eq_nat @ I @ ( minus_minus_nat @ N2 @ K ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % add_le_imp_le_diff
% 3.82/4.05 thf(fact_3789_add__le__imp__le__diff,axiom,
% 3.82/4.05 ! [I: int,K: int,N2: int] :
% 3.82/4.05 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N2 )
% 3.82/4.05 => ( ord_less_eq_int @ I @ ( minus_minus_int @ N2 @ K ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % add_le_imp_le_diff
% 3.82/4.05 thf(fact_3790_less__diff__eq,axiom,
% 3.82/4.05 ! [A: real,C: real,B2: real] :
% 3.82/4.05 ( ( ord_less_real @ A @ ( minus_minus_real @ C @ B2 ) )
% 3.82/4.05 = ( ord_less_real @ ( plus_plus_real @ A @ B2 ) @ C ) ) ).
% 3.82/4.05
% 3.82/4.05 % less_diff_eq
% 3.82/4.05 thf(fact_3791_less__diff__eq,axiom,
% 3.82/4.05 ! [A: int,C: int,B2: int] :
% 3.82/4.05 ( ( ord_less_int @ A @ ( minus_minus_int @ C @ B2 ) )
% 3.82/4.05 = ( ord_less_int @ ( plus_plus_int @ A @ B2 ) @ C ) ) ).
% 3.82/4.05
% 3.82/4.05 % less_diff_eq
% 3.82/4.05 thf(fact_3792_diff__less__eq,axiom,
% 3.82/4.05 ! [A: real,B2: real,C: real] :
% 3.82/4.05 ( ( ord_less_real @ ( minus_minus_real @ A @ B2 ) @ C )
% 3.82/4.05 = ( ord_less_real @ A @ ( plus_plus_real @ C @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_less_eq
% 3.82/4.05 thf(fact_3793_diff__less__eq,axiom,
% 3.82/4.05 ! [A: int,B2: int,C: int] :
% 3.82/4.05 ( ( ord_less_int @ ( minus_minus_int @ A @ B2 ) @ C )
% 3.82/4.05 = ( ord_less_int @ A @ ( plus_plus_int @ C @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_less_eq
% 3.82/4.05 thf(fact_3794_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 3.82/4.05 ! [A: nat,B2: nat] :
% 3.82/4.05 ( ~ ( ord_less_nat @ A @ B2 )
% 3.82/4.05 => ( ( plus_plus_nat @ B2 @ ( minus_minus_nat @ A @ B2 ) )
% 3.82/4.05 = A ) ) ).
% 3.82/4.05
% 3.82/4.05 % linordered_semidom_class.add_diff_inverse
% 3.82/4.05 thf(fact_3795_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 3.82/4.05 ! [A: real,B2: real] :
% 3.82/4.05 ( ~ ( ord_less_real @ A @ B2 )
% 3.82/4.05 => ( ( plus_plus_real @ B2 @ ( minus_minus_real @ A @ B2 ) )
% 3.82/4.05 = A ) ) ).
% 3.82/4.05
% 3.82/4.05 % linordered_semidom_class.add_diff_inverse
% 3.82/4.05 thf(fact_3796_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 3.82/4.05 ! [A: int,B2: int] :
% 3.82/4.05 ( ~ ( ord_less_int @ A @ B2 )
% 3.82/4.05 => ( ( plus_plus_int @ B2 @ ( minus_minus_int @ A @ B2 ) )
% 3.82/4.05 = A ) ) ).
% 3.82/4.05
% 3.82/4.05 % linordered_semidom_class.add_diff_inverse
% 3.82/4.05 thf(fact_3797_eq__add__iff1,axiom,
% 3.82/4.05 ! [A: int,E2: int,C: int,B2: int,D: int] :
% 3.82/4.05 ( ( ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C )
% 3.82/4.05 = ( plus_plus_int @ ( times_times_int @ B2 @ E2 ) @ D ) )
% 3.82/4.05 = ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B2 ) @ E2 ) @ C )
% 3.82/4.05 = D ) ) ).
% 3.82/4.05
% 3.82/4.05 % eq_add_iff1
% 3.82/4.05 thf(fact_3798_eq__add__iff1,axiom,
% 3.82/4.05 ! [A: real,E2: real,C: real,B2: real,D: real] :
% 3.82/4.05 ( ( ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C )
% 3.82/4.05 = ( plus_plus_real @ ( times_times_real @ B2 @ E2 ) @ D ) )
% 3.82/4.05 = ( ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B2 ) @ E2 ) @ C )
% 3.82/4.05 = D ) ) ).
% 3.82/4.05
% 3.82/4.05 % eq_add_iff1
% 3.82/4.05 thf(fact_3799_eq__add__iff1,axiom,
% 3.82/4.05 ! [A: complex,E2: complex,C: complex,B2: complex,D: complex] :
% 3.82/4.05 ( ( ( plus_plus_complex @ ( times_times_complex @ A @ E2 ) @ C )
% 3.82/4.05 = ( plus_plus_complex @ ( times_times_complex @ B2 @ E2 ) @ D ) )
% 3.82/4.05 = ( ( plus_plus_complex @ ( times_times_complex @ ( minus_minus_complex @ A @ B2 ) @ E2 ) @ C )
% 3.82/4.05 = D ) ) ).
% 3.82/4.05
% 3.82/4.05 % eq_add_iff1
% 3.82/4.05 thf(fact_3800_eq__add__iff2,axiom,
% 3.82/4.05 ! [A: int,E2: int,C: int,B2: int,D: int] :
% 3.82/4.05 ( ( ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C )
% 3.82/4.05 = ( plus_plus_int @ ( times_times_int @ B2 @ E2 ) @ D ) )
% 3.82/4.05 = ( C
% 3.82/4.05 = ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B2 @ A ) @ E2 ) @ D ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % eq_add_iff2
% 3.82/4.05 thf(fact_3801_eq__add__iff2,axiom,
% 3.82/4.05 ! [A: real,E2: real,C: real,B2: real,D: real] :
% 3.82/4.05 ( ( ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C )
% 3.82/4.05 = ( plus_plus_real @ ( times_times_real @ B2 @ E2 ) @ D ) )
% 3.82/4.05 = ( C
% 3.82/4.05 = ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B2 @ A ) @ E2 ) @ D ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % eq_add_iff2
% 3.82/4.05 thf(fact_3802_eq__add__iff2,axiom,
% 3.82/4.05 ! [A: complex,E2: complex,C: complex,B2: complex,D: complex] :
% 3.82/4.05 ( ( ( plus_plus_complex @ ( times_times_complex @ A @ E2 ) @ C )
% 3.82/4.05 = ( plus_plus_complex @ ( times_times_complex @ B2 @ E2 ) @ D ) )
% 3.82/4.05 = ( C
% 3.82/4.05 = ( plus_plus_complex @ ( times_times_complex @ ( minus_minus_complex @ B2 @ A ) @ E2 ) @ D ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % eq_add_iff2
% 3.82/4.05 thf(fact_3803_square__diff__square__factored,axiom,
% 3.82/4.05 ! [X: int,Y: int] :
% 3.82/4.05 ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) )
% 3.82/4.05 = ( times_times_int @ ( plus_plus_int @ X @ Y ) @ ( minus_minus_int @ X @ Y ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % square_diff_square_factored
% 3.82/4.05 thf(fact_3804_square__diff__square__factored,axiom,
% 3.82/4.05 ! [X: real,Y: real] :
% 3.82/4.05 ( ( minus_minus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) )
% 3.82/4.05 = ( times_times_real @ ( plus_plus_real @ X @ Y ) @ ( minus_minus_real @ X @ Y ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % square_diff_square_factored
% 3.82/4.05 thf(fact_3805_square__diff__square__factored,axiom,
% 3.82/4.05 ! [X: complex,Y: complex] :
% 3.82/4.05 ( ( minus_minus_complex @ ( times_times_complex @ X @ X ) @ ( times_times_complex @ Y @ Y ) )
% 3.82/4.05 = ( times_times_complex @ ( plus_plus_complex @ X @ Y ) @ ( minus_minus_complex @ X @ Y ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % square_diff_square_factored
% 3.82/4.05 thf(fact_3806_mult__diff__mult,axiom,
% 3.82/4.05 ! [X: int,Y: int,A: int,B2: int] :
% 3.82/4.05 ( ( minus_minus_int @ ( times_times_int @ X @ Y ) @ ( times_times_int @ A @ B2 ) )
% 3.82/4.05 = ( plus_plus_int @ ( times_times_int @ X @ ( minus_minus_int @ Y @ B2 ) ) @ ( times_times_int @ ( minus_minus_int @ X @ A ) @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % mult_diff_mult
% 3.82/4.05 thf(fact_3807_mult__diff__mult,axiom,
% 3.82/4.05 ! [X: real,Y: real,A: real,B2: real] :
% 3.82/4.05 ( ( minus_minus_real @ ( times_times_real @ X @ Y ) @ ( times_times_real @ A @ B2 ) )
% 3.82/4.05 = ( plus_plus_real @ ( times_times_real @ X @ ( minus_minus_real @ Y @ B2 ) ) @ ( times_times_real @ ( minus_minus_real @ X @ A ) @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % mult_diff_mult
% 3.82/4.05 thf(fact_3808_mult__diff__mult,axiom,
% 3.82/4.05 ! [X: complex,Y: complex,A: complex,B2: complex] :
% 3.82/4.05 ( ( minus_minus_complex @ ( times_times_complex @ X @ Y ) @ ( times_times_complex @ A @ B2 ) )
% 3.82/4.05 = ( plus_plus_complex @ ( times_times_complex @ X @ ( minus_minus_complex @ Y @ B2 ) ) @ ( times_times_complex @ ( minus_minus_complex @ X @ A ) @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % mult_diff_mult
% 3.82/4.05 thf(fact_3809_dvd__minus__mod,axiom,
% 3.82/4.05 ! [B2: nat,A: nat] : ( dvd_dvd_nat @ B2 @ ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % dvd_minus_mod
% 3.82/4.05 thf(fact_3810_dvd__minus__mod,axiom,
% 3.82/4.05 ! [B2: int,A: int] : ( dvd_dvd_int @ B2 @ ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % dvd_minus_mod
% 3.82/4.05 thf(fact_3811_diff__less__Suc,axiom,
% 3.82/4.05 ! [M2: nat,N2: nat] : ( ord_less_nat @ ( minus_minus_nat @ M2 @ N2 ) @ ( suc @ M2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_less_Suc
% 3.82/4.05 thf(fact_3812_Suc__diff__Suc,axiom,
% 3.82/4.05 ! [N2: nat,M2: nat] :
% 3.82/4.05 ( ( ord_less_nat @ N2 @ M2 )
% 3.82/4.05 => ( ( suc @ ( minus_minus_nat @ M2 @ ( suc @ N2 ) ) )
% 3.82/4.05 = ( minus_minus_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % Suc_diff_Suc
% 3.82/4.05 thf(fact_3813_diff__less,axiom,
% 3.82/4.05 ! [N2: nat,M2: nat] :
% 3.82/4.05 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.05 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 3.82/4.05 => ( ord_less_nat @ ( minus_minus_nat @ M2 @ N2 ) @ M2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_less
% 3.82/4.05 thf(fact_3814_Suc__diff__le,axiom,
% 3.82/4.05 ! [N2: nat,M2: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ N2 @ M2 )
% 3.82/4.05 => ( ( minus_minus_nat @ ( suc @ M2 ) @ N2 )
% 3.82/4.05 = ( suc @ ( minus_minus_nat @ M2 @ N2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % Suc_diff_le
% 3.82/4.05 thf(fact_3815_less__diff__iff,axiom,
% 3.82/4.05 ! [K: nat,M2: nat,N2: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ K @ M2 )
% 3.82/4.05 => ( ( ord_less_eq_nat @ K @ N2 )
% 3.82/4.05 => ( ( ord_less_nat @ ( minus_minus_nat @ M2 @ K ) @ ( minus_minus_nat @ N2 @ K ) )
% 3.82/4.05 = ( ord_less_nat @ M2 @ N2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % less_diff_iff
% 3.82/4.05 thf(fact_3816_diff__less__mono,axiom,
% 3.82/4.05 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.05 ( ( ord_less_nat @ A @ B2 )
% 3.82/4.05 => ( ( ord_less_eq_nat @ C @ A )
% 3.82/4.05 => ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B2 @ C ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_less_mono
% 3.82/4.05 thf(fact_3817_diff__add__0,axiom,
% 3.82/4.05 ! [N2: nat,M2: nat] :
% 3.82/4.05 ( ( minus_minus_nat @ N2 @ ( plus_plus_nat @ N2 @ M2 ) )
% 3.82/4.05 = zero_zero_nat ) ).
% 3.82/4.05
% 3.82/4.05 % diff_add_0
% 3.82/4.05 thf(fact_3818_set__encode__eq,axiom,
% 3.82/4.05 ! [A2: set_nat,B: set_nat] :
% 3.82/4.05 ( ( finite_finite_nat @ A2 )
% 3.82/4.05 => ( ( finite_finite_nat @ B )
% 3.82/4.05 => ( ( ( nat_set_encode @ A2 )
% 3.82/4.05 = ( nat_set_encode @ B ) )
% 3.82/4.05 = ( A2 = B ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % set_encode_eq
% 3.82/4.05 thf(fact_3819_add__diff__inverse__nat,axiom,
% 3.82/4.05 ! [M2: nat,N2: nat] :
% 3.82/4.05 ( ~ ( ord_less_nat @ M2 @ N2 )
% 3.82/4.05 => ( ( plus_plus_nat @ N2 @ ( minus_minus_nat @ M2 @ N2 ) )
% 3.82/4.05 = M2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % add_diff_inverse_nat
% 3.82/4.05 thf(fact_3820_less__diff__conv,axiom,
% 3.82/4.05 ! [I: nat,J: nat,K: nat] :
% 3.82/4.05 ( ( ord_less_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 3.82/4.05 = ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ).
% 3.82/4.05
% 3.82/4.05 % less_diff_conv
% 3.82/4.05 thf(fact_3821_Nat_Ole__imp__diff__is__add,axiom,
% 3.82/4.05 ! [I: nat,J: nat,K: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ I @ J )
% 3.82/4.05 => ( ( ( minus_minus_nat @ J @ I )
% 3.82/4.05 = K )
% 3.82/4.05 = ( J
% 3.82/4.05 = ( plus_plus_nat @ K @ I ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % Nat.le_imp_diff_is_add
% 3.82/4.05 thf(fact_3822_Nat_Odiff__add__assoc2,axiom,
% 3.82/4.05 ! [K: nat,J: nat,I: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ K @ J )
% 3.82/4.05 => ( ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K )
% 3.82/4.05 = ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % Nat.diff_add_assoc2
% 3.82/4.05 thf(fact_3823_Nat_Odiff__add__assoc,axiom,
% 3.82/4.05 ! [K: nat,J: nat,I: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ K @ J )
% 3.82/4.05 => ( ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 3.82/4.05 = ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % Nat.diff_add_assoc
% 3.82/4.05 thf(fact_3824_Nat_Ole__diff__conv2,axiom,
% 3.82/4.05 ! [K: nat,J: nat,I: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ K @ J )
% 3.82/4.05 => ( ( ord_less_eq_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 3.82/4.05 = ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % Nat.le_diff_conv2
% 3.82/4.05 thf(fact_3825_le__diff__conv,axiom,
% 3.82/4.05 ! [J: nat,K: nat,I: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 3.82/4.05 = ( ord_less_eq_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % le_diff_conv
% 3.82/4.05 thf(fact_3826_diff__Suc__eq__diff__pred,axiom,
% 3.82/4.05 ! [M2: nat,N2: nat] :
% 3.82/4.05 ( ( minus_minus_nat @ M2 @ ( suc @ N2 ) )
% 3.82/4.05 = ( minus_minus_nat @ ( minus_minus_nat @ M2 @ one_one_nat ) @ N2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_Suc_eq_diff_pred
% 3.82/4.05 thf(fact_3827_dvd__minus__self,axiom,
% 3.82/4.05 ! [M2: nat,N2: nat] :
% 3.82/4.05 ( ( dvd_dvd_nat @ M2 @ ( minus_minus_nat @ N2 @ M2 ) )
% 3.82/4.05 = ( ( ord_less_nat @ N2 @ M2 )
% 3.82/4.05 | ( dvd_dvd_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % dvd_minus_self
% 3.82/4.05 thf(fact_3828_less__eq__dvd__minus,axiom,
% 3.82/4.05 ! [M2: nat,N2: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.05 => ( ( dvd_dvd_nat @ M2 @ N2 )
% 3.82/4.05 = ( dvd_dvd_nat @ M2 @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % less_eq_dvd_minus
% 3.82/4.05 thf(fact_3829_dvd__diffD1,axiom,
% 3.82/4.05 ! [K: nat,M2: nat,N2: nat] :
% 3.82/4.05 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M2 @ N2 ) )
% 3.82/4.05 => ( ( dvd_dvd_nat @ K @ M2 )
% 3.82/4.05 => ( ( ord_less_eq_nat @ N2 @ M2 )
% 3.82/4.05 => ( dvd_dvd_nat @ K @ N2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % dvd_diffD1
% 3.82/4.05 thf(fact_3830_dvd__diffD,axiom,
% 3.82/4.05 ! [K: nat,M2: nat,N2: nat] :
% 3.82/4.05 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M2 @ N2 ) )
% 3.82/4.05 => ( ( dvd_dvd_nat @ K @ N2 )
% 3.82/4.05 => ( ( ord_less_eq_nat @ N2 @ M2 )
% 3.82/4.05 => ( dvd_dvd_nat @ K @ M2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % dvd_diffD
% 3.82/4.05 thf(fact_3831_mod__geq,axiom,
% 3.82/4.05 ! [M2: nat,N2: nat] :
% 3.82/4.05 ( ~ ( ord_less_nat @ M2 @ N2 )
% 3.82/4.05 => ( ( modulo_modulo_nat @ M2 @ N2 )
% 3.82/4.05 = ( modulo_modulo_nat @ ( minus_minus_nat @ M2 @ N2 ) @ N2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % mod_geq
% 3.82/4.05 thf(fact_3832_mod__if,axiom,
% 3.82/4.05 ( modulo_modulo_nat
% 3.82/4.05 = ( ^ [M: nat,N: nat] : ( if_nat @ ( ord_less_nat @ M @ N ) @ M @ ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % mod_if
% 3.82/4.05 thf(fact_3833_le__mod__geq,axiom,
% 3.82/4.05 ! [N2: nat,M2: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ N2 @ M2 )
% 3.82/4.05 => ( ( modulo_modulo_nat @ M2 @ N2 )
% 3.82/4.05 = ( modulo_modulo_nat @ ( minus_minus_nat @ M2 @ N2 ) @ N2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % le_mod_geq
% 3.82/4.05 thf(fact_3834_nat__minus__add__max,axiom,
% 3.82/4.05 ! [N2: nat,M2: nat] :
% 3.82/4.05 ( ( plus_plus_nat @ ( minus_minus_nat @ N2 @ M2 ) @ M2 )
% 3.82/4.05 = ( ord_max_nat @ N2 @ M2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % nat_minus_add_max
% 3.82/4.05 thf(fact_3835_ordered__ring__class_Ole__add__iff2,axiom,
% 3.82/4.05 ! [A: real,E2: real,C: real,B2: real,D: real] :
% 3.82/4.05 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B2 @ E2 ) @ D ) )
% 3.82/4.05 = ( ord_less_eq_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B2 @ A ) @ E2 ) @ D ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % ordered_ring_class.le_add_iff2
% 3.82/4.05 thf(fact_3836_ordered__ring__class_Ole__add__iff2,axiom,
% 3.82/4.05 ! [A: int,E2: int,C: int,B2: int,D: int] :
% 3.82/4.05 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B2 @ E2 ) @ D ) )
% 3.82/4.05 = ( ord_less_eq_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B2 @ A ) @ E2 ) @ D ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % ordered_ring_class.le_add_iff2
% 3.82/4.05 thf(fact_3837_ordered__ring__class_Ole__add__iff1,axiom,
% 3.82/4.05 ! [A: real,E2: real,C: real,B2: real,D: real] :
% 3.82/4.05 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B2 @ E2 ) @ D ) )
% 3.82/4.05 = ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B2 ) @ E2 ) @ C ) @ D ) ) ).
% 3.82/4.05
% 3.82/4.05 % ordered_ring_class.le_add_iff1
% 3.82/4.05 thf(fact_3838_ordered__ring__class_Ole__add__iff1,axiom,
% 3.82/4.05 ! [A: int,E2: int,C: int,B2: int,D: int] :
% 3.82/4.05 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B2 @ E2 ) @ D ) )
% 3.82/4.05 = ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B2 ) @ E2 ) @ C ) @ D ) ) ).
% 3.82/4.05
% 3.82/4.05 % ordered_ring_class.le_add_iff1
% 3.82/4.05 thf(fact_3839_less__add__iff2,axiom,
% 3.82/4.05 ! [A: real,E2: real,C: real,B2: real,D: real] :
% 3.82/4.05 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B2 @ E2 ) @ D ) )
% 3.82/4.05 = ( ord_less_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B2 @ A ) @ E2 ) @ D ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % less_add_iff2
% 3.82/4.05 thf(fact_3840_less__add__iff2,axiom,
% 3.82/4.05 ! [A: int,E2: int,C: int,B2: int,D: int] :
% 3.82/4.05 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B2 @ E2 ) @ D ) )
% 3.82/4.05 = ( ord_less_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B2 @ A ) @ E2 ) @ D ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % less_add_iff2
% 3.82/4.05 thf(fact_3841_less__add__iff1,axiom,
% 3.82/4.05 ! [A: real,E2: real,C: real,B2: real,D: real] :
% 3.82/4.05 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B2 @ E2 ) @ D ) )
% 3.82/4.05 = ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B2 ) @ E2 ) @ C ) @ D ) ) ).
% 3.82/4.05
% 3.82/4.05 % less_add_iff1
% 3.82/4.05 thf(fact_3842_less__add__iff1,axiom,
% 3.82/4.05 ! [A: int,E2: int,C: int,B2: int,D: int] :
% 3.82/4.05 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B2 @ E2 ) @ D ) )
% 3.82/4.05 = ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B2 ) @ E2 ) @ C ) @ D ) ) ).
% 3.82/4.05
% 3.82/4.05 % less_add_iff1
% 3.82/4.05 thf(fact_3843_divide__diff__eq__iff,axiom,
% 3.82/4.05 ! [Z3: complex,X: complex,Y: complex] :
% 3.82/4.05 ( ( Z3 != zero_zero_complex )
% 3.82/4.05 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X @ Z3 ) @ Y )
% 3.82/4.05 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ X @ ( times_times_complex @ Y @ Z3 ) ) @ Z3 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % divide_diff_eq_iff
% 3.82/4.05 thf(fact_3844_divide__diff__eq__iff,axiom,
% 3.82/4.05 ! [Z3: real,X: real,Y: real] :
% 3.82/4.05 ( ( Z3 != zero_zero_real )
% 3.82/4.05 => ( ( minus_minus_real @ ( divide_divide_real @ X @ Z3 ) @ Y )
% 3.82/4.05 = ( divide_divide_real @ ( minus_minus_real @ X @ ( times_times_real @ Y @ Z3 ) ) @ Z3 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % divide_diff_eq_iff
% 3.82/4.05 thf(fact_3845_diff__divide__eq__iff,axiom,
% 3.82/4.05 ! [Z3: complex,X: complex,Y: complex] :
% 3.82/4.05 ( ( Z3 != zero_zero_complex )
% 3.82/4.05 => ( ( minus_minus_complex @ X @ ( divide1717551699836669952omplex @ Y @ Z3 ) )
% 3.82/4.05 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X @ Z3 ) @ Y ) @ Z3 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_divide_eq_iff
% 3.82/4.05 thf(fact_3846_diff__divide__eq__iff,axiom,
% 3.82/4.05 ! [Z3: real,X: real,Y: real] :
% 3.82/4.05 ( ( Z3 != zero_zero_real )
% 3.82/4.05 => ( ( minus_minus_real @ X @ ( divide_divide_real @ Y @ Z3 ) )
% 3.82/4.05 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z3 ) @ Y ) @ Z3 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_divide_eq_iff
% 3.82/4.05 thf(fact_3847_diff__frac__eq,axiom,
% 3.82/4.05 ! [Y: complex,Z3: complex,X: complex,W2: complex] :
% 3.82/4.05 ( ( Y != zero_zero_complex )
% 3.82/4.05 => ( ( Z3 != zero_zero_complex )
% 3.82/4.05 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X @ Y ) @ ( divide1717551699836669952omplex @ W2 @ Z3 ) )
% 3.82/4.05 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X @ Z3 ) @ ( times_times_complex @ W2 @ Y ) ) @ ( times_times_complex @ Y @ Z3 ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_frac_eq
% 3.82/4.05 thf(fact_3848_diff__frac__eq,axiom,
% 3.82/4.05 ! [Y: real,Z3: real,X: real,W2: real] :
% 3.82/4.05 ( ( Y != zero_zero_real )
% 3.82/4.05 => ( ( Z3 != zero_zero_real )
% 3.82/4.05 => ( ( minus_minus_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W2 @ Z3 ) )
% 3.82/4.05 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z3 ) @ ( times_times_real @ W2 @ Y ) ) @ ( times_times_real @ Y @ Z3 ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_frac_eq
% 3.82/4.05 thf(fact_3849_add__divide__eq__if__simps_I4_J,axiom,
% 3.82/4.05 ! [Z3: complex,A: complex,B2: complex] :
% 3.82/4.05 ( ( ( Z3 = zero_zero_complex )
% 3.82/4.05 => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B2 @ Z3 ) )
% 3.82/4.05 = A ) )
% 3.82/4.05 & ( ( Z3 != zero_zero_complex )
% 3.82/4.05 => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B2 @ Z3 ) )
% 3.82/4.05 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ A @ Z3 ) @ B2 ) @ Z3 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % add_divide_eq_if_simps(4)
% 3.82/4.05 thf(fact_3850_add__divide__eq__if__simps_I4_J,axiom,
% 3.82/4.05 ! [Z3: real,A: real,B2: real] :
% 3.82/4.05 ( ( ( Z3 = zero_zero_real )
% 3.82/4.05 => ( ( minus_minus_real @ A @ ( divide_divide_real @ B2 @ Z3 ) )
% 3.82/4.05 = A ) )
% 3.82/4.05 & ( ( Z3 != zero_zero_real )
% 3.82/4.05 => ( ( minus_minus_real @ A @ ( divide_divide_real @ B2 @ Z3 ) )
% 3.82/4.05 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ A @ Z3 ) @ B2 ) @ Z3 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % add_divide_eq_if_simps(4)
% 3.82/4.05 thf(fact_3851_square__diff__one__factored,axiom,
% 3.82/4.05 ! [X: int] :
% 3.82/4.05 ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ one_one_int )
% 3.82/4.05 = ( times_times_int @ ( plus_plus_int @ X @ one_one_int ) @ ( minus_minus_int @ X @ one_one_int ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % square_diff_one_factored
% 3.82/4.05 thf(fact_3852_square__diff__one__factored,axiom,
% 3.82/4.05 ! [X: real] :
% 3.82/4.05 ( ( minus_minus_real @ ( times_times_real @ X @ X ) @ one_one_real )
% 3.82/4.05 = ( times_times_real @ ( plus_plus_real @ X @ one_one_real ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % square_diff_one_factored
% 3.82/4.05 thf(fact_3853_square__diff__one__factored,axiom,
% 3.82/4.05 ! [X: complex] :
% 3.82/4.05 ( ( minus_minus_complex @ ( times_times_complex @ X @ X ) @ one_one_complex )
% 3.82/4.05 = ( times_times_complex @ ( plus_plus_complex @ X @ one_one_complex ) @ ( minus_minus_complex @ X @ one_one_complex ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % square_diff_one_factored
% 3.82/4.05 thf(fact_3854_inf__period_I4_J,axiom,
% 3.82/4.05 ! [D: int,D6: int,T: int] :
% 3.82/4.05 ( ( dvd_dvd_int @ D @ D6 )
% 3.82/4.05 => ! [X2: int,K4: int] :
% 3.82/4.05 ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X2 @ T ) ) )
% 3.82/4.05 = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X2 @ ( times_times_int @ K4 @ D6 ) ) @ T ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % inf_period(4)
% 3.82/4.05 thf(fact_3855_inf__period_I4_J,axiom,
% 3.82/4.05 ! [D: real,D6: real,T: real] :
% 3.82/4.05 ( ( dvd_dvd_real @ D @ D6 )
% 3.82/4.05 => ! [X2: real,K4: real] :
% 3.82/4.05 ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X2 @ T ) ) )
% 3.82/4.05 = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ ( minus_minus_real @ X2 @ ( times_times_real @ K4 @ D6 ) ) @ T ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % inf_period(4)
% 3.82/4.05 thf(fact_3856_inf__period_I4_J,axiom,
% 3.82/4.05 ! [D: complex,D6: complex,T: complex] :
% 3.82/4.05 ( ( dvd_dvd_complex @ D @ D6 )
% 3.82/4.05 => ! [X2: complex,K4: complex] :
% 3.82/4.05 ( ( ~ ( dvd_dvd_complex @ D @ ( plus_plus_complex @ X2 @ T ) ) )
% 3.82/4.05 = ( ~ ( dvd_dvd_complex @ D @ ( plus_plus_complex @ ( minus_minus_complex @ X2 @ ( times_times_complex @ K4 @ D6 ) ) @ T ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % inf_period(4)
% 3.82/4.05 thf(fact_3857_inf__period_I3_J,axiom,
% 3.82/4.05 ! [D: int,D6: int,T: int] :
% 3.82/4.05 ( ( dvd_dvd_int @ D @ D6 )
% 3.82/4.05 => ! [X2: int,K4: int] :
% 3.82/4.05 ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X2 @ T ) )
% 3.82/4.05 = ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X2 @ ( times_times_int @ K4 @ D6 ) ) @ T ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % inf_period(3)
% 3.82/4.05 thf(fact_3858_inf__period_I3_J,axiom,
% 3.82/4.05 ! [D: real,D6: real,T: real] :
% 3.82/4.05 ( ( dvd_dvd_real @ D @ D6 )
% 3.82/4.05 => ! [X2: real,K4: real] :
% 3.82/4.05 ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X2 @ T ) )
% 3.82/4.05 = ( dvd_dvd_real @ D @ ( plus_plus_real @ ( minus_minus_real @ X2 @ ( times_times_real @ K4 @ D6 ) ) @ T ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % inf_period(3)
% 3.82/4.05 thf(fact_3859_inf__period_I3_J,axiom,
% 3.82/4.05 ! [D: complex,D6: complex,T: complex] :
% 3.82/4.05 ( ( dvd_dvd_complex @ D @ D6 )
% 3.82/4.05 => ! [X2: complex,K4: complex] :
% 3.82/4.05 ( ( dvd_dvd_complex @ D @ ( plus_plus_complex @ X2 @ T ) )
% 3.82/4.05 = ( dvd_dvd_complex @ D @ ( plus_plus_complex @ ( minus_minus_complex @ X2 @ ( times_times_complex @ K4 @ D6 ) ) @ T ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % inf_period(3)
% 3.82/4.05 thf(fact_3860_minus__mult__div__eq__mod,axiom,
% 3.82/4.05 ! [A: nat,B2: nat] :
% 3.82/4.05 ( ( minus_minus_nat @ A @ ( times_times_nat @ B2 @ ( divide_divide_nat @ A @ B2 ) ) )
% 3.82/4.05 = ( modulo_modulo_nat @ A @ B2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % minus_mult_div_eq_mod
% 3.82/4.05 thf(fact_3861_minus__mult__div__eq__mod,axiom,
% 3.82/4.05 ! [A: int,B2: int] :
% 3.82/4.05 ( ( minus_minus_int @ A @ ( times_times_int @ B2 @ ( divide_divide_int @ A @ B2 ) ) )
% 3.82/4.05 = ( modulo_modulo_int @ A @ B2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % minus_mult_div_eq_mod
% 3.82/4.05 thf(fact_3862_minus__mod__eq__mult__div,axiom,
% 3.82/4.05 ! [A: nat,B2: nat] :
% 3.82/4.05 ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B2 ) )
% 3.82/4.05 = ( times_times_nat @ B2 @ ( divide_divide_nat @ A @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % minus_mod_eq_mult_div
% 3.82/4.05 thf(fact_3863_minus__mod__eq__mult__div,axiom,
% 3.82/4.05 ! [A: int,B2: int] :
% 3.82/4.05 ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B2 ) )
% 3.82/4.05 = ( times_times_int @ B2 @ ( divide_divide_int @ A @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % minus_mod_eq_mult_div
% 3.82/4.05 thf(fact_3864_minus__mod__eq__div__mult,axiom,
% 3.82/4.05 ! [A: nat,B2: nat] :
% 3.82/4.05 ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B2 ) )
% 3.82/4.05 = ( times_times_nat @ ( divide_divide_nat @ A @ B2 ) @ B2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % minus_mod_eq_div_mult
% 3.82/4.05 thf(fact_3865_minus__mod__eq__div__mult,axiom,
% 3.82/4.05 ! [A: int,B2: int] :
% 3.82/4.05 ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B2 ) )
% 3.82/4.05 = ( times_times_int @ ( divide_divide_int @ A @ B2 ) @ B2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % minus_mod_eq_div_mult
% 3.82/4.05 thf(fact_3866_minus__div__mult__eq__mod,axiom,
% 3.82/4.05 ! [A: nat,B2: nat] :
% 3.82/4.05 ( ( minus_minus_nat @ A @ ( times_times_nat @ ( divide_divide_nat @ A @ B2 ) @ B2 ) )
% 3.82/4.05 = ( modulo_modulo_nat @ A @ B2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % minus_div_mult_eq_mod
% 3.82/4.05 thf(fact_3867_minus__div__mult__eq__mod,axiom,
% 3.82/4.05 ! [A: int,B2: int] :
% 3.82/4.05 ( ( minus_minus_int @ A @ ( times_times_int @ ( divide_divide_int @ A @ B2 ) @ B2 ) )
% 3.82/4.05 = ( modulo_modulo_int @ A @ B2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % minus_div_mult_eq_mod
% 3.82/4.05 thf(fact_3868_int__power__div__base,axiom,
% 3.82/4.05 ! [M2: nat,K: int] :
% 3.82/4.05 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 3.82/4.05 => ( ( ord_less_int @ zero_zero_int @ K )
% 3.82/4.05 => ( ( divide_divide_int @ ( power_power_int @ K @ M2 ) @ K )
% 3.82/4.05 = ( power_power_int @ K @ ( minus_minus_nat @ M2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % int_power_div_base
% 3.82/4.05 thf(fact_3869_diff__Suc__less,axiom,
% 3.82/4.05 ! [N2: nat,I: nat] :
% 3.82/4.05 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.05 => ( ord_less_nat @ ( minus_minus_nat @ N2 @ ( suc @ I ) ) @ N2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_Suc_less
% 3.82/4.05 thf(fact_3870_nat__diff__split__asm,axiom,
% 3.82/4.05 ! [P: nat > $o,A: nat,B2: nat] :
% 3.82/4.05 ( ( P @ ( minus_minus_nat @ A @ B2 ) )
% 3.82/4.05 = ( ~ ( ( ( ord_less_nat @ A @ B2 )
% 3.82/4.05 & ~ ( P @ zero_zero_nat ) )
% 3.82/4.05 | ? [D4: nat] :
% 3.82/4.05 ( ( A
% 3.82/4.05 = ( plus_plus_nat @ B2 @ D4 ) )
% 3.82/4.05 & ~ ( P @ D4 ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % nat_diff_split_asm
% 3.82/4.05 thf(fact_3871_nat__diff__split,axiom,
% 3.82/4.05 ! [P: nat > $o,A: nat,B2: nat] :
% 3.82/4.05 ( ( P @ ( minus_minus_nat @ A @ B2 ) )
% 3.82/4.05 = ( ( ( ord_less_nat @ A @ B2 )
% 3.82/4.05 => ( P @ zero_zero_nat ) )
% 3.82/4.05 & ! [D4: nat] :
% 3.82/4.05 ( ( A
% 3.82/4.05 = ( plus_plus_nat @ B2 @ D4 ) )
% 3.82/4.05 => ( P @ D4 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % nat_diff_split
% 3.82/4.05 thf(fact_3872_less__diff__conv2,axiom,
% 3.82/4.05 ! [K: nat,J: nat,I: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ K @ J )
% 3.82/4.05 => ( ( ord_less_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 3.82/4.05 = ( ord_less_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % less_diff_conv2
% 3.82/4.05 thf(fact_3873_nat__diff__add__eq2,axiom,
% 3.82/4.05 ! [I: nat,J: nat,U: nat,M2: nat,N2: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ I @ J )
% 3.82/4.05 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M2 ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 3.82/4.05 = ( minus_minus_nat @ M2 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % nat_diff_add_eq2
% 3.82/4.05 thf(fact_3874_nat__diff__add__eq1,axiom,
% 3.82/4.05 ! [J: nat,I: nat,U: nat,M2: nat,N2: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ J @ I )
% 3.82/4.05 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M2 ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 3.82/4.05 = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M2 ) @ N2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % nat_diff_add_eq1
% 3.82/4.05 thf(fact_3875_nat__le__add__iff2,axiom,
% 3.82/4.05 ! [I: nat,J: nat,U: nat,M2: nat,N2: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ I @ J )
% 3.82/4.05 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M2 ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 3.82/4.05 = ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % nat_le_add_iff2
% 3.82/4.05 thf(fact_3876_nat__le__add__iff1,axiom,
% 3.82/4.05 ! [J: nat,I: nat,U: nat,M2: nat,N2: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ J @ I )
% 3.82/4.05 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M2 ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 3.82/4.05 = ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M2 ) @ N2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % nat_le_add_iff1
% 3.82/4.05 thf(fact_3877_nat__eq__add__iff2,axiom,
% 3.82/4.05 ! [I: nat,J: nat,U: nat,M2: nat,N2: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ I @ J )
% 3.82/4.05 => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M2 )
% 3.82/4.05 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 3.82/4.05 = ( M2
% 3.82/4.05 = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % nat_eq_add_iff2
% 3.82/4.05 thf(fact_3878_nat__eq__add__iff1,axiom,
% 3.82/4.05 ! [J: nat,I: nat,U: nat,M2: nat,N2: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ J @ I )
% 3.82/4.05 => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M2 )
% 3.82/4.05 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 3.82/4.05 = ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M2 )
% 3.82/4.05 = N2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % nat_eq_add_iff1
% 3.82/4.05 thf(fact_3879_mod__eq__dvd__iff__nat,axiom,
% 3.82/4.05 ! [N2: nat,M2: nat,Q3: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ N2 @ M2 )
% 3.82/4.05 => ( ( ( modulo_modulo_nat @ M2 @ Q3 )
% 3.82/4.05 = ( modulo_modulo_nat @ N2 @ Q3 ) )
% 3.82/4.05 = ( dvd_dvd_nat @ Q3 @ ( minus_minus_nat @ M2 @ N2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % mod_eq_dvd_iff_nat
% 3.82/4.05 thf(fact_3880_set__encode__inf,axiom,
% 3.82/4.05 ! [A2: set_nat] :
% 3.82/4.05 ( ~ ( finite_finite_nat @ A2 )
% 3.82/4.05 => ( ( nat_set_encode @ A2 )
% 3.82/4.05 = zero_zero_nat ) ) ).
% 3.82/4.05
% 3.82/4.05 % set_encode_inf
% 3.82/4.05 thf(fact_3881_exp__div__exp__eq,axiom,
% 3.82/4.05 ! [M2: nat,N2: nat] :
% 3.82/4.05 ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 3.82/4.05 = ( times_times_nat
% 3.82/4.05 @ ( zero_n2687167440665602831ol_nat
% 3.82/4.05 @ ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 )
% 3.82/4.05 != zero_zero_nat )
% 3.82/4.05 & ( ord_less_eq_nat @ N2 @ M2 ) ) )
% 3.82/4.05 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M2 @ N2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % exp_div_exp_eq
% 3.82/4.05 thf(fact_3882_exp__div__exp__eq,axiom,
% 3.82/4.05 ! [M2: nat,N2: nat] :
% 3.82/4.05 ( ( divide_divide_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 3.82/4.05 = ( times_times_int
% 3.82/4.05 @ ( zero_n2684676970156552555ol_int
% 3.82/4.05 @ ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 )
% 3.82/4.05 != zero_zero_int )
% 3.82/4.05 & ( ord_less_eq_nat @ N2 @ M2 ) ) )
% 3.82/4.05 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M2 @ N2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % exp_div_exp_eq
% 3.82/4.05 thf(fact_3883_frac__le__eq,axiom,
% 3.82/4.05 ! [Y: real,Z3: real,X: real,W2: real] :
% 3.82/4.05 ( ( Y != zero_zero_real )
% 3.82/4.05 => ( ( Z3 != zero_zero_real )
% 3.82/4.05 => ( ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W2 @ Z3 ) )
% 3.82/4.05 = ( ord_less_eq_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z3 ) @ ( times_times_real @ W2 @ Y ) ) @ ( times_times_real @ Y @ Z3 ) ) @ zero_zero_real ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % frac_le_eq
% 3.82/4.05 thf(fact_3884_frac__less__eq,axiom,
% 3.82/4.05 ! [Y: real,Z3: real,X: real,W2: real] :
% 3.82/4.05 ( ( Y != zero_zero_real )
% 3.82/4.05 => ( ( Z3 != zero_zero_real )
% 3.82/4.05 => ( ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W2 @ Z3 ) )
% 3.82/4.05 = ( ord_less_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z3 ) @ ( times_times_real @ W2 @ Y ) ) @ ( times_times_real @ Y @ Z3 ) ) @ zero_zero_real ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % frac_less_eq
% 3.82/4.05 thf(fact_3885_power__diff,axiom,
% 3.82/4.05 ! [A: complex,N2: nat,M2: nat] :
% 3.82/4.05 ( ( A != zero_zero_complex )
% 3.82/4.05 => ( ( ord_less_eq_nat @ N2 @ M2 )
% 3.82/4.05 => ( ( power_power_complex @ A @ ( minus_minus_nat @ M2 @ N2 ) )
% 3.82/4.05 = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ M2 ) @ ( power_power_complex @ A @ N2 ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % power_diff
% 3.82/4.05 thf(fact_3886_power__diff,axiom,
% 3.82/4.05 ! [A: nat,N2: nat,M2: nat] :
% 3.82/4.05 ( ( A != zero_zero_nat )
% 3.82/4.05 => ( ( ord_less_eq_nat @ N2 @ M2 )
% 3.82/4.05 => ( ( power_power_nat @ A @ ( minus_minus_nat @ M2 @ N2 ) )
% 3.82/4.05 = ( divide_divide_nat @ ( power_power_nat @ A @ M2 ) @ ( power_power_nat @ A @ N2 ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % power_diff
% 3.82/4.05 thf(fact_3887_power__diff,axiom,
% 3.82/4.05 ! [A: int,N2: nat,M2: nat] :
% 3.82/4.05 ( ( A != zero_zero_int )
% 3.82/4.05 => ( ( ord_less_eq_nat @ N2 @ M2 )
% 3.82/4.05 => ( ( power_power_int @ A @ ( minus_minus_nat @ M2 @ N2 ) )
% 3.82/4.05 = ( divide_divide_int @ ( power_power_int @ A @ M2 ) @ ( power_power_int @ A @ N2 ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % power_diff
% 3.82/4.05 thf(fact_3888_power__diff,axiom,
% 3.82/4.05 ! [A: real,N2: nat,M2: nat] :
% 3.82/4.05 ( ( A != zero_zero_real )
% 3.82/4.05 => ( ( ord_less_eq_nat @ N2 @ M2 )
% 3.82/4.05 => ( ( power_power_real @ A @ ( minus_minus_nat @ M2 @ N2 ) )
% 3.82/4.05 = ( divide_divide_real @ ( power_power_real @ A @ M2 ) @ ( power_power_real @ A @ N2 ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % power_diff
% 3.82/4.05 thf(fact_3889_Suc__diff__eq__diff__pred,axiom,
% 3.82/4.05 ! [N2: nat,M2: nat] :
% 3.82/4.05 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.05 => ( ( minus_minus_nat @ ( suc @ M2 ) @ N2 )
% 3.82/4.05 = ( minus_minus_nat @ M2 @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % Suc_diff_eq_diff_pred
% 3.82/4.05 thf(fact_3890_Suc__pred_H,axiom,
% 3.82/4.05 ! [N2: nat] :
% 3.82/4.05 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.05 => ( N2
% 3.82/4.05 = ( suc @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % Suc_pred'
% 3.82/4.05 thf(fact_3891_div__geq,axiom,
% 3.82/4.05 ! [N2: nat,M2: nat] :
% 3.82/4.05 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.05 => ( ~ ( ord_less_nat @ M2 @ N2 )
% 3.82/4.05 => ( ( divide_divide_nat @ M2 @ N2 )
% 3.82/4.05 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M2 @ N2 ) @ N2 ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % div_geq
% 3.82/4.05 thf(fact_3892_div__if,axiom,
% 3.82/4.05 ( divide_divide_nat
% 3.82/4.05 = ( ^ [M: nat,N: nat] :
% 3.82/4.05 ( if_nat
% 3.82/4.05 @ ( ( ord_less_nat @ M @ N )
% 3.82/4.05 | ( N = zero_zero_nat ) )
% 3.82/4.05 @ zero_zero_nat
% 3.82/4.05 @ ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % div_if
% 3.82/4.05 thf(fact_3893_add__eq__if,axiom,
% 3.82/4.05 ( plus_plus_nat
% 3.82/4.05 = ( ^ [M: nat,N: nat] : ( if_nat @ ( M = zero_zero_nat ) @ N @ ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % add_eq_if
% 3.82/4.05 thf(fact_3894_nat__less__add__iff1,axiom,
% 3.82/4.05 ! [J: nat,I: nat,U: nat,M2: nat,N2: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ J @ I )
% 3.82/4.05 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M2 ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 3.82/4.05 = ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M2 ) @ N2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % nat_less_add_iff1
% 3.82/4.05 thf(fact_3895_nat__less__add__iff2,axiom,
% 3.82/4.05 ! [I: nat,J: nat,U: nat,M2: nat,N2: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ I @ J )
% 3.82/4.05 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M2 ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 3.82/4.05 = ( ord_less_nat @ M2 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % nat_less_add_iff2
% 3.82/4.05 thf(fact_3896_mult__eq__if,axiom,
% 3.82/4.05 ( times_times_nat
% 3.82/4.05 = ( ^ [M: nat,N: nat] : ( if_nat @ ( M = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ N @ ( times_times_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % mult_eq_if
% 3.82/4.05 thf(fact_3897_dvd__minus__add,axiom,
% 3.82/4.05 ! [Q3: nat,N2: nat,R2: nat,M2: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ Q3 @ N2 )
% 3.82/4.05 => ( ( ord_less_eq_nat @ Q3 @ ( times_times_nat @ R2 @ M2 ) )
% 3.82/4.05 => ( ( dvd_dvd_nat @ M2 @ ( minus_minus_nat @ N2 @ Q3 ) )
% 3.82/4.05 = ( dvd_dvd_nat @ M2 @ ( plus_plus_nat @ N2 @ ( minus_minus_nat @ ( times_times_nat @ R2 @ M2 ) @ Q3 ) ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % dvd_minus_add
% 3.82/4.05 thf(fact_3898_mod__nat__eqI,axiom,
% 3.82/4.05 ! [R2: nat,N2: nat,M2: nat] :
% 3.82/4.05 ( ( ord_less_nat @ R2 @ N2 )
% 3.82/4.05 => ( ( ord_less_eq_nat @ R2 @ M2 )
% 3.82/4.05 => ( ( dvd_dvd_nat @ N2 @ ( minus_minus_nat @ M2 @ R2 ) )
% 3.82/4.05 => ( ( modulo_modulo_nat @ M2 @ N2 )
% 3.82/4.05 = R2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % mod_nat_eqI
% 3.82/4.05 thf(fact_3899_scaling__mono,axiom,
% 3.82/4.05 ! [U: real,V: real,R2: real,S: real] :
% 3.82/4.05 ( ( ord_less_eq_real @ U @ V )
% 3.82/4.05 => ( ( ord_less_eq_real @ zero_zero_real @ R2 )
% 3.82/4.05 => ( ( ord_less_eq_real @ R2 @ S )
% 3.82/4.05 => ( ord_less_eq_real @ ( plus_plus_real @ U @ ( divide_divide_real @ ( times_times_real @ R2 @ ( minus_minus_real @ V @ U ) ) @ S ) ) @ V ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % scaling_mono
% 3.82/4.05 thf(fact_3900_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 3.82/4.05 ! [N2: nat,M2: nat] :
% 3.82/4.05 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 3.82/4.05 != zero_zero_nat )
% 3.82/4.05 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M2 ) )
% 3.82/4.05 != zero_zero_nat ) ) ).
% 3.82/4.05
% 3.82/4.05 % exp_not_zero_imp_exp_diff_not_zero
% 3.82/4.05 thf(fact_3901_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 3.82/4.05 ! [N2: nat,M2: nat] :
% 3.82/4.05 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 3.82/4.05 != zero_zero_int )
% 3.82/4.05 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M2 ) )
% 3.82/4.05 != zero_zero_int ) ) ).
% 3.82/4.05
% 3.82/4.05 % exp_not_zero_imp_exp_diff_not_zero
% 3.82/4.05 thf(fact_3902_power__diff__power__eq,axiom,
% 3.82/4.05 ! [A: nat,N2: nat,M2: nat] :
% 3.82/4.05 ( ( A != zero_zero_nat )
% 3.82/4.05 => ( ( ( ord_less_eq_nat @ N2 @ M2 )
% 3.82/4.05 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M2 ) @ ( power_power_nat @ A @ N2 ) )
% 3.82/4.05 = ( power_power_nat @ A @ ( minus_minus_nat @ M2 @ N2 ) ) ) )
% 3.82/4.05 & ( ~ ( ord_less_eq_nat @ N2 @ M2 )
% 3.82/4.05 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M2 ) @ ( power_power_nat @ A @ N2 ) )
% 3.82/4.05 = ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % power_diff_power_eq
% 3.82/4.05 thf(fact_3903_power__diff__power__eq,axiom,
% 3.82/4.05 ! [A: int,N2: nat,M2: nat] :
% 3.82/4.05 ( ( A != zero_zero_int )
% 3.82/4.05 => ( ( ( ord_less_eq_nat @ N2 @ M2 )
% 3.82/4.05 => ( ( divide_divide_int @ ( power_power_int @ A @ M2 ) @ ( power_power_int @ A @ N2 ) )
% 3.82/4.05 = ( power_power_int @ A @ ( minus_minus_nat @ M2 @ N2 ) ) ) )
% 3.82/4.05 & ( ~ ( ord_less_eq_nat @ N2 @ M2 )
% 3.82/4.05 => ( ( divide_divide_int @ ( power_power_int @ A @ M2 ) @ ( power_power_int @ A @ N2 ) )
% 3.82/4.05 = ( divide_divide_int @ one_one_int @ ( power_power_int @ A @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % power_diff_power_eq
% 3.82/4.05 thf(fact_3904_power__eq__if,axiom,
% 3.82/4.05 ( power_power_nat
% 3.82/4.05 = ( ^ [P6: nat,M: nat] : ( if_nat @ ( M = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ P6 @ ( power_power_nat @ P6 @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % power_eq_if
% 3.82/4.05 thf(fact_3905_power__eq__if,axiom,
% 3.82/4.05 ( power_power_int
% 3.82/4.05 = ( ^ [P6: int,M: nat] : ( if_int @ ( M = zero_zero_nat ) @ one_one_int @ ( times_times_int @ P6 @ ( power_power_int @ P6 @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % power_eq_if
% 3.82/4.05 thf(fact_3906_power__eq__if,axiom,
% 3.82/4.05 ( power_power_real
% 3.82/4.05 = ( ^ [P6: real,M: nat] : ( if_real @ ( M = zero_zero_nat ) @ one_one_real @ ( times_times_real @ P6 @ ( power_power_real @ P6 @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % power_eq_if
% 3.82/4.05 thf(fact_3907_power__eq__if,axiom,
% 3.82/4.05 ( power_power_complex
% 3.82/4.05 = ( ^ [P6: complex,M: nat] : ( if_complex @ ( M = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ P6 @ ( power_power_complex @ P6 @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % power_eq_if
% 3.82/4.05 thf(fact_3908_power__eq__if,axiom,
% 3.82/4.05 ( power_8040749407984259932d_enat
% 3.82/4.05 = ( ^ [P6: extended_enat,M: nat] : ( if_Extended_enat @ ( M = zero_zero_nat ) @ one_on7984719198319812577d_enat @ ( times_7803423173614009249d_enat @ P6 @ ( power_8040749407984259932d_enat @ P6 @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % power_eq_if
% 3.82/4.05 thf(fact_3909_power__minus__mult,axiom,
% 3.82/4.05 ! [N2: nat,A: nat] :
% 3.82/4.05 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.05 => ( ( times_times_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 3.82/4.05 = ( power_power_nat @ A @ N2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % power_minus_mult
% 3.82/4.05 thf(fact_3910_power__minus__mult,axiom,
% 3.82/4.05 ! [N2: nat,A: int] :
% 3.82/4.05 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.05 => ( ( times_times_int @ ( power_power_int @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 3.82/4.05 = ( power_power_int @ A @ N2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % power_minus_mult
% 3.82/4.05 thf(fact_3911_power__minus__mult,axiom,
% 3.82/4.05 ! [N2: nat,A: real] :
% 3.82/4.05 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.05 => ( ( times_times_real @ ( power_power_real @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 3.82/4.05 = ( power_power_real @ A @ N2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % power_minus_mult
% 3.82/4.05 thf(fact_3912_power__minus__mult,axiom,
% 3.82/4.05 ! [N2: nat,A: complex] :
% 3.82/4.05 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.05 => ( ( times_times_complex @ ( power_power_complex @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 3.82/4.05 = ( power_power_complex @ A @ N2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % power_minus_mult
% 3.82/4.05 thf(fact_3913_power__minus__mult,axiom,
% 3.82/4.05 ! [N2: nat,A: extended_enat] :
% 3.82/4.05 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.05 => ( ( times_7803423173614009249d_enat @ ( power_8040749407984259932d_enat @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 3.82/4.05 = ( power_8040749407984259932d_enat @ A @ N2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % power_minus_mult
% 3.82/4.05 thf(fact_3914_diff__le__diff__pow,axiom,
% 3.82/4.05 ! [K: nat,M2: nat,N2: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 3.82/4.05 => ( ord_less_eq_nat @ ( minus_minus_nat @ M2 @ N2 ) @ ( minus_minus_nat @ ( power_power_nat @ K @ M2 ) @ ( power_power_nat @ K @ N2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_le_diff_pow
% 3.82/4.05 thf(fact_3915_le__div__geq,axiom,
% 3.82/4.05 ! [N2: nat,M2: nat] :
% 3.82/4.05 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.05 => ( ( ord_less_eq_nat @ N2 @ M2 )
% 3.82/4.05 => ( ( divide_divide_nat @ M2 @ N2 )
% 3.82/4.05 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M2 @ N2 ) @ N2 ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % le_div_geq
% 3.82/4.05 thf(fact_3916_num_Osize__gen_I1_J,axiom,
% 3.82/4.05 ( ( size_num @ one )
% 3.82/4.05 = zero_zero_nat ) ).
% 3.82/4.05
% 3.82/4.05 % num.size_gen(1)
% 3.82/4.05 thf(fact_3917_bits__induct,axiom,
% 3.82/4.05 ! [P: nat > $o,A: nat] :
% 3.82/4.05 ( ! [A4: nat] :
% 3.82/4.05 ( ( ( divide_divide_nat @ A4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.05 = A4 )
% 3.82/4.05 => ( P @ A4 ) )
% 3.82/4.05 => ( ! [A4: nat,B4: $o] :
% 3.82/4.05 ( ( P @ A4 )
% 3.82/4.05 => ( ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B4 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A4 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.05 = A4 )
% 3.82/4.05 => ( P @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B4 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A4 ) ) ) ) )
% 3.82/4.05 => ( P @ A ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % bits_induct
% 3.82/4.05 thf(fact_3918_bits__induct,axiom,
% 3.82/4.05 ! [P: int > $o,A: int] :
% 3.82/4.05 ( ! [A4: int] :
% 3.82/4.05 ( ( ( divide_divide_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 3.82/4.05 = A4 )
% 3.82/4.05 => ( P @ A4 ) )
% 3.82/4.05 => ( ! [A4: int,B4: $o] :
% 3.82/4.05 ( ( P @ A4 )
% 3.82/4.05 => ( ( ( divide_divide_int @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B4 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A4 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 3.82/4.05 = A4 )
% 3.82/4.05 => ( P @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B4 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A4 ) ) ) ) )
% 3.82/4.05 => ( P @ A ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % bits_induct
% 3.82/4.05 thf(fact_3919_exp__mod__exp,axiom,
% 3.82/4.05 ! [M2: nat,N2: nat] :
% 3.82/4.05 ( ( modulo_modulo_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 3.82/4.05 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ M2 @ N2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % exp_mod_exp
% 3.82/4.05 thf(fact_3920_exp__mod__exp,axiom,
% 3.82/4.05 ! [M2: nat,N2: nat] :
% 3.82/4.05 ( ( modulo_modulo_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 3.82/4.05 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ M2 @ N2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % exp_mod_exp
% 3.82/4.05 thf(fact_3921_power2__diff,axiom,
% 3.82/4.05 ! [X: complex,Y: complex] :
% 3.82/4.05 ( ( power_power_complex @ ( minus_minus_complex @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.05 = ( minus_minus_complex @ ( plus_plus_complex @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % power2_diff
% 3.82/4.05 thf(fact_3922_power2__diff,axiom,
% 3.82/4.05 ! [X: int,Y: int] :
% 3.82/4.05 ( ( power_power_int @ ( minus_minus_int @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.05 = ( minus_minus_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % power2_diff
% 3.82/4.05 thf(fact_3923_power2__diff,axiom,
% 3.82/4.05 ! [X: real,Y: real] :
% 3.82/4.05 ( ( power_power_real @ ( minus_minus_real @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.05 = ( minus_minus_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % power2_diff
% 3.82/4.05 thf(fact_3924_mult__exp__mod__exp__eq,axiom,
% 3.82/4.05 ! [M2: nat,N2: nat,A: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.05 => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 3.82/4.05 = ( times_times_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M2 ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % mult_exp_mod_exp_eq
% 3.82/4.05 thf(fact_3925_mult__exp__mod__exp__eq,axiom,
% 3.82/4.05 ! [M2: nat,N2: nat,A: int] :
% 3.82/4.05 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.05 => ( ( modulo_modulo_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 3.82/4.05 = ( times_times_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M2 ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % mult_exp_mod_exp_eq
% 3.82/4.05 thf(fact_3926_divmod__digit__1_I2_J,axiom,
% 3.82/4.05 ! [A: nat,B2: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 3.82/4.05 => ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 3.82/4.05 => ( ( ord_less_eq_nat @ B2 @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) ) )
% 3.82/4.05 => ( ( minus_minus_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) ) @ B2 )
% 3.82/4.05 = ( modulo_modulo_nat @ A @ B2 ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % divmod_digit_1(2)
% 3.82/4.05 thf(fact_3927_divmod__digit__1_I2_J,axiom,
% 3.82/4.05 ! [A: int,B2: int] :
% 3.82/4.05 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 3.82/4.05 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 3.82/4.05 => ( ( ord_less_eq_int @ B2 @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) ) )
% 3.82/4.05 => ( ( minus_minus_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) ) @ B2 )
% 3.82/4.05 = ( modulo_modulo_int @ A @ B2 ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % divmod_digit_1(2)
% 3.82/4.05 thf(fact_3928_even__mask__div__iff_H,axiom,
% 3.82/4.05 ! [M2: nat,N2: nat] :
% 3.82/4.05 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 3.82/4.05 = ( ord_less_eq_nat @ M2 @ N2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % even_mask_div_iff'
% 3.82/4.05 thf(fact_3929_even__mask__div__iff_H,axiom,
% 3.82/4.05 ! [M2: nat,N2: nat] :
% 3.82/4.05 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) )
% 3.82/4.05 = ( ord_less_eq_nat @ M2 @ N2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % even_mask_div_iff'
% 3.82/4.05 thf(fact_3930_even__mod__4__div__2,axiom,
% 3.82/4.05 ! [N2: nat] :
% 3.82/4.05 ( ( ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 3.82/4.05 = ( suc @ zero_zero_nat ) )
% 3.82/4.05 => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % even_mod_4_div_2
% 3.82/4.05 thf(fact_3931_even__mask__div__iff,axiom,
% 3.82/4.05 ! [M2: nat,N2: nat] :
% 3.82/4.05 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 3.82/4.05 = ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 3.82/4.05 = zero_zero_nat )
% 3.82/4.05 | ( ord_less_eq_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % even_mask_div_iff
% 3.82/4.05 thf(fact_3932_even__mask__div__iff,axiom,
% 3.82/4.05 ! [M2: nat,N2: nat] :
% 3.82/4.05 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) )
% 3.82/4.05 = ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 3.82/4.05 = zero_zero_int )
% 3.82/4.05 | ( ord_less_eq_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % even_mask_div_iff
% 3.82/4.05 thf(fact_3933_divmod__step__eq,axiom,
% 3.82/4.05 ! [L: num,R2: int,Q3: int] :
% 3.82/4.05 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R2 )
% 3.82/4.05 => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 3.82/4.05 = ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q3 ) @ one_one_int ) @ ( minus_minus_int @ R2 @ ( numeral_numeral_int @ L ) ) ) ) )
% 3.82/4.05 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R2 )
% 3.82/4.05 => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 3.82/4.05 = ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q3 ) @ R2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % divmod_step_eq
% 3.82/4.05 thf(fact_3934_divmod__step__eq,axiom,
% 3.82/4.05 ! [L: num,R2: nat,Q3: nat] :
% 3.82/4.05 ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R2 )
% 3.82/4.05 => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q3 @ R2 ) )
% 3.82/4.05 = ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q3 ) @ one_one_nat ) @ ( minus_minus_nat @ R2 @ ( numeral_numeral_nat @ L ) ) ) ) )
% 3.82/4.05 & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R2 )
% 3.82/4.05 => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q3 @ R2 ) )
% 3.82/4.05 = ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q3 ) @ R2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % divmod_step_eq
% 3.82/4.05 thf(fact_3935_inrange,axiom,
% 3.82/4.05 ! [T: vEBT_VEBT,N2: nat] :
% 3.82/4.05 ( ( vEBT_invar_vebt @ T @ N2 )
% 3.82/4.05 => ( ord_less_eq_set_nat @ ( vEBT_VEBT_set_vebt @ T ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % inrange
% 3.82/4.05 thf(fact_3936_artanh__def,axiom,
% 3.82/4.05 ( artanh_real
% 3.82/4.05 = ( ^ [X4: real] : ( divide_divide_real @ ( ln_ln_real @ ( divide_divide_real @ ( plus_plus_real @ one_one_real @ X4 ) @ ( minus_minus_real @ one_one_real @ X4 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % artanh_def
% 3.82/4.05 thf(fact_3937_signed__take__bit__rec,axiom,
% 3.82/4.05 ( bit_ri631733984087533419it_int
% 3.82/4.05 = ( ^ [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 ) ) ) ) ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % signed_take_bit_rec
% 3.82/4.05 thf(fact_3938_diff__shunt__var,axiom,
% 3.82/4.05 ! [X: set_Extended_enat,Y: set_Extended_enat] :
% 3.82/4.05 ( ( ( minus_925952699566721837d_enat @ X @ Y )
% 3.82/4.05 = bot_bo7653980558646680370d_enat )
% 3.82/4.05 = ( ord_le7203529160286727270d_enat @ X @ Y ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_shunt_var
% 3.82/4.05 thf(fact_3939_diff__shunt__var,axiom,
% 3.82/4.05 ! [X: set_real,Y: set_real] :
% 3.82/4.05 ( ( ( minus_minus_set_real @ X @ Y )
% 3.82/4.05 = bot_bot_set_real )
% 3.82/4.05 = ( ord_less_eq_set_real @ X @ Y ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_shunt_var
% 3.82/4.05 thf(fact_3940_diff__shunt__var,axiom,
% 3.82/4.05 ! [X: set_nat,Y: set_nat] :
% 3.82/4.05 ( ( ( minus_minus_set_nat @ X @ Y )
% 3.82/4.05 = bot_bot_set_nat )
% 3.82/4.05 = ( ord_less_eq_set_nat @ X @ Y ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_shunt_var
% 3.82/4.05 thf(fact_3941_diff__shunt__var,axiom,
% 3.82/4.05 ! [X: set_int,Y: set_int] :
% 3.82/4.05 ( ( ( minus_minus_set_int @ X @ Y )
% 3.82/4.05 = bot_bot_set_int )
% 3.82/4.05 = ( ord_less_eq_set_int @ X @ Y ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_shunt_var
% 3.82/4.05 thf(fact_3942_take__bit__rec,axiom,
% 3.82/4.05 ( bit_se2925701944663578781it_nat
% 3.82/4.05 = ( ^ [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 ) ) ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % take_bit_rec
% 3.82/4.05 thf(fact_3943_take__bit__rec,axiom,
% 3.82/4.05 ( bit_se2923211474154528505it_int
% 3.82/4.05 = ( ^ [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 ) ) ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % take_bit_rec
% 3.82/4.05 thf(fact_3944_odd__mod__4__div__2,axiom,
% 3.82/4.05 ! [N2: nat] :
% 3.82/4.05 ( ( ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 3.82/4.05 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 3.82/4.05 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % odd_mod_4_div_2
% 3.82/4.05 thf(fact_3945_add_Oinverse__inverse,axiom,
% 3.82/4.05 ! [A: int] :
% 3.82/4.05 ( ( uminus_uminus_int @ ( uminus_uminus_int @ A ) )
% 3.82/4.05 = A ) ).
% 3.82/4.05
% 3.82/4.05 % add.inverse_inverse
% 3.82/4.05 thf(fact_3946_add_Oinverse__inverse,axiom,
% 3.82/4.05 ! [A: real] :
% 3.82/4.05 ( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
% 3.82/4.05 = A ) ).
% 3.82/4.05
% 3.82/4.05 % add.inverse_inverse
% 3.82/4.05 thf(fact_3947_neg__equal__iff__equal,axiom,
% 3.82/4.05 ! [A: int,B2: int] :
% 3.82/4.05 ( ( ( uminus_uminus_int @ A )
% 3.82/4.05 = ( uminus_uminus_int @ B2 ) )
% 3.82/4.05 = ( A = B2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_equal_iff_equal
% 3.82/4.05 thf(fact_3948_neg__equal__iff__equal,axiom,
% 3.82/4.05 ! [A: real,B2: real] :
% 3.82/4.05 ( ( ( uminus_uminus_real @ A )
% 3.82/4.05 = ( uminus_uminus_real @ B2 ) )
% 3.82/4.05 = ( A = B2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_equal_iff_equal
% 3.82/4.05 thf(fact_3949_Diff__cancel,axiom,
% 3.82/4.05 ! [A2: set_Extended_enat] :
% 3.82/4.05 ( ( minus_925952699566721837d_enat @ A2 @ A2 )
% 3.82/4.05 = bot_bo7653980558646680370d_enat ) ).
% 3.82/4.05
% 3.82/4.05 % Diff_cancel
% 3.82/4.05 thf(fact_3950_Diff__cancel,axiom,
% 3.82/4.05 ! [A2: set_real] :
% 3.82/4.05 ( ( minus_minus_set_real @ A2 @ A2 )
% 3.82/4.05 = bot_bot_set_real ) ).
% 3.82/4.05
% 3.82/4.05 % Diff_cancel
% 3.82/4.05 thf(fact_3951_Diff__cancel,axiom,
% 3.82/4.05 ! [A2: set_int] :
% 3.82/4.05 ( ( minus_minus_set_int @ A2 @ A2 )
% 3.82/4.05 = bot_bot_set_int ) ).
% 3.82/4.05
% 3.82/4.05 % Diff_cancel
% 3.82/4.05 thf(fact_3952_Diff__cancel,axiom,
% 3.82/4.05 ! [A2: set_nat] :
% 3.82/4.05 ( ( minus_minus_set_nat @ A2 @ A2 )
% 3.82/4.05 = bot_bot_set_nat ) ).
% 3.82/4.05
% 3.82/4.05 % Diff_cancel
% 3.82/4.05 thf(fact_3953_empty__Diff,axiom,
% 3.82/4.05 ! [A2: set_Extended_enat] :
% 3.82/4.05 ( ( minus_925952699566721837d_enat @ bot_bo7653980558646680370d_enat @ A2 )
% 3.82/4.05 = bot_bo7653980558646680370d_enat ) ).
% 3.82/4.05
% 3.82/4.05 % empty_Diff
% 3.82/4.05 thf(fact_3954_empty__Diff,axiom,
% 3.82/4.05 ! [A2: set_real] :
% 3.82/4.05 ( ( minus_minus_set_real @ bot_bot_set_real @ A2 )
% 3.82/4.05 = bot_bot_set_real ) ).
% 3.82/4.05
% 3.82/4.05 % empty_Diff
% 3.82/4.05 thf(fact_3955_empty__Diff,axiom,
% 3.82/4.05 ! [A2: set_int] :
% 3.82/4.05 ( ( minus_minus_set_int @ bot_bot_set_int @ A2 )
% 3.82/4.05 = bot_bot_set_int ) ).
% 3.82/4.05
% 3.82/4.05 % empty_Diff
% 3.82/4.05 thf(fact_3956_empty__Diff,axiom,
% 3.82/4.05 ! [A2: set_nat] :
% 3.82/4.05 ( ( minus_minus_set_nat @ bot_bot_set_nat @ A2 )
% 3.82/4.05 = bot_bot_set_nat ) ).
% 3.82/4.05
% 3.82/4.05 % empty_Diff
% 3.82/4.05 thf(fact_3957_Diff__empty,axiom,
% 3.82/4.05 ! [A2: set_Extended_enat] :
% 3.82/4.05 ( ( minus_925952699566721837d_enat @ A2 @ bot_bo7653980558646680370d_enat )
% 3.82/4.05 = A2 ) ).
% 3.82/4.05
% 3.82/4.05 % Diff_empty
% 3.82/4.05 thf(fact_3958_Diff__empty,axiom,
% 3.82/4.05 ! [A2: set_real] :
% 3.82/4.05 ( ( minus_minus_set_real @ A2 @ bot_bot_set_real )
% 3.82/4.05 = A2 ) ).
% 3.82/4.05
% 3.82/4.05 % Diff_empty
% 3.82/4.05 thf(fact_3959_Diff__empty,axiom,
% 3.82/4.05 ! [A2: set_int] :
% 3.82/4.05 ( ( minus_minus_set_int @ A2 @ bot_bot_set_int )
% 3.82/4.05 = A2 ) ).
% 3.82/4.05
% 3.82/4.05 % Diff_empty
% 3.82/4.05 thf(fact_3960_Diff__empty,axiom,
% 3.82/4.05 ! [A2: set_nat] :
% 3.82/4.05 ( ( minus_minus_set_nat @ A2 @ bot_bot_set_nat )
% 3.82/4.05 = A2 ) ).
% 3.82/4.05
% 3.82/4.05 % Diff_empty
% 3.82/4.05 thf(fact_3961_finite__Diff2,axiom,
% 3.82/4.05 ! [B: set_complex,A2: set_complex] :
% 3.82/4.05 ( ( finite3207457112153483333omplex @ B )
% 3.82/4.05 => ( ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A2 @ B ) )
% 3.82/4.05 = ( finite3207457112153483333omplex @ A2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % finite_Diff2
% 3.82/4.05 thf(fact_3962_finite__Diff2,axiom,
% 3.82/4.05 ! [B: set_int,A2: set_int] :
% 3.82/4.05 ( ( finite_finite_int @ B )
% 3.82/4.05 => ( ( finite_finite_int @ ( minus_minus_set_int @ A2 @ B ) )
% 3.82/4.05 = ( finite_finite_int @ A2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % finite_Diff2
% 3.82/4.05 thf(fact_3963_finite__Diff2,axiom,
% 3.82/4.05 ! [B: set_Extended_enat,A2: set_Extended_enat] :
% 3.82/4.05 ( ( finite4001608067531595151d_enat @ B )
% 3.82/4.05 => ( ( finite4001608067531595151d_enat @ ( minus_925952699566721837d_enat @ A2 @ B ) )
% 3.82/4.05 = ( finite4001608067531595151d_enat @ A2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % finite_Diff2
% 3.82/4.05 thf(fact_3964_finite__Diff2,axiom,
% 3.82/4.05 ! [B: set_nat,A2: set_nat] :
% 3.82/4.05 ( ( finite_finite_nat @ B )
% 3.82/4.05 => ( ( finite_finite_nat @ ( minus_minus_set_nat @ A2 @ B ) )
% 3.82/4.05 = ( finite_finite_nat @ A2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % finite_Diff2
% 3.82/4.05 thf(fact_3965_finite__Diff,axiom,
% 3.82/4.05 ! [A2: set_complex,B: set_complex] :
% 3.82/4.05 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.05 => ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A2 @ B ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % finite_Diff
% 3.82/4.05 thf(fact_3966_finite__Diff,axiom,
% 3.82/4.05 ! [A2: set_int,B: set_int] :
% 3.82/4.05 ( ( finite_finite_int @ A2 )
% 3.82/4.05 => ( finite_finite_int @ ( minus_minus_set_int @ A2 @ B ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % finite_Diff
% 3.82/4.05 thf(fact_3967_finite__Diff,axiom,
% 3.82/4.05 ! [A2: set_Extended_enat,B: set_Extended_enat] :
% 3.82/4.05 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.05 => ( finite4001608067531595151d_enat @ ( minus_925952699566721837d_enat @ A2 @ B ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % finite_Diff
% 3.82/4.05 thf(fact_3968_finite__Diff,axiom,
% 3.82/4.05 ! [A2: set_nat,B: set_nat] :
% 3.82/4.05 ( ( finite_finite_nat @ A2 )
% 3.82/4.05 => ( finite_finite_nat @ ( minus_minus_set_nat @ A2 @ B ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % finite_Diff
% 3.82/4.05 thf(fact_3969_Compl__subset__Compl__iff,axiom,
% 3.82/4.05 ! [A2: set_nat,B: set_nat] :
% 3.82/4.05 ( ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ A2 ) @ ( uminus5710092332889474511et_nat @ B ) )
% 3.82/4.05 = ( ord_less_eq_set_nat @ B @ A2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % Compl_subset_Compl_iff
% 3.82/4.05 thf(fact_3970_Compl__subset__Compl__iff,axiom,
% 3.82/4.05 ! [A2: set_int,B: set_int] :
% 3.82/4.05 ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ A2 ) @ ( uminus1532241313380277803et_int @ B ) )
% 3.82/4.05 = ( ord_less_eq_set_int @ B @ A2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % Compl_subset_Compl_iff
% 3.82/4.05 thf(fact_3971_Compl__anti__mono,axiom,
% 3.82/4.05 ! [A2: set_nat,B: set_nat] :
% 3.82/4.05 ( ( ord_less_eq_set_nat @ A2 @ B )
% 3.82/4.05 => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ B ) @ ( uminus5710092332889474511et_nat @ A2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % Compl_anti_mono
% 3.82/4.05 thf(fact_3972_Compl__anti__mono,axiom,
% 3.82/4.05 ! [A2: set_int,B: set_int] :
% 3.82/4.05 ( ( ord_less_eq_set_int @ A2 @ B )
% 3.82/4.05 => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ B ) @ ( uminus1532241313380277803et_int @ A2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % Compl_anti_mono
% 3.82/4.05 thf(fact_3973_zle__diff1__eq,axiom,
% 3.82/4.05 ! [W2: int,Z3: int] :
% 3.82/4.05 ( ( ord_less_eq_int @ W2 @ ( minus_minus_int @ Z3 @ one_one_int ) )
% 3.82/4.05 = ( ord_less_int @ W2 @ Z3 ) ) ).
% 3.82/4.05
% 3.82/4.05 % zle_diff1_eq
% 3.82/4.05 thf(fact_3974_zle__add1__eq__le,axiom,
% 3.82/4.05 ! [W2: int,Z3: int] :
% 3.82/4.05 ( ( ord_less_int @ W2 @ ( plus_plus_int @ Z3 @ one_one_int ) )
% 3.82/4.05 = ( ord_less_eq_int @ W2 @ Z3 ) ) ).
% 3.82/4.05
% 3.82/4.05 % zle_add1_eq_le
% 3.82/4.05 thf(fact_3975_finite__interval__int2,axiom,
% 3.82/4.05 ! [A: int,B2: int] :
% 3.82/4.05 ( finite_finite_int
% 3.82/4.05 @ ( collect_int
% 3.82/4.05 @ ^ [I3: int] :
% 3.82/4.05 ( ( ord_less_eq_int @ A @ I3 )
% 3.82/4.05 & ( ord_less_int @ I3 @ B2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % finite_interval_int2
% 3.82/4.05 thf(fact_3976_finite__interval__int3,axiom,
% 3.82/4.05 ! [A: int,B2: int] :
% 3.82/4.05 ( finite_finite_int
% 3.82/4.05 @ ( collect_int
% 3.82/4.05 @ ^ [I3: int] :
% 3.82/4.05 ( ( ord_less_int @ A @ I3 )
% 3.82/4.05 & ( ord_less_eq_int @ I3 @ B2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % finite_interval_int3
% 3.82/4.05 thf(fact_3977_finite__interval__int4,axiom,
% 3.82/4.05 ! [A: int,B2: int] :
% 3.82/4.05 ( finite_finite_int
% 3.82/4.05 @ ( collect_int
% 3.82/4.05 @ ^ [I3: int] :
% 3.82/4.05 ( ( ord_less_int @ A @ I3 )
% 3.82/4.05 & ( ord_less_int @ I3 @ B2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % finite_interval_int4
% 3.82/4.05 thf(fact_3978_compl__le__compl__iff,axiom,
% 3.82/4.05 ! [X: set_nat,Y: set_nat] :
% 3.82/4.05 ( ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ ( uminus5710092332889474511et_nat @ Y ) )
% 3.82/4.05 = ( ord_less_eq_set_nat @ Y @ X ) ) ).
% 3.82/4.05
% 3.82/4.05 % compl_le_compl_iff
% 3.82/4.05 thf(fact_3979_compl__le__compl__iff,axiom,
% 3.82/4.05 ! [X: set_int,Y: set_int] :
% 3.82/4.05 ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ X ) @ ( uminus1532241313380277803et_int @ Y ) )
% 3.82/4.05 = ( ord_less_eq_set_int @ Y @ X ) ) ).
% 3.82/4.05
% 3.82/4.05 % compl_le_compl_iff
% 3.82/4.05 thf(fact_3980_neg__le__iff__le,axiom,
% 3.82/4.05 ! [B2: real,A: real] :
% 3.82/4.05 ( ( ord_less_eq_real @ ( uminus_uminus_real @ B2 ) @ ( uminus_uminus_real @ A ) )
% 3.82/4.05 = ( ord_less_eq_real @ A @ B2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_le_iff_le
% 3.82/4.05 thf(fact_3981_neg__le__iff__le,axiom,
% 3.82/4.05 ! [B2: int,A: int] :
% 3.82/4.05 ( ( ord_less_eq_int @ ( uminus_uminus_int @ B2 ) @ ( uminus_uminus_int @ A ) )
% 3.82/4.05 = ( ord_less_eq_int @ A @ B2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_le_iff_le
% 3.82/4.05 thf(fact_3982_neg__equal__zero,axiom,
% 3.82/4.05 ! [A: int] :
% 3.82/4.05 ( ( ( uminus_uminus_int @ A )
% 3.82/4.05 = A )
% 3.82/4.05 = ( A = zero_zero_int ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_equal_zero
% 3.82/4.05 thf(fact_3983_neg__equal__zero,axiom,
% 3.82/4.05 ! [A: real] :
% 3.82/4.05 ( ( ( uminus_uminus_real @ A )
% 3.82/4.05 = A )
% 3.82/4.05 = ( A = zero_zero_real ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_equal_zero
% 3.82/4.05 thf(fact_3984_equal__neg__zero,axiom,
% 3.82/4.05 ! [A: int] :
% 3.82/4.05 ( ( A
% 3.82/4.05 = ( uminus_uminus_int @ A ) )
% 3.82/4.05 = ( A = zero_zero_int ) ) ).
% 3.82/4.05
% 3.82/4.05 % equal_neg_zero
% 3.82/4.05 thf(fact_3985_equal__neg__zero,axiom,
% 3.82/4.05 ! [A: real] :
% 3.82/4.05 ( ( A
% 3.82/4.05 = ( uminus_uminus_real @ A ) )
% 3.82/4.05 = ( A = zero_zero_real ) ) ).
% 3.82/4.05
% 3.82/4.05 % equal_neg_zero
% 3.82/4.05 thf(fact_3986_neg__equal__0__iff__equal,axiom,
% 3.82/4.05 ! [A: complex] :
% 3.82/4.05 ( ( ( uminus1482373934393186551omplex @ A )
% 3.82/4.05 = zero_zero_complex )
% 3.82/4.05 = ( A = zero_zero_complex ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_equal_0_iff_equal
% 3.82/4.05 thf(fact_3987_neg__equal__0__iff__equal,axiom,
% 3.82/4.05 ! [A: int] :
% 3.82/4.05 ( ( ( uminus_uminus_int @ A )
% 3.82/4.05 = zero_zero_int )
% 3.82/4.05 = ( A = zero_zero_int ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_equal_0_iff_equal
% 3.82/4.05 thf(fact_3988_neg__equal__0__iff__equal,axiom,
% 3.82/4.05 ! [A: real] :
% 3.82/4.05 ( ( ( uminus_uminus_real @ A )
% 3.82/4.05 = zero_zero_real )
% 3.82/4.05 = ( A = zero_zero_real ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_equal_0_iff_equal
% 3.82/4.05 thf(fact_3989_neg__0__equal__iff__equal,axiom,
% 3.82/4.05 ! [A: complex] :
% 3.82/4.05 ( ( zero_zero_complex
% 3.82/4.05 = ( uminus1482373934393186551omplex @ A ) )
% 3.82/4.05 = ( zero_zero_complex = A ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_0_equal_iff_equal
% 3.82/4.05 thf(fact_3990_neg__0__equal__iff__equal,axiom,
% 3.82/4.05 ! [A: int] :
% 3.82/4.05 ( ( zero_zero_int
% 3.82/4.05 = ( uminus_uminus_int @ A ) )
% 3.82/4.05 = ( zero_zero_int = A ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_0_equal_iff_equal
% 3.82/4.05 thf(fact_3991_neg__0__equal__iff__equal,axiom,
% 3.82/4.05 ! [A: real] :
% 3.82/4.05 ( ( zero_zero_real
% 3.82/4.05 = ( uminus_uminus_real @ A ) )
% 3.82/4.05 = ( zero_zero_real = A ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_0_equal_iff_equal
% 3.82/4.05 thf(fact_3992_add_Oinverse__neutral,axiom,
% 3.82/4.05 ( ( uminus1482373934393186551omplex @ zero_zero_complex )
% 3.82/4.05 = zero_zero_complex ) ).
% 3.82/4.05
% 3.82/4.05 % add.inverse_neutral
% 3.82/4.05 thf(fact_3993_add_Oinverse__neutral,axiom,
% 3.82/4.05 ( ( uminus_uminus_int @ zero_zero_int )
% 3.82/4.05 = zero_zero_int ) ).
% 3.82/4.05
% 3.82/4.05 % add.inverse_neutral
% 3.82/4.05 thf(fact_3994_add_Oinverse__neutral,axiom,
% 3.82/4.05 ( ( uminus_uminus_real @ zero_zero_real )
% 3.82/4.05 = zero_zero_real ) ).
% 3.82/4.05
% 3.82/4.05 % add.inverse_neutral
% 3.82/4.05 thf(fact_3995_neg__less__iff__less,axiom,
% 3.82/4.05 ! [B2: int,A: int] :
% 3.82/4.05 ( ( ord_less_int @ ( uminus_uminus_int @ B2 ) @ ( uminus_uminus_int @ A ) )
% 3.82/4.05 = ( ord_less_int @ A @ B2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_less_iff_less
% 3.82/4.05 thf(fact_3996_neg__less__iff__less,axiom,
% 3.82/4.05 ! [B2: real,A: real] :
% 3.82/4.05 ( ( ord_less_real @ ( uminus_uminus_real @ B2 ) @ ( uminus_uminus_real @ A ) )
% 3.82/4.05 = ( ord_less_real @ A @ B2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_less_iff_less
% 3.82/4.05 thf(fact_3997_mult__minus__left,axiom,
% 3.82/4.05 ! [A: complex,B2: complex] :
% 3.82/4.05 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B2 )
% 3.82/4.05 = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % mult_minus_left
% 3.82/4.05 thf(fact_3998_mult__minus__left,axiom,
% 3.82/4.05 ! [A: int,B2: int] :
% 3.82/4.05 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B2 )
% 3.82/4.05 = ( uminus_uminus_int @ ( times_times_int @ A @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % mult_minus_left
% 3.82/4.05 thf(fact_3999_mult__minus__left,axiom,
% 3.82/4.05 ! [A: real,B2: real] :
% 3.82/4.05 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B2 )
% 3.82/4.05 = ( uminus_uminus_real @ ( times_times_real @ A @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % mult_minus_left
% 3.82/4.05 thf(fact_4000_minus__mult__minus,axiom,
% 3.82/4.05 ! [A: complex,B2: complex] :
% 3.82/4.05 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B2 ) )
% 3.82/4.05 = ( times_times_complex @ A @ B2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % minus_mult_minus
% 3.82/4.05 thf(fact_4001_minus__mult__minus,axiom,
% 3.82/4.05 ! [A: int,B2: int] :
% 3.82/4.05 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B2 ) )
% 3.82/4.05 = ( times_times_int @ A @ B2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % minus_mult_minus
% 3.82/4.05 thf(fact_4002_minus__mult__minus,axiom,
% 3.82/4.05 ! [A: real,B2: real] :
% 3.82/4.05 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B2 ) )
% 3.82/4.05 = ( times_times_real @ A @ B2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % minus_mult_minus
% 3.82/4.05 thf(fact_4003_mult__minus__right,axiom,
% 3.82/4.05 ! [A: complex,B2: complex] :
% 3.82/4.05 ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B2 ) )
% 3.82/4.05 = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % mult_minus_right
% 3.82/4.05 thf(fact_4004_mult__minus__right,axiom,
% 3.82/4.05 ! [A: int,B2: int] :
% 3.82/4.05 ( ( times_times_int @ A @ ( uminus_uminus_int @ B2 ) )
% 3.82/4.05 = ( uminus_uminus_int @ ( times_times_int @ A @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % mult_minus_right
% 3.82/4.05 thf(fact_4005_mult__minus__right,axiom,
% 3.82/4.05 ! [A: real,B2: real] :
% 3.82/4.05 ( ( times_times_real @ A @ ( uminus_uminus_real @ B2 ) )
% 3.82/4.05 = ( uminus_uminus_real @ ( times_times_real @ A @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % mult_minus_right
% 3.82/4.05 thf(fact_4006_minus__add__distrib,axiom,
% 3.82/4.05 ! [A: int,B2: int] :
% 3.82/4.05 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B2 ) )
% 3.82/4.05 = ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % minus_add_distrib
% 3.82/4.05 thf(fact_4007_minus__add__distrib,axiom,
% 3.82/4.05 ! [A: real,B2: real] :
% 3.82/4.05 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B2 ) )
% 3.82/4.05 = ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % minus_add_distrib
% 3.82/4.05 thf(fact_4008_minus__add__cancel,axiom,
% 3.82/4.05 ! [A: int,B2: int] :
% 3.82/4.05 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( plus_plus_int @ A @ B2 ) )
% 3.82/4.05 = B2 ) ).
% 3.82/4.05
% 3.82/4.05 % minus_add_cancel
% 3.82/4.05 thf(fact_4009_minus__add__cancel,axiom,
% 3.82/4.05 ! [A: real,B2: real] :
% 3.82/4.05 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( plus_plus_real @ A @ B2 ) )
% 3.82/4.05 = B2 ) ).
% 3.82/4.05
% 3.82/4.05 % minus_add_cancel
% 3.82/4.05 thf(fact_4010_add__minus__cancel,axiom,
% 3.82/4.05 ! [A: int,B2: int] :
% 3.82/4.05 ( ( plus_plus_int @ A @ ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B2 ) )
% 3.82/4.05 = B2 ) ).
% 3.82/4.05
% 3.82/4.05 % add_minus_cancel
% 3.82/4.05 thf(fact_4011_add__minus__cancel,axiom,
% 3.82/4.05 ! [A: real,B2: real] :
% 3.82/4.05 ( ( plus_plus_real @ A @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B2 ) )
% 3.82/4.05 = B2 ) ).
% 3.82/4.05
% 3.82/4.05 % add_minus_cancel
% 3.82/4.05 thf(fact_4012_minus__diff__eq,axiom,
% 3.82/4.05 ! [A: int,B2: int] :
% 3.82/4.05 ( ( uminus_uminus_int @ ( minus_minus_int @ A @ B2 ) )
% 3.82/4.05 = ( minus_minus_int @ B2 @ A ) ) ).
% 3.82/4.05
% 3.82/4.05 % minus_diff_eq
% 3.82/4.05 thf(fact_4013_minus__diff__eq,axiom,
% 3.82/4.05 ! [A: real,B2: real] :
% 3.82/4.05 ( ( uminus_uminus_real @ ( minus_minus_real @ A @ B2 ) )
% 3.82/4.05 = ( minus_minus_real @ B2 @ A ) ) ).
% 3.82/4.05
% 3.82/4.05 % minus_diff_eq
% 3.82/4.05 thf(fact_4014_dvd__minus__iff,axiom,
% 3.82/4.05 ! [X: int,Y: int] :
% 3.82/4.05 ( ( dvd_dvd_int @ X @ ( uminus_uminus_int @ Y ) )
% 3.82/4.05 = ( dvd_dvd_int @ X @ Y ) ) ).
% 3.82/4.05
% 3.82/4.05 % dvd_minus_iff
% 3.82/4.05 thf(fact_4015_dvd__minus__iff,axiom,
% 3.82/4.05 ! [X: real,Y: real] :
% 3.82/4.05 ( ( dvd_dvd_real @ X @ ( uminus_uminus_real @ Y ) )
% 3.82/4.05 = ( dvd_dvd_real @ X @ Y ) ) ).
% 3.82/4.05
% 3.82/4.05 % dvd_minus_iff
% 3.82/4.05 thf(fact_4016_minus__dvd__iff,axiom,
% 3.82/4.05 ! [X: int,Y: int] :
% 3.82/4.05 ( ( dvd_dvd_int @ ( uminus_uminus_int @ X ) @ Y )
% 3.82/4.05 = ( dvd_dvd_int @ X @ Y ) ) ).
% 3.82/4.05
% 3.82/4.05 % minus_dvd_iff
% 3.82/4.05 thf(fact_4017_minus__dvd__iff,axiom,
% 3.82/4.05 ! [X: real,Y: real] :
% 3.82/4.05 ( ( dvd_dvd_real @ ( uminus_uminus_real @ X ) @ Y )
% 3.82/4.05 = ( dvd_dvd_real @ X @ Y ) ) ).
% 3.82/4.05
% 3.82/4.05 % minus_dvd_iff
% 3.82/4.05 thf(fact_4018_Diff__eq__empty__iff,axiom,
% 3.82/4.05 ! [A2: set_Extended_enat,B: set_Extended_enat] :
% 3.82/4.05 ( ( ( minus_925952699566721837d_enat @ A2 @ B )
% 3.82/4.05 = bot_bo7653980558646680370d_enat )
% 3.82/4.05 = ( ord_le7203529160286727270d_enat @ A2 @ B ) ) ).
% 3.82/4.05
% 3.82/4.05 % Diff_eq_empty_iff
% 3.82/4.05 thf(fact_4019_Diff__eq__empty__iff,axiom,
% 3.82/4.05 ! [A2: set_real,B: set_real] :
% 3.82/4.05 ( ( ( minus_minus_set_real @ A2 @ B )
% 3.82/4.05 = bot_bot_set_real )
% 3.82/4.05 = ( ord_less_eq_set_real @ A2 @ B ) ) ).
% 3.82/4.05
% 3.82/4.05 % Diff_eq_empty_iff
% 3.82/4.05 thf(fact_4020_Diff__eq__empty__iff,axiom,
% 3.82/4.05 ! [A2: set_nat,B: set_nat] :
% 3.82/4.05 ( ( ( minus_minus_set_nat @ A2 @ B )
% 3.82/4.05 = bot_bot_set_nat )
% 3.82/4.05 = ( ord_less_eq_set_nat @ A2 @ B ) ) ).
% 3.82/4.05
% 3.82/4.05 % Diff_eq_empty_iff
% 3.82/4.05 thf(fact_4021_Diff__eq__empty__iff,axiom,
% 3.82/4.05 ! [A2: set_int,B: set_int] :
% 3.82/4.05 ( ( ( minus_minus_set_int @ A2 @ B )
% 3.82/4.05 = bot_bot_set_int )
% 3.82/4.05 = ( ord_less_eq_set_int @ A2 @ B ) ) ).
% 3.82/4.05
% 3.82/4.05 % Diff_eq_empty_iff
% 3.82/4.05 thf(fact_4022_atLeastAtMost__iff,axiom,
% 3.82/4.05 ! [I: extended_enat,L: extended_enat,U: extended_enat] :
% 3.82/4.05 ( ( member_Extended_enat @ I @ ( set_or5403411693681687835d_enat @ L @ U ) )
% 3.82/4.05 = ( ( ord_le2932123472753598470d_enat @ L @ I )
% 3.82/4.05 & ( ord_le2932123472753598470d_enat @ I @ U ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % atLeastAtMost_iff
% 3.82/4.05 thf(fact_4023_atLeastAtMost__iff,axiom,
% 3.82/4.05 ! [I: set_nat,L: set_nat,U: set_nat] :
% 3.82/4.05 ( ( member_set_nat @ I @ ( set_or4548717258645045905et_nat @ L @ U ) )
% 3.82/4.05 = ( ( ord_less_eq_set_nat @ L @ I )
% 3.82/4.05 & ( ord_less_eq_set_nat @ I @ U ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % atLeastAtMost_iff
% 3.82/4.05 thf(fact_4024_atLeastAtMost__iff,axiom,
% 3.82/4.05 ! [I: set_int,L: set_int,U: set_int] :
% 3.82/4.05 ( ( member_set_int @ I @ ( set_or370866239135849197et_int @ L @ U ) )
% 3.82/4.05 = ( ( ord_less_eq_set_int @ L @ I )
% 3.82/4.05 & ( ord_less_eq_set_int @ I @ U ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % atLeastAtMost_iff
% 3.82/4.05 thf(fact_4025_atLeastAtMost__iff,axiom,
% 3.82/4.05 ! [I: nat,L: nat,U: nat] :
% 3.82/4.05 ( ( member_nat @ I @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 3.82/4.05 = ( ( ord_less_eq_nat @ L @ I )
% 3.82/4.05 & ( ord_less_eq_nat @ I @ U ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % atLeastAtMost_iff
% 3.82/4.05 thf(fact_4026_atLeastAtMost__iff,axiom,
% 3.82/4.05 ! [I: int,L: int,U: int] :
% 3.82/4.05 ( ( member_int @ I @ ( set_or1266510415728281911st_int @ L @ U ) )
% 3.82/4.05 = ( ( ord_less_eq_int @ L @ I )
% 3.82/4.05 & ( ord_less_eq_int @ I @ U ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % atLeastAtMost_iff
% 3.82/4.05 thf(fact_4027_atLeastAtMost__iff,axiom,
% 3.82/4.05 ! [I: real,L: real,U: real] :
% 3.82/4.05 ( ( member_real @ I @ ( set_or1222579329274155063t_real @ L @ U ) )
% 3.82/4.05 = ( ( ord_less_eq_real @ L @ I )
% 3.82/4.05 & ( ord_less_eq_real @ I @ U ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % atLeastAtMost_iff
% 3.82/4.05 thf(fact_4028_Icc__eq__Icc,axiom,
% 3.82/4.05 ! [L: set_nat,H2: set_nat,L3: set_nat,H3: set_nat] :
% 3.82/4.05 ( ( ( set_or4548717258645045905et_nat @ L @ H2 )
% 3.82/4.05 = ( set_or4548717258645045905et_nat @ L3 @ H3 ) )
% 3.82/4.05 = ( ( ( L = L3 )
% 3.82/4.05 & ( H2 = H3 ) )
% 3.82/4.05 | ( ~ ( ord_less_eq_set_nat @ L @ H2 )
% 3.82/4.05 & ~ ( ord_less_eq_set_nat @ L3 @ H3 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % Icc_eq_Icc
% 3.82/4.05 thf(fact_4029_Icc__eq__Icc,axiom,
% 3.82/4.05 ! [L: set_int,H2: set_int,L3: set_int,H3: set_int] :
% 3.82/4.05 ( ( ( set_or370866239135849197et_int @ L @ H2 )
% 3.82/4.05 = ( set_or370866239135849197et_int @ L3 @ H3 ) )
% 3.82/4.05 = ( ( ( L = L3 )
% 3.82/4.05 & ( H2 = H3 ) )
% 3.82/4.05 | ( ~ ( ord_less_eq_set_int @ L @ H2 )
% 3.82/4.05 & ~ ( ord_less_eq_set_int @ L3 @ H3 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % Icc_eq_Icc
% 3.82/4.05 thf(fact_4030_Icc__eq__Icc,axiom,
% 3.82/4.05 ! [L: nat,H2: nat,L3: nat,H3: nat] :
% 3.82/4.05 ( ( ( set_or1269000886237332187st_nat @ L @ H2 )
% 3.82/4.05 = ( set_or1269000886237332187st_nat @ L3 @ H3 ) )
% 3.82/4.05 = ( ( ( L = L3 )
% 3.82/4.05 & ( H2 = H3 ) )
% 3.82/4.05 | ( ~ ( ord_less_eq_nat @ L @ H2 )
% 3.82/4.05 & ~ ( ord_less_eq_nat @ L3 @ H3 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % Icc_eq_Icc
% 3.82/4.05 thf(fact_4031_Icc__eq__Icc,axiom,
% 3.82/4.05 ! [L: int,H2: int,L3: int,H3: int] :
% 3.82/4.05 ( ( ( set_or1266510415728281911st_int @ L @ H2 )
% 3.82/4.05 = ( set_or1266510415728281911st_int @ L3 @ H3 ) )
% 3.82/4.05 = ( ( ( L = L3 )
% 3.82/4.05 & ( H2 = H3 ) )
% 3.82/4.05 | ( ~ ( ord_less_eq_int @ L @ H2 )
% 3.82/4.05 & ~ ( ord_less_eq_int @ L3 @ H3 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % Icc_eq_Icc
% 3.82/4.05 thf(fact_4032_Icc__eq__Icc,axiom,
% 3.82/4.05 ! [L: real,H2: real,L3: real,H3: real] :
% 3.82/4.05 ( ( ( set_or1222579329274155063t_real @ L @ H2 )
% 3.82/4.05 = ( set_or1222579329274155063t_real @ L3 @ H3 ) )
% 3.82/4.05 = ( ( ( L = L3 )
% 3.82/4.05 & ( H2 = H3 ) )
% 3.82/4.05 | ( ~ ( ord_less_eq_real @ L @ H2 )
% 3.82/4.05 & ~ ( ord_less_eq_real @ L3 @ H3 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % Icc_eq_Icc
% 3.82/4.05 thf(fact_4033_take__bit__of__0,axiom,
% 3.82/4.05 ! [N2: nat] :
% 3.82/4.05 ( ( bit_se2925701944663578781it_nat @ N2 @ zero_zero_nat )
% 3.82/4.05 = zero_zero_nat ) ).
% 3.82/4.05
% 3.82/4.05 % take_bit_of_0
% 3.82/4.05 thf(fact_4034_take__bit__of__0,axiom,
% 3.82/4.05 ! [N2: nat] :
% 3.82/4.05 ( ( bit_se2923211474154528505it_int @ N2 @ zero_zero_int )
% 3.82/4.05 = zero_zero_int ) ).
% 3.82/4.05
% 3.82/4.05 % take_bit_of_0
% 3.82/4.05 thf(fact_4035_finite__atLeastAtMost,axiom,
% 3.82/4.05 ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or1269000886237332187st_nat @ L @ U ) ) ).
% 3.82/4.05
% 3.82/4.05 % finite_atLeastAtMost
% 3.82/4.05 thf(fact_4036_neg__0__le__iff__le,axiom,
% 3.82/4.05 ! [A: real] :
% 3.82/4.05 ( ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 3.82/4.05 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_0_le_iff_le
% 3.82/4.05 thf(fact_4037_neg__0__le__iff__le,axiom,
% 3.82/4.05 ! [A: int] :
% 3.82/4.05 ( ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 3.82/4.05 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_0_le_iff_le
% 3.82/4.05 thf(fact_4038_neg__le__0__iff__le,axiom,
% 3.82/4.05 ! [A: real] :
% 3.82/4.05 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 3.82/4.05 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_le_0_iff_le
% 3.82/4.05 thf(fact_4039_neg__le__0__iff__le,axiom,
% 3.82/4.05 ! [A: int] :
% 3.82/4.05 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 3.82/4.05 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_le_0_iff_le
% 3.82/4.05 thf(fact_4040_less__eq__neg__nonpos,axiom,
% 3.82/4.05 ! [A: real] :
% 3.82/4.05 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ A ) )
% 3.82/4.05 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 3.82/4.05
% 3.82/4.05 % less_eq_neg_nonpos
% 3.82/4.05 thf(fact_4041_less__eq__neg__nonpos,axiom,
% 3.82/4.05 ! [A: int] :
% 3.82/4.05 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ A ) )
% 3.82/4.05 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 3.82/4.05
% 3.82/4.05 % less_eq_neg_nonpos
% 3.82/4.05 thf(fact_4042_neg__less__eq__nonneg,axiom,
% 3.82/4.05 ! [A: real] :
% 3.82/4.05 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ A )
% 3.82/4.05 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_less_eq_nonneg
% 3.82/4.05 thf(fact_4043_neg__less__eq__nonneg,axiom,
% 3.82/4.05 ! [A: int] :
% 3.82/4.05 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ A )
% 3.82/4.05 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_less_eq_nonneg
% 3.82/4.05 thf(fact_4044_less__neg__neg,axiom,
% 3.82/4.05 ! [A: int] :
% 3.82/4.05 ( ( ord_less_int @ A @ ( uminus_uminus_int @ A ) )
% 3.82/4.05 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 3.82/4.05
% 3.82/4.05 % less_neg_neg
% 3.82/4.05 thf(fact_4045_less__neg__neg,axiom,
% 3.82/4.05 ! [A: real] :
% 3.82/4.05 ( ( ord_less_real @ A @ ( uminus_uminus_real @ A ) )
% 3.82/4.05 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 3.82/4.05
% 3.82/4.05 % less_neg_neg
% 3.82/4.05 thf(fact_4046_neg__less__pos,axiom,
% 3.82/4.05 ! [A: int] :
% 3.82/4.05 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ A )
% 3.82/4.05 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_less_pos
% 3.82/4.05 thf(fact_4047_neg__less__pos,axiom,
% 3.82/4.05 ! [A: real] :
% 3.82/4.05 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ A )
% 3.82/4.05 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_less_pos
% 3.82/4.05 thf(fact_4048_neg__0__less__iff__less,axiom,
% 3.82/4.05 ! [A: int] :
% 3.82/4.05 ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 3.82/4.05 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_0_less_iff_less
% 3.82/4.05 thf(fact_4049_neg__0__less__iff__less,axiom,
% 3.82/4.05 ! [A: real] :
% 3.82/4.05 ( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 3.82/4.05 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_0_less_iff_less
% 3.82/4.05 thf(fact_4050_neg__less__0__iff__less,axiom,
% 3.82/4.05 ! [A: int] :
% 3.82/4.05 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 3.82/4.05 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_less_0_iff_less
% 3.82/4.05 thf(fact_4051_neg__less__0__iff__less,axiom,
% 3.82/4.05 ! [A: real] :
% 3.82/4.05 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 3.82/4.05 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_less_0_iff_less
% 3.82/4.05 thf(fact_4052_ab__left__minus,axiom,
% 3.82/4.05 ! [A: complex] :
% 3.82/4.05 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 3.82/4.05 = zero_zero_complex ) ).
% 3.82/4.05
% 3.82/4.05 % ab_left_minus
% 3.82/4.05 thf(fact_4053_ab__left__minus,axiom,
% 3.82/4.05 ! [A: int] :
% 3.82/4.05 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 3.82/4.05 = zero_zero_int ) ).
% 3.82/4.05
% 3.82/4.05 % ab_left_minus
% 3.82/4.05 thf(fact_4054_ab__left__minus,axiom,
% 3.82/4.05 ! [A: real] :
% 3.82/4.05 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 3.82/4.05 = zero_zero_real ) ).
% 3.82/4.05
% 3.82/4.05 % ab_left_minus
% 3.82/4.05 thf(fact_4055_add_Oright__inverse,axiom,
% 3.82/4.05 ! [A: complex] :
% 3.82/4.05 ( ( plus_plus_complex @ A @ ( uminus1482373934393186551omplex @ A ) )
% 3.82/4.05 = zero_zero_complex ) ).
% 3.82/4.05
% 3.82/4.05 % add.right_inverse
% 3.82/4.05 thf(fact_4056_add_Oright__inverse,axiom,
% 3.82/4.05 ! [A: int] :
% 3.82/4.05 ( ( plus_plus_int @ A @ ( uminus_uminus_int @ A ) )
% 3.82/4.05 = zero_zero_int ) ).
% 3.82/4.05
% 3.82/4.05 % add.right_inverse
% 3.82/4.05 thf(fact_4057_add_Oright__inverse,axiom,
% 3.82/4.05 ! [A: real] :
% 3.82/4.05 ( ( plus_plus_real @ A @ ( uminus_uminus_real @ A ) )
% 3.82/4.05 = zero_zero_real ) ).
% 3.82/4.05
% 3.82/4.05 % add.right_inverse
% 3.82/4.05 thf(fact_4058_verit__minus__simplify_I3_J,axiom,
% 3.82/4.05 ! [B2: complex] :
% 3.82/4.05 ( ( minus_minus_complex @ zero_zero_complex @ B2 )
% 3.82/4.05 = ( uminus1482373934393186551omplex @ B2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % verit_minus_simplify(3)
% 3.82/4.05 thf(fact_4059_verit__minus__simplify_I3_J,axiom,
% 3.82/4.05 ! [B2: int] :
% 3.82/4.05 ( ( minus_minus_int @ zero_zero_int @ B2 )
% 3.82/4.05 = ( uminus_uminus_int @ B2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % verit_minus_simplify(3)
% 3.82/4.05 thf(fact_4060_verit__minus__simplify_I3_J,axiom,
% 3.82/4.05 ! [B2: real] :
% 3.82/4.05 ( ( minus_minus_real @ zero_zero_real @ B2 )
% 3.82/4.05 = ( uminus_uminus_real @ B2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % verit_minus_simplify(3)
% 3.82/4.05 thf(fact_4061_diff__0,axiom,
% 3.82/4.05 ! [A: complex] :
% 3.82/4.05 ( ( minus_minus_complex @ zero_zero_complex @ A )
% 3.82/4.05 = ( uminus1482373934393186551omplex @ A ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_0
% 3.82/4.05 thf(fact_4062_diff__0,axiom,
% 3.82/4.05 ! [A: int] :
% 3.82/4.05 ( ( minus_minus_int @ zero_zero_int @ A )
% 3.82/4.05 = ( uminus_uminus_int @ A ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_0
% 3.82/4.05 thf(fact_4063_diff__0,axiom,
% 3.82/4.05 ! [A: real] :
% 3.82/4.05 ( ( minus_minus_real @ zero_zero_real @ A )
% 3.82/4.05 = ( uminus_uminus_real @ A ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_0
% 3.82/4.05 thf(fact_4064_add__neg__numeral__simps_I3_J,axiom,
% 3.82/4.05 ! [M2: num,N2: num] :
% 3.82/4.05 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 3.82/4.05 = ( uminus_uminus_int @ ( plus_plus_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % add_neg_numeral_simps(3)
% 3.82/4.05 thf(fact_4065_add__neg__numeral__simps_I3_J,axiom,
% 3.82/4.05 ! [M2: num,N2: num] :
% 3.82/4.05 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 3.82/4.05 = ( uminus_uminus_real @ ( plus_plus_real @ ( numeral_numeral_real @ M2 ) @ ( numeral_numeral_real @ N2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % add_neg_numeral_simps(3)
% 3.82/4.05 thf(fact_4066_uminus__add__conv__diff,axiom,
% 3.82/4.05 ! [A: int,B2: int] :
% 3.82/4.05 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B2 )
% 3.82/4.05 = ( minus_minus_int @ B2 @ A ) ) ).
% 3.82/4.05
% 3.82/4.05 % uminus_add_conv_diff
% 3.82/4.05 thf(fact_4067_uminus__add__conv__diff,axiom,
% 3.82/4.05 ! [A: real,B2: real] :
% 3.82/4.05 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B2 )
% 3.82/4.05 = ( minus_minus_real @ B2 @ A ) ) ).
% 3.82/4.05
% 3.82/4.05 % uminus_add_conv_diff
% 3.82/4.05 thf(fact_4068_diff__minus__eq__add,axiom,
% 3.82/4.05 ! [A: int,B2: int] :
% 3.82/4.05 ( ( minus_minus_int @ A @ ( uminus_uminus_int @ B2 ) )
% 3.82/4.05 = ( plus_plus_int @ A @ B2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_minus_eq_add
% 3.82/4.05 thf(fact_4069_diff__minus__eq__add,axiom,
% 3.82/4.05 ! [A: real,B2: real] :
% 3.82/4.05 ( ( minus_minus_real @ A @ ( uminus_uminus_real @ B2 ) )
% 3.82/4.05 = ( plus_plus_real @ A @ B2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_minus_eq_add
% 3.82/4.05 thf(fact_4070_divide__minus1,axiom,
% 3.82/4.05 ! [X: complex] :
% 3.82/4.05 ( ( divide1717551699836669952omplex @ X @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 3.82/4.05 = ( uminus1482373934393186551omplex @ X ) ) ).
% 3.82/4.05
% 3.82/4.05 % divide_minus1
% 3.82/4.05 thf(fact_4071_divide__minus1,axiom,
% 3.82/4.05 ! [X: real] :
% 3.82/4.05 ( ( divide_divide_real @ X @ ( uminus_uminus_real @ one_one_real ) )
% 3.82/4.05 = ( uminus_uminus_real @ X ) ) ).
% 3.82/4.05
% 3.82/4.05 % divide_minus1
% 3.82/4.05 thf(fact_4072_atLeastatMost__empty__iff,axiom,
% 3.82/4.05 ! [A: extended_enat,B2: extended_enat] :
% 3.82/4.05 ( ( ( set_or5403411693681687835d_enat @ A @ B2 )
% 3.82/4.05 = bot_bo7653980558646680370d_enat )
% 3.82/4.05 = ( ~ ( ord_le2932123472753598470d_enat @ A @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % atLeastatMost_empty_iff
% 3.82/4.05 thf(fact_4073_atLeastatMost__empty__iff,axiom,
% 3.82/4.05 ! [A: set_nat,B2: set_nat] :
% 3.82/4.05 ( ( ( set_or4548717258645045905et_nat @ A @ B2 )
% 3.82/4.05 = bot_bot_set_set_nat )
% 3.82/4.05 = ( ~ ( ord_less_eq_set_nat @ A @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % atLeastatMost_empty_iff
% 3.82/4.05 thf(fact_4074_atLeastatMost__empty__iff,axiom,
% 3.82/4.05 ! [A: set_int,B2: set_int] :
% 3.82/4.05 ( ( ( set_or370866239135849197et_int @ A @ B2 )
% 3.82/4.05 = bot_bot_set_set_int )
% 3.82/4.05 = ( ~ ( ord_less_eq_set_int @ A @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % atLeastatMost_empty_iff
% 3.82/4.05 thf(fact_4075_atLeastatMost__empty__iff,axiom,
% 3.82/4.05 ! [A: nat,B2: nat] :
% 3.82/4.05 ( ( ( set_or1269000886237332187st_nat @ A @ B2 )
% 3.82/4.05 = bot_bot_set_nat )
% 3.82/4.05 = ( ~ ( ord_less_eq_nat @ A @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % atLeastatMost_empty_iff
% 3.82/4.05 thf(fact_4076_atLeastatMost__empty__iff,axiom,
% 3.82/4.05 ! [A: int,B2: int] :
% 3.82/4.05 ( ( ( set_or1266510415728281911st_int @ A @ B2 )
% 3.82/4.05 = bot_bot_set_int )
% 3.82/4.05 = ( ~ ( ord_less_eq_int @ A @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % atLeastatMost_empty_iff
% 3.82/4.05 thf(fact_4077_atLeastatMost__empty__iff,axiom,
% 3.82/4.05 ! [A: real,B2: real] :
% 3.82/4.05 ( ( ( set_or1222579329274155063t_real @ A @ B2 )
% 3.82/4.05 = bot_bot_set_real )
% 3.82/4.05 = ( ~ ( ord_less_eq_real @ A @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % atLeastatMost_empty_iff
% 3.82/4.05 thf(fact_4078_atLeastatMost__empty__iff2,axiom,
% 3.82/4.05 ! [A: extended_enat,B2: extended_enat] :
% 3.82/4.05 ( ( bot_bo7653980558646680370d_enat
% 3.82/4.05 = ( set_or5403411693681687835d_enat @ A @ B2 ) )
% 3.82/4.05 = ( ~ ( ord_le2932123472753598470d_enat @ A @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % atLeastatMost_empty_iff2
% 3.82/4.05 thf(fact_4079_atLeastatMost__empty__iff2,axiom,
% 3.82/4.05 ! [A: set_nat,B2: set_nat] :
% 3.82/4.05 ( ( bot_bot_set_set_nat
% 3.82/4.05 = ( set_or4548717258645045905et_nat @ A @ B2 ) )
% 3.82/4.05 = ( ~ ( ord_less_eq_set_nat @ A @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % atLeastatMost_empty_iff2
% 3.82/4.05 thf(fact_4080_atLeastatMost__empty__iff2,axiom,
% 3.82/4.05 ! [A: set_int,B2: set_int] :
% 3.82/4.05 ( ( bot_bot_set_set_int
% 3.82/4.05 = ( set_or370866239135849197et_int @ A @ B2 ) )
% 3.82/4.05 = ( ~ ( ord_less_eq_set_int @ A @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % atLeastatMost_empty_iff2
% 3.82/4.05 thf(fact_4081_atLeastatMost__empty__iff2,axiom,
% 3.82/4.05 ! [A: nat,B2: nat] :
% 3.82/4.05 ( ( bot_bot_set_nat
% 3.82/4.05 = ( set_or1269000886237332187st_nat @ A @ B2 ) )
% 3.82/4.05 = ( ~ ( ord_less_eq_nat @ A @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % atLeastatMost_empty_iff2
% 3.82/4.05 thf(fact_4082_atLeastatMost__empty__iff2,axiom,
% 3.82/4.05 ! [A: int,B2: int] :
% 3.82/4.05 ( ( bot_bot_set_int
% 3.82/4.05 = ( set_or1266510415728281911st_int @ A @ B2 ) )
% 3.82/4.05 = ( ~ ( ord_less_eq_int @ A @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % atLeastatMost_empty_iff2
% 3.82/4.05 thf(fact_4083_atLeastatMost__empty__iff2,axiom,
% 3.82/4.05 ! [A: real,B2: real] :
% 3.82/4.05 ( ( bot_bot_set_real
% 3.82/4.05 = ( set_or1222579329274155063t_real @ A @ B2 ) )
% 3.82/4.05 = ( ~ ( ord_less_eq_real @ A @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % atLeastatMost_empty_iff2
% 3.82/4.05 thf(fact_4084_atLeastatMost__subset__iff,axiom,
% 3.82/4.05 ! [A: set_nat,B2: set_nat,C: set_nat,D: set_nat] :
% 3.82/4.05 ( ( ord_le6893508408891458716et_nat @ ( set_or4548717258645045905et_nat @ A @ B2 ) @ ( set_or4548717258645045905et_nat @ C @ D ) )
% 3.82/4.05 = ( ~ ( ord_less_eq_set_nat @ A @ B2 )
% 3.82/4.05 | ( ( ord_less_eq_set_nat @ C @ A )
% 3.82/4.05 & ( ord_less_eq_set_nat @ B2 @ D ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % atLeastatMost_subset_iff
% 3.82/4.05 thf(fact_4085_atLeastatMost__subset__iff,axiom,
% 3.82/4.05 ! [A: set_int,B2: set_int,C: set_int,D: set_int] :
% 3.82/4.05 ( ( ord_le4403425263959731960et_int @ ( set_or370866239135849197et_int @ A @ B2 ) @ ( set_or370866239135849197et_int @ C @ D ) )
% 3.82/4.05 = ( ~ ( ord_less_eq_set_int @ A @ B2 )
% 3.82/4.05 | ( ( ord_less_eq_set_int @ C @ A )
% 3.82/4.05 & ( ord_less_eq_set_int @ B2 @ D ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % atLeastatMost_subset_iff
% 3.82/4.05 thf(fact_4086_atLeastatMost__subset__iff,axiom,
% 3.82/4.05 ! [A: nat,B2: nat,C: nat,D: nat] :
% 3.82/4.05 ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ A @ B2 ) @ ( set_or1269000886237332187st_nat @ C @ D ) )
% 3.82/4.05 = ( ~ ( ord_less_eq_nat @ A @ B2 )
% 3.82/4.05 | ( ( ord_less_eq_nat @ C @ A )
% 3.82/4.05 & ( ord_less_eq_nat @ B2 @ D ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % atLeastatMost_subset_iff
% 3.82/4.05 thf(fact_4087_atLeastatMost__subset__iff,axiom,
% 3.82/4.05 ! [A: int,B2: int,C: int,D: int] :
% 3.82/4.05 ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ A @ B2 ) @ ( set_or1266510415728281911st_int @ C @ D ) )
% 3.82/4.05 = ( ~ ( ord_less_eq_int @ A @ B2 )
% 3.82/4.05 | ( ( ord_less_eq_int @ C @ A )
% 3.82/4.05 & ( ord_less_eq_int @ B2 @ D ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % atLeastatMost_subset_iff
% 3.82/4.05 thf(fact_4088_atLeastatMost__subset__iff,axiom,
% 3.82/4.05 ! [A: real,B2: real,C: real,D: real] :
% 3.82/4.05 ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ A @ B2 ) @ ( set_or1222579329274155063t_real @ C @ D ) )
% 3.82/4.05 = ( ~ ( ord_less_eq_real @ A @ B2 )
% 3.82/4.05 | ( ( ord_less_eq_real @ C @ A )
% 3.82/4.05 & ( ord_less_eq_real @ B2 @ D ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % atLeastatMost_subset_iff
% 3.82/4.05 thf(fact_4089_atLeastatMost__empty,axiom,
% 3.82/4.05 ! [B2: extended_enat,A: extended_enat] :
% 3.82/4.05 ( ( ord_le72135733267957522d_enat @ B2 @ A )
% 3.82/4.05 => ( ( set_or5403411693681687835d_enat @ A @ B2 )
% 3.82/4.05 = bot_bo7653980558646680370d_enat ) ) ).
% 3.82/4.05
% 3.82/4.05 % atLeastatMost_empty
% 3.82/4.05 thf(fact_4090_atLeastatMost__empty,axiom,
% 3.82/4.05 ! [B2: nat,A: nat] :
% 3.82/4.05 ( ( ord_less_nat @ B2 @ A )
% 3.82/4.05 => ( ( set_or1269000886237332187st_nat @ A @ B2 )
% 3.82/4.05 = bot_bot_set_nat ) ) ).
% 3.82/4.05
% 3.82/4.05 % atLeastatMost_empty
% 3.82/4.05 thf(fact_4091_atLeastatMost__empty,axiom,
% 3.82/4.05 ! [B2: int,A: int] :
% 3.82/4.05 ( ( ord_less_int @ B2 @ A )
% 3.82/4.05 => ( ( set_or1266510415728281911st_int @ A @ B2 )
% 3.82/4.05 = bot_bot_set_int ) ) ).
% 3.82/4.05
% 3.82/4.05 % atLeastatMost_empty
% 3.82/4.05 thf(fact_4092_atLeastatMost__empty,axiom,
% 3.82/4.05 ! [B2: real,A: real] :
% 3.82/4.05 ( ( ord_less_real @ B2 @ A )
% 3.82/4.05 => ( ( set_or1222579329274155063t_real @ A @ B2 )
% 3.82/4.05 = bot_bot_set_real ) ) ).
% 3.82/4.05
% 3.82/4.05 % atLeastatMost_empty
% 3.82/4.05 thf(fact_4093_infinite__Icc__iff,axiom,
% 3.82/4.05 ! [A: real,B2: real] :
% 3.82/4.05 ( ( ~ ( finite_finite_real @ ( set_or1222579329274155063t_real @ A @ B2 ) ) )
% 3.82/4.05 = ( ord_less_real @ A @ B2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % infinite_Icc_iff
% 3.82/4.05 thf(fact_4094_take__bit__0,axiom,
% 3.82/4.05 ! [A: nat] :
% 3.82/4.05 ( ( bit_se2925701944663578781it_nat @ zero_zero_nat @ A )
% 3.82/4.05 = zero_zero_nat ) ).
% 3.82/4.05
% 3.82/4.05 % take_bit_0
% 3.82/4.05 thf(fact_4095_take__bit__0,axiom,
% 3.82/4.05 ! [A: int] :
% 3.82/4.05 ( ( bit_se2923211474154528505it_int @ zero_zero_nat @ A )
% 3.82/4.05 = zero_zero_int ) ).
% 3.82/4.05
% 3.82/4.05 % take_bit_0
% 3.82/4.05 thf(fact_4096_take__bit__Suc__1,axiom,
% 3.82/4.05 ! [N2: nat] :
% 3.82/4.05 ( ( bit_se2925701944663578781it_nat @ ( suc @ N2 ) @ one_one_nat )
% 3.82/4.05 = one_one_nat ) ).
% 3.82/4.05
% 3.82/4.05 % take_bit_Suc_1
% 3.82/4.05 thf(fact_4097_take__bit__Suc__1,axiom,
% 3.82/4.05 ! [N2: nat] :
% 3.82/4.05 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ one_one_int )
% 3.82/4.05 = one_one_int ) ).
% 3.82/4.05
% 3.82/4.05 % take_bit_Suc_1
% 3.82/4.05 thf(fact_4098_ln__one,axiom,
% 3.82/4.05 ( ( ln_ln_real @ one_one_real )
% 3.82/4.05 = zero_zero_real ) ).
% 3.82/4.05
% 3.82/4.05 % ln_one
% 3.82/4.05 thf(fact_4099_add__neg__numeral__special_I7_J,axiom,
% 3.82/4.05 ( ( plus_plus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 3.82/4.05 = zero_zero_complex ) ).
% 3.82/4.05
% 3.82/4.05 % add_neg_numeral_special(7)
% 3.82/4.05 thf(fact_4100_add__neg__numeral__special_I7_J,axiom,
% 3.82/4.05 ( ( plus_plus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 3.82/4.05 = zero_zero_int ) ).
% 3.82/4.05
% 3.82/4.05 % add_neg_numeral_special(7)
% 3.82/4.05 thf(fact_4101_add__neg__numeral__special_I7_J,axiom,
% 3.82/4.05 ( ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 3.82/4.05 = zero_zero_real ) ).
% 3.82/4.05
% 3.82/4.05 % add_neg_numeral_special(7)
% 3.82/4.05 thf(fact_4102_add__neg__numeral__special_I8_J,axiom,
% 3.82/4.05 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 3.82/4.05 = zero_zero_complex ) ).
% 3.82/4.05
% 3.82/4.05 % add_neg_numeral_special(8)
% 3.82/4.05 thf(fact_4103_add__neg__numeral__special_I8_J,axiom,
% 3.82/4.05 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 3.82/4.05 = zero_zero_int ) ).
% 3.82/4.05
% 3.82/4.05 % add_neg_numeral_special(8)
% 3.82/4.05 thf(fact_4104_add__neg__numeral__special_I8_J,axiom,
% 3.82/4.05 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 3.82/4.05 = zero_zero_real ) ).
% 3.82/4.05
% 3.82/4.05 % add_neg_numeral_special(8)
% 3.82/4.05 thf(fact_4105_diff__numeral__special_I12_J,axiom,
% 3.82/4.05 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 3.82/4.05 = zero_zero_complex ) ).
% 3.82/4.05
% 3.82/4.05 % diff_numeral_special(12)
% 3.82/4.05 thf(fact_4106_diff__numeral__special_I12_J,axiom,
% 3.82/4.05 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 3.82/4.05 = zero_zero_int ) ).
% 3.82/4.05
% 3.82/4.05 % diff_numeral_special(12)
% 3.82/4.05 thf(fact_4107_diff__numeral__special_I12_J,axiom,
% 3.82/4.05 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 3.82/4.05 = zero_zero_real ) ).
% 3.82/4.05
% 3.82/4.05 % diff_numeral_special(12)
% 3.82/4.05 thf(fact_4108_mod__minus1__right,axiom,
% 3.82/4.05 ! [A: int] :
% 3.82/4.05 ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 3.82/4.05 = zero_zero_int ) ).
% 3.82/4.05
% 3.82/4.05 % mod_minus1_right
% 3.82/4.05 thf(fact_4109_max__number__of_I2_J,axiom,
% 3.82/4.05 ! [U: num,V: num] :
% 3.82/4.05 ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 3.82/4.05 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 3.82/4.05 = ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) )
% 3.82/4.05 & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 3.82/4.05 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 3.82/4.05 = ( numeral_numeral_real @ U ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % max_number_of(2)
% 3.82/4.05 thf(fact_4110_max__number__of_I2_J,axiom,
% 3.82/4.05 ! [U: num,V: num] :
% 3.82/4.05 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 3.82/4.05 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 3.82/4.05 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) )
% 3.82/4.05 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 3.82/4.05 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 3.82/4.05 = ( numeral_numeral_int @ U ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % max_number_of(2)
% 3.82/4.05 thf(fact_4111_max__number__of_I3_J,axiom,
% 3.82/4.05 ! [U: num,V: num] :
% 3.82/4.05 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 3.82/4.05 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 3.82/4.05 = ( numeral_numeral_real @ V ) ) )
% 3.82/4.05 & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 3.82/4.05 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 3.82/4.05 = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % max_number_of(3)
% 3.82/4.05 thf(fact_4112_max__number__of_I3_J,axiom,
% 3.82/4.05 ! [U: num,V: num] :
% 3.82/4.05 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 3.82/4.05 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 3.82/4.05 = ( numeral_numeral_int @ V ) ) )
% 3.82/4.05 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 3.82/4.05 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 3.82/4.05 = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % max_number_of(3)
% 3.82/4.05 thf(fact_4113_max__number__of_I4_J,axiom,
% 3.82/4.05 ! [U: num,V: num] :
% 3.82/4.05 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 3.82/4.05 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 3.82/4.05 = ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) )
% 3.82/4.05 & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 3.82/4.05 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 3.82/4.05 = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % max_number_of(4)
% 3.82/4.05 thf(fact_4114_max__number__of_I4_J,axiom,
% 3.82/4.05 ! [U: num,V: num] :
% 3.82/4.05 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 3.82/4.05 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 3.82/4.05 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) )
% 3.82/4.05 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 3.82/4.05 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 3.82/4.05 = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % max_number_of(4)
% 3.82/4.05 thf(fact_4115_take__bit__of__1__eq__0__iff,axiom,
% 3.82/4.05 ! [N2: nat] :
% 3.82/4.05 ( ( ( bit_se2925701944663578781it_nat @ N2 @ one_one_nat )
% 3.82/4.05 = zero_zero_nat )
% 3.82/4.05 = ( N2 = zero_zero_nat ) ) ).
% 3.82/4.05
% 3.82/4.05 % take_bit_of_1_eq_0_iff
% 3.82/4.05 thf(fact_4116_take__bit__of__1__eq__0__iff,axiom,
% 3.82/4.05 ! [N2: nat] :
% 3.82/4.05 ( ( ( bit_se2923211474154528505it_int @ N2 @ one_one_int )
% 3.82/4.05 = zero_zero_int )
% 3.82/4.05 = ( N2 = zero_zero_nat ) ) ).
% 3.82/4.05
% 3.82/4.05 % take_bit_of_1_eq_0_iff
% 3.82/4.05 thf(fact_4117_semiring__norm_I168_J,axiom,
% 3.82/4.05 ! [V: num,W2: num,Y: int] :
% 3.82/4.05 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W2 ) ) @ Y ) )
% 3.82/4.05 = ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W2 ) ) ) @ Y ) ) ).
% 3.82/4.05
% 3.82/4.05 % semiring_norm(168)
% 3.82/4.05 thf(fact_4118_semiring__norm_I168_J,axiom,
% 3.82/4.05 ! [V: num,W2: num,Y: real] :
% 3.82/4.05 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ Y ) )
% 3.82/4.05 = ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W2 ) ) ) @ Y ) ) ).
% 3.82/4.05
% 3.82/4.05 % semiring_norm(168)
% 3.82/4.05 thf(fact_4119_neg__numeral__le__iff,axiom,
% 3.82/4.05 ! [M2: num,N2: num] :
% 3.82/4.05 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 3.82/4.05 = ( ord_less_eq_num @ N2 @ M2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_numeral_le_iff
% 3.82/4.05 thf(fact_4120_neg__numeral__le__iff,axiom,
% 3.82/4.05 ! [M2: num,N2: num] :
% 3.82/4.05 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 3.82/4.05 = ( ord_less_eq_num @ N2 @ M2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_numeral_le_iff
% 3.82/4.05 thf(fact_4121_neg__numeral__less__iff,axiom,
% 3.82/4.05 ! [M2: num,N2: num] :
% 3.82/4.05 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 3.82/4.05 = ( ord_less_num @ N2 @ M2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_numeral_less_iff
% 3.82/4.05 thf(fact_4122_neg__numeral__less__iff,axiom,
% 3.82/4.05 ! [M2: num,N2: num] :
% 3.82/4.05 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 3.82/4.05 = ( ord_less_num @ N2 @ M2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_numeral_less_iff
% 3.82/4.05 thf(fact_4123_take__bit__of__Suc__0,axiom,
% 3.82/4.05 ! [N2: nat] :
% 3.82/4.05 ( ( bit_se2925701944663578781it_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 3.82/4.05 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % take_bit_of_Suc_0
% 3.82/4.05 thf(fact_4124_not__neg__one__le__neg__numeral__iff,axiom,
% 3.82/4.05 ! [M2: num] :
% 3.82/4.05 ( ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) ) )
% 3.82/4.05 = ( M2 != one ) ) ).
% 3.82/4.05
% 3.82/4.05 % not_neg_one_le_neg_numeral_iff
% 3.82/4.05 thf(fact_4125_not__neg__one__le__neg__numeral__iff,axiom,
% 3.82/4.05 ! [M2: num] :
% 3.82/4.05 ( ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) ) )
% 3.82/4.05 = ( M2 != one ) ) ).
% 3.82/4.05
% 3.82/4.05 % not_neg_one_le_neg_numeral_iff
% 3.82/4.05 thf(fact_4126_le__divide__eq__numeral1_I2_J,axiom,
% 3.82/4.05 ! [A: real,B2: real,W2: num] :
% 3.82/4.05 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B2 @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) )
% 3.82/4.05 = ( ord_less_eq_real @ B2 @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % le_divide_eq_numeral1(2)
% 3.82/4.05 thf(fact_4127_divide__le__eq__numeral1_I2_J,axiom,
% 3.82/4.05 ! [B2: real,W2: num,A: real] :
% 3.82/4.05 ( ( ord_less_eq_real @ ( divide_divide_real @ B2 @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) @ A )
% 3.82/4.05 = ( ord_less_eq_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) @ B2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % divide_le_eq_numeral1(2)
% 3.82/4.05 thf(fact_4128_divide__eq__eq__numeral1_I2_J,axiom,
% 3.82/4.05 ! [B2: complex,W2: num,A: complex] :
% 3.82/4.05 ( ( ( divide1717551699836669952omplex @ B2 @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) )
% 3.82/4.05 = A )
% 3.82/4.05 = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 3.82/4.05 != zero_zero_complex )
% 3.82/4.05 => ( B2
% 3.82/4.05 = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) ) ) )
% 3.82/4.05 & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 3.82/4.05 = zero_zero_complex )
% 3.82/4.05 => ( A = zero_zero_complex ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % divide_eq_eq_numeral1(2)
% 3.82/4.05 thf(fact_4129_divide__eq__eq__numeral1_I2_J,axiom,
% 3.82/4.05 ! [B2: real,W2: num,A: real] :
% 3.82/4.05 ( ( ( divide_divide_real @ B2 @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) )
% 3.82/4.05 = A )
% 3.82/4.05 = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 3.82/4.05 != zero_zero_real )
% 3.82/4.05 => ( B2
% 3.82/4.05 = ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) ) )
% 3.82/4.05 & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 3.82/4.05 = zero_zero_real )
% 3.82/4.05 => ( A = zero_zero_real ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % divide_eq_eq_numeral1(2)
% 3.82/4.05 thf(fact_4130_eq__divide__eq__numeral1_I2_J,axiom,
% 3.82/4.05 ! [A: complex,B2: complex,W2: num] :
% 3.82/4.05 ( ( A
% 3.82/4.05 = ( divide1717551699836669952omplex @ B2 @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) ) )
% 3.82/4.05 = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 3.82/4.05 != zero_zero_complex )
% 3.82/4.05 => ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) )
% 3.82/4.05 = B2 ) )
% 3.82/4.05 & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 3.82/4.05 = zero_zero_complex )
% 3.82/4.05 => ( A = zero_zero_complex ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % eq_divide_eq_numeral1(2)
% 3.82/4.05 thf(fact_4131_eq__divide__eq__numeral1_I2_J,axiom,
% 3.82/4.05 ! [A: real,B2: real,W2: num] :
% 3.82/4.05 ( ( A
% 3.82/4.05 = ( divide_divide_real @ B2 @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) )
% 3.82/4.05 = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 3.82/4.05 != zero_zero_real )
% 3.82/4.05 => ( ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) )
% 3.82/4.05 = B2 ) )
% 3.82/4.05 & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 3.82/4.05 = zero_zero_real )
% 3.82/4.05 => ( A = zero_zero_real ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % eq_divide_eq_numeral1(2)
% 3.82/4.05 thf(fact_4132_neg__numeral__less__neg__one__iff,axiom,
% 3.82/4.05 ! [M2: num] :
% 3.82/4.05 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 3.82/4.05 = ( M2 != one ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_numeral_less_neg_one_iff
% 3.82/4.05 thf(fact_4133_neg__numeral__less__neg__one__iff,axiom,
% 3.82/4.05 ! [M2: num] :
% 3.82/4.05 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 3.82/4.05 = ( M2 != one ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_numeral_less_neg_one_iff
% 3.82/4.05 thf(fact_4134_less__divide__eq__numeral1_I2_J,axiom,
% 3.82/4.05 ! [A: real,B2: real,W2: num] :
% 3.82/4.05 ( ( ord_less_real @ A @ ( divide_divide_real @ B2 @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) )
% 3.82/4.05 = ( ord_less_real @ B2 @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % less_divide_eq_numeral1(2)
% 3.82/4.05 thf(fact_4135_divide__less__eq__numeral1_I2_J,axiom,
% 3.82/4.05 ! [B2: real,W2: num,A: real] :
% 3.82/4.05 ( ( ord_less_real @ ( divide_divide_real @ B2 @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) @ A )
% 3.82/4.05 = ( ord_less_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) @ B2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % divide_less_eq_numeral1(2)
% 3.82/4.05 thf(fact_4136_take__bit__of__1,axiom,
% 3.82/4.05 ! [N2: nat] :
% 3.82/4.05 ( ( bit_se2925701944663578781it_nat @ N2 @ one_one_nat )
% 3.82/4.05 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % take_bit_of_1
% 3.82/4.05 thf(fact_4137_take__bit__of__1,axiom,
% 3.82/4.05 ! [N2: nat] :
% 3.82/4.05 ( ( bit_se2923211474154528505it_int @ N2 @ one_one_int )
% 3.82/4.05 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % take_bit_of_1
% 3.82/4.05 thf(fact_4138_add__neg__numeral__special_I9_J,axiom,
% 3.82/4.05 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 3.82/4.05 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % add_neg_numeral_special(9)
% 3.82/4.05 thf(fact_4139_add__neg__numeral__special_I9_J,axiom,
% 3.82/4.05 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 3.82/4.05 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % add_neg_numeral_special(9)
% 3.82/4.05 thf(fact_4140_add__neg__numeral__special_I9_J,axiom,
% 3.82/4.05 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 3.82/4.05 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % add_neg_numeral_special(9)
% 3.82/4.05 thf(fact_4141_even__take__bit__eq,axiom,
% 3.82/4.05 ! [N2: nat,A: nat] :
% 3.82/4.05 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2925701944663578781it_nat @ N2 @ A ) )
% 3.82/4.05 = ( ( N2 = zero_zero_nat )
% 3.82/4.05 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % even_take_bit_eq
% 3.82/4.05 thf(fact_4142_even__take__bit__eq,axiom,
% 3.82/4.05 ! [N2: nat,A: int] :
% 3.82/4.05 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2923211474154528505it_int @ N2 @ A ) )
% 3.82/4.05 = ( ( N2 = zero_zero_nat )
% 3.82/4.05 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % even_take_bit_eq
% 3.82/4.05 thf(fact_4143_Suc__div__eq__add3__div__numeral,axiom,
% 3.82/4.05 ! [M2: nat,V: num] :
% 3.82/4.05 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M2 ) ) ) @ ( numeral_numeral_nat @ V ) )
% 3.82/4.05 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M2 ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % Suc_div_eq_add3_div_numeral
% 3.82/4.05 thf(fact_4144_div__Suc__eq__div__add3,axiom,
% 3.82/4.05 ! [M2: nat,N2: nat] :
% 3.82/4.05 ( ( divide_divide_nat @ M2 @ ( suc @ ( suc @ ( suc @ N2 ) ) ) )
% 3.82/4.05 = ( divide_divide_nat @ M2 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % div_Suc_eq_div_add3
% 3.82/4.05 thf(fact_4145_Suc__mod__eq__add3__mod__numeral,axiom,
% 3.82/4.05 ! [M2: nat,V: num] :
% 3.82/4.05 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M2 ) ) ) @ ( numeral_numeral_nat @ V ) )
% 3.82/4.05 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M2 ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % Suc_mod_eq_add3_mod_numeral
% 3.82/4.05 thf(fact_4146_mod__Suc__eq__mod__add3,axiom,
% 3.82/4.05 ! [M2: nat,N2: nat] :
% 3.82/4.05 ( ( modulo_modulo_nat @ M2 @ ( suc @ ( suc @ ( suc @ N2 ) ) ) )
% 3.82/4.05 = ( modulo_modulo_nat @ M2 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % mod_Suc_eq_mod_add3
% 3.82/4.05 thf(fact_4147_signed__take__bit__Suc__minus__bit0,axiom,
% 3.82/4.05 ! [N2: nat,K: num] :
% 3.82/4.05 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 3.82/4.05 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % signed_take_bit_Suc_minus_bit0
% 3.82/4.05 thf(fact_4148_take__bit__Suc__0,axiom,
% 3.82/4.05 ! [A: nat] :
% 3.82/4.05 ( ( bit_se2925701944663578781it_nat @ ( suc @ zero_zero_nat ) @ A )
% 3.82/4.05 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % take_bit_Suc_0
% 3.82/4.05 thf(fact_4149_take__bit__Suc__0,axiom,
% 3.82/4.05 ! [A: int] :
% 3.82/4.05 ( ( bit_se2923211474154528505it_int @ ( suc @ zero_zero_nat ) @ A )
% 3.82/4.05 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % take_bit_Suc_0
% 3.82/4.05 thf(fact_4150_signed__take__bit__0,axiom,
% 3.82/4.05 ! [A: int] :
% 3.82/4.05 ( ( bit_ri631733984087533419it_int @ zero_zero_nat @ A )
% 3.82/4.05 = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % signed_take_bit_0
% 3.82/4.05 thf(fact_4151_signed__take__bit__Suc__minus__bit1,axiom,
% 3.82/4.05 ! [N2: nat,K: num] :
% 3.82/4.05 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 3.82/4.05 = ( 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 ) ) ).
% 3.82/4.05
% 3.82/4.05 % signed_take_bit_Suc_minus_bit1
% 3.82/4.05 thf(fact_4152_signed__take__bit__Suc__bit1,axiom,
% 3.82/4.05 ! [N2: nat,K: num] :
% 3.82/4.05 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 3.82/4.05 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N2 @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 3.82/4.05
% 3.82/4.05 % signed_take_bit_Suc_bit1
% 3.82/4.05 thf(fact_4153_take__bit__of__exp,axiom,
% 3.82/4.05 ! [M2: nat,N2: nat] :
% 3.82/4.05 ( ( bit_se2925701944663578781it_nat @ M2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 3.82/4.05 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ N2 @ M2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % take_bit_of_exp
% 3.82/4.05 thf(fact_4154_take__bit__of__exp,axiom,
% 3.82/4.05 ! [M2: nat,N2: nat] :
% 3.82/4.05 ( ( bit_se2923211474154528505it_int @ M2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 3.82/4.05 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ N2 @ M2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % take_bit_of_exp
% 3.82/4.05 thf(fact_4155_take__bit__of__2,axiom,
% 3.82/4.05 ! [N2: nat] :
% 3.82/4.05 ( ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.05 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % take_bit_of_2
% 3.82/4.05 thf(fact_4156_take__bit__of__2,axiom,
% 3.82/4.05 ! [N2: nat] :
% 3.82/4.05 ( ( bit_se2923211474154528505it_int @ N2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 3.82/4.05 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % take_bit_of_2
% 3.82/4.05 thf(fact_4157_minus__int__code_I2_J,axiom,
% 3.82/4.05 ! [L: int] :
% 3.82/4.05 ( ( minus_minus_int @ zero_zero_int @ L )
% 3.82/4.05 = ( uminus_uminus_int @ L ) ) ).
% 3.82/4.05
% 3.82/4.05 % minus_int_code(2)
% 3.82/4.05 thf(fact_4158_minus__int__code_I1_J,axiom,
% 3.82/4.05 ! [K: int] :
% 3.82/4.05 ( ( minus_minus_int @ K @ zero_zero_int )
% 3.82/4.05 = K ) ).
% 3.82/4.05
% 3.82/4.05 % minus_int_code(1)
% 3.82/4.05 thf(fact_4159_int__distrib_I3_J,axiom,
% 3.82/4.05 ! [Z1: int,Z22: int,W2: int] :
% 3.82/4.05 ( ( times_times_int @ ( minus_minus_int @ Z1 @ Z22 ) @ W2 )
% 3.82/4.05 = ( minus_minus_int @ ( times_times_int @ Z1 @ W2 ) @ ( times_times_int @ Z22 @ W2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % int_distrib(3)
% 3.82/4.05 thf(fact_4160_int__distrib_I4_J,axiom,
% 3.82/4.05 ! [W2: int,Z1: int,Z22: int] :
% 3.82/4.05 ( ( times_times_int @ W2 @ ( minus_minus_int @ Z1 @ Z22 ) )
% 3.82/4.05 = ( minus_minus_int @ ( times_times_int @ W2 @ Z1 ) @ ( times_times_int @ W2 @ Z22 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % int_distrib(4)
% 3.82/4.05 thf(fact_4161_int__less__induct,axiom,
% 3.82/4.05 ! [I: int,K: int,P: int > $o] :
% 3.82/4.05 ( ( ord_less_int @ I @ K )
% 3.82/4.05 => ( ( P @ ( minus_minus_int @ K @ one_one_int ) )
% 3.82/4.05 => ( ! [I4: int] :
% 3.82/4.05 ( ( ord_less_int @ I4 @ K )
% 3.82/4.05 => ( ( P @ I4 )
% 3.82/4.05 => ( P @ ( minus_minus_int @ I4 @ one_one_int ) ) ) )
% 3.82/4.05 => ( P @ I ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % int_less_induct
% 3.82/4.05 thf(fact_4162_zdvd__mult__cancel,axiom,
% 3.82/4.05 ! [K: int,M2: int,N2: int] :
% 3.82/4.05 ( ( dvd_dvd_int @ ( times_times_int @ K @ M2 ) @ ( times_times_int @ K @ N2 ) )
% 3.82/4.05 => ( ( K != zero_zero_int )
% 3.82/4.05 => ( dvd_dvd_int @ M2 @ N2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % zdvd_mult_cancel
% 3.82/4.05 thf(fact_4163_zdvd__imp__le,axiom,
% 3.82/4.05 ! [Z3: int,N2: int] :
% 3.82/4.05 ( ( dvd_dvd_int @ Z3 @ N2 )
% 3.82/4.05 => ( ( ord_less_int @ zero_zero_int @ N2 )
% 3.82/4.05 => ( ord_less_eq_int @ Z3 @ N2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % zdvd_imp_le
% 3.82/4.05 thf(fact_4164_zdvd__not__zless,axiom,
% 3.82/4.05 ! [M2: int,N2: int] :
% 3.82/4.05 ( ( ord_less_int @ zero_zero_int @ M2 )
% 3.82/4.05 => ( ( ord_less_int @ M2 @ N2 )
% 3.82/4.05 => ~ ( dvd_dvd_int @ N2 @ M2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % zdvd_not_zless
% 3.82/4.05 thf(fact_4165_zdvd__antisym__nonneg,axiom,
% 3.82/4.05 ! [M2: int,N2: int] :
% 3.82/4.05 ( ( ord_less_eq_int @ zero_zero_int @ M2 )
% 3.82/4.05 => ( ( ord_less_eq_int @ zero_zero_int @ N2 )
% 3.82/4.05 => ( ( dvd_dvd_int @ M2 @ N2 )
% 3.82/4.05 => ( ( dvd_dvd_int @ N2 @ M2 )
% 3.82/4.05 => ( M2 = N2 ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % zdvd_antisym_nonneg
% 3.82/4.05 thf(fact_4166_zdvd__reduce,axiom,
% 3.82/4.05 ! [K: int,N2: int,M2: int] :
% 3.82/4.05 ( ( dvd_dvd_int @ K @ ( plus_plus_int @ N2 @ ( times_times_int @ K @ M2 ) ) )
% 3.82/4.05 = ( dvd_dvd_int @ K @ N2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % zdvd_reduce
% 3.82/4.05 thf(fact_4167_zdvd__period,axiom,
% 3.82/4.05 ! [A: int,D: int,X: int,T: int,C: int] :
% 3.82/4.05 ( ( dvd_dvd_int @ A @ D )
% 3.82/4.05 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ X @ T ) )
% 3.82/4.05 = ( dvd_dvd_int @ A @ ( plus_plus_int @ ( plus_plus_int @ X @ ( times_times_int @ C @ D ) ) @ T ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % zdvd_period
% 3.82/4.05 thf(fact_4168_finite__divisors__int,axiom,
% 3.82/4.05 ! [I: int] :
% 3.82/4.05 ( ( I != zero_zero_int )
% 3.82/4.05 => ( finite_finite_int
% 3.82/4.05 @ ( collect_int
% 3.82/4.05 @ ^ [D4: int] : ( dvd_dvd_int @ D4 @ I ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % finite_divisors_int
% 3.82/4.05 thf(fact_4169_compl__le__swap2,axiom,
% 3.82/4.05 ! [Y: set_nat,X: set_nat] :
% 3.82/4.05 ( ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ Y ) @ X )
% 3.82/4.05 => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ Y ) ) ).
% 3.82/4.05
% 3.82/4.05 % compl_le_swap2
% 3.82/4.05 thf(fact_4170_compl__le__swap2,axiom,
% 3.82/4.05 ! [Y: set_int,X: set_int] :
% 3.82/4.05 ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ Y ) @ X )
% 3.82/4.05 => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ X ) @ Y ) ) ).
% 3.82/4.05
% 3.82/4.05 % compl_le_swap2
% 3.82/4.05 thf(fact_4171_compl__le__swap1,axiom,
% 3.82/4.05 ! [Y: set_nat,X: set_nat] :
% 3.82/4.05 ( ( ord_less_eq_set_nat @ Y @ ( uminus5710092332889474511et_nat @ X ) )
% 3.82/4.05 => ( ord_less_eq_set_nat @ X @ ( uminus5710092332889474511et_nat @ Y ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % compl_le_swap1
% 3.82/4.05 thf(fact_4172_compl__le__swap1,axiom,
% 3.82/4.05 ! [Y: set_int,X: set_int] :
% 3.82/4.05 ( ( ord_less_eq_set_int @ Y @ ( uminus1532241313380277803et_int @ X ) )
% 3.82/4.05 => ( ord_less_eq_set_int @ X @ ( uminus1532241313380277803et_int @ Y ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % compl_le_swap1
% 3.82/4.05 thf(fact_4173_compl__mono,axiom,
% 3.82/4.05 ! [X: set_nat,Y: set_nat] :
% 3.82/4.05 ( ( ord_less_eq_set_nat @ X @ Y )
% 3.82/4.05 => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ Y ) @ ( uminus5710092332889474511et_nat @ X ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % compl_mono
% 3.82/4.05 thf(fact_4174_compl__mono,axiom,
% 3.82/4.05 ! [X: set_int,Y: set_int] :
% 3.82/4.05 ( ( ord_less_eq_set_int @ X @ Y )
% 3.82/4.05 => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ Y ) @ ( uminus1532241313380277803et_int @ X ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % compl_mono
% 3.82/4.05 thf(fact_4175_zmult__zless__mono2,axiom,
% 3.82/4.05 ! [I: int,J: int,K: int] :
% 3.82/4.05 ( ( ord_less_int @ I @ J )
% 3.82/4.05 => ( ( ord_less_int @ zero_zero_int @ K )
% 3.82/4.05 => ( ord_less_int @ ( times_times_int @ K @ I ) @ ( times_times_int @ K @ J ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % zmult_zless_mono2
% 3.82/4.05 thf(fact_4176_add1__zle__eq,axiom,
% 3.82/4.05 ! [W2: int,Z3: int] :
% 3.82/4.05 ( ( ord_less_eq_int @ ( plus_plus_int @ W2 @ one_one_int ) @ Z3 )
% 3.82/4.05 = ( ord_less_int @ W2 @ Z3 ) ) ).
% 3.82/4.05
% 3.82/4.05 % add1_zle_eq
% 3.82/4.05 thf(fact_4177_int__gr__induct,axiom,
% 3.82/4.05 ! [K: int,I: int,P: int > $o] :
% 3.82/4.05 ( ( ord_less_int @ K @ I )
% 3.82/4.05 => ( ( P @ ( plus_plus_int @ K @ one_one_int ) )
% 3.82/4.05 => ( ! [I4: int] :
% 3.82/4.05 ( ( ord_less_int @ K @ I4 )
% 3.82/4.05 => ( ( P @ I4 )
% 3.82/4.05 => ( P @ ( plus_plus_int @ I4 @ one_one_int ) ) ) )
% 3.82/4.05 => ( P @ I ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % int_gr_induct
% 3.82/4.05 thf(fact_4178_le__imp__0__less,axiom,
% 3.82/4.05 ! [Z3: int] :
% 3.82/4.05 ( ( ord_less_eq_int @ zero_zero_int @ Z3 )
% 3.82/4.05 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z3 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % le_imp_0_less
% 3.82/4.05 thf(fact_4179_zless__add1__eq,axiom,
% 3.82/4.05 ! [W2: int,Z3: int] :
% 3.82/4.05 ( ( ord_less_int @ W2 @ ( plus_plus_int @ Z3 @ one_one_int ) )
% 3.82/4.05 = ( ( ord_less_int @ W2 @ Z3 )
% 3.82/4.05 | ( W2 = Z3 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % zless_add1_eq
% 3.82/4.05 thf(fact_4180_odd__less__0__iff,axiom,
% 3.82/4.05 ! [Z3: int] :
% 3.82/4.05 ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z3 ) @ Z3 ) @ zero_zero_int )
% 3.82/4.05 = ( ord_less_int @ Z3 @ zero_zero_int ) ) ).
% 3.82/4.05
% 3.82/4.05 % odd_less_0_iff
% 3.82/4.05 thf(fact_4181_pos__zmult__eq__1__iff,axiom,
% 3.82/4.05 ! [M2: int,N2: int] :
% 3.82/4.05 ( ( ord_less_int @ zero_zero_int @ M2 )
% 3.82/4.05 => ( ( ( times_times_int @ M2 @ N2 )
% 3.82/4.05 = one_one_int )
% 3.82/4.05 = ( ( M2 = one_one_int )
% 3.82/4.05 & ( N2 = one_one_int ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % pos_zmult_eq_1_iff
% 3.82/4.05 thf(fact_4182_zless__imp__add1__zle,axiom,
% 3.82/4.05 ! [W2: int,Z3: int] :
% 3.82/4.05 ( ( ord_less_int @ W2 @ Z3 )
% 3.82/4.05 => ( ord_less_eq_int @ ( plus_plus_int @ W2 @ one_one_int ) @ Z3 ) ) ).
% 3.82/4.05
% 3.82/4.05 % zless_imp_add1_zle
% 3.82/4.05 thf(fact_4183_int__one__le__iff__zero__less,axiom,
% 3.82/4.05 ! [Z3: int] :
% 3.82/4.05 ( ( ord_less_eq_int @ one_one_int @ Z3 )
% 3.82/4.05 = ( ord_less_int @ zero_zero_int @ Z3 ) ) ).
% 3.82/4.05
% 3.82/4.05 % int_one_le_iff_zero_less
% 3.82/4.05 thf(fact_4184_odd__nonzero,axiom,
% 3.82/4.05 ! [Z3: int] :
% 3.82/4.05 ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z3 ) @ Z3 )
% 3.82/4.05 != zero_zero_int ) ).
% 3.82/4.05
% 3.82/4.05 % odd_nonzero
% 3.82/4.05 thf(fact_4185_pos__zmult__eq__1__iff__lemma,axiom,
% 3.82/4.05 ! [M2: int,N2: int] :
% 3.82/4.05 ( ( ( times_times_int @ M2 @ N2 )
% 3.82/4.05 = one_one_int )
% 3.82/4.05 => ( ( M2 = one_one_int )
% 3.82/4.05 | ( M2
% 3.82/4.05 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % pos_zmult_eq_1_iff_lemma
% 3.82/4.05 thf(fact_4186_zmult__eq__1__iff,axiom,
% 3.82/4.05 ! [M2: int,N2: int] :
% 3.82/4.05 ( ( ( times_times_int @ M2 @ N2 )
% 3.82/4.05 = one_one_int )
% 3.82/4.05 = ( ( ( M2 = one_one_int )
% 3.82/4.05 & ( N2 = one_one_int ) )
% 3.82/4.05 | ( ( M2
% 3.82/4.05 = ( uminus_uminus_int @ one_one_int ) )
% 3.82/4.05 & ( N2
% 3.82/4.05 = ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % zmult_eq_1_iff
% 3.82/4.05 thf(fact_4187_times__int__code_I2_J,axiom,
% 3.82/4.05 ! [L: int] :
% 3.82/4.05 ( ( times_times_int @ zero_zero_int @ L )
% 3.82/4.05 = zero_zero_int ) ).
% 3.82/4.05
% 3.82/4.05 % times_int_code(2)
% 3.82/4.05 thf(fact_4188_times__int__code_I1_J,axiom,
% 3.82/4.05 ! [K: int] :
% 3.82/4.05 ( ( times_times_int @ K @ zero_zero_int )
% 3.82/4.05 = zero_zero_int ) ).
% 3.82/4.05
% 3.82/4.05 % times_int_code(1)
% 3.82/4.05 thf(fact_4189_int__distrib_I1_J,axiom,
% 3.82/4.05 ! [Z1: int,Z22: int,W2: int] :
% 3.82/4.05 ( ( times_times_int @ ( plus_plus_int @ Z1 @ Z22 ) @ W2 )
% 3.82/4.05 = ( plus_plus_int @ ( times_times_int @ Z1 @ W2 ) @ ( times_times_int @ Z22 @ W2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % int_distrib(1)
% 3.82/4.05 thf(fact_4190_int__distrib_I2_J,axiom,
% 3.82/4.05 ! [W2: int,Z1: int,Z22: int] :
% 3.82/4.05 ( ( times_times_int @ W2 @ ( plus_plus_int @ Z1 @ Z22 ) )
% 3.82/4.05 = ( plus_plus_int @ ( times_times_int @ W2 @ Z1 ) @ ( times_times_int @ W2 @ Z22 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % int_distrib(2)
% 3.82/4.05 thf(fact_4191_uminus__int__code_I1_J,axiom,
% 3.82/4.05 ( ( uminus_uminus_int @ zero_zero_int )
% 3.82/4.05 = zero_zero_int ) ).
% 3.82/4.05
% 3.82/4.05 % uminus_int_code(1)
% 3.82/4.05 thf(fact_4192_equation__minus__iff,axiom,
% 3.82/4.05 ! [A: int,B2: int] :
% 3.82/4.05 ( ( A
% 3.82/4.05 = ( uminus_uminus_int @ B2 ) )
% 3.82/4.05 = ( B2
% 3.82/4.05 = ( uminus_uminus_int @ A ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % equation_minus_iff
% 3.82/4.05 thf(fact_4193_equation__minus__iff,axiom,
% 3.82/4.05 ! [A: real,B2: real] :
% 3.82/4.05 ( ( A
% 3.82/4.05 = ( uminus_uminus_real @ B2 ) )
% 3.82/4.05 = ( B2
% 3.82/4.05 = ( uminus_uminus_real @ A ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % equation_minus_iff
% 3.82/4.05 thf(fact_4194_minus__equation__iff,axiom,
% 3.82/4.05 ! [A: int,B2: int] :
% 3.82/4.05 ( ( ( uminus_uminus_int @ A )
% 3.82/4.05 = B2 )
% 3.82/4.05 = ( ( uminus_uminus_int @ B2 )
% 3.82/4.05 = A ) ) ).
% 3.82/4.05
% 3.82/4.05 % minus_equation_iff
% 3.82/4.05 thf(fact_4195_minus__equation__iff,axiom,
% 3.82/4.05 ! [A: real,B2: real] :
% 3.82/4.05 ( ( ( uminus_uminus_real @ A )
% 3.82/4.05 = B2 )
% 3.82/4.05 = ( ( uminus_uminus_real @ B2 )
% 3.82/4.05 = A ) ) ).
% 3.82/4.05
% 3.82/4.05 % minus_equation_iff
% 3.82/4.05 thf(fact_4196_take__bit__add,axiom,
% 3.82/4.05 ! [N2: nat,A: nat,B2: nat] :
% 3.82/4.05 ( ( bit_se2925701944663578781it_nat @ N2 @ ( plus_plus_nat @ ( bit_se2925701944663578781it_nat @ N2 @ A ) @ ( bit_se2925701944663578781it_nat @ N2 @ B2 ) ) )
% 3.82/4.05 = ( bit_se2925701944663578781it_nat @ N2 @ ( plus_plus_nat @ A @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % take_bit_add
% 3.82/4.05 thf(fact_4197_take__bit__add,axiom,
% 3.82/4.05 ! [N2: nat,A: int,B2: int] :
% 3.82/4.05 ( ( bit_se2923211474154528505it_int @ N2 @ ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N2 @ A ) @ ( bit_se2923211474154528505it_int @ N2 @ B2 ) ) )
% 3.82/4.05 = ( bit_se2923211474154528505it_int @ N2 @ ( plus_plus_int @ A @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % take_bit_add
% 3.82/4.05 thf(fact_4198_take__bit__tightened,axiom,
% 3.82/4.05 ! [N2: nat,A: nat,B2: nat,M2: nat] :
% 3.82/4.05 ( ( ( bit_se2925701944663578781it_nat @ N2 @ A )
% 3.82/4.05 = ( bit_se2925701944663578781it_nat @ N2 @ B2 ) )
% 3.82/4.05 => ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.05 => ( ( bit_se2925701944663578781it_nat @ M2 @ A )
% 3.82/4.05 = ( bit_se2925701944663578781it_nat @ M2 @ B2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % take_bit_tightened
% 3.82/4.05 thf(fact_4199_take__bit__tightened,axiom,
% 3.82/4.05 ! [N2: nat,A: int,B2: int,M2: nat] :
% 3.82/4.05 ( ( ( bit_se2923211474154528505it_int @ N2 @ A )
% 3.82/4.05 = ( bit_se2923211474154528505it_int @ N2 @ B2 ) )
% 3.82/4.05 => ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.05 => ( ( bit_se2923211474154528505it_int @ M2 @ A )
% 3.82/4.05 = ( bit_se2923211474154528505it_int @ M2 @ B2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % take_bit_tightened
% 3.82/4.05 thf(fact_4200_take__bit__tightened__less__eq__nat,axiom,
% 3.82/4.05 ! [M2: nat,N2: nat,Q3: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.05 => ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ M2 @ Q3 ) @ ( bit_se2925701944663578781it_nat @ N2 @ Q3 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % take_bit_tightened_less_eq_nat
% 3.82/4.05 thf(fact_4201_take__bit__nat__less__eq__self,axiom,
% 3.82/4.05 ! [N2: nat,M2: nat] : ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ N2 @ M2 ) @ M2 ) ).
% 3.82/4.05
% 3.82/4.05 % take_bit_nat_less_eq_self
% 3.82/4.05 thf(fact_4202_take__bit__tightened__less__eq__int,axiom,
% 3.82/4.05 ! [M2: nat,N2: nat,K: int] :
% 3.82/4.05 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.05 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ M2 @ K ) @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % take_bit_tightened_less_eq_int
% 3.82/4.05 thf(fact_4203_le__imp__neg__le,axiom,
% 3.82/4.05 ! [A: real,B2: real] :
% 3.82/4.05 ( ( ord_less_eq_real @ A @ B2 )
% 3.82/4.05 => ( ord_less_eq_real @ ( uminus_uminus_real @ B2 ) @ ( uminus_uminus_real @ A ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % le_imp_neg_le
% 3.82/4.05 thf(fact_4204_le__imp__neg__le,axiom,
% 3.82/4.05 ! [A: int,B2: int] :
% 3.82/4.05 ( ( ord_less_eq_int @ A @ B2 )
% 3.82/4.05 => ( ord_less_eq_int @ ( uminus_uminus_int @ B2 ) @ ( uminus_uminus_int @ A ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % le_imp_neg_le
% 3.82/4.05 thf(fact_4205_minus__le__iff,axiom,
% 3.82/4.05 ! [A: real,B2: real] :
% 3.82/4.05 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B2 )
% 3.82/4.05 = ( ord_less_eq_real @ ( uminus_uminus_real @ B2 ) @ A ) ) ).
% 3.82/4.05
% 3.82/4.05 % minus_le_iff
% 3.82/4.05 thf(fact_4206_minus__le__iff,axiom,
% 3.82/4.05 ! [A: int,B2: int] :
% 3.82/4.05 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B2 )
% 3.82/4.05 = ( ord_less_eq_int @ ( uminus_uminus_int @ B2 ) @ A ) ) ).
% 3.82/4.05
% 3.82/4.05 % minus_le_iff
% 3.82/4.05 thf(fact_4207_le__minus__iff,axiom,
% 3.82/4.05 ! [A: real,B2: real] :
% 3.82/4.05 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ B2 ) )
% 3.82/4.05 = ( ord_less_eq_real @ B2 @ ( uminus_uminus_real @ A ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % le_minus_iff
% 3.82/4.05 thf(fact_4208_le__minus__iff,axiom,
% 3.82/4.05 ! [A: int,B2: int] :
% 3.82/4.05 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ B2 ) )
% 3.82/4.05 = ( ord_less_eq_int @ B2 @ ( uminus_uminus_int @ A ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % le_minus_iff
% 3.82/4.05 thf(fact_4209_verit__negate__coefficient_I2_J,axiom,
% 3.82/4.05 ! [A: int,B2: int] :
% 3.82/4.05 ( ( ord_less_int @ A @ B2 )
% 3.82/4.05 => ( ord_less_int @ ( uminus_uminus_int @ B2 ) @ ( uminus_uminus_int @ A ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % verit_negate_coefficient(2)
% 3.82/4.05 thf(fact_4210_verit__negate__coefficient_I2_J,axiom,
% 3.82/4.05 ! [A: real,B2: real] :
% 3.82/4.05 ( ( ord_less_real @ A @ B2 )
% 3.82/4.05 => ( ord_less_real @ ( uminus_uminus_real @ B2 ) @ ( uminus_uminus_real @ A ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % verit_negate_coefficient(2)
% 3.82/4.05 thf(fact_4211_minus__less__iff,axiom,
% 3.82/4.05 ! [A: int,B2: int] :
% 3.82/4.05 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ B2 )
% 3.82/4.05 = ( ord_less_int @ ( uminus_uminus_int @ B2 ) @ A ) ) ).
% 3.82/4.05
% 3.82/4.05 % minus_less_iff
% 3.82/4.05 thf(fact_4212_minus__less__iff,axiom,
% 3.82/4.05 ! [A: real,B2: real] :
% 3.82/4.05 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ B2 )
% 3.82/4.05 = ( ord_less_real @ ( uminus_uminus_real @ B2 ) @ A ) ) ).
% 3.82/4.05
% 3.82/4.05 % minus_less_iff
% 3.82/4.05 thf(fact_4213_less__minus__iff,axiom,
% 3.82/4.05 ! [A: int,B2: int] :
% 3.82/4.05 ( ( ord_less_int @ A @ ( uminus_uminus_int @ B2 ) )
% 3.82/4.05 = ( ord_less_int @ B2 @ ( uminus_uminus_int @ A ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % less_minus_iff
% 3.82/4.05 thf(fact_4214_less__minus__iff,axiom,
% 3.82/4.05 ! [A: real,B2: real] :
% 3.82/4.05 ( ( ord_less_real @ A @ ( uminus_uminus_real @ B2 ) )
% 3.82/4.05 = ( ord_less_real @ B2 @ ( uminus_uminus_real @ A ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % less_minus_iff
% 3.82/4.05 thf(fact_4215_square__eq__iff,axiom,
% 3.82/4.05 ! [A: complex,B2: complex] :
% 3.82/4.05 ( ( ( times_times_complex @ A @ A )
% 3.82/4.05 = ( times_times_complex @ B2 @ B2 ) )
% 3.82/4.05 = ( ( A = B2 )
% 3.82/4.05 | ( A
% 3.82/4.05 = ( uminus1482373934393186551omplex @ B2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % square_eq_iff
% 3.82/4.05 thf(fact_4216_square__eq__iff,axiom,
% 3.82/4.05 ! [A: int,B2: int] :
% 3.82/4.05 ( ( ( times_times_int @ A @ A )
% 3.82/4.05 = ( times_times_int @ B2 @ B2 ) )
% 3.82/4.05 = ( ( A = B2 )
% 3.82/4.05 | ( A
% 3.82/4.05 = ( uminus_uminus_int @ B2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % square_eq_iff
% 3.82/4.05 thf(fact_4217_square__eq__iff,axiom,
% 3.82/4.05 ! [A: real,B2: real] :
% 3.82/4.05 ( ( ( times_times_real @ A @ A )
% 3.82/4.05 = ( times_times_real @ B2 @ B2 ) )
% 3.82/4.05 = ( ( A = B2 )
% 3.82/4.05 | ( A
% 3.82/4.05 = ( uminus_uminus_real @ B2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % square_eq_iff
% 3.82/4.05 thf(fact_4218_minus__mult__commute,axiom,
% 3.82/4.05 ! [A: complex,B2: complex] :
% 3.82/4.05 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B2 )
% 3.82/4.05 = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % minus_mult_commute
% 3.82/4.05 thf(fact_4219_minus__mult__commute,axiom,
% 3.82/4.05 ! [A: int,B2: int] :
% 3.82/4.05 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B2 )
% 3.82/4.05 = ( times_times_int @ A @ ( uminus_uminus_int @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % minus_mult_commute
% 3.82/4.05 thf(fact_4220_minus__mult__commute,axiom,
% 3.82/4.05 ! [A: real,B2: real] :
% 3.82/4.05 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B2 )
% 3.82/4.05 = ( times_times_real @ A @ ( uminus_uminus_real @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % minus_mult_commute
% 3.82/4.05 thf(fact_4221_is__num__normalize_I8_J,axiom,
% 3.82/4.05 ! [A: int,B2: int] :
% 3.82/4.05 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B2 ) )
% 3.82/4.05 = ( plus_plus_int @ ( uminus_uminus_int @ B2 ) @ ( uminus_uminus_int @ A ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % is_num_normalize(8)
% 3.82/4.05 thf(fact_4222_is__num__normalize_I8_J,axiom,
% 3.82/4.05 ! [A: real,B2: real] :
% 3.82/4.05 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B2 ) )
% 3.82/4.05 = ( plus_plus_real @ ( uminus_uminus_real @ B2 ) @ ( uminus_uminus_real @ A ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % is_num_normalize(8)
% 3.82/4.05 thf(fact_4223_add_Oinverse__distrib__swap,axiom,
% 3.82/4.05 ! [A: int,B2: int] :
% 3.82/4.05 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B2 ) )
% 3.82/4.05 = ( plus_plus_int @ ( uminus_uminus_int @ B2 ) @ ( uminus_uminus_int @ A ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % add.inverse_distrib_swap
% 3.82/4.05 thf(fact_4224_add_Oinverse__distrib__swap,axiom,
% 3.82/4.05 ! [A: real,B2: real] :
% 3.82/4.05 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B2 ) )
% 3.82/4.05 = ( plus_plus_real @ ( uminus_uminus_real @ B2 ) @ ( uminus_uminus_real @ A ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % add.inverse_distrib_swap
% 3.82/4.05 thf(fact_4225_group__cancel_Oneg1,axiom,
% 3.82/4.05 ! [A2: int,K: int,A: int] :
% 3.82/4.05 ( ( A2
% 3.82/4.05 = ( plus_plus_int @ K @ A ) )
% 3.82/4.05 => ( ( uminus_uminus_int @ A2 )
% 3.82/4.05 = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( uminus_uminus_int @ A ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % group_cancel.neg1
% 3.82/4.05 thf(fact_4226_group__cancel_Oneg1,axiom,
% 3.82/4.05 ! [A2: real,K: real,A: real] :
% 3.82/4.05 ( ( A2
% 3.82/4.05 = ( plus_plus_real @ K @ A ) )
% 3.82/4.05 => ( ( uminus_uminus_real @ A2 )
% 3.82/4.05 = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( uminus_uminus_real @ A ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % group_cancel.neg1
% 3.82/4.05 thf(fact_4227_minus__diff__commute,axiom,
% 3.82/4.05 ! [B2: int,A: int] :
% 3.82/4.05 ( ( minus_minus_int @ ( uminus_uminus_int @ B2 ) @ A )
% 3.82/4.05 = ( minus_minus_int @ ( uminus_uminus_int @ A ) @ B2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % minus_diff_commute
% 3.82/4.05 thf(fact_4228_minus__diff__commute,axiom,
% 3.82/4.05 ! [B2: real,A: real] :
% 3.82/4.05 ( ( minus_minus_real @ ( uminus_uminus_real @ B2 ) @ A )
% 3.82/4.05 = ( minus_minus_real @ ( uminus_uminus_real @ A ) @ B2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % minus_diff_commute
% 3.82/4.05 thf(fact_4229_minus__divide__right,axiom,
% 3.82/4.05 ! [A: real,B2: real] :
% 3.82/4.05 ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B2 ) )
% 3.82/4.05 = ( divide_divide_real @ A @ ( uminus_uminus_real @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % minus_divide_right
% 3.82/4.05 thf(fact_4230_minus__divide__divide,axiom,
% 3.82/4.05 ! [A: real,B2: real] :
% 3.82/4.05 ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B2 ) )
% 3.82/4.05 = ( divide_divide_real @ A @ B2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % minus_divide_divide
% 3.82/4.05 thf(fact_4231_minus__divide__left,axiom,
% 3.82/4.05 ! [A: real,B2: real] :
% 3.82/4.05 ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B2 ) )
% 3.82/4.05 = ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % minus_divide_left
% 3.82/4.05 thf(fact_4232_Diff__infinite__finite,axiom,
% 3.82/4.05 ! [T3: set_complex,S2: set_complex] :
% 3.82/4.05 ( ( finite3207457112153483333omplex @ T3 )
% 3.82/4.05 => ( ~ ( finite3207457112153483333omplex @ S2 )
% 3.82/4.05 => ~ ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ S2 @ T3 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % Diff_infinite_finite
% 3.82/4.05 thf(fact_4233_Diff__infinite__finite,axiom,
% 3.82/4.05 ! [T3: set_int,S2: set_int] :
% 3.82/4.05 ( ( finite_finite_int @ T3 )
% 3.82/4.05 => ( ~ ( finite_finite_int @ S2 )
% 3.82/4.05 => ~ ( finite_finite_int @ ( minus_minus_set_int @ S2 @ T3 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % Diff_infinite_finite
% 3.82/4.05 thf(fact_4234_Diff__infinite__finite,axiom,
% 3.82/4.05 ! [T3: set_Extended_enat,S2: set_Extended_enat] :
% 3.82/4.05 ( ( finite4001608067531595151d_enat @ T3 )
% 3.82/4.05 => ( ~ ( finite4001608067531595151d_enat @ S2 )
% 3.82/4.05 => ~ ( finite4001608067531595151d_enat @ ( minus_925952699566721837d_enat @ S2 @ T3 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % Diff_infinite_finite
% 3.82/4.05 thf(fact_4235_Diff__infinite__finite,axiom,
% 3.82/4.05 ! [T3: set_nat,S2: set_nat] :
% 3.82/4.05 ( ( finite_finite_nat @ T3 )
% 3.82/4.05 => ( ~ ( finite_finite_nat @ S2 )
% 3.82/4.05 => ~ ( finite_finite_nat @ ( minus_minus_set_nat @ S2 @ T3 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % Diff_infinite_finite
% 3.82/4.05 thf(fact_4236_double__diff,axiom,
% 3.82/4.05 ! [A2: set_nat,B: set_nat,C4: set_nat] :
% 3.82/4.05 ( ( ord_less_eq_set_nat @ A2 @ B )
% 3.82/4.05 => ( ( ord_less_eq_set_nat @ B @ C4 )
% 3.82/4.05 => ( ( minus_minus_set_nat @ B @ ( minus_minus_set_nat @ C4 @ A2 ) )
% 3.82/4.05 = A2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % double_diff
% 3.82/4.05 thf(fact_4237_double__diff,axiom,
% 3.82/4.05 ! [A2: set_int,B: set_int,C4: set_int] :
% 3.82/4.05 ( ( ord_less_eq_set_int @ A2 @ B )
% 3.82/4.05 => ( ( ord_less_eq_set_int @ B @ C4 )
% 3.82/4.05 => ( ( minus_minus_set_int @ B @ ( minus_minus_set_int @ C4 @ A2 ) )
% 3.82/4.05 = A2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % double_diff
% 3.82/4.05 thf(fact_4238_Diff__subset,axiom,
% 3.82/4.05 ! [A2: set_nat,B: set_nat] : ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ B ) @ A2 ) ).
% 3.82/4.05
% 3.82/4.05 % Diff_subset
% 3.82/4.05 thf(fact_4239_Diff__subset,axiom,
% 3.82/4.05 ! [A2: set_int,B: set_int] : ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ B ) @ A2 ) ).
% 3.82/4.05
% 3.82/4.05 % Diff_subset
% 3.82/4.05 thf(fact_4240_Diff__mono,axiom,
% 3.82/4.05 ! [A2: set_nat,C4: set_nat,D6: set_nat,B: set_nat] :
% 3.82/4.05 ( ( ord_less_eq_set_nat @ A2 @ C4 )
% 3.82/4.05 => ( ( ord_less_eq_set_nat @ D6 @ B )
% 3.82/4.05 => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ B ) @ ( minus_minus_set_nat @ C4 @ D6 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % Diff_mono
% 3.82/4.05 thf(fact_4241_Diff__mono,axiom,
% 3.82/4.05 ! [A2: set_int,C4: set_int,D6: set_int,B: set_int] :
% 3.82/4.05 ( ( ord_less_eq_set_int @ A2 @ C4 )
% 3.82/4.05 => ( ( ord_less_eq_set_int @ D6 @ B )
% 3.82/4.05 => ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ B ) @ ( minus_minus_set_int @ C4 @ D6 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % Diff_mono
% 3.82/4.05 thf(fact_4242_psubset__imp__ex__mem,axiom,
% 3.82/4.05 ! [A2: set_Extended_enat,B: set_Extended_enat] :
% 3.82/4.05 ( ( ord_le2529575680413868914d_enat @ A2 @ B )
% 3.82/4.05 => ? [B4: extended_enat] : ( member_Extended_enat @ B4 @ ( minus_925952699566721837d_enat @ B @ A2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % psubset_imp_ex_mem
% 3.82/4.05 thf(fact_4243_psubset__imp__ex__mem,axiom,
% 3.82/4.05 ! [A2: set_real,B: set_real] :
% 3.82/4.05 ( ( ord_less_set_real @ A2 @ B )
% 3.82/4.05 => ? [B4: real] : ( member_real @ B4 @ ( minus_minus_set_real @ B @ A2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % psubset_imp_ex_mem
% 3.82/4.05 thf(fact_4244_psubset__imp__ex__mem,axiom,
% 3.82/4.05 ! [A2: set_set_nat,B: set_set_nat] :
% 3.82/4.05 ( ( ord_less_set_set_nat @ A2 @ B )
% 3.82/4.05 => ? [B4: set_nat] : ( member_set_nat @ B4 @ ( minus_2163939370556025621et_nat @ B @ A2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % psubset_imp_ex_mem
% 3.82/4.05 thf(fact_4245_psubset__imp__ex__mem,axiom,
% 3.82/4.05 ! [A2: set_int,B: set_int] :
% 3.82/4.05 ( ( ord_less_set_int @ A2 @ B )
% 3.82/4.05 => ? [B4: int] : ( member_int @ B4 @ ( minus_minus_set_int @ B @ A2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % psubset_imp_ex_mem
% 3.82/4.05 thf(fact_4246_psubset__imp__ex__mem,axiom,
% 3.82/4.05 ! [A2: set_nat,B: set_nat] :
% 3.82/4.05 ( ( ord_less_set_nat @ A2 @ B )
% 3.82/4.05 => ? [B4: nat] : ( member_nat @ B4 @ ( minus_minus_set_nat @ B @ A2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % psubset_imp_ex_mem
% 3.82/4.05 thf(fact_4247_signed__take__bit__eq__take__bit__shift,axiom,
% 3.82/4.05 ( bit_ri631733984087533419it_int
% 3.82/4.05 = ( ^ [N: nat,K2: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( plus_plus_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % signed_take_bit_eq_take_bit_shift
% 3.82/4.05 thf(fact_4248_take__bit__Suc__minus__bit0,axiom,
% 3.82/4.05 ! [N2: nat,K: num] :
% 3.82/4.05 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 3.82/4.05 = ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % take_bit_Suc_minus_bit0
% 3.82/4.05 thf(fact_4249_take__bit__int__less__eq,axiom,
% 3.82/4.05 ! [N2: nat,K: int] :
% 3.82/4.05 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K )
% 3.82/4.05 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.05 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % take_bit_int_less_eq
% 3.82/4.05 thf(fact_4250_infinite__Icc,axiom,
% 3.82/4.05 ! [A: real,B2: real] :
% 3.82/4.05 ( ( ord_less_real @ A @ B2 )
% 3.82/4.05 => ~ ( finite_finite_real @ ( set_or1222579329274155063t_real @ A @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % infinite_Icc
% 3.82/4.05 thf(fact_4251_signed__take__bit__eq__iff__take__bit__eq,axiom,
% 3.82/4.05 ! [N2: nat,A: int,B2: int] :
% 3.82/4.05 ( ( ( bit_ri631733984087533419it_int @ N2 @ A )
% 3.82/4.05 = ( bit_ri631733984087533419it_int @ N2 @ B2 ) )
% 3.82/4.05 = ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ A )
% 3.82/4.05 = ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % signed_take_bit_eq_iff_take_bit_eq
% 3.82/4.05 thf(fact_4252_signed__take__bit__take__bit,axiom,
% 3.82/4.05 ! [M2: nat,N2: nat,A: int] :
% 3.82/4.05 ( ( bit_ri631733984087533419it_int @ M2 @ ( bit_se2923211474154528505it_int @ N2 @ A ) )
% 3.82/4.05 = ( if_int_int @ ( ord_less_eq_nat @ N2 @ M2 ) @ ( bit_se2923211474154528505it_int @ N2 ) @ ( bit_ri631733984087533419it_int @ M2 ) @ A ) ) ).
% 3.82/4.05
% 3.82/4.05 % signed_take_bit_take_bit
% 3.82/4.05 thf(fact_4253_all__nat__less,axiom,
% 3.82/4.05 ! [N2: nat,P: nat > $o] :
% 3.82/4.05 ( ( ! [M: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ M @ N2 )
% 3.82/4.05 => ( P @ M ) ) )
% 3.82/4.05 = ( ! [X4: nat] :
% 3.82/4.05 ( ( member_nat @ X4 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 3.82/4.05 => ( P @ X4 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % all_nat_less
% 3.82/4.05 thf(fact_4254_ex__nat__less,axiom,
% 3.82/4.05 ! [N2: nat,P: nat > $o] :
% 3.82/4.05 ( ( ? [M: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ M @ N2 )
% 3.82/4.05 & ( P @ M ) ) )
% 3.82/4.05 = ( ? [X4: nat] :
% 3.82/4.05 ( ( member_nat @ X4 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 3.82/4.05 & ( P @ X4 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % ex_nat_less
% 3.82/4.05 thf(fact_4255_not__numeral__le__neg__numeral,axiom,
% 3.82/4.05 ! [M2: num,N2: num] :
% 3.82/4.05 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M2 ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % not_numeral_le_neg_numeral
% 3.82/4.05 thf(fact_4256_not__numeral__le__neg__numeral,axiom,
% 3.82/4.05 ! [M2: num,N2: num] :
% 3.82/4.05 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % not_numeral_le_neg_numeral
% 3.82/4.05 thf(fact_4257_neg__numeral__le__numeral,axiom,
% 3.82/4.05 ! [M2: num,N2: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( numeral_numeral_real @ N2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_numeral_le_numeral
% 3.82/4.05 thf(fact_4258_neg__numeral__le__numeral,axiom,
% 3.82/4.05 ! [M2: num,N2: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_numeral_le_numeral
% 3.82/4.05 thf(fact_4259_zero__neq__neg__numeral,axiom,
% 3.82/4.05 ! [N2: num] :
% 3.82/4.05 ( zero_zero_complex
% 3.82/4.05 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % zero_neq_neg_numeral
% 3.82/4.05 thf(fact_4260_zero__neq__neg__numeral,axiom,
% 3.82/4.05 ! [N2: num] :
% 3.82/4.05 ( zero_zero_int
% 3.82/4.05 != ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % zero_neq_neg_numeral
% 3.82/4.05 thf(fact_4261_zero__neq__neg__numeral,axiom,
% 3.82/4.05 ! [N2: num] :
% 3.82/4.05 ( zero_zero_real
% 3.82/4.05 != ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % zero_neq_neg_numeral
% 3.82/4.05 thf(fact_4262_not__numeral__less__neg__numeral,axiom,
% 3.82/4.05 ! [M2: num,N2: num] :
% 3.82/4.05 ~ ( ord_less_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % not_numeral_less_neg_numeral
% 3.82/4.05 thf(fact_4263_not__numeral__less__neg__numeral,axiom,
% 3.82/4.05 ! [M2: num,N2: num] :
% 3.82/4.05 ~ ( ord_less_real @ ( numeral_numeral_real @ M2 ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % not_numeral_less_neg_numeral
% 3.82/4.05 thf(fact_4264_neg__numeral__less__numeral,axiom,
% 3.82/4.05 ! [M2: num,N2: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_numeral_less_numeral
% 3.82/4.05 thf(fact_4265_neg__numeral__less__numeral,axiom,
% 3.82/4.05 ! [M2: num,N2: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( numeral_numeral_real @ N2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_numeral_less_numeral
% 3.82/4.05 thf(fact_4266_le__minus__one__simps_I4_J,axiom,
% 3.82/4.05 ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 3.82/4.05
% 3.82/4.05 % le_minus_one_simps(4)
% 3.82/4.05 thf(fact_4267_le__minus__one__simps_I4_J,axiom,
% 3.82/4.05 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 3.82/4.05
% 3.82/4.05 % le_minus_one_simps(4)
% 3.82/4.05 thf(fact_4268_le__minus__one__simps_I2_J,axiom,
% 3.82/4.05 ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 3.82/4.05
% 3.82/4.05 % le_minus_one_simps(2)
% 3.82/4.05 thf(fact_4269_le__minus__one__simps_I2_J,axiom,
% 3.82/4.05 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 3.82/4.05
% 3.82/4.05 % le_minus_one_simps(2)
% 3.82/4.05 thf(fact_4270_zero__neq__neg__one,axiom,
% 3.82/4.05 ( zero_zero_complex
% 3.82/4.05 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 3.82/4.05
% 3.82/4.05 % zero_neq_neg_one
% 3.82/4.05 thf(fact_4271_zero__neq__neg__one,axiom,
% 3.82/4.05 ( zero_zero_int
% 3.82/4.05 != ( uminus_uminus_int @ one_one_int ) ) ).
% 3.82/4.05
% 3.82/4.05 % zero_neq_neg_one
% 3.82/4.05 thf(fact_4272_zero__neq__neg__one,axiom,
% 3.82/4.05 ( zero_zero_real
% 3.82/4.05 != ( uminus_uminus_real @ one_one_real ) ) ).
% 3.82/4.05
% 3.82/4.05 % zero_neq_neg_one
% 3.82/4.05 thf(fact_4273_neg__eq__iff__add__eq__0,axiom,
% 3.82/4.05 ! [A: complex,B2: complex] :
% 3.82/4.05 ( ( ( uminus1482373934393186551omplex @ A )
% 3.82/4.05 = B2 )
% 3.82/4.05 = ( ( plus_plus_complex @ A @ B2 )
% 3.82/4.05 = zero_zero_complex ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_eq_iff_add_eq_0
% 3.82/4.05 thf(fact_4274_neg__eq__iff__add__eq__0,axiom,
% 3.82/4.05 ! [A: int,B2: int] :
% 3.82/4.05 ( ( ( uminus_uminus_int @ A )
% 3.82/4.05 = B2 )
% 3.82/4.05 = ( ( plus_plus_int @ A @ B2 )
% 3.82/4.05 = zero_zero_int ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_eq_iff_add_eq_0
% 3.82/4.05 thf(fact_4275_neg__eq__iff__add__eq__0,axiom,
% 3.82/4.05 ! [A: real,B2: real] :
% 3.82/4.05 ( ( ( uminus_uminus_real @ A )
% 3.82/4.05 = B2 )
% 3.82/4.05 = ( ( plus_plus_real @ A @ B2 )
% 3.82/4.05 = zero_zero_real ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_eq_iff_add_eq_0
% 3.82/4.05 thf(fact_4276_eq__neg__iff__add__eq__0,axiom,
% 3.82/4.05 ! [A: complex,B2: complex] :
% 3.82/4.05 ( ( A
% 3.82/4.05 = ( uminus1482373934393186551omplex @ B2 ) )
% 3.82/4.05 = ( ( plus_plus_complex @ A @ B2 )
% 3.82/4.05 = zero_zero_complex ) ) ).
% 3.82/4.05
% 3.82/4.05 % eq_neg_iff_add_eq_0
% 3.82/4.05 thf(fact_4277_eq__neg__iff__add__eq__0,axiom,
% 3.82/4.05 ! [A: int,B2: int] :
% 3.82/4.05 ( ( A
% 3.82/4.05 = ( uminus_uminus_int @ B2 ) )
% 3.82/4.05 = ( ( plus_plus_int @ A @ B2 )
% 3.82/4.05 = zero_zero_int ) ) ).
% 3.82/4.05
% 3.82/4.05 % eq_neg_iff_add_eq_0
% 3.82/4.05 thf(fact_4278_eq__neg__iff__add__eq__0,axiom,
% 3.82/4.05 ! [A: real,B2: real] :
% 3.82/4.05 ( ( A
% 3.82/4.05 = ( uminus_uminus_real @ B2 ) )
% 3.82/4.05 = ( ( plus_plus_real @ A @ B2 )
% 3.82/4.05 = zero_zero_real ) ) ).
% 3.82/4.05
% 3.82/4.05 % eq_neg_iff_add_eq_0
% 3.82/4.05 thf(fact_4279_add_Oinverse__unique,axiom,
% 3.82/4.05 ! [A: complex,B2: complex] :
% 3.82/4.05 ( ( ( plus_plus_complex @ A @ B2 )
% 3.82/4.05 = zero_zero_complex )
% 3.82/4.05 => ( ( uminus1482373934393186551omplex @ A )
% 3.82/4.05 = B2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % add.inverse_unique
% 3.82/4.05 thf(fact_4280_add_Oinverse__unique,axiom,
% 3.82/4.05 ! [A: int,B2: int] :
% 3.82/4.05 ( ( ( plus_plus_int @ A @ B2 )
% 3.82/4.05 = zero_zero_int )
% 3.82/4.05 => ( ( uminus_uminus_int @ A )
% 3.82/4.05 = B2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % add.inverse_unique
% 3.82/4.05 thf(fact_4281_add_Oinverse__unique,axiom,
% 3.82/4.05 ! [A: real,B2: real] :
% 3.82/4.05 ( ( ( plus_plus_real @ A @ B2 )
% 3.82/4.05 = zero_zero_real )
% 3.82/4.05 => ( ( uminus_uminus_real @ A )
% 3.82/4.05 = B2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % add.inverse_unique
% 3.82/4.05 thf(fact_4282_ab__group__add__class_Oab__left__minus,axiom,
% 3.82/4.05 ! [A: complex] :
% 3.82/4.05 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 3.82/4.05 = zero_zero_complex ) ).
% 3.82/4.05
% 3.82/4.05 % ab_group_add_class.ab_left_minus
% 3.82/4.05 thf(fact_4283_ab__group__add__class_Oab__left__minus,axiom,
% 3.82/4.05 ! [A: int] :
% 3.82/4.05 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 3.82/4.05 = zero_zero_int ) ).
% 3.82/4.05
% 3.82/4.05 % ab_group_add_class.ab_left_minus
% 3.82/4.05 thf(fact_4284_ab__group__add__class_Oab__left__minus,axiom,
% 3.82/4.05 ! [A: real] :
% 3.82/4.05 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 3.82/4.05 = zero_zero_real ) ).
% 3.82/4.05
% 3.82/4.05 % ab_group_add_class.ab_left_minus
% 3.82/4.05 thf(fact_4285_add__eq__0__iff,axiom,
% 3.82/4.05 ! [A: complex,B2: complex] :
% 3.82/4.05 ( ( ( plus_plus_complex @ A @ B2 )
% 3.82/4.05 = zero_zero_complex )
% 3.82/4.05 = ( B2
% 3.82/4.05 = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % add_eq_0_iff
% 3.82/4.05 thf(fact_4286_add__eq__0__iff,axiom,
% 3.82/4.05 ! [A: int,B2: int] :
% 3.82/4.05 ( ( ( plus_plus_int @ A @ B2 )
% 3.82/4.05 = zero_zero_int )
% 3.82/4.05 = ( B2
% 3.82/4.05 = ( uminus_uminus_int @ A ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % add_eq_0_iff
% 3.82/4.05 thf(fact_4287_add__eq__0__iff,axiom,
% 3.82/4.05 ! [A: real,B2: real] :
% 3.82/4.05 ( ( ( plus_plus_real @ A @ B2 )
% 3.82/4.05 = zero_zero_real )
% 3.82/4.05 = ( B2
% 3.82/4.05 = ( uminus_uminus_real @ A ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % add_eq_0_iff
% 3.82/4.05 thf(fact_4288_less__minus__one__simps_I4_J,axiom,
% 3.82/4.05 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 3.82/4.05
% 3.82/4.05 % less_minus_one_simps(4)
% 3.82/4.05 thf(fact_4289_less__minus__one__simps_I4_J,axiom,
% 3.82/4.05 ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 3.82/4.05
% 3.82/4.05 % less_minus_one_simps(4)
% 3.82/4.05 thf(fact_4290_less__minus__one__simps_I2_J,axiom,
% 3.82/4.05 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 3.82/4.05
% 3.82/4.05 % less_minus_one_simps(2)
% 3.82/4.05 thf(fact_4291_less__minus__one__simps_I2_J,axiom,
% 3.82/4.05 ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 3.82/4.05
% 3.82/4.05 % less_minus_one_simps(2)
% 3.82/4.05 thf(fact_4292_nonzero__minus__divide__right,axiom,
% 3.82/4.05 ! [B2: complex,A: complex] :
% 3.82/4.05 ( ( B2 != zero_zero_complex )
% 3.82/4.05 => ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B2 ) )
% 3.82/4.05 = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % nonzero_minus_divide_right
% 3.82/4.05 thf(fact_4293_nonzero__minus__divide__right,axiom,
% 3.82/4.05 ! [B2: real,A: real] :
% 3.82/4.05 ( ( B2 != zero_zero_real )
% 3.82/4.05 => ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B2 ) )
% 3.82/4.05 = ( divide_divide_real @ A @ ( uminus_uminus_real @ B2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % nonzero_minus_divide_right
% 3.82/4.05 thf(fact_4294_nonzero__minus__divide__divide,axiom,
% 3.82/4.05 ! [B2: complex,A: complex] :
% 3.82/4.05 ( ( B2 != zero_zero_complex )
% 3.82/4.05 => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B2 ) )
% 3.82/4.05 = ( divide1717551699836669952omplex @ A @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % nonzero_minus_divide_divide
% 3.82/4.05 thf(fact_4295_nonzero__minus__divide__divide,axiom,
% 3.82/4.05 ! [B2: real,A: real] :
% 3.82/4.05 ( ( B2 != zero_zero_real )
% 3.82/4.05 => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B2 ) )
% 3.82/4.05 = ( divide_divide_real @ A @ B2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % nonzero_minus_divide_divide
% 3.82/4.05 thf(fact_4296_square__eq__1__iff,axiom,
% 3.82/4.05 ! [X: complex] :
% 3.82/4.05 ( ( ( times_times_complex @ X @ X )
% 3.82/4.05 = one_one_complex )
% 3.82/4.05 = ( ( X = one_one_complex )
% 3.82/4.05 | ( X
% 3.82/4.05 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % square_eq_1_iff
% 3.82/4.05 thf(fact_4297_square__eq__1__iff,axiom,
% 3.82/4.05 ! [X: int] :
% 3.82/4.05 ( ( ( times_times_int @ X @ X )
% 3.82/4.05 = one_one_int )
% 3.82/4.05 = ( ( X = one_one_int )
% 3.82/4.05 | ( X
% 3.82/4.05 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % square_eq_1_iff
% 3.82/4.05 thf(fact_4298_square__eq__1__iff,axiom,
% 3.82/4.05 ! [X: real] :
% 3.82/4.05 ( ( ( times_times_real @ X @ X )
% 3.82/4.05 = one_one_real )
% 3.82/4.05 = ( ( X = one_one_real )
% 3.82/4.05 | ( X
% 3.82/4.05 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % square_eq_1_iff
% 3.82/4.05 thf(fact_4299_group__cancel_Osub2,axiom,
% 3.82/4.05 ! [B: int,K: int,B2: int,A: int] :
% 3.82/4.05 ( ( B
% 3.82/4.05 = ( plus_plus_int @ K @ B2 ) )
% 3.82/4.05 => ( ( minus_minus_int @ A @ B )
% 3.82/4.05 = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( minus_minus_int @ A @ B2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % group_cancel.sub2
% 3.82/4.05 thf(fact_4300_group__cancel_Osub2,axiom,
% 3.82/4.05 ! [B: real,K: real,B2: real,A: real] :
% 3.82/4.05 ( ( B
% 3.82/4.05 = ( plus_plus_real @ K @ B2 ) )
% 3.82/4.05 => ( ( minus_minus_real @ A @ B )
% 3.82/4.05 = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( minus_minus_real @ A @ B2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % group_cancel.sub2
% 3.82/4.05 thf(fact_4301_diff__conv__add__uminus,axiom,
% 3.82/4.05 ( minus_minus_int
% 3.82/4.05 = ( ^ [A3: int,B3: int] : ( plus_plus_int @ A3 @ ( uminus_uminus_int @ B3 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_conv_add_uminus
% 3.82/4.05 thf(fact_4302_diff__conv__add__uminus,axiom,
% 3.82/4.05 ( minus_minus_real
% 3.82/4.05 = ( ^ [A3: real,B3: real] : ( plus_plus_real @ A3 @ ( uminus_uminus_real @ B3 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % diff_conv_add_uminus
% 3.82/4.05 thf(fact_4303_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 3.82/4.05 ( minus_minus_int
% 3.82/4.05 = ( ^ [A3: int,B3: int] : ( plus_plus_int @ A3 @ ( uminus_uminus_int @ B3 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % ab_group_add_class.ab_diff_conv_add_uminus
% 3.82/4.05 thf(fact_4304_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 3.82/4.05 ( minus_minus_real
% 3.82/4.05 = ( ^ [A3: real,B3: real] : ( plus_plus_real @ A3 @ ( uminus_uminus_real @ B3 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % ab_group_add_class.ab_diff_conv_add_uminus
% 3.82/4.05 thf(fact_4305_take__bit__unset__bit__eq,axiom,
% 3.82/4.05 ! [N2: nat,M2: nat,A: nat] :
% 3.82/4.05 ( ( ( ord_less_eq_nat @ N2 @ M2 )
% 3.82/4.05 => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se4205575877204974255it_nat @ M2 @ A ) )
% 3.82/4.05 = ( bit_se2925701944663578781it_nat @ N2 @ A ) ) )
% 3.82/4.05 & ( ~ ( ord_less_eq_nat @ N2 @ M2 )
% 3.82/4.05 => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se4205575877204974255it_nat @ M2 @ A ) )
% 3.82/4.05 = ( bit_se4205575877204974255it_nat @ M2 @ ( bit_se2925701944663578781it_nat @ N2 @ A ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % take_bit_unset_bit_eq
% 3.82/4.05 thf(fact_4306_take__bit__unset__bit__eq,axiom,
% 3.82/4.05 ! [N2: nat,M2: nat,A: int] :
% 3.82/4.05 ( ( ( ord_less_eq_nat @ N2 @ M2 )
% 3.82/4.05 => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se4203085406695923979it_int @ M2 @ A ) )
% 3.82/4.05 = ( bit_se2923211474154528505it_int @ N2 @ A ) ) )
% 3.82/4.05 & ( ~ ( ord_less_eq_nat @ N2 @ M2 )
% 3.82/4.05 => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se4203085406695923979it_int @ M2 @ A ) )
% 3.82/4.05 = ( bit_se4203085406695923979it_int @ M2 @ ( bit_se2923211474154528505it_int @ N2 @ A ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % take_bit_unset_bit_eq
% 3.82/4.05 thf(fact_4307_take__bit__set__bit__eq,axiom,
% 3.82/4.05 ! [N2: nat,M2: nat,A: nat] :
% 3.82/4.05 ( ( ( ord_less_eq_nat @ N2 @ M2 )
% 3.82/4.05 => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se7882103937844011126it_nat @ M2 @ A ) )
% 3.82/4.05 = ( bit_se2925701944663578781it_nat @ N2 @ A ) ) )
% 3.82/4.05 & ( ~ ( ord_less_eq_nat @ N2 @ M2 )
% 3.82/4.05 => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se7882103937844011126it_nat @ M2 @ A ) )
% 3.82/4.05 = ( bit_se7882103937844011126it_nat @ M2 @ ( bit_se2925701944663578781it_nat @ N2 @ A ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % take_bit_set_bit_eq
% 3.82/4.05 thf(fact_4308_take__bit__set__bit__eq,axiom,
% 3.82/4.05 ! [N2: nat,M2: nat,A: int] :
% 3.82/4.05 ( ( ( ord_less_eq_nat @ N2 @ M2 )
% 3.82/4.05 => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se7879613467334960850it_int @ M2 @ A ) )
% 3.82/4.05 = ( bit_se2923211474154528505it_int @ N2 @ A ) ) )
% 3.82/4.05 & ( ~ ( ord_less_eq_nat @ N2 @ M2 )
% 3.82/4.05 => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se7879613467334960850it_int @ M2 @ A ) )
% 3.82/4.05 = ( bit_se7879613467334960850it_int @ M2 @ ( bit_se2923211474154528505it_int @ N2 @ A ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % take_bit_set_bit_eq
% 3.82/4.05 thf(fact_4309_take__bit__flip__bit__eq,axiom,
% 3.82/4.05 ! [N2: nat,M2: nat,A: nat] :
% 3.82/4.05 ( ( ( ord_less_eq_nat @ N2 @ M2 )
% 3.82/4.05 => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se2161824704523386999it_nat @ M2 @ A ) )
% 3.82/4.05 = ( bit_se2925701944663578781it_nat @ N2 @ A ) ) )
% 3.82/4.05 & ( ~ ( ord_less_eq_nat @ N2 @ M2 )
% 3.82/4.05 => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se2161824704523386999it_nat @ M2 @ A ) )
% 3.82/4.05 = ( bit_se2161824704523386999it_nat @ M2 @ ( bit_se2925701944663578781it_nat @ N2 @ A ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % take_bit_flip_bit_eq
% 3.82/4.05 thf(fact_4310_take__bit__flip__bit__eq,axiom,
% 3.82/4.05 ! [N2: nat,M2: nat,A: int] :
% 3.82/4.05 ( ( ( ord_less_eq_nat @ N2 @ M2 )
% 3.82/4.05 => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se2159334234014336723it_int @ M2 @ A ) )
% 3.82/4.05 = ( bit_se2923211474154528505it_int @ N2 @ A ) ) )
% 3.82/4.05 & ( ~ ( ord_less_eq_nat @ N2 @ M2 )
% 3.82/4.05 => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se2159334234014336723it_int @ M2 @ A ) )
% 3.82/4.05 = ( bit_se2159334234014336723it_int @ M2 @ ( bit_se2923211474154528505it_int @ N2 @ A ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % take_bit_flip_bit_eq
% 3.82/4.05 thf(fact_4311_dvd__div__neg,axiom,
% 3.82/4.05 ! [B2: int,A: int] :
% 3.82/4.05 ( ( dvd_dvd_int @ B2 @ A )
% 3.82/4.05 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B2 ) )
% 3.82/4.05 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % dvd_div_neg
% 3.82/4.05 thf(fact_4312_dvd__div__neg,axiom,
% 3.82/4.05 ! [B2: real,A: real] :
% 3.82/4.05 ( ( dvd_dvd_real @ B2 @ A )
% 3.82/4.05 => ( ( divide_divide_real @ A @ ( uminus_uminus_real @ B2 ) )
% 3.82/4.05 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % dvd_div_neg
% 3.82/4.05 thf(fact_4313_dvd__neg__div,axiom,
% 3.82/4.05 ! [B2: int,A: int] :
% 3.82/4.05 ( ( dvd_dvd_int @ B2 @ A )
% 3.82/4.05 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B2 )
% 3.82/4.05 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % dvd_neg_div
% 3.82/4.05 thf(fact_4314_dvd__neg__div,axiom,
% 3.82/4.05 ! [B2: real,A: real] :
% 3.82/4.05 ( ( dvd_dvd_real @ B2 @ A )
% 3.82/4.05 => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B2 )
% 3.82/4.05 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % dvd_neg_div
% 3.82/4.05 thf(fact_4315_subset__Compl__self__eq,axiom,
% 3.82/4.05 ! [A2: set_Extended_enat] :
% 3.82/4.05 ( ( ord_le7203529160286727270d_enat @ A2 @ ( uminus417252749190364093d_enat @ A2 ) )
% 3.82/4.05 = ( A2 = bot_bo7653980558646680370d_enat ) ) ).
% 3.82/4.05
% 3.82/4.05 % subset_Compl_self_eq
% 3.82/4.05 thf(fact_4316_subset__Compl__self__eq,axiom,
% 3.82/4.05 ! [A2: set_real] :
% 3.82/4.05 ( ( ord_less_eq_set_real @ A2 @ ( uminus612125837232591019t_real @ A2 ) )
% 3.82/4.05 = ( A2 = bot_bot_set_real ) ) ).
% 3.82/4.05
% 3.82/4.05 % subset_Compl_self_eq
% 3.82/4.05 thf(fact_4317_subset__Compl__self__eq,axiom,
% 3.82/4.05 ! [A2: set_nat] :
% 3.82/4.05 ( ( ord_less_eq_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ A2 ) )
% 3.82/4.05 = ( A2 = bot_bot_set_nat ) ) ).
% 3.82/4.05
% 3.82/4.05 % subset_Compl_self_eq
% 3.82/4.05 thf(fact_4318_subset__Compl__self__eq,axiom,
% 3.82/4.05 ! [A2: set_int] :
% 3.82/4.05 ( ( ord_less_eq_set_int @ A2 @ ( uminus1532241313380277803et_int @ A2 ) )
% 3.82/4.05 = ( A2 = bot_bot_set_int ) ) ).
% 3.82/4.05
% 3.82/4.05 % subset_Compl_self_eq
% 3.82/4.05 thf(fact_4319_atLeastatMost__psubset__iff,axiom,
% 3.82/4.05 ! [A: extended_enat,B2: extended_enat,C: extended_enat,D: extended_enat] :
% 3.82/4.05 ( ( ord_le2529575680413868914d_enat @ ( set_or5403411693681687835d_enat @ A @ B2 ) @ ( set_or5403411693681687835d_enat @ C @ D ) )
% 3.82/4.05 = ( ( ~ ( ord_le2932123472753598470d_enat @ A @ B2 )
% 3.82/4.05 | ( ( ord_le2932123472753598470d_enat @ C @ A )
% 3.82/4.05 & ( ord_le2932123472753598470d_enat @ B2 @ D )
% 3.82/4.05 & ( ( ord_le72135733267957522d_enat @ C @ A )
% 3.82/4.05 | ( ord_le72135733267957522d_enat @ B2 @ D ) ) ) )
% 3.82/4.05 & ( ord_le2932123472753598470d_enat @ C @ D ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % atLeastatMost_psubset_iff
% 3.82/4.05 thf(fact_4320_atLeastatMost__psubset__iff,axiom,
% 3.82/4.05 ! [A: set_nat,B2: set_nat,C: set_nat,D: set_nat] :
% 3.82/4.05 ( ( ord_less_set_set_nat @ ( set_or4548717258645045905et_nat @ A @ B2 ) @ ( set_or4548717258645045905et_nat @ C @ D ) )
% 3.82/4.05 = ( ( ~ ( ord_less_eq_set_nat @ A @ B2 )
% 3.82/4.05 | ( ( ord_less_eq_set_nat @ C @ A )
% 3.82/4.05 & ( ord_less_eq_set_nat @ B2 @ D )
% 3.82/4.05 & ( ( ord_less_set_nat @ C @ A )
% 3.82/4.05 | ( ord_less_set_nat @ B2 @ D ) ) ) )
% 3.82/4.05 & ( ord_less_eq_set_nat @ C @ D ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % atLeastatMost_psubset_iff
% 3.82/4.05 thf(fact_4321_atLeastatMost__psubset__iff,axiom,
% 3.82/4.05 ! [A: set_int,B2: set_int,C: set_int,D: set_int] :
% 3.82/4.05 ( ( ord_less_set_set_int @ ( set_or370866239135849197et_int @ A @ B2 ) @ ( set_or370866239135849197et_int @ C @ D ) )
% 3.82/4.05 = ( ( ~ ( ord_less_eq_set_int @ A @ B2 )
% 3.82/4.05 | ( ( ord_less_eq_set_int @ C @ A )
% 3.82/4.05 & ( ord_less_eq_set_int @ B2 @ D )
% 3.82/4.05 & ( ( ord_less_set_int @ C @ A )
% 3.82/4.05 | ( ord_less_set_int @ B2 @ D ) ) ) )
% 3.82/4.05 & ( ord_less_eq_set_int @ C @ D ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % atLeastatMost_psubset_iff
% 3.82/4.05 thf(fact_4322_atLeastatMost__psubset__iff,axiom,
% 3.82/4.05 ! [A: nat,B2: nat,C: nat,D: nat] :
% 3.82/4.05 ( ( ord_less_set_nat @ ( set_or1269000886237332187st_nat @ A @ B2 ) @ ( set_or1269000886237332187st_nat @ C @ D ) )
% 3.82/4.05 = ( ( ~ ( ord_less_eq_nat @ A @ B2 )
% 3.82/4.05 | ( ( ord_less_eq_nat @ C @ A )
% 3.82/4.05 & ( ord_less_eq_nat @ B2 @ D )
% 3.82/4.05 & ( ( ord_less_nat @ C @ A )
% 3.82/4.05 | ( ord_less_nat @ B2 @ D ) ) ) )
% 3.82/4.05 & ( ord_less_eq_nat @ C @ D ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % atLeastatMost_psubset_iff
% 3.82/4.05 thf(fact_4323_atLeastatMost__psubset__iff,axiom,
% 3.82/4.05 ! [A: int,B2: int,C: int,D: int] :
% 3.82/4.05 ( ( ord_less_set_int @ ( set_or1266510415728281911st_int @ A @ B2 ) @ ( set_or1266510415728281911st_int @ C @ D ) )
% 3.82/4.05 = ( ( ~ ( ord_less_eq_int @ A @ B2 )
% 3.82/4.05 | ( ( ord_less_eq_int @ C @ A )
% 3.82/4.05 & ( ord_less_eq_int @ B2 @ D )
% 3.82/4.05 & ( ( ord_less_int @ C @ A )
% 3.82/4.05 | ( ord_less_int @ B2 @ D ) ) ) )
% 3.82/4.05 & ( ord_less_eq_int @ C @ D ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % atLeastatMost_psubset_iff
% 3.82/4.05 thf(fact_4324_atLeastatMost__psubset__iff,axiom,
% 3.82/4.05 ! [A: real,B2: real,C: real,D: real] :
% 3.82/4.05 ( ( ord_less_set_real @ ( set_or1222579329274155063t_real @ A @ B2 ) @ ( set_or1222579329274155063t_real @ C @ D ) )
% 3.82/4.05 = ( ( ~ ( ord_less_eq_real @ A @ B2 )
% 3.82/4.05 | ( ( ord_less_eq_real @ C @ A )
% 3.82/4.05 & ( ord_less_eq_real @ B2 @ D )
% 3.82/4.05 & ( ( ord_less_real @ C @ A )
% 3.82/4.05 | ( ord_less_real @ B2 @ D ) ) ) )
% 3.82/4.05 & ( ord_less_eq_real @ C @ D ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % atLeastatMost_psubset_iff
% 3.82/4.05 thf(fact_4325_take__bit__signed__take__bit,axiom,
% 3.82/4.05 ! [M2: nat,N2: nat,A: int] :
% 3.82/4.05 ( ( ord_less_eq_nat @ M2 @ ( suc @ N2 ) )
% 3.82/4.05 => ( ( bit_se2923211474154528505it_int @ M2 @ ( bit_ri631733984087533419it_int @ N2 @ A ) )
% 3.82/4.05 = ( bit_se2923211474154528505it_int @ M2 @ A ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % take_bit_signed_take_bit
% 3.82/4.05 thf(fact_4326_neg__numeral__le__zero,axiom,
% 3.82/4.05 ! [N2: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) @ zero_zero_real ) ).
% 3.82/4.05
% 3.82/4.05 % neg_numeral_le_zero
% 3.82/4.05 thf(fact_4327_neg__numeral__le__zero,axiom,
% 3.82/4.05 ! [N2: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) @ zero_zero_int ) ).
% 3.82/4.05
% 3.82/4.05 % neg_numeral_le_zero
% 3.82/4.05 thf(fact_4328_not__zero__le__neg__numeral,axiom,
% 3.82/4.05 ! [N2: num] :
% 3.82/4.05 ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % not_zero_le_neg_numeral
% 3.82/4.05 thf(fact_4329_not__zero__le__neg__numeral,axiom,
% 3.82/4.05 ! [N2: num] :
% 3.82/4.05 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % not_zero_le_neg_numeral
% 3.82/4.05 thf(fact_4330_neg__numeral__less__zero,axiom,
% 3.82/4.05 ! [N2: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) @ zero_zero_int ) ).
% 3.82/4.05
% 3.82/4.05 % neg_numeral_less_zero
% 3.82/4.05 thf(fact_4331_neg__numeral__less__zero,axiom,
% 3.82/4.05 ! [N2: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) @ zero_zero_real ) ).
% 3.82/4.05
% 3.82/4.05 % neg_numeral_less_zero
% 3.82/4.05 thf(fact_4332_not__zero__less__neg__numeral,axiom,
% 3.82/4.05 ! [N2: num] :
% 3.82/4.05 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % not_zero_less_neg_numeral
% 3.82/4.05 thf(fact_4333_not__zero__less__neg__numeral,axiom,
% 3.82/4.05 ! [N2: num] :
% 3.82/4.05 ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % not_zero_less_neg_numeral
% 3.82/4.05 thf(fact_4334_le__minus__one__simps_I3_J,axiom,
% 3.82/4.05 ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 3.82/4.05
% 3.82/4.05 % le_minus_one_simps(3)
% 3.82/4.05 thf(fact_4335_le__minus__one__simps_I3_J,axiom,
% 3.82/4.05 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 3.82/4.05
% 3.82/4.05 % le_minus_one_simps(3)
% 3.82/4.05 thf(fact_4336_le__minus__one__simps_I1_J,axiom,
% 3.82/4.05 ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 3.82/4.05
% 3.82/4.05 % le_minus_one_simps(1)
% 3.82/4.05 thf(fact_4337_le__minus__one__simps_I1_J,axiom,
% 3.82/4.05 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 3.82/4.05
% 3.82/4.05 % le_minus_one_simps(1)
% 3.82/4.05 thf(fact_4338_numeral__Bit1,axiom,
% 3.82/4.05 ! [N2: num] :
% 3.82/4.05 ( ( numera6690914467698888265omplex @ ( bit1 @ N2 ) )
% 3.82/4.05 = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N2 ) @ ( numera6690914467698888265omplex @ N2 ) ) @ one_one_complex ) ) ).
% 3.82/4.05
% 3.82/4.05 % numeral_Bit1
% 3.82/4.05 thf(fact_4339_numeral__Bit1,axiom,
% 3.82/4.05 ! [N2: num] :
% 3.82/4.05 ( ( numeral_numeral_nat @ ( bit1 @ N2 ) )
% 3.82/4.05 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) @ one_one_nat ) ) ).
% 3.82/4.05
% 3.82/4.05 % numeral_Bit1
% 3.82/4.05 thf(fact_4340_numeral__Bit1,axiom,
% 3.82/4.05 ! [N2: num] :
% 3.82/4.05 ( ( numera1916890842035813515d_enat @ ( bit1 @ N2 ) )
% 3.82/4.05 = ( plus_p3455044024723400733d_enat @ ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ ( numera1916890842035813515d_enat @ N2 ) ) @ one_on7984719198319812577d_enat ) ) ).
% 3.82/4.05
% 3.82/4.05 % numeral_Bit1
% 3.82/4.05 thf(fact_4341_numeral__Bit1,axiom,
% 3.82/4.05 ! [N2: num] :
% 3.82/4.05 ( ( numeral_numeral_int @ ( bit1 @ N2 ) )
% 3.82/4.05 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) @ one_one_int ) ) ).
% 3.82/4.05
% 3.82/4.05 % numeral_Bit1
% 3.82/4.05 thf(fact_4342_numeral__Bit1,axiom,
% 3.82/4.05 ! [N2: num] :
% 3.82/4.05 ( ( numeral_numeral_real @ ( bit1 @ N2 ) )
% 3.82/4.05 = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N2 ) @ ( numeral_numeral_real @ N2 ) ) @ one_one_real ) ) ).
% 3.82/4.05
% 3.82/4.05 % numeral_Bit1
% 3.82/4.05 thf(fact_4343_less__minus__one__simps_I3_J,axiom,
% 3.82/4.05 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 3.82/4.05
% 3.82/4.05 % less_minus_one_simps(3)
% 3.82/4.05 thf(fact_4344_less__minus__one__simps_I3_J,axiom,
% 3.82/4.05 ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 3.82/4.05
% 3.82/4.05 % less_minus_one_simps(3)
% 3.82/4.05 thf(fact_4345_less__minus__one__simps_I1_J,axiom,
% 3.82/4.05 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 3.82/4.05
% 3.82/4.05 % less_minus_one_simps(1)
% 3.82/4.05 thf(fact_4346_less__minus__one__simps_I1_J,axiom,
% 3.82/4.05 ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 3.82/4.05
% 3.82/4.05 % less_minus_one_simps(1)
% 3.82/4.05 thf(fact_4347_not__one__le__neg__numeral,axiom,
% 3.82/4.05 ! [M2: num] :
% 3.82/4.05 ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % not_one_le_neg_numeral
% 3.82/4.05 thf(fact_4348_not__one__le__neg__numeral,axiom,
% 3.82/4.05 ! [M2: num] :
% 3.82/4.05 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % not_one_le_neg_numeral
% 3.82/4.05 thf(fact_4349_not__numeral__le__neg__one,axiom,
% 3.82/4.05 ! [M2: num] :
% 3.82/4.05 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M2 ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 3.82/4.05
% 3.82/4.05 % not_numeral_le_neg_one
% 3.82/4.05 thf(fact_4350_not__numeral__le__neg__one,axiom,
% 3.82/4.05 ! [M2: num] :
% 3.82/4.05 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 3.82/4.05
% 3.82/4.05 % not_numeral_le_neg_one
% 3.82/4.05 thf(fact_4351_neg__numeral__le__neg__one,axiom,
% 3.82/4.05 ! [M2: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_numeral_le_neg_one
% 3.82/4.05 thf(fact_4352_neg__numeral__le__neg__one,axiom,
% 3.82/4.05 ! [M2: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_numeral_le_neg_one
% 3.82/4.05 thf(fact_4353_neg__one__le__numeral,axiom,
% 3.82/4.05 ! [M2: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_one_le_numeral
% 3.82/4.05 thf(fact_4354_neg__one__le__numeral,axiom,
% 3.82/4.05 ! [M2: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_one_le_numeral
% 3.82/4.05 thf(fact_4355_neg__numeral__le__one,axiom,
% 3.82/4.05 ! [M2: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ one_one_real ) ).
% 3.82/4.05
% 3.82/4.05 % neg_numeral_le_one
% 3.82/4.05 thf(fact_4356_neg__numeral__le__one,axiom,
% 3.82/4.05 ! [M2: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ one_one_int ) ).
% 3.82/4.05
% 3.82/4.05 % neg_numeral_le_one
% 3.82/4.05 thf(fact_4357_not__neg__one__less__neg__numeral,axiom,
% 3.82/4.05 ! [M2: num] :
% 3.82/4.05 ~ ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % not_neg_one_less_neg_numeral
% 3.82/4.05 thf(fact_4358_not__neg__one__less__neg__numeral,axiom,
% 3.82/4.05 ! [M2: num] :
% 3.82/4.05 ~ ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % not_neg_one_less_neg_numeral
% 3.82/4.05 thf(fact_4359_not__one__less__neg__numeral,axiom,
% 3.82/4.05 ! [M2: num] :
% 3.82/4.05 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % not_one_less_neg_numeral
% 3.82/4.05 thf(fact_4360_not__one__less__neg__numeral,axiom,
% 3.82/4.05 ! [M2: num] :
% 3.82/4.05 ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % not_one_less_neg_numeral
% 3.82/4.05 thf(fact_4361_not__numeral__less__neg__one,axiom,
% 3.82/4.05 ! [M2: num] :
% 3.82/4.05 ~ ( ord_less_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 3.82/4.05
% 3.82/4.05 % not_numeral_less_neg_one
% 3.82/4.05 thf(fact_4362_not__numeral__less__neg__one,axiom,
% 3.82/4.05 ! [M2: num] :
% 3.82/4.05 ~ ( ord_less_real @ ( numeral_numeral_real @ M2 ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 3.82/4.05
% 3.82/4.05 % not_numeral_less_neg_one
% 3.82/4.05 thf(fact_4363_neg__one__less__numeral,axiom,
% 3.82/4.05 ! [M2: num] : ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_one_less_numeral
% 3.82/4.05 thf(fact_4364_neg__one__less__numeral,axiom,
% 3.82/4.05 ! [M2: num] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_one_less_numeral
% 3.82/4.05 thf(fact_4365_neg__numeral__less__one,axiom,
% 3.82/4.05 ! [M2: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ one_one_int ) ).
% 3.82/4.05
% 3.82/4.05 % neg_numeral_less_one
% 3.82/4.05 thf(fact_4366_neg__numeral__less__one,axiom,
% 3.82/4.05 ! [M2: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ one_one_real ) ).
% 3.82/4.05
% 3.82/4.05 % neg_numeral_less_one
% 3.82/4.05 thf(fact_4367_eq__minus__divide__eq,axiom,
% 3.82/4.05 ! [A: complex,B2: complex,C: complex] :
% 3.82/4.05 ( ( A
% 3.82/4.05 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B2 @ C ) ) )
% 3.82/4.05 = ( ( ( C != zero_zero_complex )
% 3.82/4.05 => ( ( times_times_complex @ A @ C )
% 3.82/4.05 = ( uminus1482373934393186551omplex @ B2 ) ) )
% 3.82/4.05 & ( ( C = zero_zero_complex )
% 3.82/4.05 => ( A = zero_zero_complex ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % eq_minus_divide_eq
% 3.82/4.05 thf(fact_4368_eq__minus__divide__eq,axiom,
% 3.82/4.05 ! [A: real,B2: real,C: real] :
% 3.82/4.05 ( ( A
% 3.82/4.05 = ( uminus_uminus_real @ ( divide_divide_real @ B2 @ C ) ) )
% 3.82/4.05 = ( ( ( C != zero_zero_real )
% 3.82/4.05 => ( ( times_times_real @ A @ C )
% 3.82/4.05 = ( uminus_uminus_real @ B2 ) ) )
% 3.82/4.05 & ( ( C = zero_zero_real )
% 3.82/4.05 => ( A = zero_zero_real ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % eq_minus_divide_eq
% 3.82/4.05 thf(fact_4369_minus__divide__eq__eq,axiom,
% 3.82/4.05 ! [B2: complex,C: complex,A: complex] :
% 3.82/4.05 ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B2 @ C ) )
% 3.82/4.05 = A )
% 3.82/4.05 = ( ( ( C != zero_zero_complex )
% 3.82/4.05 => ( ( uminus1482373934393186551omplex @ B2 )
% 3.82/4.05 = ( times_times_complex @ A @ C ) ) )
% 3.82/4.05 & ( ( C = zero_zero_complex )
% 3.82/4.05 => ( A = zero_zero_complex ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % minus_divide_eq_eq
% 3.82/4.05 thf(fact_4370_minus__divide__eq__eq,axiom,
% 3.82/4.05 ! [B2: real,C: real,A: real] :
% 3.82/4.05 ( ( ( uminus_uminus_real @ ( divide_divide_real @ B2 @ C ) )
% 3.82/4.05 = A )
% 3.82/4.05 = ( ( ( C != zero_zero_real )
% 3.82/4.05 => ( ( uminus_uminus_real @ B2 )
% 3.82/4.05 = ( times_times_real @ A @ C ) ) )
% 3.82/4.05 & ( ( C = zero_zero_real )
% 3.82/4.05 => ( A = zero_zero_real ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % minus_divide_eq_eq
% 3.82/4.05 thf(fact_4371_nonzero__neg__divide__eq__eq,axiom,
% 3.82/4.05 ! [B2: complex,A: complex,C: complex] :
% 3.82/4.05 ( ( B2 != zero_zero_complex )
% 3.82/4.05 => ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B2 ) )
% 3.82/4.05 = C )
% 3.82/4.05 = ( ( uminus1482373934393186551omplex @ A )
% 3.82/4.05 = ( times_times_complex @ C @ B2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % nonzero_neg_divide_eq_eq
% 3.82/4.05 thf(fact_4372_nonzero__neg__divide__eq__eq,axiom,
% 3.82/4.05 ! [B2: real,A: real,C: real] :
% 3.82/4.05 ( ( B2 != zero_zero_real )
% 3.82/4.05 => ( ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B2 ) )
% 3.82/4.05 = C )
% 3.82/4.05 = ( ( uminus_uminus_real @ A )
% 3.82/4.05 = ( times_times_real @ C @ B2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % nonzero_neg_divide_eq_eq
% 3.82/4.05 thf(fact_4373_nonzero__neg__divide__eq__eq2,axiom,
% 3.82/4.05 ! [B2: complex,C: complex,A: complex] :
% 3.82/4.05 ( ( B2 != zero_zero_complex )
% 3.82/4.05 => ( ( C
% 3.82/4.05 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B2 ) ) )
% 3.82/4.05 = ( ( times_times_complex @ C @ B2 )
% 3.82/4.05 = ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % nonzero_neg_divide_eq_eq2
% 3.82/4.05 thf(fact_4374_nonzero__neg__divide__eq__eq2,axiom,
% 3.82/4.05 ! [B2: real,C: real,A: real] :
% 3.82/4.05 ( ( B2 != zero_zero_real )
% 3.82/4.05 => ( ( C
% 3.82/4.05 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B2 ) ) )
% 3.82/4.05 = ( ( times_times_real @ C @ B2 )
% 3.82/4.05 = ( uminus_uminus_real @ A ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % nonzero_neg_divide_eq_eq2
% 3.82/4.05 thf(fact_4375_divide__eq__minus__1__iff,axiom,
% 3.82/4.05 ! [A: complex,B2: complex] :
% 3.82/4.05 ( ( ( divide1717551699836669952omplex @ A @ B2 )
% 3.82/4.05 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 3.82/4.05 = ( ( B2 != zero_zero_complex )
% 3.82/4.05 & ( A
% 3.82/4.05 = ( uminus1482373934393186551omplex @ B2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % divide_eq_minus_1_iff
% 3.82/4.05 thf(fact_4376_divide__eq__minus__1__iff,axiom,
% 3.82/4.05 ! [A: real,B2: real] :
% 3.82/4.05 ( ( ( divide_divide_real @ A @ B2 )
% 3.82/4.05 = ( uminus_uminus_real @ one_one_real ) )
% 3.82/4.05 = ( ( B2 != zero_zero_real )
% 3.82/4.05 & ( A
% 3.82/4.05 = ( uminus_uminus_real @ B2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % divide_eq_minus_1_iff
% 3.82/4.05 thf(fact_4377_eval__nat__numeral_I3_J,axiom,
% 3.82/4.05 ! [N2: num] :
% 3.82/4.05 ( ( numeral_numeral_nat @ ( bit1 @ N2 ) )
% 3.82/4.05 = ( suc @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % eval_nat_numeral(3)
% 3.82/4.05 thf(fact_4378_signed__take__bit__int__less__eq,axiom,
% 3.82/4.05 ! [N2: nat,K: int] :
% 3.82/4.05 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K )
% 3.82/4.05 => ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % signed_take_bit_int_less_eq
% 3.82/4.05 thf(fact_4379_signed__take__bit__int__greater__eq,axiom,
% 3.82/4.05 ! [K: int,N2: nat] :
% 3.82/4.05 ( ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) )
% 3.82/4.05 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) ) @ ( bit_ri631733984087533419it_int @ N2 @ K ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % signed_take_bit_int_greater_eq
% 3.82/4.05 thf(fact_4380_take__bit__Suc__bit1,axiom,
% 3.82/4.05 ! [N2: nat,K: num] :
% 3.82/4.05 ( ( bit_se2925701944663578781it_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 3.82/4.05 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 3.82/4.05
% 3.82/4.05 % take_bit_Suc_bit1
% 3.82/4.05 thf(fact_4381_take__bit__Suc__bit1,axiom,
% 3.82/4.05 ! [N2: nat,K: num] :
% 3.82/4.05 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 3.82/4.05 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 3.82/4.05
% 3.82/4.05 % take_bit_Suc_bit1
% 3.82/4.05 thf(fact_4382_take__bit__Suc__minus__1__eq,axiom,
% 3.82/4.05 ! [N2: nat] :
% 3.82/4.05 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ one_one_int ) )
% 3.82/4.05 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) @ one_one_int ) ) ).
% 3.82/4.05
% 3.82/4.05 % take_bit_Suc_minus_1_eq
% 3.82/4.05 thf(fact_4383_numeral__code_I3_J,axiom,
% 3.82/4.05 ! [N2: num] :
% 3.82/4.05 ( ( numera6690914467698888265omplex @ ( bit1 @ N2 ) )
% 3.82/4.05 = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N2 ) @ ( numera6690914467698888265omplex @ N2 ) ) @ one_one_complex ) ) ).
% 3.82/4.05
% 3.82/4.05 % numeral_code(3)
% 3.82/4.05 thf(fact_4384_numeral__code_I3_J,axiom,
% 3.82/4.05 ! [N2: num] :
% 3.82/4.05 ( ( numeral_numeral_nat @ ( bit1 @ N2 ) )
% 3.82/4.05 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) @ one_one_nat ) ) ).
% 3.82/4.05
% 3.82/4.05 % numeral_code(3)
% 3.82/4.05 thf(fact_4385_numeral__code_I3_J,axiom,
% 3.82/4.05 ! [N2: num] :
% 3.82/4.05 ( ( numera1916890842035813515d_enat @ ( bit1 @ N2 ) )
% 3.82/4.05 = ( plus_p3455044024723400733d_enat @ ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ ( numera1916890842035813515d_enat @ N2 ) ) @ one_on7984719198319812577d_enat ) ) ).
% 3.82/4.05
% 3.82/4.05 % numeral_code(3)
% 3.82/4.05 thf(fact_4386_numeral__code_I3_J,axiom,
% 3.82/4.05 ! [N2: num] :
% 3.82/4.05 ( ( numeral_numeral_int @ ( bit1 @ N2 ) )
% 3.82/4.05 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) @ one_one_int ) ) ).
% 3.82/4.05
% 3.82/4.05 % numeral_code(3)
% 3.82/4.05 thf(fact_4387_numeral__code_I3_J,axiom,
% 3.82/4.05 ! [N2: num] :
% 3.82/4.05 ( ( numeral_numeral_real @ ( bit1 @ N2 ) )
% 3.82/4.05 = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N2 ) @ ( numeral_numeral_real @ N2 ) ) @ one_one_real ) ) ).
% 3.82/4.05
% 3.82/4.05 % numeral_code(3)
% 3.82/4.05 thf(fact_4388_subset__eq__atLeast0__atMost__finite,axiom,
% 3.82/4.05 ! [N6: set_nat,N2: nat] :
% 3.82/4.05 ( ( ord_less_eq_set_nat @ N6 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 3.82/4.05 => ( finite_finite_nat @ N6 ) ) ).
% 3.82/4.05
% 3.82/4.05 % subset_eq_atLeast0_atMost_finite
% 3.82/4.05 thf(fact_4389_pos__minus__divide__less__eq,axiom,
% 3.82/4.05 ! [C: real,B2: real,A: real] :
% 3.82/4.05 ( ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.05 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B2 @ C ) ) @ A )
% 3.82/4.05 = ( ord_less_real @ ( uminus_uminus_real @ B2 ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % pos_minus_divide_less_eq
% 3.82/4.05 thf(fact_4390_pos__less__minus__divide__eq,axiom,
% 3.82/4.05 ! [C: real,A: real,B2: real] :
% 3.82/4.05 ( ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.05 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B2 @ C ) ) )
% 3.82/4.05 = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % pos_less_minus_divide_eq
% 3.82/4.05 thf(fact_4391_neg__minus__divide__less__eq,axiom,
% 3.82/4.05 ! [C: real,B2: real,A: real] :
% 3.82/4.05 ( ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.05 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B2 @ C ) ) @ A )
% 3.82/4.05 = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_minus_divide_less_eq
% 3.82/4.05 thf(fact_4392_neg__less__minus__divide__eq,axiom,
% 3.82/4.05 ! [C: real,A: real,B2: real] :
% 3.82/4.05 ( ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.05 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B2 @ C ) ) )
% 3.82/4.05 = ( ord_less_real @ ( uminus_uminus_real @ B2 ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_less_minus_divide_eq
% 3.82/4.05 thf(fact_4393_minus__divide__less__eq,axiom,
% 3.82/4.05 ! [B2: real,C: real,A: real] :
% 3.82/4.05 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B2 @ C ) ) @ A )
% 3.82/4.05 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.05 => ( ord_less_real @ ( uminus_uminus_real @ B2 ) @ ( times_times_real @ A @ C ) ) )
% 3.82/4.05 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.05 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.05 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B2 ) ) )
% 3.82/4.05 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.05 => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % minus_divide_less_eq
% 3.82/4.05 thf(fact_4394_less__minus__divide__eq,axiom,
% 3.82/4.05 ! [A: real,B2: real,C: real] :
% 3.82/4.05 ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B2 @ C ) ) )
% 3.82/4.05 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.05 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B2 ) ) )
% 3.82/4.05 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.05 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.05 => ( ord_less_real @ ( uminus_uminus_real @ B2 ) @ ( times_times_real @ A @ C ) ) )
% 3.82/4.05 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.05 => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % less_minus_divide_eq
% 3.82/4.05 thf(fact_4395_divide__eq__eq__numeral_I2_J,axiom,
% 3.82/4.05 ! [B2: complex,C: complex,W2: num] :
% 3.82/4.05 ( ( ( divide1717551699836669952omplex @ B2 @ C )
% 3.82/4.05 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) )
% 3.82/4.05 = ( ( ( C != zero_zero_complex )
% 3.82/4.05 => ( B2
% 3.82/4.05 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) @ C ) ) )
% 3.82/4.05 & ( ( C = zero_zero_complex )
% 3.82/4.05 => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 3.82/4.05 = zero_zero_complex ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % divide_eq_eq_numeral(2)
% 3.82/4.05 thf(fact_4396_divide__eq__eq__numeral_I2_J,axiom,
% 3.82/4.05 ! [B2: real,C: real,W2: num] :
% 3.82/4.05 ( ( ( divide_divide_real @ B2 @ C )
% 3.82/4.05 = ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) )
% 3.82/4.05 = ( ( ( C != zero_zero_real )
% 3.82/4.05 => ( B2
% 3.82/4.05 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) ) )
% 3.82/4.05 & ( ( C = zero_zero_real )
% 3.82/4.05 => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 3.82/4.05 = zero_zero_real ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % divide_eq_eq_numeral(2)
% 3.82/4.05 thf(fact_4397_eq__divide__eq__numeral_I2_J,axiom,
% 3.82/4.05 ! [W2: num,B2: complex,C: complex] :
% 3.82/4.05 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 3.82/4.05 = ( divide1717551699836669952omplex @ B2 @ C ) )
% 3.82/4.05 = ( ( ( C != zero_zero_complex )
% 3.82/4.05 => ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) @ C )
% 3.82/4.05 = B2 ) )
% 3.82/4.05 & ( ( C = zero_zero_complex )
% 3.82/4.05 => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 3.82/4.05 = zero_zero_complex ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % eq_divide_eq_numeral(2)
% 3.82/4.05 thf(fact_4398_eq__divide__eq__numeral_I2_J,axiom,
% 3.82/4.05 ! [W2: num,B2: real,C: real] :
% 3.82/4.05 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 3.82/4.05 = ( divide_divide_real @ B2 @ C ) )
% 3.82/4.05 = ( ( ( C != zero_zero_real )
% 3.82/4.05 => ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C )
% 3.82/4.05 = B2 ) )
% 3.82/4.05 & ( ( C = zero_zero_real )
% 3.82/4.05 => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 3.82/4.05 = zero_zero_real ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % eq_divide_eq_numeral(2)
% 3.82/4.05 thf(fact_4399_cong__exp__iff__simps_I3_J,axiom,
% 3.82/4.05 ! [N2: num,Q3: num] :
% 3.82/4.05 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 3.82/4.05 != zero_zero_nat ) ).
% 3.82/4.05
% 3.82/4.05 % cong_exp_iff_simps(3)
% 3.82/4.05 thf(fact_4400_cong__exp__iff__simps_I3_J,axiom,
% 3.82/4.05 ! [N2: num,Q3: num] :
% 3.82/4.05 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 3.82/4.05 != zero_zero_int ) ).
% 3.82/4.05
% 3.82/4.05 % cong_exp_iff_simps(3)
% 3.82/4.05 thf(fact_4401_add__divide__eq__if__simps_I3_J,axiom,
% 3.82/4.05 ! [Z3: complex,A: complex,B2: complex] :
% 3.82/4.05 ( ( ( Z3 = zero_zero_complex )
% 3.82/4.05 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z3 ) ) @ B2 )
% 3.82/4.05 = B2 ) )
% 3.82/4.05 & ( ( Z3 != zero_zero_complex )
% 3.82/4.05 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z3 ) ) @ B2 )
% 3.82/4.05 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B2 @ Z3 ) ) @ Z3 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % add_divide_eq_if_simps(3)
% 3.82/4.05 thf(fact_4402_add__divide__eq__if__simps_I3_J,axiom,
% 3.82/4.05 ! [Z3: real,A: real,B2: real] :
% 3.82/4.05 ( ( ( Z3 = zero_zero_real )
% 3.82/4.05 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z3 ) ) @ B2 )
% 3.82/4.05 = B2 ) )
% 3.82/4.05 & ( ( Z3 != zero_zero_real )
% 3.82/4.05 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z3 ) ) @ B2 )
% 3.82/4.05 = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B2 @ Z3 ) ) @ Z3 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % add_divide_eq_if_simps(3)
% 3.82/4.05 thf(fact_4403_minus__divide__add__eq__iff,axiom,
% 3.82/4.05 ! [Z3: complex,X: complex,Y: complex] :
% 3.82/4.05 ( ( Z3 != zero_zero_complex )
% 3.82/4.05 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X @ Z3 ) ) @ Y )
% 3.82/4.05 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ X ) @ ( times_times_complex @ Y @ Z3 ) ) @ Z3 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % minus_divide_add_eq_iff
% 3.82/4.05 thf(fact_4404_minus__divide__add__eq__iff,axiom,
% 3.82/4.05 ! [Z3: real,X: real,Y: real] :
% 3.82/4.05 ( ( Z3 != zero_zero_real )
% 3.82/4.05 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X @ Z3 ) ) @ Y )
% 3.82/4.05 = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ X ) @ ( times_times_real @ Y @ Z3 ) ) @ Z3 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % minus_divide_add_eq_iff
% 3.82/4.05 thf(fact_4405_add__divide__eq__if__simps_I6_J,axiom,
% 3.82/4.05 ! [Z3: complex,A: complex,B2: complex] :
% 3.82/4.05 ( ( ( Z3 = zero_zero_complex )
% 3.82/4.05 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z3 ) ) @ B2 )
% 3.82/4.05 = ( uminus1482373934393186551omplex @ B2 ) ) )
% 3.82/4.05 & ( ( Z3 != zero_zero_complex )
% 3.82/4.05 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z3 ) ) @ B2 )
% 3.82/4.05 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B2 @ Z3 ) ) @ Z3 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % add_divide_eq_if_simps(6)
% 3.82/4.05 thf(fact_4406_add__divide__eq__if__simps_I6_J,axiom,
% 3.82/4.05 ! [Z3: real,A: real,B2: real] :
% 3.82/4.05 ( ( ( Z3 = zero_zero_real )
% 3.82/4.05 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z3 ) ) @ B2 )
% 3.82/4.05 = ( uminus_uminus_real @ B2 ) ) )
% 3.82/4.05 & ( ( Z3 != zero_zero_real )
% 3.82/4.05 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z3 ) ) @ B2 )
% 3.82/4.05 = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B2 @ Z3 ) ) @ Z3 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % add_divide_eq_if_simps(6)
% 3.82/4.05 thf(fact_4407_add__divide__eq__if__simps_I5_J,axiom,
% 3.82/4.05 ! [Z3: complex,A: complex,B2: complex] :
% 3.82/4.05 ( ( ( Z3 = zero_zero_complex )
% 3.82/4.05 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z3 ) @ B2 )
% 3.82/4.05 = ( uminus1482373934393186551omplex @ B2 ) ) )
% 3.82/4.05 & ( ( Z3 != zero_zero_complex )
% 3.82/4.05 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z3 ) @ B2 )
% 3.82/4.05 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ ( times_times_complex @ B2 @ Z3 ) ) @ Z3 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % add_divide_eq_if_simps(5)
% 3.82/4.05 thf(fact_4408_add__divide__eq__if__simps_I5_J,axiom,
% 3.82/4.05 ! [Z3: real,A: real,B2: real] :
% 3.82/4.05 ( ( ( Z3 = zero_zero_real )
% 3.82/4.05 => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z3 ) @ B2 )
% 3.82/4.05 = ( uminus_uminus_real @ B2 ) ) )
% 3.82/4.05 & ( ( Z3 != zero_zero_real )
% 3.82/4.05 => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z3 ) @ B2 )
% 3.82/4.05 = ( divide_divide_real @ ( minus_minus_real @ A @ ( times_times_real @ B2 @ Z3 ) ) @ Z3 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % add_divide_eq_if_simps(5)
% 3.82/4.05 thf(fact_4409_minus__divide__diff__eq__iff,axiom,
% 3.82/4.05 ! [Z3: complex,X: complex,Y: complex] :
% 3.82/4.05 ( ( Z3 != zero_zero_complex )
% 3.82/4.05 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X @ Z3 ) ) @ Y )
% 3.82/4.05 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X ) @ ( times_times_complex @ Y @ Z3 ) ) @ Z3 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % minus_divide_diff_eq_iff
% 3.82/4.05 thf(fact_4410_minus__divide__diff__eq__iff,axiom,
% 3.82/4.05 ! [Z3: real,X: real,Y: real] :
% 3.82/4.05 ( ( Z3 != zero_zero_real )
% 3.82/4.05 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X @ Z3 ) ) @ Y )
% 3.82/4.05 = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ X ) @ ( times_times_real @ Y @ Z3 ) ) @ Z3 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % minus_divide_diff_eq_iff
% 3.82/4.05 thf(fact_4411_numeral__3__eq__3,axiom,
% 3.82/4.05 ( ( numeral_numeral_nat @ ( bit1 @ one ) )
% 3.82/4.05 = ( suc @ ( suc @ ( suc @ zero_zero_nat ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % numeral_3_eq_3
% 3.82/4.05 thf(fact_4412_Suc3__eq__add__3,axiom,
% 3.82/4.05 ! [N2: nat] :
% 3.82/4.05 ( ( suc @ ( suc @ ( suc @ N2 ) ) )
% 3.82/4.05 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % Suc3_eq_add_3
% 3.82/4.05 thf(fact_4413_take__bit__Suc__bit0,axiom,
% 3.82/4.05 ! [N2: nat,K: num] :
% 3.82/4.05 ( ( bit_se2925701944663578781it_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 3.82/4.05 = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % take_bit_Suc_bit0
% 3.82/4.05 thf(fact_4414_take__bit__Suc__bit0,axiom,
% 3.82/4.05 ! [N2: nat,K: num] :
% 3.82/4.05 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 3.82/4.05 = ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % take_bit_Suc_bit0
% 3.82/4.05 thf(fact_4415_take__bit__nat__eq__self,axiom,
% 3.82/4.05 ! [M2: nat,N2: nat] :
% 3.82/4.05 ( ( ord_less_nat @ M2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 3.82/4.05 => ( ( bit_se2925701944663578781it_nat @ N2 @ M2 )
% 3.82/4.05 = M2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % take_bit_nat_eq_self
% 3.82/4.05 thf(fact_4416_take__bit__nat__less__exp,axiom,
% 3.82/4.05 ! [N2: nat,M2: nat] : ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N2 @ M2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % take_bit_nat_less_exp
% 3.82/4.05 thf(fact_4417_take__bit__nat__eq__self__iff,axiom,
% 3.82/4.05 ! [N2: nat,M2: nat] :
% 3.82/4.05 ( ( ( bit_se2925701944663578781it_nat @ N2 @ M2 )
% 3.82/4.05 = M2 )
% 3.82/4.05 = ( ord_less_nat @ M2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % take_bit_nat_eq_self_iff
% 3.82/4.05 thf(fact_4418_num_Osize_I6_J,axiom,
% 3.82/4.05 ! [X32: num] :
% 3.82/4.05 ( ( size_size_num @ ( bit1 @ X32 ) )
% 3.82/4.05 = ( plus_plus_nat @ ( size_size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % num.size(6)
% 3.82/4.05 thf(fact_4419_num_Osize__gen_I3_J,axiom,
% 3.82/4.05 ! [X32: num] :
% 3.82/4.05 ( ( size_num @ ( bit1 @ X32 ) )
% 3.82/4.05 = ( plus_plus_nat @ ( size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % num.size_gen(3)
% 3.82/4.05 thf(fact_4420_le__minus__divide__eq,axiom,
% 3.82/4.05 ! [A: real,B2: real,C: real] :
% 3.82/4.05 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B2 @ C ) ) )
% 3.82/4.05 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.05 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B2 ) ) )
% 3.82/4.05 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.05 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.05 => ( ord_less_eq_real @ ( uminus_uminus_real @ B2 ) @ ( times_times_real @ A @ C ) ) )
% 3.82/4.05 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.05 => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % le_minus_divide_eq
% 3.82/4.05 thf(fact_4421_minus__divide__le__eq,axiom,
% 3.82/4.05 ! [B2: real,C: real,A: real] :
% 3.82/4.05 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B2 @ C ) ) @ A )
% 3.82/4.05 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.05 => ( ord_less_eq_real @ ( uminus_uminus_real @ B2 ) @ ( times_times_real @ A @ C ) ) )
% 3.82/4.05 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.05 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.05 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B2 ) ) )
% 3.82/4.05 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.05 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % minus_divide_le_eq
% 3.82/4.05 thf(fact_4422_neg__le__minus__divide__eq,axiom,
% 3.82/4.05 ! [C: real,A: real,B2: real] :
% 3.82/4.05 ( ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.05 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B2 @ C ) ) )
% 3.82/4.05 = ( ord_less_eq_real @ ( uminus_uminus_real @ B2 ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_le_minus_divide_eq
% 3.82/4.05 thf(fact_4423_neg__minus__divide__le__eq,axiom,
% 3.82/4.05 ! [C: real,B2: real,A: real] :
% 3.82/4.05 ( ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.05 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B2 @ C ) ) @ A )
% 3.82/4.05 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_minus_divide_le_eq
% 3.82/4.05 thf(fact_4424_pos__le__minus__divide__eq,axiom,
% 3.82/4.05 ! [C: real,A: real,B2: real] :
% 3.82/4.05 ( ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.05 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B2 @ C ) ) )
% 3.82/4.05 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B2 ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % pos_le_minus_divide_eq
% 3.82/4.05 thf(fact_4425_pos__minus__divide__le__eq,axiom,
% 3.82/4.05 ! [C: real,B2: real,A: real] :
% 3.82/4.05 ( ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.05 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B2 @ C ) ) @ A )
% 3.82/4.05 = ( ord_less_eq_real @ ( uminus_uminus_real @ B2 ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % pos_minus_divide_le_eq
% 3.82/4.05 thf(fact_4426_divide__less__eq__numeral_I2_J,axiom,
% 3.82/4.05 ! [B2: real,C: real,W2: num] :
% 3.82/4.05 ( ( ord_less_real @ ( divide_divide_real @ B2 @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) )
% 3.82/4.05 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.05 => ( ord_less_real @ B2 @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) ) )
% 3.82/4.05 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.05 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.05 => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) @ B2 ) )
% 3.82/4.05 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.05 => ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % divide_less_eq_numeral(2)
% 3.82/4.05 thf(fact_4427_less__divide__eq__numeral_I2_J,axiom,
% 3.82/4.05 ! [W2: num,B2: real,C: real] :
% 3.82/4.05 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ ( divide_divide_real @ B2 @ C ) )
% 3.82/4.05 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.05 => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) @ B2 ) )
% 3.82/4.05 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.05 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.05 => ( ord_less_real @ B2 @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) ) )
% 3.82/4.05 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.05 => ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % less_divide_eq_numeral(2)
% 3.82/4.05 thf(fact_4428_cong__exp__iff__simps_I7_J,axiom,
% 3.82/4.05 ! [Q3: num,N2: num] :
% 3.82/4.05 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 3.82/4.05 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) )
% 3.82/4.05 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ Q3 ) )
% 3.82/4.05 = zero_zero_nat ) ) ).
% 3.82/4.05
% 3.82/4.05 % cong_exp_iff_simps(7)
% 3.82/4.05 thf(fact_4429_cong__exp__iff__simps_I7_J,axiom,
% 3.82/4.05 ! [Q3: num,N2: num] :
% 3.82/4.05 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 3.82/4.05 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) )
% 3.82/4.05 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ Q3 ) )
% 3.82/4.05 = zero_zero_int ) ) ).
% 3.82/4.05
% 3.82/4.05 % cong_exp_iff_simps(7)
% 3.82/4.05 thf(fact_4430_cong__exp__iff__simps_I11_J,axiom,
% 3.82/4.05 ! [M2: num,Q3: num] :
% 3.82/4.05 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 3.82/4.05 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) )
% 3.82/4.05 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ Q3 ) )
% 3.82/4.05 = zero_zero_nat ) ) ).
% 3.82/4.05
% 3.82/4.05 % cong_exp_iff_simps(11)
% 3.82/4.05 thf(fact_4431_cong__exp__iff__simps_I11_J,axiom,
% 3.82/4.05 ! [M2: num,Q3: num] :
% 3.82/4.05 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 3.82/4.05 = ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) )
% 3.82/4.05 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ Q3 ) )
% 3.82/4.05 = zero_zero_int ) ) ).
% 3.82/4.05
% 3.82/4.05 % cong_exp_iff_simps(11)
% 3.82/4.05 thf(fact_4432_Suc__div__eq__add3__div,axiom,
% 3.82/4.05 ! [M2: nat,N2: nat] :
% 3.82/4.05 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M2 ) ) ) @ N2 )
% 3.82/4.05 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M2 ) @ N2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % Suc_div_eq_add3_div
% 3.82/4.05 thf(fact_4433_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 3.82/4.05 ! [K: nat,N2: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ K @ N2 )
% 3.82/4.05 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( plus_plus_nat @ N2 @ K ) )
% 3.82/4.05 = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_one_power_add_eq_neg_one_power_diff
% 3.82/4.05 thf(fact_4434_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 3.82/4.05 ! [K: nat,N2: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ K @ N2 )
% 3.82/4.05 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ N2 @ K ) )
% 3.82/4.05 = ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_one_power_add_eq_neg_one_power_diff
% 3.82/4.05 thf(fact_4435_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 3.82/4.05 ! [K: nat,N2: nat] :
% 3.82/4.05 ( ( ord_less_eq_nat @ K @ N2 )
% 3.82/4.05 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( plus_plus_nat @ N2 @ K ) )
% 3.82/4.05 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % neg_one_power_add_eq_neg_one_power_diff
% 3.82/4.05 thf(fact_4436_Suc__mod__eq__add3__mod,axiom,
% 3.82/4.05 ! [M2: nat,N2: nat] :
% 3.82/4.05 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M2 ) ) ) @ N2 )
% 3.82/4.05 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M2 ) @ N2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % Suc_mod_eq_add3_mod
% 3.82/4.05 thf(fact_4437_take__bit__eq__0__iff,axiom,
% 3.82/4.05 ! [N2: nat,A: nat] :
% 3.82/4.05 ( ( ( bit_se2925701944663578781it_nat @ N2 @ A )
% 3.82/4.05 = zero_zero_nat )
% 3.82/4.05 = ( dvd_dvd_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ A ) ) ).
% 3.82/4.05
% 3.82/4.05 % take_bit_eq_0_iff
% 3.82/4.05 thf(fact_4438_take__bit__eq__0__iff,axiom,
% 3.82/4.05 ! [N2: nat,A: int] :
% 3.82/4.05 ( ( ( bit_se2923211474154528505it_int @ N2 @ A )
% 3.82/4.05 = zero_zero_int )
% 3.82/4.05 = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ A ) ) ).
% 3.82/4.05
% 3.82/4.05 % take_bit_eq_0_iff
% 3.82/4.05 thf(fact_4439_take__bit__nat__less__self__iff,axiom,
% 3.82/4.05 ! [N2: nat,M2: nat] :
% 3.82/4.05 ( ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N2 @ M2 ) @ M2 )
% 3.82/4.05 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ M2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % take_bit_nat_less_self_iff
% 3.82/4.05 thf(fact_4440_divide__le__eq__numeral_I2_J,axiom,
% 3.82/4.05 ! [B2: real,C: real,W2: num] :
% 3.82/4.05 ( ( ord_less_eq_real @ ( divide_divide_real @ B2 @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) )
% 3.82/4.05 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.05 => ( ord_less_eq_real @ B2 @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) ) )
% 3.82/4.05 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.05 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.05 => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) @ B2 ) )
% 3.82/4.05 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.05 => ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % divide_le_eq_numeral(2)
% 3.82/4.05 thf(fact_4441_le__divide__eq__numeral_I2_J,axiom,
% 3.82/4.05 ! [W2: num,B2: real,C: real] :
% 3.82/4.05 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ ( divide_divide_real @ B2 @ C ) )
% 3.82/4.05 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.05 => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) @ B2 ) )
% 3.82/4.05 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.05 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.05 => ( ord_less_eq_real @ B2 @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) ) )
% 3.82/4.05 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.05 => ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % le_divide_eq_numeral(2)
% 3.82/4.05 thf(fact_4442_square__le__1,axiom,
% 3.82/4.05 ! [X: real] :
% 3.82/4.05 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 3.82/4.05 => ( ( ord_less_eq_real @ X @ one_one_real )
% 3.82/4.05 => ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % square_le_1
% 3.82/4.05 thf(fact_4443_square__le__1,axiom,
% 3.82/4.05 ! [X: int] :
% 3.82/4.05 ( ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ X )
% 3.82/4.05 => ( ( ord_less_eq_int @ X @ one_one_int )
% 3.82/4.05 => ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % square_le_1
% 3.82/4.05 thf(fact_4444_power__minus1__odd,axiom,
% 3.82/4.05 ! [N2: nat] :
% 3.82/4.05 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 3.82/4.05 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 3.82/4.05
% 3.82/4.05 % power_minus1_odd
% 3.82/4.05 thf(fact_4445_power__minus1__odd,axiom,
% 3.82/4.05 ! [N2: nat] :
% 3.82/4.05 ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 3.82/4.05 = ( uminus_uminus_int @ one_one_int ) ) ).
% 3.82/4.05
% 3.82/4.05 % power_minus1_odd
% 3.82/4.05 thf(fact_4446_power__minus1__odd,axiom,
% 3.82/4.05 ! [N2: nat] :
% 3.82/4.05 ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 3.82/4.05 = ( uminus_uminus_real @ one_one_real ) ) ).
% 3.82/4.05
% 3.82/4.05 % power_minus1_odd
% 3.82/4.05 thf(fact_4447_take__bit__Suc,axiom,
% 3.82/4.05 ! [N2: nat,A: nat] :
% 3.82/4.05 ( ( bit_se2925701944663578781it_nat @ ( suc @ N2 ) @ A )
% 3.82/4.05 = ( 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 ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % take_bit_Suc
% 3.82/4.05 thf(fact_4448_take__bit__Suc,axiom,
% 3.82/4.05 ! [N2: nat,A: int] :
% 3.82/4.05 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ A )
% 3.82/4.05 = ( 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 ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % take_bit_Suc
% 3.82/4.05 thf(fact_4449_stable__imp__take__bit__eq,axiom,
% 3.82/4.05 ! [A: nat,N2: nat] :
% 3.82/4.05 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.05 = A )
% 3.82/4.05 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 3.82/4.05 => ( ( bit_se2925701944663578781it_nat @ N2 @ A )
% 3.82/4.05 = zero_zero_nat ) )
% 3.82/4.05 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 3.82/4.05 => ( ( bit_se2925701944663578781it_nat @ N2 @ A )
% 3.82/4.05 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % stable_imp_take_bit_eq
% 3.82/4.05 thf(fact_4450_stable__imp__take__bit__eq,axiom,
% 3.82/4.05 ! [A: int,N2: nat] :
% 3.82/4.05 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 3.82/4.05 = A )
% 3.82/4.05 => ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 3.82/4.05 => ( ( bit_se2923211474154528505it_int @ N2 @ A )
% 3.82/4.05 = zero_zero_int ) )
% 3.82/4.05 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 3.82/4.05 => ( ( bit_se2923211474154528505it_int @ N2 @ A )
% 3.82/4.05 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % stable_imp_take_bit_eq
% 3.82/4.05 thf(fact_4451_mod__exhaust__less__4,axiom,
% 3.82/4.05 ! [M2: nat] :
% 3.82/4.05 ( ( ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 3.82/4.05 = zero_zero_nat )
% 3.82/4.05 | ( ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 3.82/4.05 = one_one_nat )
% 3.82/4.05 | ( ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 3.82/4.05 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.05 | ( ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 3.82/4.05 = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % mod_exhaust_less_4
% 3.82/4.05 thf(fact_4452_divmod__algorithm__code_I8_J,axiom,
% 3.82/4.05 ! [M2: num,N2: num] :
% 3.82/4.05 ( ( ( ord_less_num @ M2 @ N2 )
% 3.82/4.05 => ( ( unique5052692396658037445od_int @ ( bit1 @ M2 ) @ ( bit1 @ N2 ) )
% 3.82/4.05 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit1 @ M2 ) ) ) ) )
% 3.82/4.05 & ( ~ ( ord_less_num @ M2 @ N2 )
% 3.82/4.05 => ( ( unique5052692396658037445od_int @ ( bit1 @ M2 ) @ ( bit1 @ N2 ) )
% 3.82/4.05 = ( unique5024387138958732305ep_int @ ( bit1 @ N2 ) @ ( unique5052692396658037445od_int @ ( bit1 @ M2 ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % divmod_algorithm_code(8)
% 3.82/4.05 thf(fact_4453_divmod__algorithm__code_I8_J,axiom,
% 3.82/4.05 ! [M2: num,N2: num] :
% 3.82/4.05 ( ( ( ord_less_num @ M2 @ N2 )
% 3.82/4.05 => ( ( unique5055182867167087721od_nat @ ( bit1 @ M2 ) @ ( bit1 @ N2 ) )
% 3.82/4.05 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit1 @ M2 ) ) ) ) )
% 3.82/4.05 & ( ~ ( ord_less_num @ M2 @ N2 )
% 3.82/4.05 => ( ( unique5055182867167087721od_nat @ ( bit1 @ M2 ) @ ( bit1 @ N2 ) )
% 3.82/4.05 = ( unique5026877609467782581ep_nat @ ( bit1 @ N2 ) @ ( unique5055182867167087721od_nat @ ( bit1 @ M2 ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % divmod_algorithm_code(8)
% 3.82/4.05 thf(fact_4454_divmod__algorithm__code_I7_J,axiom,
% 3.82/4.05 ! [M2: num,N2: num] :
% 3.82/4.05 ( ( ( ord_less_eq_num @ M2 @ N2 )
% 3.82/4.05 => ( ( unique5052692396658037445od_int @ ( bit0 @ M2 ) @ ( bit1 @ N2 ) )
% 3.82/4.05 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit0 @ M2 ) ) ) ) )
% 3.82/4.05 & ( ~ ( ord_less_eq_num @ M2 @ N2 )
% 3.82/4.05 => ( ( unique5052692396658037445od_int @ ( bit0 @ M2 ) @ ( bit1 @ N2 ) )
% 3.82/4.05 = ( unique5024387138958732305ep_int @ ( bit1 @ N2 ) @ ( unique5052692396658037445od_int @ ( bit0 @ M2 ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % divmod_algorithm_code(7)
% 3.82/4.05 thf(fact_4455_divmod__algorithm__code_I7_J,axiom,
% 3.82/4.05 ! [M2: num,N2: num] :
% 3.82/4.05 ( ( ( ord_less_eq_num @ M2 @ N2 )
% 3.82/4.05 => ( ( unique5055182867167087721od_nat @ ( bit0 @ M2 ) @ ( bit1 @ N2 ) )
% 3.82/4.05 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ M2 ) ) ) ) )
% 3.82/4.05 & ( ~ ( ord_less_eq_num @ M2 @ N2 )
% 3.82/4.05 => ( ( unique5055182867167087721od_nat @ ( bit0 @ M2 ) @ ( bit1 @ N2 ) )
% 3.82/4.05 = ( unique5026877609467782581ep_nat @ ( bit1 @ N2 ) @ ( unique5055182867167087721od_nat @ ( bit0 @ M2 ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % divmod_algorithm_code(7)
% 3.82/4.05 thf(fact_4456_divmod__step__def,axiom,
% 3.82/4.05 ( unique5024387138958732305ep_int
% 3.82/4.05 = ( ^ [L2: num] :
% 3.82/4.05 ( produc4245557441103728435nt_int
% 3.82/4.05 @ ^ [Q5: int,R4: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ R4 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q5 ) @ one_one_int ) @ ( minus_minus_int @ R4 @ ( numeral_numeral_int @ L2 ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q5 ) @ R4 ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % divmod_step_def
% 3.82/4.05 thf(fact_4457_divmod__step__def,axiom,
% 3.82/4.05 ( unique5026877609467782581ep_nat
% 3.82/4.05 = ( ^ [L2: num] :
% 3.82/4.05 ( produc2626176000494625587at_nat
% 3.82/4.05 @ ^ [Q5: nat,R4: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R4 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ one_one_nat ) @ ( minus_minus_nat @ R4 @ ( numeral_numeral_nat @ L2 ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ R4 ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % divmod_step_def
% 3.82/4.05 thf(fact_4458_take__bit__numeral__bit1,axiom,
% 3.82/4.05 ! [L: num,K: num] :
% 3.82/4.05 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 3.82/4.05 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 3.82/4.05
% 3.82/4.05 % take_bit_numeral_bit1
% 3.82/4.05 thf(fact_4459_take__bit__numeral__bit1,axiom,
% 3.82/4.05 ! [L: num,K: num] :
% 3.82/4.05 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 3.82/4.05 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 3.82/4.05
% 3.82/4.05 % take_bit_numeral_bit1
% 3.82/4.05 thf(fact_4460_divmod__divmod__step,axiom,
% 3.82/4.05 ( unique5052692396658037445od_int
% 3.82/4.05 = ( ^ [M: num,N: num] : ( if_Pro3027730157355071871nt_int @ ( ord_less_num @ M @ N ) @ ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ M ) ) @ ( unique5024387138958732305ep_int @ N @ ( unique5052692396658037445od_int @ M @ ( bit0 @ N ) ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % divmod_divmod_step
% 3.82/4.05 thf(fact_4461_divmod__divmod__step,axiom,
% 3.82/4.05 ( unique5055182867167087721od_nat
% 3.82/4.05 = ( ^ [M: num,N: num] : ( if_Pro6206227464963214023at_nat @ ( ord_less_num @ M @ N ) @ ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ M ) ) @ ( unique5026877609467782581ep_nat @ N @ ( unique5055182867167087721od_nat @ M @ ( bit0 @ N ) ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % divmod_divmod_step
% 3.82/4.05 thf(fact_4462_set__encode__insert,axiom,
% 3.82/4.05 ! [A2: set_nat,N2: nat] :
% 3.82/4.05 ( ( finite_finite_nat @ A2 )
% 3.82/4.05 => ( ~ ( member_nat @ N2 @ A2 )
% 3.82/4.05 => ( ( nat_set_encode @ ( insert_nat @ N2 @ A2 ) )
% 3.82/4.05 = ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ ( nat_set_encode @ A2 ) ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % set_encode_insert
% 3.82/4.05 thf(fact_4463_insert__absorb2,axiom,
% 3.82/4.05 ! [X: nat,A2: set_nat] :
% 3.82/4.05 ( ( insert_nat @ X @ ( insert_nat @ X @ A2 ) )
% 3.82/4.05 = ( insert_nat @ X @ A2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % insert_absorb2
% 3.82/4.05 thf(fact_4464_insert__absorb2,axiom,
% 3.82/4.05 ! [X: int,A2: set_int] :
% 3.82/4.05 ( ( insert_int @ X @ ( insert_int @ X @ A2 ) )
% 3.82/4.05 = ( insert_int @ X @ A2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % insert_absorb2
% 3.82/4.05 thf(fact_4465_insert__absorb2,axiom,
% 3.82/4.05 ! [X: real,A2: set_real] :
% 3.82/4.05 ( ( insert_real @ X @ ( insert_real @ X @ A2 ) )
% 3.82/4.05 = ( insert_real @ X @ A2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % insert_absorb2
% 3.82/4.05 thf(fact_4466_insert__iff,axiom,
% 3.82/4.05 ! [A: extended_enat,B2: extended_enat,A2: set_Extended_enat] :
% 3.82/4.05 ( ( member_Extended_enat @ A @ ( insert_Extended_enat @ B2 @ A2 ) )
% 3.82/4.05 = ( ( A = B2 )
% 3.82/4.05 | ( member_Extended_enat @ A @ A2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % insert_iff
% 3.82/4.05 thf(fact_4467_insert__iff,axiom,
% 3.82/4.05 ! [A: real,B2: real,A2: set_real] :
% 3.82/4.05 ( ( member_real @ A @ ( insert_real @ B2 @ A2 ) )
% 3.82/4.05 = ( ( A = B2 )
% 3.82/4.05 | ( member_real @ A @ A2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % insert_iff
% 3.82/4.05 thf(fact_4468_insert__iff,axiom,
% 3.82/4.05 ! [A: set_nat,B2: set_nat,A2: set_set_nat] :
% 3.82/4.05 ( ( member_set_nat @ A @ ( insert_set_nat @ B2 @ A2 ) )
% 3.82/4.05 = ( ( A = B2 )
% 3.82/4.05 | ( member_set_nat @ A @ A2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % insert_iff
% 3.82/4.05 thf(fact_4469_insert__iff,axiom,
% 3.82/4.05 ! [A: nat,B2: nat,A2: set_nat] :
% 3.82/4.05 ( ( member_nat @ A @ ( insert_nat @ B2 @ A2 ) )
% 3.82/4.05 = ( ( A = B2 )
% 3.82/4.05 | ( member_nat @ A @ A2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % insert_iff
% 3.82/4.05 thf(fact_4470_insert__iff,axiom,
% 3.82/4.05 ! [A: int,B2: int,A2: set_int] :
% 3.82/4.05 ( ( member_int @ A @ ( insert_int @ B2 @ A2 ) )
% 3.82/4.05 = ( ( A = B2 )
% 3.82/4.05 | ( member_int @ A @ A2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % insert_iff
% 3.82/4.05 thf(fact_4471_insertCI,axiom,
% 3.82/4.05 ! [A: extended_enat,B: set_Extended_enat,B2: extended_enat] :
% 3.82/4.05 ( ( ~ ( member_Extended_enat @ A @ B )
% 3.82/4.05 => ( A = B2 ) )
% 3.82/4.05 => ( member_Extended_enat @ A @ ( insert_Extended_enat @ B2 @ B ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % insertCI
% 3.82/4.05 thf(fact_4472_insertCI,axiom,
% 3.82/4.05 ! [A: real,B: set_real,B2: real] :
% 3.82/4.05 ( ( ~ ( member_real @ A @ B )
% 3.82/4.05 => ( A = B2 ) )
% 3.82/4.05 => ( member_real @ A @ ( insert_real @ B2 @ B ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % insertCI
% 3.82/4.05 thf(fact_4473_insertCI,axiom,
% 3.82/4.05 ! [A: set_nat,B: set_set_nat,B2: set_nat] :
% 3.82/4.05 ( ( ~ ( member_set_nat @ A @ B )
% 3.82/4.05 => ( A = B2 ) )
% 3.82/4.05 => ( member_set_nat @ A @ ( insert_set_nat @ B2 @ B ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % insertCI
% 3.82/4.05 thf(fact_4474_insertCI,axiom,
% 3.82/4.05 ! [A: nat,B: set_nat,B2: nat] :
% 3.82/4.05 ( ( ~ ( member_nat @ A @ B )
% 3.82/4.05 => ( A = B2 ) )
% 3.82/4.05 => ( member_nat @ A @ ( insert_nat @ B2 @ B ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % insertCI
% 3.82/4.05 thf(fact_4475_insertCI,axiom,
% 3.82/4.05 ! [A: int,B: set_int,B2: int] :
% 3.82/4.05 ( ( ~ ( member_int @ A @ B )
% 3.82/4.05 => ( A = B2 ) )
% 3.82/4.05 => ( member_int @ A @ ( insert_int @ B2 @ B ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % insertCI
% 3.82/4.05 thf(fact_4476_Diff__idemp,axiom,
% 3.82/4.05 ! [A2: set_nat,B: set_nat] :
% 3.82/4.05 ( ( minus_minus_set_nat @ ( minus_minus_set_nat @ A2 @ B ) @ B )
% 3.82/4.05 = ( minus_minus_set_nat @ A2 @ B ) ) ).
% 3.82/4.05
% 3.82/4.05 % Diff_idemp
% 3.82/4.05 thf(fact_4477_Diff__iff,axiom,
% 3.82/4.05 ! [C: extended_enat,A2: set_Extended_enat,B: set_Extended_enat] :
% 3.82/4.05 ( ( member_Extended_enat @ C @ ( minus_925952699566721837d_enat @ A2 @ B ) )
% 3.82/4.05 = ( ( member_Extended_enat @ C @ A2 )
% 3.82/4.05 & ~ ( member_Extended_enat @ C @ B ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % Diff_iff
% 3.82/4.05 thf(fact_4478_Diff__iff,axiom,
% 3.82/4.05 ! [C: real,A2: set_real,B: set_real] :
% 3.82/4.05 ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B ) )
% 3.82/4.05 = ( ( member_real @ C @ A2 )
% 3.82/4.05 & ~ ( member_real @ C @ B ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % Diff_iff
% 3.82/4.05 thf(fact_4479_Diff__iff,axiom,
% 3.82/4.05 ! [C: set_nat,A2: set_set_nat,B: set_set_nat] :
% 3.82/4.05 ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B ) )
% 3.82/4.05 = ( ( member_set_nat @ C @ A2 )
% 3.82/4.05 & ~ ( member_set_nat @ C @ B ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % Diff_iff
% 3.82/4.05 thf(fact_4480_Diff__iff,axiom,
% 3.82/4.05 ! [C: int,A2: set_int,B: set_int] :
% 3.82/4.05 ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B ) )
% 3.82/4.05 = ( ( member_int @ C @ A2 )
% 3.82/4.05 & ~ ( member_int @ C @ B ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % Diff_iff
% 3.82/4.05 thf(fact_4481_Diff__iff,axiom,
% 3.82/4.05 ! [C: nat,A2: set_nat,B: set_nat] :
% 3.82/4.05 ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B ) )
% 3.82/4.05 = ( ( member_nat @ C @ A2 )
% 3.82/4.05 & ~ ( member_nat @ C @ B ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % Diff_iff
% 3.82/4.05 thf(fact_4482_DiffI,axiom,
% 3.82/4.05 ! [C: extended_enat,A2: set_Extended_enat,B: set_Extended_enat] :
% 3.82/4.05 ( ( member_Extended_enat @ C @ A2 )
% 3.82/4.05 => ( ~ ( member_Extended_enat @ C @ B )
% 3.82/4.05 => ( member_Extended_enat @ C @ ( minus_925952699566721837d_enat @ A2 @ B ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % DiffI
% 3.82/4.05 thf(fact_4483_DiffI,axiom,
% 3.82/4.05 ! [C: real,A2: set_real,B: set_real] :
% 3.82/4.05 ( ( member_real @ C @ A2 )
% 3.82/4.05 => ( ~ ( member_real @ C @ B )
% 3.82/4.05 => ( member_real @ C @ ( minus_minus_set_real @ A2 @ B ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % DiffI
% 3.82/4.05 thf(fact_4484_DiffI,axiom,
% 3.82/4.05 ! [C: set_nat,A2: set_set_nat,B: set_set_nat] :
% 3.82/4.05 ( ( member_set_nat @ C @ A2 )
% 3.82/4.05 => ( ~ ( member_set_nat @ C @ B )
% 3.82/4.05 => ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % DiffI
% 3.82/4.05 thf(fact_4485_DiffI,axiom,
% 3.82/4.05 ! [C: int,A2: set_int,B: set_int] :
% 3.82/4.05 ( ( member_int @ C @ A2 )
% 3.82/4.05 => ( ~ ( member_int @ C @ B )
% 3.82/4.05 => ( member_int @ C @ ( minus_minus_set_int @ A2 @ B ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % DiffI
% 3.82/4.05 thf(fact_4486_DiffI,axiom,
% 3.82/4.05 ! [C: nat,A2: set_nat,B: set_nat] :
% 3.82/4.05 ( ( member_nat @ C @ A2 )
% 3.82/4.05 => ( ~ ( member_nat @ C @ B )
% 3.82/4.05 => ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B ) ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % DiffI
% 3.82/4.05 thf(fact_4487_ComplI,axiom,
% 3.82/4.05 ! [C: extended_enat,A2: set_Extended_enat] :
% 3.82/4.05 ( ~ ( member_Extended_enat @ C @ A2 )
% 3.82/4.05 => ( member_Extended_enat @ C @ ( uminus417252749190364093d_enat @ A2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % ComplI
% 3.82/4.05 thf(fact_4488_ComplI,axiom,
% 3.82/4.05 ! [C: real,A2: set_real] :
% 3.82/4.05 ( ~ ( member_real @ C @ A2 )
% 3.82/4.05 => ( member_real @ C @ ( uminus612125837232591019t_real @ A2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % ComplI
% 3.82/4.05 thf(fact_4489_ComplI,axiom,
% 3.82/4.05 ! [C: set_nat,A2: set_set_nat] :
% 3.82/4.05 ( ~ ( member_set_nat @ C @ A2 )
% 3.82/4.05 => ( member_set_nat @ C @ ( uminus613421341184616069et_nat @ A2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % ComplI
% 3.82/4.05 thf(fact_4490_ComplI,axiom,
% 3.82/4.05 ! [C: nat,A2: set_nat] :
% 3.82/4.05 ( ~ ( member_nat @ C @ A2 )
% 3.82/4.05 => ( member_nat @ C @ ( uminus5710092332889474511et_nat @ A2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % ComplI
% 3.82/4.05 thf(fact_4491_ComplI,axiom,
% 3.82/4.05 ! [C: int,A2: set_int] :
% 3.82/4.05 ( ~ ( member_int @ C @ A2 )
% 3.82/4.05 => ( member_int @ C @ ( uminus1532241313380277803et_int @ A2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % ComplI
% 3.82/4.05 thf(fact_4492_Compl__iff,axiom,
% 3.82/4.05 ! [C: extended_enat,A2: set_Extended_enat] :
% 3.82/4.05 ( ( member_Extended_enat @ C @ ( uminus417252749190364093d_enat @ A2 ) )
% 3.82/4.05 = ( ~ ( member_Extended_enat @ C @ A2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % Compl_iff
% 3.82/4.05 thf(fact_4493_Compl__iff,axiom,
% 3.82/4.05 ! [C: real,A2: set_real] :
% 3.82/4.05 ( ( member_real @ C @ ( uminus612125837232591019t_real @ A2 ) )
% 3.82/4.05 = ( ~ ( member_real @ C @ A2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % Compl_iff
% 3.82/4.05 thf(fact_4494_Compl__iff,axiom,
% 3.82/4.05 ! [C: set_nat,A2: set_set_nat] :
% 3.82/4.05 ( ( member_set_nat @ C @ ( uminus613421341184616069et_nat @ A2 ) )
% 3.82/4.05 = ( ~ ( member_set_nat @ C @ A2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % Compl_iff
% 3.82/4.05 thf(fact_4495_Compl__iff,axiom,
% 3.82/4.05 ! [C: nat,A2: set_nat] :
% 3.82/4.05 ( ( member_nat @ C @ ( uminus5710092332889474511et_nat @ A2 ) )
% 3.82/4.05 = ( ~ ( member_nat @ C @ A2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % Compl_iff
% 3.82/4.05 thf(fact_4496_Compl__iff,axiom,
% 3.82/4.05 ! [C: int,A2: set_int] :
% 3.82/4.05 ( ( member_int @ C @ ( uminus1532241313380277803et_int @ A2 ) )
% 3.82/4.05 = ( ~ ( member_int @ C @ A2 ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % Compl_iff
% 3.82/4.05 thf(fact_4497_finite__atLeastAtMost__int,axiom,
% 3.82/4.05 ! [L: int,U: int] : ( finite_finite_int @ ( set_or1266510415728281911st_int @ L @ U ) ) ).
% 3.82/4.05
% 3.82/4.05 % finite_atLeastAtMost_int
% 3.82/4.05 thf(fact_4498_singletonI,axiom,
% 3.82/4.05 ! [A: set_nat] : ( member_set_nat @ A @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) ).
% 3.82/4.05
% 3.82/4.05 % singletonI
% 3.82/4.05 thf(fact_4499_singletonI,axiom,
% 3.82/4.05 ! [A: extended_enat] : ( member_Extended_enat @ A @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) ).
% 3.82/4.05
% 3.82/4.05 % singletonI
% 3.82/4.05 thf(fact_4500_singletonI,axiom,
% 3.82/4.05 ! [A: real] : ( member_real @ A @ ( insert_real @ A @ bot_bot_set_real ) ) ).
% 3.82/4.05
% 3.82/4.05 % singletonI
% 3.82/4.05 thf(fact_4501_singletonI,axiom,
% 3.82/4.05 ! [A: nat] : ( member_nat @ A @ ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 3.82/4.05
% 3.82/4.05 % singletonI
% 3.82/4.05 thf(fact_4502_singletonI,axiom,
% 3.82/4.05 ! [A: int] : ( member_int @ A @ ( insert_int @ A @ bot_bot_set_int ) ) ).
% 3.82/4.05
% 3.82/4.05 % singletonI
% 3.82/4.05 thf(fact_4503_finite__insert,axiom,
% 3.82/4.05 ! [A: real,A2: set_real] :
% 3.82/4.05 ( ( finite_finite_real @ ( insert_real @ A @ A2 ) )
% 3.82/4.05 = ( finite_finite_real @ A2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % finite_insert
% 3.82/4.05 thf(fact_4504_finite__insert,axiom,
% 3.82/4.05 ! [A: nat,A2: set_nat] :
% 3.82/4.05 ( ( finite_finite_nat @ ( insert_nat @ A @ A2 ) )
% 3.82/4.05 = ( finite_finite_nat @ A2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % finite_insert
% 3.82/4.05 thf(fact_4505_finite__insert,axiom,
% 3.82/4.05 ! [A: complex,A2: set_complex] :
% 3.82/4.05 ( ( finite3207457112153483333omplex @ ( insert_complex @ A @ A2 ) )
% 3.82/4.05 = ( finite3207457112153483333omplex @ A2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % finite_insert
% 3.82/4.05 thf(fact_4506_finite__insert,axiom,
% 3.82/4.05 ! [A: int,A2: set_int] :
% 3.82/4.05 ( ( finite_finite_int @ ( insert_int @ A @ A2 ) )
% 3.82/4.05 = ( finite_finite_int @ A2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % finite_insert
% 3.82/4.05 thf(fact_4507_finite__insert,axiom,
% 3.82/4.05 ! [A: extended_enat,A2: set_Extended_enat] :
% 3.82/4.05 ( ( finite4001608067531595151d_enat @ ( insert_Extended_enat @ A @ A2 ) )
% 3.82/4.05 = ( finite4001608067531595151d_enat @ A2 ) ) ).
% 3.82/4.05
% 3.82/4.05 % finite_insert
% 3.82/4.05 thf(fact_4508_insert__subset,axiom,
% 3.82/4.05 ! [X: extended_enat,A2: set_Extended_enat,B: set_Extended_enat] :
% 3.82/4.05 ( ( ord_le7203529160286727270d_enat @ ( insert_Extended_enat @ X @ A2 ) @ B )
% 3.82/4.05 = ( ( member_Extended_enat @ X @ B )
% 3.82/4.05 & ( ord_le7203529160286727270d_enat @ A2 @ B ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % insert_subset
% 3.82/4.05 thf(fact_4509_insert__subset,axiom,
% 3.82/4.05 ! [X: real,A2: set_real,B: set_real] :
% 3.82/4.05 ( ( ord_less_eq_set_real @ ( insert_real @ X @ A2 ) @ B )
% 3.82/4.05 = ( ( member_real @ X @ B )
% 3.82/4.05 & ( ord_less_eq_set_real @ A2 @ B ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % insert_subset
% 3.82/4.05 thf(fact_4510_insert__subset,axiom,
% 3.82/4.05 ! [X: set_nat,A2: set_set_nat,B: set_set_nat] :
% 3.82/4.05 ( ( ord_le6893508408891458716et_nat @ ( insert_set_nat @ X @ A2 ) @ B )
% 3.82/4.05 = ( ( member_set_nat @ X @ B )
% 3.82/4.05 & ( ord_le6893508408891458716et_nat @ A2 @ B ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % insert_subset
% 3.82/4.05 thf(fact_4511_insert__subset,axiom,
% 3.82/4.05 ! [X: nat,A2: set_nat,B: set_nat] :
% 3.82/4.05 ( ( ord_less_eq_set_nat @ ( insert_nat @ X @ A2 ) @ B )
% 3.82/4.05 = ( ( member_nat @ X @ B )
% 3.82/4.05 & ( ord_less_eq_set_nat @ A2 @ B ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % insert_subset
% 3.82/4.05 thf(fact_4512_insert__subset,axiom,
% 3.82/4.05 ! [X: int,A2: set_int,B: set_int] :
% 3.82/4.05 ( ( ord_less_eq_set_int @ ( insert_int @ X @ A2 ) @ B )
% 3.82/4.05 = ( ( member_int @ X @ B )
% 3.82/4.05 & ( ord_less_eq_set_int @ A2 @ B ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % insert_subset
% 3.82/4.05 thf(fact_4513_insert__Diff1,axiom,
% 3.82/4.05 ! [X: extended_enat,B: set_Extended_enat,A2: set_Extended_enat] :
% 3.82/4.05 ( ( member_Extended_enat @ X @ B )
% 3.82/4.05 => ( ( minus_925952699566721837d_enat @ ( insert_Extended_enat @ X @ A2 ) @ B )
% 3.82/4.05 = ( minus_925952699566721837d_enat @ A2 @ B ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % insert_Diff1
% 3.82/4.05 thf(fact_4514_insert__Diff1,axiom,
% 3.82/4.05 ! [X: real,B: set_real,A2: set_real] :
% 3.82/4.05 ( ( member_real @ X @ B )
% 3.82/4.05 => ( ( minus_minus_set_real @ ( insert_real @ X @ A2 ) @ B )
% 3.82/4.05 = ( minus_minus_set_real @ A2 @ B ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % insert_Diff1
% 3.82/4.05 thf(fact_4515_insert__Diff1,axiom,
% 3.82/4.05 ! [X: set_nat,B: set_set_nat,A2: set_set_nat] :
% 3.82/4.05 ( ( member_set_nat @ X @ B )
% 3.82/4.05 => ( ( minus_2163939370556025621et_nat @ ( insert_set_nat @ X @ A2 ) @ B )
% 3.82/4.05 = ( minus_2163939370556025621et_nat @ A2 @ B ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % insert_Diff1
% 3.82/4.05 thf(fact_4516_insert__Diff1,axiom,
% 3.82/4.05 ! [X: int,B: set_int,A2: set_int] :
% 3.82/4.05 ( ( member_int @ X @ B )
% 3.82/4.05 => ( ( minus_minus_set_int @ ( insert_int @ X @ A2 ) @ B )
% 3.82/4.05 = ( minus_minus_set_int @ A2 @ B ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % insert_Diff1
% 3.82/4.05 thf(fact_4517_insert__Diff1,axiom,
% 3.82/4.05 ! [X: nat,B: set_nat,A2: set_nat] :
% 3.82/4.05 ( ( member_nat @ X @ B )
% 3.82/4.05 => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A2 ) @ B )
% 3.82/4.05 = ( minus_minus_set_nat @ A2 @ B ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % insert_Diff1
% 3.82/4.05 thf(fact_4518_Diff__insert0,axiom,
% 3.82/4.05 ! [X: extended_enat,A2: set_Extended_enat,B: set_Extended_enat] :
% 3.82/4.05 ( ~ ( member_Extended_enat @ X @ A2 )
% 3.82/4.05 => ( ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ X @ B ) )
% 3.82/4.05 = ( minus_925952699566721837d_enat @ A2 @ B ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % Diff_insert0
% 3.82/4.05 thf(fact_4519_Diff__insert0,axiom,
% 3.82/4.05 ! [X: real,A2: set_real,B: set_real] :
% 3.82/4.05 ( ~ ( member_real @ X @ A2 )
% 3.82/4.05 => ( ( minus_minus_set_real @ A2 @ ( insert_real @ X @ B ) )
% 3.82/4.05 = ( minus_minus_set_real @ A2 @ B ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % Diff_insert0
% 3.82/4.05 thf(fact_4520_Diff__insert0,axiom,
% 3.82/4.05 ! [X: set_nat,A2: set_set_nat,B: set_set_nat] :
% 3.82/4.05 ( ~ ( member_set_nat @ X @ A2 )
% 3.82/4.05 => ( ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ X @ B ) )
% 3.82/4.05 = ( minus_2163939370556025621et_nat @ A2 @ B ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % Diff_insert0
% 3.82/4.05 thf(fact_4521_Diff__insert0,axiom,
% 3.82/4.05 ! [X: int,A2: set_int,B: set_int] :
% 3.82/4.05 ( ~ ( member_int @ X @ A2 )
% 3.82/4.05 => ( ( minus_minus_set_int @ A2 @ ( insert_int @ X @ B ) )
% 3.82/4.05 = ( minus_minus_set_int @ A2 @ B ) ) ) ).
% 3.82/4.05
% 3.82/4.05 % Diff_insert0
% 3.82/4.05 thf(fact_4522_Diff__insert0,axiom,
% 3.82/4.06 ! [X: nat,A2: set_nat,B: set_nat] :
% 3.82/4.06 ( ~ ( member_nat @ X @ A2 )
% 3.82/4.06 => ( ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ B ) )
% 3.82/4.06 = ( minus_minus_set_nat @ A2 @ B ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % Diff_insert0
% 3.82/4.06 thf(fact_4523_singleton__conv,axiom,
% 3.82/4.06 ! [A: list_nat] :
% 3.82/4.06 ( ( collect_list_nat
% 3.82/4.06 @ ^ [X4: list_nat] : ( X4 = A ) )
% 3.82/4.06 = ( insert_list_nat @ A @ bot_bot_set_list_nat ) ) ).
% 3.82/4.06
% 3.82/4.06 % singleton_conv
% 3.82/4.06 thf(fact_4524_singleton__conv,axiom,
% 3.82/4.06 ! [A: set_nat] :
% 3.82/4.06 ( ( collect_set_nat
% 3.82/4.06 @ ^ [X4: set_nat] : ( X4 = A ) )
% 3.82/4.06 = ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) ).
% 3.82/4.06
% 3.82/4.06 % singleton_conv
% 3.82/4.06 thf(fact_4525_singleton__conv,axiom,
% 3.82/4.06 ! [A: extended_enat] :
% 3.82/4.06 ( ( collec4429806609662206161d_enat
% 3.82/4.06 @ ^ [X4: extended_enat] : ( X4 = A ) )
% 3.82/4.06 = ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) ).
% 3.82/4.06
% 3.82/4.06 % singleton_conv
% 3.82/4.06 thf(fact_4526_singleton__conv,axiom,
% 3.82/4.06 ! [A: real] :
% 3.82/4.06 ( ( collect_real
% 3.82/4.06 @ ^ [X4: real] : ( X4 = A ) )
% 3.82/4.06 = ( insert_real @ A @ bot_bot_set_real ) ) ).
% 3.82/4.06
% 3.82/4.06 % singleton_conv
% 3.82/4.06 thf(fact_4527_singleton__conv,axiom,
% 3.82/4.06 ! [A: nat] :
% 3.82/4.06 ( ( collect_nat
% 3.82/4.06 @ ^ [X4: nat] : ( X4 = A ) )
% 3.82/4.06 = ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 3.82/4.06
% 3.82/4.06 % singleton_conv
% 3.82/4.06 thf(fact_4528_singleton__conv,axiom,
% 3.82/4.06 ! [A: int] :
% 3.82/4.06 ( ( collect_int
% 3.82/4.06 @ ^ [X4: int] : ( X4 = A ) )
% 3.82/4.06 = ( insert_int @ A @ bot_bot_set_int ) ) ).
% 3.82/4.06
% 3.82/4.06 % singleton_conv
% 3.82/4.06 thf(fact_4529_singleton__conv2,axiom,
% 3.82/4.06 ! [A: list_nat] :
% 3.82/4.06 ( ( collect_list_nat
% 3.82/4.06 @ ( ^ [Y4: list_nat,Z2: list_nat] : ( Y4 = Z2 )
% 3.82/4.06 @ A ) )
% 3.82/4.06 = ( insert_list_nat @ A @ bot_bot_set_list_nat ) ) ).
% 3.82/4.06
% 3.82/4.06 % singleton_conv2
% 3.82/4.06 thf(fact_4530_singleton__conv2,axiom,
% 3.82/4.06 ! [A: set_nat] :
% 3.82/4.06 ( ( collect_set_nat
% 3.82/4.06 @ ( ^ [Y4: set_nat,Z2: set_nat] : ( Y4 = Z2 )
% 3.82/4.06 @ A ) )
% 3.82/4.06 = ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) ).
% 3.82/4.06
% 3.82/4.06 % singleton_conv2
% 3.82/4.06 thf(fact_4531_singleton__conv2,axiom,
% 3.82/4.06 ! [A: extended_enat] :
% 3.82/4.06 ( ( collec4429806609662206161d_enat
% 3.82/4.06 @ ( ^ [Y4: extended_enat,Z2: extended_enat] : ( Y4 = Z2 )
% 3.82/4.06 @ A ) )
% 3.82/4.06 = ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) ).
% 3.82/4.06
% 3.82/4.06 % singleton_conv2
% 3.82/4.06 thf(fact_4532_singleton__conv2,axiom,
% 3.82/4.06 ! [A: real] :
% 3.82/4.06 ( ( collect_real
% 3.82/4.06 @ ( ^ [Y4: real,Z2: real] : ( Y4 = Z2 )
% 3.82/4.06 @ A ) )
% 3.82/4.06 = ( insert_real @ A @ bot_bot_set_real ) ) ).
% 3.82/4.06
% 3.82/4.06 % singleton_conv2
% 3.82/4.06 thf(fact_4533_singleton__conv2,axiom,
% 3.82/4.06 ! [A: nat] :
% 3.82/4.06 ( ( collect_nat
% 3.82/4.06 @ ( ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 3.82/4.06 @ A ) )
% 3.82/4.06 = ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 3.82/4.06
% 3.82/4.06 % singleton_conv2
% 3.82/4.06 thf(fact_4534_singleton__conv2,axiom,
% 3.82/4.06 ! [A: int] :
% 3.82/4.06 ( ( collect_int
% 3.82/4.06 @ ( ^ [Y4: int,Z2: int] : ( Y4 = Z2 )
% 3.82/4.06 @ A ) )
% 3.82/4.06 = ( insert_int @ A @ bot_bot_set_int ) ) ).
% 3.82/4.06
% 3.82/4.06 % singleton_conv2
% 3.82/4.06 thf(fact_4535_finite__interval__int1,axiom,
% 3.82/4.06 ! [A: int,B2: int] :
% 3.82/4.06 ( finite_finite_int
% 3.82/4.06 @ ( collect_int
% 3.82/4.06 @ ^ [I3: int] :
% 3.82/4.06 ( ( ord_less_eq_int @ A @ I3 )
% 3.82/4.06 & ( ord_less_eq_int @ I3 @ B2 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_interval_int1
% 3.82/4.06 thf(fact_4536_singleton__insert__inj__eq_H,axiom,
% 3.82/4.06 ! [A: extended_enat,A2: set_Extended_enat,B2: extended_enat] :
% 3.82/4.06 ( ( ( insert_Extended_enat @ A @ A2 )
% 3.82/4.06 = ( insert_Extended_enat @ B2 @ bot_bo7653980558646680370d_enat ) )
% 3.82/4.06 = ( ( A = B2 )
% 3.82/4.06 & ( ord_le7203529160286727270d_enat @ A2 @ ( insert_Extended_enat @ B2 @ bot_bo7653980558646680370d_enat ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % singleton_insert_inj_eq'
% 3.82/4.06 thf(fact_4537_singleton__insert__inj__eq_H,axiom,
% 3.82/4.06 ! [A: real,A2: set_real,B2: real] :
% 3.82/4.06 ( ( ( insert_real @ A @ A2 )
% 3.82/4.06 = ( insert_real @ B2 @ bot_bot_set_real ) )
% 3.82/4.06 = ( ( A = B2 )
% 3.82/4.06 & ( ord_less_eq_set_real @ A2 @ ( insert_real @ B2 @ bot_bot_set_real ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % singleton_insert_inj_eq'
% 3.82/4.06 thf(fact_4538_singleton__insert__inj__eq_H,axiom,
% 3.82/4.06 ! [A: nat,A2: set_nat,B2: nat] :
% 3.82/4.06 ( ( ( insert_nat @ A @ A2 )
% 3.82/4.06 = ( insert_nat @ B2 @ bot_bot_set_nat ) )
% 3.82/4.06 = ( ( A = B2 )
% 3.82/4.06 & ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ B2 @ bot_bot_set_nat ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % singleton_insert_inj_eq'
% 3.82/4.06 thf(fact_4539_singleton__insert__inj__eq_H,axiom,
% 3.82/4.06 ! [A: int,A2: set_int,B2: int] :
% 3.82/4.06 ( ( ( insert_int @ A @ A2 )
% 3.82/4.06 = ( insert_int @ B2 @ bot_bot_set_int ) )
% 3.82/4.06 = ( ( A = B2 )
% 3.82/4.06 & ( ord_less_eq_set_int @ A2 @ ( insert_int @ B2 @ bot_bot_set_int ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % singleton_insert_inj_eq'
% 3.82/4.06 thf(fact_4540_singleton__insert__inj__eq,axiom,
% 3.82/4.06 ! [B2: extended_enat,A: extended_enat,A2: set_Extended_enat] :
% 3.82/4.06 ( ( ( insert_Extended_enat @ B2 @ bot_bo7653980558646680370d_enat )
% 3.82/4.06 = ( insert_Extended_enat @ A @ A2 ) )
% 3.82/4.06 = ( ( A = B2 )
% 3.82/4.06 & ( ord_le7203529160286727270d_enat @ A2 @ ( insert_Extended_enat @ B2 @ bot_bo7653980558646680370d_enat ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % singleton_insert_inj_eq
% 3.82/4.06 thf(fact_4541_singleton__insert__inj__eq,axiom,
% 3.82/4.06 ! [B2: real,A: real,A2: set_real] :
% 3.82/4.06 ( ( ( insert_real @ B2 @ bot_bot_set_real )
% 3.82/4.06 = ( insert_real @ A @ A2 ) )
% 3.82/4.06 = ( ( A = B2 )
% 3.82/4.06 & ( ord_less_eq_set_real @ A2 @ ( insert_real @ B2 @ bot_bot_set_real ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % singleton_insert_inj_eq
% 3.82/4.06 thf(fact_4542_singleton__insert__inj__eq,axiom,
% 3.82/4.06 ! [B2: nat,A: nat,A2: set_nat] :
% 3.82/4.06 ( ( ( insert_nat @ B2 @ bot_bot_set_nat )
% 3.82/4.06 = ( insert_nat @ A @ A2 ) )
% 3.82/4.06 = ( ( A = B2 )
% 3.82/4.06 & ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ B2 @ bot_bot_set_nat ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % singleton_insert_inj_eq
% 3.82/4.06 thf(fact_4543_singleton__insert__inj__eq,axiom,
% 3.82/4.06 ! [B2: int,A: int,A2: set_int] :
% 3.82/4.06 ( ( ( insert_int @ B2 @ bot_bot_set_int )
% 3.82/4.06 = ( insert_int @ A @ A2 ) )
% 3.82/4.06 = ( ( A = B2 )
% 3.82/4.06 & ( ord_less_eq_set_int @ A2 @ ( insert_int @ B2 @ bot_bot_set_int ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % singleton_insert_inj_eq
% 3.82/4.06 thf(fact_4544_atLeastAtMost__singleton__iff,axiom,
% 3.82/4.06 ! [A: extended_enat,B2: extended_enat,C: extended_enat] :
% 3.82/4.06 ( ( ( set_or5403411693681687835d_enat @ A @ B2 )
% 3.82/4.06 = ( insert_Extended_enat @ C @ bot_bo7653980558646680370d_enat ) )
% 3.82/4.06 = ( ( A = B2 )
% 3.82/4.06 & ( B2 = C ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % atLeastAtMost_singleton_iff
% 3.82/4.06 thf(fact_4545_atLeastAtMost__singleton__iff,axiom,
% 3.82/4.06 ! [A: nat,B2: nat,C: nat] :
% 3.82/4.06 ( ( ( set_or1269000886237332187st_nat @ A @ B2 )
% 3.82/4.06 = ( insert_nat @ C @ bot_bot_set_nat ) )
% 3.82/4.06 = ( ( A = B2 )
% 3.82/4.06 & ( B2 = C ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % atLeastAtMost_singleton_iff
% 3.82/4.06 thf(fact_4546_atLeastAtMost__singleton__iff,axiom,
% 3.82/4.06 ! [A: int,B2: int,C: int] :
% 3.82/4.06 ( ( ( set_or1266510415728281911st_int @ A @ B2 )
% 3.82/4.06 = ( insert_int @ C @ bot_bot_set_int ) )
% 3.82/4.06 = ( ( A = B2 )
% 3.82/4.06 & ( B2 = C ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % atLeastAtMost_singleton_iff
% 3.82/4.06 thf(fact_4547_atLeastAtMost__singleton__iff,axiom,
% 3.82/4.06 ! [A: real,B2: real,C: real] :
% 3.82/4.06 ( ( ( set_or1222579329274155063t_real @ A @ B2 )
% 3.82/4.06 = ( insert_real @ C @ bot_bot_set_real ) )
% 3.82/4.06 = ( ( A = B2 )
% 3.82/4.06 & ( B2 = C ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % atLeastAtMost_singleton_iff
% 3.82/4.06 thf(fact_4548_atLeastAtMost__singleton,axiom,
% 3.82/4.06 ! [A: extended_enat] :
% 3.82/4.06 ( ( set_or5403411693681687835d_enat @ A @ A )
% 3.82/4.06 = ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) ).
% 3.82/4.06
% 3.82/4.06 % atLeastAtMost_singleton
% 3.82/4.06 thf(fact_4549_atLeastAtMost__singleton,axiom,
% 3.82/4.06 ! [A: nat] :
% 3.82/4.06 ( ( set_or1269000886237332187st_nat @ A @ A )
% 3.82/4.06 = ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 3.82/4.06
% 3.82/4.06 % atLeastAtMost_singleton
% 3.82/4.06 thf(fact_4550_atLeastAtMost__singleton,axiom,
% 3.82/4.06 ! [A: int] :
% 3.82/4.06 ( ( set_or1266510415728281911st_int @ A @ A )
% 3.82/4.06 = ( insert_int @ A @ bot_bot_set_int ) ) ).
% 3.82/4.06
% 3.82/4.06 % atLeastAtMost_singleton
% 3.82/4.06 thf(fact_4551_atLeastAtMost__singleton,axiom,
% 3.82/4.06 ! [A: real] :
% 3.82/4.06 ( ( set_or1222579329274155063t_real @ A @ A )
% 3.82/4.06 = ( insert_real @ A @ bot_bot_set_real ) ) ).
% 3.82/4.06
% 3.82/4.06 % atLeastAtMost_singleton
% 3.82/4.06 thf(fact_4552_insert__Diff__single,axiom,
% 3.82/4.06 ! [A: extended_enat,A2: set_Extended_enat] :
% 3.82/4.06 ( ( insert_Extended_enat @ A @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) )
% 3.82/4.06 = ( insert_Extended_enat @ A @ A2 ) ) ).
% 3.82/4.06
% 3.82/4.06 % insert_Diff_single
% 3.82/4.06 thf(fact_4553_insert__Diff__single,axiom,
% 3.82/4.06 ! [A: real,A2: set_real] :
% 3.82/4.06 ( ( insert_real @ A @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 3.82/4.06 = ( insert_real @ A @ A2 ) ) ).
% 3.82/4.06
% 3.82/4.06 % insert_Diff_single
% 3.82/4.06 thf(fact_4554_insert__Diff__single,axiom,
% 3.82/4.06 ! [A: int,A2: set_int] :
% 3.82/4.06 ( ( insert_int @ A @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 3.82/4.06 = ( insert_int @ A @ A2 ) ) ).
% 3.82/4.06
% 3.82/4.06 % insert_Diff_single
% 3.82/4.06 thf(fact_4555_insert__Diff__single,axiom,
% 3.82/4.06 ! [A: nat,A2: set_nat] :
% 3.82/4.06 ( ( insert_nat @ A @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 3.82/4.06 = ( insert_nat @ A @ A2 ) ) ).
% 3.82/4.06
% 3.82/4.06 % insert_Diff_single
% 3.82/4.06 thf(fact_4556_finite__Diff__insert,axiom,
% 3.82/4.06 ! [A2: set_real,A: real,B: set_real] :
% 3.82/4.06 ( ( finite_finite_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ B ) ) )
% 3.82/4.06 = ( finite_finite_real @ ( minus_minus_set_real @ A2 @ B ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_Diff_insert
% 3.82/4.06 thf(fact_4557_finite__Diff__insert,axiom,
% 3.82/4.06 ! [A2: set_complex,A: complex,B: set_complex] :
% 3.82/4.06 ( ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ B ) ) )
% 3.82/4.06 = ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A2 @ B ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_Diff_insert
% 3.82/4.06 thf(fact_4558_finite__Diff__insert,axiom,
% 3.82/4.06 ! [A2: set_int,A: int,B: set_int] :
% 3.82/4.06 ( ( finite_finite_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ B ) ) )
% 3.82/4.06 = ( finite_finite_int @ ( minus_minus_set_int @ A2 @ B ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_Diff_insert
% 3.82/4.06 thf(fact_4559_finite__Diff__insert,axiom,
% 3.82/4.06 ! [A2: set_Extended_enat,A: extended_enat,B: set_Extended_enat] :
% 3.82/4.06 ( ( finite4001608067531595151d_enat @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ A @ B ) ) )
% 3.82/4.06 = ( finite4001608067531595151d_enat @ ( minus_925952699566721837d_enat @ A2 @ B ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_Diff_insert
% 3.82/4.06 thf(fact_4560_finite__Diff__insert,axiom,
% 3.82/4.06 ! [A2: set_nat,A: nat,B: set_nat] :
% 3.82/4.06 ( ( finite_finite_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ B ) ) )
% 3.82/4.06 = ( finite_finite_nat @ ( minus_minus_set_nat @ A2 @ B ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_Diff_insert
% 3.82/4.06 thf(fact_4561_pred__numeral__simps_I1_J,axiom,
% 3.82/4.06 ( ( pred_numeral @ one )
% 3.82/4.06 = zero_zero_nat ) ).
% 3.82/4.06
% 3.82/4.06 % pred_numeral_simps(1)
% 3.82/4.06 thf(fact_4562_eq__numeral__Suc,axiom,
% 3.82/4.06 ! [K: num,N2: nat] :
% 3.82/4.06 ( ( ( numeral_numeral_nat @ K )
% 3.82/4.06 = ( suc @ N2 ) )
% 3.82/4.06 = ( ( pred_numeral @ K )
% 3.82/4.06 = N2 ) ) ).
% 3.82/4.06
% 3.82/4.06 % eq_numeral_Suc
% 3.82/4.06 thf(fact_4563_Suc__eq__numeral,axiom,
% 3.82/4.06 ! [N2: nat,K: num] :
% 3.82/4.06 ( ( ( suc @ N2 )
% 3.82/4.06 = ( numeral_numeral_nat @ K ) )
% 3.82/4.06 = ( N2
% 3.82/4.06 = ( pred_numeral @ K ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % Suc_eq_numeral
% 3.82/4.06 thf(fact_4564_subset__Compl__singleton,axiom,
% 3.82/4.06 ! [A2: set_set_nat,B2: set_nat] :
% 3.82/4.06 ( ( ord_le6893508408891458716et_nat @ A2 @ ( uminus613421341184616069et_nat @ ( insert_set_nat @ B2 @ bot_bot_set_set_nat ) ) )
% 3.82/4.06 = ( ~ ( member_set_nat @ B2 @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % subset_Compl_singleton
% 3.82/4.06 thf(fact_4565_subset__Compl__singleton,axiom,
% 3.82/4.06 ! [A2: set_Extended_enat,B2: extended_enat] :
% 3.82/4.06 ( ( ord_le7203529160286727270d_enat @ A2 @ ( uminus417252749190364093d_enat @ ( insert_Extended_enat @ B2 @ bot_bo7653980558646680370d_enat ) ) )
% 3.82/4.06 = ( ~ ( member_Extended_enat @ B2 @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % subset_Compl_singleton
% 3.82/4.06 thf(fact_4566_subset__Compl__singleton,axiom,
% 3.82/4.06 ! [A2: set_real,B2: real] :
% 3.82/4.06 ( ( ord_less_eq_set_real @ A2 @ ( uminus612125837232591019t_real @ ( insert_real @ B2 @ bot_bot_set_real ) ) )
% 3.82/4.06 = ( ~ ( member_real @ B2 @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % subset_Compl_singleton
% 3.82/4.06 thf(fact_4567_subset__Compl__singleton,axiom,
% 3.82/4.06 ! [A2: set_nat,B2: nat] :
% 3.82/4.06 ( ( ord_less_eq_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ ( insert_nat @ B2 @ bot_bot_set_nat ) ) )
% 3.82/4.06 = ( ~ ( member_nat @ B2 @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % subset_Compl_singleton
% 3.82/4.06 thf(fact_4568_subset__Compl__singleton,axiom,
% 3.82/4.06 ! [A2: set_int,B2: int] :
% 3.82/4.06 ( ( ord_less_eq_set_int @ A2 @ ( uminus1532241313380277803et_int @ ( insert_int @ B2 @ bot_bot_set_int ) ) )
% 3.82/4.06 = ( ~ ( member_int @ B2 @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % subset_Compl_singleton
% 3.82/4.06 thf(fact_4569_less__numeral__Suc,axiom,
% 3.82/4.06 ! [K: num,N2: nat] :
% 3.82/4.06 ( ( ord_less_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N2 ) )
% 3.82/4.06 = ( ord_less_nat @ ( pred_numeral @ K ) @ N2 ) ) ).
% 3.82/4.06
% 3.82/4.06 % less_numeral_Suc
% 3.82/4.06 thf(fact_4570_less__Suc__numeral,axiom,
% 3.82/4.06 ! [N2: nat,K: num] :
% 3.82/4.06 ( ( ord_less_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 3.82/4.06 = ( ord_less_nat @ N2 @ ( pred_numeral @ K ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % less_Suc_numeral
% 3.82/4.06 thf(fact_4571_le__numeral__Suc,axiom,
% 3.82/4.06 ! [K: num,N2: nat] :
% 3.82/4.06 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N2 ) )
% 3.82/4.06 = ( ord_less_eq_nat @ ( pred_numeral @ K ) @ N2 ) ) ).
% 3.82/4.06
% 3.82/4.06 % le_numeral_Suc
% 3.82/4.06 thf(fact_4572_le__Suc__numeral,axiom,
% 3.82/4.06 ! [N2: nat,K: num] :
% 3.82/4.06 ( ( ord_less_eq_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 3.82/4.06 = ( ord_less_eq_nat @ N2 @ ( pred_numeral @ K ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % le_Suc_numeral
% 3.82/4.06 thf(fact_4573_diff__Suc__numeral,axiom,
% 3.82/4.06 ! [N2: nat,K: num] :
% 3.82/4.06 ( ( minus_minus_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 3.82/4.06 = ( minus_minus_nat @ N2 @ ( pred_numeral @ K ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % diff_Suc_numeral
% 3.82/4.06 thf(fact_4574_diff__numeral__Suc,axiom,
% 3.82/4.06 ! [K: num,N2: nat] :
% 3.82/4.06 ( ( minus_minus_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N2 ) )
% 3.82/4.06 = ( minus_minus_nat @ ( pred_numeral @ K ) @ N2 ) ) ).
% 3.82/4.06
% 3.82/4.06 % diff_numeral_Suc
% 3.82/4.06 thf(fact_4575_max__Suc__numeral,axiom,
% 3.82/4.06 ! [N2: nat,K: num] :
% 3.82/4.06 ( ( ord_max_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 3.82/4.06 = ( suc @ ( ord_max_nat @ N2 @ ( pred_numeral @ K ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % max_Suc_numeral
% 3.82/4.06 thf(fact_4576_max__numeral__Suc,axiom,
% 3.82/4.06 ! [K: num,N2: nat] :
% 3.82/4.06 ( ( ord_max_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N2 ) )
% 3.82/4.06 = ( suc @ ( ord_max_nat @ ( pred_numeral @ K ) @ N2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % max_numeral_Suc
% 3.82/4.06 thf(fact_4577_divmod__algorithm__code_I2_J,axiom,
% 3.82/4.06 ! [M2: num] :
% 3.82/4.06 ( ( unique5052692396658037445od_int @ M2 @ one )
% 3.82/4.06 = ( product_Pair_int_int @ ( numeral_numeral_int @ M2 ) @ zero_zero_int ) ) ).
% 3.82/4.06
% 3.82/4.06 % divmod_algorithm_code(2)
% 3.82/4.06 thf(fact_4578_divmod__algorithm__code_I2_J,axiom,
% 3.82/4.06 ! [M2: num] :
% 3.82/4.06 ( ( unique5055182867167087721od_nat @ M2 @ one )
% 3.82/4.06 = ( product_Pair_nat_nat @ ( numeral_numeral_nat @ M2 ) @ zero_zero_nat ) ) ).
% 3.82/4.06
% 3.82/4.06 % divmod_algorithm_code(2)
% 3.82/4.06 thf(fact_4579_set__replicate,axiom,
% 3.82/4.06 ! [N2: nat,X: vEBT_VEBT] :
% 3.82/4.06 ( ( N2 != zero_zero_nat )
% 3.82/4.06 => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N2 @ X ) )
% 3.82/4.06 = ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % set_replicate
% 3.82/4.06 thf(fact_4580_set__replicate,axiom,
% 3.82/4.06 ! [N2: nat,X: extended_enat] :
% 3.82/4.06 ( ( N2 != zero_zero_nat )
% 3.82/4.06 => ( ( set_Extended_enat2 @ ( replic7216382294607269926d_enat @ N2 @ X ) )
% 3.82/4.06 = ( insert_Extended_enat @ X @ bot_bo7653980558646680370d_enat ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % set_replicate
% 3.82/4.06 thf(fact_4581_set__replicate,axiom,
% 3.82/4.06 ! [N2: nat,X: real] :
% 3.82/4.06 ( ( N2 != zero_zero_nat )
% 3.82/4.06 => ( ( set_real2 @ ( replicate_real @ N2 @ X ) )
% 3.82/4.06 = ( insert_real @ X @ bot_bot_set_real ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % set_replicate
% 3.82/4.06 thf(fact_4582_set__replicate,axiom,
% 3.82/4.06 ! [N2: nat,X: nat] :
% 3.82/4.06 ( ( N2 != zero_zero_nat )
% 3.82/4.06 => ( ( set_nat2 @ ( replicate_nat @ N2 @ X ) )
% 3.82/4.06 = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % set_replicate
% 3.82/4.06 thf(fact_4583_set__replicate,axiom,
% 3.82/4.06 ! [N2: nat,X: int] :
% 3.82/4.06 ( ( N2 != zero_zero_nat )
% 3.82/4.06 => ( ( set_int2 @ ( replicate_int @ N2 @ X ) )
% 3.82/4.06 = ( insert_int @ X @ bot_bot_set_int ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % set_replicate
% 3.82/4.06 thf(fact_4584_divmod__algorithm__code_I3_J,axiom,
% 3.82/4.06 ! [N2: num] :
% 3.82/4.06 ( ( unique5052692396658037445od_int @ one @ ( bit0 @ N2 ) )
% 3.82/4.06 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % divmod_algorithm_code(3)
% 3.82/4.06 thf(fact_4585_divmod__algorithm__code_I3_J,axiom,
% 3.82/4.06 ! [N2: num] :
% 3.82/4.06 ( ( unique5055182867167087721od_nat @ one @ ( bit0 @ N2 ) )
% 3.82/4.06 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % divmod_algorithm_code(3)
% 3.82/4.06 thf(fact_4586_divmod__algorithm__code_I4_J,axiom,
% 3.82/4.06 ! [N2: num] :
% 3.82/4.06 ( ( unique5052692396658037445od_int @ one @ ( bit1 @ N2 ) )
% 3.82/4.06 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % divmod_algorithm_code(4)
% 3.82/4.06 thf(fact_4587_divmod__algorithm__code_I4_J,axiom,
% 3.82/4.06 ! [N2: num] :
% 3.82/4.06 ( ( unique5055182867167087721od_nat @ one @ ( bit1 @ N2 ) )
% 3.82/4.06 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % divmod_algorithm_code(4)
% 3.82/4.06 thf(fact_4588_divmod__algorithm__code_I6_J,axiom,
% 3.82/4.06 ! [M2: num,N2: num] :
% 3.82/4.06 ( ( unique5052692396658037445od_int @ ( bit1 @ M2 ) @ ( bit0 @ N2 ) )
% 3.82/4.06 = ( produc4245557441103728435nt_int
% 3.82/4.06 @ ^ [Q5: int,R4: int] : ( product_Pair_int_int @ Q5 @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R4 ) @ one_one_int ) )
% 3.82/4.06 @ ( unique5052692396658037445od_int @ M2 @ N2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % divmod_algorithm_code(6)
% 3.82/4.06 thf(fact_4589_divmod__algorithm__code_I6_J,axiom,
% 3.82/4.06 ! [M2: num,N2: num] :
% 3.82/4.06 ( ( unique5055182867167087721od_nat @ ( bit1 @ M2 ) @ ( bit0 @ N2 ) )
% 3.82/4.06 = ( produc2626176000494625587at_nat
% 3.82/4.06 @ ^ [Q5: nat,R4: nat] : ( product_Pair_nat_nat @ Q5 @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ R4 ) @ one_one_nat ) )
% 3.82/4.06 @ ( unique5055182867167087721od_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % divmod_algorithm_code(6)
% 3.82/4.06 thf(fact_4590_set__diff__eq,axiom,
% 3.82/4.06 ( minus_925952699566721837d_enat
% 3.82/4.06 = ( ^ [A5: set_Extended_enat,B5: set_Extended_enat] :
% 3.82/4.06 ( collec4429806609662206161d_enat
% 3.82/4.06 @ ^ [X4: extended_enat] :
% 3.82/4.06 ( ( member_Extended_enat @ X4 @ A5 )
% 3.82/4.06 & ~ ( member_Extended_enat @ X4 @ B5 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % set_diff_eq
% 3.82/4.06 thf(fact_4591_set__diff__eq,axiom,
% 3.82/4.06 ( minus_minus_set_real
% 3.82/4.06 = ( ^ [A5: set_real,B5: set_real] :
% 3.82/4.06 ( collect_real
% 3.82/4.06 @ ^ [X4: real] :
% 3.82/4.06 ( ( member_real @ X4 @ A5 )
% 3.82/4.06 & ~ ( member_real @ X4 @ B5 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % set_diff_eq
% 3.82/4.06 thf(fact_4592_set__diff__eq,axiom,
% 3.82/4.06 ( minus_7954133019191499631st_nat
% 3.82/4.06 = ( ^ [A5: set_list_nat,B5: set_list_nat] :
% 3.82/4.06 ( collect_list_nat
% 3.82/4.06 @ ^ [X4: list_nat] :
% 3.82/4.06 ( ( member_list_nat @ X4 @ A5 )
% 3.82/4.06 & ~ ( member_list_nat @ X4 @ B5 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % set_diff_eq
% 3.82/4.06 thf(fact_4593_set__diff__eq,axiom,
% 3.82/4.06 ( minus_2163939370556025621et_nat
% 3.82/4.06 = ( ^ [A5: set_set_nat,B5: set_set_nat] :
% 3.82/4.06 ( collect_set_nat
% 3.82/4.06 @ ^ [X4: set_nat] :
% 3.82/4.06 ( ( member_set_nat @ X4 @ A5 )
% 3.82/4.06 & ~ ( member_set_nat @ X4 @ B5 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % set_diff_eq
% 3.82/4.06 thf(fact_4594_set__diff__eq,axiom,
% 3.82/4.06 ( minus_minus_set_int
% 3.82/4.06 = ( ^ [A5: set_int,B5: set_int] :
% 3.82/4.06 ( collect_int
% 3.82/4.06 @ ^ [X4: int] :
% 3.82/4.06 ( ( member_int @ X4 @ A5 )
% 3.82/4.06 & ~ ( member_int @ X4 @ B5 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % set_diff_eq
% 3.82/4.06 thf(fact_4595_set__diff__eq,axiom,
% 3.82/4.06 ( minus_minus_set_nat
% 3.82/4.06 = ( ^ [A5: set_nat,B5: set_nat] :
% 3.82/4.06 ( collect_nat
% 3.82/4.06 @ ^ [X4: nat] :
% 3.82/4.06 ( ( member_nat @ X4 @ A5 )
% 3.82/4.06 & ~ ( member_nat @ X4 @ B5 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % set_diff_eq
% 3.82/4.06 thf(fact_4596_minus__set__def,axiom,
% 3.82/4.06 ( minus_925952699566721837d_enat
% 3.82/4.06 = ( ^ [A5: set_Extended_enat,B5: set_Extended_enat] :
% 3.82/4.06 ( collec4429806609662206161d_enat
% 3.82/4.06 @ ( minus_2020553357622893040enat_o
% 3.82/4.06 @ ^ [X4: extended_enat] : ( member_Extended_enat @ X4 @ A5 )
% 3.82/4.06 @ ^ [X4: extended_enat] : ( member_Extended_enat @ X4 @ B5 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % minus_set_def
% 3.82/4.06 thf(fact_4597_minus__set__def,axiom,
% 3.82/4.06 ( minus_minus_set_real
% 3.82/4.06 = ( ^ [A5: set_real,B5: set_real] :
% 3.82/4.06 ( collect_real
% 3.82/4.06 @ ( minus_minus_real_o
% 3.82/4.06 @ ^ [X4: real] : ( member_real @ X4 @ A5 )
% 3.82/4.06 @ ^ [X4: real] : ( member_real @ X4 @ B5 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % minus_set_def
% 3.82/4.06 thf(fact_4598_minus__set__def,axiom,
% 3.82/4.06 ( minus_7954133019191499631st_nat
% 3.82/4.06 = ( ^ [A5: set_list_nat,B5: set_list_nat] :
% 3.82/4.06 ( collect_list_nat
% 3.82/4.06 @ ( minus_1139252259498527702_nat_o
% 3.82/4.06 @ ^ [X4: list_nat] : ( member_list_nat @ X4 @ A5 )
% 3.82/4.06 @ ^ [X4: list_nat] : ( member_list_nat @ X4 @ B5 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % minus_set_def
% 3.82/4.06 thf(fact_4599_minus__set__def,axiom,
% 3.82/4.06 ( minus_2163939370556025621et_nat
% 3.82/4.06 = ( ^ [A5: set_set_nat,B5: set_set_nat] :
% 3.82/4.06 ( collect_set_nat
% 3.82/4.06 @ ( minus_6910147592129066416_nat_o
% 3.82/4.06 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ A5 )
% 3.82/4.06 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ B5 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % minus_set_def
% 3.82/4.06 thf(fact_4600_minus__set__def,axiom,
% 3.82/4.06 ( minus_minus_set_int
% 3.82/4.06 = ( ^ [A5: set_int,B5: set_int] :
% 3.82/4.06 ( collect_int
% 3.82/4.06 @ ( minus_minus_int_o
% 3.82/4.06 @ ^ [X4: int] : ( member_int @ X4 @ A5 )
% 3.82/4.06 @ ^ [X4: int] : ( member_int @ X4 @ B5 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % minus_set_def
% 3.82/4.06 thf(fact_4601_minus__set__def,axiom,
% 3.82/4.06 ( minus_minus_set_nat
% 3.82/4.06 = ( ^ [A5: set_nat,B5: set_nat] :
% 3.82/4.06 ( collect_nat
% 3.82/4.06 @ ( minus_minus_nat_o
% 3.82/4.06 @ ^ [X4: nat] : ( member_nat @ X4 @ A5 )
% 3.82/4.06 @ ^ [X4: nat] : ( member_nat @ X4 @ B5 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % minus_set_def
% 3.82/4.06 thf(fact_4602_insert__Diff__if,axiom,
% 3.82/4.06 ! [X: extended_enat,B: set_Extended_enat,A2: set_Extended_enat] :
% 3.82/4.06 ( ( ( member_Extended_enat @ X @ B )
% 3.82/4.06 => ( ( minus_925952699566721837d_enat @ ( insert_Extended_enat @ X @ A2 ) @ B )
% 3.82/4.06 = ( minus_925952699566721837d_enat @ A2 @ B ) ) )
% 3.82/4.06 & ( ~ ( member_Extended_enat @ X @ B )
% 3.82/4.06 => ( ( minus_925952699566721837d_enat @ ( insert_Extended_enat @ X @ A2 ) @ B )
% 3.82/4.06 = ( insert_Extended_enat @ X @ ( minus_925952699566721837d_enat @ A2 @ B ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % insert_Diff_if
% 3.82/4.06 thf(fact_4603_insert__Diff__if,axiom,
% 3.82/4.06 ! [X: real,B: set_real,A2: set_real] :
% 3.82/4.06 ( ( ( member_real @ X @ B )
% 3.82/4.06 => ( ( minus_minus_set_real @ ( insert_real @ X @ A2 ) @ B )
% 3.82/4.06 = ( minus_minus_set_real @ A2 @ B ) ) )
% 3.82/4.06 & ( ~ ( member_real @ X @ B )
% 3.82/4.06 => ( ( minus_minus_set_real @ ( insert_real @ X @ A2 ) @ B )
% 3.82/4.06 = ( insert_real @ X @ ( minus_minus_set_real @ A2 @ B ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % insert_Diff_if
% 3.82/4.06 thf(fact_4604_insert__Diff__if,axiom,
% 3.82/4.06 ! [X: set_nat,B: set_set_nat,A2: set_set_nat] :
% 3.82/4.06 ( ( ( member_set_nat @ X @ B )
% 3.82/4.06 => ( ( minus_2163939370556025621et_nat @ ( insert_set_nat @ X @ A2 ) @ B )
% 3.82/4.06 = ( minus_2163939370556025621et_nat @ A2 @ B ) ) )
% 3.82/4.06 & ( ~ ( member_set_nat @ X @ B )
% 3.82/4.06 => ( ( minus_2163939370556025621et_nat @ ( insert_set_nat @ X @ A2 ) @ B )
% 3.82/4.06 = ( insert_set_nat @ X @ ( minus_2163939370556025621et_nat @ A2 @ B ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % insert_Diff_if
% 3.82/4.06 thf(fact_4605_insert__Diff__if,axiom,
% 3.82/4.06 ! [X: int,B: set_int,A2: set_int] :
% 3.82/4.06 ( ( ( member_int @ X @ B )
% 3.82/4.06 => ( ( minus_minus_set_int @ ( insert_int @ X @ A2 ) @ B )
% 3.82/4.06 = ( minus_minus_set_int @ A2 @ B ) ) )
% 3.82/4.06 & ( ~ ( member_int @ X @ B )
% 3.82/4.06 => ( ( minus_minus_set_int @ ( insert_int @ X @ A2 ) @ B )
% 3.82/4.06 = ( insert_int @ X @ ( minus_minus_set_int @ A2 @ B ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % insert_Diff_if
% 3.82/4.06 thf(fact_4606_insert__Diff__if,axiom,
% 3.82/4.06 ! [X: nat,B: set_nat,A2: set_nat] :
% 3.82/4.06 ( ( ( member_nat @ X @ B )
% 3.82/4.06 => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A2 ) @ B )
% 3.82/4.06 = ( minus_minus_set_nat @ A2 @ B ) ) )
% 3.82/4.06 & ( ~ ( member_nat @ X @ B )
% 3.82/4.06 => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A2 ) @ B )
% 3.82/4.06 = ( insert_nat @ X @ ( minus_minus_set_nat @ A2 @ B ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % insert_Diff_if
% 3.82/4.06 thf(fact_4607_DiffD2,axiom,
% 3.82/4.06 ! [C: extended_enat,A2: set_Extended_enat,B: set_Extended_enat] :
% 3.82/4.06 ( ( member_Extended_enat @ C @ ( minus_925952699566721837d_enat @ A2 @ B ) )
% 3.82/4.06 => ~ ( member_Extended_enat @ C @ B ) ) ).
% 3.82/4.06
% 3.82/4.06 % DiffD2
% 3.82/4.06 thf(fact_4608_DiffD2,axiom,
% 3.82/4.06 ! [C: real,A2: set_real,B: set_real] :
% 3.82/4.06 ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B ) )
% 3.82/4.06 => ~ ( member_real @ C @ B ) ) ).
% 3.82/4.06
% 3.82/4.06 % DiffD2
% 3.82/4.06 thf(fact_4609_DiffD2,axiom,
% 3.82/4.06 ! [C: set_nat,A2: set_set_nat,B: set_set_nat] :
% 3.82/4.06 ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B ) )
% 3.82/4.06 => ~ ( member_set_nat @ C @ B ) ) ).
% 3.82/4.06
% 3.82/4.06 % DiffD2
% 3.82/4.06 thf(fact_4610_DiffD2,axiom,
% 3.82/4.06 ! [C: int,A2: set_int,B: set_int] :
% 3.82/4.06 ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B ) )
% 3.82/4.06 => ~ ( member_int @ C @ B ) ) ).
% 3.82/4.06
% 3.82/4.06 % DiffD2
% 3.82/4.06 thf(fact_4611_DiffD2,axiom,
% 3.82/4.06 ! [C: nat,A2: set_nat,B: set_nat] :
% 3.82/4.06 ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B ) )
% 3.82/4.06 => ~ ( member_nat @ C @ B ) ) ).
% 3.82/4.06
% 3.82/4.06 % DiffD2
% 3.82/4.06 thf(fact_4612_DiffD1,axiom,
% 3.82/4.06 ! [C: extended_enat,A2: set_Extended_enat,B: set_Extended_enat] :
% 3.82/4.06 ( ( member_Extended_enat @ C @ ( minus_925952699566721837d_enat @ A2 @ B ) )
% 3.82/4.06 => ( member_Extended_enat @ C @ A2 ) ) ).
% 3.82/4.06
% 3.82/4.06 % DiffD1
% 3.82/4.06 thf(fact_4613_DiffD1,axiom,
% 3.82/4.06 ! [C: real,A2: set_real,B: set_real] :
% 3.82/4.06 ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B ) )
% 3.82/4.06 => ( member_real @ C @ A2 ) ) ).
% 3.82/4.06
% 3.82/4.06 % DiffD1
% 3.82/4.06 thf(fact_4614_DiffD1,axiom,
% 3.82/4.06 ! [C: set_nat,A2: set_set_nat,B: set_set_nat] :
% 3.82/4.06 ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B ) )
% 3.82/4.06 => ( member_set_nat @ C @ A2 ) ) ).
% 3.82/4.06
% 3.82/4.06 % DiffD1
% 3.82/4.06 thf(fact_4615_DiffD1,axiom,
% 3.82/4.06 ! [C: int,A2: set_int,B: set_int] :
% 3.82/4.06 ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B ) )
% 3.82/4.06 => ( member_int @ C @ A2 ) ) ).
% 3.82/4.06
% 3.82/4.06 % DiffD1
% 3.82/4.06 thf(fact_4616_DiffD1,axiom,
% 3.82/4.06 ! [C: nat,A2: set_nat,B: set_nat] :
% 3.82/4.06 ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B ) )
% 3.82/4.06 => ( member_nat @ C @ A2 ) ) ).
% 3.82/4.06
% 3.82/4.06 % DiffD1
% 3.82/4.06 thf(fact_4617_DiffE,axiom,
% 3.82/4.06 ! [C: extended_enat,A2: set_Extended_enat,B: set_Extended_enat] :
% 3.82/4.06 ( ( member_Extended_enat @ C @ ( minus_925952699566721837d_enat @ A2 @ B ) )
% 3.82/4.06 => ~ ( ( member_Extended_enat @ C @ A2 )
% 3.82/4.06 => ( member_Extended_enat @ C @ B ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % DiffE
% 3.82/4.06 thf(fact_4618_DiffE,axiom,
% 3.82/4.06 ! [C: real,A2: set_real,B: set_real] :
% 3.82/4.06 ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B ) )
% 3.82/4.06 => ~ ( ( member_real @ C @ A2 )
% 3.82/4.06 => ( member_real @ C @ B ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % DiffE
% 3.82/4.06 thf(fact_4619_DiffE,axiom,
% 3.82/4.06 ! [C: set_nat,A2: set_set_nat,B: set_set_nat] :
% 3.82/4.06 ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B ) )
% 3.82/4.06 => ~ ( ( member_set_nat @ C @ A2 )
% 3.82/4.06 => ( member_set_nat @ C @ B ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % DiffE
% 3.82/4.06 thf(fact_4620_DiffE,axiom,
% 3.82/4.06 ! [C: int,A2: set_int,B: set_int] :
% 3.82/4.06 ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B ) )
% 3.82/4.06 => ~ ( ( member_int @ C @ A2 )
% 3.82/4.06 => ( member_int @ C @ B ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % DiffE
% 3.82/4.06 thf(fact_4621_DiffE,axiom,
% 3.82/4.06 ! [C: nat,A2: set_nat,B: set_nat] :
% 3.82/4.06 ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B ) )
% 3.82/4.06 => ~ ( ( member_nat @ C @ A2 )
% 3.82/4.06 => ( member_nat @ C @ B ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % DiffE
% 3.82/4.06 thf(fact_4622_int__induct,axiom,
% 3.82/4.06 ! [P: int > $o,K: int,I: int] :
% 3.82/4.06 ( ( P @ K )
% 3.82/4.06 => ( ! [I4: int] :
% 3.82/4.06 ( ( ord_less_eq_int @ K @ I4 )
% 3.82/4.06 => ( ( P @ I4 )
% 3.82/4.06 => ( P @ ( plus_plus_int @ I4 @ one_one_int ) ) ) )
% 3.82/4.06 => ( ! [I4: int] :
% 3.82/4.06 ( ( ord_less_eq_int @ I4 @ K )
% 3.82/4.06 => ( ( P @ I4 )
% 3.82/4.06 => ( P @ ( minus_minus_int @ I4 @ one_one_int ) ) ) )
% 3.82/4.06 => ( P @ I ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % int_induct
% 3.82/4.06 thf(fact_4623_int__le__induct,axiom,
% 3.82/4.06 ! [I: int,K: int,P: int > $o] :
% 3.82/4.06 ( ( ord_less_eq_int @ I @ K )
% 3.82/4.06 => ( ( P @ K )
% 3.82/4.06 => ( ! [I4: int] :
% 3.82/4.06 ( ( ord_less_eq_int @ I4 @ K )
% 3.82/4.06 => ( ( P @ I4 )
% 3.82/4.06 => ( P @ ( minus_minus_int @ I4 @ one_one_int ) ) ) )
% 3.82/4.06 => ( P @ I ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % int_le_induct
% 3.82/4.06 thf(fact_4624_zdvd__zdiffD,axiom,
% 3.82/4.06 ! [K: int,M2: int,N2: int] :
% 3.82/4.06 ( ( dvd_dvd_int @ K @ ( minus_minus_int @ M2 @ N2 ) )
% 3.82/4.06 => ( ( dvd_dvd_int @ K @ N2 )
% 3.82/4.06 => ( dvd_dvd_int @ K @ M2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % zdvd_zdiffD
% 3.82/4.06 thf(fact_4625_ComplD,axiom,
% 3.82/4.06 ! [C: extended_enat,A2: set_Extended_enat] :
% 3.82/4.06 ( ( member_Extended_enat @ C @ ( uminus417252749190364093d_enat @ A2 ) )
% 3.82/4.06 => ~ ( member_Extended_enat @ C @ A2 ) ) ).
% 3.82/4.06
% 3.82/4.06 % ComplD
% 3.82/4.06 thf(fact_4626_ComplD,axiom,
% 3.82/4.06 ! [C: real,A2: set_real] :
% 3.82/4.06 ( ( member_real @ C @ ( uminus612125837232591019t_real @ A2 ) )
% 3.82/4.06 => ~ ( member_real @ C @ A2 ) ) ).
% 3.82/4.06
% 3.82/4.06 % ComplD
% 3.82/4.06 thf(fact_4627_ComplD,axiom,
% 3.82/4.06 ! [C: set_nat,A2: set_set_nat] :
% 3.82/4.06 ( ( member_set_nat @ C @ ( uminus613421341184616069et_nat @ A2 ) )
% 3.82/4.06 => ~ ( member_set_nat @ C @ A2 ) ) ).
% 3.82/4.06
% 3.82/4.06 % ComplD
% 3.82/4.06 thf(fact_4628_ComplD,axiom,
% 3.82/4.06 ! [C: nat,A2: set_nat] :
% 3.82/4.06 ( ( member_nat @ C @ ( uminus5710092332889474511et_nat @ A2 ) )
% 3.82/4.06 => ~ ( member_nat @ C @ A2 ) ) ).
% 3.82/4.06
% 3.82/4.06 % ComplD
% 3.82/4.06 thf(fact_4629_ComplD,axiom,
% 3.82/4.06 ! [C: int,A2: set_int] :
% 3.82/4.06 ( ( member_int @ C @ ( uminus1532241313380277803et_int @ A2 ) )
% 3.82/4.06 => ~ ( member_int @ C @ A2 ) ) ).
% 3.82/4.06
% 3.82/4.06 % ComplD
% 3.82/4.06 thf(fact_4630_uminus__set__def,axiom,
% 3.82/4.06 ( uminus417252749190364093d_enat
% 3.82/4.06 = ( ^ [A5: set_Extended_enat] :
% 3.82/4.06 ( collec4429806609662206161d_enat
% 3.82/4.06 @ ( uminus6636779312473996640enat_o
% 3.82/4.06 @ ^ [X4: extended_enat] : ( member_Extended_enat @ X4 @ A5 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % uminus_set_def
% 3.82/4.06 thf(fact_4631_uminus__set__def,axiom,
% 3.82/4.06 ( uminus612125837232591019t_real
% 3.82/4.06 = ( ^ [A5: set_real] :
% 3.82/4.06 ( collect_real
% 3.82/4.06 @ ( uminus_uminus_real_o
% 3.82/4.06 @ ^ [X4: real] : ( member_real @ X4 @ A5 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % uminus_set_def
% 3.82/4.06 thf(fact_4632_uminus__set__def,axiom,
% 3.82/4.06 ( uminus3195874150345416415st_nat
% 3.82/4.06 = ( ^ [A5: set_list_nat] :
% 3.82/4.06 ( collect_list_nat
% 3.82/4.06 @ ( uminus5770388063884162150_nat_o
% 3.82/4.06 @ ^ [X4: list_nat] : ( member_list_nat @ X4 @ A5 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % uminus_set_def
% 3.82/4.06 thf(fact_4633_uminus__set__def,axiom,
% 3.82/4.06 ( uminus613421341184616069et_nat
% 3.82/4.06 = ( ^ [A5: set_set_nat] :
% 3.82/4.06 ( collect_set_nat
% 3.82/4.06 @ ( uminus6401447641752708672_nat_o
% 3.82/4.06 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ A5 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % uminus_set_def
% 3.82/4.06 thf(fact_4634_uminus__set__def,axiom,
% 3.82/4.06 ( uminus5710092332889474511et_nat
% 3.82/4.06 = ( ^ [A5: set_nat] :
% 3.82/4.06 ( collect_nat
% 3.82/4.06 @ ( uminus_uminus_nat_o
% 3.82/4.06 @ ^ [X4: nat] : ( member_nat @ X4 @ A5 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % uminus_set_def
% 3.82/4.06 thf(fact_4635_uminus__set__def,axiom,
% 3.82/4.06 ( uminus1532241313380277803et_int
% 3.82/4.06 = ( ^ [A5: set_int] :
% 3.82/4.06 ( collect_int
% 3.82/4.06 @ ( uminus_uminus_int_o
% 3.82/4.06 @ ^ [X4: int] : ( member_int @ X4 @ A5 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % uminus_set_def
% 3.82/4.06 thf(fact_4636_Collect__neg__eq,axiom,
% 3.82/4.06 ! [P: real > $o] :
% 3.82/4.06 ( ( collect_real
% 3.82/4.06 @ ^ [X4: real] :
% 3.82/4.06 ~ ( P @ X4 ) )
% 3.82/4.06 = ( uminus612125837232591019t_real @ ( collect_real @ P ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % Collect_neg_eq
% 3.82/4.06 thf(fact_4637_Collect__neg__eq,axiom,
% 3.82/4.06 ! [P: list_nat > $o] :
% 3.82/4.06 ( ( collect_list_nat
% 3.82/4.06 @ ^ [X4: list_nat] :
% 3.82/4.06 ~ ( P @ X4 ) )
% 3.82/4.06 = ( uminus3195874150345416415st_nat @ ( collect_list_nat @ P ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % Collect_neg_eq
% 3.82/4.06 thf(fact_4638_Collect__neg__eq,axiom,
% 3.82/4.06 ! [P: set_nat > $o] :
% 3.82/4.06 ( ( collect_set_nat
% 3.82/4.06 @ ^ [X4: set_nat] :
% 3.82/4.06 ~ ( P @ X4 ) )
% 3.82/4.06 = ( uminus613421341184616069et_nat @ ( collect_set_nat @ P ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % Collect_neg_eq
% 3.82/4.06 thf(fact_4639_Collect__neg__eq,axiom,
% 3.82/4.06 ! [P: nat > $o] :
% 3.82/4.06 ( ( collect_nat
% 3.82/4.06 @ ^ [X4: nat] :
% 3.82/4.06 ~ ( P @ X4 ) )
% 3.82/4.06 = ( uminus5710092332889474511et_nat @ ( collect_nat @ P ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % Collect_neg_eq
% 3.82/4.06 thf(fact_4640_Collect__neg__eq,axiom,
% 3.82/4.06 ! [P: int > $o] :
% 3.82/4.06 ( ( collect_int
% 3.82/4.06 @ ^ [X4: int] :
% 3.82/4.06 ~ ( P @ X4 ) )
% 3.82/4.06 = ( uminus1532241313380277803et_int @ ( collect_int @ P ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % Collect_neg_eq
% 3.82/4.06 thf(fact_4641_Compl__eq,axiom,
% 3.82/4.06 ( uminus417252749190364093d_enat
% 3.82/4.06 = ( ^ [A5: set_Extended_enat] :
% 3.82/4.06 ( collec4429806609662206161d_enat
% 3.82/4.06 @ ^ [X4: extended_enat] :
% 3.82/4.06 ~ ( member_Extended_enat @ X4 @ A5 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % Compl_eq
% 3.82/4.06 thf(fact_4642_Compl__eq,axiom,
% 3.82/4.06 ( uminus612125837232591019t_real
% 3.82/4.06 = ( ^ [A5: set_real] :
% 3.82/4.06 ( collect_real
% 3.82/4.06 @ ^ [X4: real] :
% 3.82/4.06 ~ ( member_real @ X4 @ A5 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % Compl_eq
% 3.82/4.06 thf(fact_4643_Compl__eq,axiom,
% 3.82/4.06 ( uminus3195874150345416415st_nat
% 3.82/4.06 = ( ^ [A5: set_list_nat] :
% 3.82/4.06 ( collect_list_nat
% 3.82/4.06 @ ^ [X4: list_nat] :
% 3.82/4.06 ~ ( member_list_nat @ X4 @ A5 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % Compl_eq
% 3.82/4.06 thf(fact_4644_Compl__eq,axiom,
% 3.82/4.06 ( uminus613421341184616069et_nat
% 3.82/4.06 = ( ^ [A5: set_set_nat] :
% 3.82/4.06 ( collect_set_nat
% 3.82/4.06 @ ^ [X4: set_nat] :
% 3.82/4.06 ~ ( member_set_nat @ X4 @ A5 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % Compl_eq
% 3.82/4.06 thf(fact_4645_Compl__eq,axiom,
% 3.82/4.06 ( uminus5710092332889474511et_nat
% 3.82/4.06 = ( ^ [A5: set_nat] :
% 3.82/4.06 ( collect_nat
% 3.82/4.06 @ ^ [X4: nat] :
% 3.82/4.06 ~ ( member_nat @ X4 @ A5 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % Compl_eq
% 3.82/4.06 thf(fact_4646_Compl__eq,axiom,
% 3.82/4.06 ( uminus1532241313380277803et_int
% 3.82/4.06 = ( ^ [A5: set_int] :
% 3.82/4.06 ( collect_int
% 3.82/4.06 @ ^ [X4: int] :
% 3.82/4.06 ~ ( member_int @ X4 @ A5 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % Compl_eq
% 3.82/4.06 thf(fact_4647_insert__compr,axiom,
% 3.82/4.06 ( insert_Extended_enat
% 3.82/4.06 = ( ^ [A3: extended_enat,B5: set_Extended_enat] :
% 3.82/4.06 ( collec4429806609662206161d_enat
% 3.82/4.06 @ ^ [X4: extended_enat] :
% 3.82/4.06 ( ( X4 = A3 )
% 3.82/4.06 | ( member_Extended_enat @ X4 @ B5 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % insert_compr
% 3.82/4.06 thf(fact_4648_insert__compr,axiom,
% 3.82/4.06 ( insert_real
% 3.82/4.06 = ( ^ [A3: real,B5: set_real] :
% 3.82/4.06 ( collect_real
% 3.82/4.06 @ ^ [X4: real] :
% 3.82/4.06 ( ( X4 = A3 )
% 3.82/4.06 | ( member_real @ X4 @ B5 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % insert_compr
% 3.82/4.06 thf(fact_4649_insert__compr,axiom,
% 3.82/4.06 ( insert_list_nat
% 3.82/4.06 = ( ^ [A3: list_nat,B5: set_list_nat] :
% 3.82/4.06 ( collect_list_nat
% 3.82/4.06 @ ^ [X4: list_nat] :
% 3.82/4.06 ( ( X4 = A3 )
% 3.82/4.06 | ( member_list_nat @ X4 @ B5 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % insert_compr
% 3.82/4.06 thf(fact_4650_insert__compr,axiom,
% 3.82/4.06 ( insert_set_nat
% 3.82/4.06 = ( ^ [A3: set_nat,B5: set_set_nat] :
% 3.82/4.06 ( collect_set_nat
% 3.82/4.06 @ ^ [X4: set_nat] :
% 3.82/4.06 ( ( X4 = A3 )
% 3.82/4.06 | ( member_set_nat @ X4 @ B5 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % insert_compr
% 3.82/4.06 thf(fact_4651_insert__compr,axiom,
% 3.82/4.06 ( insert_nat
% 3.82/4.06 = ( ^ [A3: nat,B5: set_nat] :
% 3.82/4.06 ( collect_nat
% 3.82/4.06 @ ^ [X4: nat] :
% 3.82/4.06 ( ( X4 = A3 )
% 3.82/4.06 | ( member_nat @ X4 @ B5 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % insert_compr
% 3.82/4.06 thf(fact_4652_insert__compr,axiom,
% 3.82/4.06 ( insert_int
% 3.82/4.06 = ( ^ [A3: int,B5: set_int] :
% 3.82/4.06 ( collect_int
% 3.82/4.06 @ ^ [X4: int] :
% 3.82/4.06 ( ( X4 = A3 )
% 3.82/4.06 | ( member_int @ X4 @ B5 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % insert_compr
% 3.82/4.06 thf(fact_4653_insert__Collect,axiom,
% 3.82/4.06 ! [A: real,P: real > $o] :
% 3.82/4.06 ( ( insert_real @ A @ ( collect_real @ P ) )
% 3.82/4.06 = ( collect_real
% 3.82/4.06 @ ^ [U2: real] :
% 3.82/4.06 ( ( U2 != A )
% 3.82/4.06 => ( P @ U2 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % insert_Collect
% 3.82/4.06 thf(fact_4654_insert__Collect,axiom,
% 3.82/4.06 ! [A: list_nat,P: list_nat > $o] :
% 3.82/4.06 ( ( insert_list_nat @ A @ ( collect_list_nat @ P ) )
% 3.82/4.06 = ( collect_list_nat
% 3.82/4.06 @ ^ [U2: list_nat] :
% 3.82/4.06 ( ( U2 != A )
% 3.82/4.06 => ( P @ U2 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % insert_Collect
% 3.82/4.06 thf(fact_4655_insert__Collect,axiom,
% 3.82/4.06 ! [A: set_nat,P: set_nat > $o] :
% 3.82/4.06 ( ( insert_set_nat @ A @ ( collect_set_nat @ P ) )
% 3.82/4.06 = ( collect_set_nat
% 3.82/4.06 @ ^ [U2: set_nat] :
% 3.82/4.06 ( ( U2 != A )
% 3.82/4.06 => ( P @ U2 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % insert_Collect
% 3.82/4.06 thf(fact_4656_insert__Collect,axiom,
% 3.82/4.06 ! [A: nat,P: nat > $o] :
% 3.82/4.06 ( ( insert_nat @ A @ ( collect_nat @ P ) )
% 3.82/4.06 = ( collect_nat
% 3.82/4.06 @ ^ [U2: nat] :
% 3.82/4.06 ( ( U2 != A )
% 3.82/4.06 => ( P @ U2 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % insert_Collect
% 3.82/4.06 thf(fact_4657_insert__Collect,axiom,
% 3.82/4.06 ! [A: int,P: int > $o] :
% 3.82/4.06 ( ( insert_int @ A @ ( collect_int @ P ) )
% 3.82/4.06 = ( collect_int
% 3.82/4.06 @ ^ [U2: int] :
% 3.82/4.06 ( ( U2 != A )
% 3.82/4.06 => ( P @ U2 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % insert_Collect
% 3.82/4.06 thf(fact_4658_mk__disjoint__insert,axiom,
% 3.82/4.06 ! [A: extended_enat,A2: set_Extended_enat] :
% 3.82/4.06 ( ( member_Extended_enat @ A @ A2 )
% 3.82/4.06 => ? [B8: set_Extended_enat] :
% 3.82/4.06 ( ( A2
% 3.82/4.06 = ( insert_Extended_enat @ A @ B8 ) )
% 3.82/4.06 & ~ ( member_Extended_enat @ A @ B8 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % mk_disjoint_insert
% 3.82/4.06 thf(fact_4659_mk__disjoint__insert,axiom,
% 3.82/4.06 ! [A: real,A2: set_real] :
% 3.82/4.06 ( ( member_real @ A @ A2 )
% 3.82/4.06 => ? [B8: set_real] :
% 3.82/4.06 ( ( A2
% 3.82/4.06 = ( insert_real @ A @ B8 ) )
% 3.82/4.06 & ~ ( member_real @ A @ B8 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % mk_disjoint_insert
% 3.82/4.06 thf(fact_4660_mk__disjoint__insert,axiom,
% 3.82/4.06 ! [A: set_nat,A2: set_set_nat] :
% 3.82/4.06 ( ( member_set_nat @ A @ A2 )
% 3.82/4.06 => ? [B8: set_set_nat] :
% 3.82/4.06 ( ( A2
% 3.82/4.06 = ( insert_set_nat @ A @ B8 ) )
% 3.82/4.06 & ~ ( member_set_nat @ A @ B8 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % mk_disjoint_insert
% 3.82/4.06 thf(fact_4661_mk__disjoint__insert,axiom,
% 3.82/4.06 ! [A: nat,A2: set_nat] :
% 3.82/4.06 ( ( member_nat @ A @ A2 )
% 3.82/4.06 => ? [B8: set_nat] :
% 3.82/4.06 ( ( A2
% 3.82/4.06 = ( insert_nat @ A @ B8 ) )
% 3.82/4.06 & ~ ( member_nat @ A @ B8 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % mk_disjoint_insert
% 3.82/4.06 thf(fact_4662_mk__disjoint__insert,axiom,
% 3.82/4.06 ! [A: int,A2: set_int] :
% 3.82/4.06 ( ( member_int @ A @ A2 )
% 3.82/4.06 => ? [B8: set_int] :
% 3.82/4.06 ( ( A2
% 3.82/4.06 = ( insert_int @ A @ B8 ) )
% 3.82/4.06 & ~ ( member_int @ A @ B8 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % mk_disjoint_insert
% 3.82/4.06 thf(fact_4663_insert__commute,axiom,
% 3.82/4.06 ! [X: nat,Y: nat,A2: set_nat] :
% 3.82/4.06 ( ( insert_nat @ X @ ( insert_nat @ Y @ A2 ) )
% 3.82/4.06 = ( insert_nat @ Y @ ( insert_nat @ X @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % insert_commute
% 3.82/4.06 thf(fact_4664_insert__commute,axiom,
% 3.82/4.06 ! [X: int,Y: int,A2: set_int] :
% 3.82/4.06 ( ( insert_int @ X @ ( insert_int @ Y @ A2 ) )
% 3.82/4.06 = ( insert_int @ Y @ ( insert_int @ X @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % insert_commute
% 3.82/4.06 thf(fact_4665_insert__commute,axiom,
% 3.82/4.06 ! [X: real,Y: real,A2: set_real] :
% 3.82/4.06 ( ( insert_real @ X @ ( insert_real @ Y @ A2 ) )
% 3.82/4.06 = ( insert_real @ Y @ ( insert_real @ X @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % insert_commute
% 3.82/4.06 thf(fact_4666_insert__eq__iff,axiom,
% 3.82/4.06 ! [A: extended_enat,A2: set_Extended_enat,B2: extended_enat,B: set_Extended_enat] :
% 3.82/4.06 ( ~ ( member_Extended_enat @ A @ A2 )
% 3.82/4.06 => ( ~ ( member_Extended_enat @ B2 @ B )
% 3.82/4.06 => ( ( ( insert_Extended_enat @ A @ A2 )
% 3.82/4.06 = ( insert_Extended_enat @ B2 @ B ) )
% 3.82/4.06 = ( ( ( A = B2 )
% 3.82/4.06 => ( A2 = B ) )
% 3.82/4.06 & ( ( A != B2 )
% 3.82/4.06 => ? [C5: set_Extended_enat] :
% 3.82/4.06 ( ( A2
% 3.82/4.06 = ( insert_Extended_enat @ B2 @ C5 ) )
% 3.82/4.06 & ~ ( member_Extended_enat @ B2 @ C5 )
% 3.82/4.06 & ( B
% 3.82/4.06 = ( insert_Extended_enat @ A @ C5 ) )
% 3.82/4.06 & ~ ( member_Extended_enat @ A @ C5 ) ) ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % insert_eq_iff
% 3.82/4.06 thf(fact_4667_insert__eq__iff,axiom,
% 3.82/4.06 ! [A: real,A2: set_real,B2: real,B: set_real] :
% 3.82/4.06 ( ~ ( member_real @ A @ A2 )
% 3.82/4.06 => ( ~ ( member_real @ B2 @ B )
% 3.82/4.06 => ( ( ( insert_real @ A @ A2 )
% 3.82/4.06 = ( insert_real @ B2 @ B ) )
% 3.82/4.06 = ( ( ( A = B2 )
% 3.82/4.06 => ( A2 = B ) )
% 3.82/4.06 & ( ( A != B2 )
% 3.82/4.06 => ? [C5: set_real] :
% 3.82/4.06 ( ( A2
% 3.82/4.06 = ( insert_real @ B2 @ C5 ) )
% 3.82/4.06 & ~ ( member_real @ B2 @ C5 )
% 3.82/4.06 & ( B
% 3.82/4.06 = ( insert_real @ A @ C5 ) )
% 3.82/4.06 & ~ ( member_real @ A @ C5 ) ) ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % insert_eq_iff
% 3.82/4.06 thf(fact_4668_insert__eq__iff,axiom,
% 3.82/4.06 ! [A: set_nat,A2: set_set_nat,B2: set_nat,B: set_set_nat] :
% 3.82/4.06 ( ~ ( member_set_nat @ A @ A2 )
% 3.82/4.06 => ( ~ ( member_set_nat @ B2 @ B )
% 3.82/4.06 => ( ( ( insert_set_nat @ A @ A2 )
% 3.82/4.06 = ( insert_set_nat @ B2 @ B ) )
% 3.82/4.06 = ( ( ( A = B2 )
% 3.82/4.06 => ( A2 = B ) )
% 3.82/4.06 & ( ( A != B2 )
% 3.82/4.06 => ? [C5: set_set_nat] :
% 3.82/4.06 ( ( A2
% 3.82/4.06 = ( insert_set_nat @ B2 @ C5 ) )
% 3.82/4.06 & ~ ( member_set_nat @ B2 @ C5 )
% 3.82/4.06 & ( B
% 3.82/4.06 = ( insert_set_nat @ A @ C5 ) )
% 3.82/4.06 & ~ ( member_set_nat @ A @ C5 ) ) ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % insert_eq_iff
% 3.82/4.06 thf(fact_4669_insert__eq__iff,axiom,
% 3.82/4.06 ! [A: nat,A2: set_nat,B2: nat,B: set_nat] :
% 3.82/4.06 ( ~ ( member_nat @ A @ A2 )
% 3.82/4.06 => ( ~ ( member_nat @ B2 @ B )
% 3.82/4.06 => ( ( ( insert_nat @ A @ A2 )
% 3.82/4.06 = ( insert_nat @ B2 @ B ) )
% 3.82/4.06 = ( ( ( A = B2 )
% 3.82/4.06 => ( A2 = B ) )
% 3.82/4.06 & ( ( A != B2 )
% 3.82/4.06 => ? [C5: set_nat] :
% 3.82/4.06 ( ( A2
% 3.82/4.06 = ( insert_nat @ B2 @ C5 ) )
% 3.82/4.06 & ~ ( member_nat @ B2 @ C5 )
% 3.82/4.06 & ( B
% 3.82/4.06 = ( insert_nat @ A @ C5 ) )
% 3.82/4.06 & ~ ( member_nat @ A @ C5 ) ) ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % insert_eq_iff
% 3.82/4.06 thf(fact_4670_insert__eq__iff,axiom,
% 3.82/4.06 ! [A: int,A2: set_int,B2: int,B: set_int] :
% 3.82/4.06 ( ~ ( member_int @ A @ A2 )
% 3.82/4.06 => ( ~ ( member_int @ B2 @ B )
% 3.82/4.06 => ( ( ( insert_int @ A @ A2 )
% 3.82/4.06 = ( insert_int @ B2 @ B ) )
% 3.82/4.06 = ( ( ( A = B2 )
% 3.82/4.06 => ( A2 = B ) )
% 3.82/4.06 & ( ( A != B2 )
% 3.82/4.06 => ? [C5: set_int] :
% 3.82/4.06 ( ( A2
% 3.82/4.06 = ( insert_int @ B2 @ C5 ) )
% 3.82/4.06 & ~ ( member_int @ B2 @ C5 )
% 3.82/4.06 & ( B
% 3.82/4.06 = ( insert_int @ A @ C5 ) )
% 3.82/4.06 & ~ ( member_int @ A @ C5 ) ) ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % insert_eq_iff
% 3.82/4.06 thf(fact_4671_insert__absorb,axiom,
% 3.82/4.06 ! [A: extended_enat,A2: set_Extended_enat] :
% 3.82/4.06 ( ( member_Extended_enat @ A @ A2 )
% 3.82/4.06 => ( ( insert_Extended_enat @ A @ A2 )
% 3.82/4.06 = A2 ) ) ).
% 3.82/4.06
% 3.82/4.06 % insert_absorb
% 3.82/4.06 thf(fact_4672_insert__absorb,axiom,
% 3.82/4.06 ! [A: real,A2: set_real] :
% 3.82/4.06 ( ( member_real @ A @ A2 )
% 3.82/4.06 => ( ( insert_real @ A @ A2 )
% 3.82/4.06 = A2 ) ) ).
% 3.82/4.06
% 3.82/4.06 % insert_absorb
% 3.82/4.06 thf(fact_4673_insert__absorb,axiom,
% 3.82/4.06 ! [A: set_nat,A2: set_set_nat] :
% 3.82/4.06 ( ( member_set_nat @ A @ A2 )
% 3.82/4.06 => ( ( insert_set_nat @ A @ A2 )
% 3.82/4.06 = A2 ) ) ).
% 3.82/4.06
% 3.82/4.06 % insert_absorb
% 3.82/4.06 thf(fact_4674_insert__absorb,axiom,
% 3.82/4.06 ! [A: nat,A2: set_nat] :
% 3.82/4.06 ( ( member_nat @ A @ A2 )
% 3.82/4.06 => ( ( insert_nat @ A @ A2 )
% 3.82/4.06 = A2 ) ) ).
% 3.82/4.06
% 3.82/4.06 % insert_absorb
% 3.82/4.06 thf(fact_4675_insert__absorb,axiom,
% 3.82/4.06 ! [A: int,A2: set_int] :
% 3.82/4.06 ( ( member_int @ A @ A2 )
% 3.82/4.06 => ( ( insert_int @ A @ A2 )
% 3.82/4.06 = A2 ) ) ).
% 3.82/4.06
% 3.82/4.06 % insert_absorb
% 3.82/4.06 thf(fact_4676_insert__ident,axiom,
% 3.82/4.06 ! [X: extended_enat,A2: set_Extended_enat,B: set_Extended_enat] :
% 3.82/4.06 ( ~ ( member_Extended_enat @ X @ A2 )
% 3.82/4.06 => ( ~ ( member_Extended_enat @ X @ B )
% 3.82/4.06 => ( ( ( insert_Extended_enat @ X @ A2 )
% 3.82/4.06 = ( insert_Extended_enat @ X @ B ) )
% 3.82/4.06 = ( A2 = B ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % insert_ident
% 3.82/4.06 thf(fact_4677_insert__ident,axiom,
% 3.82/4.06 ! [X: real,A2: set_real,B: set_real] :
% 3.82/4.06 ( ~ ( member_real @ X @ A2 )
% 3.82/4.06 => ( ~ ( member_real @ X @ B )
% 3.82/4.06 => ( ( ( insert_real @ X @ A2 )
% 3.82/4.06 = ( insert_real @ X @ B ) )
% 3.82/4.06 = ( A2 = B ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % insert_ident
% 3.82/4.06 thf(fact_4678_insert__ident,axiom,
% 3.82/4.06 ! [X: set_nat,A2: set_set_nat,B: set_set_nat] :
% 3.82/4.06 ( ~ ( member_set_nat @ X @ A2 )
% 3.82/4.06 => ( ~ ( member_set_nat @ X @ B )
% 3.82/4.06 => ( ( ( insert_set_nat @ X @ A2 )
% 3.82/4.06 = ( insert_set_nat @ X @ B ) )
% 3.82/4.06 = ( A2 = B ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % insert_ident
% 3.82/4.06 thf(fact_4679_insert__ident,axiom,
% 3.82/4.06 ! [X: nat,A2: set_nat,B: set_nat] :
% 3.82/4.06 ( ~ ( member_nat @ X @ A2 )
% 3.82/4.06 => ( ~ ( member_nat @ X @ B )
% 3.82/4.06 => ( ( ( insert_nat @ X @ A2 )
% 3.82/4.06 = ( insert_nat @ X @ B ) )
% 3.82/4.06 = ( A2 = B ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % insert_ident
% 3.82/4.06 thf(fact_4680_insert__ident,axiom,
% 3.82/4.06 ! [X: int,A2: set_int,B: set_int] :
% 3.82/4.06 ( ~ ( member_int @ X @ A2 )
% 3.82/4.06 => ( ~ ( member_int @ X @ B )
% 3.82/4.06 => ( ( ( insert_int @ X @ A2 )
% 3.82/4.06 = ( insert_int @ X @ B ) )
% 3.82/4.06 = ( A2 = B ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % insert_ident
% 3.82/4.06 thf(fact_4681_Set_Oset__insert,axiom,
% 3.82/4.06 ! [X: extended_enat,A2: set_Extended_enat] :
% 3.82/4.06 ( ( member_Extended_enat @ X @ A2 )
% 3.82/4.06 => ~ ! [B8: set_Extended_enat] :
% 3.82/4.06 ( ( A2
% 3.82/4.06 = ( insert_Extended_enat @ X @ B8 ) )
% 3.82/4.06 => ( member_Extended_enat @ X @ B8 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % Set.set_insert
% 3.82/4.06 thf(fact_4682_Set_Oset__insert,axiom,
% 3.82/4.06 ! [X: real,A2: set_real] :
% 3.82/4.06 ( ( member_real @ X @ A2 )
% 3.82/4.06 => ~ ! [B8: set_real] :
% 3.82/4.06 ( ( A2
% 3.82/4.06 = ( insert_real @ X @ B8 ) )
% 3.82/4.06 => ( member_real @ X @ B8 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % Set.set_insert
% 3.82/4.06 thf(fact_4683_Set_Oset__insert,axiom,
% 3.82/4.06 ! [X: set_nat,A2: set_set_nat] :
% 3.82/4.06 ( ( member_set_nat @ X @ A2 )
% 3.82/4.06 => ~ ! [B8: set_set_nat] :
% 3.82/4.06 ( ( A2
% 3.82/4.06 = ( insert_set_nat @ X @ B8 ) )
% 3.82/4.06 => ( member_set_nat @ X @ B8 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % Set.set_insert
% 3.82/4.06 thf(fact_4684_Set_Oset__insert,axiom,
% 3.82/4.06 ! [X: nat,A2: set_nat] :
% 3.82/4.06 ( ( member_nat @ X @ A2 )
% 3.82/4.06 => ~ ! [B8: set_nat] :
% 3.82/4.06 ( ( A2
% 3.82/4.06 = ( insert_nat @ X @ B8 ) )
% 3.82/4.06 => ( member_nat @ X @ B8 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % Set.set_insert
% 3.82/4.06 thf(fact_4685_Set_Oset__insert,axiom,
% 3.82/4.06 ! [X: int,A2: set_int] :
% 3.82/4.06 ( ( member_int @ X @ A2 )
% 3.82/4.06 => ~ ! [B8: set_int] :
% 3.82/4.06 ( ( A2
% 3.82/4.06 = ( insert_int @ X @ B8 ) )
% 3.82/4.06 => ( member_int @ X @ B8 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % Set.set_insert
% 3.82/4.06 thf(fact_4686_insertI2,axiom,
% 3.82/4.06 ! [A: extended_enat,B: set_Extended_enat,B2: extended_enat] :
% 3.82/4.06 ( ( member_Extended_enat @ A @ B )
% 3.82/4.06 => ( member_Extended_enat @ A @ ( insert_Extended_enat @ B2 @ B ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % insertI2
% 3.82/4.06 thf(fact_4687_insertI2,axiom,
% 3.82/4.06 ! [A: real,B: set_real,B2: real] :
% 3.82/4.06 ( ( member_real @ A @ B )
% 3.82/4.06 => ( member_real @ A @ ( insert_real @ B2 @ B ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % insertI2
% 3.82/4.06 thf(fact_4688_insertI2,axiom,
% 3.82/4.06 ! [A: set_nat,B: set_set_nat,B2: set_nat] :
% 3.82/4.06 ( ( member_set_nat @ A @ B )
% 3.82/4.06 => ( member_set_nat @ A @ ( insert_set_nat @ B2 @ B ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % insertI2
% 3.82/4.06 thf(fact_4689_insertI2,axiom,
% 3.82/4.06 ! [A: nat,B: set_nat,B2: nat] :
% 3.82/4.06 ( ( member_nat @ A @ B )
% 3.82/4.06 => ( member_nat @ A @ ( insert_nat @ B2 @ B ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % insertI2
% 3.82/4.06 thf(fact_4690_insertI2,axiom,
% 3.82/4.06 ! [A: int,B: set_int,B2: int] :
% 3.82/4.06 ( ( member_int @ A @ B )
% 3.82/4.06 => ( member_int @ A @ ( insert_int @ B2 @ B ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % insertI2
% 3.82/4.06 thf(fact_4691_insertI1,axiom,
% 3.82/4.06 ! [A: extended_enat,B: set_Extended_enat] : ( member_Extended_enat @ A @ ( insert_Extended_enat @ A @ B ) ) ).
% 3.82/4.06
% 3.82/4.06 % insertI1
% 3.82/4.06 thf(fact_4692_insertI1,axiom,
% 3.82/4.06 ! [A: real,B: set_real] : ( member_real @ A @ ( insert_real @ A @ B ) ) ).
% 3.82/4.06
% 3.82/4.06 % insertI1
% 3.82/4.06 thf(fact_4693_insertI1,axiom,
% 3.82/4.06 ! [A: set_nat,B: set_set_nat] : ( member_set_nat @ A @ ( insert_set_nat @ A @ B ) ) ).
% 3.82/4.06
% 3.82/4.06 % insertI1
% 3.82/4.06 thf(fact_4694_insertI1,axiom,
% 3.82/4.06 ! [A: nat,B: set_nat] : ( member_nat @ A @ ( insert_nat @ A @ B ) ) ).
% 3.82/4.06
% 3.82/4.06 % insertI1
% 3.82/4.06 thf(fact_4695_insertI1,axiom,
% 3.82/4.06 ! [A: int,B: set_int] : ( member_int @ A @ ( insert_int @ A @ B ) ) ).
% 3.82/4.06
% 3.82/4.06 % insertI1
% 3.82/4.06 thf(fact_4696_insertE,axiom,
% 3.82/4.06 ! [A: extended_enat,B2: extended_enat,A2: set_Extended_enat] :
% 3.82/4.06 ( ( member_Extended_enat @ A @ ( insert_Extended_enat @ B2 @ A2 ) )
% 3.82/4.06 => ( ( A != B2 )
% 3.82/4.06 => ( member_Extended_enat @ A @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % insertE
% 3.82/4.06 thf(fact_4697_insertE,axiom,
% 3.82/4.06 ! [A: real,B2: real,A2: set_real] :
% 3.82/4.06 ( ( member_real @ A @ ( insert_real @ B2 @ A2 ) )
% 3.82/4.06 => ( ( A != B2 )
% 3.82/4.06 => ( member_real @ A @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % insertE
% 3.82/4.06 thf(fact_4698_insertE,axiom,
% 3.82/4.06 ! [A: set_nat,B2: set_nat,A2: set_set_nat] :
% 3.82/4.06 ( ( member_set_nat @ A @ ( insert_set_nat @ B2 @ A2 ) )
% 3.82/4.06 => ( ( A != B2 )
% 3.82/4.06 => ( member_set_nat @ A @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % insertE
% 3.82/4.06 thf(fact_4699_insertE,axiom,
% 3.82/4.06 ! [A: nat,B2: nat,A2: set_nat] :
% 3.82/4.06 ( ( member_nat @ A @ ( insert_nat @ B2 @ A2 ) )
% 3.82/4.06 => ( ( A != B2 )
% 3.82/4.06 => ( member_nat @ A @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % insertE
% 3.82/4.06 thf(fact_4700_insertE,axiom,
% 3.82/4.06 ! [A: int,B2: int,A2: set_int] :
% 3.82/4.06 ( ( member_int @ A @ ( insert_int @ B2 @ A2 ) )
% 3.82/4.06 => ( ( A != B2 )
% 3.82/4.06 => ( member_int @ A @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % insertE
% 3.82/4.06 thf(fact_4701_int__ge__induct,axiom,
% 3.82/4.06 ! [K: int,I: int,P: int > $o] :
% 3.82/4.06 ( ( ord_less_eq_int @ K @ I )
% 3.82/4.06 => ( ( P @ K )
% 3.82/4.06 => ( ! [I4: int] :
% 3.82/4.06 ( ( ord_less_eq_int @ K @ I4 )
% 3.82/4.06 => ( ( P @ I4 )
% 3.82/4.06 => ( P @ ( plus_plus_int @ I4 @ one_one_int ) ) ) )
% 3.82/4.06 => ( P @ I ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % int_ge_induct
% 3.82/4.06 thf(fact_4702_singletonD,axiom,
% 3.82/4.06 ! [B2: set_nat,A: set_nat] :
% 3.82/4.06 ( ( member_set_nat @ B2 @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) )
% 3.82/4.06 => ( B2 = A ) ) ).
% 3.82/4.06
% 3.82/4.06 % singletonD
% 3.82/4.06 thf(fact_4703_singletonD,axiom,
% 3.82/4.06 ! [B2: extended_enat,A: extended_enat] :
% 3.82/4.06 ( ( member_Extended_enat @ B2 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) )
% 3.82/4.06 => ( B2 = A ) ) ).
% 3.82/4.06
% 3.82/4.06 % singletonD
% 3.82/4.06 thf(fact_4704_singletonD,axiom,
% 3.82/4.06 ! [B2: real,A: real] :
% 3.82/4.06 ( ( member_real @ B2 @ ( insert_real @ A @ bot_bot_set_real ) )
% 3.82/4.06 => ( B2 = A ) ) ).
% 3.82/4.06
% 3.82/4.06 % singletonD
% 3.82/4.06 thf(fact_4705_singletonD,axiom,
% 3.82/4.06 ! [B2: nat,A: nat] :
% 3.82/4.06 ( ( member_nat @ B2 @ ( insert_nat @ A @ bot_bot_set_nat ) )
% 3.82/4.06 => ( B2 = A ) ) ).
% 3.82/4.06
% 3.82/4.06 % singletonD
% 3.82/4.06 thf(fact_4706_singletonD,axiom,
% 3.82/4.06 ! [B2: int,A: int] :
% 3.82/4.06 ( ( member_int @ B2 @ ( insert_int @ A @ bot_bot_set_int ) )
% 3.82/4.06 => ( B2 = A ) ) ).
% 3.82/4.06
% 3.82/4.06 % singletonD
% 3.82/4.06 thf(fact_4707_singleton__iff,axiom,
% 3.82/4.06 ! [B2: set_nat,A: set_nat] :
% 3.82/4.06 ( ( member_set_nat @ B2 @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) )
% 3.82/4.06 = ( B2 = A ) ) ).
% 3.82/4.06
% 3.82/4.06 % singleton_iff
% 3.82/4.06 thf(fact_4708_singleton__iff,axiom,
% 3.82/4.06 ! [B2: extended_enat,A: extended_enat] :
% 3.82/4.06 ( ( member_Extended_enat @ B2 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) )
% 3.82/4.06 = ( B2 = A ) ) ).
% 3.82/4.06
% 3.82/4.06 % singleton_iff
% 3.82/4.06 thf(fact_4709_singleton__iff,axiom,
% 3.82/4.06 ! [B2: real,A: real] :
% 3.82/4.06 ( ( member_real @ B2 @ ( insert_real @ A @ bot_bot_set_real ) )
% 3.82/4.06 = ( B2 = A ) ) ).
% 3.82/4.06
% 3.82/4.06 % singleton_iff
% 3.82/4.06 thf(fact_4710_singleton__iff,axiom,
% 3.82/4.06 ! [B2: nat,A: nat] :
% 3.82/4.06 ( ( member_nat @ B2 @ ( insert_nat @ A @ bot_bot_set_nat ) )
% 3.82/4.06 = ( B2 = A ) ) ).
% 3.82/4.06
% 3.82/4.06 % singleton_iff
% 3.82/4.06 thf(fact_4711_singleton__iff,axiom,
% 3.82/4.06 ! [B2: int,A: int] :
% 3.82/4.06 ( ( member_int @ B2 @ ( insert_int @ A @ bot_bot_set_int ) )
% 3.82/4.06 = ( B2 = A ) ) ).
% 3.82/4.06
% 3.82/4.06 % singleton_iff
% 3.82/4.06 thf(fact_4712_doubleton__eq__iff,axiom,
% 3.82/4.06 ! [A: extended_enat,B2: extended_enat,C: extended_enat,D: extended_enat] :
% 3.82/4.06 ( ( ( insert_Extended_enat @ A @ ( insert_Extended_enat @ B2 @ bot_bo7653980558646680370d_enat ) )
% 3.82/4.06 = ( insert_Extended_enat @ C @ ( insert_Extended_enat @ D @ bot_bo7653980558646680370d_enat ) ) )
% 3.82/4.06 = ( ( ( A = C )
% 3.82/4.06 & ( B2 = D ) )
% 3.82/4.06 | ( ( A = D )
% 3.82/4.06 & ( B2 = C ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % doubleton_eq_iff
% 3.82/4.06 thf(fact_4713_doubleton__eq__iff,axiom,
% 3.82/4.06 ! [A: real,B2: real,C: real,D: real] :
% 3.82/4.06 ( ( ( insert_real @ A @ ( insert_real @ B2 @ bot_bot_set_real ) )
% 3.82/4.06 = ( insert_real @ C @ ( insert_real @ D @ bot_bot_set_real ) ) )
% 3.82/4.06 = ( ( ( A = C )
% 3.82/4.06 & ( B2 = D ) )
% 3.82/4.06 | ( ( A = D )
% 3.82/4.06 & ( B2 = C ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % doubleton_eq_iff
% 3.82/4.06 thf(fact_4714_doubleton__eq__iff,axiom,
% 3.82/4.06 ! [A: nat,B2: nat,C: nat,D: nat] :
% 3.82/4.06 ( ( ( insert_nat @ A @ ( insert_nat @ B2 @ bot_bot_set_nat ) )
% 3.82/4.06 = ( insert_nat @ C @ ( insert_nat @ D @ bot_bot_set_nat ) ) )
% 3.82/4.06 = ( ( ( A = C )
% 3.82/4.06 & ( B2 = D ) )
% 3.82/4.06 | ( ( A = D )
% 3.82/4.06 & ( B2 = C ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % doubleton_eq_iff
% 3.82/4.06 thf(fact_4715_doubleton__eq__iff,axiom,
% 3.82/4.06 ! [A: int,B2: int,C: int,D: int] :
% 3.82/4.06 ( ( ( insert_int @ A @ ( insert_int @ B2 @ bot_bot_set_int ) )
% 3.82/4.06 = ( insert_int @ C @ ( insert_int @ D @ bot_bot_set_int ) ) )
% 3.82/4.06 = ( ( ( A = C )
% 3.82/4.06 & ( B2 = D ) )
% 3.82/4.06 | ( ( A = D )
% 3.82/4.06 & ( B2 = C ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % doubleton_eq_iff
% 3.82/4.06 thf(fact_4716_insert__not__empty,axiom,
% 3.82/4.06 ! [A: extended_enat,A2: set_Extended_enat] :
% 3.82/4.06 ( ( insert_Extended_enat @ A @ A2 )
% 3.82/4.06 != bot_bo7653980558646680370d_enat ) ).
% 3.82/4.06
% 3.82/4.06 % insert_not_empty
% 3.82/4.06 thf(fact_4717_insert__not__empty,axiom,
% 3.82/4.06 ! [A: real,A2: set_real] :
% 3.82/4.06 ( ( insert_real @ A @ A2 )
% 3.82/4.06 != bot_bot_set_real ) ).
% 3.82/4.06
% 3.82/4.06 % insert_not_empty
% 3.82/4.06 thf(fact_4718_insert__not__empty,axiom,
% 3.82/4.06 ! [A: nat,A2: set_nat] :
% 3.82/4.06 ( ( insert_nat @ A @ A2 )
% 3.82/4.06 != bot_bot_set_nat ) ).
% 3.82/4.06
% 3.82/4.06 % insert_not_empty
% 3.82/4.06 thf(fact_4719_insert__not__empty,axiom,
% 3.82/4.06 ! [A: int,A2: set_int] :
% 3.82/4.06 ( ( insert_int @ A @ A2 )
% 3.82/4.06 != bot_bot_set_int ) ).
% 3.82/4.06
% 3.82/4.06 % insert_not_empty
% 3.82/4.06 thf(fact_4720_singleton__inject,axiom,
% 3.82/4.06 ! [A: extended_enat,B2: extended_enat] :
% 3.82/4.06 ( ( ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat )
% 3.82/4.06 = ( insert_Extended_enat @ B2 @ bot_bo7653980558646680370d_enat ) )
% 3.82/4.06 => ( A = B2 ) ) ).
% 3.82/4.06
% 3.82/4.06 % singleton_inject
% 3.82/4.06 thf(fact_4721_singleton__inject,axiom,
% 3.82/4.06 ! [A: real,B2: real] :
% 3.82/4.06 ( ( ( insert_real @ A @ bot_bot_set_real )
% 3.82/4.06 = ( insert_real @ B2 @ bot_bot_set_real ) )
% 3.82/4.06 => ( A = B2 ) ) ).
% 3.82/4.06
% 3.82/4.06 % singleton_inject
% 3.82/4.06 thf(fact_4722_singleton__inject,axiom,
% 3.82/4.06 ! [A: nat,B2: nat] :
% 3.82/4.06 ( ( ( insert_nat @ A @ bot_bot_set_nat )
% 3.82/4.06 = ( insert_nat @ B2 @ bot_bot_set_nat ) )
% 3.82/4.06 => ( A = B2 ) ) ).
% 3.82/4.06
% 3.82/4.06 % singleton_inject
% 3.82/4.06 thf(fact_4723_singleton__inject,axiom,
% 3.82/4.06 ! [A: int,B2: int] :
% 3.82/4.06 ( ( ( insert_int @ A @ bot_bot_set_int )
% 3.82/4.06 = ( insert_int @ B2 @ bot_bot_set_int ) )
% 3.82/4.06 => ( A = B2 ) ) ).
% 3.82/4.06
% 3.82/4.06 % singleton_inject
% 3.82/4.06 thf(fact_4724_Compl__insert,axiom,
% 3.82/4.06 ! [X: extended_enat,A2: set_Extended_enat] :
% 3.82/4.06 ( ( uminus417252749190364093d_enat @ ( insert_Extended_enat @ X @ A2 ) )
% 3.82/4.06 = ( minus_925952699566721837d_enat @ ( uminus417252749190364093d_enat @ A2 ) @ ( insert_Extended_enat @ X @ bot_bo7653980558646680370d_enat ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % Compl_insert
% 3.82/4.06 thf(fact_4725_Compl__insert,axiom,
% 3.82/4.06 ! [X: real,A2: set_real] :
% 3.82/4.06 ( ( uminus612125837232591019t_real @ ( insert_real @ X @ A2 ) )
% 3.82/4.06 = ( minus_minus_set_real @ ( uminus612125837232591019t_real @ A2 ) @ ( insert_real @ X @ bot_bot_set_real ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % Compl_insert
% 3.82/4.06 thf(fact_4726_Compl__insert,axiom,
% 3.82/4.06 ! [X: int,A2: set_int] :
% 3.82/4.06 ( ( uminus1532241313380277803et_int @ ( insert_int @ X @ A2 ) )
% 3.82/4.06 = ( minus_minus_set_int @ ( uminus1532241313380277803et_int @ A2 ) @ ( insert_int @ X @ bot_bot_set_int ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % Compl_insert
% 3.82/4.06 thf(fact_4727_Compl__insert,axiom,
% 3.82/4.06 ! [X: nat,A2: set_nat] :
% 3.82/4.06 ( ( uminus5710092332889474511et_nat @ ( insert_nat @ X @ A2 ) )
% 3.82/4.06 = ( minus_minus_set_nat @ ( uminus5710092332889474511et_nat @ A2 ) @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % Compl_insert
% 3.82/4.06 thf(fact_4728_Diff__insert,axiom,
% 3.82/4.06 ! [A2: set_Extended_enat,A: extended_enat,B: set_Extended_enat] :
% 3.82/4.06 ( ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ A @ B ) )
% 3.82/4.06 = ( minus_925952699566721837d_enat @ ( minus_925952699566721837d_enat @ A2 @ B ) @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % Diff_insert
% 3.82/4.06 thf(fact_4729_Diff__insert,axiom,
% 3.82/4.06 ! [A2: set_real,A: real,B: set_real] :
% 3.82/4.06 ( ( minus_minus_set_real @ A2 @ ( insert_real @ A @ B ) )
% 3.82/4.06 = ( minus_minus_set_real @ ( minus_minus_set_real @ A2 @ B ) @ ( insert_real @ A @ bot_bot_set_real ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % Diff_insert
% 3.82/4.06 thf(fact_4730_Diff__insert,axiom,
% 3.82/4.06 ! [A2: set_int,A: int,B: set_int] :
% 3.82/4.06 ( ( minus_minus_set_int @ A2 @ ( insert_int @ A @ B ) )
% 3.82/4.06 = ( minus_minus_set_int @ ( minus_minus_set_int @ A2 @ B ) @ ( insert_int @ A @ bot_bot_set_int ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % Diff_insert
% 3.82/4.06 thf(fact_4731_Diff__insert,axiom,
% 3.82/4.06 ! [A2: set_nat,A: nat,B: set_nat] :
% 3.82/4.06 ( ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ B ) )
% 3.82/4.06 = ( minus_minus_set_nat @ ( minus_minus_set_nat @ A2 @ B ) @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % Diff_insert
% 3.82/4.06 thf(fact_4732_insert__Diff,axiom,
% 3.82/4.06 ! [A: set_nat,A2: set_set_nat] :
% 3.82/4.06 ( ( member_set_nat @ A @ A2 )
% 3.82/4.06 => ( ( insert_set_nat @ A @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 3.82/4.06 = A2 ) ) ).
% 3.82/4.06
% 3.82/4.06 % insert_Diff
% 3.82/4.06 thf(fact_4733_insert__Diff,axiom,
% 3.82/4.06 ! [A: extended_enat,A2: set_Extended_enat] :
% 3.82/4.06 ( ( member_Extended_enat @ A @ A2 )
% 3.82/4.06 => ( ( insert_Extended_enat @ A @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) )
% 3.82/4.06 = A2 ) ) ).
% 3.82/4.06
% 3.82/4.06 % insert_Diff
% 3.82/4.06 thf(fact_4734_insert__Diff,axiom,
% 3.82/4.06 ! [A: real,A2: set_real] :
% 3.82/4.06 ( ( member_real @ A @ A2 )
% 3.82/4.06 => ( ( insert_real @ A @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 3.82/4.06 = A2 ) ) ).
% 3.82/4.06
% 3.82/4.06 % insert_Diff
% 3.82/4.06 thf(fact_4735_insert__Diff,axiom,
% 3.82/4.06 ! [A: int,A2: set_int] :
% 3.82/4.06 ( ( member_int @ A @ A2 )
% 3.82/4.06 => ( ( insert_int @ A @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 3.82/4.06 = A2 ) ) ).
% 3.82/4.06
% 3.82/4.06 % insert_Diff
% 3.82/4.06 thf(fact_4736_insert__Diff,axiom,
% 3.82/4.06 ! [A: nat,A2: set_nat] :
% 3.82/4.06 ( ( member_nat @ A @ A2 )
% 3.82/4.06 => ( ( insert_nat @ A @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 3.82/4.06 = A2 ) ) ).
% 3.82/4.06
% 3.82/4.06 % insert_Diff
% 3.82/4.06 thf(fact_4737_Diff__insert2,axiom,
% 3.82/4.06 ! [A2: set_Extended_enat,A: extended_enat,B: set_Extended_enat] :
% 3.82/4.06 ( ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ A @ B ) )
% 3.82/4.06 = ( minus_925952699566721837d_enat @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) @ B ) ) ).
% 3.82/4.06
% 3.82/4.06 % Diff_insert2
% 3.82/4.06 thf(fact_4738_Diff__insert2,axiom,
% 3.82/4.06 ! [A2: set_real,A: real,B: set_real] :
% 3.82/4.06 ( ( minus_minus_set_real @ A2 @ ( insert_real @ A @ B ) )
% 3.82/4.06 = ( minus_minus_set_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) @ B ) ) ).
% 3.82/4.06
% 3.82/4.06 % Diff_insert2
% 3.82/4.06 thf(fact_4739_Diff__insert2,axiom,
% 3.82/4.06 ! [A2: set_int,A: int,B: set_int] :
% 3.82/4.06 ( ( minus_minus_set_int @ A2 @ ( insert_int @ A @ B ) )
% 3.82/4.06 = ( minus_minus_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) @ B ) ) ).
% 3.82/4.06
% 3.82/4.06 % Diff_insert2
% 3.82/4.06 thf(fact_4740_Diff__insert2,axiom,
% 3.82/4.06 ! [A2: set_nat,A: nat,B: set_nat] :
% 3.82/4.06 ( ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ B ) )
% 3.82/4.06 = ( minus_minus_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) @ B ) ) ).
% 3.82/4.06
% 3.82/4.06 % Diff_insert2
% 3.82/4.06 thf(fact_4741_Diff__insert__absorb,axiom,
% 3.82/4.06 ! [X: set_nat,A2: set_set_nat] :
% 3.82/4.06 ( ~ ( member_set_nat @ X @ A2 )
% 3.82/4.06 => ( ( minus_2163939370556025621et_nat @ ( insert_set_nat @ X @ A2 ) @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) )
% 3.82/4.06 = A2 ) ) ).
% 3.82/4.06
% 3.82/4.06 % Diff_insert_absorb
% 3.82/4.06 thf(fact_4742_Diff__insert__absorb,axiom,
% 3.82/4.06 ! [X: extended_enat,A2: set_Extended_enat] :
% 3.82/4.06 ( ~ ( member_Extended_enat @ X @ A2 )
% 3.82/4.06 => ( ( minus_925952699566721837d_enat @ ( insert_Extended_enat @ X @ A2 ) @ ( insert_Extended_enat @ X @ bot_bo7653980558646680370d_enat ) )
% 3.82/4.06 = A2 ) ) ).
% 3.82/4.06
% 3.82/4.06 % Diff_insert_absorb
% 3.82/4.06 thf(fact_4743_Diff__insert__absorb,axiom,
% 3.82/4.06 ! [X: real,A2: set_real] :
% 3.82/4.06 ( ~ ( member_real @ X @ A2 )
% 3.82/4.06 => ( ( minus_minus_set_real @ ( insert_real @ X @ A2 ) @ ( insert_real @ X @ bot_bot_set_real ) )
% 3.82/4.06 = A2 ) ) ).
% 3.82/4.06
% 3.82/4.06 % Diff_insert_absorb
% 3.82/4.06 thf(fact_4744_Diff__insert__absorb,axiom,
% 3.82/4.06 ! [X: int,A2: set_int] :
% 3.82/4.06 ( ~ ( member_int @ X @ A2 )
% 3.82/4.06 => ( ( minus_minus_set_int @ ( insert_int @ X @ A2 ) @ ( insert_int @ X @ bot_bot_set_int ) )
% 3.82/4.06 = A2 ) ) ).
% 3.82/4.06
% 3.82/4.06 % Diff_insert_absorb
% 3.82/4.06 thf(fact_4745_Diff__insert__absorb,axiom,
% 3.82/4.06 ! [X: nat,A2: set_nat] :
% 3.82/4.06 ( ~ ( member_nat @ X @ A2 )
% 3.82/4.06 => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A2 ) @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 3.82/4.06 = A2 ) ) ).
% 3.82/4.06
% 3.82/4.06 % Diff_insert_absorb
% 3.82/4.06 thf(fact_4746_finite_OinsertI,axiom,
% 3.82/4.06 ! [A2: set_real,A: real] :
% 3.82/4.06 ( ( finite_finite_real @ A2 )
% 3.82/4.06 => ( finite_finite_real @ ( insert_real @ A @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite.insertI
% 3.82/4.06 thf(fact_4747_finite_OinsertI,axiom,
% 3.82/4.06 ! [A2: set_nat,A: nat] :
% 3.82/4.06 ( ( finite_finite_nat @ A2 )
% 3.82/4.06 => ( finite_finite_nat @ ( insert_nat @ A @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite.insertI
% 3.82/4.06 thf(fact_4748_finite_OinsertI,axiom,
% 3.82/4.06 ! [A2: set_complex,A: complex] :
% 3.82/4.06 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.06 => ( finite3207457112153483333omplex @ ( insert_complex @ A @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite.insertI
% 3.82/4.06 thf(fact_4749_finite_OinsertI,axiom,
% 3.82/4.06 ! [A2: set_int,A: int] :
% 3.82/4.06 ( ( finite_finite_int @ A2 )
% 3.82/4.06 => ( finite_finite_int @ ( insert_int @ A @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite.insertI
% 3.82/4.06 thf(fact_4750_finite_OinsertI,axiom,
% 3.82/4.06 ! [A2: set_Extended_enat,A: extended_enat] :
% 3.82/4.06 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.06 => ( finite4001608067531595151d_enat @ ( insert_Extended_enat @ A @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite.insertI
% 3.82/4.06 thf(fact_4751_insert__mono,axiom,
% 3.82/4.06 ! [C4: set_real,D6: set_real,A: real] :
% 3.82/4.06 ( ( ord_less_eq_set_real @ C4 @ D6 )
% 3.82/4.06 => ( ord_less_eq_set_real @ ( insert_real @ A @ C4 ) @ ( insert_real @ A @ D6 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % insert_mono
% 3.82/4.06 thf(fact_4752_insert__mono,axiom,
% 3.82/4.06 ! [C4: set_nat,D6: set_nat,A: nat] :
% 3.82/4.06 ( ( ord_less_eq_set_nat @ C4 @ D6 )
% 3.82/4.06 => ( ord_less_eq_set_nat @ ( insert_nat @ A @ C4 ) @ ( insert_nat @ A @ D6 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % insert_mono
% 3.82/4.06 thf(fact_4753_insert__mono,axiom,
% 3.82/4.06 ! [C4: set_int,D6: set_int,A: int] :
% 3.82/4.06 ( ( ord_less_eq_set_int @ C4 @ D6 )
% 3.82/4.06 => ( ord_less_eq_set_int @ ( insert_int @ A @ C4 ) @ ( insert_int @ A @ D6 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % insert_mono
% 3.82/4.06 thf(fact_4754_subset__insert,axiom,
% 3.82/4.06 ! [X: extended_enat,A2: set_Extended_enat,B: set_Extended_enat] :
% 3.82/4.06 ( ~ ( member_Extended_enat @ X @ A2 )
% 3.82/4.06 => ( ( ord_le7203529160286727270d_enat @ A2 @ ( insert_Extended_enat @ X @ B ) )
% 3.82/4.06 = ( ord_le7203529160286727270d_enat @ A2 @ B ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % subset_insert
% 3.82/4.06 thf(fact_4755_subset__insert,axiom,
% 3.82/4.06 ! [X: real,A2: set_real,B: set_real] :
% 3.82/4.06 ( ~ ( member_real @ X @ A2 )
% 3.82/4.06 => ( ( ord_less_eq_set_real @ A2 @ ( insert_real @ X @ B ) )
% 3.82/4.06 = ( ord_less_eq_set_real @ A2 @ B ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % subset_insert
% 3.82/4.06 thf(fact_4756_subset__insert,axiom,
% 3.82/4.06 ! [X: set_nat,A2: set_set_nat,B: set_set_nat] :
% 3.82/4.06 ( ~ ( member_set_nat @ X @ A2 )
% 3.82/4.06 => ( ( ord_le6893508408891458716et_nat @ A2 @ ( insert_set_nat @ X @ B ) )
% 3.82/4.06 = ( ord_le6893508408891458716et_nat @ A2 @ B ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % subset_insert
% 3.82/4.06 thf(fact_4757_subset__insert,axiom,
% 3.82/4.06 ! [X: nat,A2: set_nat,B: set_nat] :
% 3.82/4.06 ( ~ ( member_nat @ X @ A2 )
% 3.82/4.06 => ( ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X @ B ) )
% 3.82/4.06 = ( ord_less_eq_set_nat @ A2 @ B ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % subset_insert
% 3.82/4.06 thf(fact_4758_subset__insert,axiom,
% 3.82/4.06 ! [X: int,A2: set_int,B: set_int] :
% 3.82/4.06 ( ~ ( member_int @ X @ A2 )
% 3.82/4.06 => ( ( ord_less_eq_set_int @ A2 @ ( insert_int @ X @ B ) )
% 3.82/4.06 = ( ord_less_eq_set_int @ A2 @ B ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % subset_insert
% 3.82/4.06 thf(fact_4759_subset__insertI,axiom,
% 3.82/4.06 ! [B: set_real,A: real] : ( ord_less_eq_set_real @ B @ ( insert_real @ A @ B ) ) ).
% 3.82/4.06
% 3.82/4.06 % subset_insertI
% 3.82/4.06 thf(fact_4760_subset__insertI,axiom,
% 3.82/4.06 ! [B: set_nat,A: nat] : ( ord_less_eq_set_nat @ B @ ( insert_nat @ A @ B ) ) ).
% 3.82/4.06
% 3.82/4.06 % subset_insertI
% 3.82/4.06 thf(fact_4761_subset__insertI,axiom,
% 3.82/4.06 ! [B: set_int,A: int] : ( ord_less_eq_set_int @ B @ ( insert_int @ A @ B ) ) ).
% 3.82/4.06
% 3.82/4.06 % subset_insertI
% 3.82/4.06 thf(fact_4762_subset__insertI2,axiom,
% 3.82/4.06 ! [A2: set_real,B: set_real,B2: real] :
% 3.82/4.06 ( ( ord_less_eq_set_real @ A2 @ B )
% 3.82/4.06 => ( ord_less_eq_set_real @ A2 @ ( insert_real @ B2 @ B ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % subset_insertI2
% 3.82/4.06 thf(fact_4763_subset__insertI2,axiom,
% 3.82/4.06 ! [A2: set_nat,B: set_nat,B2: nat] :
% 3.82/4.06 ( ( ord_less_eq_set_nat @ A2 @ B )
% 3.82/4.06 => ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ B2 @ B ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % subset_insertI2
% 3.82/4.06 thf(fact_4764_subset__insertI2,axiom,
% 3.82/4.06 ! [A2: set_int,B: set_int,B2: int] :
% 3.82/4.06 ( ( ord_less_eq_set_int @ A2 @ B )
% 3.82/4.06 => ( ord_less_eq_set_int @ A2 @ ( insert_int @ B2 @ B ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % subset_insertI2
% 3.82/4.06 thf(fact_4765_insert__subsetI,axiom,
% 3.82/4.06 ! [X: extended_enat,A2: set_Extended_enat,X8: set_Extended_enat] :
% 3.82/4.06 ( ( member_Extended_enat @ X @ A2 )
% 3.82/4.06 => ( ( ord_le7203529160286727270d_enat @ X8 @ A2 )
% 3.82/4.06 => ( ord_le7203529160286727270d_enat @ ( insert_Extended_enat @ X @ X8 ) @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % insert_subsetI
% 3.82/4.06 thf(fact_4766_insert__subsetI,axiom,
% 3.82/4.06 ! [X: real,A2: set_real,X8: set_real] :
% 3.82/4.06 ( ( member_real @ X @ A2 )
% 3.82/4.06 => ( ( ord_less_eq_set_real @ X8 @ A2 )
% 3.82/4.06 => ( ord_less_eq_set_real @ ( insert_real @ X @ X8 ) @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % insert_subsetI
% 3.82/4.06 thf(fact_4767_insert__subsetI,axiom,
% 3.82/4.06 ! [X: set_nat,A2: set_set_nat,X8: set_set_nat] :
% 3.82/4.06 ( ( member_set_nat @ X @ A2 )
% 3.82/4.06 => ( ( ord_le6893508408891458716et_nat @ X8 @ A2 )
% 3.82/4.06 => ( ord_le6893508408891458716et_nat @ ( insert_set_nat @ X @ X8 ) @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % insert_subsetI
% 3.82/4.06 thf(fact_4768_insert__subsetI,axiom,
% 3.82/4.06 ! [X: nat,A2: set_nat,X8: set_nat] :
% 3.82/4.06 ( ( member_nat @ X @ A2 )
% 3.82/4.06 => ( ( ord_less_eq_set_nat @ X8 @ A2 )
% 3.82/4.06 => ( ord_less_eq_set_nat @ ( insert_nat @ X @ X8 ) @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % insert_subsetI
% 3.82/4.06 thf(fact_4769_insert__subsetI,axiom,
% 3.82/4.06 ! [X: int,A2: set_int,X8: set_int] :
% 3.82/4.06 ( ( member_int @ X @ A2 )
% 3.82/4.06 => ( ( ord_less_eq_set_int @ X8 @ A2 )
% 3.82/4.06 => ( ord_less_eq_set_int @ ( insert_int @ X @ X8 ) @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % insert_subsetI
% 3.82/4.06 thf(fact_4770_subset__Diff__insert,axiom,
% 3.82/4.06 ! [A2: set_Extended_enat,B: set_Extended_enat,X: extended_enat,C4: set_Extended_enat] :
% 3.82/4.06 ( ( ord_le7203529160286727270d_enat @ A2 @ ( minus_925952699566721837d_enat @ B @ ( insert_Extended_enat @ X @ C4 ) ) )
% 3.82/4.06 = ( ( ord_le7203529160286727270d_enat @ A2 @ ( minus_925952699566721837d_enat @ B @ C4 ) )
% 3.82/4.06 & ~ ( member_Extended_enat @ X @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % subset_Diff_insert
% 3.82/4.06 thf(fact_4771_subset__Diff__insert,axiom,
% 3.82/4.06 ! [A2: set_real,B: set_real,X: real,C4: set_real] :
% 3.82/4.06 ( ( ord_less_eq_set_real @ A2 @ ( minus_minus_set_real @ B @ ( insert_real @ X @ C4 ) ) )
% 3.82/4.06 = ( ( ord_less_eq_set_real @ A2 @ ( minus_minus_set_real @ B @ C4 ) )
% 3.82/4.06 & ~ ( member_real @ X @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % subset_Diff_insert
% 3.82/4.06 thf(fact_4772_subset__Diff__insert,axiom,
% 3.82/4.06 ! [A2: set_set_nat,B: set_set_nat,X: set_nat,C4: set_set_nat] :
% 3.82/4.06 ( ( ord_le6893508408891458716et_nat @ A2 @ ( minus_2163939370556025621et_nat @ B @ ( insert_set_nat @ X @ C4 ) ) )
% 3.82/4.06 = ( ( ord_le6893508408891458716et_nat @ A2 @ ( minus_2163939370556025621et_nat @ B @ C4 ) )
% 3.82/4.06 & ~ ( member_set_nat @ X @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % subset_Diff_insert
% 3.82/4.06 thf(fact_4773_subset__Diff__insert,axiom,
% 3.82/4.06 ! [A2: set_nat,B: set_nat,X: nat,C4: set_nat] :
% 3.82/4.06 ( ( ord_less_eq_set_nat @ A2 @ ( minus_minus_set_nat @ B @ ( insert_nat @ X @ C4 ) ) )
% 3.82/4.06 = ( ( ord_less_eq_set_nat @ A2 @ ( minus_minus_set_nat @ B @ C4 ) )
% 3.82/4.06 & ~ ( member_nat @ X @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % subset_Diff_insert
% 3.82/4.06 thf(fact_4774_subset__Diff__insert,axiom,
% 3.82/4.06 ! [A2: set_int,B: set_int,X: int,C4: set_int] :
% 3.82/4.06 ( ( ord_less_eq_set_int @ A2 @ ( minus_minus_set_int @ B @ ( insert_int @ X @ C4 ) ) )
% 3.82/4.06 = ( ( ord_less_eq_set_int @ A2 @ ( minus_minus_set_int @ B @ C4 ) )
% 3.82/4.06 & ~ ( member_int @ X @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % subset_Diff_insert
% 3.82/4.06 thf(fact_4775_Collect__conv__if,axiom,
% 3.82/4.06 ! [P: list_nat > $o,A: list_nat] :
% 3.82/4.06 ( ( ( P @ A )
% 3.82/4.06 => ( ( collect_list_nat
% 3.82/4.06 @ ^ [X4: list_nat] :
% 3.82/4.06 ( ( X4 = A )
% 3.82/4.06 & ( P @ X4 ) ) )
% 3.82/4.06 = ( insert_list_nat @ A @ bot_bot_set_list_nat ) ) )
% 3.82/4.06 & ( ~ ( P @ A )
% 3.82/4.06 => ( ( collect_list_nat
% 3.82/4.06 @ ^ [X4: list_nat] :
% 3.82/4.06 ( ( X4 = A )
% 3.82/4.06 & ( P @ X4 ) ) )
% 3.82/4.06 = bot_bot_set_list_nat ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % Collect_conv_if
% 3.82/4.06 thf(fact_4776_Collect__conv__if,axiom,
% 3.82/4.06 ! [P: set_nat > $o,A: set_nat] :
% 3.82/4.06 ( ( ( P @ A )
% 3.82/4.06 => ( ( collect_set_nat
% 3.82/4.06 @ ^ [X4: set_nat] :
% 3.82/4.06 ( ( X4 = A )
% 3.82/4.06 & ( P @ X4 ) ) )
% 3.82/4.06 = ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 3.82/4.06 & ( ~ ( P @ A )
% 3.82/4.06 => ( ( collect_set_nat
% 3.82/4.06 @ ^ [X4: set_nat] :
% 3.82/4.06 ( ( X4 = A )
% 3.82/4.06 & ( P @ X4 ) ) )
% 3.82/4.06 = bot_bot_set_set_nat ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % Collect_conv_if
% 3.82/4.06 thf(fact_4777_Collect__conv__if,axiom,
% 3.82/4.06 ! [P: extended_enat > $o,A: extended_enat] :
% 3.82/4.06 ( ( ( P @ A )
% 3.82/4.06 => ( ( collec4429806609662206161d_enat
% 3.82/4.06 @ ^ [X4: extended_enat] :
% 3.82/4.06 ( ( X4 = A )
% 3.82/4.06 & ( P @ X4 ) ) )
% 3.82/4.06 = ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) )
% 3.82/4.06 & ( ~ ( P @ A )
% 3.82/4.06 => ( ( collec4429806609662206161d_enat
% 3.82/4.06 @ ^ [X4: extended_enat] :
% 3.82/4.06 ( ( X4 = A )
% 3.82/4.06 & ( P @ X4 ) ) )
% 3.82/4.06 = bot_bo7653980558646680370d_enat ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % Collect_conv_if
% 3.82/4.06 thf(fact_4778_Collect__conv__if,axiom,
% 3.82/4.06 ! [P: real > $o,A: real] :
% 3.82/4.06 ( ( ( P @ A )
% 3.82/4.06 => ( ( collect_real
% 3.82/4.06 @ ^ [X4: real] :
% 3.82/4.06 ( ( X4 = A )
% 3.82/4.06 & ( P @ X4 ) ) )
% 3.82/4.06 = ( insert_real @ A @ bot_bot_set_real ) ) )
% 3.82/4.06 & ( ~ ( P @ A )
% 3.82/4.06 => ( ( collect_real
% 3.82/4.06 @ ^ [X4: real] :
% 3.82/4.06 ( ( X4 = A )
% 3.82/4.06 & ( P @ X4 ) ) )
% 3.82/4.06 = bot_bot_set_real ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % Collect_conv_if
% 3.82/4.06 thf(fact_4779_Collect__conv__if,axiom,
% 3.82/4.06 ! [P: nat > $o,A: nat] :
% 3.82/4.06 ( ( ( P @ A )
% 3.82/4.06 => ( ( collect_nat
% 3.82/4.06 @ ^ [X4: nat] :
% 3.82/4.06 ( ( X4 = A )
% 3.82/4.06 & ( P @ X4 ) ) )
% 3.82/4.06 = ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 3.82/4.06 & ( ~ ( P @ A )
% 3.82/4.06 => ( ( collect_nat
% 3.82/4.06 @ ^ [X4: nat] :
% 3.82/4.06 ( ( X4 = A )
% 3.82/4.06 & ( P @ X4 ) ) )
% 3.82/4.06 = bot_bot_set_nat ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % Collect_conv_if
% 3.82/4.06 thf(fact_4780_Collect__conv__if,axiom,
% 3.82/4.06 ! [P: int > $o,A: int] :
% 3.82/4.06 ( ( ( P @ A )
% 3.82/4.06 => ( ( collect_int
% 3.82/4.06 @ ^ [X4: int] :
% 3.82/4.06 ( ( X4 = A )
% 3.82/4.06 & ( P @ X4 ) ) )
% 3.82/4.06 = ( insert_int @ A @ bot_bot_set_int ) ) )
% 3.82/4.06 & ( ~ ( P @ A )
% 3.82/4.06 => ( ( collect_int
% 3.82/4.06 @ ^ [X4: int] :
% 3.82/4.06 ( ( X4 = A )
% 3.82/4.06 & ( P @ X4 ) ) )
% 3.82/4.06 = bot_bot_set_int ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % Collect_conv_if
% 3.82/4.06 thf(fact_4781_Collect__conv__if2,axiom,
% 3.82/4.06 ! [P: list_nat > $o,A: list_nat] :
% 3.82/4.06 ( ( ( P @ A )
% 3.82/4.06 => ( ( collect_list_nat
% 3.82/4.06 @ ^ [X4: list_nat] :
% 3.82/4.06 ( ( A = X4 )
% 3.82/4.06 & ( P @ X4 ) ) )
% 3.82/4.06 = ( insert_list_nat @ A @ bot_bot_set_list_nat ) ) )
% 3.82/4.06 & ( ~ ( P @ A )
% 3.82/4.06 => ( ( collect_list_nat
% 3.82/4.06 @ ^ [X4: list_nat] :
% 3.82/4.06 ( ( A = X4 )
% 3.82/4.06 & ( P @ X4 ) ) )
% 3.82/4.06 = bot_bot_set_list_nat ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % Collect_conv_if2
% 3.82/4.06 thf(fact_4782_Collect__conv__if2,axiom,
% 3.82/4.06 ! [P: set_nat > $o,A: set_nat] :
% 3.82/4.06 ( ( ( P @ A )
% 3.82/4.06 => ( ( collect_set_nat
% 3.82/4.06 @ ^ [X4: set_nat] :
% 3.82/4.06 ( ( A = X4 )
% 3.82/4.06 & ( P @ X4 ) ) )
% 3.82/4.06 = ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 3.82/4.06 & ( ~ ( P @ A )
% 3.82/4.06 => ( ( collect_set_nat
% 3.82/4.06 @ ^ [X4: set_nat] :
% 3.82/4.06 ( ( A = X4 )
% 3.82/4.06 & ( P @ X4 ) ) )
% 3.82/4.06 = bot_bot_set_set_nat ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % Collect_conv_if2
% 3.82/4.06 thf(fact_4783_Collect__conv__if2,axiom,
% 3.82/4.06 ! [P: extended_enat > $o,A: extended_enat] :
% 3.82/4.06 ( ( ( P @ A )
% 3.82/4.06 => ( ( collec4429806609662206161d_enat
% 3.82/4.06 @ ^ [X4: extended_enat] :
% 3.82/4.06 ( ( A = X4 )
% 3.82/4.06 & ( P @ X4 ) ) )
% 3.82/4.06 = ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) )
% 3.82/4.06 & ( ~ ( P @ A )
% 3.82/4.06 => ( ( collec4429806609662206161d_enat
% 3.82/4.06 @ ^ [X4: extended_enat] :
% 3.82/4.06 ( ( A = X4 )
% 3.82/4.06 & ( P @ X4 ) ) )
% 3.82/4.06 = bot_bo7653980558646680370d_enat ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % Collect_conv_if2
% 3.82/4.06 thf(fact_4784_Collect__conv__if2,axiom,
% 3.82/4.06 ! [P: real > $o,A: real] :
% 3.82/4.06 ( ( ( P @ A )
% 3.82/4.06 => ( ( collect_real
% 3.82/4.06 @ ^ [X4: real] :
% 3.82/4.06 ( ( A = X4 )
% 3.82/4.06 & ( P @ X4 ) ) )
% 3.82/4.06 = ( insert_real @ A @ bot_bot_set_real ) ) )
% 3.82/4.06 & ( ~ ( P @ A )
% 3.82/4.06 => ( ( collect_real
% 3.82/4.06 @ ^ [X4: real] :
% 3.82/4.06 ( ( A = X4 )
% 3.82/4.06 & ( P @ X4 ) ) )
% 3.82/4.06 = bot_bot_set_real ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % Collect_conv_if2
% 3.82/4.06 thf(fact_4785_Collect__conv__if2,axiom,
% 3.82/4.06 ! [P: nat > $o,A: nat] :
% 3.82/4.06 ( ( ( P @ A )
% 3.82/4.06 => ( ( collect_nat
% 3.82/4.06 @ ^ [X4: nat] :
% 3.82/4.06 ( ( A = X4 )
% 3.82/4.06 & ( P @ X4 ) ) )
% 3.82/4.06 = ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 3.82/4.06 & ( ~ ( P @ A )
% 3.82/4.06 => ( ( collect_nat
% 3.82/4.06 @ ^ [X4: nat] :
% 3.82/4.06 ( ( A = X4 )
% 3.82/4.06 & ( P @ X4 ) ) )
% 3.82/4.06 = bot_bot_set_nat ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % Collect_conv_if2
% 3.82/4.06 thf(fact_4786_Collect__conv__if2,axiom,
% 3.82/4.06 ! [P: int > $o,A: int] :
% 3.82/4.06 ( ( ( P @ A )
% 3.82/4.06 => ( ( collect_int
% 3.82/4.06 @ ^ [X4: int] :
% 3.82/4.06 ( ( A = X4 )
% 3.82/4.06 & ( P @ X4 ) ) )
% 3.82/4.06 = ( insert_int @ A @ bot_bot_set_int ) ) )
% 3.82/4.06 & ( ~ ( P @ A )
% 3.82/4.06 => ( ( collect_int
% 3.82/4.06 @ ^ [X4: int] :
% 3.82/4.06 ( ( A = X4 )
% 3.82/4.06 & ( P @ X4 ) ) )
% 3.82/4.06 = bot_bot_set_int ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % Collect_conv_if2
% 3.82/4.06 thf(fact_4787_finite_Ocases,axiom,
% 3.82/4.06 ! [A: set_complex] :
% 3.82/4.06 ( ( finite3207457112153483333omplex @ A )
% 3.82/4.06 => ( ( A != bot_bot_set_complex )
% 3.82/4.06 => ~ ! [A6: set_complex] :
% 3.82/4.06 ( ? [A4: complex] :
% 3.82/4.06 ( A
% 3.82/4.06 = ( insert_complex @ A4 @ A6 ) )
% 3.82/4.06 => ~ ( finite3207457112153483333omplex @ A6 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite.cases
% 3.82/4.06 thf(fact_4788_finite_Ocases,axiom,
% 3.82/4.06 ! [A: set_Extended_enat] :
% 3.82/4.06 ( ( finite4001608067531595151d_enat @ A )
% 3.82/4.06 => ( ( A != bot_bo7653980558646680370d_enat )
% 3.82/4.06 => ~ ! [A6: set_Extended_enat] :
% 3.82/4.06 ( ? [A4: extended_enat] :
% 3.82/4.06 ( A
% 3.82/4.06 = ( insert_Extended_enat @ A4 @ A6 ) )
% 3.82/4.06 => ~ ( finite4001608067531595151d_enat @ A6 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite.cases
% 3.82/4.06 thf(fact_4789_finite_Ocases,axiom,
% 3.82/4.06 ! [A: set_real] :
% 3.82/4.06 ( ( finite_finite_real @ A )
% 3.82/4.06 => ( ( A != bot_bot_set_real )
% 3.82/4.06 => ~ ! [A6: set_real] :
% 3.82/4.06 ( ? [A4: real] :
% 3.82/4.06 ( A
% 3.82/4.06 = ( insert_real @ A4 @ A6 ) )
% 3.82/4.06 => ~ ( finite_finite_real @ A6 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite.cases
% 3.82/4.06 thf(fact_4790_finite_Ocases,axiom,
% 3.82/4.06 ! [A: set_nat] :
% 3.82/4.06 ( ( finite_finite_nat @ A )
% 3.82/4.06 => ( ( A != bot_bot_set_nat )
% 3.82/4.06 => ~ ! [A6: set_nat] :
% 3.82/4.06 ( ? [A4: nat] :
% 3.82/4.06 ( A
% 3.82/4.06 = ( insert_nat @ A4 @ A6 ) )
% 3.82/4.06 => ~ ( finite_finite_nat @ A6 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite.cases
% 3.82/4.06 thf(fact_4791_finite_Ocases,axiom,
% 3.82/4.06 ! [A: set_int] :
% 3.82/4.06 ( ( finite_finite_int @ A )
% 3.82/4.06 => ( ( A != bot_bot_set_int )
% 3.82/4.06 => ~ ! [A6: set_int] :
% 3.82/4.06 ( ? [A4: int] :
% 3.82/4.06 ( A
% 3.82/4.06 = ( insert_int @ A4 @ A6 ) )
% 3.82/4.06 => ~ ( finite_finite_int @ A6 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite.cases
% 3.82/4.06 thf(fact_4792_finite_Osimps,axiom,
% 3.82/4.06 ( finite3207457112153483333omplex
% 3.82/4.06 = ( ^ [A3: set_complex] :
% 3.82/4.06 ( ( A3 = bot_bot_set_complex )
% 3.82/4.06 | ? [A5: set_complex,B3: complex] :
% 3.82/4.06 ( ( A3
% 3.82/4.06 = ( insert_complex @ B3 @ A5 ) )
% 3.82/4.06 & ( finite3207457112153483333omplex @ A5 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite.simps
% 3.82/4.06 thf(fact_4793_finite_Osimps,axiom,
% 3.82/4.06 ( finite4001608067531595151d_enat
% 3.82/4.06 = ( ^ [A3: set_Extended_enat] :
% 3.82/4.06 ( ( A3 = bot_bo7653980558646680370d_enat )
% 3.82/4.06 | ? [A5: set_Extended_enat,B3: extended_enat] :
% 3.82/4.06 ( ( A3
% 3.82/4.06 = ( insert_Extended_enat @ B3 @ A5 ) )
% 3.82/4.06 & ( finite4001608067531595151d_enat @ A5 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite.simps
% 3.82/4.06 thf(fact_4794_finite_Osimps,axiom,
% 3.82/4.06 ( finite_finite_real
% 3.82/4.06 = ( ^ [A3: set_real] :
% 3.82/4.06 ( ( A3 = bot_bot_set_real )
% 3.82/4.06 | ? [A5: set_real,B3: real] :
% 3.82/4.06 ( ( A3
% 3.82/4.06 = ( insert_real @ B3 @ A5 ) )
% 3.82/4.06 & ( finite_finite_real @ A5 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite.simps
% 3.82/4.06 thf(fact_4795_finite_Osimps,axiom,
% 3.82/4.06 ( finite_finite_nat
% 3.82/4.06 = ( ^ [A3: set_nat] :
% 3.82/4.06 ( ( A3 = bot_bot_set_nat )
% 3.82/4.06 | ? [A5: set_nat,B3: nat] :
% 3.82/4.06 ( ( A3
% 3.82/4.06 = ( insert_nat @ B3 @ A5 ) )
% 3.82/4.06 & ( finite_finite_nat @ A5 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite.simps
% 3.82/4.06 thf(fact_4796_finite_Osimps,axiom,
% 3.82/4.06 ( finite_finite_int
% 3.82/4.06 = ( ^ [A3: set_int] :
% 3.82/4.06 ( ( A3 = bot_bot_set_int )
% 3.82/4.06 | ? [A5: set_int,B3: int] :
% 3.82/4.06 ( ( A3
% 3.82/4.06 = ( insert_int @ B3 @ A5 ) )
% 3.82/4.06 & ( finite_finite_int @ A5 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite.simps
% 3.82/4.06 thf(fact_4797_finite__induct,axiom,
% 3.82/4.06 ! [F3: set_set_nat,P: set_set_nat > $o] :
% 3.82/4.06 ( ( finite1152437895449049373et_nat @ F3 )
% 3.82/4.06 => ( ( P @ bot_bot_set_set_nat )
% 3.82/4.06 => ( ! [X5: set_nat,F4: set_set_nat] :
% 3.82/4.06 ( ( finite1152437895449049373et_nat @ F4 )
% 3.82/4.06 => ( ~ ( member_set_nat @ X5 @ F4 )
% 3.82/4.06 => ( ( P @ F4 )
% 3.82/4.06 => ( P @ ( insert_set_nat @ X5 @ F4 ) ) ) ) )
% 3.82/4.06 => ( P @ F3 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_induct
% 3.82/4.06 thf(fact_4798_finite__induct,axiom,
% 3.82/4.06 ! [F3: set_complex,P: set_complex > $o] :
% 3.82/4.06 ( ( finite3207457112153483333omplex @ F3 )
% 3.82/4.06 => ( ( P @ bot_bot_set_complex )
% 3.82/4.06 => ( ! [X5: complex,F4: set_complex] :
% 3.82/4.06 ( ( finite3207457112153483333omplex @ F4 )
% 3.82/4.06 => ( ~ ( member_complex @ X5 @ F4 )
% 3.82/4.06 => ( ( P @ F4 )
% 3.82/4.06 => ( P @ ( insert_complex @ X5 @ F4 ) ) ) ) )
% 3.82/4.06 => ( P @ F3 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_induct
% 3.82/4.06 thf(fact_4799_finite__induct,axiom,
% 3.82/4.06 ! [F3: set_Extended_enat,P: set_Extended_enat > $o] :
% 3.82/4.06 ( ( finite4001608067531595151d_enat @ F3 )
% 3.82/4.06 => ( ( P @ bot_bo7653980558646680370d_enat )
% 3.82/4.06 => ( ! [X5: extended_enat,F4: set_Extended_enat] :
% 3.82/4.06 ( ( finite4001608067531595151d_enat @ F4 )
% 3.82/4.06 => ( ~ ( member_Extended_enat @ X5 @ F4 )
% 3.82/4.06 => ( ( P @ F4 )
% 3.82/4.06 => ( P @ ( insert_Extended_enat @ X5 @ F4 ) ) ) ) )
% 3.82/4.06 => ( P @ F3 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_induct
% 3.82/4.06 thf(fact_4800_finite__induct,axiom,
% 3.82/4.06 ! [F3: set_real,P: set_real > $o] :
% 3.82/4.06 ( ( finite_finite_real @ F3 )
% 3.82/4.06 => ( ( P @ bot_bot_set_real )
% 3.82/4.06 => ( ! [X5: real,F4: set_real] :
% 3.82/4.06 ( ( finite_finite_real @ F4 )
% 3.82/4.06 => ( ~ ( member_real @ X5 @ F4 )
% 3.82/4.06 => ( ( P @ F4 )
% 3.82/4.06 => ( P @ ( insert_real @ X5 @ F4 ) ) ) ) )
% 3.82/4.06 => ( P @ F3 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_induct
% 3.82/4.06 thf(fact_4801_finite__induct,axiom,
% 3.82/4.06 ! [F3: set_nat,P: set_nat > $o] :
% 3.82/4.06 ( ( finite_finite_nat @ F3 )
% 3.82/4.06 => ( ( P @ bot_bot_set_nat )
% 3.82/4.06 => ( ! [X5: nat,F4: set_nat] :
% 3.82/4.06 ( ( finite_finite_nat @ F4 )
% 3.82/4.06 => ( ~ ( member_nat @ X5 @ F4 )
% 3.82/4.06 => ( ( P @ F4 )
% 3.82/4.06 => ( P @ ( insert_nat @ X5 @ F4 ) ) ) ) )
% 3.82/4.06 => ( P @ F3 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_induct
% 3.82/4.06 thf(fact_4802_finite__induct,axiom,
% 3.82/4.06 ! [F3: set_int,P: set_int > $o] :
% 3.82/4.06 ( ( finite_finite_int @ F3 )
% 3.82/4.06 => ( ( P @ bot_bot_set_int )
% 3.82/4.06 => ( ! [X5: int,F4: set_int] :
% 3.82/4.06 ( ( finite_finite_int @ F4 )
% 3.82/4.06 => ( ~ ( member_int @ X5 @ F4 )
% 3.82/4.06 => ( ( P @ F4 )
% 3.82/4.06 => ( P @ ( insert_int @ X5 @ F4 ) ) ) ) )
% 3.82/4.06 => ( P @ F3 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_induct
% 3.82/4.06 thf(fact_4803_finite__ne__induct,axiom,
% 3.82/4.06 ! [F3: set_set_nat,P: set_set_nat > $o] :
% 3.82/4.06 ( ( finite1152437895449049373et_nat @ F3 )
% 3.82/4.06 => ( ( F3 != bot_bot_set_set_nat )
% 3.82/4.06 => ( ! [X5: set_nat] : ( P @ ( insert_set_nat @ X5 @ bot_bot_set_set_nat ) )
% 3.82/4.06 => ( ! [X5: set_nat,F4: set_set_nat] :
% 3.82/4.06 ( ( finite1152437895449049373et_nat @ F4 )
% 3.82/4.06 => ( ( F4 != bot_bot_set_set_nat )
% 3.82/4.06 => ( ~ ( member_set_nat @ X5 @ F4 )
% 3.82/4.06 => ( ( P @ F4 )
% 3.82/4.06 => ( P @ ( insert_set_nat @ X5 @ F4 ) ) ) ) ) )
% 3.82/4.06 => ( P @ F3 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_ne_induct
% 3.82/4.06 thf(fact_4804_finite__ne__induct,axiom,
% 3.82/4.06 ! [F3: set_complex,P: set_complex > $o] :
% 3.82/4.06 ( ( finite3207457112153483333omplex @ F3 )
% 3.82/4.06 => ( ( F3 != bot_bot_set_complex )
% 3.82/4.06 => ( ! [X5: complex] : ( P @ ( insert_complex @ X5 @ bot_bot_set_complex ) )
% 3.82/4.06 => ( ! [X5: complex,F4: set_complex] :
% 3.82/4.06 ( ( finite3207457112153483333omplex @ F4 )
% 3.82/4.06 => ( ( F4 != bot_bot_set_complex )
% 3.82/4.06 => ( ~ ( member_complex @ X5 @ F4 )
% 3.82/4.06 => ( ( P @ F4 )
% 3.82/4.06 => ( P @ ( insert_complex @ X5 @ F4 ) ) ) ) ) )
% 3.82/4.06 => ( P @ F3 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_ne_induct
% 3.82/4.06 thf(fact_4805_finite__ne__induct,axiom,
% 3.82/4.06 ! [F3: set_Extended_enat,P: set_Extended_enat > $o] :
% 3.82/4.06 ( ( finite4001608067531595151d_enat @ F3 )
% 3.82/4.06 => ( ( F3 != bot_bo7653980558646680370d_enat )
% 3.82/4.06 => ( ! [X5: extended_enat] : ( P @ ( insert_Extended_enat @ X5 @ bot_bo7653980558646680370d_enat ) )
% 3.82/4.06 => ( ! [X5: extended_enat,F4: set_Extended_enat] :
% 3.82/4.06 ( ( finite4001608067531595151d_enat @ F4 )
% 3.82/4.06 => ( ( F4 != bot_bo7653980558646680370d_enat )
% 3.82/4.06 => ( ~ ( member_Extended_enat @ X5 @ F4 )
% 3.82/4.06 => ( ( P @ F4 )
% 3.82/4.06 => ( P @ ( insert_Extended_enat @ X5 @ F4 ) ) ) ) ) )
% 3.82/4.06 => ( P @ F3 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_ne_induct
% 3.82/4.06 thf(fact_4806_finite__ne__induct,axiom,
% 3.82/4.06 ! [F3: set_real,P: set_real > $o] :
% 3.82/4.06 ( ( finite_finite_real @ F3 )
% 3.82/4.06 => ( ( F3 != bot_bot_set_real )
% 3.82/4.06 => ( ! [X5: real] : ( P @ ( insert_real @ X5 @ bot_bot_set_real ) )
% 3.82/4.06 => ( ! [X5: real,F4: set_real] :
% 3.82/4.06 ( ( finite_finite_real @ F4 )
% 3.82/4.06 => ( ( F4 != bot_bot_set_real )
% 3.82/4.06 => ( ~ ( member_real @ X5 @ F4 )
% 3.82/4.06 => ( ( P @ F4 )
% 3.82/4.06 => ( P @ ( insert_real @ X5 @ F4 ) ) ) ) ) )
% 3.82/4.06 => ( P @ F3 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_ne_induct
% 3.82/4.06 thf(fact_4807_finite__ne__induct,axiom,
% 3.82/4.06 ! [F3: set_nat,P: set_nat > $o] :
% 3.82/4.06 ( ( finite_finite_nat @ F3 )
% 3.82/4.06 => ( ( F3 != bot_bot_set_nat )
% 3.82/4.06 => ( ! [X5: nat] : ( P @ ( insert_nat @ X5 @ bot_bot_set_nat ) )
% 3.82/4.06 => ( ! [X5: nat,F4: set_nat] :
% 3.82/4.06 ( ( finite_finite_nat @ F4 )
% 3.82/4.06 => ( ( F4 != bot_bot_set_nat )
% 3.82/4.06 => ( ~ ( member_nat @ X5 @ F4 )
% 3.82/4.06 => ( ( P @ F4 )
% 3.82/4.06 => ( P @ ( insert_nat @ X5 @ F4 ) ) ) ) ) )
% 3.82/4.06 => ( P @ F3 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_ne_induct
% 3.82/4.06 thf(fact_4808_finite__ne__induct,axiom,
% 3.82/4.06 ! [F3: set_int,P: set_int > $o] :
% 3.82/4.06 ( ( finite_finite_int @ F3 )
% 3.82/4.06 => ( ( F3 != bot_bot_set_int )
% 3.82/4.06 => ( ! [X5: int] : ( P @ ( insert_int @ X5 @ bot_bot_set_int ) )
% 3.82/4.06 => ( ! [X5: int,F4: set_int] :
% 3.82/4.06 ( ( finite_finite_int @ F4 )
% 3.82/4.06 => ( ( F4 != bot_bot_set_int )
% 3.82/4.06 => ( ~ ( member_int @ X5 @ F4 )
% 3.82/4.06 => ( ( P @ F4 )
% 3.82/4.06 => ( P @ ( insert_int @ X5 @ F4 ) ) ) ) ) )
% 3.82/4.06 => ( P @ F3 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_ne_induct
% 3.82/4.06 thf(fact_4809_infinite__finite__induct,axiom,
% 3.82/4.06 ! [P: set_set_nat > $o,A2: set_set_nat] :
% 3.82/4.06 ( ! [A6: set_set_nat] :
% 3.82/4.06 ( ~ ( finite1152437895449049373et_nat @ A6 )
% 3.82/4.06 => ( P @ A6 ) )
% 3.82/4.06 => ( ( P @ bot_bot_set_set_nat )
% 3.82/4.06 => ( ! [X5: set_nat,F4: set_set_nat] :
% 3.82/4.06 ( ( finite1152437895449049373et_nat @ F4 )
% 3.82/4.06 => ( ~ ( member_set_nat @ X5 @ F4 )
% 3.82/4.06 => ( ( P @ F4 )
% 3.82/4.06 => ( P @ ( insert_set_nat @ X5 @ F4 ) ) ) ) )
% 3.82/4.06 => ( P @ A2 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % infinite_finite_induct
% 3.82/4.06 thf(fact_4810_infinite__finite__induct,axiom,
% 3.82/4.06 ! [P: set_complex > $o,A2: set_complex] :
% 3.82/4.06 ( ! [A6: set_complex] :
% 3.82/4.06 ( ~ ( finite3207457112153483333omplex @ A6 )
% 3.82/4.06 => ( P @ A6 ) )
% 3.82/4.06 => ( ( P @ bot_bot_set_complex )
% 3.82/4.06 => ( ! [X5: complex,F4: set_complex] :
% 3.82/4.06 ( ( finite3207457112153483333omplex @ F4 )
% 3.82/4.06 => ( ~ ( member_complex @ X5 @ F4 )
% 3.82/4.06 => ( ( P @ F4 )
% 3.82/4.06 => ( P @ ( insert_complex @ X5 @ F4 ) ) ) ) )
% 3.82/4.06 => ( P @ A2 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % infinite_finite_induct
% 3.82/4.06 thf(fact_4811_infinite__finite__induct,axiom,
% 3.82/4.06 ! [P: set_Extended_enat > $o,A2: set_Extended_enat] :
% 3.82/4.06 ( ! [A6: set_Extended_enat] :
% 3.82/4.06 ( ~ ( finite4001608067531595151d_enat @ A6 )
% 3.82/4.06 => ( P @ A6 ) )
% 3.82/4.06 => ( ( P @ bot_bo7653980558646680370d_enat )
% 3.82/4.06 => ( ! [X5: extended_enat,F4: set_Extended_enat] :
% 3.82/4.06 ( ( finite4001608067531595151d_enat @ F4 )
% 3.82/4.06 => ( ~ ( member_Extended_enat @ X5 @ F4 )
% 3.82/4.06 => ( ( P @ F4 )
% 3.82/4.06 => ( P @ ( insert_Extended_enat @ X5 @ F4 ) ) ) ) )
% 3.82/4.06 => ( P @ A2 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % infinite_finite_induct
% 3.82/4.06 thf(fact_4812_infinite__finite__induct,axiom,
% 3.82/4.06 ! [P: set_real > $o,A2: set_real] :
% 3.82/4.06 ( ! [A6: set_real] :
% 3.82/4.06 ( ~ ( finite_finite_real @ A6 )
% 3.82/4.06 => ( P @ A6 ) )
% 3.82/4.06 => ( ( P @ bot_bot_set_real )
% 3.82/4.06 => ( ! [X5: real,F4: set_real] :
% 3.82/4.06 ( ( finite_finite_real @ F4 )
% 3.82/4.06 => ( ~ ( member_real @ X5 @ F4 )
% 3.82/4.06 => ( ( P @ F4 )
% 3.82/4.06 => ( P @ ( insert_real @ X5 @ F4 ) ) ) ) )
% 3.82/4.06 => ( P @ A2 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % infinite_finite_induct
% 3.82/4.06 thf(fact_4813_infinite__finite__induct,axiom,
% 3.82/4.06 ! [P: set_nat > $o,A2: set_nat] :
% 3.82/4.06 ( ! [A6: set_nat] :
% 3.82/4.06 ( ~ ( finite_finite_nat @ A6 )
% 3.82/4.06 => ( P @ A6 ) )
% 3.82/4.06 => ( ( P @ bot_bot_set_nat )
% 3.82/4.06 => ( ! [X5: nat,F4: set_nat] :
% 3.82/4.06 ( ( finite_finite_nat @ F4 )
% 3.82/4.06 => ( ~ ( member_nat @ X5 @ F4 )
% 3.82/4.06 => ( ( P @ F4 )
% 3.82/4.06 => ( P @ ( insert_nat @ X5 @ F4 ) ) ) ) )
% 3.82/4.06 => ( P @ A2 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % infinite_finite_induct
% 3.82/4.06 thf(fact_4814_infinite__finite__induct,axiom,
% 3.82/4.06 ! [P: set_int > $o,A2: set_int] :
% 3.82/4.06 ( ! [A6: set_int] :
% 3.82/4.06 ( ~ ( finite_finite_int @ A6 )
% 3.82/4.06 => ( P @ A6 ) )
% 3.82/4.06 => ( ( P @ bot_bot_set_int )
% 3.82/4.06 => ( ! [X5: int,F4: set_int] :
% 3.82/4.06 ( ( finite_finite_int @ F4 )
% 3.82/4.06 => ( ~ ( member_int @ X5 @ F4 )
% 3.82/4.06 => ( ( P @ F4 )
% 3.82/4.06 => ( P @ ( insert_int @ X5 @ F4 ) ) ) ) )
% 3.82/4.06 => ( P @ A2 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % infinite_finite_induct
% 3.82/4.06 thf(fact_4815_infinite__remove,axiom,
% 3.82/4.06 ! [S2: set_complex,A: complex] :
% 3.82/4.06 ( ~ ( finite3207457112153483333omplex @ S2 )
% 3.82/4.06 => ~ ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % infinite_remove
% 3.82/4.06 thf(fact_4816_infinite__remove,axiom,
% 3.82/4.06 ! [S2: set_Extended_enat,A: extended_enat] :
% 3.82/4.06 ( ~ ( finite4001608067531595151d_enat @ S2 )
% 3.82/4.06 => ~ ( finite4001608067531595151d_enat @ ( minus_925952699566721837d_enat @ S2 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % infinite_remove
% 3.82/4.06 thf(fact_4817_infinite__remove,axiom,
% 3.82/4.06 ! [S2: set_real,A: real] :
% 3.82/4.06 ( ~ ( finite_finite_real @ S2 )
% 3.82/4.06 => ~ ( finite_finite_real @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % infinite_remove
% 3.82/4.06 thf(fact_4818_infinite__remove,axiom,
% 3.82/4.06 ! [S2: set_int,A: int] :
% 3.82/4.06 ( ~ ( finite_finite_int @ S2 )
% 3.82/4.06 => ~ ( finite_finite_int @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % infinite_remove
% 3.82/4.06 thf(fact_4819_infinite__remove,axiom,
% 3.82/4.06 ! [S2: set_nat,A: nat] :
% 3.82/4.06 ( ~ ( finite_finite_nat @ S2 )
% 3.82/4.06 => ~ ( finite_finite_nat @ ( minus_minus_set_nat @ S2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % infinite_remove
% 3.82/4.06 thf(fact_4820_infinite__coinduct,axiom,
% 3.82/4.06 ! [X8: set_complex > $o,A2: set_complex] :
% 3.82/4.06 ( ( X8 @ A2 )
% 3.82/4.06 => ( ! [A6: set_complex] :
% 3.82/4.06 ( ( X8 @ A6 )
% 3.82/4.06 => ? [X2: complex] :
% 3.82/4.06 ( ( member_complex @ X2 @ A6 )
% 3.82/4.06 & ( ( X8 @ ( minus_811609699411566653omplex @ A6 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) )
% 3.82/4.06 | ~ ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A6 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) ) ) )
% 3.82/4.06 => ~ ( finite3207457112153483333omplex @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % infinite_coinduct
% 3.82/4.06 thf(fact_4821_infinite__coinduct,axiom,
% 3.82/4.06 ! [X8: set_Extended_enat > $o,A2: set_Extended_enat] :
% 3.82/4.06 ( ( X8 @ A2 )
% 3.82/4.06 => ( ! [A6: set_Extended_enat] :
% 3.82/4.06 ( ( X8 @ A6 )
% 3.82/4.06 => ? [X2: extended_enat] :
% 3.82/4.06 ( ( member_Extended_enat @ X2 @ A6 )
% 3.82/4.06 & ( ( X8 @ ( minus_925952699566721837d_enat @ A6 @ ( insert_Extended_enat @ X2 @ bot_bo7653980558646680370d_enat ) ) )
% 3.82/4.06 | ~ ( finite4001608067531595151d_enat @ ( minus_925952699566721837d_enat @ A6 @ ( insert_Extended_enat @ X2 @ bot_bo7653980558646680370d_enat ) ) ) ) ) )
% 3.82/4.06 => ~ ( finite4001608067531595151d_enat @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % infinite_coinduct
% 3.82/4.06 thf(fact_4822_infinite__coinduct,axiom,
% 3.82/4.06 ! [X8: set_real > $o,A2: set_real] :
% 3.82/4.06 ( ( X8 @ A2 )
% 3.82/4.06 => ( ! [A6: set_real] :
% 3.82/4.06 ( ( X8 @ A6 )
% 3.82/4.06 => ? [X2: real] :
% 3.82/4.06 ( ( member_real @ X2 @ A6 )
% 3.82/4.06 & ( ( X8 @ ( minus_minus_set_real @ A6 @ ( insert_real @ X2 @ bot_bot_set_real ) ) )
% 3.82/4.06 | ~ ( finite_finite_real @ ( minus_minus_set_real @ A6 @ ( insert_real @ X2 @ bot_bot_set_real ) ) ) ) ) )
% 3.82/4.06 => ~ ( finite_finite_real @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % infinite_coinduct
% 3.82/4.06 thf(fact_4823_infinite__coinduct,axiom,
% 3.82/4.06 ! [X8: set_int > $o,A2: set_int] :
% 3.82/4.06 ( ( X8 @ A2 )
% 3.82/4.06 => ( ! [A6: set_int] :
% 3.82/4.06 ( ( X8 @ A6 )
% 3.82/4.06 => ? [X2: int] :
% 3.82/4.06 ( ( member_int @ X2 @ A6 )
% 3.82/4.06 & ( ( X8 @ ( minus_minus_set_int @ A6 @ ( insert_int @ X2 @ bot_bot_set_int ) ) )
% 3.82/4.06 | ~ ( finite_finite_int @ ( minus_minus_set_int @ A6 @ ( insert_int @ X2 @ bot_bot_set_int ) ) ) ) ) )
% 3.82/4.06 => ~ ( finite_finite_int @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % infinite_coinduct
% 3.82/4.06 thf(fact_4824_infinite__coinduct,axiom,
% 3.82/4.06 ! [X8: set_nat > $o,A2: set_nat] :
% 3.82/4.06 ( ( X8 @ A2 )
% 3.82/4.06 => ( ! [A6: set_nat] :
% 3.82/4.06 ( ( X8 @ A6 )
% 3.82/4.06 => ? [X2: nat] :
% 3.82/4.06 ( ( member_nat @ X2 @ A6 )
% 3.82/4.06 & ( ( X8 @ ( minus_minus_set_nat @ A6 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) )
% 3.82/4.06 | ~ ( finite_finite_nat @ ( minus_minus_set_nat @ A6 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) ) ) )
% 3.82/4.06 => ~ ( finite_finite_nat @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % infinite_coinduct
% 3.82/4.06 thf(fact_4825_finite__empty__induct,axiom,
% 3.82/4.06 ! [A2: set_set_nat,P: set_set_nat > $o] :
% 3.82/4.06 ( ( finite1152437895449049373et_nat @ A2 )
% 3.82/4.06 => ( ( P @ A2 )
% 3.82/4.06 => ( ! [A4: set_nat,A6: set_set_nat] :
% 3.82/4.06 ( ( finite1152437895449049373et_nat @ A6 )
% 3.82/4.06 => ( ( member_set_nat @ A4 @ A6 )
% 3.82/4.06 => ( ( P @ A6 )
% 3.82/4.06 => ( P @ ( minus_2163939370556025621et_nat @ A6 @ ( insert_set_nat @ A4 @ bot_bot_set_set_nat ) ) ) ) ) )
% 3.82/4.06 => ( P @ bot_bot_set_set_nat ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_empty_induct
% 3.82/4.06 thf(fact_4826_finite__empty__induct,axiom,
% 3.82/4.06 ! [A2: set_complex,P: set_complex > $o] :
% 3.82/4.06 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.06 => ( ( P @ A2 )
% 3.82/4.06 => ( ! [A4: complex,A6: set_complex] :
% 3.82/4.06 ( ( finite3207457112153483333omplex @ A6 )
% 3.82/4.06 => ( ( member_complex @ A4 @ A6 )
% 3.82/4.06 => ( ( P @ A6 )
% 3.82/4.06 => ( P @ ( minus_811609699411566653omplex @ A6 @ ( insert_complex @ A4 @ bot_bot_set_complex ) ) ) ) ) )
% 3.82/4.06 => ( P @ bot_bot_set_complex ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_empty_induct
% 3.82/4.06 thf(fact_4827_finite__empty__induct,axiom,
% 3.82/4.06 ! [A2: set_Extended_enat,P: set_Extended_enat > $o] :
% 3.82/4.06 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.06 => ( ( P @ A2 )
% 3.82/4.06 => ( ! [A4: extended_enat,A6: set_Extended_enat] :
% 3.82/4.06 ( ( finite4001608067531595151d_enat @ A6 )
% 3.82/4.06 => ( ( member_Extended_enat @ A4 @ A6 )
% 3.82/4.06 => ( ( P @ A6 )
% 3.82/4.06 => ( P @ ( minus_925952699566721837d_enat @ A6 @ ( insert_Extended_enat @ A4 @ bot_bo7653980558646680370d_enat ) ) ) ) ) )
% 3.82/4.06 => ( P @ bot_bo7653980558646680370d_enat ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_empty_induct
% 3.82/4.06 thf(fact_4828_finite__empty__induct,axiom,
% 3.82/4.06 ! [A2: set_real,P: set_real > $o] :
% 3.82/4.06 ( ( finite_finite_real @ A2 )
% 3.82/4.06 => ( ( P @ A2 )
% 3.82/4.06 => ( ! [A4: real,A6: set_real] :
% 3.82/4.06 ( ( finite_finite_real @ A6 )
% 3.82/4.06 => ( ( member_real @ A4 @ A6 )
% 3.82/4.06 => ( ( P @ A6 )
% 3.82/4.06 => ( P @ ( minus_minus_set_real @ A6 @ ( insert_real @ A4 @ bot_bot_set_real ) ) ) ) ) )
% 3.82/4.06 => ( P @ bot_bot_set_real ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_empty_induct
% 3.82/4.06 thf(fact_4829_finite__empty__induct,axiom,
% 3.82/4.06 ! [A2: set_int,P: set_int > $o] :
% 3.82/4.06 ( ( finite_finite_int @ A2 )
% 3.82/4.06 => ( ( P @ A2 )
% 3.82/4.06 => ( ! [A4: int,A6: set_int] :
% 3.82/4.06 ( ( finite_finite_int @ A6 )
% 3.82/4.06 => ( ( member_int @ A4 @ A6 )
% 3.82/4.06 => ( ( P @ A6 )
% 3.82/4.06 => ( P @ ( minus_minus_set_int @ A6 @ ( insert_int @ A4 @ bot_bot_set_int ) ) ) ) ) )
% 3.82/4.06 => ( P @ bot_bot_set_int ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_empty_induct
% 3.82/4.06 thf(fact_4830_finite__empty__induct,axiom,
% 3.82/4.06 ! [A2: set_nat,P: set_nat > $o] :
% 3.82/4.06 ( ( finite_finite_nat @ A2 )
% 3.82/4.06 => ( ( P @ A2 )
% 3.82/4.06 => ( ! [A4: nat,A6: set_nat] :
% 3.82/4.06 ( ( finite_finite_nat @ A6 )
% 3.82/4.06 => ( ( member_nat @ A4 @ A6 )
% 3.82/4.06 => ( ( P @ A6 )
% 3.82/4.06 => ( P @ ( minus_minus_set_nat @ A6 @ ( insert_nat @ A4 @ bot_bot_set_nat ) ) ) ) ) )
% 3.82/4.06 => ( P @ bot_bot_set_nat ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_empty_induct
% 3.82/4.06 thf(fact_4831_subset__singleton__iff,axiom,
% 3.82/4.06 ! [X8: set_Extended_enat,A: extended_enat] :
% 3.82/4.06 ( ( ord_le7203529160286727270d_enat @ X8 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) )
% 3.82/4.06 = ( ( X8 = bot_bo7653980558646680370d_enat )
% 3.82/4.06 | ( X8
% 3.82/4.06 = ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % subset_singleton_iff
% 3.82/4.06 thf(fact_4832_subset__singleton__iff,axiom,
% 3.82/4.06 ! [X8: set_real,A: real] :
% 3.82/4.06 ( ( ord_less_eq_set_real @ X8 @ ( insert_real @ A @ bot_bot_set_real ) )
% 3.82/4.06 = ( ( X8 = bot_bot_set_real )
% 3.82/4.06 | ( X8
% 3.82/4.06 = ( insert_real @ A @ bot_bot_set_real ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % subset_singleton_iff
% 3.82/4.06 thf(fact_4833_subset__singleton__iff,axiom,
% 3.82/4.06 ! [X8: set_nat,A: nat] :
% 3.82/4.06 ( ( ord_less_eq_set_nat @ X8 @ ( insert_nat @ A @ bot_bot_set_nat ) )
% 3.82/4.06 = ( ( X8 = bot_bot_set_nat )
% 3.82/4.06 | ( X8
% 3.82/4.06 = ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % subset_singleton_iff
% 3.82/4.06 thf(fact_4834_subset__singleton__iff,axiom,
% 3.82/4.06 ! [X8: set_int,A: int] :
% 3.82/4.06 ( ( ord_less_eq_set_int @ X8 @ ( insert_int @ A @ bot_bot_set_int ) )
% 3.82/4.06 = ( ( X8 = bot_bot_set_int )
% 3.82/4.06 | ( X8
% 3.82/4.06 = ( insert_int @ A @ bot_bot_set_int ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % subset_singleton_iff
% 3.82/4.06 thf(fact_4835_subset__singletonD,axiom,
% 3.82/4.06 ! [A2: set_Extended_enat,X: extended_enat] :
% 3.82/4.06 ( ( ord_le7203529160286727270d_enat @ A2 @ ( insert_Extended_enat @ X @ bot_bo7653980558646680370d_enat ) )
% 3.82/4.06 => ( ( A2 = bot_bo7653980558646680370d_enat )
% 3.82/4.06 | ( A2
% 3.82/4.06 = ( insert_Extended_enat @ X @ bot_bo7653980558646680370d_enat ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % subset_singletonD
% 3.82/4.06 thf(fact_4836_subset__singletonD,axiom,
% 3.82/4.06 ! [A2: set_real,X: real] :
% 3.82/4.06 ( ( ord_less_eq_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) )
% 3.82/4.06 => ( ( A2 = bot_bot_set_real )
% 3.82/4.06 | ( A2
% 3.82/4.06 = ( insert_real @ X @ bot_bot_set_real ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % subset_singletonD
% 3.82/4.06 thf(fact_4837_subset__singletonD,axiom,
% 3.82/4.06 ! [A2: set_nat,X: nat] :
% 3.82/4.06 ( ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 3.82/4.06 => ( ( A2 = bot_bot_set_nat )
% 3.82/4.06 | ( A2
% 3.82/4.06 = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % subset_singletonD
% 3.82/4.06 thf(fact_4838_subset__singletonD,axiom,
% 3.82/4.06 ! [A2: set_int,X: int] :
% 3.82/4.06 ( ( ord_less_eq_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) )
% 3.82/4.06 => ( ( A2 = bot_bot_set_int )
% 3.82/4.06 | ( A2
% 3.82/4.06 = ( insert_int @ X @ bot_bot_set_int ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % subset_singletonD
% 3.82/4.06 thf(fact_4839_Diff__single__insert,axiom,
% 3.82/4.06 ! [A2: set_Extended_enat,X: extended_enat,B: set_Extended_enat] :
% 3.82/4.06 ( ( ord_le7203529160286727270d_enat @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ X @ bot_bo7653980558646680370d_enat ) ) @ B )
% 3.82/4.06 => ( ord_le7203529160286727270d_enat @ A2 @ ( insert_Extended_enat @ X @ B ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % Diff_single_insert
% 3.82/4.06 thf(fact_4840_Diff__single__insert,axiom,
% 3.82/4.06 ! [A2: set_real,X: real,B: set_real] :
% 3.82/4.06 ( ( ord_less_eq_set_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) @ B )
% 3.82/4.06 => ( ord_less_eq_set_real @ A2 @ ( insert_real @ X @ B ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % Diff_single_insert
% 3.82/4.06 thf(fact_4841_Diff__single__insert,axiom,
% 3.82/4.06 ! [A2: set_nat,X: nat,B: set_nat] :
% 3.82/4.06 ( ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ B )
% 3.82/4.06 => ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X @ B ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % Diff_single_insert
% 3.82/4.06 thf(fact_4842_Diff__single__insert,axiom,
% 3.82/4.06 ! [A2: set_int,X: int,B: set_int] :
% 3.82/4.06 ( ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) @ B )
% 3.82/4.06 => ( ord_less_eq_set_int @ A2 @ ( insert_int @ X @ B ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % Diff_single_insert
% 3.82/4.06 thf(fact_4843_subset__insert__iff,axiom,
% 3.82/4.06 ! [A2: set_set_nat,X: set_nat,B: set_set_nat] :
% 3.82/4.06 ( ( ord_le6893508408891458716et_nat @ A2 @ ( insert_set_nat @ X @ B ) )
% 3.82/4.06 = ( ( ( member_set_nat @ X @ A2 )
% 3.82/4.06 => ( ord_le6893508408891458716et_nat @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) @ B ) )
% 3.82/4.06 & ( ~ ( member_set_nat @ X @ A2 )
% 3.82/4.06 => ( ord_le6893508408891458716et_nat @ A2 @ B ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % subset_insert_iff
% 3.82/4.06 thf(fact_4844_subset__insert__iff,axiom,
% 3.82/4.06 ! [A2: set_Extended_enat,X: extended_enat,B: set_Extended_enat] :
% 3.82/4.06 ( ( ord_le7203529160286727270d_enat @ A2 @ ( insert_Extended_enat @ X @ B ) )
% 3.82/4.06 = ( ( ( member_Extended_enat @ X @ A2 )
% 3.82/4.06 => ( ord_le7203529160286727270d_enat @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ X @ bot_bo7653980558646680370d_enat ) ) @ B ) )
% 3.82/4.06 & ( ~ ( member_Extended_enat @ X @ A2 )
% 3.82/4.06 => ( ord_le7203529160286727270d_enat @ A2 @ B ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % subset_insert_iff
% 3.82/4.06 thf(fact_4845_subset__insert__iff,axiom,
% 3.82/4.06 ! [A2: set_real,X: real,B: set_real] :
% 3.82/4.06 ( ( ord_less_eq_set_real @ A2 @ ( insert_real @ X @ B ) )
% 3.82/4.06 = ( ( ( member_real @ X @ A2 )
% 3.82/4.06 => ( ord_less_eq_set_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) @ B ) )
% 3.82/4.06 & ( ~ ( member_real @ X @ A2 )
% 3.82/4.06 => ( ord_less_eq_set_real @ A2 @ B ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % subset_insert_iff
% 3.82/4.06 thf(fact_4846_subset__insert__iff,axiom,
% 3.82/4.06 ! [A2: set_nat,X: nat,B: set_nat] :
% 3.82/4.06 ( ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X @ B ) )
% 3.82/4.06 = ( ( ( member_nat @ X @ A2 )
% 3.82/4.06 => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ B ) )
% 3.82/4.06 & ( ~ ( member_nat @ X @ A2 )
% 3.82/4.06 => ( ord_less_eq_set_nat @ A2 @ B ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % subset_insert_iff
% 3.82/4.06 thf(fact_4847_subset__insert__iff,axiom,
% 3.82/4.06 ! [A2: set_int,X: int,B: set_int] :
% 3.82/4.06 ( ( ord_less_eq_set_int @ A2 @ ( insert_int @ X @ B ) )
% 3.82/4.06 = ( ( ( member_int @ X @ A2 )
% 3.82/4.06 => ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) @ B ) )
% 3.82/4.06 & ( ~ ( member_int @ X @ A2 )
% 3.82/4.06 => ( ord_less_eq_set_int @ A2 @ B ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % subset_insert_iff
% 3.82/4.06 thf(fact_4848_atLeastAtMost__singleton_H,axiom,
% 3.82/4.06 ! [A: extended_enat,B2: extended_enat] :
% 3.82/4.06 ( ( A = B2 )
% 3.82/4.06 => ( ( set_or5403411693681687835d_enat @ A @ B2 )
% 3.82/4.06 = ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % atLeastAtMost_singleton'
% 3.82/4.06 thf(fact_4849_atLeastAtMost__singleton_H,axiom,
% 3.82/4.06 ! [A: nat,B2: nat] :
% 3.82/4.06 ( ( A = B2 )
% 3.82/4.06 => ( ( set_or1269000886237332187st_nat @ A @ B2 )
% 3.82/4.06 = ( insert_nat @ A @ bot_bot_set_nat ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % atLeastAtMost_singleton'
% 3.82/4.06 thf(fact_4850_atLeastAtMost__singleton_H,axiom,
% 3.82/4.06 ! [A: int,B2: int] :
% 3.82/4.06 ( ( A = B2 )
% 3.82/4.06 => ( ( set_or1266510415728281911st_int @ A @ B2 )
% 3.82/4.06 = ( insert_int @ A @ bot_bot_set_int ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % atLeastAtMost_singleton'
% 3.82/4.06 thf(fact_4851_atLeastAtMost__singleton_H,axiom,
% 3.82/4.06 ! [A: real,B2: real] :
% 3.82/4.06 ( ( A = B2 )
% 3.82/4.06 => ( ( set_or1222579329274155063t_real @ A @ B2 )
% 3.82/4.06 = ( insert_real @ A @ bot_bot_set_real ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % atLeastAtMost_singleton'
% 3.82/4.06 thf(fact_4852_numeral__eq__Suc,axiom,
% 3.82/4.06 ( numeral_numeral_nat
% 3.82/4.06 = ( ^ [K2: num] : ( suc @ ( pred_numeral @ K2 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % numeral_eq_Suc
% 3.82/4.06 thf(fact_4853_finite__ranking__induct,axiom,
% 3.82/4.06 ! [S2: set_complex,P: set_complex > $o,F: complex > real] :
% 3.82/4.06 ( ( finite3207457112153483333omplex @ S2 )
% 3.82/4.06 => ( ( P @ bot_bot_set_complex )
% 3.82/4.06 => ( ! [X5: complex,S4: set_complex] :
% 3.82/4.06 ( ( finite3207457112153483333omplex @ S4 )
% 3.82/4.06 => ( ! [Y6: complex] :
% 3.82/4.06 ( ( member_complex @ Y6 @ S4 )
% 3.82/4.06 => ( ord_less_eq_real @ ( F @ Y6 ) @ ( F @ X5 ) ) )
% 3.82/4.06 => ( ( P @ S4 )
% 3.82/4.06 => ( P @ ( insert_complex @ X5 @ S4 ) ) ) ) )
% 3.82/4.06 => ( P @ S2 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_ranking_induct
% 3.82/4.06 thf(fact_4854_finite__ranking__induct,axiom,
% 3.82/4.06 ! [S2: set_Extended_enat,P: set_Extended_enat > $o,F: extended_enat > real] :
% 3.82/4.06 ( ( finite4001608067531595151d_enat @ S2 )
% 3.82/4.06 => ( ( P @ bot_bo7653980558646680370d_enat )
% 3.82/4.06 => ( ! [X5: extended_enat,S4: set_Extended_enat] :
% 3.82/4.06 ( ( finite4001608067531595151d_enat @ S4 )
% 3.82/4.06 => ( ! [Y6: extended_enat] :
% 3.82/4.06 ( ( member_Extended_enat @ Y6 @ S4 )
% 3.82/4.06 => ( ord_less_eq_real @ ( F @ Y6 ) @ ( F @ X5 ) ) )
% 3.82/4.06 => ( ( P @ S4 )
% 3.82/4.06 => ( P @ ( insert_Extended_enat @ X5 @ S4 ) ) ) ) )
% 3.82/4.06 => ( P @ S2 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_ranking_induct
% 3.82/4.06 thf(fact_4855_finite__ranking__induct,axiom,
% 3.82/4.06 ! [S2: set_real,P: set_real > $o,F: real > real] :
% 3.82/4.06 ( ( finite_finite_real @ S2 )
% 3.82/4.06 => ( ( P @ bot_bot_set_real )
% 3.82/4.06 => ( ! [X5: real,S4: set_real] :
% 3.82/4.06 ( ( finite_finite_real @ S4 )
% 3.82/4.06 => ( ! [Y6: real] :
% 3.82/4.06 ( ( member_real @ Y6 @ S4 )
% 3.82/4.06 => ( ord_less_eq_real @ ( F @ Y6 ) @ ( F @ X5 ) ) )
% 3.82/4.06 => ( ( P @ S4 )
% 3.82/4.06 => ( P @ ( insert_real @ X5 @ S4 ) ) ) ) )
% 3.82/4.06 => ( P @ S2 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_ranking_induct
% 3.82/4.06 thf(fact_4856_finite__ranking__induct,axiom,
% 3.82/4.06 ! [S2: set_nat,P: set_nat > $o,F: nat > real] :
% 3.82/4.06 ( ( finite_finite_nat @ S2 )
% 3.82/4.06 => ( ( P @ bot_bot_set_nat )
% 3.82/4.06 => ( ! [X5: nat,S4: set_nat] :
% 3.82/4.06 ( ( finite_finite_nat @ S4 )
% 3.82/4.06 => ( ! [Y6: nat] :
% 3.82/4.06 ( ( member_nat @ Y6 @ S4 )
% 3.82/4.06 => ( ord_less_eq_real @ ( F @ Y6 ) @ ( F @ X5 ) ) )
% 3.82/4.06 => ( ( P @ S4 )
% 3.82/4.06 => ( P @ ( insert_nat @ X5 @ S4 ) ) ) ) )
% 3.82/4.06 => ( P @ S2 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_ranking_induct
% 3.82/4.06 thf(fact_4857_finite__ranking__induct,axiom,
% 3.82/4.06 ! [S2: set_int,P: set_int > $o,F: int > real] :
% 3.82/4.06 ( ( finite_finite_int @ S2 )
% 3.82/4.06 => ( ( P @ bot_bot_set_int )
% 3.82/4.06 => ( ! [X5: int,S4: set_int] :
% 3.82/4.06 ( ( finite_finite_int @ S4 )
% 3.82/4.06 => ( ! [Y6: int] :
% 3.82/4.06 ( ( member_int @ Y6 @ S4 )
% 3.82/4.06 => ( ord_less_eq_real @ ( F @ Y6 ) @ ( F @ X5 ) ) )
% 3.82/4.06 => ( ( P @ S4 )
% 3.82/4.06 => ( P @ ( insert_int @ X5 @ S4 ) ) ) ) )
% 3.82/4.06 => ( P @ S2 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_ranking_induct
% 3.82/4.06 thf(fact_4858_finite__ranking__induct,axiom,
% 3.82/4.06 ! [S2: set_complex,P: set_complex > $o,F: complex > nat] :
% 3.82/4.06 ( ( finite3207457112153483333omplex @ S2 )
% 3.82/4.06 => ( ( P @ bot_bot_set_complex )
% 3.82/4.06 => ( ! [X5: complex,S4: set_complex] :
% 3.82/4.06 ( ( finite3207457112153483333omplex @ S4 )
% 3.82/4.06 => ( ! [Y6: complex] :
% 3.82/4.06 ( ( member_complex @ Y6 @ S4 )
% 3.82/4.06 => ( ord_less_eq_nat @ ( F @ Y6 ) @ ( F @ X5 ) ) )
% 3.82/4.06 => ( ( P @ S4 )
% 3.82/4.06 => ( P @ ( insert_complex @ X5 @ S4 ) ) ) ) )
% 3.82/4.06 => ( P @ S2 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_ranking_induct
% 3.82/4.06 thf(fact_4859_finite__ranking__induct,axiom,
% 3.82/4.06 ! [S2: set_Extended_enat,P: set_Extended_enat > $o,F: extended_enat > nat] :
% 3.82/4.06 ( ( finite4001608067531595151d_enat @ S2 )
% 3.82/4.06 => ( ( P @ bot_bo7653980558646680370d_enat )
% 3.82/4.06 => ( ! [X5: extended_enat,S4: set_Extended_enat] :
% 3.82/4.06 ( ( finite4001608067531595151d_enat @ S4 )
% 3.82/4.06 => ( ! [Y6: extended_enat] :
% 3.82/4.06 ( ( member_Extended_enat @ Y6 @ S4 )
% 3.82/4.06 => ( ord_less_eq_nat @ ( F @ Y6 ) @ ( F @ X5 ) ) )
% 3.82/4.06 => ( ( P @ S4 )
% 3.82/4.06 => ( P @ ( insert_Extended_enat @ X5 @ S4 ) ) ) ) )
% 3.82/4.06 => ( P @ S2 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_ranking_induct
% 3.82/4.06 thf(fact_4860_finite__ranking__induct,axiom,
% 3.82/4.06 ! [S2: set_real,P: set_real > $o,F: real > nat] :
% 3.82/4.06 ( ( finite_finite_real @ S2 )
% 3.82/4.06 => ( ( P @ bot_bot_set_real )
% 3.82/4.06 => ( ! [X5: real,S4: set_real] :
% 3.82/4.06 ( ( finite_finite_real @ S4 )
% 3.82/4.06 => ( ! [Y6: real] :
% 3.82/4.06 ( ( member_real @ Y6 @ S4 )
% 3.82/4.06 => ( ord_less_eq_nat @ ( F @ Y6 ) @ ( F @ X5 ) ) )
% 3.82/4.06 => ( ( P @ S4 )
% 3.82/4.06 => ( P @ ( insert_real @ X5 @ S4 ) ) ) ) )
% 3.82/4.06 => ( P @ S2 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_ranking_induct
% 3.82/4.06 thf(fact_4861_finite__ranking__induct,axiom,
% 3.82/4.06 ! [S2: set_nat,P: set_nat > $o,F: nat > nat] :
% 3.82/4.06 ( ( finite_finite_nat @ S2 )
% 3.82/4.06 => ( ( P @ bot_bot_set_nat )
% 3.82/4.06 => ( ! [X5: nat,S4: set_nat] :
% 3.82/4.06 ( ( finite_finite_nat @ S4 )
% 3.82/4.06 => ( ! [Y6: nat] :
% 3.82/4.06 ( ( member_nat @ Y6 @ S4 )
% 3.82/4.06 => ( ord_less_eq_nat @ ( F @ Y6 ) @ ( F @ X5 ) ) )
% 3.82/4.06 => ( ( P @ S4 )
% 3.82/4.06 => ( P @ ( insert_nat @ X5 @ S4 ) ) ) ) )
% 3.82/4.06 => ( P @ S2 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_ranking_induct
% 3.82/4.06 thf(fact_4862_finite__ranking__induct,axiom,
% 3.82/4.06 ! [S2: set_int,P: set_int > $o,F: int > nat] :
% 3.82/4.06 ( ( finite_finite_int @ S2 )
% 3.82/4.06 => ( ( P @ bot_bot_set_int )
% 3.82/4.06 => ( ! [X5: int,S4: set_int] :
% 3.82/4.06 ( ( finite_finite_int @ S4 )
% 3.82/4.06 => ( ! [Y6: int] :
% 3.82/4.06 ( ( member_int @ Y6 @ S4 )
% 3.82/4.06 => ( ord_less_eq_nat @ ( F @ Y6 ) @ ( F @ X5 ) ) )
% 3.82/4.06 => ( ( P @ S4 )
% 3.82/4.06 => ( P @ ( insert_int @ X5 @ S4 ) ) ) ) )
% 3.82/4.06 => ( P @ S2 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_ranking_induct
% 3.82/4.06 thf(fact_4863_finite__linorder__max__induct,axiom,
% 3.82/4.06 ! [A2: set_nat,P: set_nat > $o] :
% 3.82/4.06 ( ( finite_finite_nat @ A2 )
% 3.82/4.06 => ( ( P @ bot_bot_set_nat )
% 3.82/4.06 => ( ! [B4: nat,A6: set_nat] :
% 3.82/4.06 ( ( finite_finite_nat @ A6 )
% 3.82/4.06 => ( ! [X2: nat] :
% 3.82/4.06 ( ( member_nat @ X2 @ A6 )
% 3.82/4.06 => ( ord_less_nat @ X2 @ B4 ) )
% 3.82/4.06 => ( ( P @ A6 )
% 3.82/4.06 => ( P @ ( insert_nat @ B4 @ A6 ) ) ) ) )
% 3.82/4.06 => ( P @ A2 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_linorder_max_induct
% 3.82/4.06 thf(fact_4864_finite__linorder__max__induct,axiom,
% 3.82/4.06 ! [A2: set_Extended_enat,P: set_Extended_enat > $o] :
% 3.82/4.06 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.06 => ( ( P @ bot_bo7653980558646680370d_enat )
% 3.82/4.06 => ( ! [B4: extended_enat,A6: set_Extended_enat] :
% 3.82/4.06 ( ( finite4001608067531595151d_enat @ A6 )
% 3.82/4.06 => ( ! [X2: extended_enat] :
% 3.82/4.06 ( ( member_Extended_enat @ X2 @ A6 )
% 3.82/4.06 => ( ord_le72135733267957522d_enat @ X2 @ B4 ) )
% 3.82/4.06 => ( ( P @ A6 )
% 3.82/4.06 => ( P @ ( insert_Extended_enat @ B4 @ A6 ) ) ) ) )
% 3.82/4.06 => ( P @ A2 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_linorder_max_induct
% 3.82/4.06 thf(fact_4865_finite__linorder__max__induct,axiom,
% 3.82/4.06 ! [A2: set_real,P: set_real > $o] :
% 3.82/4.06 ( ( finite_finite_real @ A2 )
% 3.82/4.06 => ( ( P @ bot_bot_set_real )
% 3.82/4.06 => ( ! [B4: real,A6: set_real] :
% 3.82/4.06 ( ( finite_finite_real @ A6 )
% 3.82/4.06 => ( ! [X2: real] :
% 3.82/4.06 ( ( member_real @ X2 @ A6 )
% 3.82/4.06 => ( ord_less_real @ X2 @ B4 ) )
% 3.82/4.06 => ( ( P @ A6 )
% 3.82/4.06 => ( P @ ( insert_real @ B4 @ A6 ) ) ) ) )
% 3.82/4.06 => ( P @ A2 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_linorder_max_induct
% 3.82/4.06 thf(fact_4866_finite__linorder__max__induct,axiom,
% 3.82/4.06 ! [A2: set_int,P: set_int > $o] :
% 3.82/4.06 ( ( finite_finite_int @ A2 )
% 3.82/4.06 => ( ( P @ bot_bot_set_int )
% 3.82/4.06 => ( ! [B4: int,A6: set_int] :
% 3.82/4.06 ( ( finite_finite_int @ A6 )
% 3.82/4.06 => ( ! [X2: int] :
% 3.82/4.06 ( ( member_int @ X2 @ A6 )
% 3.82/4.06 => ( ord_less_int @ X2 @ B4 ) )
% 3.82/4.06 => ( ( P @ A6 )
% 3.82/4.06 => ( P @ ( insert_int @ B4 @ A6 ) ) ) ) )
% 3.82/4.06 => ( P @ A2 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_linorder_max_induct
% 3.82/4.06 thf(fact_4867_finite__linorder__min__induct,axiom,
% 3.82/4.06 ! [A2: set_nat,P: set_nat > $o] :
% 3.82/4.06 ( ( finite_finite_nat @ A2 )
% 3.82/4.06 => ( ( P @ bot_bot_set_nat )
% 3.82/4.06 => ( ! [B4: nat,A6: set_nat] :
% 3.82/4.06 ( ( finite_finite_nat @ A6 )
% 3.82/4.06 => ( ! [X2: nat] :
% 3.82/4.06 ( ( member_nat @ X2 @ A6 )
% 3.82/4.06 => ( ord_less_nat @ B4 @ X2 ) )
% 3.82/4.06 => ( ( P @ A6 )
% 3.82/4.06 => ( P @ ( insert_nat @ B4 @ A6 ) ) ) ) )
% 3.82/4.06 => ( P @ A2 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_linorder_min_induct
% 3.82/4.06 thf(fact_4868_finite__linorder__min__induct,axiom,
% 3.82/4.06 ! [A2: set_Extended_enat,P: set_Extended_enat > $o] :
% 3.82/4.06 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.06 => ( ( P @ bot_bo7653980558646680370d_enat )
% 3.82/4.06 => ( ! [B4: extended_enat,A6: set_Extended_enat] :
% 3.82/4.06 ( ( finite4001608067531595151d_enat @ A6 )
% 3.82/4.06 => ( ! [X2: extended_enat] :
% 3.82/4.06 ( ( member_Extended_enat @ X2 @ A6 )
% 3.82/4.06 => ( ord_le72135733267957522d_enat @ B4 @ X2 ) )
% 3.82/4.06 => ( ( P @ A6 )
% 3.82/4.06 => ( P @ ( insert_Extended_enat @ B4 @ A6 ) ) ) ) )
% 3.82/4.06 => ( P @ A2 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_linorder_min_induct
% 3.82/4.06 thf(fact_4869_finite__linorder__min__induct,axiom,
% 3.82/4.06 ! [A2: set_real,P: set_real > $o] :
% 3.82/4.06 ( ( finite_finite_real @ A2 )
% 3.82/4.06 => ( ( P @ bot_bot_set_real )
% 3.82/4.06 => ( ! [B4: real,A6: set_real] :
% 3.82/4.06 ( ( finite_finite_real @ A6 )
% 3.82/4.06 => ( ! [X2: real] :
% 3.82/4.06 ( ( member_real @ X2 @ A6 )
% 3.82/4.06 => ( ord_less_real @ B4 @ X2 ) )
% 3.82/4.06 => ( ( P @ A6 )
% 3.82/4.06 => ( P @ ( insert_real @ B4 @ A6 ) ) ) ) )
% 3.82/4.06 => ( P @ A2 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_linorder_min_induct
% 3.82/4.06 thf(fact_4870_finite__linorder__min__induct,axiom,
% 3.82/4.06 ! [A2: set_int,P: set_int > $o] :
% 3.82/4.06 ( ( finite_finite_int @ A2 )
% 3.82/4.06 => ( ( P @ bot_bot_set_int )
% 3.82/4.06 => ( ! [B4: int,A6: set_int] :
% 3.82/4.06 ( ( finite_finite_int @ A6 )
% 3.82/4.06 => ( ! [X2: int] :
% 3.82/4.06 ( ( member_int @ X2 @ A6 )
% 3.82/4.06 => ( ord_less_int @ B4 @ X2 ) )
% 3.82/4.06 => ( ( P @ A6 )
% 3.82/4.06 => ( P @ ( insert_int @ B4 @ A6 ) ) ) ) )
% 3.82/4.06 => ( P @ A2 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_linorder_min_induct
% 3.82/4.06 thf(fact_4871_finite__subset__induct_H,axiom,
% 3.82/4.06 ! [F3: set_set_nat,A2: set_set_nat,P: set_set_nat > $o] :
% 3.82/4.06 ( ( finite1152437895449049373et_nat @ F3 )
% 3.82/4.06 => ( ( ord_le6893508408891458716et_nat @ F3 @ A2 )
% 3.82/4.06 => ( ( P @ bot_bot_set_set_nat )
% 3.82/4.06 => ( ! [A4: set_nat,F4: set_set_nat] :
% 3.82/4.06 ( ( finite1152437895449049373et_nat @ F4 )
% 3.82/4.06 => ( ( member_set_nat @ A4 @ A2 )
% 3.82/4.06 => ( ( ord_le6893508408891458716et_nat @ F4 @ A2 )
% 3.82/4.06 => ( ~ ( member_set_nat @ A4 @ F4 )
% 3.82/4.06 => ( ( P @ F4 )
% 3.82/4.06 => ( P @ ( insert_set_nat @ A4 @ F4 ) ) ) ) ) ) )
% 3.82/4.06 => ( P @ F3 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_subset_induct'
% 3.82/4.06 thf(fact_4872_finite__subset__induct_H,axiom,
% 3.82/4.06 ! [F3: set_complex,A2: set_complex,P: set_complex > $o] :
% 3.82/4.06 ( ( finite3207457112153483333omplex @ F3 )
% 3.82/4.06 => ( ( ord_le211207098394363844omplex @ F3 @ A2 )
% 3.82/4.06 => ( ( P @ bot_bot_set_complex )
% 3.82/4.06 => ( ! [A4: complex,F4: set_complex] :
% 3.82/4.06 ( ( finite3207457112153483333omplex @ F4 )
% 3.82/4.06 => ( ( member_complex @ A4 @ A2 )
% 3.82/4.06 => ( ( ord_le211207098394363844omplex @ F4 @ A2 )
% 3.82/4.06 => ( ~ ( member_complex @ A4 @ F4 )
% 3.82/4.06 => ( ( P @ F4 )
% 3.82/4.06 => ( P @ ( insert_complex @ A4 @ F4 ) ) ) ) ) ) )
% 3.82/4.06 => ( P @ F3 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_subset_induct'
% 3.82/4.06 thf(fact_4873_finite__subset__induct_H,axiom,
% 3.82/4.06 ! [F3: set_Extended_enat,A2: set_Extended_enat,P: set_Extended_enat > $o] :
% 3.82/4.06 ( ( finite4001608067531595151d_enat @ F3 )
% 3.82/4.06 => ( ( ord_le7203529160286727270d_enat @ F3 @ A2 )
% 3.82/4.06 => ( ( P @ bot_bo7653980558646680370d_enat )
% 3.82/4.06 => ( ! [A4: extended_enat,F4: set_Extended_enat] :
% 3.82/4.06 ( ( finite4001608067531595151d_enat @ F4 )
% 3.82/4.06 => ( ( member_Extended_enat @ A4 @ A2 )
% 3.82/4.06 => ( ( ord_le7203529160286727270d_enat @ F4 @ A2 )
% 3.82/4.06 => ( ~ ( member_Extended_enat @ A4 @ F4 )
% 3.82/4.06 => ( ( P @ F4 )
% 3.82/4.06 => ( P @ ( insert_Extended_enat @ A4 @ F4 ) ) ) ) ) ) )
% 3.82/4.06 => ( P @ F3 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_subset_induct'
% 3.82/4.06 thf(fact_4874_finite__subset__induct_H,axiom,
% 3.82/4.06 ! [F3: set_real,A2: set_real,P: set_real > $o] :
% 3.82/4.06 ( ( finite_finite_real @ F3 )
% 3.82/4.06 => ( ( ord_less_eq_set_real @ F3 @ A2 )
% 3.82/4.06 => ( ( P @ bot_bot_set_real )
% 3.82/4.06 => ( ! [A4: real,F4: set_real] :
% 3.82/4.06 ( ( finite_finite_real @ F4 )
% 3.82/4.06 => ( ( member_real @ A4 @ A2 )
% 3.82/4.06 => ( ( ord_less_eq_set_real @ F4 @ A2 )
% 3.82/4.06 => ( ~ ( member_real @ A4 @ F4 )
% 3.82/4.06 => ( ( P @ F4 )
% 3.82/4.06 => ( P @ ( insert_real @ A4 @ F4 ) ) ) ) ) ) )
% 3.82/4.06 => ( P @ F3 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_subset_induct'
% 3.82/4.06 thf(fact_4875_finite__subset__induct_H,axiom,
% 3.82/4.06 ! [F3: set_nat,A2: set_nat,P: set_nat > $o] :
% 3.82/4.06 ( ( finite_finite_nat @ F3 )
% 3.82/4.06 => ( ( ord_less_eq_set_nat @ F3 @ A2 )
% 3.82/4.06 => ( ( P @ bot_bot_set_nat )
% 3.82/4.06 => ( ! [A4: nat,F4: set_nat] :
% 3.82/4.06 ( ( finite_finite_nat @ F4 )
% 3.82/4.06 => ( ( member_nat @ A4 @ A2 )
% 3.82/4.06 => ( ( ord_less_eq_set_nat @ F4 @ A2 )
% 3.82/4.06 => ( ~ ( member_nat @ A4 @ F4 )
% 3.82/4.06 => ( ( P @ F4 )
% 3.82/4.06 => ( P @ ( insert_nat @ A4 @ F4 ) ) ) ) ) ) )
% 3.82/4.06 => ( P @ F3 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_subset_induct'
% 3.82/4.06 thf(fact_4876_finite__subset__induct_H,axiom,
% 3.82/4.06 ! [F3: set_int,A2: set_int,P: set_int > $o] :
% 3.82/4.06 ( ( finite_finite_int @ F3 )
% 3.82/4.06 => ( ( ord_less_eq_set_int @ F3 @ A2 )
% 3.82/4.06 => ( ( P @ bot_bot_set_int )
% 3.82/4.06 => ( ! [A4: int,F4: set_int] :
% 3.82/4.06 ( ( finite_finite_int @ F4 )
% 3.82/4.06 => ( ( member_int @ A4 @ A2 )
% 3.82/4.06 => ( ( ord_less_eq_set_int @ F4 @ A2 )
% 3.82/4.06 => ( ~ ( member_int @ A4 @ F4 )
% 3.82/4.06 => ( ( P @ F4 )
% 3.82/4.06 => ( P @ ( insert_int @ A4 @ F4 ) ) ) ) ) ) )
% 3.82/4.06 => ( P @ F3 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_subset_induct'
% 3.82/4.06 thf(fact_4877_finite__subset__induct,axiom,
% 3.82/4.06 ! [F3: set_set_nat,A2: set_set_nat,P: set_set_nat > $o] :
% 3.82/4.06 ( ( finite1152437895449049373et_nat @ F3 )
% 3.82/4.06 => ( ( ord_le6893508408891458716et_nat @ F3 @ A2 )
% 3.82/4.06 => ( ( P @ bot_bot_set_set_nat )
% 3.82/4.06 => ( ! [A4: set_nat,F4: set_set_nat] :
% 3.82/4.06 ( ( finite1152437895449049373et_nat @ F4 )
% 3.82/4.06 => ( ( member_set_nat @ A4 @ A2 )
% 3.82/4.06 => ( ~ ( member_set_nat @ A4 @ F4 )
% 3.82/4.06 => ( ( P @ F4 )
% 3.82/4.06 => ( P @ ( insert_set_nat @ A4 @ F4 ) ) ) ) ) )
% 3.82/4.06 => ( P @ F3 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_subset_induct
% 3.82/4.06 thf(fact_4878_finite__subset__induct,axiom,
% 3.82/4.06 ! [F3: set_complex,A2: set_complex,P: set_complex > $o] :
% 3.82/4.06 ( ( finite3207457112153483333omplex @ F3 )
% 3.82/4.06 => ( ( ord_le211207098394363844omplex @ F3 @ A2 )
% 3.82/4.06 => ( ( P @ bot_bot_set_complex )
% 3.82/4.06 => ( ! [A4: complex,F4: set_complex] :
% 3.82/4.06 ( ( finite3207457112153483333omplex @ F4 )
% 3.82/4.06 => ( ( member_complex @ A4 @ A2 )
% 3.82/4.06 => ( ~ ( member_complex @ A4 @ F4 )
% 3.82/4.06 => ( ( P @ F4 )
% 3.82/4.06 => ( P @ ( insert_complex @ A4 @ F4 ) ) ) ) ) )
% 3.82/4.06 => ( P @ F3 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_subset_induct
% 3.82/4.06 thf(fact_4879_finite__subset__induct,axiom,
% 3.82/4.06 ! [F3: set_Extended_enat,A2: set_Extended_enat,P: set_Extended_enat > $o] :
% 3.82/4.06 ( ( finite4001608067531595151d_enat @ F3 )
% 3.82/4.06 => ( ( ord_le7203529160286727270d_enat @ F3 @ A2 )
% 3.82/4.06 => ( ( P @ bot_bo7653980558646680370d_enat )
% 3.82/4.06 => ( ! [A4: extended_enat,F4: set_Extended_enat] :
% 3.82/4.06 ( ( finite4001608067531595151d_enat @ F4 )
% 3.82/4.06 => ( ( member_Extended_enat @ A4 @ A2 )
% 3.82/4.06 => ( ~ ( member_Extended_enat @ A4 @ F4 )
% 3.82/4.06 => ( ( P @ F4 )
% 3.82/4.06 => ( P @ ( insert_Extended_enat @ A4 @ F4 ) ) ) ) ) )
% 3.82/4.06 => ( P @ F3 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_subset_induct
% 3.82/4.06 thf(fact_4880_finite__subset__induct,axiom,
% 3.82/4.06 ! [F3: set_real,A2: set_real,P: set_real > $o] :
% 3.82/4.06 ( ( finite_finite_real @ F3 )
% 3.82/4.06 => ( ( ord_less_eq_set_real @ F3 @ A2 )
% 3.82/4.06 => ( ( P @ bot_bot_set_real )
% 3.82/4.06 => ( ! [A4: real,F4: set_real] :
% 3.82/4.06 ( ( finite_finite_real @ F4 )
% 3.82/4.06 => ( ( member_real @ A4 @ A2 )
% 3.82/4.06 => ( ~ ( member_real @ A4 @ F4 )
% 3.82/4.06 => ( ( P @ F4 )
% 3.82/4.06 => ( P @ ( insert_real @ A4 @ F4 ) ) ) ) ) )
% 3.82/4.06 => ( P @ F3 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_subset_induct
% 3.82/4.06 thf(fact_4881_finite__subset__induct,axiom,
% 3.82/4.06 ! [F3: set_nat,A2: set_nat,P: set_nat > $o] :
% 3.82/4.06 ( ( finite_finite_nat @ F3 )
% 3.82/4.06 => ( ( ord_less_eq_set_nat @ F3 @ A2 )
% 3.82/4.06 => ( ( P @ bot_bot_set_nat )
% 3.82/4.06 => ( ! [A4: nat,F4: set_nat] :
% 3.82/4.06 ( ( finite_finite_nat @ F4 )
% 3.82/4.06 => ( ( member_nat @ A4 @ A2 )
% 3.82/4.06 => ( ~ ( member_nat @ A4 @ F4 )
% 3.82/4.06 => ( ( P @ F4 )
% 3.82/4.06 => ( P @ ( insert_nat @ A4 @ F4 ) ) ) ) ) )
% 3.82/4.06 => ( P @ F3 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_subset_induct
% 3.82/4.06 thf(fact_4882_finite__subset__induct,axiom,
% 3.82/4.06 ! [F3: set_int,A2: set_int,P: set_int > $o] :
% 3.82/4.06 ( ( finite_finite_int @ F3 )
% 3.82/4.06 => ( ( ord_less_eq_set_int @ F3 @ A2 )
% 3.82/4.06 => ( ( P @ bot_bot_set_int )
% 3.82/4.06 => ( ! [A4: int,F4: set_int] :
% 3.82/4.06 ( ( finite_finite_int @ F4 )
% 3.82/4.06 => ( ( member_int @ A4 @ A2 )
% 3.82/4.06 => ( ~ ( member_int @ A4 @ F4 )
% 3.82/4.06 => ( ( P @ F4 )
% 3.82/4.06 => ( P @ ( insert_int @ A4 @ F4 ) ) ) ) ) )
% 3.82/4.06 => ( P @ F3 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_subset_induct
% 3.82/4.06 thf(fact_4883_finite__remove__induct,axiom,
% 3.82/4.06 ! [B: set_set_nat,P: set_set_nat > $o] :
% 3.82/4.06 ( ( finite1152437895449049373et_nat @ B )
% 3.82/4.06 => ( ( P @ bot_bot_set_set_nat )
% 3.82/4.06 => ( ! [A6: set_set_nat] :
% 3.82/4.06 ( ( finite1152437895449049373et_nat @ A6 )
% 3.82/4.06 => ( ( A6 != bot_bot_set_set_nat )
% 3.82/4.06 => ( ( ord_le6893508408891458716et_nat @ A6 @ B )
% 3.82/4.06 => ( ! [X2: set_nat] :
% 3.82/4.06 ( ( member_set_nat @ X2 @ A6 )
% 3.82/4.06 => ( P @ ( minus_2163939370556025621et_nat @ A6 @ ( insert_set_nat @ X2 @ bot_bot_set_set_nat ) ) ) )
% 3.82/4.06 => ( P @ A6 ) ) ) ) )
% 3.82/4.06 => ( P @ B ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_remove_induct
% 3.82/4.06 thf(fact_4884_finite__remove__induct,axiom,
% 3.82/4.06 ! [B: set_complex,P: set_complex > $o] :
% 3.82/4.06 ( ( finite3207457112153483333omplex @ B )
% 3.82/4.06 => ( ( P @ bot_bot_set_complex )
% 3.82/4.06 => ( ! [A6: set_complex] :
% 3.82/4.06 ( ( finite3207457112153483333omplex @ A6 )
% 3.82/4.06 => ( ( A6 != bot_bot_set_complex )
% 3.82/4.06 => ( ( ord_le211207098394363844omplex @ A6 @ B )
% 3.82/4.06 => ( ! [X2: complex] :
% 3.82/4.06 ( ( member_complex @ X2 @ A6 )
% 3.82/4.06 => ( P @ ( minus_811609699411566653omplex @ A6 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) )
% 3.82/4.06 => ( P @ A6 ) ) ) ) )
% 3.82/4.06 => ( P @ B ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_remove_induct
% 3.82/4.06 thf(fact_4885_finite__remove__induct,axiom,
% 3.82/4.06 ! [B: set_Extended_enat,P: set_Extended_enat > $o] :
% 3.82/4.06 ( ( finite4001608067531595151d_enat @ B )
% 3.82/4.06 => ( ( P @ bot_bo7653980558646680370d_enat )
% 3.82/4.06 => ( ! [A6: set_Extended_enat] :
% 3.82/4.06 ( ( finite4001608067531595151d_enat @ A6 )
% 3.82/4.06 => ( ( A6 != bot_bo7653980558646680370d_enat )
% 3.82/4.06 => ( ( ord_le7203529160286727270d_enat @ A6 @ B )
% 3.82/4.06 => ( ! [X2: extended_enat] :
% 3.82/4.06 ( ( member_Extended_enat @ X2 @ A6 )
% 3.82/4.06 => ( P @ ( minus_925952699566721837d_enat @ A6 @ ( insert_Extended_enat @ X2 @ bot_bo7653980558646680370d_enat ) ) ) )
% 3.82/4.06 => ( P @ A6 ) ) ) ) )
% 3.82/4.06 => ( P @ B ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_remove_induct
% 3.82/4.06 thf(fact_4886_finite__remove__induct,axiom,
% 3.82/4.06 ! [B: set_real,P: set_real > $o] :
% 3.82/4.06 ( ( finite_finite_real @ B )
% 3.82/4.06 => ( ( P @ bot_bot_set_real )
% 3.82/4.06 => ( ! [A6: set_real] :
% 3.82/4.06 ( ( finite_finite_real @ A6 )
% 3.82/4.06 => ( ( A6 != bot_bot_set_real )
% 3.82/4.06 => ( ( ord_less_eq_set_real @ A6 @ B )
% 3.82/4.06 => ( ! [X2: real] :
% 3.82/4.06 ( ( member_real @ X2 @ A6 )
% 3.82/4.06 => ( P @ ( minus_minus_set_real @ A6 @ ( insert_real @ X2 @ bot_bot_set_real ) ) ) )
% 3.82/4.06 => ( P @ A6 ) ) ) ) )
% 3.82/4.06 => ( P @ B ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_remove_induct
% 3.82/4.06 thf(fact_4887_finite__remove__induct,axiom,
% 3.82/4.06 ! [B: set_nat,P: set_nat > $o] :
% 3.82/4.06 ( ( finite_finite_nat @ B )
% 3.82/4.06 => ( ( P @ bot_bot_set_nat )
% 3.82/4.06 => ( ! [A6: set_nat] :
% 3.82/4.06 ( ( finite_finite_nat @ A6 )
% 3.82/4.06 => ( ( A6 != bot_bot_set_nat )
% 3.82/4.06 => ( ( ord_less_eq_set_nat @ A6 @ B )
% 3.82/4.06 => ( ! [X2: nat] :
% 3.82/4.06 ( ( member_nat @ X2 @ A6 )
% 3.82/4.06 => ( P @ ( minus_minus_set_nat @ A6 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) )
% 3.82/4.06 => ( P @ A6 ) ) ) ) )
% 3.82/4.06 => ( P @ B ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_remove_induct
% 3.82/4.06 thf(fact_4888_finite__remove__induct,axiom,
% 3.82/4.06 ! [B: set_int,P: set_int > $o] :
% 3.82/4.06 ( ( finite_finite_int @ B )
% 3.82/4.06 => ( ( P @ bot_bot_set_int )
% 3.82/4.06 => ( ! [A6: set_int] :
% 3.82/4.06 ( ( finite_finite_int @ A6 )
% 3.82/4.06 => ( ( A6 != bot_bot_set_int )
% 3.82/4.06 => ( ( ord_less_eq_set_int @ A6 @ B )
% 3.82/4.06 => ( ! [X2: int] :
% 3.82/4.06 ( ( member_int @ X2 @ A6 )
% 3.82/4.06 => ( P @ ( minus_minus_set_int @ A6 @ ( insert_int @ X2 @ bot_bot_set_int ) ) ) )
% 3.82/4.06 => ( P @ A6 ) ) ) ) )
% 3.82/4.06 => ( P @ B ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_remove_induct
% 3.82/4.06 thf(fact_4889_remove__induct,axiom,
% 3.82/4.06 ! [P: set_set_nat > $o,B: set_set_nat] :
% 3.82/4.06 ( ( P @ bot_bot_set_set_nat )
% 3.82/4.06 => ( ( ~ ( finite1152437895449049373et_nat @ B )
% 3.82/4.06 => ( P @ B ) )
% 3.82/4.06 => ( ! [A6: set_set_nat] :
% 3.82/4.06 ( ( finite1152437895449049373et_nat @ A6 )
% 3.82/4.06 => ( ( A6 != bot_bot_set_set_nat )
% 3.82/4.06 => ( ( ord_le6893508408891458716et_nat @ A6 @ B )
% 3.82/4.06 => ( ! [X2: set_nat] :
% 3.82/4.06 ( ( member_set_nat @ X2 @ A6 )
% 3.82/4.06 => ( P @ ( minus_2163939370556025621et_nat @ A6 @ ( insert_set_nat @ X2 @ bot_bot_set_set_nat ) ) ) )
% 3.82/4.06 => ( P @ A6 ) ) ) ) )
% 3.82/4.06 => ( P @ B ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % remove_induct
% 3.82/4.06 thf(fact_4890_remove__induct,axiom,
% 3.82/4.06 ! [P: set_complex > $o,B: set_complex] :
% 3.82/4.06 ( ( P @ bot_bot_set_complex )
% 3.82/4.06 => ( ( ~ ( finite3207457112153483333omplex @ B )
% 3.82/4.06 => ( P @ B ) )
% 3.82/4.06 => ( ! [A6: set_complex] :
% 3.82/4.06 ( ( finite3207457112153483333omplex @ A6 )
% 3.82/4.06 => ( ( A6 != bot_bot_set_complex )
% 3.82/4.06 => ( ( ord_le211207098394363844omplex @ A6 @ B )
% 3.82/4.06 => ( ! [X2: complex] :
% 3.82/4.06 ( ( member_complex @ X2 @ A6 )
% 3.82/4.06 => ( P @ ( minus_811609699411566653omplex @ A6 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) )
% 3.82/4.06 => ( P @ A6 ) ) ) ) )
% 3.82/4.06 => ( P @ B ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % remove_induct
% 3.82/4.06 thf(fact_4891_remove__induct,axiom,
% 3.82/4.06 ! [P: set_Extended_enat > $o,B: set_Extended_enat] :
% 3.82/4.06 ( ( P @ bot_bo7653980558646680370d_enat )
% 3.82/4.06 => ( ( ~ ( finite4001608067531595151d_enat @ B )
% 3.82/4.06 => ( P @ B ) )
% 3.82/4.06 => ( ! [A6: set_Extended_enat] :
% 3.82/4.06 ( ( finite4001608067531595151d_enat @ A6 )
% 3.82/4.06 => ( ( A6 != bot_bo7653980558646680370d_enat )
% 3.82/4.06 => ( ( ord_le7203529160286727270d_enat @ A6 @ B )
% 3.82/4.06 => ( ! [X2: extended_enat] :
% 3.82/4.06 ( ( member_Extended_enat @ X2 @ A6 )
% 3.82/4.06 => ( P @ ( minus_925952699566721837d_enat @ A6 @ ( insert_Extended_enat @ X2 @ bot_bo7653980558646680370d_enat ) ) ) )
% 3.82/4.06 => ( P @ A6 ) ) ) ) )
% 3.82/4.06 => ( P @ B ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % remove_induct
% 3.82/4.06 thf(fact_4892_remove__induct,axiom,
% 3.82/4.06 ! [P: set_real > $o,B: set_real] :
% 3.82/4.06 ( ( P @ bot_bot_set_real )
% 3.82/4.06 => ( ( ~ ( finite_finite_real @ B )
% 3.82/4.06 => ( P @ B ) )
% 3.82/4.06 => ( ! [A6: set_real] :
% 3.82/4.06 ( ( finite_finite_real @ A6 )
% 3.82/4.06 => ( ( A6 != bot_bot_set_real )
% 3.82/4.06 => ( ( ord_less_eq_set_real @ A6 @ B )
% 3.82/4.06 => ( ! [X2: real] :
% 3.82/4.06 ( ( member_real @ X2 @ A6 )
% 3.82/4.06 => ( P @ ( minus_minus_set_real @ A6 @ ( insert_real @ X2 @ bot_bot_set_real ) ) ) )
% 3.82/4.06 => ( P @ A6 ) ) ) ) )
% 3.82/4.06 => ( P @ B ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % remove_induct
% 3.82/4.06 thf(fact_4893_remove__induct,axiom,
% 3.82/4.06 ! [P: set_nat > $o,B: set_nat] :
% 3.82/4.06 ( ( P @ bot_bot_set_nat )
% 3.82/4.06 => ( ( ~ ( finite_finite_nat @ B )
% 3.82/4.06 => ( P @ B ) )
% 3.82/4.06 => ( ! [A6: set_nat] :
% 3.82/4.06 ( ( finite_finite_nat @ A6 )
% 3.82/4.06 => ( ( A6 != bot_bot_set_nat )
% 3.82/4.06 => ( ( ord_less_eq_set_nat @ A6 @ B )
% 3.82/4.06 => ( ! [X2: nat] :
% 3.82/4.06 ( ( member_nat @ X2 @ A6 )
% 3.82/4.06 => ( P @ ( minus_minus_set_nat @ A6 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) )
% 3.82/4.06 => ( P @ A6 ) ) ) ) )
% 3.82/4.06 => ( P @ B ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % remove_induct
% 3.82/4.06 thf(fact_4894_remove__induct,axiom,
% 3.82/4.06 ! [P: set_int > $o,B: set_int] :
% 3.82/4.06 ( ( P @ bot_bot_set_int )
% 3.82/4.06 => ( ( ~ ( finite_finite_int @ B )
% 3.82/4.06 => ( P @ B ) )
% 3.82/4.06 => ( ! [A6: set_int] :
% 3.82/4.06 ( ( finite_finite_int @ A6 )
% 3.82/4.06 => ( ( A6 != bot_bot_set_int )
% 3.82/4.06 => ( ( ord_less_eq_set_int @ A6 @ B )
% 3.82/4.06 => ( ! [X2: int] :
% 3.82/4.06 ( ( member_int @ X2 @ A6 )
% 3.82/4.06 => ( P @ ( minus_minus_set_int @ A6 @ ( insert_int @ X2 @ bot_bot_set_int ) ) ) )
% 3.82/4.06 => ( P @ A6 ) ) ) ) )
% 3.82/4.06 => ( P @ B ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % remove_induct
% 3.82/4.06 thf(fact_4895_atLeast0__atMost__Suc,axiom,
% 3.82/4.06 ! [N2: nat] :
% 3.82/4.06 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 3.82/4.06 = ( insert_nat @ ( suc @ N2 ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % atLeast0_atMost_Suc
% 3.82/4.06 thf(fact_4896_finite__induct__select,axiom,
% 3.82/4.06 ! [S2: set_complex,P: set_complex > $o] :
% 3.82/4.06 ( ( finite3207457112153483333omplex @ S2 )
% 3.82/4.06 => ( ( P @ bot_bot_set_complex )
% 3.82/4.06 => ( ! [T4: set_complex] :
% 3.82/4.06 ( ( ord_less_set_complex @ T4 @ S2 )
% 3.82/4.06 => ( ( P @ T4 )
% 3.82/4.06 => ? [X2: complex] :
% 3.82/4.06 ( ( member_complex @ X2 @ ( minus_811609699411566653omplex @ S2 @ T4 ) )
% 3.82/4.06 & ( P @ ( insert_complex @ X2 @ T4 ) ) ) ) )
% 3.82/4.06 => ( P @ S2 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_induct_select
% 3.82/4.06 thf(fact_4897_finite__induct__select,axiom,
% 3.82/4.06 ! [S2: set_Extended_enat,P: set_Extended_enat > $o] :
% 3.82/4.06 ( ( finite4001608067531595151d_enat @ S2 )
% 3.82/4.06 => ( ( P @ bot_bo7653980558646680370d_enat )
% 3.82/4.06 => ( ! [T4: set_Extended_enat] :
% 3.82/4.06 ( ( ord_le2529575680413868914d_enat @ T4 @ S2 )
% 3.82/4.06 => ( ( P @ T4 )
% 3.82/4.06 => ? [X2: extended_enat] :
% 3.82/4.06 ( ( member_Extended_enat @ X2 @ ( minus_925952699566721837d_enat @ S2 @ T4 ) )
% 3.82/4.06 & ( P @ ( insert_Extended_enat @ X2 @ T4 ) ) ) ) )
% 3.82/4.06 => ( P @ S2 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_induct_select
% 3.82/4.06 thf(fact_4898_finite__induct__select,axiom,
% 3.82/4.06 ! [S2: set_real,P: set_real > $o] :
% 3.82/4.06 ( ( finite_finite_real @ S2 )
% 3.82/4.06 => ( ( P @ bot_bot_set_real )
% 3.82/4.06 => ( ! [T4: set_real] :
% 3.82/4.06 ( ( ord_less_set_real @ T4 @ S2 )
% 3.82/4.06 => ( ( P @ T4 )
% 3.82/4.06 => ? [X2: real] :
% 3.82/4.06 ( ( member_real @ X2 @ ( minus_minus_set_real @ S2 @ T4 ) )
% 3.82/4.06 & ( P @ ( insert_real @ X2 @ T4 ) ) ) ) )
% 3.82/4.06 => ( P @ S2 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_induct_select
% 3.82/4.06 thf(fact_4899_finite__induct__select,axiom,
% 3.82/4.06 ! [S2: set_int,P: set_int > $o] :
% 3.82/4.06 ( ( finite_finite_int @ S2 )
% 3.82/4.06 => ( ( P @ bot_bot_set_int )
% 3.82/4.06 => ( ! [T4: set_int] :
% 3.82/4.06 ( ( ord_less_set_int @ T4 @ S2 )
% 3.82/4.06 => ( ( P @ T4 )
% 3.82/4.06 => ? [X2: int] :
% 3.82/4.06 ( ( member_int @ X2 @ ( minus_minus_set_int @ S2 @ T4 ) )
% 3.82/4.06 & ( P @ ( insert_int @ X2 @ T4 ) ) ) ) )
% 3.82/4.06 => ( P @ S2 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_induct_select
% 3.82/4.06 thf(fact_4900_finite__induct__select,axiom,
% 3.82/4.06 ! [S2: set_nat,P: set_nat > $o] :
% 3.82/4.06 ( ( finite_finite_nat @ S2 )
% 3.82/4.06 => ( ( P @ bot_bot_set_nat )
% 3.82/4.06 => ( ! [T4: set_nat] :
% 3.82/4.06 ( ( ord_less_set_nat @ T4 @ S2 )
% 3.82/4.06 => ( ( P @ T4 )
% 3.82/4.06 => ? [X2: nat] :
% 3.82/4.06 ( ( member_nat @ X2 @ ( minus_minus_set_nat @ S2 @ T4 ) )
% 3.82/4.06 & ( P @ ( insert_nat @ X2 @ T4 ) ) ) ) )
% 3.82/4.06 => ( P @ S2 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % finite_induct_select
% 3.82/4.06 thf(fact_4901_psubset__insert__iff,axiom,
% 3.82/4.06 ! [A2: set_set_nat,X: set_nat,B: set_set_nat] :
% 3.82/4.06 ( ( ord_less_set_set_nat @ A2 @ ( insert_set_nat @ X @ B ) )
% 3.82/4.06 = ( ( ( member_set_nat @ X @ B )
% 3.82/4.06 => ( ord_less_set_set_nat @ A2 @ B ) )
% 3.82/4.06 & ( ~ ( member_set_nat @ X @ B )
% 3.82/4.06 => ( ( ( member_set_nat @ X @ A2 )
% 3.82/4.06 => ( ord_less_set_set_nat @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) @ B ) )
% 3.82/4.06 & ( ~ ( member_set_nat @ X @ A2 )
% 3.82/4.06 => ( ord_le6893508408891458716et_nat @ A2 @ B ) ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % psubset_insert_iff
% 3.82/4.06 thf(fact_4902_psubset__insert__iff,axiom,
% 3.82/4.06 ! [A2: set_Extended_enat,X: extended_enat,B: set_Extended_enat] :
% 3.82/4.06 ( ( ord_le2529575680413868914d_enat @ A2 @ ( insert_Extended_enat @ X @ B ) )
% 3.82/4.06 = ( ( ( member_Extended_enat @ X @ B )
% 3.82/4.06 => ( ord_le2529575680413868914d_enat @ A2 @ B ) )
% 3.82/4.06 & ( ~ ( member_Extended_enat @ X @ B )
% 3.82/4.06 => ( ( ( member_Extended_enat @ X @ A2 )
% 3.82/4.06 => ( ord_le2529575680413868914d_enat @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ X @ bot_bo7653980558646680370d_enat ) ) @ B ) )
% 3.82/4.06 & ( ~ ( member_Extended_enat @ X @ A2 )
% 3.82/4.06 => ( ord_le7203529160286727270d_enat @ A2 @ B ) ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % psubset_insert_iff
% 3.82/4.06 thf(fact_4903_psubset__insert__iff,axiom,
% 3.82/4.06 ! [A2: set_real,X: real,B: set_real] :
% 3.82/4.06 ( ( ord_less_set_real @ A2 @ ( insert_real @ X @ B ) )
% 3.82/4.06 = ( ( ( member_real @ X @ B )
% 3.82/4.06 => ( ord_less_set_real @ A2 @ B ) )
% 3.82/4.06 & ( ~ ( member_real @ X @ B )
% 3.82/4.06 => ( ( ( member_real @ X @ A2 )
% 3.82/4.06 => ( ord_less_set_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) @ B ) )
% 3.82/4.06 & ( ~ ( member_real @ X @ A2 )
% 3.82/4.06 => ( ord_less_eq_set_real @ A2 @ B ) ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % psubset_insert_iff
% 3.82/4.06 thf(fact_4904_psubset__insert__iff,axiom,
% 3.82/4.06 ! [A2: set_nat,X: nat,B: set_nat] :
% 3.82/4.06 ( ( ord_less_set_nat @ A2 @ ( insert_nat @ X @ B ) )
% 3.82/4.06 = ( ( ( member_nat @ X @ B )
% 3.82/4.06 => ( ord_less_set_nat @ A2 @ B ) )
% 3.82/4.06 & ( ~ ( member_nat @ X @ B )
% 3.82/4.06 => ( ( ( member_nat @ X @ A2 )
% 3.82/4.06 => ( ord_less_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ B ) )
% 3.82/4.06 & ( ~ ( member_nat @ X @ A2 )
% 3.82/4.06 => ( ord_less_eq_set_nat @ A2 @ B ) ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % psubset_insert_iff
% 3.82/4.06 thf(fact_4905_psubset__insert__iff,axiom,
% 3.82/4.06 ! [A2: set_int,X: int,B: set_int] :
% 3.82/4.06 ( ( ord_less_set_int @ A2 @ ( insert_int @ X @ B ) )
% 3.82/4.06 = ( ( ( member_int @ X @ B )
% 3.82/4.06 => ( ord_less_set_int @ A2 @ B ) )
% 3.82/4.06 & ( ~ ( member_int @ X @ B )
% 3.82/4.06 => ( ( ( member_int @ X @ A2 )
% 3.82/4.06 => ( ord_less_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) @ B ) )
% 3.82/4.06 & ( ~ ( member_int @ X @ A2 )
% 3.82/4.06 => ( ord_less_eq_set_int @ A2 @ B ) ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % psubset_insert_iff
% 3.82/4.06 thf(fact_4906_atLeastAtMost__insertL,axiom,
% 3.82/4.06 ! [M2: nat,N2: nat] :
% 3.82/4.06 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.06 => ( ( insert_nat @ M2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N2 ) )
% 3.82/4.06 = ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % atLeastAtMost_insertL
% 3.82/4.06 thf(fact_4907_atLeastAtMostSuc__conv,axiom,
% 3.82/4.06 ! [M2: nat,N2: nat] :
% 3.82/4.06 ( ( ord_less_eq_nat @ M2 @ ( suc @ N2 ) )
% 3.82/4.06 => ( ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) )
% 3.82/4.06 = ( insert_nat @ ( suc @ N2 ) @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % atLeastAtMostSuc_conv
% 3.82/4.06 thf(fact_4908_Icc__eq__insert__lb__nat,axiom,
% 3.82/4.06 ! [M2: nat,N2: nat] :
% 3.82/4.06 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.06 => ( ( set_or1269000886237332187st_nat @ M2 @ N2 )
% 3.82/4.06 = ( insert_nat @ M2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N2 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % Icc_eq_insert_lb_nat
% 3.82/4.06 thf(fact_4909_set__update__subset__insert,axiom,
% 3.82/4.06 ! [Xs: list_real,I: nat,X: real] : ( ord_less_eq_set_real @ ( set_real2 @ ( list_update_real @ Xs @ I @ X ) ) @ ( insert_real @ X @ ( set_real2 @ Xs ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % set_update_subset_insert
% 3.82/4.06 thf(fact_4910_set__update__subset__insert,axiom,
% 3.82/4.06 ! [Xs: list_VEBT_VEBT,I: nat,X: vEBT_VEBT] : ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) ) @ ( insert_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % set_update_subset_insert
% 3.82/4.06 thf(fact_4911_set__update__subset__insert,axiom,
% 3.82/4.06 ! [Xs: list_nat,I: nat,X: nat] : ( ord_less_eq_set_nat @ ( set_nat2 @ ( list_update_nat @ Xs @ I @ X ) ) @ ( insert_nat @ X @ ( set_nat2 @ Xs ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % set_update_subset_insert
% 3.82/4.06 thf(fact_4912_set__update__subset__insert,axiom,
% 3.82/4.06 ! [Xs: list_int,I: nat,X: int] : ( ord_less_eq_set_int @ ( set_int2 @ ( list_update_int @ Xs @ I @ X ) ) @ ( insert_int @ X @ ( set_int2 @ Xs ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % set_update_subset_insert
% 3.82/4.06 thf(fact_4913_set__replicate__Suc,axiom,
% 3.82/4.06 ! [N2: nat,X: vEBT_VEBT] :
% 3.82/4.06 ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ ( suc @ N2 ) @ X ) )
% 3.82/4.06 = ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ).
% 3.82/4.06
% 3.82/4.06 % set_replicate_Suc
% 3.82/4.06 thf(fact_4914_set__replicate__Suc,axiom,
% 3.82/4.06 ! [N2: nat,X: extended_enat] :
% 3.82/4.06 ( ( set_Extended_enat2 @ ( replic7216382294607269926d_enat @ ( suc @ N2 ) @ X ) )
% 3.82/4.06 = ( insert_Extended_enat @ X @ bot_bo7653980558646680370d_enat ) ) ).
% 3.82/4.06
% 3.82/4.06 % set_replicate_Suc
% 3.82/4.06 thf(fact_4915_set__replicate__Suc,axiom,
% 3.82/4.06 ! [N2: nat,X: real] :
% 3.82/4.06 ( ( set_real2 @ ( replicate_real @ ( suc @ N2 ) @ X ) )
% 3.82/4.06 = ( insert_real @ X @ bot_bot_set_real ) ) ).
% 3.82/4.06
% 3.82/4.06 % set_replicate_Suc
% 3.82/4.06 thf(fact_4916_set__replicate__Suc,axiom,
% 3.82/4.06 ! [N2: nat,X: nat] :
% 3.82/4.06 ( ( set_nat2 @ ( replicate_nat @ ( suc @ N2 ) @ X ) )
% 3.82/4.06 = ( insert_nat @ X @ bot_bot_set_nat ) ) ).
% 3.82/4.06
% 3.82/4.06 % set_replicate_Suc
% 3.82/4.06 thf(fact_4917_set__replicate__Suc,axiom,
% 3.82/4.06 ! [N2: nat,X: int] :
% 3.82/4.06 ( ( set_int2 @ ( replicate_int @ ( suc @ N2 ) @ X ) )
% 3.82/4.06 = ( insert_int @ X @ bot_bot_set_int ) ) ).
% 3.82/4.06
% 3.82/4.06 % set_replicate_Suc
% 3.82/4.06 thf(fact_4918_set__replicate__conv__if,axiom,
% 3.82/4.06 ! [N2: nat,X: vEBT_VEBT] :
% 3.82/4.06 ( ( ( N2 = zero_zero_nat )
% 3.82/4.06 => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N2 @ X ) )
% 3.82/4.06 = bot_bo8194388402131092736T_VEBT ) )
% 3.82/4.06 & ( ( N2 != zero_zero_nat )
% 3.82/4.06 => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N2 @ X ) )
% 3.82/4.06 = ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % set_replicate_conv_if
% 3.82/4.06 thf(fact_4919_set__replicate__conv__if,axiom,
% 3.82/4.06 ! [N2: nat,X: extended_enat] :
% 3.82/4.06 ( ( ( N2 = zero_zero_nat )
% 3.82/4.06 => ( ( set_Extended_enat2 @ ( replic7216382294607269926d_enat @ N2 @ X ) )
% 3.82/4.06 = bot_bo7653980558646680370d_enat ) )
% 3.82/4.06 & ( ( N2 != zero_zero_nat )
% 3.82/4.06 => ( ( set_Extended_enat2 @ ( replic7216382294607269926d_enat @ N2 @ X ) )
% 3.82/4.06 = ( insert_Extended_enat @ X @ bot_bo7653980558646680370d_enat ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % set_replicate_conv_if
% 3.82/4.06 thf(fact_4920_set__replicate__conv__if,axiom,
% 3.82/4.06 ! [N2: nat,X: real] :
% 3.82/4.06 ( ( ( N2 = zero_zero_nat )
% 3.82/4.06 => ( ( set_real2 @ ( replicate_real @ N2 @ X ) )
% 3.82/4.06 = bot_bot_set_real ) )
% 3.82/4.06 & ( ( N2 != zero_zero_nat )
% 3.82/4.06 => ( ( set_real2 @ ( replicate_real @ N2 @ X ) )
% 3.82/4.06 = ( insert_real @ X @ bot_bot_set_real ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % set_replicate_conv_if
% 3.82/4.06 thf(fact_4921_set__replicate__conv__if,axiom,
% 3.82/4.06 ! [N2: nat,X: nat] :
% 3.82/4.06 ( ( ( N2 = zero_zero_nat )
% 3.82/4.06 => ( ( set_nat2 @ ( replicate_nat @ N2 @ X ) )
% 3.82/4.06 = bot_bot_set_nat ) )
% 3.82/4.06 & ( ( N2 != zero_zero_nat )
% 3.82/4.06 => ( ( set_nat2 @ ( replicate_nat @ N2 @ X ) )
% 3.82/4.06 = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % set_replicate_conv_if
% 3.82/4.06 thf(fact_4922_set__replicate__conv__if,axiom,
% 3.82/4.06 ! [N2: nat,X: int] :
% 3.82/4.06 ( ( ( N2 = zero_zero_nat )
% 3.82/4.06 => ( ( set_int2 @ ( replicate_int @ N2 @ X ) )
% 3.82/4.06 = bot_bot_set_int ) )
% 3.82/4.06 & ( ( N2 != zero_zero_nat )
% 3.82/4.06 => ( ( set_int2 @ ( replicate_int @ N2 @ X ) )
% 3.82/4.06 = ( insert_int @ X @ bot_bot_set_int ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % set_replicate_conv_if
% 3.82/4.06 thf(fact_4923_set__decode__plus__power__2,axiom,
% 3.82/4.06 ! [N2: nat,Z3: nat] :
% 3.82/4.06 ( ~ ( member_nat @ N2 @ ( nat_set_decode @ Z3 ) )
% 3.82/4.06 => ( ( nat_set_decode @ ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ Z3 ) )
% 3.82/4.06 = ( insert_nat @ N2 @ ( nat_set_decode @ Z3 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % set_decode_plus_power_2
% 3.82/4.06 thf(fact_4924_divmod__step__nat__def,axiom,
% 3.82/4.06 ( unique5026877609467782581ep_nat
% 3.82/4.06 = ( ^ [L2: num] :
% 3.82/4.06 ( produc2626176000494625587at_nat
% 3.82/4.06 @ ^ [Q5: nat,R4: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R4 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ one_one_nat ) @ ( minus_minus_nat @ R4 @ ( numeral_numeral_nat @ L2 ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ R4 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % divmod_step_nat_def
% 3.82/4.06 thf(fact_4925_take__bit__Suc__minus__bit1,axiom,
% 3.82/4.06 ! [N2: nat,K: num] :
% 3.82/4.06 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 3.82/4.06 = ( 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 ) ) ).
% 3.82/4.06
% 3.82/4.06 % take_bit_Suc_minus_bit1
% 3.82/4.06 thf(fact_4926_divmod__nat__if,axiom,
% 3.82/4.06 ( divmod_nat
% 3.82/4.06 = ( ^ [M: nat,N: nat] :
% 3.82/4.06 ( if_Pro6206227464963214023at_nat
% 3.82/4.06 @ ( ( N = zero_zero_nat )
% 3.82/4.06 | ( ord_less_nat @ M @ N ) )
% 3.82/4.06 @ ( product_Pair_nat_nat @ zero_zero_nat @ M )
% 3.82/4.06 @ ( produc2626176000494625587at_nat
% 3.82/4.06 @ ^ [Q5: nat] : ( product_Pair_nat_nat @ ( suc @ Q5 ) )
% 3.82/4.06 @ ( divmod_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % divmod_nat_if
% 3.82/4.06 thf(fact_4927_mask__numeral,axiom,
% 3.82/4.06 ! [N2: num] :
% 3.82/4.06 ( ( bit_se2000444600071755411sk_int @ ( numeral_numeral_nat @ N2 ) )
% 3.82/4.06 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ ( pred_numeral @ N2 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % mask_numeral
% 3.82/4.06 thf(fact_4928_mask__numeral,axiom,
% 3.82/4.06 ! [N2: num] :
% 3.82/4.06 ( ( bit_se2002935070580805687sk_nat @ ( numeral_numeral_nat @ N2 ) )
% 3.82/4.06 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ ( pred_numeral @ N2 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % mask_numeral
% 3.82/4.06 thf(fact_4929_of__int__code__if,axiom,
% 3.82/4.06 ( ring_17405671764205052669omplex
% 3.82/4.06 = ( ^ [K2: int] :
% 3.82/4.06 ( if_complex @ ( K2 = zero_zero_int ) @ zero_zero_complex
% 3.82/4.06 @ ( if_complex @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus1482373934393186551omplex @ ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ K2 ) ) )
% 3.82/4.06 @ ( if_complex
% 3.82/4.06 @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 3.82/4.06 = zero_zero_int )
% 3.82/4.06 @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 3.82/4.06 @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_complex ) ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_code_if
% 3.82/4.06 thf(fact_4930_of__int__code__if,axiom,
% 3.82/4.06 ( ring_1_of_int_int
% 3.82/4.06 = ( ^ [K2: int] :
% 3.82/4.06 ( if_int @ ( K2 = zero_zero_int ) @ zero_zero_int
% 3.82/4.06 @ ( if_int @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus_uminus_int @ ( ring_1_of_int_int @ ( uminus_uminus_int @ K2 ) ) )
% 3.82/4.06 @ ( if_int
% 3.82/4.06 @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 3.82/4.06 = zero_zero_int )
% 3.82/4.06 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 3.82/4.06 @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_int ) ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_code_if
% 3.82/4.06 thf(fact_4931_of__int__code__if,axiom,
% 3.82/4.06 ( ring_1_of_int_real
% 3.82/4.06 = ( ^ [K2: int] :
% 3.82/4.06 ( if_real @ ( K2 = zero_zero_int ) @ zero_zero_real
% 3.82/4.06 @ ( if_real @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus_uminus_real @ ( ring_1_of_int_real @ ( uminus_uminus_int @ K2 ) ) )
% 3.82/4.06 @ ( if_real
% 3.82/4.06 @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 3.82/4.06 = zero_zero_int )
% 3.82/4.06 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 3.82/4.06 @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_code_if
% 3.82/4.06 thf(fact_4932_concat__bit__Suc,axiom,
% 3.82/4.06 ! [N2: nat,K: int,L: int] :
% 3.82/4.06 ( ( bit_concat_bit @ ( suc @ N2 ) @ K @ L )
% 3.82/4.06 = ( 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 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % concat_bit_Suc
% 3.82/4.06 thf(fact_4933_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 3.82/4.06 ! [A: int,X: num,N2: nat] :
% 3.82/4.06 ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) )
% 3.82/4.06 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_less_neg_numeral_power_cancel_iff
% 3.82/4.06 thf(fact_4934_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 3.82/4.06 ! [A: int,X: num,N2: nat] :
% 3.82/4.06 ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N2 ) )
% 3.82/4.06 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_less_neg_numeral_power_cancel_iff
% 3.82/4.06 thf(fact_4935_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 3.82/4.06 ! [X: num,N2: nat,A: int] :
% 3.82/4.06 ( ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) @ ( ring_1_of_int_int @ A ) )
% 3.82/4.06 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) @ A ) ) ).
% 3.82/4.06
% 3.82/4.06 % neg_numeral_power_less_of_int_cancel_iff
% 3.82/4.06 thf(fact_4936_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 3.82/4.06 ! [X: num,N2: nat,A: int] :
% 3.82/4.06 ( ( ord_less_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N2 ) @ ( ring_1_of_int_real @ A ) )
% 3.82/4.06 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) @ A ) ) ).
% 3.82/4.06
% 3.82/4.06 % neg_numeral_power_less_of_int_cancel_iff
% 3.82/4.06 thf(fact_4937_of__int__eq__iff,axiom,
% 3.82/4.06 ! [W2: int,Z3: int] :
% 3.82/4.06 ( ( ( ring_1_of_int_real @ W2 )
% 3.82/4.06 = ( ring_1_of_int_real @ Z3 ) )
% 3.82/4.06 = ( W2 = Z3 ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_eq_iff
% 3.82/4.06 thf(fact_4938_mask__nat__positive__iff,axiom,
% 3.82/4.06 ! [N2: nat] :
% 3.82/4.06 ( ( ord_less_nat @ zero_zero_nat @ ( bit_se2002935070580805687sk_nat @ N2 ) )
% 3.82/4.06 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 3.82/4.06
% 3.82/4.06 % mask_nat_positive_iff
% 3.82/4.06 thf(fact_4939_of__int__of__bool,axiom,
% 3.82/4.06 ! [P: $o] :
% 3.82/4.06 ( ( ring_1_of_int_real @ ( zero_n2684676970156552555ol_int @ P ) )
% 3.82/4.06 = ( zero_n3304061248610475627l_real @ P ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_of_bool
% 3.82/4.06 thf(fact_4940_of__int__of__bool,axiom,
% 3.82/4.06 ! [P: $o] :
% 3.82/4.06 ( ( ring_1_of_int_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 3.82/4.06 = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_of_bool
% 3.82/4.06 thf(fact_4941_concat__bit__0,axiom,
% 3.82/4.06 ! [K: int,L: int] :
% 3.82/4.06 ( ( bit_concat_bit @ zero_zero_nat @ K @ L )
% 3.82/4.06 = L ) ).
% 3.82/4.06
% 3.82/4.06 % concat_bit_0
% 3.82/4.06 thf(fact_4942_of__int__eq__0__iff,axiom,
% 3.82/4.06 ! [Z3: int] :
% 3.82/4.06 ( ( ( ring_1_of_int_int @ Z3 )
% 3.82/4.06 = zero_zero_int )
% 3.82/4.06 = ( Z3 = zero_zero_int ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_eq_0_iff
% 3.82/4.06 thf(fact_4943_of__int__eq__0__iff,axiom,
% 3.82/4.06 ! [Z3: int] :
% 3.82/4.06 ( ( ( ring_17405671764205052669omplex @ Z3 )
% 3.82/4.06 = zero_zero_complex )
% 3.82/4.06 = ( Z3 = zero_zero_int ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_eq_0_iff
% 3.82/4.06 thf(fact_4944_of__int__eq__0__iff,axiom,
% 3.82/4.06 ! [Z3: int] :
% 3.82/4.06 ( ( ( ring_1_of_int_real @ Z3 )
% 3.82/4.06 = zero_zero_real )
% 3.82/4.06 = ( Z3 = zero_zero_int ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_eq_0_iff
% 3.82/4.06 thf(fact_4945_of__int__0__eq__iff,axiom,
% 3.82/4.06 ! [Z3: int] :
% 3.82/4.06 ( ( zero_zero_int
% 3.82/4.06 = ( ring_1_of_int_int @ Z3 ) )
% 3.82/4.06 = ( Z3 = zero_zero_int ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_0_eq_iff
% 3.82/4.06 thf(fact_4946_of__int__0__eq__iff,axiom,
% 3.82/4.06 ! [Z3: int] :
% 3.82/4.06 ( ( zero_zero_complex
% 3.82/4.06 = ( ring_17405671764205052669omplex @ Z3 ) )
% 3.82/4.06 = ( Z3 = zero_zero_int ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_0_eq_iff
% 3.82/4.06 thf(fact_4947_of__int__0__eq__iff,axiom,
% 3.82/4.06 ! [Z3: int] :
% 3.82/4.06 ( ( zero_zero_real
% 3.82/4.06 = ( ring_1_of_int_real @ Z3 ) )
% 3.82/4.06 = ( Z3 = zero_zero_int ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_0_eq_iff
% 3.82/4.06 thf(fact_4948_of__int__0,axiom,
% 3.82/4.06 ( ( ring_1_of_int_int @ zero_zero_int )
% 3.82/4.06 = zero_zero_int ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_0
% 3.82/4.06 thf(fact_4949_of__int__0,axiom,
% 3.82/4.06 ( ( ring_17405671764205052669omplex @ zero_zero_int )
% 3.82/4.06 = zero_zero_complex ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_0
% 3.82/4.06 thf(fact_4950_of__int__0,axiom,
% 3.82/4.06 ( ( ring_1_of_int_real @ zero_zero_int )
% 3.82/4.06 = zero_zero_real ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_0
% 3.82/4.06 thf(fact_4951_of__int__le__iff,axiom,
% 3.82/4.06 ! [W2: int,Z3: int] :
% 3.82/4.06 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ W2 ) @ ( ring_1_of_int_real @ Z3 ) )
% 3.82/4.06 = ( ord_less_eq_int @ W2 @ Z3 ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_le_iff
% 3.82/4.06 thf(fact_4952_of__int__le__iff,axiom,
% 3.82/4.06 ! [W2: int,Z3: int] :
% 3.82/4.06 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ W2 ) @ ( ring_1_of_int_int @ Z3 ) )
% 3.82/4.06 = ( ord_less_eq_int @ W2 @ Z3 ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_le_iff
% 3.82/4.06 thf(fact_4953_of__int__numeral,axiom,
% 3.82/4.06 ! [K: num] :
% 3.82/4.06 ( ( ring_1_of_int_int @ ( numeral_numeral_int @ K ) )
% 3.82/4.06 = ( numeral_numeral_int @ K ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_numeral
% 3.82/4.06 thf(fact_4954_of__int__numeral,axiom,
% 3.82/4.06 ! [K: num] :
% 3.82/4.06 ( ( ring_1_of_int_real @ ( numeral_numeral_int @ K ) )
% 3.82/4.06 = ( numeral_numeral_real @ K ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_numeral
% 3.82/4.06 thf(fact_4955_of__int__eq__numeral__iff,axiom,
% 3.82/4.06 ! [Z3: int,N2: num] :
% 3.82/4.06 ( ( ( ring_1_of_int_int @ Z3 )
% 3.82/4.06 = ( numeral_numeral_int @ N2 ) )
% 3.82/4.06 = ( Z3
% 3.82/4.06 = ( numeral_numeral_int @ N2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_eq_numeral_iff
% 3.82/4.06 thf(fact_4956_of__int__eq__numeral__iff,axiom,
% 3.82/4.06 ! [Z3: int,N2: num] :
% 3.82/4.06 ( ( ( ring_1_of_int_real @ Z3 )
% 3.82/4.06 = ( numeral_numeral_real @ N2 ) )
% 3.82/4.06 = ( Z3
% 3.82/4.06 = ( numeral_numeral_int @ N2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_eq_numeral_iff
% 3.82/4.06 thf(fact_4957_of__int__less__iff,axiom,
% 3.82/4.06 ! [W2: int,Z3: int] :
% 3.82/4.06 ( ( ord_less_real @ ( ring_1_of_int_real @ W2 ) @ ( ring_1_of_int_real @ Z3 ) )
% 3.82/4.06 = ( ord_less_int @ W2 @ Z3 ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_less_iff
% 3.82/4.06 thf(fact_4958_of__int__less__iff,axiom,
% 3.82/4.06 ! [W2: int,Z3: int] :
% 3.82/4.06 ( ( ord_less_int @ ( ring_1_of_int_int @ W2 ) @ ( ring_1_of_int_int @ Z3 ) )
% 3.82/4.06 = ( ord_less_int @ W2 @ Z3 ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_less_iff
% 3.82/4.06 thf(fact_4959_of__int__1,axiom,
% 3.82/4.06 ( ( ring_1_of_int_int @ one_one_int )
% 3.82/4.06 = one_one_int ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_1
% 3.82/4.06 thf(fact_4960_of__int__1,axiom,
% 3.82/4.06 ( ( ring_17405671764205052669omplex @ one_one_int )
% 3.82/4.06 = one_one_complex ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_1
% 3.82/4.06 thf(fact_4961_of__int__1,axiom,
% 3.82/4.06 ( ( ring_1_of_int_real @ one_one_int )
% 3.82/4.06 = one_one_real ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_1
% 3.82/4.06 thf(fact_4962_of__int__eq__1__iff,axiom,
% 3.82/4.06 ! [Z3: int] :
% 3.82/4.06 ( ( ( ring_1_of_int_int @ Z3 )
% 3.82/4.06 = one_one_int )
% 3.82/4.06 = ( Z3 = one_one_int ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_eq_1_iff
% 3.82/4.06 thf(fact_4963_of__int__eq__1__iff,axiom,
% 3.82/4.06 ! [Z3: int] :
% 3.82/4.06 ( ( ( ring_17405671764205052669omplex @ Z3 )
% 3.82/4.06 = one_one_complex )
% 3.82/4.06 = ( Z3 = one_one_int ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_eq_1_iff
% 3.82/4.06 thf(fact_4964_of__int__eq__1__iff,axiom,
% 3.82/4.06 ! [Z3: int] :
% 3.82/4.06 ( ( ( ring_1_of_int_real @ Z3 )
% 3.82/4.06 = one_one_real )
% 3.82/4.06 = ( Z3 = one_one_int ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_eq_1_iff
% 3.82/4.06 thf(fact_4965_of__int__mult,axiom,
% 3.82/4.06 ! [W2: int,Z3: int] :
% 3.82/4.06 ( ( ring_1_of_int_int @ ( times_times_int @ W2 @ Z3 ) )
% 3.82/4.06 = ( times_times_int @ ( ring_1_of_int_int @ W2 ) @ ( ring_1_of_int_int @ Z3 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_mult
% 3.82/4.06 thf(fact_4966_of__int__mult,axiom,
% 3.82/4.06 ! [W2: int,Z3: int] :
% 3.82/4.06 ( ( ring_1_of_int_real @ ( times_times_int @ W2 @ Z3 ) )
% 3.82/4.06 = ( times_times_real @ ( ring_1_of_int_real @ W2 ) @ ( ring_1_of_int_real @ Z3 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_mult
% 3.82/4.06 thf(fact_4967_of__int__mult,axiom,
% 3.82/4.06 ! [W2: int,Z3: int] :
% 3.82/4.06 ( ( ring_17405671764205052669omplex @ ( times_times_int @ W2 @ Z3 ) )
% 3.82/4.06 = ( times_times_complex @ ( ring_17405671764205052669omplex @ W2 ) @ ( ring_17405671764205052669omplex @ Z3 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_mult
% 3.82/4.06 thf(fact_4968_of__int__add,axiom,
% 3.82/4.06 ! [W2: int,Z3: int] :
% 3.82/4.06 ( ( ring_1_of_int_int @ ( plus_plus_int @ W2 @ Z3 ) )
% 3.82/4.06 = ( plus_plus_int @ ( ring_1_of_int_int @ W2 ) @ ( ring_1_of_int_int @ Z3 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_add
% 3.82/4.06 thf(fact_4969_of__int__add,axiom,
% 3.82/4.06 ! [W2: int,Z3: int] :
% 3.82/4.06 ( ( ring_1_of_int_real @ ( plus_plus_int @ W2 @ Z3 ) )
% 3.82/4.06 = ( plus_plus_real @ ( ring_1_of_int_real @ W2 ) @ ( ring_1_of_int_real @ Z3 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_add
% 3.82/4.06 thf(fact_4970_of__int__minus,axiom,
% 3.82/4.06 ! [Z3: int] :
% 3.82/4.06 ( ( ring_1_of_int_int @ ( uminus_uminus_int @ Z3 ) )
% 3.82/4.06 = ( uminus_uminus_int @ ( ring_1_of_int_int @ Z3 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_minus
% 3.82/4.06 thf(fact_4971_of__int__minus,axiom,
% 3.82/4.06 ! [Z3: int] :
% 3.82/4.06 ( ( ring_1_of_int_real @ ( uminus_uminus_int @ Z3 ) )
% 3.82/4.06 = ( uminus_uminus_real @ ( ring_1_of_int_real @ Z3 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_minus
% 3.82/4.06 thf(fact_4972_mask__0,axiom,
% 3.82/4.06 ( ( bit_se2000444600071755411sk_int @ zero_zero_nat )
% 3.82/4.06 = zero_zero_int ) ).
% 3.82/4.06
% 3.82/4.06 % mask_0
% 3.82/4.06 thf(fact_4973_mask__0,axiom,
% 3.82/4.06 ( ( bit_se2002935070580805687sk_nat @ zero_zero_nat )
% 3.82/4.06 = zero_zero_nat ) ).
% 3.82/4.06
% 3.82/4.06 % mask_0
% 3.82/4.06 thf(fact_4974_mask__eq__0__iff,axiom,
% 3.82/4.06 ! [N2: nat] :
% 3.82/4.06 ( ( ( bit_se2000444600071755411sk_int @ N2 )
% 3.82/4.06 = zero_zero_int )
% 3.82/4.06 = ( N2 = zero_zero_nat ) ) ).
% 3.82/4.06
% 3.82/4.06 % mask_eq_0_iff
% 3.82/4.06 thf(fact_4975_mask__eq__0__iff,axiom,
% 3.82/4.06 ! [N2: nat] :
% 3.82/4.06 ( ( ( bit_se2002935070580805687sk_nat @ N2 )
% 3.82/4.06 = zero_zero_nat )
% 3.82/4.06 = ( N2 = zero_zero_nat ) ) ).
% 3.82/4.06
% 3.82/4.06 % mask_eq_0_iff
% 3.82/4.06 thf(fact_4976_of__int__diff,axiom,
% 3.82/4.06 ! [W2: int,Z3: int] :
% 3.82/4.06 ( ( ring_1_of_int_int @ ( minus_minus_int @ W2 @ Z3 ) )
% 3.82/4.06 = ( minus_minus_int @ ( ring_1_of_int_int @ W2 ) @ ( ring_1_of_int_int @ Z3 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_diff
% 3.82/4.06 thf(fact_4977_of__int__diff,axiom,
% 3.82/4.06 ! [W2: int,Z3: int] :
% 3.82/4.06 ( ( ring_1_of_int_real @ ( minus_minus_int @ W2 @ Z3 ) )
% 3.82/4.06 = ( minus_minus_real @ ( ring_1_of_int_real @ W2 ) @ ( ring_1_of_int_real @ Z3 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_diff
% 3.82/4.06 thf(fact_4978_of__int__power,axiom,
% 3.82/4.06 ! [Z3: int,N2: nat] :
% 3.82/4.06 ( ( ring_1_of_int_real @ ( power_power_int @ Z3 @ N2 ) )
% 3.82/4.06 = ( power_power_real @ ( ring_1_of_int_real @ Z3 ) @ N2 ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_power
% 3.82/4.06 thf(fact_4979_of__int__power,axiom,
% 3.82/4.06 ! [Z3: int,N2: nat] :
% 3.82/4.06 ( ( ring_17405671764205052669omplex @ ( power_power_int @ Z3 @ N2 ) )
% 3.82/4.06 = ( power_power_complex @ ( ring_17405671764205052669omplex @ Z3 ) @ N2 ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_power
% 3.82/4.06 thf(fact_4980_of__int__power,axiom,
% 3.82/4.06 ! [Z3: int,N2: nat] :
% 3.82/4.06 ( ( ring_1_of_int_int @ ( power_power_int @ Z3 @ N2 ) )
% 3.82/4.06 = ( power_power_int @ ( ring_1_of_int_int @ Z3 ) @ N2 ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_power
% 3.82/4.06 thf(fact_4981_of__int__eq__of__int__power__cancel__iff,axiom,
% 3.82/4.06 ! [B2: int,W2: nat,X: int] :
% 3.82/4.06 ( ( ( power_power_real @ ( ring_1_of_int_real @ B2 ) @ W2 )
% 3.82/4.06 = ( ring_1_of_int_real @ X ) )
% 3.82/4.06 = ( ( power_power_int @ B2 @ W2 )
% 3.82/4.06 = X ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_eq_of_int_power_cancel_iff
% 3.82/4.06 thf(fact_4982_of__int__eq__of__int__power__cancel__iff,axiom,
% 3.82/4.06 ! [B2: int,W2: nat,X: int] :
% 3.82/4.06 ( ( ( power_power_complex @ ( ring_17405671764205052669omplex @ B2 ) @ W2 )
% 3.82/4.06 = ( ring_17405671764205052669omplex @ X ) )
% 3.82/4.06 = ( ( power_power_int @ B2 @ W2 )
% 3.82/4.06 = X ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_eq_of_int_power_cancel_iff
% 3.82/4.06 thf(fact_4983_of__int__eq__of__int__power__cancel__iff,axiom,
% 3.82/4.06 ! [B2: int,W2: nat,X: int] :
% 3.82/4.06 ( ( ( power_power_int @ ( ring_1_of_int_int @ B2 ) @ W2 )
% 3.82/4.06 = ( ring_1_of_int_int @ X ) )
% 3.82/4.06 = ( ( power_power_int @ B2 @ W2 )
% 3.82/4.06 = X ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_eq_of_int_power_cancel_iff
% 3.82/4.06 thf(fact_4984_of__int__power__eq__of__int__cancel__iff,axiom,
% 3.82/4.06 ! [X: int,B2: int,W2: nat] :
% 3.82/4.06 ( ( ( ring_1_of_int_real @ X )
% 3.82/4.06 = ( power_power_real @ ( ring_1_of_int_real @ B2 ) @ W2 ) )
% 3.82/4.06 = ( X
% 3.82/4.06 = ( power_power_int @ B2 @ W2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_power_eq_of_int_cancel_iff
% 3.82/4.06 thf(fact_4985_of__int__power__eq__of__int__cancel__iff,axiom,
% 3.82/4.06 ! [X: int,B2: int,W2: nat] :
% 3.82/4.06 ( ( ( ring_17405671764205052669omplex @ X )
% 3.82/4.06 = ( power_power_complex @ ( ring_17405671764205052669omplex @ B2 ) @ W2 ) )
% 3.82/4.06 = ( X
% 3.82/4.06 = ( power_power_int @ B2 @ W2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_power_eq_of_int_cancel_iff
% 3.82/4.06 thf(fact_4986_of__int__power__eq__of__int__cancel__iff,axiom,
% 3.82/4.06 ! [X: int,B2: int,W2: nat] :
% 3.82/4.06 ( ( ( ring_1_of_int_int @ X )
% 3.82/4.06 = ( power_power_int @ ( ring_1_of_int_int @ B2 ) @ W2 ) )
% 3.82/4.06 = ( X
% 3.82/4.06 = ( power_power_int @ B2 @ W2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_power_eq_of_int_cancel_iff
% 3.82/4.06 thf(fact_4987_mask__Suc__0,axiom,
% 3.82/4.06 ( ( bit_se2000444600071755411sk_int @ ( suc @ zero_zero_nat ) )
% 3.82/4.06 = one_one_int ) ).
% 3.82/4.06
% 3.82/4.06 % mask_Suc_0
% 3.82/4.06 thf(fact_4988_mask__Suc__0,axiom,
% 3.82/4.06 ( ( bit_se2002935070580805687sk_nat @ ( suc @ zero_zero_nat ) )
% 3.82/4.06 = one_one_nat ) ).
% 3.82/4.06
% 3.82/4.06 % mask_Suc_0
% 3.82/4.06 thf(fact_4989_of__int__0__le__iff,axiom,
% 3.82/4.06 ! [Z3: int] :
% 3.82/4.06 ( ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z3 ) )
% 3.82/4.06 = ( ord_less_eq_int @ zero_zero_int @ Z3 ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_0_le_iff
% 3.82/4.06 thf(fact_4990_of__int__0__le__iff,axiom,
% 3.82/4.06 ! [Z3: int] :
% 3.82/4.06 ( ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z3 ) )
% 3.82/4.06 = ( ord_less_eq_int @ zero_zero_int @ Z3 ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_0_le_iff
% 3.82/4.06 thf(fact_4991_of__int__le__0__iff,axiom,
% 3.82/4.06 ! [Z3: int] :
% 3.82/4.06 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z3 ) @ zero_zero_real )
% 3.82/4.06 = ( ord_less_eq_int @ Z3 @ zero_zero_int ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_le_0_iff
% 3.82/4.06 thf(fact_4992_of__int__le__0__iff,axiom,
% 3.82/4.06 ! [Z3: int] :
% 3.82/4.06 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z3 ) @ zero_zero_int )
% 3.82/4.06 = ( ord_less_eq_int @ Z3 @ zero_zero_int ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_le_0_iff
% 3.82/4.06 thf(fact_4993_of__int__0__less__iff,axiom,
% 3.82/4.06 ! [Z3: int] :
% 3.82/4.06 ( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z3 ) )
% 3.82/4.06 = ( ord_less_int @ zero_zero_int @ Z3 ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_0_less_iff
% 3.82/4.06 thf(fact_4994_of__int__0__less__iff,axiom,
% 3.82/4.06 ! [Z3: int] :
% 3.82/4.06 ( ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z3 ) )
% 3.82/4.06 = ( ord_less_int @ zero_zero_int @ Z3 ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_0_less_iff
% 3.82/4.06 thf(fact_4995_of__int__less__0__iff,axiom,
% 3.82/4.06 ! [Z3: int] :
% 3.82/4.06 ( ( ord_less_real @ ( ring_1_of_int_real @ Z3 ) @ zero_zero_real )
% 3.82/4.06 = ( ord_less_int @ Z3 @ zero_zero_int ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_less_0_iff
% 3.82/4.06 thf(fact_4996_of__int__less__0__iff,axiom,
% 3.82/4.06 ! [Z3: int] :
% 3.82/4.06 ( ( ord_less_int @ ( ring_1_of_int_int @ Z3 ) @ zero_zero_int )
% 3.82/4.06 = ( ord_less_int @ Z3 @ zero_zero_int ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_less_0_iff
% 3.82/4.06 thf(fact_4997_of__int__numeral__le__iff,axiom,
% 3.82/4.06 ! [N2: num,Z3: int] :
% 3.82/4.06 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N2 ) @ ( ring_1_of_int_real @ Z3 ) )
% 3.82/4.06 = ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ Z3 ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_numeral_le_iff
% 3.82/4.06 thf(fact_4998_of__int__numeral__le__iff,axiom,
% 3.82/4.06 ! [N2: num,Z3: int] :
% 3.82/4.06 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ ( ring_1_of_int_int @ Z3 ) )
% 3.82/4.06 = ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ Z3 ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_numeral_le_iff
% 3.82/4.06 thf(fact_4999_of__int__le__numeral__iff,axiom,
% 3.82/4.06 ! [Z3: int,N2: num] :
% 3.82/4.06 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z3 ) @ ( numeral_numeral_real @ N2 ) )
% 3.82/4.06 = ( ord_less_eq_int @ Z3 @ ( numeral_numeral_int @ N2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_le_numeral_iff
% 3.82/4.06 thf(fact_5000_of__int__le__numeral__iff,axiom,
% 3.82/4.06 ! [Z3: int,N2: num] :
% 3.82/4.06 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z3 ) @ ( numeral_numeral_int @ N2 ) )
% 3.82/4.06 = ( ord_less_eq_int @ Z3 @ ( numeral_numeral_int @ N2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_le_numeral_iff
% 3.82/4.06 thf(fact_5001_of__int__less__numeral__iff,axiom,
% 3.82/4.06 ! [Z3: int,N2: num] :
% 3.82/4.06 ( ( ord_less_int @ ( ring_1_of_int_int @ Z3 ) @ ( numeral_numeral_int @ N2 ) )
% 3.82/4.06 = ( ord_less_int @ Z3 @ ( numeral_numeral_int @ N2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_less_numeral_iff
% 3.82/4.06 thf(fact_5002_of__int__less__numeral__iff,axiom,
% 3.82/4.06 ! [Z3: int,N2: num] :
% 3.82/4.06 ( ( ord_less_real @ ( ring_1_of_int_real @ Z3 ) @ ( numeral_numeral_real @ N2 ) )
% 3.82/4.06 = ( ord_less_int @ Z3 @ ( numeral_numeral_int @ N2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_less_numeral_iff
% 3.82/4.06 thf(fact_5003_of__int__numeral__less__iff,axiom,
% 3.82/4.06 ! [N2: num,Z3: int] :
% 3.82/4.06 ( ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ ( ring_1_of_int_int @ Z3 ) )
% 3.82/4.06 = ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ Z3 ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_numeral_less_iff
% 3.82/4.06 thf(fact_5004_of__int__numeral__less__iff,axiom,
% 3.82/4.06 ! [N2: num,Z3: int] :
% 3.82/4.06 ( ( ord_less_real @ ( numeral_numeral_real @ N2 ) @ ( ring_1_of_int_real @ Z3 ) )
% 3.82/4.06 = ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ Z3 ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_numeral_less_iff
% 3.82/4.06 thf(fact_5005_of__int__1__le__iff,axiom,
% 3.82/4.06 ! [Z3: int] :
% 3.82/4.06 ( ( ord_less_eq_real @ one_one_real @ ( ring_1_of_int_real @ Z3 ) )
% 3.82/4.06 = ( ord_less_eq_int @ one_one_int @ Z3 ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_1_le_iff
% 3.82/4.06 thf(fact_5006_of__int__1__le__iff,axiom,
% 3.82/4.06 ! [Z3: int] :
% 3.82/4.06 ( ( ord_less_eq_int @ one_one_int @ ( ring_1_of_int_int @ Z3 ) )
% 3.82/4.06 = ( ord_less_eq_int @ one_one_int @ Z3 ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_1_le_iff
% 3.82/4.06 thf(fact_5007_of__int__le__1__iff,axiom,
% 3.82/4.06 ! [Z3: int] :
% 3.82/4.06 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z3 ) @ one_one_real )
% 3.82/4.06 = ( ord_less_eq_int @ Z3 @ one_one_int ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_le_1_iff
% 3.82/4.06 thf(fact_5008_of__int__le__1__iff,axiom,
% 3.82/4.06 ! [Z3: int] :
% 3.82/4.06 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z3 ) @ one_one_int )
% 3.82/4.06 = ( ord_less_eq_int @ Z3 @ one_one_int ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_le_1_iff
% 3.82/4.06 thf(fact_5009_of__int__less__1__iff,axiom,
% 3.82/4.06 ! [Z3: int] :
% 3.82/4.06 ( ( ord_less_real @ ( ring_1_of_int_real @ Z3 ) @ one_one_real )
% 3.82/4.06 = ( ord_less_int @ Z3 @ one_one_int ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_less_1_iff
% 3.82/4.06 thf(fact_5010_of__int__less__1__iff,axiom,
% 3.82/4.06 ! [Z3: int] :
% 3.82/4.06 ( ( ord_less_int @ ( ring_1_of_int_int @ Z3 ) @ one_one_int )
% 3.82/4.06 = ( ord_less_int @ Z3 @ one_one_int ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_less_1_iff
% 3.82/4.06 thf(fact_5011_of__int__1__less__iff,axiom,
% 3.82/4.06 ! [Z3: int] :
% 3.82/4.06 ( ( ord_less_real @ one_one_real @ ( ring_1_of_int_real @ Z3 ) )
% 3.82/4.06 = ( ord_less_int @ one_one_int @ Z3 ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_1_less_iff
% 3.82/4.06 thf(fact_5012_of__int__1__less__iff,axiom,
% 3.82/4.06 ! [Z3: int] :
% 3.82/4.06 ( ( ord_less_int @ one_one_int @ ( ring_1_of_int_int @ Z3 ) )
% 3.82/4.06 = ( ord_less_int @ one_one_int @ Z3 ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_1_less_iff
% 3.82/4.06 thf(fact_5013_of__int__power__le__of__int__cancel__iff,axiom,
% 3.82/4.06 ! [X: int,B2: int,W2: nat] :
% 3.82/4.06 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X ) @ ( power_power_real @ ( ring_1_of_int_real @ B2 ) @ W2 ) )
% 3.82/4.06 = ( ord_less_eq_int @ X @ ( power_power_int @ B2 @ W2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_power_le_of_int_cancel_iff
% 3.82/4.06 thf(fact_5014_of__int__power__le__of__int__cancel__iff,axiom,
% 3.82/4.06 ! [X: int,B2: int,W2: nat] :
% 3.82/4.06 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ X ) @ ( power_power_int @ ( ring_1_of_int_int @ B2 ) @ W2 ) )
% 3.82/4.06 = ( ord_less_eq_int @ X @ ( power_power_int @ B2 @ W2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_power_le_of_int_cancel_iff
% 3.82/4.06 thf(fact_5015_of__int__le__of__int__power__cancel__iff,axiom,
% 3.82/4.06 ! [B2: int,W2: nat,X: int] :
% 3.82/4.06 ( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ B2 ) @ W2 ) @ ( ring_1_of_int_real @ X ) )
% 3.82/4.06 = ( ord_less_eq_int @ ( power_power_int @ B2 @ W2 ) @ X ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_le_of_int_power_cancel_iff
% 3.82/4.06 thf(fact_5016_of__int__le__of__int__power__cancel__iff,axiom,
% 3.82/4.06 ! [B2: int,W2: nat,X: int] :
% 3.82/4.06 ( ( ord_less_eq_int @ ( power_power_int @ ( ring_1_of_int_int @ B2 ) @ W2 ) @ ( ring_1_of_int_int @ X ) )
% 3.82/4.06 = ( ord_less_eq_int @ ( power_power_int @ B2 @ W2 ) @ X ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_le_of_int_power_cancel_iff
% 3.82/4.06 thf(fact_5017_numeral__power__eq__of__int__cancel__iff,axiom,
% 3.82/4.06 ! [X: num,N2: nat,Y: int] :
% 3.82/4.06 ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N2 )
% 3.82/4.06 = ( ring_17405671764205052669omplex @ Y ) )
% 3.82/4.06 = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 )
% 3.82/4.06 = Y ) ) ).
% 3.82/4.06
% 3.82/4.06 % numeral_power_eq_of_int_cancel_iff
% 3.82/4.06 thf(fact_5018_numeral__power__eq__of__int__cancel__iff,axiom,
% 3.82/4.06 ! [X: num,N2: nat,Y: int] :
% 3.82/4.06 ( ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 )
% 3.82/4.06 = ( ring_1_of_int_int @ Y ) )
% 3.82/4.06 = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 )
% 3.82/4.06 = Y ) ) ).
% 3.82/4.06
% 3.82/4.06 % numeral_power_eq_of_int_cancel_iff
% 3.82/4.06 thf(fact_5019_numeral__power__eq__of__int__cancel__iff,axiom,
% 3.82/4.06 ! [X: num,N2: nat,Y: int] :
% 3.82/4.06 ( ( ( power_power_real @ ( numeral_numeral_real @ X ) @ N2 )
% 3.82/4.06 = ( ring_1_of_int_real @ Y ) )
% 3.82/4.06 = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 )
% 3.82/4.06 = Y ) ) ).
% 3.82/4.06
% 3.82/4.06 % numeral_power_eq_of_int_cancel_iff
% 3.82/4.06 thf(fact_5020_of__int__eq__numeral__power__cancel__iff,axiom,
% 3.82/4.06 ! [Y: int,X: num,N2: nat] :
% 3.82/4.06 ( ( ( ring_17405671764205052669omplex @ Y )
% 3.82/4.06 = ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N2 ) )
% 3.82/4.06 = ( Y
% 3.82/4.06 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_eq_numeral_power_cancel_iff
% 3.82/4.06 thf(fact_5021_of__int__eq__numeral__power__cancel__iff,axiom,
% 3.82/4.06 ! [Y: int,X: num,N2: nat] :
% 3.82/4.06 ( ( ( ring_1_of_int_int @ Y )
% 3.82/4.06 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) )
% 3.82/4.06 = ( Y
% 3.82/4.06 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_eq_numeral_power_cancel_iff
% 3.82/4.06 thf(fact_5022_of__int__eq__numeral__power__cancel__iff,axiom,
% 3.82/4.06 ! [Y: int,X: num,N2: nat] :
% 3.82/4.06 ( ( ( ring_1_of_int_real @ Y )
% 3.82/4.06 = ( power_power_real @ ( numeral_numeral_real @ X ) @ N2 ) )
% 3.82/4.06 = ( Y
% 3.82/4.06 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_eq_numeral_power_cancel_iff
% 3.82/4.06 thf(fact_5023_add__neg__numeral__special_I6_J,axiom,
% 3.82/4.06 ! [M2: num] :
% 3.82/4.06 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M2 ) ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 3.82/4.06 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ M2 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % add_neg_numeral_special(6)
% 3.82/4.06 thf(fact_5024_add__neg__numeral__special_I6_J,axiom,
% 3.82/4.06 ! [M2: num] :
% 3.82/4.06 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 3.82/4.06 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ M2 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % add_neg_numeral_special(6)
% 3.82/4.06 thf(fact_5025_add__neg__numeral__special_I6_J,axiom,
% 3.82/4.06 ! [M2: num] :
% 3.82/4.06 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 3.82/4.06 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ M2 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % add_neg_numeral_special(6)
% 3.82/4.06 thf(fact_5026_add__neg__numeral__special_I5_J,axiom,
% 3.82/4.06 ! [N2: num] :
% 3.82/4.06 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 3.82/4.06 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ N2 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % add_neg_numeral_special(5)
% 3.82/4.06 thf(fact_5027_add__neg__numeral__special_I5_J,axiom,
% 3.82/4.06 ! [N2: num] :
% 3.82/4.06 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 3.82/4.06 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N2 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % add_neg_numeral_special(5)
% 3.82/4.06 thf(fact_5028_add__neg__numeral__special_I5_J,axiom,
% 3.82/4.06 ! [N2: num] :
% 3.82/4.06 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 3.82/4.06 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ N2 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % add_neg_numeral_special(5)
% 3.82/4.06 thf(fact_5029_of__int__less__of__int__power__cancel__iff,axiom,
% 3.82/4.06 ! [B2: int,W2: nat,X: int] :
% 3.82/4.06 ( ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ B2 ) @ W2 ) @ ( ring_1_of_int_real @ X ) )
% 3.82/4.06 = ( ord_less_int @ ( power_power_int @ B2 @ W2 ) @ X ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_less_of_int_power_cancel_iff
% 3.82/4.06 thf(fact_5030_of__int__less__of__int__power__cancel__iff,axiom,
% 3.82/4.06 ! [B2: int,W2: nat,X: int] :
% 3.82/4.06 ( ( ord_less_int @ ( power_power_int @ ( ring_1_of_int_int @ B2 ) @ W2 ) @ ( ring_1_of_int_int @ X ) )
% 3.82/4.06 = ( ord_less_int @ ( power_power_int @ B2 @ W2 ) @ X ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_less_of_int_power_cancel_iff
% 3.82/4.06 thf(fact_5031_of__int__power__less__of__int__cancel__iff,axiom,
% 3.82/4.06 ! [X: int,B2: int,W2: nat] :
% 3.82/4.06 ( ( ord_less_real @ ( ring_1_of_int_real @ X ) @ ( power_power_real @ ( ring_1_of_int_real @ B2 ) @ W2 ) )
% 3.82/4.06 = ( ord_less_int @ X @ ( power_power_int @ B2 @ W2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_power_less_of_int_cancel_iff
% 3.82/4.06 thf(fact_5032_of__int__power__less__of__int__cancel__iff,axiom,
% 3.82/4.06 ! [X: int,B2: int,W2: nat] :
% 3.82/4.06 ( ( ord_less_int @ ( ring_1_of_int_int @ X ) @ ( power_power_int @ ( ring_1_of_int_int @ B2 ) @ W2 ) )
% 3.82/4.06 = ( ord_less_int @ X @ ( power_power_int @ B2 @ W2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_power_less_of_int_cancel_iff
% 3.82/4.06 thf(fact_5033_of__int__le__numeral__power__cancel__iff,axiom,
% 3.82/4.06 ! [A: int,X: num,N2: nat] :
% 3.82/4.06 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N2 ) )
% 3.82/4.06 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_le_numeral_power_cancel_iff
% 3.82/4.06 thf(fact_5034_of__int__le__numeral__power__cancel__iff,axiom,
% 3.82/4.06 ! [A: int,X: num,N2: nat] :
% 3.82/4.06 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) )
% 3.82/4.06 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_le_numeral_power_cancel_iff
% 3.82/4.06 thf(fact_5035_numeral__power__le__of__int__cancel__iff,axiom,
% 3.82/4.06 ! [X: num,N2: nat,A: int] :
% 3.82/4.06 ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N2 ) @ ( ring_1_of_int_real @ A ) )
% 3.82/4.06 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) @ A ) ) ).
% 3.82/4.06
% 3.82/4.06 % numeral_power_le_of_int_cancel_iff
% 3.82/4.06 thf(fact_5036_numeral__power__le__of__int__cancel__iff,axiom,
% 3.82/4.06 ! [X: num,N2: nat,A: int] :
% 3.82/4.06 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) @ ( ring_1_of_int_int @ A ) )
% 3.82/4.06 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) @ A ) ) ).
% 3.82/4.06
% 3.82/4.06 % numeral_power_le_of_int_cancel_iff
% 3.82/4.06 thf(fact_5037_numeral__power__less__of__int__cancel__iff,axiom,
% 3.82/4.06 ! [X: num,N2: nat,A: int] :
% 3.82/4.06 ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) @ ( ring_1_of_int_int @ A ) )
% 3.82/4.06 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) @ A ) ) ).
% 3.82/4.06
% 3.82/4.06 % numeral_power_less_of_int_cancel_iff
% 3.82/4.06 thf(fact_5038_numeral__power__less__of__int__cancel__iff,axiom,
% 3.82/4.06 ! [X: num,N2: nat,A: int] :
% 3.82/4.06 ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N2 ) @ ( ring_1_of_int_real @ A ) )
% 3.82/4.06 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) @ A ) ) ).
% 3.82/4.06
% 3.82/4.06 % numeral_power_less_of_int_cancel_iff
% 3.82/4.06 thf(fact_5039_of__int__less__numeral__power__cancel__iff,axiom,
% 3.82/4.06 ! [A: int,X: num,N2: nat] :
% 3.82/4.06 ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) )
% 3.82/4.06 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_less_numeral_power_cancel_iff
% 3.82/4.06 thf(fact_5040_of__int__less__numeral__power__cancel__iff,axiom,
% 3.82/4.06 ! [A: int,X: num,N2: nat] :
% 3.82/4.06 ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N2 ) )
% 3.82/4.06 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_less_numeral_power_cancel_iff
% 3.82/4.06 thf(fact_5041_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 3.82/4.06 ! [X: num,N2: nat,Y: int] :
% 3.82/4.06 ( ( ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X ) ) @ N2 )
% 3.82/4.06 = ( ring_17405671764205052669omplex @ Y ) )
% 3.82/4.06 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 )
% 3.82/4.06 = Y ) ) ).
% 3.82/4.06
% 3.82/4.06 % neg_numeral_power_eq_of_int_cancel_iff
% 3.82/4.06 thf(fact_5042_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 3.82/4.06 ! [X: num,N2: nat,Y: int] :
% 3.82/4.06 ( ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 )
% 3.82/4.06 = ( ring_1_of_int_int @ Y ) )
% 3.82/4.06 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 )
% 3.82/4.06 = Y ) ) ).
% 3.82/4.06
% 3.82/4.06 % neg_numeral_power_eq_of_int_cancel_iff
% 3.82/4.06 thf(fact_5043_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 3.82/4.06 ! [X: num,N2: nat,Y: int] :
% 3.82/4.06 ( ( ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N2 )
% 3.82/4.06 = ( ring_1_of_int_real @ Y ) )
% 3.82/4.06 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 )
% 3.82/4.06 = Y ) ) ).
% 3.82/4.06
% 3.82/4.06 % neg_numeral_power_eq_of_int_cancel_iff
% 3.82/4.06 thf(fact_5044_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 3.82/4.06 ! [Y: int,X: num,N2: nat] :
% 3.82/4.06 ( ( ( ring_17405671764205052669omplex @ Y )
% 3.82/4.06 = ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X ) ) @ N2 ) )
% 3.82/4.06 = ( Y
% 3.82/4.06 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_eq_neg_numeral_power_cancel_iff
% 3.82/4.06 thf(fact_5045_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 3.82/4.06 ! [Y: int,X: num,N2: nat] :
% 3.82/4.06 ( ( ( ring_1_of_int_int @ Y )
% 3.82/4.06 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) )
% 3.82/4.06 = ( Y
% 3.82/4.06 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_eq_neg_numeral_power_cancel_iff
% 3.82/4.06 thf(fact_5046_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 3.82/4.06 ! [Y: int,X: num,N2: nat] :
% 3.82/4.06 ( ( ( ring_1_of_int_real @ Y )
% 3.82/4.06 = ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N2 ) )
% 3.82/4.06 = ( Y
% 3.82/4.06 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_eq_neg_numeral_power_cancel_iff
% 3.82/4.06 thf(fact_5047_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 3.82/4.06 ! [A: int,X: num,N2: nat] :
% 3.82/4.06 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N2 ) )
% 3.82/4.06 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_le_neg_numeral_power_cancel_iff
% 3.82/4.06 thf(fact_5048_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 3.82/4.06 ! [A: int,X: num,N2: nat] :
% 3.82/4.06 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) )
% 3.82/4.06 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_le_neg_numeral_power_cancel_iff
% 3.82/4.06 thf(fact_5049_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 3.82/4.06 ! [X: num,N2: nat,A: int] :
% 3.82/4.06 ( ( ord_less_eq_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N2 ) @ ( ring_1_of_int_real @ A ) )
% 3.82/4.06 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) @ A ) ) ).
% 3.82/4.06
% 3.82/4.06 % neg_numeral_power_le_of_int_cancel_iff
% 3.82/4.06 thf(fact_5050_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 3.82/4.06 ! [X: num,N2: nat,A: int] :
% 3.82/4.06 ( ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) @ ( ring_1_of_int_int @ A ) )
% 3.82/4.06 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) @ A ) ) ).
% 3.82/4.06
% 3.82/4.06 % neg_numeral_power_le_of_int_cancel_iff
% 3.82/4.06 thf(fact_5051_ex__le__of__int,axiom,
% 3.82/4.06 ! [X: real] :
% 3.82/4.06 ? [Z: int] : ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ Z ) ) ).
% 3.82/4.06
% 3.82/4.06 % ex_le_of_int
% 3.82/4.06 thf(fact_5052_ex__of__int__less,axiom,
% 3.82/4.06 ! [X: real] :
% 3.82/4.06 ? [Z: int] : ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ X ) ).
% 3.82/4.06
% 3.82/4.06 % ex_of_int_less
% 3.82/4.06 thf(fact_5053_ex__less__of__int,axiom,
% 3.82/4.06 ! [X: real] :
% 3.82/4.06 ? [Z: int] : ( ord_less_real @ X @ ( ring_1_of_int_real @ Z ) ) ).
% 3.82/4.06
% 3.82/4.06 % ex_less_of_int
% 3.82/4.06 thf(fact_5054_mult__of__int__commute,axiom,
% 3.82/4.06 ! [X: int,Y: int] :
% 3.82/4.06 ( ( times_times_int @ ( ring_1_of_int_int @ X ) @ Y )
% 3.82/4.06 = ( times_times_int @ Y @ ( ring_1_of_int_int @ X ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % mult_of_int_commute
% 3.82/4.06 thf(fact_5055_mult__of__int__commute,axiom,
% 3.82/4.06 ! [X: int,Y: real] :
% 3.82/4.06 ( ( times_times_real @ ( ring_1_of_int_real @ X ) @ Y )
% 3.82/4.06 = ( times_times_real @ Y @ ( ring_1_of_int_real @ X ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % mult_of_int_commute
% 3.82/4.06 thf(fact_5056_mult__of__int__commute,axiom,
% 3.82/4.06 ! [X: int,Y: complex] :
% 3.82/4.06 ( ( times_times_complex @ ( ring_17405671764205052669omplex @ X ) @ Y )
% 3.82/4.06 = ( times_times_complex @ Y @ ( ring_17405671764205052669omplex @ X ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % mult_of_int_commute
% 3.82/4.06 thf(fact_5057_of__int__max,axiom,
% 3.82/4.06 ! [X: int,Y: int] :
% 3.82/4.06 ( ( ring_1_of_int_real @ ( ord_max_int @ X @ Y ) )
% 3.82/4.06 = ( ord_max_real @ ( ring_1_of_int_real @ X ) @ ( ring_1_of_int_real @ Y ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_max
% 3.82/4.06 thf(fact_5058_of__int__max,axiom,
% 3.82/4.06 ! [X: int,Y: int] :
% 3.82/4.06 ( ( ring_1_of_int_int @ ( ord_max_int @ X @ Y ) )
% 3.82/4.06 = ( ord_max_int @ ( ring_1_of_int_int @ X ) @ ( ring_1_of_int_int @ Y ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_max
% 3.82/4.06 thf(fact_5059_less__eq__mask,axiom,
% 3.82/4.06 ! [N2: nat] : ( ord_less_eq_nat @ N2 @ ( bit_se2002935070580805687sk_nat @ N2 ) ) ).
% 3.82/4.06
% 3.82/4.06 % less_eq_mask
% 3.82/4.06 thf(fact_5060_concat__bit__assoc,axiom,
% 3.82/4.06 ! [N2: nat,K: int,M2: nat,L: int,R2: int] :
% 3.82/4.06 ( ( bit_concat_bit @ N2 @ K @ ( bit_concat_bit @ M2 @ L @ R2 ) )
% 3.82/4.06 = ( bit_concat_bit @ ( plus_plus_nat @ M2 @ N2 ) @ ( bit_concat_bit @ N2 @ K @ L ) @ R2 ) ) ).
% 3.82/4.06
% 3.82/4.06 % concat_bit_assoc
% 3.82/4.06 thf(fact_5061_atLeastAtMostPlus1__int__conv,axiom,
% 3.82/4.06 ! [M2: int,N2: int] :
% 3.82/4.06 ( ( ord_less_eq_int @ M2 @ ( plus_plus_int @ one_one_int @ N2 ) )
% 3.82/4.06 => ( ( set_or1266510415728281911st_int @ M2 @ ( plus_plus_int @ one_one_int @ N2 ) )
% 3.82/4.06 = ( insert_int @ ( plus_plus_int @ one_one_int @ N2 ) @ ( set_or1266510415728281911st_int @ M2 @ N2 ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % atLeastAtMostPlus1_int_conv
% 3.82/4.06 thf(fact_5062_simp__from__to,axiom,
% 3.82/4.06 ( set_or1266510415728281911st_int
% 3.82/4.06 = ( ^ [I3: int,J2: int] : ( if_set_int @ ( ord_less_int @ J2 @ I3 ) @ bot_bot_set_int @ ( insert_int @ I3 @ ( set_or1266510415728281911st_int @ ( plus_plus_int @ I3 @ one_one_int ) @ J2 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % simp_from_to
% 3.82/4.06 thf(fact_5063_less__mask,axiom,
% 3.82/4.06 ! [N2: nat] :
% 3.82/4.06 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 3.82/4.06 => ( ord_less_nat @ N2 @ ( bit_se2002935070580805687sk_nat @ N2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % less_mask
% 3.82/4.06 thf(fact_5064_of__int__nonneg,axiom,
% 3.82/4.06 ! [Z3: int] :
% 3.82/4.06 ( ( ord_less_eq_int @ zero_zero_int @ Z3 )
% 3.82/4.06 => ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z3 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_nonneg
% 3.82/4.06 thf(fact_5065_of__int__nonneg,axiom,
% 3.82/4.06 ! [Z3: int] :
% 3.82/4.06 ( ( ord_less_eq_int @ zero_zero_int @ Z3 )
% 3.82/4.06 => ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z3 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_nonneg
% 3.82/4.06 thf(fact_5066_of__int__pos,axiom,
% 3.82/4.06 ! [Z3: int] :
% 3.82/4.06 ( ( ord_less_int @ zero_zero_int @ Z3 )
% 3.82/4.06 => ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z3 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_pos
% 3.82/4.06 thf(fact_5067_of__int__pos,axiom,
% 3.82/4.06 ! [Z3: int] :
% 3.82/4.06 ( ( ord_less_int @ zero_zero_int @ Z3 )
% 3.82/4.06 => ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z3 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_pos
% 3.82/4.06 thf(fact_5068_floor__exists1,axiom,
% 3.82/4.06 ! [X: real] :
% 3.82/4.06 ? [X5: int] :
% 3.82/4.06 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X5 ) @ X )
% 3.82/4.06 & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ X5 @ one_one_int ) ) )
% 3.82/4.06 & ! [Y6: int] :
% 3.82/4.06 ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y6 ) @ X )
% 3.82/4.06 & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ Y6 @ one_one_int ) ) ) )
% 3.82/4.06 => ( Y6 = X5 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % floor_exists1
% 3.82/4.06 thf(fact_5069_floor__exists,axiom,
% 3.82/4.06 ! [X: real] :
% 3.82/4.06 ? [Z: int] :
% 3.82/4.06 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ X )
% 3.82/4.06 & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ Z @ one_one_int ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % floor_exists
% 3.82/4.06 thf(fact_5070_numeral__inc,axiom,
% 3.82/4.06 ! [X: num] :
% 3.82/4.06 ( ( numera6690914467698888265omplex @ ( inc @ X ) )
% 3.82/4.06 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X ) @ one_one_complex ) ) ).
% 3.82/4.06
% 3.82/4.06 % numeral_inc
% 3.82/4.06 thf(fact_5071_numeral__inc,axiom,
% 3.82/4.06 ! [X: num] :
% 3.82/4.06 ( ( numeral_numeral_nat @ ( inc @ X ) )
% 3.82/4.06 = ( plus_plus_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat ) ) ).
% 3.82/4.06
% 3.82/4.06 % numeral_inc
% 3.82/4.06 thf(fact_5072_numeral__inc,axiom,
% 3.82/4.06 ! [X: num] :
% 3.82/4.06 ( ( numera1916890842035813515d_enat @ ( inc @ X ) )
% 3.82/4.06 = ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ X ) @ one_on7984719198319812577d_enat ) ) ).
% 3.82/4.06
% 3.82/4.06 % numeral_inc
% 3.82/4.06 thf(fact_5073_numeral__inc,axiom,
% 3.82/4.06 ! [X: num] :
% 3.82/4.06 ( ( numeral_numeral_int @ ( inc @ X ) )
% 3.82/4.06 = ( plus_plus_int @ ( numeral_numeral_int @ X ) @ one_one_int ) ) ).
% 3.82/4.06
% 3.82/4.06 % numeral_inc
% 3.82/4.06 thf(fact_5074_numeral__inc,axiom,
% 3.82/4.06 ! [X: num] :
% 3.82/4.06 ( ( numeral_numeral_real @ ( inc @ X ) )
% 3.82/4.06 = ( plus_plus_real @ ( numeral_numeral_real @ X ) @ one_one_real ) ) ).
% 3.82/4.06
% 3.82/4.06 % numeral_inc
% 3.82/4.06 thf(fact_5075_of__int__neg__numeral,axiom,
% 3.82/4.06 ! [K: num] :
% 3.82/4.06 ( ( ring_1_of_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 3.82/4.06 = ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_neg_numeral
% 3.82/4.06 thf(fact_5076_of__int__neg__numeral,axiom,
% 3.82/4.06 ! [K: num] :
% 3.82/4.06 ( ( ring_1_of_int_real @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 3.82/4.06 = ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_neg_numeral
% 3.82/4.06 thf(fact_5077_Suc__mask__eq__exp,axiom,
% 3.82/4.06 ! [N2: nat] :
% 3.82/4.06 ( ( suc @ ( bit_se2002935070580805687sk_nat @ N2 ) )
% 3.82/4.06 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 3.82/4.06
% 3.82/4.06 % Suc_mask_eq_exp
% 3.82/4.06 thf(fact_5078_mask__nat__less__exp,axiom,
% 3.82/4.06 ! [N2: nat] : ( ord_less_nat @ ( bit_se2002935070580805687sk_nat @ N2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 3.82/4.06
% 3.82/4.06 % mask_nat_less_exp
% 3.82/4.06 thf(fact_5079_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 3.82/4.06 ! [N2: nat] :
% 3.82/4.06 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ N2 ) )
% 3.82/4.06 = ( N2 = zero_zero_nat ) ) ).
% 3.82/4.06
% 3.82/4.06 % semiring_bit_operations_class.even_mask_iff
% 3.82/4.06 thf(fact_5080_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 3.82/4.06 ! [N2: nat] :
% 3.82/4.06 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ N2 ) )
% 3.82/4.06 = ( N2 = zero_zero_nat ) ) ).
% 3.82/4.06
% 3.82/4.06 % semiring_bit_operations_class.even_mask_iff
% 3.82/4.06 thf(fact_5081_round__unique,axiom,
% 3.82/4.06 ! [X: real,Y: int] :
% 3.82/4.06 ( ( ord_less_real @ ( minus_minus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ Y ) )
% 3.82/4.06 => ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y ) @ ( plus_plus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 3.82/4.06 => ( ( archim8280529875227126926d_real @ X )
% 3.82/4.06 = Y ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % round_unique
% 3.82/4.06 thf(fact_5082_of__int__round__gt,axiom,
% 3.82/4.06 ! [X: real] : ( ord_less_real @ ( minus_minus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_round_gt
% 3.82/4.06 thf(fact_5083_of__int__round__ge,axiom,
% 3.82/4.06 ! [X: real] : ( ord_less_eq_real @ ( minus_minus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_round_ge
% 3.82/4.06 thf(fact_5084_of__int__round__le,axiom,
% 3.82/4.06 ! [X: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X ) ) @ ( plus_plus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_round_le
% 3.82/4.06 thf(fact_5085_Sum__Icc__int,axiom,
% 3.82/4.06 ! [M2: int,N2: int] :
% 3.82/4.06 ( ( ord_less_eq_int @ M2 @ N2 )
% 3.82/4.06 => ( ( groups4538972089207619220nt_int
% 3.82/4.06 @ ^ [X4: int] : X4
% 3.82/4.06 @ ( set_or1266510415728281911st_int @ M2 @ N2 ) )
% 3.82/4.06 = ( divide_divide_int @ ( minus_minus_int @ ( times_times_int @ N2 @ ( plus_plus_int @ N2 @ one_one_int ) ) @ ( times_times_int @ M2 @ ( minus_minus_int @ M2 @ one_one_int ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % Sum_Icc_int
% 3.82/4.06 thf(fact_5086_and__int_Oelims,axiom,
% 3.82/4.06 ! [X: int,Xa2: int,Y: int] :
% 3.82/4.06 ( ( ( bit_se725231765392027082nd_int @ X @ Xa2 )
% 3.82/4.06 = Y )
% 3.82/4.06 => ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 3.82/4.06 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 3.82/4.06 => ( Y
% 3.82/4.06 = ( uminus_uminus_int
% 3.82/4.06 @ ( zero_n2684676970156552555ol_int
% 3.82/4.06 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 3.82/4.06 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) ) ) ) )
% 3.82/4.06 & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 3.82/4.06 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 3.82/4.06 => ( Y
% 3.82/4.06 = ( plus_plus_int
% 3.82/4.06 @ ( zero_n2684676970156552555ol_int
% 3.82/4.06 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 3.82/4.06 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) )
% 3.82/4.06 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % and_int.elims
% 3.82/4.06 thf(fact_5087_and__int_Osimps,axiom,
% 3.82/4.06 ( bit_se725231765392027082nd_int
% 3.82/4.06 = ( ^ [K2: int,L2: int] :
% 3.82/4.06 ( if_int
% 3.82/4.06 @ ( ( member_int @ K2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 3.82/4.06 & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 3.82/4.06 @ ( uminus_uminus_int
% 3.82/4.06 @ ( zero_n2684676970156552555ol_int
% 3.82/4.06 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 3.82/4.06 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) )
% 3.82/4.06 @ ( plus_plus_int
% 3.82/4.06 @ ( zero_n2684676970156552555ol_int
% 3.82/4.06 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 3.82/4.06 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 3.82/4.06 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % and_int.simps
% 3.82/4.06 thf(fact_5088_and__zero__eq,axiom,
% 3.82/4.06 ! [A: int] :
% 3.82/4.06 ( ( bit_se725231765392027082nd_int @ A @ zero_zero_int )
% 3.82/4.06 = zero_zero_int ) ).
% 3.82/4.06
% 3.82/4.06 % and_zero_eq
% 3.82/4.06 thf(fact_5089_and__zero__eq,axiom,
% 3.82/4.06 ! [A: nat] :
% 3.82/4.06 ( ( bit_se727722235901077358nd_nat @ A @ zero_zero_nat )
% 3.82/4.06 = zero_zero_nat ) ).
% 3.82/4.06
% 3.82/4.06 % and_zero_eq
% 3.82/4.06 thf(fact_5090_zero__and__eq,axiom,
% 3.82/4.06 ! [A: int] :
% 3.82/4.06 ( ( bit_se725231765392027082nd_int @ zero_zero_int @ A )
% 3.82/4.06 = zero_zero_int ) ).
% 3.82/4.06
% 3.82/4.06 % zero_and_eq
% 3.82/4.06 thf(fact_5091_zero__and__eq,axiom,
% 3.82/4.06 ! [A: nat] :
% 3.82/4.06 ( ( bit_se727722235901077358nd_nat @ zero_zero_nat @ A )
% 3.82/4.06 = zero_zero_nat ) ).
% 3.82/4.06
% 3.82/4.06 % zero_and_eq
% 3.82/4.06 thf(fact_5092_bit_Oconj__zero__left,axiom,
% 3.82/4.06 ! [X: int] :
% 3.82/4.06 ( ( bit_se725231765392027082nd_int @ zero_zero_int @ X )
% 3.82/4.06 = zero_zero_int ) ).
% 3.82/4.06
% 3.82/4.06 % bit.conj_zero_left
% 3.82/4.06 thf(fact_5093_bit_Oconj__zero__right,axiom,
% 3.82/4.06 ! [X: int] :
% 3.82/4.06 ( ( bit_se725231765392027082nd_int @ X @ zero_zero_int )
% 3.82/4.06 = zero_zero_int ) ).
% 3.82/4.06
% 3.82/4.06 % bit.conj_zero_right
% 3.82/4.06 thf(fact_5094_sum_Oneutral__const,axiom,
% 3.82/4.06 ! [A2: set_int] :
% 3.82/4.06 ( ( groups4538972089207619220nt_int
% 3.82/4.06 @ ^ [Uu3: int] : zero_zero_int
% 3.82/4.06 @ A2 )
% 3.82/4.06 = zero_zero_int ) ).
% 3.82/4.06
% 3.82/4.06 % sum.neutral_const
% 3.82/4.06 thf(fact_5095_sum_Oneutral__const,axiom,
% 3.82/4.06 ! [A2: set_nat] :
% 3.82/4.06 ( ( groups3542108847815614940at_nat
% 3.82/4.06 @ ^ [Uu3: nat] : zero_zero_nat
% 3.82/4.06 @ A2 )
% 3.82/4.06 = zero_zero_nat ) ).
% 3.82/4.06
% 3.82/4.06 % sum.neutral_const
% 3.82/4.06 thf(fact_5096_sum_Oneutral__const,axiom,
% 3.82/4.06 ! [A2: set_complex] :
% 3.82/4.06 ( ( groups7754918857620584856omplex
% 3.82/4.06 @ ^ [Uu3: complex] : zero_zero_complex
% 3.82/4.06 @ A2 )
% 3.82/4.06 = zero_zero_complex ) ).
% 3.82/4.06
% 3.82/4.06 % sum.neutral_const
% 3.82/4.06 thf(fact_5097_sum_Oneutral__const,axiom,
% 3.82/4.06 ! [A2: set_nat] :
% 3.82/4.06 ( ( groups6591440286371151544t_real
% 3.82/4.06 @ ^ [Uu3: nat] : zero_zero_real
% 3.82/4.06 @ A2 )
% 3.82/4.06 = zero_zero_real ) ).
% 3.82/4.06
% 3.82/4.06 % sum.neutral_const
% 3.82/4.06 thf(fact_5098_sum_Oempty,axiom,
% 3.82/4.06 ! [G: extended_enat > nat] :
% 3.82/4.06 ( ( groups2027974829824023292at_nat @ G @ bot_bo7653980558646680370d_enat )
% 3.82/4.06 = zero_zero_nat ) ).
% 3.82/4.06
% 3.82/4.06 % sum.empty
% 3.82/4.06 thf(fact_5099_sum_Oempty,axiom,
% 3.82/4.06 ! [G: extended_enat > real] :
% 3.82/4.06 ( ( groups4148127829035722712t_real @ G @ bot_bo7653980558646680370d_enat )
% 3.82/4.06 = zero_zero_real ) ).
% 3.82/4.06
% 3.82/4.06 % sum.empty
% 3.82/4.06 thf(fact_5100_sum_Oempty,axiom,
% 3.82/4.06 ! [G: extended_enat > int] :
% 3.82/4.06 ( ( groups2025484359314973016at_int @ G @ bot_bo7653980558646680370d_enat )
% 3.82/4.06 = zero_zero_int ) ).
% 3.82/4.06
% 3.82/4.06 % sum.empty
% 3.82/4.06 thf(fact_5101_sum_Oempty,axiom,
% 3.82/4.06 ! [G: extended_enat > complex] :
% 3.82/4.06 ( ( groups6818542070133387226omplex @ G @ bot_bo7653980558646680370d_enat )
% 3.82/4.06 = zero_zero_complex ) ).
% 3.82/4.06
% 3.82/4.06 % sum.empty
% 3.82/4.06 thf(fact_5102_sum_Oempty,axiom,
% 3.82/4.06 ! [G: extended_enat > extended_enat] :
% 3.82/4.06 ( ( groups2433450451889696826d_enat @ G @ bot_bo7653980558646680370d_enat )
% 3.82/4.06 = zero_z5237406670263579293d_enat ) ).
% 3.82/4.06
% 3.82/4.06 % sum.empty
% 3.82/4.06 thf(fact_5103_sum_Oempty,axiom,
% 3.82/4.06 ! [G: real > nat] :
% 3.82/4.06 ( ( groups1935376822645274424al_nat @ G @ bot_bot_set_real )
% 3.82/4.06 = zero_zero_nat ) ).
% 3.82/4.06
% 3.82/4.06 % sum.empty
% 3.82/4.06 thf(fact_5104_sum_Oempty,axiom,
% 3.82/4.06 ! [G: real > real] :
% 3.82/4.06 ( ( groups8097168146408367636l_real @ G @ bot_bot_set_real )
% 3.82/4.06 = zero_zero_real ) ).
% 3.82/4.06
% 3.82/4.06 % sum.empty
% 3.82/4.06 thf(fact_5105_sum_Oempty,axiom,
% 3.82/4.06 ! [G: real > int] :
% 3.82/4.06 ( ( groups1932886352136224148al_int @ G @ bot_bot_set_real )
% 3.82/4.06 = zero_zero_int ) ).
% 3.82/4.06
% 3.82/4.06 % sum.empty
% 3.82/4.06 thf(fact_5106_sum_Oempty,axiom,
% 3.82/4.06 ! [G: real > complex] :
% 3.82/4.06 ( ( groups5754745047067104278omplex @ G @ bot_bot_set_real )
% 3.82/4.06 = zero_zero_complex ) ).
% 3.82/4.06
% 3.82/4.06 % sum.empty
% 3.82/4.06 thf(fact_5107_sum_Oempty,axiom,
% 3.82/4.06 ! [G: real > extended_enat] :
% 3.82/4.06 ( ( groups2800946370649118462d_enat @ G @ bot_bot_set_real )
% 3.82/4.06 = zero_z5237406670263579293d_enat ) ).
% 3.82/4.06
% 3.82/4.06 % sum.empty
% 3.82/4.06 thf(fact_5108_sum_Oinfinite,axiom,
% 3.82/4.06 ! [A2: set_complex,G: complex > nat] :
% 3.82/4.06 ( ~ ( finite3207457112153483333omplex @ A2 )
% 3.82/4.06 => ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 3.82/4.06 = zero_zero_nat ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.infinite
% 3.82/4.06 thf(fact_5109_sum_Oinfinite,axiom,
% 3.82/4.06 ! [A2: set_int,G: int > nat] :
% 3.82/4.06 ( ~ ( finite_finite_int @ A2 )
% 3.82/4.06 => ( ( groups4541462559716669496nt_nat @ G @ A2 )
% 3.82/4.06 = zero_zero_nat ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.infinite
% 3.82/4.06 thf(fact_5110_sum_Oinfinite,axiom,
% 3.82/4.06 ! [A2: set_Extended_enat,G: extended_enat > nat] :
% 3.82/4.06 ( ~ ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.06 => ( ( groups2027974829824023292at_nat @ G @ A2 )
% 3.82/4.06 = zero_zero_nat ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.infinite
% 3.82/4.06 thf(fact_5111_sum_Oinfinite,axiom,
% 3.82/4.06 ! [A2: set_complex,G: complex > real] :
% 3.82/4.06 ( ~ ( finite3207457112153483333omplex @ A2 )
% 3.82/4.06 => ( ( groups5808333547571424918x_real @ G @ A2 )
% 3.82/4.06 = zero_zero_real ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.infinite
% 3.82/4.06 thf(fact_5112_sum_Oinfinite,axiom,
% 3.82/4.06 ! [A2: set_int,G: int > real] :
% 3.82/4.06 ( ~ ( finite_finite_int @ A2 )
% 3.82/4.06 => ( ( groups8778361861064173332t_real @ G @ A2 )
% 3.82/4.06 = zero_zero_real ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.infinite
% 3.82/4.06 thf(fact_5113_sum_Oinfinite,axiom,
% 3.82/4.06 ! [A2: set_Extended_enat,G: extended_enat > real] :
% 3.82/4.06 ( ~ ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.06 => ( ( groups4148127829035722712t_real @ G @ A2 )
% 3.82/4.06 = zero_zero_real ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.infinite
% 3.82/4.06 thf(fact_5114_sum_Oinfinite,axiom,
% 3.82/4.06 ! [A2: set_nat,G: nat > int] :
% 3.82/4.06 ( ~ ( finite_finite_nat @ A2 )
% 3.82/4.06 => ( ( groups3539618377306564664at_int @ G @ A2 )
% 3.82/4.06 = zero_zero_int ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.infinite
% 3.82/4.06 thf(fact_5115_sum_Oinfinite,axiom,
% 3.82/4.06 ! [A2: set_complex,G: complex > int] :
% 3.82/4.06 ( ~ ( finite3207457112153483333omplex @ A2 )
% 3.82/4.06 => ( ( groups5690904116761175830ex_int @ G @ A2 )
% 3.82/4.06 = zero_zero_int ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.infinite
% 3.82/4.06 thf(fact_5116_sum_Oinfinite,axiom,
% 3.82/4.06 ! [A2: set_Extended_enat,G: extended_enat > int] :
% 3.82/4.06 ( ~ ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.06 => ( ( groups2025484359314973016at_int @ G @ A2 )
% 3.82/4.06 = zero_zero_int ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.infinite
% 3.82/4.06 thf(fact_5117_sum_Oinfinite,axiom,
% 3.82/4.06 ! [A2: set_nat,G: nat > complex] :
% 3.82/4.06 ( ~ ( finite_finite_nat @ A2 )
% 3.82/4.06 => ( ( groups2073611262835488442omplex @ G @ A2 )
% 3.82/4.06 = zero_zero_complex ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.infinite
% 3.82/4.06 thf(fact_5118_sum__eq__0__iff,axiom,
% 3.82/4.06 ! [F3: set_complex,F: complex > nat] :
% 3.82/4.06 ( ( finite3207457112153483333omplex @ F3 )
% 3.82/4.06 => ( ( ( groups5693394587270226106ex_nat @ F @ F3 )
% 3.82/4.06 = zero_zero_nat )
% 3.82/4.06 = ( ! [X4: complex] :
% 3.82/4.06 ( ( member_complex @ X4 @ F3 )
% 3.82/4.06 => ( ( F @ X4 )
% 3.82/4.06 = zero_zero_nat ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum_eq_0_iff
% 3.82/4.06 thf(fact_5119_sum__eq__0__iff,axiom,
% 3.82/4.06 ! [F3: set_int,F: int > nat] :
% 3.82/4.06 ( ( finite_finite_int @ F3 )
% 3.82/4.06 => ( ( ( groups4541462559716669496nt_nat @ F @ F3 )
% 3.82/4.06 = zero_zero_nat )
% 3.82/4.06 = ( ! [X4: int] :
% 3.82/4.06 ( ( member_int @ X4 @ F3 )
% 3.82/4.06 => ( ( F @ X4 )
% 3.82/4.06 = zero_zero_nat ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum_eq_0_iff
% 3.82/4.06 thf(fact_5120_sum__eq__0__iff,axiom,
% 3.82/4.06 ! [F3: set_Extended_enat,F: extended_enat > nat] :
% 3.82/4.06 ( ( finite4001608067531595151d_enat @ F3 )
% 3.82/4.06 => ( ( ( groups2027974829824023292at_nat @ F @ F3 )
% 3.82/4.06 = zero_zero_nat )
% 3.82/4.06 = ( ! [X4: extended_enat] :
% 3.82/4.06 ( ( member_Extended_enat @ X4 @ F3 )
% 3.82/4.06 => ( ( F @ X4 )
% 3.82/4.06 = zero_zero_nat ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum_eq_0_iff
% 3.82/4.06 thf(fact_5121_sum__eq__0__iff,axiom,
% 3.82/4.06 ! [F3: set_nat,F: nat > extended_enat] :
% 3.82/4.06 ( ( finite_finite_nat @ F3 )
% 3.82/4.06 => ( ( ( groups7108830773950497114d_enat @ F @ F3 )
% 3.82/4.06 = zero_z5237406670263579293d_enat )
% 3.82/4.06 = ( ! [X4: nat] :
% 3.82/4.06 ( ( member_nat @ X4 @ F3 )
% 3.82/4.06 => ( ( F @ X4 )
% 3.82/4.06 = zero_z5237406670263579293d_enat ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum_eq_0_iff
% 3.82/4.06 thf(fact_5122_sum__eq__0__iff,axiom,
% 3.82/4.06 ! [F3: set_complex,F: complex > extended_enat] :
% 3.82/4.06 ( ( finite3207457112153483333omplex @ F3 )
% 3.82/4.06 => ( ( ( groups1752964319039525884d_enat @ F @ F3 )
% 3.82/4.06 = zero_z5237406670263579293d_enat )
% 3.82/4.06 = ( ! [X4: complex] :
% 3.82/4.06 ( ( member_complex @ X4 @ F3 )
% 3.82/4.06 => ( ( F @ X4 )
% 3.82/4.06 = zero_z5237406670263579293d_enat ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum_eq_0_iff
% 3.82/4.06 thf(fact_5123_sum__eq__0__iff,axiom,
% 3.82/4.06 ! [F3: set_int,F: int > extended_enat] :
% 3.82/4.06 ( ( finite_finite_int @ F3 )
% 3.82/4.06 => ( ( ( groups4225252721152677374d_enat @ F @ F3 )
% 3.82/4.06 = zero_z5237406670263579293d_enat )
% 3.82/4.06 = ( ! [X4: int] :
% 3.82/4.06 ( ( member_int @ X4 @ F3 )
% 3.82/4.06 => ( ( F @ X4 )
% 3.82/4.06 = zero_z5237406670263579293d_enat ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum_eq_0_iff
% 3.82/4.06 thf(fact_5124_sum__eq__0__iff,axiom,
% 3.82/4.06 ! [F3: set_Extended_enat,F: extended_enat > extended_enat] :
% 3.82/4.06 ( ( finite4001608067531595151d_enat @ F3 )
% 3.82/4.06 => ( ( ( groups2433450451889696826d_enat @ F @ F3 )
% 3.82/4.06 = zero_z5237406670263579293d_enat )
% 3.82/4.06 = ( ! [X4: extended_enat] :
% 3.82/4.06 ( ( member_Extended_enat @ X4 @ F3 )
% 3.82/4.06 => ( ( F @ X4 )
% 3.82/4.06 = zero_z5237406670263579293d_enat ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum_eq_0_iff
% 3.82/4.06 thf(fact_5125_sum__eq__0__iff,axiom,
% 3.82/4.06 ! [F3: set_nat,F: nat > nat] :
% 3.82/4.06 ( ( finite_finite_nat @ F3 )
% 3.82/4.06 => ( ( ( groups3542108847815614940at_nat @ F @ F3 )
% 3.82/4.06 = zero_zero_nat )
% 3.82/4.06 = ( ! [X4: nat] :
% 3.82/4.06 ( ( member_nat @ X4 @ F3 )
% 3.82/4.06 => ( ( F @ X4 )
% 3.82/4.06 = zero_zero_nat ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum_eq_0_iff
% 3.82/4.06 thf(fact_5126_round__0,axiom,
% 3.82/4.06 ( ( archim8280529875227126926d_real @ zero_zero_real )
% 3.82/4.06 = zero_zero_int ) ).
% 3.82/4.06
% 3.82/4.06 % round_0
% 3.82/4.06 thf(fact_5127_sum_Odelta,axiom,
% 3.82/4.06 ! [S2: set_real,A: real,B2: real > nat] :
% 3.82/4.06 ( ( finite_finite_real @ S2 )
% 3.82/4.06 => ( ( ( member_real @ A @ S2 )
% 3.82/4.06 => ( ( groups1935376822645274424al_nat
% 3.82/4.06 @ ^ [K2: real] : ( if_nat @ ( K2 = A ) @ ( B2 @ K2 ) @ zero_zero_nat )
% 3.82/4.06 @ S2 )
% 3.82/4.06 = ( B2 @ A ) ) )
% 3.82/4.06 & ( ~ ( member_real @ A @ S2 )
% 3.82/4.06 => ( ( groups1935376822645274424al_nat
% 3.82/4.06 @ ^ [K2: real] : ( if_nat @ ( K2 = A ) @ ( B2 @ K2 ) @ zero_zero_nat )
% 3.82/4.06 @ S2 )
% 3.82/4.06 = zero_zero_nat ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.delta
% 3.82/4.06 thf(fact_5128_sum_Odelta,axiom,
% 3.82/4.06 ! [S2: set_complex,A: complex,B2: complex > nat] :
% 3.82/4.06 ( ( finite3207457112153483333omplex @ S2 )
% 3.82/4.06 => ( ( ( member_complex @ A @ S2 )
% 3.82/4.06 => ( ( groups5693394587270226106ex_nat
% 3.82/4.06 @ ^ [K2: complex] : ( if_nat @ ( K2 = A ) @ ( B2 @ K2 ) @ zero_zero_nat )
% 3.82/4.06 @ S2 )
% 3.82/4.06 = ( B2 @ A ) ) )
% 3.82/4.06 & ( ~ ( member_complex @ A @ S2 )
% 3.82/4.06 => ( ( groups5693394587270226106ex_nat
% 3.82/4.06 @ ^ [K2: complex] : ( if_nat @ ( K2 = A ) @ ( B2 @ K2 ) @ zero_zero_nat )
% 3.82/4.06 @ S2 )
% 3.82/4.06 = zero_zero_nat ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.delta
% 3.82/4.06 thf(fact_5129_sum_Odelta,axiom,
% 3.82/4.06 ! [S2: set_int,A: int,B2: int > nat] :
% 3.82/4.06 ( ( finite_finite_int @ S2 )
% 3.82/4.06 => ( ( ( member_int @ A @ S2 )
% 3.82/4.06 => ( ( groups4541462559716669496nt_nat
% 3.82/4.06 @ ^ [K2: int] : ( if_nat @ ( K2 = A ) @ ( B2 @ K2 ) @ zero_zero_nat )
% 3.82/4.06 @ S2 )
% 3.82/4.06 = ( B2 @ A ) ) )
% 3.82/4.06 & ( ~ ( member_int @ A @ S2 )
% 3.82/4.06 => ( ( groups4541462559716669496nt_nat
% 3.82/4.06 @ ^ [K2: int] : ( if_nat @ ( K2 = A ) @ ( B2 @ K2 ) @ zero_zero_nat )
% 3.82/4.06 @ S2 )
% 3.82/4.06 = zero_zero_nat ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.delta
% 3.82/4.06 thf(fact_5130_sum_Odelta,axiom,
% 3.82/4.06 ! [S2: set_Extended_enat,A: extended_enat,B2: extended_enat > nat] :
% 3.82/4.06 ( ( finite4001608067531595151d_enat @ S2 )
% 3.82/4.06 => ( ( ( member_Extended_enat @ A @ S2 )
% 3.82/4.06 => ( ( groups2027974829824023292at_nat
% 3.82/4.06 @ ^ [K2: extended_enat] : ( if_nat @ ( K2 = A ) @ ( B2 @ K2 ) @ zero_zero_nat )
% 3.82/4.06 @ S2 )
% 3.82/4.06 = ( B2 @ A ) ) )
% 3.82/4.06 & ( ~ ( member_Extended_enat @ A @ S2 )
% 3.82/4.06 => ( ( groups2027974829824023292at_nat
% 3.82/4.06 @ ^ [K2: extended_enat] : ( if_nat @ ( K2 = A ) @ ( B2 @ K2 ) @ zero_zero_nat )
% 3.82/4.06 @ S2 )
% 3.82/4.06 = zero_zero_nat ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.delta
% 3.82/4.06 thf(fact_5131_sum_Odelta,axiom,
% 3.82/4.06 ! [S2: set_real,A: real,B2: real > real] :
% 3.82/4.06 ( ( finite_finite_real @ S2 )
% 3.82/4.06 => ( ( ( member_real @ A @ S2 )
% 3.82/4.06 => ( ( groups8097168146408367636l_real
% 3.82/4.06 @ ^ [K2: real] : ( if_real @ ( K2 = A ) @ ( B2 @ K2 ) @ zero_zero_real )
% 3.82/4.06 @ S2 )
% 3.82/4.06 = ( B2 @ A ) ) )
% 3.82/4.06 & ( ~ ( member_real @ A @ S2 )
% 3.82/4.06 => ( ( groups8097168146408367636l_real
% 3.82/4.06 @ ^ [K2: real] : ( if_real @ ( K2 = A ) @ ( B2 @ K2 ) @ zero_zero_real )
% 3.82/4.06 @ S2 )
% 3.82/4.06 = zero_zero_real ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.delta
% 3.82/4.06 thf(fact_5132_sum_Odelta,axiom,
% 3.82/4.06 ! [S2: set_complex,A: complex,B2: complex > real] :
% 3.82/4.06 ( ( finite3207457112153483333omplex @ S2 )
% 3.82/4.06 => ( ( ( member_complex @ A @ S2 )
% 3.82/4.06 => ( ( groups5808333547571424918x_real
% 3.82/4.06 @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B2 @ K2 ) @ zero_zero_real )
% 3.82/4.06 @ S2 )
% 3.82/4.06 = ( B2 @ A ) ) )
% 3.82/4.06 & ( ~ ( member_complex @ A @ S2 )
% 3.82/4.06 => ( ( groups5808333547571424918x_real
% 3.82/4.06 @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B2 @ K2 ) @ zero_zero_real )
% 3.82/4.06 @ S2 )
% 3.82/4.06 = zero_zero_real ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.delta
% 3.82/4.06 thf(fact_5133_sum_Odelta,axiom,
% 3.82/4.06 ! [S2: set_int,A: int,B2: int > real] :
% 3.82/4.06 ( ( finite_finite_int @ S2 )
% 3.82/4.06 => ( ( ( member_int @ A @ S2 )
% 3.82/4.06 => ( ( groups8778361861064173332t_real
% 3.82/4.06 @ ^ [K2: int] : ( if_real @ ( K2 = A ) @ ( B2 @ K2 ) @ zero_zero_real )
% 3.82/4.06 @ S2 )
% 3.82/4.06 = ( B2 @ A ) ) )
% 3.82/4.06 & ( ~ ( member_int @ A @ S2 )
% 3.82/4.06 => ( ( groups8778361861064173332t_real
% 3.82/4.06 @ ^ [K2: int] : ( if_real @ ( K2 = A ) @ ( B2 @ K2 ) @ zero_zero_real )
% 3.82/4.06 @ S2 )
% 3.82/4.06 = zero_zero_real ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.delta
% 3.82/4.06 thf(fact_5134_sum_Odelta,axiom,
% 3.82/4.06 ! [S2: set_Extended_enat,A: extended_enat,B2: extended_enat > real] :
% 3.82/4.06 ( ( finite4001608067531595151d_enat @ S2 )
% 3.82/4.06 => ( ( ( member_Extended_enat @ A @ S2 )
% 3.82/4.06 => ( ( groups4148127829035722712t_real
% 3.82/4.06 @ ^ [K2: extended_enat] : ( if_real @ ( K2 = A ) @ ( B2 @ K2 ) @ zero_zero_real )
% 3.82/4.06 @ S2 )
% 3.82/4.06 = ( B2 @ A ) ) )
% 3.82/4.06 & ( ~ ( member_Extended_enat @ A @ S2 )
% 3.82/4.06 => ( ( groups4148127829035722712t_real
% 3.82/4.06 @ ^ [K2: extended_enat] : ( if_real @ ( K2 = A ) @ ( B2 @ K2 ) @ zero_zero_real )
% 3.82/4.06 @ S2 )
% 3.82/4.06 = zero_zero_real ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.delta
% 3.82/4.06 thf(fact_5135_sum_Odelta,axiom,
% 3.82/4.06 ! [S2: set_real,A: real,B2: real > int] :
% 3.82/4.06 ( ( finite_finite_real @ S2 )
% 3.82/4.06 => ( ( ( member_real @ A @ S2 )
% 3.82/4.06 => ( ( groups1932886352136224148al_int
% 3.82/4.06 @ ^ [K2: real] : ( if_int @ ( K2 = A ) @ ( B2 @ K2 ) @ zero_zero_int )
% 3.82/4.06 @ S2 )
% 3.82/4.06 = ( B2 @ A ) ) )
% 3.82/4.06 & ( ~ ( member_real @ A @ S2 )
% 3.82/4.06 => ( ( groups1932886352136224148al_int
% 3.82/4.06 @ ^ [K2: real] : ( if_int @ ( K2 = A ) @ ( B2 @ K2 ) @ zero_zero_int )
% 3.82/4.06 @ S2 )
% 3.82/4.06 = zero_zero_int ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.delta
% 3.82/4.06 thf(fact_5136_sum_Odelta,axiom,
% 3.82/4.06 ! [S2: set_nat,A: nat,B2: nat > int] :
% 3.82/4.06 ( ( finite_finite_nat @ S2 )
% 3.82/4.06 => ( ( ( member_nat @ A @ S2 )
% 3.82/4.06 => ( ( groups3539618377306564664at_int
% 3.82/4.06 @ ^ [K2: nat] : ( if_int @ ( K2 = A ) @ ( B2 @ K2 ) @ zero_zero_int )
% 3.82/4.06 @ S2 )
% 3.82/4.06 = ( B2 @ A ) ) )
% 3.82/4.06 & ( ~ ( member_nat @ A @ S2 )
% 3.82/4.06 => ( ( groups3539618377306564664at_int
% 3.82/4.06 @ ^ [K2: nat] : ( if_int @ ( K2 = A ) @ ( B2 @ K2 ) @ zero_zero_int )
% 3.82/4.06 @ S2 )
% 3.82/4.06 = zero_zero_int ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.delta
% 3.82/4.06 thf(fact_5137_sum_Odelta_H,axiom,
% 3.82/4.06 ! [S2: set_real,A: real,B2: real > nat] :
% 3.82/4.06 ( ( finite_finite_real @ S2 )
% 3.82/4.06 => ( ( ( member_real @ A @ S2 )
% 3.82/4.06 => ( ( groups1935376822645274424al_nat
% 3.82/4.06 @ ^ [K2: real] : ( if_nat @ ( A = K2 ) @ ( B2 @ K2 ) @ zero_zero_nat )
% 3.82/4.06 @ S2 )
% 3.82/4.06 = ( B2 @ A ) ) )
% 3.82/4.06 & ( ~ ( member_real @ A @ S2 )
% 3.82/4.06 => ( ( groups1935376822645274424al_nat
% 3.82/4.06 @ ^ [K2: real] : ( if_nat @ ( A = K2 ) @ ( B2 @ K2 ) @ zero_zero_nat )
% 3.82/4.06 @ S2 )
% 3.82/4.06 = zero_zero_nat ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.delta'
% 3.82/4.06 thf(fact_5138_sum_Odelta_H,axiom,
% 3.82/4.06 ! [S2: set_complex,A: complex,B2: complex > nat] :
% 3.82/4.06 ( ( finite3207457112153483333omplex @ S2 )
% 3.82/4.06 => ( ( ( member_complex @ A @ S2 )
% 3.82/4.06 => ( ( groups5693394587270226106ex_nat
% 3.82/4.06 @ ^ [K2: complex] : ( if_nat @ ( A = K2 ) @ ( B2 @ K2 ) @ zero_zero_nat )
% 3.82/4.06 @ S2 )
% 3.82/4.06 = ( B2 @ A ) ) )
% 3.82/4.06 & ( ~ ( member_complex @ A @ S2 )
% 3.82/4.06 => ( ( groups5693394587270226106ex_nat
% 3.82/4.06 @ ^ [K2: complex] : ( if_nat @ ( A = K2 ) @ ( B2 @ K2 ) @ zero_zero_nat )
% 3.82/4.06 @ S2 )
% 3.82/4.06 = zero_zero_nat ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.delta'
% 3.82/4.06 thf(fact_5139_sum_Odelta_H,axiom,
% 3.82/4.06 ! [S2: set_int,A: int,B2: int > nat] :
% 3.82/4.06 ( ( finite_finite_int @ S2 )
% 3.82/4.06 => ( ( ( member_int @ A @ S2 )
% 3.82/4.06 => ( ( groups4541462559716669496nt_nat
% 3.82/4.06 @ ^ [K2: int] : ( if_nat @ ( A = K2 ) @ ( B2 @ K2 ) @ zero_zero_nat )
% 3.82/4.06 @ S2 )
% 3.82/4.06 = ( B2 @ A ) ) )
% 3.82/4.06 & ( ~ ( member_int @ A @ S2 )
% 3.82/4.06 => ( ( groups4541462559716669496nt_nat
% 3.82/4.06 @ ^ [K2: int] : ( if_nat @ ( A = K2 ) @ ( B2 @ K2 ) @ zero_zero_nat )
% 3.82/4.06 @ S2 )
% 3.82/4.06 = zero_zero_nat ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.delta'
% 3.82/4.06 thf(fact_5140_sum_Odelta_H,axiom,
% 3.82/4.06 ! [S2: set_Extended_enat,A: extended_enat,B2: extended_enat > nat] :
% 3.82/4.06 ( ( finite4001608067531595151d_enat @ S2 )
% 3.82/4.06 => ( ( ( member_Extended_enat @ A @ S2 )
% 3.82/4.06 => ( ( groups2027974829824023292at_nat
% 3.82/4.06 @ ^ [K2: extended_enat] : ( if_nat @ ( A = K2 ) @ ( B2 @ K2 ) @ zero_zero_nat )
% 3.82/4.06 @ S2 )
% 3.82/4.06 = ( B2 @ A ) ) )
% 3.82/4.06 & ( ~ ( member_Extended_enat @ A @ S2 )
% 3.82/4.06 => ( ( groups2027974829824023292at_nat
% 3.82/4.06 @ ^ [K2: extended_enat] : ( if_nat @ ( A = K2 ) @ ( B2 @ K2 ) @ zero_zero_nat )
% 3.82/4.06 @ S2 )
% 3.82/4.06 = zero_zero_nat ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.delta'
% 3.82/4.06 thf(fact_5141_sum_Odelta_H,axiom,
% 3.82/4.06 ! [S2: set_real,A: real,B2: real > real] :
% 3.82/4.06 ( ( finite_finite_real @ S2 )
% 3.82/4.06 => ( ( ( member_real @ A @ S2 )
% 3.82/4.06 => ( ( groups8097168146408367636l_real
% 3.82/4.06 @ ^ [K2: real] : ( if_real @ ( A = K2 ) @ ( B2 @ K2 ) @ zero_zero_real )
% 3.82/4.06 @ S2 )
% 3.82/4.06 = ( B2 @ A ) ) )
% 3.82/4.06 & ( ~ ( member_real @ A @ S2 )
% 3.82/4.06 => ( ( groups8097168146408367636l_real
% 3.82/4.06 @ ^ [K2: real] : ( if_real @ ( A = K2 ) @ ( B2 @ K2 ) @ zero_zero_real )
% 3.82/4.06 @ S2 )
% 3.82/4.06 = zero_zero_real ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.delta'
% 3.82/4.06 thf(fact_5142_sum_Odelta_H,axiom,
% 3.82/4.06 ! [S2: set_complex,A: complex,B2: complex > real] :
% 3.82/4.06 ( ( finite3207457112153483333omplex @ S2 )
% 3.82/4.06 => ( ( ( member_complex @ A @ S2 )
% 3.82/4.06 => ( ( groups5808333547571424918x_real
% 3.82/4.06 @ ^ [K2: complex] : ( if_real @ ( A = K2 ) @ ( B2 @ K2 ) @ zero_zero_real )
% 3.82/4.06 @ S2 )
% 3.82/4.06 = ( B2 @ A ) ) )
% 3.82/4.06 & ( ~ ( member_complex @ A @ S2 )
% 3.82/4.06 => ( ( groups5808333547571424918x_real
% 3.82/4.06 @ ^ [K2: complex] : ( if_real @ ( A = K2 ) @ ( B2 @ K2 ) @ zero_zero_real )
% 3.82/4.06 @ S2 )
% 3.82/4.06 = zero_zero_real ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.delta'
% 3.82/4.06 thf(fact_5143_sum_Odelta_H,axiom,
% 3.82/4.06 ! [S2: set_int,A: int,B2: int > real] :
% 3.82/4.06 ( ( finite_finite_int @ S2 )
% 3.82/4.06 => ( ( ( member_int @ A @ S2 )
% 3.82/4.06 => ( ( groups8778361861064173332t_real
% 3.82/4.06 @ ^ [K2: int] : ( if_real @ ( A = K2 ) @ ( B2 @ K2 ) @ zero_zero_real )
% 3.82/4.06 @ S2 )
% 3.82/4.06 = ( B2 @ A ) ) )
% 3.82/4.06 & ( ~ ( member_int @ A @ S2 )
% 3.82/4.06 => ( ( groups8778361861064173332t_real
% 3.82/4.06 @ ^ [K2: int] : ( if_real @ ( A = K2 ) @ ( B2 @ K2 ) @ zero_zero_real )
% 3.82/4.06 @ S2 )
% 3.82/4.06 = zero_zero_real ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.delta'
% 3.82/4.06 thf(fact_5144_sum_Odelta_H,axiom,
% 3.82/4.06 ! [S2: set_Extended_enat,A: extended_enat,B2: extended_enat > real] :
% 3.82/4.06 ( ( finite4001608067531595151d_enat @ S2 )
% 3.82/4.06 => ( ( ( member_Extended_enat @ A @ S2 )
% 3.82/4.06 => ( ( groups4148127829035722712t_real
% 3.82/4.06 @ ^ [K2: extended_enat] : ( if_real @ ( A = K2 ) @ ( B2 @ K2 ) @ zero_zero_real )
% 3.82/4.06 @ S2 )
% 3.82/4.06 = ( B2 @ A ) ) )
% 3.82/4.06 & ( ~ ( member_Extended_enat @ A @ S2 )
% 3.82/4.06 => ( ( groups4148127829035722712t_real
% 3.82/4.06 @ ^ [K2: extended_enat] : ( if_real @ ( A = K2 ) @ ( B2 @ K2 ) @ zero_zero_real )
% 3.82/4.06 @ S2 )
% 3.82/4.06 = zero_zero_real ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.delta'
% 3.82/4.06 thf(fact_5145_sum_Odelta_H,axiom,
% 3.82/4.06 ! [S2: set_real,A: real,B2: real > int] :
% 3.82/4.06 ( ( finite_finite_real @ S2 )
% 3.82/4.06 => ( ( ( member_real @ A @ S2 )
% 3.82/4.06 => ( ( groups1932886352136224148al_int
% 3.82/4.06 @ ^ [K2: real] : ( if_int @ ( A = K2 ) @ ( B2 @ K2 ) @ zero_zero_int )
% 3.82/4.06 @ S2 )
% 3.82/4.06 = ( B2 @ A ) ) )
% 3.82/4.06 & ( ~ ( member_real @ A @ S2 )
% 3.82/4.06 => ( ( groups1932886352136224148al_int
% 3.82/4.06 @ ^ [K2: real] : ( if_int @ ( A = K2 ) @ ( B2 @ K2 ) @ zero_zero_int )
% 3.82/4.06 @ S2 )
% 3.82/4.06 = zero_zero_int ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.delta'
% 3.82/4.06 thf(fact_5146_sum_Odelta_H,axiom,
% 3.82/4.06 ! [S2: set_nat,A: nat,B2: nat > int] :
% 3.82/4.06 ( ( finite_finite_nat @ S2 )
% 3.82/4.06 => ( ( ( member_nat @ A @ S2 )
% 3.82/4.06 => ( ( groups3539618377306564664at_int
% 3.82/4.06 @ ^ [K2: nat] : ( if_int @ ( A = K2 ) @ ( B2 @ K2 ) @ zero_zero_int )
% 3.82/4.06 @ S2 )
% 3.82/4.06 = ( B2 @ A ) ) )
% 3.82/4.06 & ( ~ ( member_nat @ A @ S2 )
% 3.82/4.06 => ( ( groups3539618377306564664at_int
% 3.82/4.06 @ ^ [K2: nat] : ( if_int @ ( A = K2 ) @ ( B2 @ K2 ) @ zero_zero_int )
% 3.82/4.06 @ S2 )
% 3.82/4.06 = zero_zero_int ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.delta'
% 3.82/4.06 thf(fact_5147_sum_Oinsert,axiom,
% 3.82/4.06 ! [A2: set_real,X: real,G: real > nat] :
% 3.82/4.06 ( ( finite_finite_real @ A2 )
% 3.82/4.06 => ( ~ ( member_real @ X @ A2 )
% 3.82/4.06 => ( ( groups1935376822645274424al_nat @ G @ ( insert_real @ X @ A2 ) )
% 3.82/4.06 = ( plus_plus_nat @ ( G @ X ) @ ( groups1935376822645274424al_nat @ G @ A2 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.insert
% 3.82/4.06 thf(fact_5148_sum_Oinsert,axiom,
% 3.82/4.06 ! [A2: set_complex,X: complex,G: complex > nat] :
% 3.82/4.06 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.06 => ( ~ ( member_complex @ X @ A2 )
% 3.82/4.06 => ( ( groups5693394587270226106ex_nat @ G @ ( insert_complex @ X @ A2 ) )
% 3.82/4.06 = ( plus_plus_nat @ ( G @ X ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.insert
% 3.82/4.06 thf(fact_5149_sum_Oinsert,axiom,
% 3.82/4.06 ! [A2: set_int,X: int,G: int > nat] :
% 3.82/4.06 ( ( finite_finite_int @ A2 )
% 3.82/4.06 => ( ~ ( member_int @ X @ A2 )
% 3.82/4.06 => ( ( groups4541462559716669496nt_nat @ G @ ( insert_int @ X @ A2 ) )
% 3.82/4.06 = ( plus_plus_nat @ ( G @ X ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.insert
% 3.82/4.06 thf(fact_5150_sum_Oinsert,axiom,
% 3.82/4.06 ! [A2: set_Extended_enat,X: extended_enat,G: extended_enat > nat] :
% 3.82/4.06 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.06 => ( ~ ( member_Extended_enat @ X @ A2 )
% 3.82/4.06 => ( ( groups2027974829824023292at_nat @ G @ ( insert_Extended_enat @ X @ A2 ) )
% 3.82/4.06 = ( plus_plus_nat @ ( G @ X ) @ ( groups2027974829824023292at_nat @ G @ A2 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.insert
% 3.82/4.06 thf(fact_5151_sum_Oinsert,axiom,
% 3.82/4.06 ! [A2: set_real,X: real,G: real > int] :
% 3.82/4.06 ( ( finite_finite_real @ A2 )
% 3.82/4.06 => ( ~ ( member_real @ X @ A2 )
% 3.82/4.06 => ( ( groups1932886352136224148al_int @ G @ ( insert_real @ X @ A2 ) )
% 3.82/4.06 = ( plus_plus_int @ ( G @ X ) @ ( groups1932886352136224148al_int @ G @ A2 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.insert
% 3.82/4.06 thf(fact_5152_sum_Oinsert,axiom,
% 3.82/4.06 ! [A2: set_nat,X: nat,G: nat > int] :
% 3.82/4.06 ( ( finite_finite_nat @ A2 )
% 3.82/4.06 => ( ~ ( member_nat @ X @ A2 )
% 3.82/4.06 => ( ( groups3539618377306564664at_int @ G @ ( insert_nat @ X @ A2 ) )
% 3.82/4.06 = ( plus_plus_int @ ( G @ X ) @ ( groups3539618377306564664at_int @ G @ A2 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.insert
% 3.82/4.06 thf(fact_5153_sum_Oinsert,axiom,
% 3.82/4.06 ! [A2: set_complex,X: complex,G: complex > int] :
% 3.82/4.06 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.06 => ( ~ ( member_complex @ X @ A2 )
% 3.82/4.06 => ( ( groups5690904116761175830ex_int @ G @ ( insert_complex @ X @ A2 ) )
% 3.82/4.06 = ( plus_plus_int @ ( G @ X ) @ ( groups5690904116761175830ex_int @ G @ A2 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.insert
% 3.82/4.06 thf(fact_5154_sum_Oinsert,axiom,
% 3.82/4.06 ! [A2: set_Extended_enat,X: extended_enat,G: extended_enat > int] :
% 3.82/4.06 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.06 => ( ~ ( member_Extended_enat @ X @ A2 )
% 3.82/4.06 => ( ( groups2025484359314973016at_int @ G @ ( insert_Extended_enat @ X @ A2 ) )
% 3.82/4.06 = ( plus_plus_int @ ( G @ X ) @ ( groups2025484359314973016at_int @ G @ A2 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.insert
% 3.82/4.06 thf(fact_5155_sum_Oinsert,axiom,
% 3.82/4.06 ! [A2: set_real,X: real,G: real > real] :
% 3.82/4.06 ( ( finite_finite_real @ A2 )
% 3.82/4.06 => ( ~ ( member_real @ X @ A2 )
% 3.82/4.06 => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X @ A2 ) )
% 3.82/4.06 = ( plus_plus_real @ ( G @ X ) @ ( groups8097168146408367636l_real @ G @ A2 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.insert
% 3.82/4.06 thf(fact_5156_sum_Oinsert,axiom,
% 3.82/4.06 ! [A2: set_complex,X: complex,G: complex > real] :
% 3.82/4.06 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.06 => ( ~ ( member_complex @ X @ A2 )
% 3.82/4.06 => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X @ A2 ) )
% 3.82/4.06 = ( plus_plus_real @ ( G @ X ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.insert
% 3.82/4.06 thf(fact_5157_of__int__sum,axiom,
% 3.82/4.06 ! [F: complex > int,A2: set_complex] :
% 3.82/4.06 ( ( ring_17405671764205052669omplex @ ( groups5690904116761175830ex_int @ F @ A2 ) )
% 3.82/4.06 = ( groups7754918857620584856omplex
% 3.82/4.06 @ ^ [X4: complex] : ( ring_17405671764205052669omplex @ ( F @ X4 ) )
% 3.82/4.06 @ A2 ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_sum
% 3.82/4.06 thf(fact_5158_of__int__sum,axiom,
% 3.82/4.06 ! [F: nat > int,A2: set_nat] :
% 3.82/4.06 ( ( ring_1_of_int_real @ ( groups3539618377306564664at_int @ F @ A2 ) )
% 3.82/4.06 = ( groups6591440286371151544t_real
% 3.82/4.06 @ ^ [X4: nat] : ( ring_1_of_int_real @ ( F @ X4 ) )
% 3.82/4.06 @ A2 ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_sum
% 3.82/4.06 thf(fact_5159_of__int__sum,axiom,
% 3.82/4.06 ! [F: int > int,A2: set_int] :
% 3.82/4.06 ( ( ring_1_of_int_real @ ( groups4538972089207619220nt_int @ F @ A2 ) )
% 3.82/4.06 = ( groups8778361861064173332t_real
% 3.82/4.06 @ ^ [X4: int] : ( ring_1_of_int_real @ ( F @ X4 ) )
% 3.82/4.06 @ A2 ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_sum
% 3.82/4.06 thf(fact_5160_of__int__sum,axiom,
% 3.82/4.06 ! [F: int > int,A2: set_int] :
% 3.82/4.06 ( ( ring_1_of_int_int @ ( groups4538972089207619220nt_int @ F @ A2 ) )
% 3.82/4.06 = ( groups4538972089207619220nt_int
% 3.82/4.06 @ ^ [X4: int] : ( ring_1_of_int_int @ ( F @ X4 ) )
% 3.82/4.06 @ A2 ) ) ).
% 3.82/4.06
% 3.82/4.06 % of_int_sum
% 3.82/4.06 thf(fact_5161_and__numerals_I5_J,axiom,
% 3.82/4.06 ! [X: num] :
% 3.82/4.06 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ one_one_int )
% 3.82/4.06 = zero_zero_int ) ).
% 3.82/4.06
% 3.82/4.06 % and_numerals(5)
% 3.82/4.06 thf(fact_5162_and__numerals_I5_J,axiom,
% 3.82/4.06 ! [X: num] :
% 3.82/4.06 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ one_one_nat )
% 3.82/4.06 = zero_zero_nat ) ).
% 3.82/4.06
% 3.82/4.06 % and_numerals(5)
% 3.82/4.06 thf(fact_5163_and__numerals_I1_J,axiom,
% 3.82/4.06 ! [Y: num] :
% 3.82/4.06 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 3.82/4.06 = zero_zero_int ) ).
% 3.82/4.06
% 3.82/4.06 % and_numerals(1)
% 3.82/4.06 thf(fact_5164_and__numerals_I1_J,axiom,
% 3.82/4.06 ! [Y: num] :
% 3.82/4.06 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 3.82/4.06 = zero_zero_nat ) ).
% 3.82/4.06
% 3.82/4.06 % and_numerals(1)
% 3.82/4.06 thf(fact_5165_and__numerals_I7_J,axiom,
% 3.82/4.06 ! [X: num,Y: num] :
% 3.82/4.06 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 3.82/4.06 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % and_numerals(7)
% 3.82/4.06 thf(fact_5166_and__numerals_I7_J,axiom,
% 3.82/4.06 ! [X: num,Y: num] :
% 3.82/4.06 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 3.82/4.06 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % and_numerals(7)
% 3.82/4.06 thf(fact_5167_sum_Oneutral,axiom,
% 3.82/4.06 ! [A2: set_int,G: int > int] :
% 3.82/4.06 ( ! [X5: int] :
% 3.82/4.06 ( ( member_int @ X5 @ A2 )
% 3.82/4.06 => ( ( G @ X5 )
% 3.82/4.06 = zero_zero_int ) )
% 3.82/4.06 => ( ( groups4538972089207619220nt_int @ G @ A2 )
% 3.82/4.06 = zero_zero_int ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.neutral
% 3.82/4.06 thf(fact_5168_sum_Oneutral,axiom,
% 3.82/4.06 ! [A2: set_nat,G: nat > nat] :
% 3.82/4.06 ( ! [X5: nat] :
% 3.82/4.06 ( ( member_nat @ X5 @ A2 )
% 3.82/4.06 => ( ( G @ X5 )
% 3.82/4.06 = zero_zero_nat ) )
% 3.82/4.06 => ( ( groups3542108847815614940at_nat @ G @ A2 )
% 3.82/4.06 = zero_zero_nat ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.neutral
% 3.82/4.06 thf(fact_5169_sum_Oneutral,axiom,
% 3.82/4.06 ! [A2: set_complex,G: complex > complex] :
% 3.82/4.06 ( ! [X5: complex] :
% 3.82/4.06 ( ( member_complex @ X5 @ A2 )
% 3.82/4.06 => ( ( G @ X5 )
% 3.82/4.06 = zero_zero_complex ) )
% 3.82/4.06 => ( ( groups7754918857620584856omplex @ G @ A2 )
% 3.82/4.06 = zero_zero_complex ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.neutral
% 3.82/4.06 thf(fact_5170_sum_Oneutral,axiom,
% 3.82/4.06 ! [A2: set_nat,G: nat > real] :
% 3.82/4.06 ( ! [X5: nat] :
% 3.82/4.06 ( ( member_nat @ X5 @ A2 )
% 3.82/4.06 => ( ( G @ X5 )
% 3.82/4.06 = zero_zero_real ) )
% 3.82/4.06 => ( ( groups6591440286371151544t_real @ G @ A2 )
% 3.82/4.06 = zero_zero_real ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.neutral
% 3.82/4.06 thf(fact_5171_sum_Onot__neutral__contains__not__neutral,axiom,
% 3.82/4.06 ! [G: extended_enat > nat,A2: set_Extended_enat] :
% 3.82/4.06 ( ( ( groups2027974829824023292at_nat @ G @ A2 )
% 3.82/4.06 != zero_zero_nat )
% 3.82/4.06 => ~ ! [A4: extended_enat] :
% 3.82/4.06 ( ( member_Extended_enat @ A4 @ A2 )
% 3.82/4.06 => ( ( G @ A4 )
% 3.82/4.06 = zero_zero_nat ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.not_neutral_contains_not_neutral
% 3.82/4.06 thf(fact_5172_sum_Onot__neutral__contains__not__neutral,axiom,
% 3.82/4.06 ! [G: real > nat,A2: set_real] :
% 3.82/4.06 ( ( ( groups1935376822645274424al_nat @ G @ A2 )
% 3.82/4.06 != zero_zero_nat )
% 3.82/4.06 => ~ ! [A4: real] :
% 3.82/4.06 ( ( member_real @ A4 @ A2 )
% 3.82/4.06 => ( ( G @ A4 )
% 3.82/4.06 = zero_zero_nat ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.not_neutral_contains_not_neutral
% 3.82/4.06 thf(fact_5173_sum_Onot__neutral__contains__not__neutral,axiom,
% 3.82/4.06 ! [G: int > nat,A2: set_int] :
% 3.82/4.06 ( ( ( groups4541462559716669496nt_nat @ G @ A2 )
% 3.82/4.06 != zero_zero_nat )
% 3.82/4.06 => ~ ! [A4: int] :
% 3.82/4.06 ( ( member_int @ A4 @ A2 )
% 3.82/4.06 => ( ( G @ A4 )
% 3.82/4.06 = zero_zero_nat ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.not_neutral_contains_not_neutral
% 3.82/4.06 thf(fact_5174_sum_Onot__neutral__contains__not__neutral,axiom,
% 3.82/4.06 ! [G: extended_enat > real,A2: set_Extended_enat] :
% 3.82/4.06 ( ( ( groups4148127829035722712t_real @ G @ A2 )
% 3.82/4.06 != zero_zero_real )
% 3.82/4.06 => ~ ! [A4: extended_enat] :
% 3.82/4.06 ( ( member_Extended_enat @ A4 @ A2 )
% 3.82/4.06 => ( ( G @ A4 )
% 3.82/4.06 = zero_zero_real ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.not_neutral_contains_not_neutral
% 3.82/4.06 thf(fact_5175_sum_Onot__neutral__contains__not__neutral,axiom,
% 3.82/4.06 ! [G: real > real,A2: set_real] :
% 3.82/4.06 ( ( ( groups8097168146408367636l_real @ G @ A2 )
% 3.82/4.06 != zero_zero_real )
% 3.82/4.06 => ~ ! [A4: real] :
% 3.82/4.06 ( ( member_real @ A4 @ A2 )
% 3.82/4.06 => ( ( G @ A4 )
% 3.82/4.06 = zero_zero_real ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.not_neutral_contains_not_neutral
% 3.82/4.06 thf(fact_5176_sum_Onot__neutral__contains__not__neutral,axiom,
% 3.82/4.06 ! [G: int > real,A2: set_int] :
% 3.82/4.06 ( ( ( groups8778361861064173332t_real @ G @ A2 )
% 3.82/4.06 != zero_zero_real )
% 3.82/4.06 => ~ ! [A4: int] :
% 3.82/4.06 ( ( member_int @ A4 @ A2 )
% 3.82/4.06 => ( ( G @ A4 )
% 3.82/4.06 = zero_zero_real ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.not_neutral_contains_not_neutral
% 3.82/4.06 thf(fact_5177_sum_Onot__neutral__contains__not__neutral,axiom,
% 3.82/4.06 ! [G: extended_enat > int,A2: set_Extended_enat] :
% 3.82/4.06 ( ( ( groups2025484359314973016at_int @ G @ A2 )
% 3.82/4.06 != zero_zero_int )
% 3.82/4.06 => ~ ! [A4: extended_enat] :
% 3.82/4.06 ( ( member_Extended_enat @ A4 @ A2 )
% 3.82/4.06 => ( ( G @ A4 )
% 3.82/4.06 = zero_zero_int ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.not_neutral_contains_not_neutral
% 3.82/4.06 thf(fact_5178_sum_Onot__neutral__contains__not__neutral,axiom,
% 3.82/4.06 ! [G: real > int,A2: set_real] :
% 3.82/4.06 ( ( ( groups1932886352136224148al_int @ G @ A2 )
% 3.82/4.06 != zero_zero_int )
% 3.82/4.06 => ~ ! [A4: real] :
% 3.82/4.06 ( ( member_real @ A4 @ A2 )
% 3.82/4.06 => ( ( G @ A4 )
% 3.82/4.06 = zero_zero_int ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.not_neutral_contains_not_neutral
% 3.82/4.06 thf(fact_5179_sum_Onot__neutral__contains__not__neutral,axiom,
% 3.82/4.06 ! [G: nat > int,A2: set_nat] :
% 3.82/4.06 ( ( ( groups3539618377306564664at_int @ G @ A2 )
% 3.82/4.06 != zero_zero_int )
% 3.82/4.06 => ~ ! [A4: nat] :
% 3.82/4.06 ( ( member_nat @ A4 @ A2 )
% 3.82/4.06 => ( ( G @ A4 )
% 3.82/4.06 = zero_zero_int ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.not_neutral_contains_not_neutral
% 3.82/4.06 thf(fact_5180_sum_Onot__neutral__contains__not__neutral,axiom,
% 3.82/4.06 ! [G: extended_enat > complex,A2: set_Extended_enat] :
% 3.82/4.06 ( ( ( groups6818542070133387226omplex @ G @ A2 )
% 3.82/4.06 != zero_zero_complex )
% 3.82/4.06 => ~ ! [A4: extended_enat] :
% 3.82/4.06 ( ( member_Extended_enat @ A4 @ A2 )
% 3.82/4.06 => ( ( G @ A4 )
% 3.82/4.06 = zero_zero_complex ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.not_neutral_contains_not_neutral
% 3.82/4.06 thf(fact_5181_sum__mono,axiom,
% 3.82/4.06 ! [K5: set_Extended_enat,F: extended_enat > real,G: extended_enat > real] :
% 3.82/4.06 ( ! [I4: extended_enat] :
% 3.82/4.06 ( ( member_Extended_enat @ I4 @ K5 )
% 3.82/4.06 => ( ord_less_eq_real @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 3.82/4.06 => ( ord_less_eq_real @ ( groups4148127829035722712t_real @ F @ K5 ) @ ( groups4148127829035722712t_real @ G @ K5 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum_mono
% 3.82/4.06 thf(fact_5182_sum__mono,axiom,
% 3.82/4.06 ! [K5: set_real,F: real > real,G: real > real] :
% 3.82/4.06 ( ! [I4: real] :
% 3.82/4.06 ( ( member_real @ I4 @ K5 )
% 3.82/4.06 => ( ord_less_eq_real @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 3.82/4.06 => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ K5 ) @ ( groups8097168146408367636l_real @ G @ K5 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum_mono
% 3.82/4.06 thf(fact_5183_sum__mono,axiom,
% 3.82/4.06 ! [K5: set_int,F: int > real,G: int > real] :
% 3.82/4.06 ( ! [I4: int] :
% 3.82/4.06 ( ( member_int @ I4 @ K5 )
% 3.82/4.06 => ( ord_less_eq_real @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 3.82/4.06 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ K5 ) @ ( groups8778361861064173332t_real @ G @ K5 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum_mono
% 3.82/4.06 thf(fact_5184_sum__mono,axiom,
% 3.82/4.06 ! [K5: set_Extended_enat,F: extended_enat > nat,G: extended_enat > nat] :
% 3.82/4.06 ( ! [I4: extended_enat] :
% 3.82/4.06 ( ( member_Extended_enat @ I4 @ K5 )
% 3.82/4.06 => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 3.82/4.06 => ( ord_less_eq_nat @ ( groups2027974829824023292at_nat @ F @ K5 ) @ ( groups2027974829824023292at_nat @ G @ K5 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum_mono
% 3.82/4.06 thf(fact_5185_sum__mono,axiom,
% 3.82/4.06 ! [K5: set_real,F: real > nat,G: real > nat] :
% 3.82/4.06 ( ! [I4: real] :
% 3.82/4.06 ( ( member_real @ I4 @ K5 )
% 3.82/4.06 => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 3.82/4.06 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ K5 ) @ ( groups1935376822645274424al_nat @ G @ K5 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum_mono
% 3.82/4.06 thf(fact_5186_sum__mono,axiom,
% 3.82/4.06 ! [K5: set_int,F: int > nat,G: int > nat] :
% 3.82/4.06 ( ! [I4: int] :
% 3.82/4.06 ( ( member_int @ I4 @ K5 )
% 3.82/4.06 => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 3.82/4.06 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ K5 ) @ ( groups4541462559716669496nt_nat @ G @ K5 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum_mono
% 3.82/4.06 thf(fact_5187_sum__mono,axiom,
% 3.82/4.06 ! [K5: set_Extended_enat,F: extended_enat > int,G: extended_enat > int] :
% 3.82/4.06 ( ! [I4: extended_enat] :
% 3.82/4.06 ( ( member_Extended_enat @ I4 @ K5 )
% 3.82/4.06 => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 3.82/4.06 => ( ord_less_eq_int @ ( groups2025484359314973016at_int @ F @ K5 ) @ ( groups2025484359314973016at_int @ G @ K5 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum_mono
% 3.82/4.06 thf(fact_5188_sum__mono,axiom,
% 3.82/4.06 ! [K5: set_real,F: real > int,G: real > int] :
% 3.82/4.06 ( ! [I4: real] :
% 3.82/4.06 ( ( member_real @ I4 @ K5 )
% 3.82/4.06 => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 3.82/4.06 => ( ord_less_eq_int @ ( groups1932886352136224148al_int @ F @ K5 ) @ ( groups1932886352136224148al_int @ G @ K5 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum_mono
% 3.82/4.06 thf(fact_5189_sum__mono,axiom,
% 3.82/4.06 ! [K5: set_nat,F: nat > int,G: nat > int] :
% 3.82/4.06 ( ! [I4: nat] :
% 3.82/4.06 ( ( member_nat @ I4 @ K5 )
% 3.82/4.06 => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 3.82/4.06 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ K5 ) @ ( groups3539618377306564664at_int @ G @ K5 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum_mono
% 3.82/4.06 thf(fact_5190_sum__mono,axiom,
% 3.82/4.06 ! [K5: set_int,F: int > int,G: int > int] :
% 3.82/4.06 ( ! [I4: int] :
% 3.82/4.06 ( ( member_int @ I4 @ K5 )
% 3.82/4.06 => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 3.82/4.06 => ( ord_less_eq_int @ ( groups4538972089207619220nt_int @ F @ K5 ) @ ( groups4538972089207619220nt_int @ G @ K5 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum_mono
% 3.82/4.06 thf(fact_5191_sum_Odistrib,axiom,
% 3.82/4.06 ! [G: int > int,H2: int > int,A2: set_int] :
% 3.82/4.06 ( ( groups4538972089207619220nt_int
% 3.82/4.06 @ ^ [X4: int] : ( plus_plus_int @ ( G @ X4 ) @ ( H2 @ X4 ) )
% 3.82/4.06 @ A2 )
% 3.82/4.06 = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G @ A2 ) @ ( groups4538972089207619220nt_int @ H2 @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.distrib
% 3.82/4.06 thf(fact_5192_sum_Odistrib,axiom,
% 3.82/4.06 ! [G: nat > nat,H2: nat > nat,A2: set_nat] :
% 3.82/4.06 ( ( groups3542108847815614940at_nat
% 3.82/4.06 @ ^ [X4: nat] : ( plus_plus_nat @ ( G @ X4 ) @ ( H2 @ X4 ) )
% 3.82/4.06 @ A2 )
% 3.82/4.06 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ A2 ) @ ( groups3542108847815614940at_nat @ H2 @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.distrib
% 3.82/4.06 thf(fact_5193_sum_Odistrib,axiom,
% 3.82/4.06 ! [G: complex > complex,H2: complex > complex,A2: set_complex] :
% 3.82/4.06 ( ( groups7754918857620584856omplex
% 3.82/4.06 @ ^ [X4: complex] : ( plus_plus_complex @ ( G @ X4 ) @ ( H2 @ X4 ) )
% 3.82/4.06 @ A2 )
% 3.82/4.06 = ( plus_plus_complex @ ( groups7754918857620584856omplex @ G @ A2 ) @ ( groups7754918857620584856omplex @ H2 @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.distrib
% 3.82/4.06 thf(fact_5194_sum_Odistrib,axiom,
% 3.82/4.06 ! [G: nat > real,H2: nat > real,A2: set_nat] :
% 3.82/4.06 ( ( groups6591440286371151544t_real
% 3.82/4.06 @ ^ [X4: nat] : ( plus_plus_real @ ( G @ X4 ) @ ( H2 @ X4 ) )
% 3.82/4.06 @ A2 )
% 3.82/4.06 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ A2 ) @ ( groups6591440286371151544t_real @ H2 @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.distrib
% 3.82/4.06 thf(fact_5195_sum_Oswap__restrict,axiom,
% 3.82/4.06 ! [A2: set_real,B: set_int,G: real > int > int,R: real > int > $o] :
% 3.82/4.06 ( ( finite_finite_real @ A2 )
% 3.82/4.06 => ( ( finite_finite_int @ B )
% 3.82/4.06 => ( ( groups1932886352136224148al_int
% 3.82/4.06 @ ^ [X4: real] :
% 3.82/4.06 ( groups4538972089207619220nt_int @ ( G @ X4 )
% 3.82/4.06 @ ( collect_int
% 3.82/4.06 @ ^ [Y5: int] :
% 3.82/4.06 ( ( member_int @ Y5 @ B )
% 3.82/4.06 & ( R @ X4 @ Y5 ) ) ) )
% 3.82/4.06 @ A2 )
% 3.82/4.06 = ( groups4538972089207619220nt_int
% 3.82/4.06 @ ^ [Y5: int] :
% 3.82/4.06 ( groups1932886352136224148al_int
% 3.82/4.06 @ ^ [X4: real] : ( G @ X4 @ Y5 )
% 3.82/4.06 @ ( collect_real
% 3.82/4.06 @ ^ [X4: real] :
% 3.82/4.06 ( ( member_real @ X4 @ A2 )
% 3.82/4.06 & ( R @ X4 @ Y5 ) ) ) )
% 3.82/4.06 @ B ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.swap_restrict
% 3.82/4.06 thf(fact_5196_sum_Oswap__restrict,axiom,
% 3.82/4.06 ! [A2: set_nat,B: set_int,G: nat > int > int,R: nat > int > $o] :
% 3.82/4.06 ( ( finite_finite_nat @ A2 )
% 3.82/4.06 => ( ( finite_finite_int @ B )
% 3.82/4.06 => ( ( groups3539618377306564664at_int
% 3.82/4.06 @ ^ [X4: nat] :
% 3.82/4.06 ( groups4538972089207619220nt_int @ ( G @ X4 )
% 3.82/4.06 @ ( collect_int
% 3.82/4.06 @ ^ [Y5: int] :
% 3.82/4.06 ( ( member_int @ Y5 @ B )
% 3.82/4.06 & ( R @ X4 @ Y5 ) ) ) )
% 3.82/4.06 @ A2 )
% 3.82/4.06 = ( groups4538972089207619220nt_int
% 3.82/4.06 @ ^ [Y5: int] :
% 3.82/4.06 ( groups3539618377306564664at_int
% 3.82/4.06 @ ^ [X4: nat] : ( G @ X4 @ Y5 )
% 3.82/4.06 @ ( collect_nat
% 3.82/4.06 @ ^ [X4: nat] :
% 3.82/4.06 ( ( member_nat @ X4 @ A2 )
% 3.82/4.06 & ( R @ X4 @ Y5 ) ) ) )
% 3.82/4.06 @ B ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.swap_restrict
% 3.82/4.06 thf(fact_5197_sum_Oswap__restrict,axiom,
% 3.82/4.06 ! [A2: set_complex,B: set_int,G: complex > int > int,R: complex > int > $o] :
% 3.82/4.06 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.06 => ( ( finite_finite_int @ B )
% 3.82/4.06 => ( ( groups5690904116761175830ex_int
% 3.82/4.06 @ ^ [X4: complex] :
% 3.82/4.06 ( groups4538972089207619220nt_int @ ( G @ X4 )
% 3.82/4.06 @ ( collect_int
% 3.82/4.06 @ ^ [Y5: int] :
% 3.82/4.06 ( ( member_int @ Y5 @ B )
% 3.82/4.06 & ( R @ X4 @ Y5 ) ) ) )
% 3.82/4.06 @ A2 )
% 3.82/4.06 = ( groups4538972089207619220nt_int
% 3.82/4.06 @ ^ [Y5: int] :
% 3.82/4.06 ( groups5690904116761175830ex_int
% 3.82/4.06 @ ^ [X4: complex] : ( G @ X4 @ Y5 )
% 3.82/4.06 @ ( collect_complex
% 3.82/4.06 @ ^ [X4: complex] :
% 3.82/4.06 ( ( member_complex @ X4 @ A2 )
% 3.82/4.06 & ( R @ X4 @ Y5 ) ) ) )
% 3.82/4.06 @ B ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.swap_restrict
% 3.82/4.06 thf(fact_5198_sum_Oswap__restrict,axiom,
% 3.82/4.06 ! [A2: set_Extended_enat,B: set_int,G: extended_enat > int > int,R: extended_enat > int > $o] :
% 3.82/4.06 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.06 => ( ( finite_finite_int @ B )
% 3.82/4.06 => ( ( groups2025484359314973016at_int
% 3.82/4.06 @ ^ [X4: extended_enat] :
% 3.82/4.06 ( groups4538972089207619220nt_int @ ( G @ X4 )
% 3.82/4.06 @ ( collect_int
% 3.82/4.06 @ ^ [Y5: int] :
% 3.82/4.06 ( ( member_int @ Y5 @ B )
% 3.82/4.06 & ( R @ X4 @ Y5 ) ) ) )
% 3.82/4.06 @ A2 )
% 3.82/4.06 = ( groups4538972089207619220nt_int
% 3.82/4.06 @ ^ [Y5: int] :
% 3.82/4.06 ( groups2025484359314973016at_int
% 3.82/4.06 @ ^ [X4: extended_enat] : ( G @ X4 @ Y5 )
% 3.82/4.06 @ ( collec4429806609662206161d_enat
% 3.82/4.06 @ ^ [X4: extended_enat] :
% 3.82/4.06 ( ( member_Extended_enat @ X4 @ A2 )
% 3.82/4.06 & ( R @ X4 @ Y5 ) ) ) )
% 3.82/4.06 @ B ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.swap_restrict
% 3.82/4.06 thf(fact_5199_sum_Oswap__restrict,axiom,
% 3.82/4.06 ! [A2: set_real,B: set_nat,G: real > nat > nat,R: real > nat > $o] :
% 3.82/4.06 ( ( finite_finite_real @ A2 )
% 3.82/4.06 => ( ( finite_finite_nat @ B )
% 3.82/4.06 => ( ( groups1935376822645274424al_nat
% 3.82/4.06 @ ^ [X4: real] :
% 3.82/4.06 ( groups3542108847815614940at_nat @ ( G @ X4 )
% 3.82/4.06 @ ( collect_nat
% 3.82/4.06 @ ^ [Y5: nat] :
% 3.82/4.06 ( ( member_nat @ Y5 @ B )
% 3.82/4.06 & ( R @ X4 @ Y5 ) ) ) )
% 3.82/4.06 @ A2 )
% 3.82/4.06 = ( groups3542108847815614940at_nat
% 3.82/4.06 @ ^ [Y5: nat] :
% 3.82/4.06 ( groups1935376822645274424al_nat
% 3.82/4.06 @ ^ [X4: real] : ( G @ X4 @ Y5 )
% 3.82/4.06 @ ( collect_real
% 3.82/4.06 @ ^ [X4: real] :
% 3.82/4.06 ( ( member_real @ X4 @ A2 )
% 3.82/4.06 & ( R @ X4 @ Y5 ) ) ) )
% 3.82/4.06 @ B ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.swap_restrict
% 3.82/4.06 thf(fact_5200_sum_Oswap__restrict,axiom,
% 3.82/4.06 ! [A2: set_complex,B: set_nat,G: complex > nat > nat,R: complex > nat > $o] :
% 3.82/4.06 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.06 => ( ( finite_finite_nat @ B )
% 3.82/4.06 => ( ( groups5693394587270226106ex_nat
% 3.82/4.06 @ ^ [X4: complex] :
% 3.82/4.06 ( groups3542108847815614940at_nat @ ( G @ X4 )
% 3.82/4.06 @ ( collect_nat
% 3.82/4.06 @ ^ [Y5: nat] :
% 3.82/4.06 ( ( member_nat @ Y5 @ B )
% 3.82/4.06 & ( R @ X4 @ Y5 ) ) ) )
% 3.82/4.06 @ A2 )
% 3.82/4.06 = ( groups3542108847815614940at_nat
% 3.82/4.06 @ ^ [Y5: nat] :
% 3.82/4.06 ( groups5693394587270226106ex_nat
% 3.82/4.06 @ ^ [X4: complex] : ( G @ X4 @ Y5 )
% 3.82/4.06 @ ( collect_complex
% 3.82/4.06 @ ^ [X4: complex] :
% 3.82/4.06 ( ( member_complex @ X4 @ A2 )
% 3.82/4.06 & ( R @ X4 @ Y5 ) ) ) )
% 3.82/4.06 @ B ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.swap_restrict
% 3.82/4.06 thf(fact_5201_sum_Oswap__restrict,axiom,
% 3.82/4.06 ! [A2: set_int,B: set_nat,G: int > nat > nat,R: int > nat > $o] :
% 3.82/4.06 ( ( finite_finite_int @ A2 )
% 3.82/4.06 => ( ( finite_finite_nat @ B )
% 3.82/4.06 => ( ( groups4541462559716669496nt_nat
% 3.82/4.06 @ ^ [X4: int] :
% 3.82/4.06 ( groups3542108847815614940at_nat @ ( G @ X4 )
% 3.82/4.06 @ ( collect_nat
% 3.82/4.06 @ ^ [Y5: nat] :
% 3.82/4.06 ( ( member_nat @ Y5 @ B )
% 3.82/4.06 & ( R @ X4 @ Y5 ) ) ) )
% 3.82/4.06 @ A2 )
% 3.82/4.06 = ( groups3542108847815614940at_nat
% 3.82/4.06 @ ^ [Y5: nat] :
% 3.82/4.06 ( groups4541462559716669496nt_nat
% 3.82/4.06 @ ^ [X4: int] : ( G @ X4 @ Y5 )
% 3.82/4.06 @ ( collect_int
% 3.82/4.06 @ ^ [X4: int] :
% 3.82/4.06 ( ( member_int @ X4 @ A2 )
% 3.82/4.06 & ( R @ X4 @ Y5 ) ) ) )
% 3.82/4.06 @ B ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.swap_restrict
% 3.82/4.06 thf(fact_5202_sum_Oswap__restrict,axiom,
% 3.82/4.06 ! [A2: set_Extended_enat,B: set_nat,G: extended_enat > nat > nat,R: extended_enat > nat > $o] :
% 3.82/4.06 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.06 => ( ( finite_finite_nat @ B )
% 3.82/4.06 => ( ( groups2027974829824023292at_nat
% 3.82/4.06 @ ^ [X4: extended_enat] :
% 3.82/4.06 ( groups3542108847815614940at_nat @ ( G @ X4 )
% 3.82/4.06 @ ( collect_nat
% 3.82/4.06 @ ^ [Y5: nat] :
% 3.82/4.06 ( ( member_nat @ Y5 @ B )
% 3.82/4.06 & ( R @ X4 @ Y5 ) ) ) )
% 3.82/4.06 @ A2 )
% 3.82/4.06 = ( groups3542108847815614940at_nat
% 3.82/4.06 @ ^ [Y5: nat] :
% 3.82/4.06 ( groups2027974829824023292at_nat
% 3.82/4.06 @ ^ [X4: extended_enat] : ( G @ X4 @ Y5 )
% 3.82/4.06 @ ( collec4429806609662206161d_enat
% 3.82/4.06 @ ^ [X4: extended_enat] :
% 3.82/4.06 ( ( member_Extended_enat @ X4 @ A2 )
% 3.82/4.06 & ( R @ X4 @ Y5 ) ) ) )
% 3.82/4.06 @ B ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.swap_restrict
% 3.82/4.06 thf(fact_5203_sum_Oswap__restrict,axiom,
% 3.82/4.06 ! [A2: set_real,B: set_complex,G: real > complex > complex,R: real > complex > $o] :
% 3.82/4.06 ( ( finite_finite_real @ A2 )
% 3.82/4.06 => ( ( finite3207457112153483333omplex @ B )
% 3.82/4.06 => ( ( groups5754745047067104278omplex
% 3.82/4.06 @ ^ [X4: real] :
% 3.82/4.06 ( groups7754918857620584856omplex @ ( G @ X4 )
% 3.82/4.06 @ ( collect_complex
% 3.82/4.06 @ ^ [Y5: complex] :
% 3.82/4.06 ( ( member_complex @ Y5 @ B )
% 3.82/4.06 & ( R @ X4 @ Y5 ) ) ) )
% 3.82/4.06 @ A2 )
% 3.82/4.06 = ( groups7754918857620584856omplex
% 3.82/4.06 @ ^ [Y5: complex] :
% 3.82/4.06 ( groups5754745047067104278omplex
% 3.82/4.06 @ ^ [X4: real] : ( G @ X4 @ Y5 )
% 3.82/4.06 @ ( collect_real
% 3.82/4.06 @ ^ [X4: real] :
% 3.82/4.06 ( ( member_real @ X4 @ A2 )
% 3.82/4.06 & ( R @ X4 @ Y5 ) ) ) )
% 3.82/4.06 @ B ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.swap_restrict
% 3.82/4.06 thf(fact_5204_sum_Oswap__restrict,axiom,
% 3.82/4.06 ! [A2: set_nat,B: set_complex,G: nat > complex > complex,R: nat > complex > $o] :
% 3.82/4.06 ( ( finite_finite_nat @ A2 )
% 3.82/4.06 => ( ( finite3207457112153483333omplex @ B )
% 3.82/4.06 => ( ( groups2073611262835488442omplex
% 3.82/4.06 @ ^ [X4: nat] :
% 3.82/4.06 ( groups7754918857620584856omplex @ ( G @ X4 )
% 3.82/4.06 @ ( collect_complex
% 3.82/4.06 @ ^ [Y5: complex] :
% 3.82/4.06 ( ( member_complex @ Y5 @ B )
% 3.82/4.06 & ( R @ X4 @ Y5 ) ) ) )
% 3.82/4.06 @ A2 )
% 3.82/4.06 = ( groups7754918857620584856omplex
% 3.82/4.06 @ ^ [Y5: complex] :
% 3.82/4.06 ( groups2073611262835488442omplex
% 3.82/4.06 @ ^ [X4: nat] : ( G @ X4 @ Y5 )
% 3.82/4.06 @ ( collect_nat
% 3.82/4.06 @ ^ [X4: nat] :
% 3.82/4.06 ( ( member_nat @ X4 @ A2 )
% 3.82/4.06 & ( R @ X4 @ Y5 ) ) ) )
% 3.82/4.06 @ B ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.swap_restrict
% 3.82/4.06 thf(fact_5205_sum__nonpos,axiom,
% 3.82/4.06 ! [A2: set_Extended_enat,F: extended_enat > extended_enat] :
% 3.82/4.06 ( ! [X5: extended_enat] :
% 3.82/4.06 ( ( member_Extended_enat @ X5 @ A2 )
% 3.82/4.06 => ( ord_le2932123472753598470d_enat @ ( F @ X5 ) @ zero_z5237406670263579293d_enat ) )
% 3.82/4.06 => ( ord_le2932123472753598470d_enat @ ( groups2433450451889696826d_enat @ F @ A2 ) @ zero_z5237406670263579293d_enat ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum_nonpos
% 3.82/4.06 thf(fact_5206_sum__nonpos,axiom,
% 3.82/4.06 ! [A2: set_real,F: real > extended_enat] :
% 3.82/4.06 ( ! [X5: real] :
% 3.82/4.06 ( ( member_real @ X5 @ A2 )
% 3.82/4.06 => ( ord_le2932123472753598470d_enat @ ( F @ X5 ) @ zero_z5237406670263579293d_enat ) )
% 3.82/4.06 => ( ord_le2932123472753598470d_enat @ ( groups2800946370649118462d_enat @ F @ A2 ) @ zero_z5237406670263579293d_enat ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum_nonpos
% 3.82/4.06 thf(fact_5207_sum__nonpos,axiom,
% 3.82/4.06 ! [A2: set_nat,F: nat > extended_enat] :
% 3.82/4.06 ( ! [X5: nat] :
% 3.82/4.06 ( ( member_nat @ X5 @ A2 )
% 3.82/4.06 => ( ord_le2932123472753598470d_enat @ ( F @ X5 ) @ zero_z5237406670263579293d_enat ) )
% 3.82/4.06 => ( ord_le2932123472753598470d_enat @ ( groups7108830773950497114d_enat @ F @ A2 ) @ zero_z5237406670263579293d_enat ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum_nonpos
% 3.82/4.06 thf(fact_5208_sum__nonpos,axiom,
% 3.82/4.06 ! [A2: set_int,F: int > extended_enat] :
% 3.82/4.06 ( ! [X5: int] :
% 3.82/4.06 ( ( member_int @ X5 @ A2 )
% 3.82/4.06 => ( ord_le2932123472753598470d_enat @ ( F @ X5 ) @ zero_z5237406670263579293d_enat ) )
% 3.82/4.06 => ( ord_le2932123472753598470d_enat @ ( groups4225252721152677374d_enat @ F @ A2 ) @ zero_z5237406670263579293d_enat ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum_nonpos
% 3.82/4.06 thf(fact_5209_sum__nonpos,axiom,
% 3.82/4.06 ! [A2: set_Extended_enat,F: extended_enat > real] :
% 3.82/4.06 ( ! [X5: extended_enat] :
% 3.82/4.06 ( ( member_Extended_enat @ X5 @ A2 )
% 3.82/4.06 => ( ord_less_eq_real @ ( F @ X5 ) @ zero_zero_real ) )
% 3.82/4.06 => ( ord_less_eq_real @ ( groups4148127829035722712t_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum_nonpos
% 3.82/4.06 thf(fact_5210_sum__nonpos,axiom,
% 3.82/4.06 ! [A2: set_real,F: real > real] :
% 3.82/4.06 ( ! [X5: real] :
% 3.82/4.06 ( ( member_real @ X5 @ A2 )
% 3.82/4.06 => ( ord_less_eq_real @ ( F @ X5 ) @ zero_zero_real ) )
% 3.82/4.06 => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum_nonpos
% 3.82/4.06 thf(fact_5211_sum__nonpos,axiom,
% 3.82/4.06 ! [A2: set_int,F: int > real] :
% 3.82/4.06 ( ! [X5: int] :
% 3.82/4.06 ( ( member_int @ X5 @ A2 )
% 3.82/4.06 => ( ord_less_eq_real @ ( F @ X5 ) @ zero_zero_real ) )
% 3.82/4.06 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum_nonpos
% 3.82/4.06 thf(fact_5212_sum__nonpos,axiom,
% 3.82/4.06 ! [A2: set_Extended_enat,F: extended_enat > nat] :
% 3.82/4.06 ( ! [X5: extended_enat] :
% 3.82/4.06 ( ( member_Extended_enat @ X5 @ A2 )
% 3.82/4.06 => ( ord_less_eq_nat @ ( F @ X5 ) @ zero_zero_nat ) )
% 3.82/4.06 => ( ord_less_eq_nat @ ( groups2027974829824023292at_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum_nonpos
% 3.82/4.06 thf(fact_5213_sum__nonpos,axiom,
% 3.82/4.06 ! [A2: set_real,F: real > nat] :
% 3.82/4.06 ( ! [X5: real] :
% 3.82/4.06 ( ( member_real @ X5 @ A2 )
% 3.82/4.06 => ( ord_less_eq_nat @ ( F @ X5 ) @ zero_zero_nat ) )
% 3.82/4.06 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum_nonpos
% 3.82/4.06 thf(fact_5214_sum__nonpos,axiom,
% 3.82/4.06 ! [A2: set_int,F: int > nat] :
% 3.82/4.06 ( ! [X5: int] :
% 3.82/4.06 ( ( member_int @ X5 @ A2 )
% 3.82/4.06 => ( ord_less_eq_nat @ ( F @ X5 ) @ zero_zero_nat ) )
% 3.82/4.06 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum_nonpos
% 3.82/4.06 thf(fact_5215_sum__nonneg,axiom,
% 3.82/4.06 ! [A2: set_Extended_enat,F: extended_enat > extended_enat] :
% 3.82/4.06 ( ! [X5: extended_enat] :
% 3.82/4.06 ( ( member_Extended_enat @ X5 @ A2 )
% 3.82/4.06 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ X5 ) ) )
% 3.82/4.06 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( groups2433450451889696826d_enat @ F @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum_nonneg
% 3.82/4.06 thf(fact_5216_sum__nonneg,axiom,
% 3.82/4.06 ! [A2: set_real,F: real > extended_enat] :
% 3.82/4.06 ( ! [X5: real] :
% 3.82/4.06 ( ( member_real @ X5 @ A2 )
% 3.82/4.06 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ X5 ) ) )
% 3.82/4.06 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( groups2800946370649118462d_enat @ F @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum_nonneg
% 3.82/4.06 thf(fact_5217_sum__nonneg,axiom,
% 3.82/4.06 ! [A2: set_nat,F: nat > extended_enat] :
% 3.82/4.06 ( ! [X5: nat] :
% 3.82/4.06 ( ( member_nat @ X5 @ A2 )
% 3.82/4.06 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ X5 ) ) )
% 3.82/4.06 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( groups7108830773950497114d_enat @ F @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum_nonneg
% 3.82/4.06 thf(fact_5218_sum__nonneg,axiom,
% 3.82/4.06 ! [A2: set_int,F: int > extended_enat] :
% 3.82/4.06 ( ! [X5: int] :
% 3.82/4.06 ( ( member_int @ X5 @ A2 )
% 3.82/4.06 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ X5 ) ) )
% 3.82/4.06 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( groups4225252721152677374d_enat @ F @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum_nonneg
% 3.82/4.06 thf(fact_5219_sum__nonneg,axiom,
% 3.82/4.06 ! [A2: set_Extended_enat,F: extended_enat > real] :
% 3.82/4.06 ( ! [X5: extended_enat] :
% 3.82/4.06 ( ( member_Extended_enat @ X5 @ A2 )
% 3.82/4.06 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 3.82/4.06 => ( ord_less_eq_real @ zero_zero_real @ ( groups4148127829035722712t_real @ F @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum_nonneg
% 3.82/4.06 thf(fact_5220_sum__nonneg,axiom,
% 3.82/4.06 ! [A2: set_real,F: real > real] :
% 3.82/4.06 ( ! [X5: real] :
% 3.82/4.06 ( ( member_real @ X5 @ A2 )
% 3.82/4.06 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 3.82/4.06 => ( ord_less_eq_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum_nonneg
% 3.82/4.06 thf(fact_5221_sum__nonneg,axiom,
% 3.82/4.06 ! [A2: set_int,F: int > real] :
% 3.82/4.06 ( ! [X5: int] :
% 3.82/4.06 ( ( member_int @ X5 @ A2 )
% 3.82/4.06 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 3.82/4.06 => ( ord_less_eq_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum_nonneg
% 3.82/4.06 thf(fact_5222_sum__nonneg,axiom,
% 3.82/4.06 ! [A2: set_Extended_enat,F: extended_enat > nat] :
% 3.82/4.06 ( ! [X5: extended_enat] :
% 3.82/4.06 ( ( member_Extended_enat @ X5 @ A2 )
% 3.82/4.06 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) ) )
% 3.82/4.06 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups2027974829824023292at_nat @ F @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum_nonneg
% 3.82/4.06 thf(fact_5223_sum__nonneg,axiom,
% 3.82/4.06 ! [A2: set_real,F: real > nat] :
% 3.82/4.06 ( ! [X5: real] :
% 3.82/4.06 ( ( member_real @ X5 @ A2 )
% 3.82/4.06 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) ) )
% 3.82/4.06 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum_nonneg
% 3.82/4.06 thf(fact_5224_sum__nonneg,axiom,
% 3.82/4.06 ! [A2: set_int,F: int > nat] :
% 3.82/4.06 ( ! [X5: int] :
% 3.82/4.06 ( ( member_int @ X5 @ A2 )
% 3.82/4.06 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) ) )
% 3.82/4.06 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum_nonneg
% 3.82/4.06 thf(fact_5225_sum__mono__inv,axiom,
% 3.82/4.06 ! [F: real > real,I6: set_real,G: real > real,I: real] :
% 3.82/4.06 ( ( ( groups8097168146408367636l_real @ F @ I6 )
% 3.82/4.06 = ( groups8097168146408367636l_real @ G @ I6 ) )
% 3.82/4.06 => ( ! [I4: real] :
% 3.82/4.06 ( ( member_real @ I4 @ I6 )
% 3.82/4.06 => ( ord_less_eq_real @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 3.82/4.06 => ( ( member_real @ I @ I6 )
% 3.82/4.06 => ( ( finite_finite_real @ I6 )
% 3.82/4.06 => ( ( F @ I )
% 3.82/4.06 = ( G @ I ) ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum_mono_inv
% 3.82/4.06 thf(fact_5226_sum__mono__inv,axiom,
% 3.82/4.06 ! [F: complex > real,I6: set_complex,G: complex > real,I: complex] :
% 3.82/4.06 ( ( ( groups5808333547571424918x_real @ F @ I6 )
% 3.82/4.06 = ( groups5808333547571424918x_real @ G @ I6 ) )
% 3.82/4.06 => ( ! [I4: complex] :
% 3.82/4.06 ( ( member_complex @ I4 @ I6 )
% 3.82/4.06 => ( ord_less_eq_real @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 3.82/4.06 => ( ( member_complex @ I @ I6 )
% 3.82/4.06 => ( ( finite3207457112153483333omplex @ I6 )
% 3.82/4.06 => ( ( F @ I )
% 3.82/4.06 = ( G @ I ) ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum_mono_inv
% 3.82/4.06 thf(fact_5227_sum__mono__inv,axiom,
% 3.82/4.06 ! [F: int > real,I6: set_int,G: int > real,I: int] :
% 3.82/4.06 ( ( ( groups8778361861064173332t_real @ F @ I6 )
% 3.82/4.06 = ( groups8778361861064173332t_real @ G @ I6 ) )
% 3.82/4.06 => ( ! [I4: int] :
% 3.82/4.06 ( ( member_int @ I4 @ I6 )
% 3.82/4.06 => ( ord_less_eq_real @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 3.82/4.06 => ( ( member_int @ I @ I6 )
% 3.82/4.06 => ( ( finite_finite_int @ I6 )
% 3.82/4.06 => ( ( F @ I )
% 3.82/4.06 = ( G @ I ) ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum_mono_inv
% 3.82/4.06 thf(fact_5228_sum__mono__inv,axiom,
% 3.82/4.06 ! [F: extended_enat > real,I6: set_Extended_enat,G: extended_enat > real,I: extended_enat] :
% 3.82/4.06 ( ( ( groups4148127829035722712t_real @ F @ I6 )
% 3.82/4.06 = ( groups4148127829035722712t_real @ G @ I6 ) )
% 3.82/4.06 => ( ! [I4: extended_enat] :
% 3.82/4.06 ( ( member_Extended_enat @ I4 @ I6 )
% 3.82/4.06 => ( ord_less_eq_real @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 3.82/4.06 => ( ( member_Extended_enat @ I @ I6 )
% 3.82/4.06 => ( ( finite4001608067531595151d_enat @ I6 )
% 3.82/4.06 => ( ( F @ I )
% 3.82/4.06 = ( G @ I ) ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum_mono_inv
% 3.82/4.06 thf(fact_5229_sum__mono__inv,axiom,
% 3.82/4.06 ! [F: real > nat,I6: set_real,G: real > nat,I: real] :
% 3.82/4.06 ( ( ( groups1935376822645274424al_nat @ F @ I6 )
% 3.82/4.06 = ( groups1935376822645274424al_nat @ G @ I6 ) )
% 3.82/4.06 => ( ! [I4: real] :
% 3.82/4.06 ( ( member_real @ I4 @ I6 )
% 3.82/4.06 => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 3.82/4.06 => ( ( member_real @ I @ I6 )
% 3.82/4.06 => ( ( finite_finite_real @ I6 )
% 3.82/4.06 => ( ( F @ I )
% 3.82/4.06 = ( G @ I ) ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum_mono_inv
% 3.82/4.06 thf(fact_5230_sum__mono__inv,axiom,
% 3.82/4.06 ! [F: complex > nat,I6: set_complex,G: complex > nat,I: complex] :
% 3.82/4.06 ( ( ( groups5693394587270226106ex_nat @ F @ I6 )
% 3.82/4.06 = ( groups5693394587270226106ex_nat @ G @ I6 ) )
% 3.82/4.06 => ( ! [I4: complex] :
% 3.82/4.06 ( ( member_complex @ I4 @ I6 )
% 3.82/4.06 => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 3.82/4.06 => ( ( member_complex @ I @ I6 )
% 3.82/4.06 => ( ( finite3207457112153483333omplex @ I6 )
% 3.82/4.06 => ( ( F @ I )
% 3.82/4.06 = ( G @ I ) ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum_mono_inv
% 3.82/4.06 thf(fact_5231_sum__mono__inv,axiom,
% 3.82/4.06 ! [F: int > nat,I6: set_int,G: int > nat,I: int] :
% 3.82/4.06 ( ( ( groups4541462559716669496nt_nat @ F @ I6 )
% 3.82/4.06 = ( groups4541462559716669496nt_nat @ G @ I6 ) )
% 3.82/4.06 => ( ! [I4: int] :
% 3.82/4.06 ( ( member_int @ I4 @ I6 )
% 3.82/4.06 => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 3.82/4.06 => ( ( member_int @ I @ I6 )
% 3.82/4.06 => ( ( finite_finite_int @ I6 )
% 3.82/4.06 => ( ( F @ I )
% 3.82/4.06 = ( G @ I ) ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum_mono_inv
% 3.82/4.06 thf(fact_5232_sum__mono__inv,axiom,
% 3.82/4.06 ! [F: extended_enat > nat,I6: set_Extended_enat,G: extended_enat > nat,I: extended_enat] :
% 3.82/4.06 ( ( ( groups2027974829824023292at_nat @ F @ I6 )
% 3.82/4.06 = ( groups2027974829824023292at_nat @ G @ I6 ) )
% 3.82/4.06 => ( ! [I4: extended_enat] :
% 3.82/4.06 ( ( member_Extended_enat @ I4 @ I6 )
% 3.82/4.06 => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 3.82/4.06 => ( ( member_Extended_enat @ I @ I6 )
% 3.82/4.06 => ( ( finite4001608067531595151d_enat @ I6 )
% 3.82/4.06 => ( ( F @ I )
% 3.82/4.06 = ( G @ I ) ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum_mono_inv
% 3.82/4.06 thf(fact_5233_sum__mono__inv,axiom,
% 3.82/4.06 ! [F: real > int,I6: set_real,G: real > int,I: real] :
% 3.82/4.06 ( ( ( groups1932886352136224148al_int @ F @ I6 )
% 3.82/4.06 = ( groups1932886352136224148al_int @ G @ I6 ) )
% 3.82/4.06 => ( ! [I4: real] :
% 3.82/4.06 ( ( member_real @ I4 @ I6 )
% 3.82/4.06 => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 3.82/4.06 => ( ( member_real @ I @ I6 )
% 3.82/4.06 => ( ( finite_finite_real @ I6 )
% 3.82/4.06 => ( ( F @ I )
% 3.82/4.06 = ( G @ I ) ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum_mono_inv
% 3.82/4.06 thf(fact_5234_sum__mono__inv,axiom,
% 3.82/4.06 ! [F: nat > int,I6: set_nat,G: nat > int,I: nat] :
% 3.82/4.06 ( ( ( groups3539618377306564664at_int @ F @ I6 )
% 3.82/4.06 = ( groups3539618377306564664at_int @ G @ I6 ) )
% 3.82/4.06 => ( ! [I4: nat] :
% 3.82/4.06 ( ( member_nat @ I4 @ I6 )
% 3.82/4.06 => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 3.82/4.06 => ( ( member_nat @ I @ I6 )
% 3.82/4.06 => ( ( finite_finite_nat @ I6 )
% 3.82/4.06 => ( ( F @ I )
% 3.82/4.06 = ( G @ I ) ) ) ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum_mono_inv
% 3.82/4.06 thf(fact_5235_sum_Ointer__filter,axiom,
% 3.82/4.06 ! [A2: set_real,G: real > nat,P: real > $o] :
% 3.82/4.06 ( ( finite_finite_real @ A2 )
% 3.82/4.06 => ( ( groups1935376822645274424al_nat @ G
% 3.82/4.06 @ ( collect_real
% 3.82/4.06 @ ^ [X4: real] :
% 3.82/4.06 ( ( member_real @ X4 @ A2 )
% 3.82/4.06 & ( P @ X4 ) ) ) )
% 3.82/4.06 = ( groups1935376822645274424al_nat
% 3.82/4.06 @ ^ [X4: real] : ( if_nat @ ( P @ X4 ) @ ( G @ X4 ) @ zero_zero_nat )
% 3.82/4.06 @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.inter_filter
% 3.82/4.06 thf(fact_5236_sum_Ointer__filter,axiom,
% 3.82/4.06 ! [A2: set_complex,G: complex > nat,P: complex > $o] :
% 3.82/4.06 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.06 => ( ( groups5693394587270226106ex_nat @ G
% 3.82/4.06 @ ( collect_complex
% 3.82/4.06 @ ^ [X4: complex] :
% 3.82/4.06 ( ( member_complex @ X4 @ A2 )
% 3.82/4.06 & ( P @ X4 ) ) ) )
% 3.82/4.06 = ( groups5693394587270226106ex_nat
% 3.82/4.06 @ ^ [X4: complex] : ( if_nat @ ( P @ X4 ) @ ( G @ X4 ) @ zero_zero_nat )
% 3.82/4.06 @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.inter_filter
% 3.82/4.06 thf(fact_5237_sum_Ointer__filter,axiom,
% 3.82/4.06 ! [A2: set_int,G: int > nat,P: int > $o] :
% 3.82/4.06 ( ( finite_finite_int @ A2 )
% 3.82/4.06 => ( ( groups4541462559716669496nt_nat @ G
% 3.82/4.06 @ ( collect_int
% 3.82/4.06 @ ^ [X4: int] :
% 3.82/4.06 ( ( member_int @ X4 @ A2 )
% 3.82/4.06 & ( P @ X4 ) ) ) )
% 3.82/4.06 = ( groups4541462559716669496nt_nat
% 3.82/4.06 @ ^ [X4: int] : ( if_nat @ ( P @ X4 ) @ ( G @ X4 ) @ zero_zero_nat )
% 3.82/4.06 @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.inter_filter
% 3.82/4.06 thf(fact_5238_sum_Ointer__filter,axiom,
% 3.82/4.06 ! [A2: set_Extended_enat,G: extended_enat > nat,P: extended_enat > $o] :
% 3.82/4.06 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.06 => ( ( groups2027974829824023292at_nat @ G
% 3.82/4.06 @ ( collec4429806609662206161d_enat
% 3.82/4.06 @ ^ [X4: extended_enat] :
% 3.82/4.06 ( ( member_Extended_enat @ X4 @ A2 )
% 3.82/4.06 & ( P @ X4 ) ) ) )
% 3.82/4.06 = ( groups2027974829824023292at_nat
% 3.82/4.06 @ ^ [X4: extended_enat] : ( if_nat @ ( P @ X4 ) @ ( G @ X4 ) @ zero_zero_nat )
% 3.82/4.06 @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.inter_filter
% 3.82/4.06 thf(fact_5239_sum_Ointer__filter,axiom,
% 3.82/4.06 ! [A2: set_real,G: real > real,P: real > $o] :
% 3.82/4.06 ( ( finite_finite_real @ A2 )
% 3.82/4.06 => ( ( groups8097168146408367636l_real @ G
% 3.82/4.06 @ ( collect_real
% 3.82/4.06 @ ^ [X4: real] :
% 3.82/4.06 ( ( member_real @ X4 @ A2 )
% 3.82/4.06 & ( P @ X4 ) ) ) )
% 3.82/4.06 = ( groups8097168146408367636l_real
% 3.82/4.06 @ ^ [X4: real] : ( if_real @ ( P @ X4 ) @ ( G @ X4 ) @ zero_zero_real )
% 3.82/4.06 @ A2 ) ) ) ).
% 3.82/4.06
% 3.82/4.06 % sum.inter_filter
% 3.82/4.06 thf(fact_5240_sum_Ointer__filter,axiom,
% 3.82/4.06 ! [A2: set_complex,G: complex > real,P: complex > $o] :
% 3.82/4.06 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.06 => ( ( groups5808333547571424918x_real @ G
% 3.82/4.07 @ ( collect_complex
% 3.82/4.07 @ ^ [X4: complex] :
% 3.82/4.07 ( ( member_complex @ X4 @ A2 )
% 3.82/4.07 & ( P @ X4 ) ) ) )
% 3.82/4.07 = ( groups5808333547571424918x_real
% 3.82/4.07 @ ^ [X4: complex] : ( if_real @ ( P @ X4 ) @ ( G @ X4 ) @ zero_zero_real )
% 3.82/4.07 @ A2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.inter_filter
% 3.82/4.07 thf(fact_5241_sum_Ointer__filter,axiom,
% 3.82/4.07 ! [A2: set_int,G: int > real,P: int > $o] :
% 3.82/4.07 ( ( finite_finite_int @ A2 )
% 3.82/4.07 => ( ( groups8778361861064173332t_real @ G
% 3.82/4.07 @ ( collect_int
% 3.82/4.07 @ ^ [X4: int] :
% 3.82/4.07 ( ( member_int @ X4 @ A2 )
% 3.82/4.07 & ( P @ X4 ) ) ) )
% 3.82/4.07 = ( groups8778361861064173332t_real
% 3.82/4.07 @ ^ [X4: int] : ( if_real @ ( P @ X4 ) @ ( G @ X4 ) @ zero_zero_real )
% 3.82/4.07 @ A2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.inter_filter
% 3.82/4.07 thf(fact_5242_sum_Ointer__filter,axiom,
% 3.82/4.07 ! [A2: set_Extended_enat,G: extended_enat > real,P: extended_enat > $o] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.07 => ( ( groups4148127829035722712t_real @ G
% 3.82/4.07 @ ( collec4429806609662206161d_enat
% 3.82/4.07 @ ^ [X4: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ X4 @ A2 )
% 3.82/4.07 & ( P @ X4 ) ) ) )
% 3.82/4.07 = ( groups4148127829035722712t_real
% 3.82/4.07 @ ^ [X4: extended_enat] : ( if_real @ ( P @ X4 ) @ ( G @ X4 ) @ zero_zero_real )
% 3.82/4.07 @ A2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.inter_filter
% 3.82/4.07 thf(fact_5243_sum_Ointer__filter,axiom,
% 3.82/4.07 ! [A2: set_real,G: real > int,P: real > $o] :
% 3.82/4.07 ( ( finite_finite_real @ A2 )
% 3.82/4.07 => ( ( groups1932886352136224148al_int @ G
% 3.82/4.07 @ ( collect_real
% 3.82/4.07 @ ^ [X4: real] :
% 3.82/4.07 ( ( member_real @ X4 @ A2 )
% 3.82/4.07 & ( P @ X4 ) ) ) )
% 3.82/4.07 = ( groups1932886352136224148al_int
% 3.82/4.07 @ ^ [X4: real] : ( if_int @ ( P @ X4 ) @ ( G @ X4 ) @ zero_zero_int )
% 3.82/4.07 @ A2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.inter_filter
% 3.82/4.07 thf(fact_5244_sum_Ointer__filter,axiom,
% 3.82/4.07 ! [A2: set_nat,G: nat > int,P: nat > $o] :
% 3.82/4.07 ( ( finite_finite_nat @ A2 )
% 3.82/4.07 => ( ( groups3539618377306564664at_int @ G
% 3.82/4.07 @ ( collect_nat
% 3.82/4.07 @ ^ [X4: nat] :
% 3.82/4.07 ( ( member_nat @ X4 @ A2 )
% 3.82/4.07 & ( P @ X4 ) ) ) )
% 3.82/4.07 = ( groups3539618377306564664at_int
% 3.82/4.07 @ ^ [X4: nat] : ( if_int @ ( P @ X4 ) @ ( G @ X4 ) @ zero_zero_int )
% 3.82/4.07 @ A2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.inter_filter
% 3.82/4.07 thf(fact_5245_sum__nonneg__eq__0__iff,axiom,
% 3.82/4.07 ! [A2: set_real,F: real > extended_enat] :
% 3.82/4.07 ( ( finite_finite_real @ A2 )
% 3.82/4.07 => ( ! [X5: real] :
% 3.82/4.07 ( ( member_real @ X5 @ A2 )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ X5 ) ) )
% 3.82/4.07 => ( ( ( groups2800946370649118462d_enat @ F @ A2 )
% 3.82/4.07 = zero_z5237406670263579293d_enat )
% 3.82/4.07 = ( ! [X4: real] :
% 3.82/4.07 ( ( member_real @ X4 @ A2 )
% 3.82/4.07 => ( ( F @ X4 )
% 3.82/4.07 = zero_z5237406670263579293d_enat ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_nonneg_eq_0_iff
% 3.82/4.07 thf(fact_5246_sum__nonneg__eq__0__iff,axiom,
% 3.82/4.07 ! [A2: set_nat,F: nat > extended_enat] :
% 3.82/4.07 ( ( finite_finite_nat @ A2 )
% 3.82/4.07 => ( ! [X5: nat] :
% 3.82/4.07 ( ( member_nat @ X5 @ A2 )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ X5 ) ) )
% 3.82/4.07 => ( ( ( groups7108830773950497114d_enat @ F @ A2 )
% 3.82/4.07 = zero_z5237406670263579293d_enat )
% 3.82/4.07 = ( ! [X4: nat] :
% 3.82/4.07 ( ( member_nat @ X4 @ A2 )
% 3.82/4.07 => ( ( F @ X4 )
% 3.82/4.07 = zero_z5237406670263579293d_enat ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_nonneg_eq_0_iff
% 3.82/4.07 thf(fact_5247_sum__nonneg__eq__0__iff,axiom,
% 3.82/4.07 ! [A2: set_complex,F: complex > extended_enat] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.07 => ( ! [X5: complex] :
% 3.82/4.07 ( ( member_complex @ X5 @ A2 )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ X5 ) ) )
% 3.82/4.07 => ( ( ( groups1752964319039525884d_enat @ F @ A2 )
% 3.82/4.07 = zero_z5237406670263579293d_enat )
% 3.82/4.07 = ( ! [X4: complex] :
% 3.82/4.07 ( ( member_complex @ X4 @ A2 )
% 3.82/4.07 => ( ( F @ X4 )
% 3.82/4.07 = zero_z5237406670263579293d_enat ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_nonneg_eq_0_iff
% 3.82/4.07 thf(fact_5248_sum__nonneg__eq__0__iff,axiom,
% 3.82/4.07 ! [A2: set_int,F: int > extended_enat] :
% 3.82/4.07 ( ( finite_finite_int @ A2 )
% 3.82/4.07 => ( ! [X5: int] :
% 3.82/4.07 ( ( member_int @ X5 @ A2 )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ X5 ) ) )
% 3.82/4.07 => ( ( ( groups4225252721152677374d_enat @ F @ A2 )
% 3.82/4.07 = zero_z5237406670263579293d_enat )
% 3.82/4.07 = ( ! [X4: int] :
% 3.82/4.07 ( ( member_int @ X4 @ A2 )
% 3.82/4.07 => ( ( F @ X4 )
% 3.82/4.07 = zero_z5237406670263579293d_enat ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_nonneg_eq_0_iff
% 3.82/4.07 thf(fact_5249_sum__nonneg__eq__0__iff,axiom,
% 3.82/4.07 ! [A2: set_Extended_enat,F: extended_enat > extended_enat] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.07 => ( ! [X5: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ X5 @ A2 )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ X5 ) ) )
% 3.82/4.07 => ( ( ( groups2433450451889696826d_enat @ F @ A2 )
% 3.82/4.07 = zero_z5237406670263579293d_enat )
% 3.82/4.07 = ( ! [X4: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ X4 @ A2 )
% 3.82/4.07 => ( ( F @ X4 )
% 3.82/4.07 = zero_z5237406670263579293d_enat ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_nonneg_eq_0_iff
% 3.82/4.07 thf(fact_5250_sum__nonneg__eq__0__iff,axiom,
% 3.82/4.07 ! [A2: set_real,F: real > real] :
% 3.82/4.07 ( ( finite_finite_real @ A2 )
% 3.82/4.07 => ( ! [X5: real] :
% 3.82/4.07 ( ( member_real @ X5 @ A2 )
% 3.82/4.07 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 3.82/4.07 => ( ( ( groups8097168146408367636l_real @ F @ A2 )
% 3.82/4.07 = zero_zero_real )
% 3.82/4.07 = ( ! [X4: real] :
% 3.82/4.07 ( ( member_real @ X4 @ A2 )
% 3.82/4.07 => ( ( F @ X4 )
% 3.82/4.07 = zero_zero_real ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_nonneg_eq_0_iff
% 3.82/4.07 thf(fact_5251_sum__nonneg__eq__0__iff,axiom,
% 3.82/4.07 ! [A2: set_complex,F: complex > real] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.07 => ( ! [X5: complex] :
% 3.82/4.07 ( ( member_complex @ X5 @ A2 )
% 3.82/4.07 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 3.82/4.07 => ( ( ( groups5808333547571424918x_real @ F @ A2 )
% 3.82/4.07 = zero_zero_real )
% 3.82/4.07 = ( ! [X4: complex] :
% 3.82/4.07 ( ( member_complex @ X4 @ A2 )
% 3.82/4.07 => ( ( F @ X4 )
% 3.82/4.07 = zero_zero_real ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_nonneg_eq_0_iff
% 3.82/4.07 thf(fact_5252_sum__nonneg__eq__0__iff,axiom,
% 3.82/4.07 ! [A2: set_int,F: int > real] :
% 3.82/4.07 ( ( finite_finite_int @ A2 )
% 3.82/4.07 => ( ! [X5: int] :
% 3.82/4.07 ( ( member_int @ X5 @ A2 )
% 3.82/4.07 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 3.82/4.07 => ( ( ( groups8778361861064173332t_real @ F @ A2 )
% 3.82/4.07 = zero_zero_real )
% 3.82/4.07 = ( ! [X4: int] :
% 3.82/4.07 ( ( member_int @ X4 @ A2 )
% 3.82/4.07 => ( ( F @ X4 )
% 3.82/4.07 = zero_zero_real ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_nonneg_eq_0_iff
% 3.82/4.07 thf(fact_5253_sum__nonneg__eq__0__iff,axiom,
% 3.82/4.07 ! [A2: set_Extended_enat,F: extended_enat > real] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.07 => ( ! [X5: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ X5 @ A2 )
% 3.82/4.07 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 3.82/4.07 => ( ( ( groups4148127829035722712t_real @ F @ A2 )
% 3.82/4.07 = zero_zero_real )
% 3.82/4.07 = ( ! [X4: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ X4 @ A2 )
% 3.82/4.07 => ( ( F @ X4 )
% 3.82/4.07 = zero_zero_real ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_nonneg_eq_0_iff
% 3.82/4.07 thf(fact_5254_sum__nonneg__eq__0__iff,axiom,
% 3.82/4.07 ! [A2: set_real,F: real > nat] :
% 3.82/4.07 ( ( finite_finite_real @ A2 )
% 3.82/4.07 => ( ! [X5: real] :
% 3.82/4.07 ( ( member_real @ X5 @ A2 )
% 3.82/4.07 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) ) )
% 3.82/4.07 => ( ( ( groups1935376822645274424al_nat @ F @ A2 )
% 3.82/4.07 = zero_zero_nat )
% 3.82/4.07 = ( ! [X4: real] :
% 3.82/4.07 ( ( member_real @ X4 @ A2 )
% 3.82/4.07 => ( ( F @ X4 )
% 3.82/4.07 = zero_zero_nat ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_nonneg_eq_0_iff
% 3.82/4.07 thf(fact_5255_sum__le__included,axiom,
% 3.82/4.07 ! [S: set_nat,T: set_nat,G: nat > extended_enat,I: nat > nat,F: nat > extended_enat] :
% 3.82/4.07 ( ( finite_finite_nat @ S )
% 3.82/4.07 => ( ( finite_finite_nat @ T )
% 3.82/4.07 => ( ! [X5: nat] :
% 3.82/4.07 ( ( member_nat @ X5 @ T )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( G @ X5 ) ) )
% 3.82/4.07 => ( ! [X5: nat] :
% 3.82/4.07 ( ( member_nat @ X5 @ S )
% 3.82/4.07 => ? [Xa: nat] :
% 3.82/4.07 ( ( member_nat @ Xa @ T )
% 3.82/4.07 & ( ( I @ Xa )
% 3.82/4.07 = X5 )
% 3.82/4.07 & ( ord_le2932123472753598470d_enat @ ( F @ X5 ) @ ( G @ Xa ) ) ) )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ ( groups7108830773950497114d_enat @ F @ S ) @ ( groups7108830773950497114d_enat @ G @ T ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_le_included
% 3.82/4.07 thf(fact_5256_sum__le__included,axiom,
% 3.82/4.07 ! [S: set_nat,T: set_complex,G: complex > extended_enat,I: complex > nat,F: nat > extended_enat] :
% 3.82/4.07 ( ( finite_finite_nat @ S )
% 3.82/4.07 => ( ( finite3207457112153483333omplex @ T )
% 3.82/4.07 => ( ! [X5: complex] :
% 3.82/4.07 ( ( member_complex @ X5 @ T )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( G @ X5 ) ) )
% 3.82/4.07 => ( ! [X5: nat] :
% 3.82/4.07 ( ( member_nat @ X5 @ S )
% 3.82/4.07 => ? [Xa: complex] :
% 3.82/4.07 ( ( member_complex @ Xa @ T )
% 3.82/4.07 & ( ( I @ Xa )
% 3.82/4.07 = X5 )
% 3.82/4.07 & ( ord_le2932123472753598470d_enat @ ( F @ X5 ) @ ( G @ Xa ) ) ) )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ ( groups7108830773950497114d_enat @ F @ S ) @ ( groups1752964319039525884d_enat @ G @ T ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_le_included
% 3.82/4.07 thf(fact_5257_sum__le__included,axiom,
% 3.82/4.07 ! [S: set_nat,T: set_int,G: int > extended_enat,I: int > nat,F: nat > extended_enat] :
% 3.82/4.07 ( ( finite_finite_nat @ S )
% 3.82/4.07 => ( ( finite_finite_int @ T )
% 3.82/4.07 => ( ! [X5: int] :
% 3.82/4.07 ( ( member_int @ X5 @ T )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( G @ X5 ) ) )
% 3.82/4.07 => ( ! [X5: nat] :
% 3.82/4.07 ( ( member_nat @ X5 @ S )
% 3.82/4.07 => ? [Xa: int] :
% 3.82/4.07 ( ( member_int @ Xa @ T )
% 3.82/4.07 & ( ( I @ Xa )
% 3.82/4.07 = X5 )
% 3.82/4.07 & ( ord_le2932123472753598470d_enat @ ( F @ X5 ) @ ( G @ Xa ) ) ) )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ ( groups7108830773950497114d_enat @ F @ S ) @ ( groups4225252721152677374d_enat @ G @ T ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_le_included
% 3.82/4.07 thf(fact_5258_sum__le__included,axiom,
% 3.82/4.07 ! [S: set_nat,T: set_Extended_enat,G: extended_enat > extended_enat,I: extended_enat > nat,F: nat > extended_enat] :
% 3.82/4.07 ( ( finite_finite_nat @ S )
% 3.82/4.07 => ( ( finite4001608067531595151d_enat @ T )
% 3.82/4.07 => ( ! [X5: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ X5 @ T )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( G @ X5 ) ) )
% 3.82/4.07 => ( ! [X5: nat] :
% 3.82/4.07 ( ( member_nat @ X5 @ S )
% 3.82/4.07 => ? [Xa: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ Xa @ T )
% 3.82/4.07 & ( ( I @ Xa )
% 3.82/4.07 = X5 )
% 3.82/4.07 & ( ord_le2932123472753598470d_enat @ ( F @ X5 ) @ ( G @ Xa ) ) ) )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ ( groups7108830773950497114d_enat @ F @ S ) @ ( groups2433450451889696826d_enat @ G @ T ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_le_included
% 3.82/4.07 thf(fact_5259_sum__le__included,axiom,
% 3.82/4.07 ! [S: set_complex,T: set_nat,G: nat > extended_enat,I: nat > complex,F: complex > extended_enat] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ S )
% 3.82/4.07 => ( ( finite_finite_nat @ T )
% 3.82/4.07 => ( ! [X5: nat] :
% 3.82/4.07 ( ( member_nat @ X5 @ T )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( G @ X5 ) ) )
% 3.82/4.07 => ( ! [X5: complex] :
% 3.82/4.07 ( ( member_complex @ X5 @ S )
% 3.82/4.07 => ? [Xa: nat] :
% 3.82/4.07 ( ( member_nat @ Xa @ T )
% 3.82/4.07 & ( ( I @ Xa )
% 3.82/4.07 = X5 )
% 3.82/4.07 & ( ord_le2932123472753598470d_enat @ ( F @ X5 ) @ ( G @ Xa ) ) ) )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ ( groups1752964319039525884d_enat @ F @ S ) @ ( groups7108830773950497114d_enat @ G @ T ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_le_included
% 3.82/4.07 thf(fact_5260_sum__le__included,axiom,
% 3.82/4.07 ! [S: set_complex,T: set_complex,G: complex > extended_enat,I: complex > complex,F: complex > extended_enat] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ S )
% 3.82/4.07 => ( ( finite3207457112153483333omplex @ T )
% 3.82/4.07 => ( ! [X5: complex] :
% 3.82/4.07 ( ( member_complex @ X5 @ T )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( G @ X5 ) ) )
% 3.82/4.07 => ( ! [X5: complex] :
% 3.82/4.07 ( ( member_complex @ X5 @ S )
% 3.82/4.07 => ? [Xa: complex] :
% 3.82/4.07 ( ( member_complex @ Xa @ T )
% 3.82/4.07 & ( ( I @ Xa )
% 3.82/4.07 = X5 )
% 3.82/4.07 & ( ord_le2932123472753598470d_enat @ ( F @ X5 ) @ ( G @ Xa ) ) ) )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ ( groups1752964319039525884d_enat @ F @ S ) @ ( groups1752964319039525884d_enat @ G @ T ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_le_included
% 3.82/4.07 thf(fact_5261_sum__le__included,axiom,
% 3.82/4.07 ! [S: set_complex,T: set_int,G: int > extended_enat,I: int > complex,F: complex > extended_enat] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ S )
% 3.82/4.07 => ( ( finite_finite_int @ T )
% 3.82/4.07 => ( ! [X5: int] :
% 3.82/4.07 ( ( member_int @ X5 @ T )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( G @ X5 ) ) )
% 3.82/4.07 => ( ! [X5: complex] :
% 3.82/4.07 ( ( member_complex @ X5 @ S )
% 3.82/4.07 => ? [Xa: int] :
% 3.82/4.07 ( ( member_int @ Xa @ T )
% 3.82/4.07 & ( ( I @ Xa )
% 3.82/4.07 = X5 )
% 3.82/4.07 & ( ord_le2932123472753598470d_enat @ ( F @ X5 ) @ ( G @ Xa ) ) ) )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ ( groups1752964319039525884d_enat @ F @ S ) @ ( groups4225252721152677374d_enat @ G @ T ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_le_included
% 3.82/4.07 thf(fact_5262_sum__le__included,axiom,
% 3.82/4.07 ! [S: set_complex,T: set_Extended_enat,G: extended_enat > extended_enat,I: extended_enat > complex,F: complex > extended_enat] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ S )
% 3.82/4.07 => ( ( finite4001608067531595151d_enat @ T )
% 3.82/4.07 => ( ! [X5: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ X5 @ T )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( G @ X5 ) ) )
% 3.82/4.07 => ( ! [X5: complex] :
% 3.82/4.07 ( ( member_complex @ X5 @ S )
% 3.82/4.07 => ? [Xa: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ Xa @ T )
% 3.82/4.07 & ( ( I @ Xa )
% 3.82/4.07 = X5 )
% 3.82/4.07 & ( ord_le2932123472753598470d_enat @ ( F @ X5 ) @ ( G @ Xa ) ) ) )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ ( groups1752964319039525884d_enat @ F @ S ) @ ( groups2433450451889696826d_enat @ G @ T ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_le_included
% 3.82/4.07 thf(fact_5263_sum__le__included,axiom,
% 3.82/4.07 ! [S: set_int,T: set_nat,G: nat > extended_enat,I: nat > int,F: int > extended_enat] :
% 3.82/4.07 ( ( finite_finite_int @ S )
% 3.82/4.07 => ( ( finite_finite_nat @ T )
% 3.82/4.07 => ( ! [X5: nat] :
% 3.82/4.07 ( ( member_nat @ X5 @ T )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( G @ X5 ) ) )
% 3.82/4.07 => ( ! [X5: int] :
% 3.82/4.07 ( ( member_int @ X5 @ S )
% 3.82/4.07 => ? [Xa: nat] :
% 3.82/4.07 ( ( member_nat @ Xa @ T )
% 3.82/4.07 & ( ( I @ Xa )
% 3.82/4.07 = X5 )
% 3.82/4.07 & ( ord_le2932123472753598470d_enat @ ( F @ X5 ) @ ( G @ Xa ) ) ) )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ ( groups4225252721152677374d_enat @ F @ S ) @ ( groups7108830773950497114d_enat @ G @ T ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_le_included
% 3.82/4.07 thf(fact_5264_sum__le__included,axiom,
% 3.82/4.07 ! [S: set_int,T: set_complex,G: complex > extended_enat,I: complex > int,F: int > extended_enat] :
% 3.82/4.07 ( ( finite_finite_int @ S )
% 3.82/4.07 => ( ( finite3207457112153483333omplex @ T )
% 3.82/4.07 => ( ! [X5: complex] :
% 3.82/4.07 ( ( member_complex @ X5 @ T )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( G @ X5 ) ) )
% 3.82/4.07 => ( ! [X5: int] :
% 3.82/4.07 ( ( member_int @ X5 @ S )
% 3.82/4.07 => ? [Xa: complex] :
% 3.82/4.07 ( ( member_complex @ Xa @ T )
% 3.82/4.07 & ( ( I @ Xa )
% 3.82/4.07 = X5 )
% 3.82/4.07 & ( ord_le2932123472753598470d_enat @ ( F @ X5 ) @ ( G @ Xa ) ) ) )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ ( groups4225252721152677374d_enat @ F @ S ) @ ( groups1752964319039525884d_enat @ G @ T ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_le_included
% 3.82/4.07 thf(fact_5265_sum__strict__mono__ex1,axiom,
% 3.82/4.07 ! [A2: set_complex,F: complex > real,G: complex > real] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.07 => ( ! [X5: complex] :
% 3.82/4.07 ( ( member_complex @ X5 @ A2 )
% 3.82/4.07 => ( ord_less_eq_real @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 3.82/4.07 => ( ? [X2: complex] :
% 3.82/4.07 ( ( member_complex @ X2 @ A2 )
% 3.82/4.07 & ( ord_less_real @ ( F @ X2 ) @ ( G @ X2 ) ) )
% 3.82/4.07 => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_strict_mono_ex1
% 3.82/4.07 thf(fact_5266_sum__strict__mono__ex1,axiom,
% 3.82/4.07 ! [A2: set_int,F: int > real,G: int > real] :
% 3.82/4.07 ( ( finite_finite_int @ A2 )
% 3.82/4.07 => ( ! [X5: int] :
% 3.82/4.07 ( ( member_int @ X5 @ A2 )
% 3.82/4.07 => ( ord_less_eq_real @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 3.82/4.07 => ( ? [X2: int] :
% 3.82/4.07 ( ( member_int @ X2 @ A2 )
% 3.82/4.07 & ( ord_less_real @ ( F @ X2 ) @ ( G @ X2 ) ) )
% 3.82/4.07 => ( ord_less_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( groups8778361861064173332t_real @ G @ A2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_strict_mono_ex1
% 3.82/4.07 thf(fact_5267_sum__strict__mono__ex1,axiom,
% 3.82/4.07 ! [A2: set_Extended_enat,F: extended_enat > real,G: extended_enat > real] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.07 => ( ! [X5: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ X5 @ A2 )
% 3.82/4.07 => ( ord_less_eq_real @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 3.82/4.07 => ( ? [X2: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ X2 @ A2 )
% 3.82/4.07 & ( ord_less_real @ ( F @ X2 ) @ ( G @ X2 ) ) )
% 3.82/4.07 => ( ord_less_real @ ( groups4148127829035722712t_real @ F @ A2 ) @ ( groups4148127829035722712t_real @ G @ A2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_strict_mono_ex1
% 3.82/4.07 thf(fact_5268_sum__strict__mono__ex1,axiom,
% 3.82/4.07 ! [A2: set_complex,F: complex > nat,G: complex > nat] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.07 => ( ! [X5: complex] :
% 3.82/4.07 ( ( member_complex @ X5 @ A2 )
% 3.82/4.07 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 3.82/4.07 => ( ? [X2: complex] :
% 3.82/4.07 ( ( member_complex @ X2 @ A2 )
% 3.82/4.07 & ( ord_less_nat @ ( F @ X2 ) @ ( G @ X2 ) ) )
% 3.82/4.07 => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_strict_mono_ex1
% 3.82/4.07 thf(fact_5269_sum__strict__mono__ex1,axiom,
% 3.82/4.07 ! [A2: set_int,F: int > nat,G: int > nat] :
% 3.82/4.07 ( ( finite_finite_int @ A2 )
% 3.82/4.07 => ( ! [X5: int] :
% 3.82/4.07 ( ( member_int @ X5 @ A2 )
% 3.82/4.07 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 3.82/4.07 => ( ? [X2: int] :
% 3.82/4.07 ( ( member_int @ X2 @ A2 )
% 3.82/4.07 & ( ord_less_nat @ ( F @ X2 ) @ ( G @ X2 ) ) )
% 3.82/4.07 => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_strict_mono_ex1
% 3.82/4.07 thf(fact_5270_sum__strict__mono__ex1,axiom,
% 3.82/4.07 ! [A2: set_Extended_enat,F: extended_enat > nat,G: extended_enat > nat] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.07 => ( ! [X5: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ X5 @ A2 )
% 3.82/4.07 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 3.82/4.07 => ( ? [X2: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ X2 @ A2 )
% 3.82/4.07 & ( ord_less_nat @ ( F @ X2 ) @ ( G @ X2 ) ) )
% 3.82/4.07 => ( ord_less_nat @ ( groups2027974829824023292at_nat @ F @ A2 ) @ ( groups2027974829824023292at_nat @ G @ A2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_strict_mono_ex1
% 3.82/4.07 thf(fact_5271_sum__strict__mono__ex1,axiom,
% 3.82/4.07 ! [A2: set_nat,F: nat > int,G: nat > int] :
% 3.82/4.07 ( ( finite_finite_nat @ A2 )
% 3.82/4.07 => ( ! [X5: nat] :
% 3.82/4.07 ( ( member_nat @ X5 @ A2 )
% 3.82/4.07 => ( ord_less_eq_int @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 3.82/4.07 => ( ? [X2: nat] :
% 3.82/4.07 ( ( member_nat @ X2 @ A2 )
% 3.82/4.07 & ( ord_less_int @ ( F @ X2 ) @ ( G @ X2 ) ) )
% 3.82/4.07 => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ A2 ) @ ( groups3539618377306564664at_int @ G @ A2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_strict_mono_ex1
% 3.82/4.07 thf(fact_5272_sum__strict__mono__ex1,axiom,
% 3.82/4.07 ! [A2: set_complex,F: complex > int,G: complex > int] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.07 => ( ! [X5: complex] :
% 3.82/4.07 ( ( member_complex @ X5 @ A2 )
% 3.82/4.07 => ( ord_less_eq_int @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 3.82/4.07 => ( ? [X2: complex] :
% 3.82/4.07 ( ( member_complex @ X2 @ A2 )
% 3.82/4.07 & ( ord_less_int @ ( F @ X2 ) @ ( G @ X2 ) ) )
% 3.82/4.07 => ( ord_less_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( groups5690904116761175830ex_int @ G @ A2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_strict_mono_ex1
% 3.82/4.07 thf(fact_5273_sum__strict__mono__ex1,axiom,
% 3.82/4.07 ! [A2: set_Extended_enat,F: extended_enat > int,G: extended_enat > int] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.07 => ( ! [X5: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ X5 @ A2 )
% 3.82/4.07 => ( ord_less_eq_int @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 3.82/4.07 => ( ? [X2: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ X2 @ A2 )
% 3.82/4.07 & ( ord_less_int @ ( F @ X2 ) @ ( G @ X2 ) ) )
% 3.82/4.07 => ( ord_less_int @ ( groups2025484359314973016at_int @ F @ A2 ) @ ( groups2025484359314973016at_int @ G @ A2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_strict_mono_ex1
% 3.82/4.07 thf(fact_5274_sum__strict__mono__ex1,axiom,
% 3.82/4.07 ! [A2: set_int,F: int > int,G: int > int] :
% 3.82/4.07 ( ( finite_finite_int @ A2 )
% 3.82/4.07 => ( ! [X5: int] :
% 3.82/4.07 ( ( member_int @ X5 @ A2 )
% 3.82/4.07 => ( ord_less_eq_int @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 3.82/4.07 => ( ? [X2: int] :
% 3.82/4.07 ( ( member_int @ X2 @ A2 )
% 3.82/4.07 & ( ord_less_int @ ( F @ X2 ) @ ( G @ X2 ) ) )
% 3.82/4.07 => ( ord_less_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( groups4538972089207619220nt_int @ G @ A2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_strict_mono_ex1
% 3.82/4.07 thf(fact_5275_sum_Orelated,axiom,
% 3.82/4.07 ! [R: nat > nat > $o,S2: set_complex,H2: complex > nat,G: complex > nat] :
% 3.82/4.07 ( ( R @ zero_zero_nat @ zero_zero_nat )
% 3.82/4.07 => ( ! [X1: nat,Y1: nat,X23: nat,Y22: nat] :
% 3.82/4.07 ( ( ( R @ X1 @ X23 )
% 3.82/4.07 & ( R @ Y1 @ Y22 ) )
% 3.82/4.07 => ( R @ ( plus_plus_nat @ X1 @ Y1 ) @ ( plus_plus_nat @ X23 @ Y22 ) ) )
% 3.82/4.07 => ( ( finite3207457112153483333omplex @ S2 )
% 3.82/4.07 => ( ! [X5: complex] :
% 3.82/4.07 ( ( member_complex @ X5 @ S2 )
% 3.82/4.07 => ( R @ ( H2 @ X5 ) @ ( G @ X5 ) ) )
% 3.82/4.07 => ( R @ ( groups5693394587270226106ex_nat @ H2 @ S2 ) @ ( groups5693394587270226106ex_nat @ G @ S2 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.related
% 3.82/4.07 thf(fact_5276_sum_Orelated,axiom,
% 3.82/4.07 ! [R: nat > nat > $o,S2: set_int,H2: int > nat,G: int > nat] :
% 3.82/4.07 ( ( R @ zero_zero_nat @ zero_zero_nat )
% 3.82/4.07 => ( ! [X1: nat,Y1: nat,X23: nat,Y22: nat] :
% 3.82/4.07 ( ( ( R @ X1 @ X23 )
% 3.82/4.07 & ( R @ Y1 @ Y22 ) )
% 3.82/4.07 => ( R @ ( plus_plus_nat @ X1 @ Y1 ) @ ( plus_plus_nat @ X23 @ Y22 ) ) )
% 3.82/4.07 => ( ( finite_finite_int @ S2 )
% 3.82/4.07 => ( ! [X5: int] :
% 3.82/4.07 ( ( member_int @ X5 @ S2 )
% 3.82/4.07 => ( R @ ( H2 @ X5 ) @ ( G @ X5 ) ) )
% 3.82/4.07 => ( R @ ( groups4541462559716669496nt_nat @ H2 @ S2 ) @ ( groups4541462559716669496nt_nat @ G @ S2 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.related
% 3.82/4.07 thf(fact_5277_sum_Orelated,axiom,
% 3.82/4.07 ! [R: nat > nat > $o,S2: set_Extended_enat,H2: extended_enat > nat,G: extended_enat > nat] :
% 3.82/4.07 ( ( R @ zero_zero_nat @ zero_zero_nat )
% 3.82/4.07 => ( ! [X1: nat,Y1: nat,X23: nat,Y22: nat] :
% 3.82/4.07 ( ( ( R @ X1 @ X23 )
% 3.82/4.07 & ( R @ Y1 @ Y22 ) )
% 3.82/4.07 => ( R @ ( plus_plus_nat @ X1 @ Y1 ) @ ( plus_plus_nat @ X23 @ Y22 ) ) )
% 3.82/4.07 => ( ( finite4001608067531595151d_enat @ S2 )
% 3.82/4.07 => ( ! [X5: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ X5 @ S2 )
% 3.82/4.07 => ( R @ ( H2 @ X5 ) @ ( G @ X5 ) ) )
% 3.82/4.07 => ( R @ ( groups2027974829824023292at_nat @ H2 @ S2 ) @ ( groups2027974829824023292at_nat @ G @ S2 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.related
% 3.82/4.07 thf(fact_5278_sum_Orelated,axiom,
% 3.82/4.07 ! [R: real > real > $o,S2: set_complex,H2: complex > real,G: complex > real] :
% 3.82/4.07 ( ( R @ zero_zero_real @ zero_zero_real )
% 3.82/4.07 => ( ! [X1: real,Y1: real,X23: real,Y22: real] :
% 3.82/4.07 ( ( ( R @ X1 @ X23 )
% 3.82/4.07 & ( R @ Y1 @ Y22 ) )
% 3.82/4.07 => ( R @ ( plus_plus_real @ X1 @ Y1 ) @ ( plus_plus_real @ X23 @ Y22 ) ) )
% 3.82/4.07 => ( ( finite3207457112153483333omplex @ S2 )
% 3.82/4.07 => ( ! [X5: complex] :
% 3.82/4.07 ( ( member_complex @ X5 @ S2 )
% 3.82/4.07 => ( R @ ( H2 @ X5 ) @ ( G @ X5 ) ) )
% 3.82/4.07 => ( R @ ( groups5808333547571424918x_real @ H2 @ S2 ) @ ( groups5808333547571424918x_real @ G @ S2 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.related
% 3.82/4.07 thf(fact_5279_sum_Orelated,axiom,
% 3.82/4.07 ! [R: real > real > $o,S2: set_int,H2: int > real,G: int > real] :
% 3.82/4.07 ( ( R @ zero_zero_real @ zero_zero_real )
% 3.82/4.07 => ( ! [X1: real,Y1: real,X23: real,Y22: real] :
% 3.82/4.07 ( ( ( R @ X1 @ X23 )
% 3.82/4.07 & ( R @ Y1 @ Y22 ) )
% 3.82/4.07 => ( R @ ( plus_plus_real @ X1 @ Y1 ) @ ( plus_plus_real @ X23 @ Y22 ) ) )
% 3.82/4.07 => ( ( finite_finite_int @ S2 )
% 3.82/4.07 => ( ! [X5: int] :
% 3.82/4.07 ( ( member_int @ X5 @ S2 )
% 3.82/4.07 => ( R @ ( H2 @ X5 ) @ ( G @ X5 ) ) )
% 3.82/4.07 => ( R @ ( groups8778361861064173332t_real @ H2 @ S2 ) @ ( groups8778361861064173332t_real @ G @ S2 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.related
% 3.82/4.07 thf(fact_5280_sum_Orelated,axiom,
% 3.82/4.07 ! [R: real > real > $o,S2: set_Extended_enat,H2: extended_enat > real,G: extended_enat > real] :
% 3.82/4.07 ( ( R @ zero_zero_real @ zero_zero_real )
% 3.82/4.07 => ( ! [X1: real,Y1: real,X23: real,Y22: real] :
% 3.82/4.07 ( ( ( R @ X1 @ X23 )
% 3.82/4.07 & ( R @ Y1 @ Y22 ) )
% 3.82/4.07 => ( R @ ( plus_plus_real @ X1 @ Y1 ) @ ( plus_plus_real @ X23 @ Y22 ) ) )
% 3.82/4.07 => ( ( finite4001608067531595151d_enat @ S2 )
% 3.82/4.07 => ( ! [X5: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ X5 @ S2 )
% 3.82/4.07 => ( R @ ( H2 @ X5 ) @ ( G @ X5 ) ) )
% 3.82/4.07 => ( R @ ( groups4148127829035722712t_real @ H2 @ S2 ) @ ( groups4148127829035722712t_real @ G @ S2 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.related
% 3.82/4.07 thf(fact_5281_sum_Orelated,axiom,
% 3.82/4.07 ! [R: int > int > $o,S2: set_nat,H2: nat > int,G: nat > int] :
% 3.82/4.07 ( ( R @ zero_zero_int @ zero_zero_int )
% 3.82/4.07 => ( ! [X1: int,Y1: int,X23: int,Y22: int] :
% 3.82/4.07 ( ( ( R @ X1 @ X23 )
% 3.82/4.07 & ( R @ Y1 @ Y22 ) )
% 3.82/4.07 => ( R @ ( plus_plus_int @ X1 @ Y1 ) @ ( plus_plus_int @ X23 @ Y22 ) ) )
% 3.82/4.07 => ( ( finite_finite_nat @ S2 )
% 3.82/4.07 => ( ! [X5: nat] :
% 3.82/4.07 ( ( member_nat @ X5 @ S2 )
% 3.82/4.07 => ( R @ ( H2 @ X5 ) @ ( G @ X5 ) ) )
% 3.82/4.07 => ( R @ ( groups3539618377306564664at_int @ H2 @ S2 ) @ ( groups3539618377306564664at_int @ G @ S2 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.related
% 3.82/4.07 thf(fact_5282_sum_Orelated,axiom,
% 3.82/4.07 ! [R: int > int > $o,S2: set_complex,H2: complex > int,G: complex > int] :
% 3.82/4.07 ( ( R @ zero_zero_int @ zero_zero_int )
% 3.82/4.07 => ( ! [X1: int,Y1: int,X23: int,Y22: int] :
% 3.82/4.07 ( ( ( R @ X1 @ X23 )
% 3.82/4.07 & ( R @ Y1 @ Y22 ) )
% 3.82/4.07 => ( R @ ( plus_plus_int @ X1 @ Y1 ) @ ( plus_plus_int @ X23 @ Y22 ) ) )
% 3.82/4.07 => ( ( finite3207457112153483333omplex @ S2 )
% 3.82/4.07 => ( ! [X5: complex] :
% 3.82/4.07 ( ( member_complex @ X5 @ S2 )
% 3.82/4.07 => ( R @ ( H2 @ X5 ) @ ( G @ X5 ) ) )
% 3.82/4.07 => ( R @ ( groups5690904116761175830ex_int @ H2 @ S2 ) @ ( groups5690904116761175830ex_int @ G @ S2 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.related
% 3.82/4.07 thf(fact_5283_sum_Orelated,axiom,
% 3.82/4.07 ! [R: int > int > $o,S2: set_Extended_enat,H2: extended_enat > int,G: extended_enat > int] :
% 3.82/4.07 ( ( R @ zero_zero_int @ zero_zero_int )
% 3.82/4.07 => ( ! [X1: int,Y1: int,X23: int,Y22: int] :
% 3.82/4.07 ( ( ( R @ X1 @ X23 )
% 3.82/4.07 & ( R @ Y1 @ Y22 ) )
% 3.82/4.07 => ( R @ ( plus_plus_int @ X1 @ Y1 ) @ ( plus_plus_int @ X23 @ Y22 ) ) )
% 3.82/4.07 => ( ( finite4001608067531595151d_enat @ S2 )
% 3.82/4.07 => ( ! [X5: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ X5 @ S2 )
% 3.82/4.07 => ( R @ ( H2 @ X5 ) @ ( G @ X5 ) ) )
% 3.82/4.07 => ( R @ ( groups2025484359314973016at_int @ H2 @ S2 ) @ ( groups2025484359314973016at_int @ G @ S2 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.related
% 3.82/4.07 thf(fact_5284_sum_Orelated,axiom,
% 3.82/4.07 ! [R: complex > complex > $o,S2: set_nat,H2: nat > complex,G: nat > complex] :
% 3.82/4.07 ( ( R @ zero_zero_complex @ zero_zero_complex )
% 3.82/4.07 => ( ! [X1: complex,Y1: complex,X23: complex,Y22: complex] :
% 3.82/4.07 ( ( ( R @ X1 @ X23 )
% 3.82/4.07 & ( R @ Y1 @ Y22 ) )
% 3.82/4.07 => ( R @ ( plus_plus_complex @ X1 @ Y1 ) @ ( plus_plus_complex @ X23 @ Y22 ) ) )
% 3.82/4.07 => ( ( finite_finite_nat @ S2 )
% 3.82/4.07 => ( ! [X5: nat] :
% 3.82/4.07 ( ( member_nat @ X5 @ S2 )
% 3.82/4.07 => ( R @ ( H2 @ X5 ) @ ( G @ X5 ) ) )
% 3.82/4.07 => ( R @ ( groups2073611262835488442omplex @ H2 @ S2 ) @ ( groups2073611262835488442omplex @ G @ S2 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.related
% 3.82/4.07 thf(fact_5285_sum__strict__mono,axiom,
% 3.82/4.07 ! [A2: set_complex,F: complex > nat,G: complex > nat] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.07 => ( ( A2 != bot_bot_set_complex )
% 3.82/4.07 => ( ! [X5: complex] :
% 3.82/4.07 ( ( member_complex @ X5 @ A2 )
% 3.82/4.07 => ( ord_less_nat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 3.82/4.07 => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_strict_mono
% 3.82/4.07 thf(fact_5286_sum__strict__mono,axiom,
% 3.82/4.07 ! [A2: set_Extended_enat,F: extended_enat > nat,G: extended_enat > nat] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.07 => ( ( A2 != bot_bo7653980558646680370d_enat )
% 3.82/4.07 => ( ! [X5: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ X5 @ A2 )
% 3.82/4.07 => ( ord_less_nat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 3.82/4.07 => ( ord_less_nat @ ( groups2027974829824023292at_nat @ F @ A2 ) @ ( groups2027974829824023292at_nat @ G @ A2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_strict_mono
% 3.82/4.07 thf(fact_5287_sum__strict__mono,axiom,
% 3.82/4.07 ! [A2: set_real,F: real > nat,G: real > nat] :
% 3.82/4.07 ( ( finite_finite_real @ A2 )
% 3.82/4.07 => ( ( A2 != bot_bot_set_real )
% 3.82/4.07 => ( ! [X5: real] :
% 3.82/4.07 ( ( member_real @ X5 @ A2 )
% 3.82/4.07 => ( ord_less_nat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 3.82/4.07 => ( ord_less_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ G @ A2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_strict_mono
% 3.82/4.07 thf(fact_5288_sum__strict__mono,axiom,
% 3.82/4.07 ! [A2: set_int,F: int > nat,G: int > nat] :
% 3.82/4.07 ( ( finite_finite_int @ A2 )
% 3.82/4.07 => ( ( A2 != bot_bot_set_int )
% 3.82/4.07 => ( ! [X5: int] :
% 3.82/4.07 ( ( member_int @ X5 @ A2 )
% 3.82/4.07 => ( ord_less_nat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 3.82/4.07 => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_strict_mono
% 3.82/4.07 thf(fact_5289_sum__strict__mono,axiom,
% 3.82/4.07 ! [A2: set_complex,F: complex > extended_enat,G: complex > extended_enat] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.07 => ( ( A2 != bot_bot_set_complex )
% 3.82/4.07 => ( ! [X5: complex] :
% 3.82/4.07 ( ( member_complex @ X5 @ A2 )
% 3.82/4.07 => ( ord_le72135733267957522d_enat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 3.82/4.07 => ( ord_le72135733267957522d_enat @ ( groups1752964319039525884d_enat @ F @ A2 ) @ ( groups1752964319039525884d_enat @ G @ A2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_strict_mono
% 3.82/4.07 thf(fact_5290_sum__strict__mono,axiom,
% 3.82/4.07 ! [A2: set_Extended_enat,F: extended_enat > extended_enat,G: extended_enat > extended_enat] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.07 => ( ( A2 != bot_bo7653980558646680370d_enat )
% 3.82/4.07 => ( ! [X5: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ X5 @ A2 )
% 3.82/4.07 => ( ord_le72135733267957522d_enat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 3.82/4.07 => ( ord_le72135733267957522d_enat @ ( groups2433450451889696826d_enat @ F @ A2 ) @ ( groups2433450451889696826d_enat @ G @ A2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_strict_mono
% 3.82/4.07 thf(fact_5291_sum__strict__mono,axiom,
% 3.82/4.07 ! [A2: set_real,F: real > extended_enat,G: real > extended_enat] :
% 3.82/4.07 ( ( finite_finite_real @ A2 )
% 3.82/4.07 => ( ( A2 != bot_bot_set_real )
% 3.82/4.07 => ( ! [X5: real] :
% 3.82/4.07 ( ( member_real @ X5 @ A2 )
% 3.82/4.07 => ( ord_le72135733267957522d_enat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 3.82/4.07 => ( ord_le72135733267957522d_enat @ ( groups2800946370649118462d_enat @ F @ A2 ) @ ( groups2800946370649118462d_enat @ G @ A2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_strict_mono
% 3.82/4.07 thf(fact_5292_sum__strict__mono,axiom,
% 3.82/4.07 ! [A2: set_nat,F: nat > extended_enat,G: nat > extended_enat] :
% 3.82/4.07 ( ( finite_finite_nat @ A2 )
% 3.82/4.07 => ( ( A2 != bot_bot_set_nat )
% 3.82/4.07 => ( ! [X5: nat] :
% 3.82/4.07 ( ( member_nat @ X5 @ A2 )
% 3.82/4.07 => ( ord_le72135733267957522d_enat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 3.82/4.07 => ( ord_le72135733267957522d_enat @ ( groups7108830773950497114d_enat @ F @ A2 ) @ ( groups7108830773950497114d_enat @ G @ A2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_strict_mono
% 3.82/4.07 thf(fact_5293_sum__strict__mono,axiom,
% 3.82/4.07 ! [A2: set_int,F: int > extended_enat,G: int > extended_enat] :
% 3.82/4.07 ( ( finite_finite_int @ A2 )
% 3.82/4.07 => ( ( A2 != bot_bot_set_int )
% 3.82/4.07 => ( ! [X5: int] :
% 3.82/4.07 ( ( member_int @ X5 @ A2 )
% 3.82/4.07 => ( ord_le72135733267957522d_enat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 3.82/4.07 => ( ord_le72135733267957522d_enat @ ( groups4225252721152677374d_enat @ F @ A2 ) @ ( groups4225252721152677374d_enat @ G @ A2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_strict_mono
% 3.82/4.07 thf(fact_5294_sum__strict__mono,axiom,
% 3.82/4.07 ! [A2: set_complex,F: complex > real,G: complex > real] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.07 => ( ( A2 != bot_bot_set_complex )
% 3.82/4.07 => ( ! [X5: complex] :
% 3.82/4.07 ( ( member_complex @ X5 @ A2 )
% 3.82/4.07 => ( ord_less_real @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 3.82/4.07 => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_strict_mono
% 3.82/4.07 thf(fact_5295_sum_Oinsert__if,axiom,
% 3.82/4.07 ! [A2: set_real,X: real,G: real > nat] :
% 3.82/4.07 ( ( finite_finite_real @ A2 )
% 3.82/4.07 => ( ( ( member_real @ X @ A2 )
% 3.82/4.07 => ( ( groups1935376822645274424al_nat @ G @ ( insert_real @ X @ A2 ) )
% 3.82/4.07 = ( groups1935376822645274424al_nat @ G @ A2 ) ) )
% 3.82/4.07 & ( ~ ( member_real @ X @ A2 )
% 3.82/4.07 => ( ( groups1935376822645274424al_nat @ G @ ( insert_real @ X @ A2 ) )
% 3.82/4.07 = ( plus_plus_nat @ ( G @ X ) @ ( groups1935376822645274424al_nat @ G @ A2 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.insert_if
% 3.82/4.07 thf(fact_5296_sum_Oinsert__if,axiom,
% 3.82/4.07 ! [A2: set_complex,X: complex,G: complex > nat] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.07 => ( ( ( member_complex @ X @ A2 )
% 3.82/4.07 => ( ( groups5693394587270226106ex_nat @ G @ ( insert_complex @ X @ A2 ) )
% 3.82/4.07 = ( groups5693394587270226106ex_nat @ G @ A2 ) ) )
% 3.82/4.07 & ( ~ ( member_complex @ X @ A2 )
% 3.82/4.07 => ( ( groups5693394587270226106ex_nat @ G @ ( insert_complex @ X @ A2 ) )
% 3.82/4.07 = ( plus_plus_nat @ ( G @ X ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.insert_if
% 3.82/4.07 thf(fact_5297_sum_Oinsert__if,axiom,
% 3.82/4.07 ! [A2: set_int,X: int,G: int > nat] :
% 3.82/4.07 ( ( finite_finite_int @ A2 )
% 3.82/4.07 => ( ( ( member_int @ X @ A2 )
% 3.82/4.07 => ( ( groups4541462559716669496nt_nat @ G @ ( insert_int @ X @ A2 ) )
% 3.82/4.07 = ( groups4541462559716669496nt_nat @ G @ A2 ) ) )
% 3.82/4.07 & ( ~ ( member_int @ X @ A2 )
% 3.82/4.07 => ( ( groups4541462559716669496nt_nat @ G @ ( insert_int @ X @ A2 ) )
% 3.82/4.07 = ( plus_plus_nat @ ( G @ X ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.insert_if
% 3.82/4.07 thf(fact_5298_sum_Oinsert__if,axiom,
% 3.82/4.07 ! [A2: set_Extended_enat,X: extended_enat,G: extended_enat > nat] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.07 => ( ( ( member_Extended_enat @ X @ A2 )
% 3.82/4.07 => ( ( groups2027974829824023292at_nat @ G @ ( insert_Extended_enat @ X @ A2 ) )
% 3.82/4.07 = ( groups2027974829824023292at_nat @ G @ A2 ) ) )
% 3.82/4.07 & ( ~ ( member_Extended_enat @ X @ A2 )
% 3.82/4.07 => ( ( groups2027974829824023292at_nat @ G @ ( insert_Extended_enat @ X @ A2 ) )
% 3.82/4.07 = ( plus_plus_nat @ ( G @ X ) @ ( groups2027974829824023292at_nat @ G @ A2 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.insert_if
% 3.82/4.07 thf(fact_5299_sum_Oinsert__if,axiom,
% 3.82/4.07 ! [A2: set_real,X: real,G: real > int] :
% 3.82/4.07 ( ( finite_finite_real @ A2 )
% 3.82/4.07 => ( ( ( member_real @ X @ A2 )
% 3.82/4.07 => ( ( groups1932886352136224148al_int @ G @ ( insert_real @ X @ A2 ) )
% 3.82/4.07 = ( groups1932886352136224148al_int @ G @ A2 ) ) )
% 3.82/4.07 & ( ~ ( member_real @ X @ A2 )
% 3.82/4.07 => ( ( groups1932886352136224148al_int @ G @ ( insert_real @ X @ A2 ) )
% 3.82/4.07 = ( plus_plus_int @ ( G @ X ) @ ( groups1932886352136224148al_int @ G @ A2 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.insert_if
% 3.82/4.07 thf(fact_5300_sum_Oinsert__if,axiom,
% 3.82/4.07 ! [A2: set_nat,X: nat,G: nat > int] :
% 3.82/4.07 ( ( finite_finite_nat @ A2 )
% 3.82/4.07 => ( ( ( member_nat @ X @ A2 )
% 3.82/4.07 => ( ( groups3539618377306564664at_int @ G @ ( insert_nat @ X @ A2 ) )
% 3.82/4.07 = ( groups3539618377306564664at_int @ G @ A2 ) ) )
% 3.82/4.07 & ( ~ ( member_nat @ X @ A2 )
% 3.82/4.07 => ( ( groups3539618377306564664at_int @ G @ ( insert_nat @ X @ A2 ) )
% 3.82/4.07 = ( plus_plus_int @ ( G @ X ) @ ( groups3539618377306564664at_int @ G @ A2 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.insert_if
% 3.82/4.07 thf(fact_5301_sum_Oinsert__if,axiom,
% 3.82/4.07 ! [A2: set_complex,X: complex,G: complex > int] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.07 => ( ( ( member_complex @ X @ A2 )
% 3.82/4.07 => ( ( groups5690904116761175830ex_int @ G @ ( insert_complex @ X @ A2 ) )
% 3.82/4.07 = ( groups5690904116761175830ex_int @ G @ A2 ) ) )
% 3.82/4.07 & ( ~ ( member_complex @ X @ A2 )
% 3.82/4.07 => ( ( groups5690904116761175830ex_int @ G @ ( insert_complex @ X @ A2 ) )
% 3.82/4.07 = ( plus_plus_int @ ( G @ X ) @ ( groups5690904116761175830ex_int @ G @ A2 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.insert_if
% 3.82/4.07 thf(fact_5302_sum_Oinsert__if,axiom,
% 3.82/4.07 ! [A2: set_Extended_enat,X: extended_enat,G: extended_enat > int] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.07 => ( ( ( member_Extended_enat @ X @ A2 )
% 3.82/4.07 => ( ( groups2025484359314973016at_int @ G @ ( insert_Extended_enat @ X @ A2 ) )
% 3.82/4.07 = ( groups2025484359314973016at_int @ G @ A2 ) ) )
% 3.82/4.07 & ( ~ ( member_Extended_enat @ X @ A2 )
% 3.82/4.07 => ( ( groups2025484359314973016at_int @ G @ ( insert_Extended_enat @ X @ A2 ) )
% 3.82/4.07 = ( plus_plus_int @ ( G @ X ) @ ( groups2025484359314973016at_int @ G @ A2 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.insert_if
% 3.82/4.07 thf(fact_5303_sum_Oinsert__if,axiom,
% 3.82/4.07 ! [A2: set_real,X: real,G: real > real] :
% 3.82/4.07 ( ( finite_finite_real @ A2 )
% 3.82/4.07 => ( ( ( member_real @ X @ A2 )
% 3.82/4.07 => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X @ A2 ) )
% 3.82/4.07 = ( groups8097168146408367636l_real @ G @ A2 ) ) )
% 3.82/4.07 & ( ~ ( member_real @ X @ A2 )
% 3.82/4.07 => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X @ A2 ) )
% 3.82/4.07 = ( plus_plus_real @ ( G @ X ) @ ( groups8097168146408367636l_real @ G @ A2 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.insert_if
% 3.82/4.07 thf(fact_5304_sum_Oinsert__if,axiom,
% 3.82/4.07 ! [A2: set_complex,X: complex,G: complex > real] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.07 => ( ( ( member_complex @ X @ A2 )
% 3.82/4.07 => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X @ A2 ) )
% 3.82/4.07 = ( groups5808333547571424918x_real @ G @ A2 ) ) )
% 3.82/4.07 & ( ~ ( member_complex @ X @ A2 )
% 3.82/4.07 => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X @ A2 ) )
% 3.82/4.07 = ( plus_plus_real @ ( G @ X ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.insert_if
% 3.82/4.07 thf(fact_5305_sum_Oreindex__bij__witness__not__neutral,axiom,
% 3.82/4.07 ! [S5: set_real,T5: set_real,S2: set_real,I: real > real,J: real > real,T3: set_real,G: real > nat,H2: real > nat] :
% 3.82/4.07 ( ( finite_finite_real @ S5 )
% 3.82/4.07 => ( ( finite_finite_real @ T5 )
% 3.82/4.07 => ( ! [A4: real] :
% 3.82/4.07 ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 3.82/4.07 => ( ( I @ ( J @ A4 ) )
% 3.82/4.07 = A4 ) )
% 3.82/4.07 => ( ! [A4: real] :
% 3.82/4.07 ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 3.82/4.07 => ( member_real @ ( J @ A4 ) @ ( minus_minus_set_real @ T3 @ T5 ) ) )
% 3.82/4.07 => ( ! [B4: real] :
% 3.82/4.07 ( ( member_real @ B4 @ ( minus_minus_set_real @ T3 @ T5 ) )
% 3.82/4.07 => ( ( J @ ( I @ B4 ) )
% 3.82/4.07 = B4 ) )
% 3.82/4.07 => ( ! [B4: real] :
% 3.82/4.07 ( ( member_real @ B4 @ ( minus_minus_set_real @ T3 @ T5 ) )
% 3.82/4.07 => ( member_real @ ( I @ B4 ) @ ( minus_minus_set_real @ S2 @ S5 ) ) )
% 3.82/4.07 => ( ! [A4: real] :
% 3.82/4.07 ( ( member_real @ A4 @ S5 )
% 3.82/4.07 => ( ( G @ A4 )
% 3.82/4.07 = zero_zero_nat ) )
% 3.82/4.07 => ( ! [B4: real] :
% 3.82/4.07 ( ( member_real @ B4 @ T5 )
% 3.82/4.07 => ( ( H2 @ B4 )
% 3.82/4.07 = zero_zero_nat ) )
% 3.82/4.07 => ( ! [A4: real] :
% 3.82/4.07 ( ( member_real @ A4 @ S2 )
% 3.82/4.07 => ( ( H2 @ ( J @ A4 ) )
% 3.82/4.07 = ( G @ A4 ) ) )
% 3.82/4.07 => ( ( groups1935376822645274424al_nat @ G @ S2 )
% 3.82/4.07 = ( groups1935376822645274424al_nat @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.reindex_bij_witness_not_neutral
% 3.82/4.07 thf(fact_5306_sum_Oreindex__bij__witness__not__neutral,axiom,
% 3.82/4.07 ! [S5: set_real,T5: set_complex,S2: set_real,I: complex > real,J: real > complex,T3: set_complex,G: real > nat,H2: complex > nat] :
% 3.82/4.07 ( ( finite_finite_real @ S5 )
% 3.82/4.07 => ( ( finite3207457112153483333omplex @ T5 )
% 3.82/4.07 => ( ! [A4: real] :
% 3.82/4.07 ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 3.82/4.07 => ( ( I @ ( J @ A4 ) )
% 3.82/4.07 = A4 ) )
% 3.82/4.07 => ( ! [A4: real] :
% 3.82/4.07 ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 3.82/4.07 => ( member_complex @ ( J @ A4 ) @ ( minus_811609699411566653omplex @ T3 @ T5 ) ) )
% 3.82/4.07 => ( ! [B4: complex] :
% 3.82/4.07 ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ T3 @ T5 ) )
% 3.82/4.07 => ( ( J @ ( I @ B4 ) )
% 3.82/4.07 = B4 ) )
% 3.82/4.07 => ( ! [B4: complex] :
% 3.82/4.07 ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ T3 @ T5 ) )
% 3.82/4.07 => ( member_real @ ( I @ B4 ) @ ( minus_minus_set_real @ S2 @ S5 ) ) )
% 3.82/4.07 => ( ! [A4: real] :
% 3.82/4.07 ( ( member_real @ A4 @ S5 )
% 3.82/4.07 => ( ( G @ A4 )
% 3.82/4.07 = zero_zero_nat ) )
% 3.82/4.07 => ( ! [B4: complex] :
% 3.82/4.07 ( ( member_complex @ B4 @ T5 )
% 3.82/4.07 => ( ( H2 @ B4 )
% 3.82/4.07 = zero_zero_nat ) )
% 3.82/4.07 => ( ! [A4: real] :
% 3.82/4.07 ( ( member_real @ A4 @ S2 )
% 3.82/4.07 => ( ( H2 @ ( J @ A4 ) )
% 3.82/4.07 = ( G @ A4 ) ) )
% 3.82/4.07 => ( ( groups1935376822645274424al_nat @ G @ S2 )
% 3.82/4.07 = ( groups5693394587270226106ex_nat @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.reindex_bij_witness_not_neutral
% 3.82/4.07 thf(fact_5307_sum_Oreindex__bij__witness__not__neutral,axiom,
% 3.82/4.07 ! [S5: set_real,T5: set_int,S2: set_real,I: int > real,J: real > int,T3: set_int,G: real > nat,H2: int > nat] :
% 3.82/4.07 ( ( finite_finite_real @ S5 )
% 3.82/4.07 => ( ( finite_finite_int @ T5 )
% 3.82/4.07 => ( ! [A4: real] :
% 3.82/4.07 ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 3.82/4.07 => ( ( I @ ( J @ A4 ) )
% 3.82/4.07 = A4 ) )
% 3.82/4.07 => ( ! [A4: real] :
% 3.82/4.07 ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 3.82/4.07 => ( member_int @ ( J @ A4 ) @ ( minus_minus_set_int @ T3 @ T5 ) ) )
% 3.82/4.07 => ( ! [B4: int] :
% 3.82/4.07 ( ( member_int @ B4 @ ( minus_minus_set_int @ T3 @ T5 ) )
% 3.82/4.07 => ( ( J @ ( I @ B4 ) )
% 3.82/4.07 = B4 ) )
% 3.82/4.07 => ( ! [B4: int] :
% 3.82/4.07 ( ( member_int @ B4 @ ( minus_minus_set_int @ T3 @ T5 ) )
% 3.82/4.07 => ( member_real @ ( I @ B4 ) @ ( minus_minus_set_real @ S2 @ S5 ) ) )
% 3.82/4.07 => ( ! [A4: real] :
% 3.82/4.07 ( ( member_real @ A4 @ S5 )
% 3.82/4.07 => ( ( G @ A4 )
% 3.82/4.07 = zero_zero_nat ) )
% 3.82/4.07 => ( ! [B4: int] :
% 3.82/4.07 ( ( member_int @ B4 @ T5 )
% 3.82/4.07 => ( ( H2 @ B4 )
% 3.82/4.07 = zero_zero_nat ) )
% 3.82/4.07 => ( ! [A4: real] :
% 3.82/4.07 ( ( member_real @ A4 @ S2 )
% 3.82/4.07 => ( ( H2 @ ( J @ A4 ) )
% 3.82/4.07 = ( G @ A4 ) ) )
% 3.82/4.07 => ( ( groups1935376822645274424al_nat @ G @ S2 )
% 3.82/4.07 = ( groups4541462559716669496nt_nat @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.reindex_bij_witness_not_neutral
% 3.82/4.07 thf(fact_5308_sum_Oreindex__bij__witness__not__neutral,axiom,
% 3.82/4.07 ! [S5: set_real,T5: set_Extended_enat,S2: set_real,I: extended_enat > real,J: real > extended_enat,T3: set_Extended_enat,G: real > nat,H2: extended_enat > nat] :
% 3.82/4.07 ( ( finite_finite_real @ S5 )
% 3.82/4.07 => ( ( finite4001608067531595151d_enat @ T5 )
% 3.82/4.07 => ( ! [A4: real] :
% 3.82/4.07 ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 3.82/4.07 => ( ( I @ ( J @ A4 ) )
% 3.82/4.07 = A4 ) )
% 3.82/4.07 => ( ! [A4: real] :
% 3.82/4.07 ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 3.82/4.07 => ( member_Extended_enat @ ( J @ A4 ) @ ( minus_925952699566721837d_enat @ T3 @ T5 ) ) )
% 3.82/4.07 => ( ! [B4: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ B4 @ ( minus_925952699566721837d_enat @ T3 @ T5 ) )
% 3.82/4.07 => ( ( J @ ( I @ B4 ) )
% 3.82/4.07 = B4 ) )
% 3.82/4.07 => ( ! [B4: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ B4 @ ( minus_925952699566721837d_enat @ T3 @ T5 ) )
% 3.82/4.07 => ( member_real @ ( I @ B4 ) @ ( minus_minus_set_real @ S2 @ S5 ) ) )
% 3.82/4.07 => ( ! [A4: real] :
% 3.82/4.07 ( ( member_real @ A4 @ S5 )
% 3.82/4.07 => ( ( G @ A4 )
% 3.82/4.07 = zero_zero_nat ) )
% 3.82/4.07 => ( ! [B4: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ B4 @ T5 )
% 3.82/4.07 => ( ( H2 @ B4 )
% 3.82/4.07 = zero_zero_nat ) )
% 3.82/4.07 => ( ! [A4: real] :
% 3.82/4.07 ( ( member_real @ A4 @ S2 )
% 3.82/4.07 => ( ( H2 @ ( J @ A4 ) )
% 3.82/4.07 = ( G @ A4 ) ) )
% 3.82/4.07 => ( ( groups1935376822645274424al_nat @ G @ S2 )
% 3.82/4.07 = ( groups2027974829824023292at_nat @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.reindex_bij_witness_not_neutral
% 3.82/4.07 thf(fact_5309_sum_Oreindex__bij__witness__not__neutral,axiom,
% 3.82/4.07 ! [S5: set_complex,T5: set_real,S2: set_complex,I: real > complex,J: complex > real,T3: set_real,G: complex > nat,H2: real > nat] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ S5 )
% 3.82/4.07 => ( ( finite_finite_real @ T5 )
% 3.82/4.07 => ( ! [A4: complex] :
% 3.82/4.07 ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ S2 @ S5 ) )
% 3.82/4.07 => ( ( I @ ( J @ A4 ) )
% 3.82/4.07 = A4 ) )
% 3.82/4.07 => ( ! [A4: complex] :
% 3.82/4.07 ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ S2 @ S5 ) )
% 3.82/4.07 => ( member_real @ ( J @ A4 ) @ ( minus_minus_set_real @ T3 @ T5 ) ) )
% 3.82/4.07 => ( ! [B4: real] :
% 3.82/4.07 ( ( member_real @ B4 @ ( minus_minus_set_real @ T3 @ T5 ) )
% 3.82/4.07 => ( ( J @ ( I @ B4 ) )
% 3.82/4.07 = B4 ) )
% 3.82/4.07 => ( ! [B4: real] :
% 3.82/4.07 ( ( member_real @ B4 @ ( minus_minus_set_real @ T3 @ T5 ) )
% 3.82/4.07 => ( member_complex @ ( I @ B4 ) @ ( minus_811609699411566653omplex @ S2 @ S5 ) ) )
% 3.82/4.07 => ( ! [A4: complex] :
% 3.82/4.07 ( ( member_complex @ A4 @ S5 )
% 3.82/4.07 => ( ( G @ A4 )
% 3.82/4.07 = zero_zero_nat ) )
% 3.82/4.07 => ( ! [B4: real] :
% 3.82/4.07 ( ( member_real @ B4 @ T5 )
% 3.82/4.07 => ( ( H2 @ B4 )
% 3.82/4.07 = zero_zero_nat ) )
% 3.82/4.07 => ( ! [A4: complex] :
% 3.82/4.07 ( ( member_complex @ A4 @ S2 )
% 3.82/4.07 => ( ( H2 @ ( J @ A4 ) )
% 3.82/4.07 = ( G @ A4 ) ) )
% 3.82/4.07 => ( ( groups5693394587270226106ex_nat @ G @ S2 )
% 3.82/4.07 = ( groups1935376822645274424al_nat @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.reindex_bij_witness_not_neutral
% 3.82/4.07 thf(fact_5310_sum_Oreindex__bij__witness__not__neutral,axiom,
% 3.82/4.07 ! [S5: set_complex,T5: set_complex,S2: set_complex,I: complex > complex,J: complex > complex,T3: set_complex,G: complex > nat,H2: complex > nat] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ S5 )
% 3.82/4.07 => ( ( finite3207457112153483333omplex @ T5 )
% 3.82/4.07 => ( ! [A4: complex] :
% 3.82/4.07 ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ S2 @ S5 ) )
% 3.82/4.07 => ( ( I @ ( J @ A4 ) )
% 3.82/4.07 = A4 ) )
% 3.82/4.07 => ( ! [A4: complex] :
% 3.82/4.07 ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ S2 @ S5 ) )
% 3.82/4.07 => ( member_complex @ ( J @ A4 ) @ ( minus_811609699411566653omplex @ T3 @ T5 ) ) )
% 3.82/4.07 => ( ! [B4: complex] :
% 3.82/4.07 ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ T3 @ T5 ) )
% 3.82/4.07 => ( ( J @ ( I @ B4 ) )
% 3.82/4.07 = B4 ) )
% 3.82/4.07 => ( ! [B4: complex] :
% 3.82/4.07 ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ T3 @ T5 ) )
% 3.82/4.07 => ( member_complex @ ( I @ B4 ) @ ( minus_811609699411566653omplex @ S2 @ S5 ) ) )
% 3.82/4.07 => ( ! [A4: complex] :
% 3.82/4.07 ( ( member_complex @ A4 @ S5 )
% 3.82/4.07 => ( ( G @ A4 )
% 3.82/4.07 = zero_zero_nat ) )
% 3.82/4.07 => ( ! [B4: complex] :
% 3.82/4.07 ( ( member_complex @ B4 @ T5 )
% 3.82/4.07 => ( ( H2 @ B4 )
% 3.82/4.07 = zero_zero_nat ) )
% 3.82/4.07 => ( ! [A4: complex] :
% 3.82/4.07 ( ( member_complex @ A4 @ S2 )
% 3.82/4.07 => ( ( H2 @ ( J @ A4 ) )
% 3.82/4.07 = ( G @ A4 ) ) )
% 3.82/4.07 => ( ( groups5693394587270226106ex_nat @ G @ S2 )
% 3.82/4.07 = ( groups5693394587270226106ex_nat @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.reindex_bij_witness_not_neutral
% 3.82/4.07 thf(fact_5311_sum_Oreindex__bij__witness__not__neutral,axiom,
% 3.82/4.07 ! [S5: set_complex,T5: set_int,S2: set_complex,I: int > complex,J: complex > int,T3: set_int,G: complex > nat,H2: int > nat] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ S5 )
% 3.82/4.07 => ( ( finite_finite_int @ T5 )
% 3.82/4.07 => ( ! [A4: complex] :
% 3.82/4.07 ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ S2 @ S5 ) )
% 3.82/4.07 => ( ( I @ ( J @ A4 ) )
% 3.82/4.07 = A4 ) )
% 3.82/4.07 => ( ! [A4: complex] :
% 3.82/4.07 ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ S2 @ S5 ) )
% 3.82/4.07 => ( member_int @ ( J @ A4 ) @ ( minus_minus_set_int @ T3 @ T5 ) ) )
% 3.82/4.07 => ( ! [B4: int] :
% 3.82/4.07 ( ( member_int @ B4 @ ( minus_minus_set_int @ T3 @ T5 ) )
% 3.82/4.07 => ( ( J @ ( I @ B4 ) )
% 3.82/4.07 = B4 ) )
% 3.82/4.07 => ( ! [B4: int] :
% 3.82/4.07 ( ( member_int @ B4 @ ( minus_minus_set_int @ T3 @ T5 ) )
% 3.82/4.07 => ( member_complex @ ( I @ B4 ) @ ( minus_811609699411566653omplex @ S2 @ S5 ) ) )
% 3.82/4.07 => ( ! [A4: complex] :
% 3.82/4.07 ( ( member_complex @ A4 @ S5 )
% 3.82/4.07 => ( ( G @ A4 )
% 3.82/4.07 = zero_zero_nat ) )
% 3.82/4.07 => ( ! [B4: int] :
% 3.82/4.07 ( ( member_int @ B4 @ T5 )
% 3.82/4.07 => ( ( H2 @ B4 )
% 3.82/4.07 = zero_zero_nat ) )
% 3.82/4.07 => ( ! [A4: complex] :
% 3.82/4.07 ( ( member_complex @ A4 @ S2 )
% 3.82/4.07 => ( ( H2 @ ( J @ A4 ) )
% 3.82/4.07 = ( G @ A4 ) ) )
% 3.82/4.07 => ( ( groups5693394587270226106ex_nat @ G @ S2 )
% 3.82/4.07 = ( groups4541462559716669496nt_nat @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.reindex_bij_witness_not_neutral
% 3.82/4.07 thf(fact_5312_sum_Oreindex__bij__witness__not__neutral,axiom,
% 3.82/4.07 ! [S5: set_complex,T5: set_Extended_enat,S2: set_complex,I: extended_enat > complex,J: complex > extended_enat,T3: set_Extended_enat,G: complex > nat,H2: extended_enat > nat] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ S5 )
% 3.82/4.07 => ( ( finite4001608067531595151d_enat @ T5 )
% 3.82/4.07 => ( ! [A4: complex] :
% 3.82/4.07 ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ S2 @ S5 ) )
% 3.82/4.07 => ( ( I @ ( J @ A4 ) )
% 3.82/4.07 = A4 ) )
% 3.82/4.07 => ( ! [A4: complex] :
% 3.82/4.07 ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ S2 @ S5 ) )
% 3.82/4.07 => ( member_Extended_enat @ ( J @ A4 ) @ ( minus_925952699566721837d_enat @ T3 @ T5 ) ) )
% 3.82/4.07 => ( ! [B4: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ B4 @ ( minus_925952699566721837d_enat @ T3 @ T5 ) )
% 3.82/4.07 => ( ( J @ ( I @ B4 ) )
% 3.82/4.07 = B4 ) )
% 3.82/4.07 => ( ! [B4: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ B4 @ ( minus_925952699566721837d_enat @ T3 @ T5 ) )
% 3.82/4.07 => ( member_complex @ ( I @ B4 ) @ ( minus_811609699411566653omplex @ S2 @ S5 ) ) )
% 3.82/4.07 => ( ! [A4: complex] :
% 3.82/4.07 ( ( member_complex @ A4 @ S5 )
% 3.82/4.07 => ( ( G @ A4 )
% 3.82/4.07 = zero_zero_nat ) )
% 3.82/4.07 => ( ! [B4: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ B4 @ T5 )
% 3.82/4.07 => ( ( H2 @ B4 )
% 3.82/4.07 = zero_zero_nat ) )
% 3.82/4.07 => ( ! [A4: complex] :
% 3.82/4.07 ( ( member_complex @ A4 @ S2 )
% 3.82/4.07 => ( ( H2 @ ( J @ A4 ) )
% 3.82/4.07 = ( G @ A4 ) ) )
% 3.82/4.07 => ( ( groups5693394587270226106ex_nat @ G @ S2 )
% 3.82/4.07 = ( groups2027974829824023292at_nat @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.reindex_bij_witness_not_neutral
% 3.82/4.07 thf(fact_5313_sum_Oreindex__bij__witness__not__neutral,axiom,
% 3.82/4.07 ! [S5: set_int,T5: set_real,S2: set_int,I: real > int,J: int > real,T3: set_real,G: int > nat,H2: real > nat] :
% 3.82/4.07 ( ( finite_finite_int @ S5 )
% 3.82/4.07 => ( ( finite_finite_real @ T5 )
% 3.82/4.07 => ( ! [A4: int] :
% 3.82/4.07 ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 3.82/4.07 => ( ( I @ ( J @ A4 ) )
% 3.82/4.07 = A4 ) )
% 3.82/4.07 => ( ! [A4: int] :
% 3.82/4.07 ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 3.82/4.07 => ( member_real @ ( J @ A4 ) @ ( minus_minus_set_real @ T3 @ T5 ) ) )
% 3.82/4.07 => ( ! [B4: real] :
% 3.82/4.07 ( ( member_real @ B4 @ ( minus_minus_set_real @ T3 @ T5 ) )
% 3.82/4.07 => ( ( J @ ( I @ B4 ) )
% 3.82/4.07 = B4 ) )
% 3.82/4.07 => ( ! [B4: real] :
% 3.82/4.07 ( ( member_real @ B4 @ ( minus_minus_set_real @ T3 @ T5 ) )
% 3.82/4.07 => ( member_int @ ( I @ B4 ) @ ( minus_minus_set_int @ S2 @ S5 ) ) )
% 3.82/4.07 => ( ! [A4: int] :
% 3.82/4.07 ( ( member_int @ A4 @ S5 )
% 3.82/4.07 => ( ( G @ A4 )
% 3.82/4.07 = zero_zero_nat ) )
% 3.82/4.07 => ( ! [B4: real] :
% 3.82/4.07 ( ( member_real @ B4 @ T5 )
% 3.82/4.07 => ( ( H2 @ B4 )
% 3.82/4.07 = zero_zero_nat ) )
% 3.82/4.07 => ( ! [A4: int] :
% 3.82/4.07 ( ( member_int @ A4 @ S2 )
% 3.82/4.07 => ( ( H2 @ ( J @ A4 ) )
% 3.82/4.07 = ( G @ A4 ) ) )
% 3.82/4.07 => ( ( groups4541462559716669496nt_nat @ G @ S2 )
% 3.82/4.07 = ( groups1935376822645274424al_nat @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.reindex_bij_witness_not_neutral
% 3.82/4.07 thf(fact_5314_sum_Oreindex__bij__witness__not__neutral,axiom,
% 3.82/4.07 ! [S5: set_int,T5: set_complex,S2: set_int,I: complex > int,J: int > complex,T3: set_complex,G: int > nat,H2: complex > nat] :
% 3.82/4.07 ( ( finite_finite_int @ S5 )
% 3.82/4.07 => ( ( finite3207457112153483333omplex @ T5 )
% 3.82/4.07 => ( ! [A4: int] :
% 3.82/4.07 ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 3.82/4.07 => ( ( I @ ( J @ A4 ) )
% 3.82/4.07 = A4 ) )
% 3.82/4.07 => ( ! [A4: int] :
% 3.82/4.07 ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 3.82/4.07 => ( member_complex @ ( J @ A4 ) @ ( minus_811609699411566653omplex @ T3 @ T5 ) ) )
% 3.82/4.07 => ( ! [B4: complex] :
% 3.82/4.07 ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ T3 @ T5 ) )
% 3.82/4.07 => ( ( J @ ( I @ B4 ) )
% 3.82/4.07 = B4 ) )
% 3.82/4.07 => ( ! [B4: complex] :
% 3.82/4.07 ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ T3 @ T5 ) )
% 3.82/4.07 => ( member_int @ ( I @ B4 ) @ ( minus_minus_set_int @ S2 @ S5 ) ) )
% 3.82/4.07 => ( ! [A4: int] :
% 3.82/4.07 ( ( member_int @ A4 @ S5 )
% 3.82/4.07 => ( ( G @ A4 )
% 3.82/4.07 = zero_zero_nat ) )
% 3.82/4.07 => ( ! [B4: complex] :
% 3.82/4.07 ( ( member_complex @ B4 @ T5 )
% 3.82/4.07 => ( ( H2 @ B4 )
% 3.82/4.07 = zero_zero_nat ) )
% 3.82/4.07 => ( ! [A4: int] :
% 3.82/4.07 ( ( member_int @ A4 @ S2 )
% 3.82/4.07 => ( ( H2 @ ( J @ A4 ) )
% 3.82/4.07 = ( G @ A4 ) ) )
% 3.82/4.07 => ( ( groups4541462559716669496nt_nat @ G @ S2 )
% 3.82/4.07 = ( groups5693394587270226106ex_nat @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.reindex_bij_witness_not_neutral
% 3.82/4.07 thf(fact_5315_round__mono,axiom,
% 3.82/4.07 ! [X: real,Y: real] :
% 3.82/4.07 ( ( ord_less_eq_real @ X @ Y )
% 3.82/4.07 => ( ord_less_eq_int @ ( archim8280529875227126926d_real @ X ) @ ( archim8280529875227126926d_real @ Y ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % round_mono
% 3.82/4.07 thf(fact_5316_sum__nonneg__0,axiom,
% 3.82/4.07 ! [S: set_real,F: real > extended_enat,I: real] :
% 3.82/4.07 ( ( finite_finite_real @ S )
% 3.82/4.07 => ( ! [I4: real] :
% 3.82/4.07 ( ( member_real @ I4 @ S )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ I4 ) ) )
% 3.82/4.07 => ( ( ( groups2800946370649118462d_enat @ F @ S )
% 3.82/4.07 = zero_z5237406670263579293d_enat )
% 3.82/4.07 => ( ( member_real @ I @ S )
% 3.82/4.07 => ( ( F @ I )
% 3.82/4.07 = zero_z5237406670263579293d_enat ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_nonneg_0
% 3.82/4.07 thf(fact_5317_sum__nonneg__0,axiom,
% 3.82/4.07 ! [S: set_nat,F: nat > extended_enat,I: nat] :
% 3.82/4.07 ( ( finite_finite_nat @ S )
% 3.82/4.07 => ( ! [I4: nat] :
% 3.82/4.07 ( ( member_nat @ I4 @ S )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ I4 ) ) )
% 3.82/4.07 => ( ( ( groups7108830773950497114d_enat @ F @ S )
% 3.82/4.07 = zero_z5237406670263579293d_enat )
% 3.82/4.07 => ( ( member_nat @ I @ S )
% 3.82/4.07 => ( ( F @ I )
% 3.82/4.07 = zero_z5237406670263579293d_enat ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_nonneg_0
% 3.82/4.07 thf(fact_5318_sum__nonneg__0,axiom,
% 3.82/4.07 ! [S: set_complex,F: complex > extended_enat,I: complex] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ S )
% 3.82/4.07 => ( ! [I4: complex] :
% 3.82/4.07 ( ( member_complex @ I4 @ S )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ I4 ) ) )
% 3.82/4.07 => ( ( ( groups1752964319039525884d_enat @ F @ S )
% 3.82/4.07 = zero_z5237406670263579293d_enat )
% 3.82/4.07 => ( ( member_complex @ I @ S )
% 3.82/4.07 => ( ( F @ I )
% 3.82/4.07 = zero_z5237406670263579293d_enat ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_nonneg_0
% 3.82/4.07 thf(fact_5319_sum__nonneg__0,axiom,
% 3.82/4.07 ! [S: set_int,F: int > extended_enat,I: int] :
% 3.82/4.07 ( ( finite_finite_int @ S )
% 3.82/4.07 => ( ! [I4: int] :
% 3.82/4.07 ( ( member_int @ I4 @ S )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ I4 ) ) )
% 3.82/4.07 => ( ( ( groups4225252721152677374d_enat @ F @ S )
% 3.82/4.07 = zero_z5237406670263579293d_enat )
% 3.82/4.07 => ( ( member_int @ I @ S )
% 3.82/4.07 => ( ( F @ I )
% 3.82/4.07 = zero_z5237406670263579293d_enat ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_nonneg_0
% 3.82/4.07 thf(fact_5320_sum__nonneg__0,axiom,
% 3.82/4.07 ! [S: set_Extended_enat,F: extended_enat > extended_enat,I: extended_enat] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ S )
% 3.82/4.07 => ( ! [I4: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ I4 @ S )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ I4 ) ) )
% 3.82/4.07 => ( ( ( groups2433450451889696826d_enat @ F @ S )
% 3.82/4.07 = zero_z5237406670263579293d_enat )
% 3.82/4.07 => ( ( member_Extended_enat @ I @ S )
% 3.82/4.07 => ( ( F @ I )
% 3.82/4.07 = zero_z5237406670263579293d_enat ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_nonneg_0
% 3.82/4.07 thf(fact_5321_sum__nonneg__0,axiom,
% 3.82/4.07 ! [S: set_real,F: real > real,I: real] :
% 3.82/4.07 ( ( finite_finite_real @ S )
% 3.82/4.07 => ( ! [I4: real] :
% 3.82/4.07 ( ( member_real @ I4 @ S )
% 3.82/4.07 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 3.82/4.07 => ( ( ( groups8097168146408367636l_real @ F @ S )
% 3.82/4.07 = zero_zero_real )
% 3.82/4.07 => ( ( member_real @ I @ S )
% 3.82/4.07 => ( ( F @ I )
% 3.82/4.07 = zero_zero_real ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_nonneg_0
% 3.82/4.07 thf(fact_5322_sum__nonneg__0,axiom,
% 3.82/4.07 ! [S: set_complex,F: complex > real,I: complex] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ S )
% 3.82/4.07 => ( ! [I4: complex] :
% 3.82/4.07 ( ( member_complex @ I4 @ S )
% 3.82/4.07 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 3.82/4.07 => ( ( ( groups5808333547571424918x_real @ F @ S )
% 3.82/4.07 = zero_zero_real )
% 3.82/4.07 => ( ( member_complex @ I @ S )
% 3.82/4.07 => ( ( F @ I )
% 3.82/4.07 = zero_zero_real ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_nonneg_0
% 3.82/4.07 thf(fact_5323_sum__nonneg__0,axiom,
% 3.82/4.07 ! [S: set_int,F: int > real,I: int] :
% 3.82/4.07 ( ( finite_finite_int @ S )
% 3.82/4.07 => ( ! [I4: int] :
% 3.82/4.07 ( ( member_int @ I4 @ S )
% 3.82/4.07 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 3.82/4.07 => ( ( ( groups8778361861064173332t_real @ F @ S )
% 3.82/4.07 = zero_zero_real )
% 3.82/4.07 => ( ( member_int @ I @ S )
% 3.82/4.07 => ( ( F @ I )
% 3.82/4.07 = zero_zero_real ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_nonneg_0
% 3.82/4.07 thf(fact_5324_sum__nonneg__0,axiom,
% 3.82/4.07 ! [S: set_Extended_enat,F: extended_enat > real,I: extended_enat] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ S )
% 3.82/4.07 => ( ! [I4: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ I4 @ S )
% 3.82/4.07 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 3.82/4.07 => ( ( ( groups4148127829035722712t_real @ F @ S )
% 3.82/4.07 = zero_zero_real )
% 3.82/4.07 => ( ( member_Extended_enat @ I @ S )
% 3.82/4.07 => ( ( F @ I )
% 3.82/4.07 = zero_zero_real ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_nonneg_0
% 3.82/4.07 thf(fact_5325_sum__nonneg__0,axiom,
% 3.82/4.07 ! [S: set_real,F: real > nat,I: real] :
% 3.82/4.07 ( ( finite_finite_real @ S )
% 3.82/4.07 => ( ! [I4: real] :
% 3.82/4.07 ( ( member_real @ I4 @ S )
% 3.82/4.07 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 3.82/4.07 => ( ( ( groups1935376822645274424al_nat @ F @ S )
% 3.82/4.07 = zero_zero_nat )
% 3.82/4.07 => ( ( member_real @ I @ S )
% 3.82/4.07 => ( ( F @ I )
% 3.82/4.07 = zero_zero_nat ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_nonneg_0
% 3.82/4.07 thf(fact_5326_sum__nonneg__leq__bound,axiom,
% 3.82/4.07 ! [S: set_real,F: real > extended_enat,B: extended_enat,I: real] :
% 3.82/4.07 ( ( finite_finite_real @ S )
% 3.82/4.07 => ( ! [I4: real] :
% 3.82/4.07 ( ( member_real @ I4 @ S )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ I4 ) ) )
% 3.82/4.07 => ( ( ( groups2800946370649118462d_enat @ F @ S )
% 3.82/4.07 = B )
% 3.82/4.07 => ( ( member_real @ I @ S )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ ( F @ I ) @ B ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_nonneg_leq_bound
% 3.82/4.07 thf(fact_5327_sum__nonneg__leq__bound,axiom,
% 3.82/4.07 ! [S: set_nat,F: nat > extended_enat,B: extended_enat,I: nat] :
% 3.82/4.07 ( ( finite_finite_nat @ S )
% 3.82/4.07 => ( ! [I4: nat] :
% 3.82/4.07 ( ( member_nat @ I4 @ S )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ I4 ) ) )
% 3.82/4.07 => ( ( ( groups7108830773950497114d_enat @ F @ S )
% 3.82/4.07 = B )
% 3.82/4.07 => ( ( member_nat @ I @ S )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ ( F @ I ) @ B ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_nonneg_leq_bound
% 3.82/4.07 thf(fact_5328_sum__nonneg__leq__bound,axiom,
% 3.82/4.07 ! [S: set_complex,F: complex > extended_enat,B: extended_enat,I: complex] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ S )
% 3.82/4.07 => ( ! [I4: complex] :
% 3.82/4.07 ( ( member_complex @ I4 @ S )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ I4 ) ) )
% 3.82/4.07 => ( ( ( groups1752964319039525884d_enat @ F @ S )
% 3.82/4.07 = B )
% 3.82/4.07 => ( ( member_complex @ I @ S )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ ( F @ I ) @ B ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_nonneg_leq_bound
% 3.82/4.07 thf(fact_5329_sum__nonneg__leq__bound,axiom,
% 3.82/4.07 ! [S: set_int,F: int > extended_enat,B: extended_enat,I: int] :
% 3.82/4.07 ( ( finite_finite_int @ S )
% 3.82/4.07 => ( ! [I4: int] :
% 3.82/4.07 ( ( member_int @ I4 @ S )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ I4 ) ) )
% 3.82/4.07 => ( ( ( groups4225252721152677374d_enat @ F @ S )
% 3.82/4.07 = B )
% 3.82/4.07 => ( ( member_int @ I @ S )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ ( F @ I ) @ B ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_nonneg_leq_bound
% 3.82/4.07 thf(fact_5330_sum__nonneg__leq__bound,axiom,
% 3.82/4.07 ! [S: set_Extended_enat,F: extended_enat > extended_enat,B: extended_enat,I: extended_enat] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ S )
% 3.82/4.07 => ( ! [I4: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ I4 @ S )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ I4 ) ) )
% 3.82/4.07 => ( ( ( groups2433450451889696826d_enat @ F @ S )
% 3.82/4.07 = B )
% 3.82/4.07 => ( ( member_Extended_enat @ I @ S )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ ( F @ I ) @ B ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_nonneg_leq_bound
% 3.82/4.07 thf(fact_5331_sum__nonneg__leq__bound,axiom,
% 3.82/4.07 ! [S: set_real,F: real > real,B: real,I: real] :
% 3.82/4.07 ( ( finite_finite_real @ S )
% 3.82/4.07 => ( ! [I4: real] :
% 3.82/4.07 ( ( member_real @ I4 @ S )
% 3.82/4.07 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 3.82/4.07 => ( ( ( groups8097168146408367636l_real @ F @ S )
% 3.82/4.07 = B )
% 3.82/4.07 => ( ( member_real @ I @ S )
% 3.82/4.07 => ( ord_less_eq_real @ ( F @ I ) @ B ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_nonneg_leq_bound
% 3.82/4.07 thf(fact_5332_sum__nonneg__leq__bound,axiom,
% 3.82/4.07 ! [S: set_complex,F: complex > real,B: real,I: complex] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ S )
% 3.82/4.07 => ( ! [I4: complex] :
% 3.82/4.07 ( ( member_complex @ I4 @ S )
% 3.82/4.07 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 3.82/4.07 => ( ( ( groups5808333547571424918x_real @ F @ S )
% 3.82/4.07 = B )
% 3.82/4.07 => ( ( member_complex @ I @ S )
% 3.82/4.07 => ( ord_less_eq_real @ ( F @ I ) @ B ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_nonneg_leq_bound
% 3.82/4.07 thf(fact_5333_sum__nonneg__leq__bound,axiom,
% 3.82/4.07 ! [S: set_int,F: int > real,B: real,I: int] :
% 3.82/4.07 ( ( finite_finite_int @ S )
% 3.82/4.07 => ( ! [I4: int] :
% 3.82/4.07 ( ( member_int @ I4 @ S )
% 3.82/4.07 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 3.82/4.07 => ( ( ( groups8778361861064173332t_real @ F @ S )
% 3.82/4.07 = B )
% 3.82/4.07 => ( ( member_int @ I @ S )
% 3.82/4.07 => ( ord_less_eq_real @ ( F @ I ) @ B ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_nonneg_leq_bound
% 3.82/4.07 thf(fact_5334_sum__nonneg__leq__bound,axiom,
% 3.82/4.07 ! [S: set_Extended_enat,F: extended_enat > real,B: real,I: extended_enat] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ S )
% 3.82/4.07 => ( ! [I4: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ I4 @ S )
% 3.82/4.07 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 3.82/4.07 => ( ( ( groups4148127829035722712t_real @ F @ S )
% 3.82/4.07 = B )
% 3.82/4.07 => ( ( member_Extended_enat @ I @ S )
% 3.82/4.07 => ( ord_less_eq_real @ ( F @ I ) @ B ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_nonneg_leq_bound
% 3.82/4.07 thf(fact_5335_sum__nonneg__leq__bound,axiom,
% 3.82/4.07 ! [S: set_real,F: real > nat,B: nat,I: real] :
% 3.82/4.07 ( ( finite_finite_real @ S )
% 3.82/4.07 => ( ! [I4: real] :
% 3.82/4.07 ( ( member_real @ I4 @ S )
% 3.82/4.07 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 3.82/4.07 => ( ( ( groups1935376822645274424al_nat @ F @ S )
% 3.82/4.07 = B )
% 3.82/4.07 => ( ( member_real @ I @ S )
% 3.82/4.07 => ( ord_less_eq_nat @ ( F @ I ) @ B ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_nonneg_leq_bound
% 3.82/4.07 thf(fact_5336_sum_Osetdiff__irrelevant,axiom,
% 3.82/4.07 ! [A2: set_real,G: real > nat] :
% 3.82/4.07 ( ( finite_finite_real @ A2 )
% 3.82/4.07 => ( ( groups1935376822645274424al_nat @ G
% 3.82/4.07 @ ( minus_minus_set_real @ A2
% 3.82/4.07 @ ( collect_real
% 3.82/4.07 @ ^ [X4: real] :
% 3.82/4.07 ( ( G @ X4 )
% 3.82/4.07 = zero_zero_nat ) ) ) )
% 3.82/4.07 = ( groups1935376822645274424al_nat @ G @ A2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.setdiff_irrelevant
% 3.82/4.07 thf(fact_5337_sum_Osetdiff__irrelevant,axiom,
% 3.82/4.07 ! [A2: set_complex,G: complex > nat] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.07 => ( ( groups5693394587270226106ex_nat @ G
% 3.82/4.07 @ ( minus_811609699411566653omplex @ A2
% 3.82/4.07 @ ( collect_complex
% 3.82/4.07 @ ^ [X4: complex] :
% 3.82/4.07 ( ( G @ X4 )
% 3.82/4.07 = zero_zero_nat ) ) ) )
% 3.82/4.07 = ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.setdiff_irrelevant
% 3.82/4.07 thf(fact_5338_sum_Osetdiff__irrelevant,axiom,
% 3.82/4.07 ! [A2: set_int,G: int > nat] :
% 3.82/4.07 ( ( finite_finite_int @ A2 )
% 3.82/4.07 => ( ( groups4541462559716669496nt_nat @ G
% 3.82/4.07 @ ( minus_minus_set_int @ A2
% 3.82/4.07 @ ( collect_int
% 3.82/4.07 @ ^ [X4: int] :
% 3.82/4.07 ( ( G @ X4 )
% 3.82/4.07 = zero_zero_nat ) ) ) )
% 3.82/4.07 = ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.setdiff_irrelevant
% 3.82/4.07 thf(fact_5339_sum_Osetdiff__irrelevant,axiom,
% 3.82/4.07 ! [A2: set_Extended_enat,G: extended_enat > nat] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.07 => ( ( groups2027974829824023292at_nat @ G
% 3.82/4.07 @ ( minus_925952699566721837d_enat @ A2
% 3.82/4.07 @ ( collec4429806609662206161d_enat
% 3.82/4.07 @ ^ [X4: extended_enat] :
% 3.82/4.07 ( ( G @ X4 )
% 3.82/4.07 = zero_zero_nat ) ) ) )
% 3.82/4.07 = ( groups2027974829824023292at_nat @ G @ A2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.setdiff_irrelevant
% 3.82/4.07 thf(fact_5340_sum_Osetdiff__irrelevant,axiom,
% 3.82/4.07 ! [A2: set_real,G: real > real] :
% 3.82/4.07 ( ( finite_finite_real @ A2 )
% 3.82/4.07 => ( ( groups8097168146408367636l_real @ G
% 3.82/4.07 @ ( minus_minus_set_real @ A2
% 3.82/4.07 @ ( collect_real
% 3.82/4.07 @ ^ [X4: real] :
% 3.82/4.07 ( ( G @ X4 )
% 3.82/4.07 = zero_zero_real ) ) ) )
% 3.82/4.07 = ( groups8097168146408367636l_real @ G @ A2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.setdiff_irrelevant
% 3.82/4.07 thf(fact_5341_sum_Osetdiff__irrelevant,axiom,
% 3.82/4.07 ! [A2: set_complex,G: complex > real] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.07 => ( ( groups5808333547571424918x_real @ G
% 3.82/4.07 @ ( minus_811609699411566653omplex @ A2
% 3.82/4.07 @ ( collect_complex
% 3.82/4.07 @ ^ [X4: complex] :
% 3.82/4.07 ( ( G @ X4 )
% 3.82/4.07 = zero_zero_real ) ) ) )
% 3.82/4.07 = ( groups5808333547571424918x_real @ G @ A2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.setdiff_irrelevant
% 3.82/4.07 thf(fact_5342_sum_Osetdiff__irrelevant,axiom,
% 3.82/4.07 ! [A2: set_int,G: int > real] :
% 3.82/4.07 ( ( finite_finite_int @ A2 )
% 3.82/4.07 => ( ( groups8778361861064173332t_real @ G
% 3.82/4.07 @ ( minus_minus_set_int @ A2
% 3.82/4.07 @ ( collect_int
% 3.82/4.07 @ ^ [X4: int] :
% 3.82/4.07 ( ( G @ X4 )
% 3.82/4.07 = zero_zero_real ) ) ) )
% 3.82/4.07 = ( groups8778361861064173332t_real @ G @ A2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.setdiff_irrelevant
% 3.82/4.07 thf(fact_5343_sum_Osetdiff__irrelevant,axiom,
% 3.82/4.07 ! [A2: set_Extended_enat,G: extended_enat > real] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.07 => ( ( groups4148127829035722712t_real @ G
% 3.82/4.07 @ ( minus_925952699566721837d_enat @ A2
% 3.82/4.07 @ ( collec4429806609662206161d_enat
% 3.82/4.07 @ ^ [X4: extended_enat] :
% 3.82/4.07 ( ( G @ X4 )
% 3.82/4.07 = zero_zero_real ) ) ) )
% 3.82/4.07 = ( groups4148127829035722712t_real @ G @ A2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.setdiff_irrelevant
% 3.82/4.07 thf(fact_5344_sum_Osetdiff__irrelevant,axiom,
% 3.82/4.07 ! [A2: set_real,G: real > int] :
% 3.82/4.07 ( ( finite_finite_real @ A2 )
% 3.82/4.07 => ( ( groups1932886352136224148al_int @ G
% 3.82/4.07 @ ( minus_minus_set_real @ A2
% 3.82/4.07 @ ( collect_real
% 3.82/4.07 @ ^ [X4: real] :
% 3.82/4.07 ( ( G @ X4 )
% 3.82/4.07 = zero_zero_int ) ) ) )
% 3.82/4.07 = ( groups1932886352136224148al_int @ G @ A2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.setdiff_irrelevant
% 3.82/4.07 thf(fact_5345_sum_Osetdiff__irrelevant,axiom,
% 3.82/4.07 ! [A2: set_complex,G: complex > int] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.07 => ( ( groups5690904116761175830ex_int @ G
% 3.82/4.07 @ ( minus_811609699411566653omplex @ A2
% 3.82/4.07 @ ( collect_complex
% 3.82/4.07 @ ^ [X4: complex] :
% 3.82/4.07 ( ( G @ X4 )
% 3.82/4.07 = zero_zero_int ) ) ) )
% 3.82/4.07 = ( groups5690904116761175830ex_int @ G @ A2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.setdiff_irrelevant
% 3.82/4.07 thf(fact_5346_sum__pos2,axiom,
% 3.82/4.07 ! [I6: set_real,I: real,F: real > extended_enat] :
% 3.82/4.07 ( ( finite_finite_real @ I6 )
% 3.82/4.07 => ( ( member_real @ I @ I6 )
% 3.82/4.07 => ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( F @ I ) )
% 3.82/4.07 => ( ! [I4: real] :
% 3.82/4.07 ( ( member_real @ I4 @ I6 )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ I4 ) ) )
% 3.82/4.07 => ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( groups2800946370649118462d_enat @ F @ I6 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_pos2
% 3.82/4.07 thf(fact_5347_sum__pos2,axiom,
% 3.82/4.07 ! [I6: set_nat,I: nat,F: nat > extended_enat] :
% 3.82/4.07 ( ( finite_finite_nat @ I6 )
% 3.82/4.07 => ( ( member_nat @ I @ I6 )
% 3.82/4.07 => ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( F @ I ) )
% 3.82/4.07 => ( ! [I4: nat] :
% 3.82/4.07 ( ( member_nat @ I4 @ I6 )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ I4 ) ) )
% 3.82/4.07 => ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( groups7108830773950497114d_enat @ F @ I6 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_pos2
% 3.82/4.07 thf(fact_5348_sum__pos2,axiom,
% 3.82/4.07 ! [I6: set_complex,I: complex,F: complex > extended_enat] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ I6 )
% 3.82/4.07 => ( ( member_complex @ I @ I6 )
% 3.82/4.07 => ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( F @ I ) )
% 3.82/4.07 => ( ! [I4: complex] :
% 3.82/4.07 ( ( member_complex @ I4 @ I6 )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ I4 ) ) )
% 3.82/4.07 => ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( groups1752964319039525884d_enat @ F @ I6 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_pos2
% 3.82/4.07 thf(fact_5349_sum__pos2,axiom,
% 3.82/4.07 ! [I6: set_int,I: int,F: int > extended_enat] :
% 3.82/4.07 ( ( finite_finite_int @ I6 )
% 3.82/4.07 => ( ( member_int @ I @ I6 )
% 3.82/4.07 => ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( F @ I ) )
% 3.82/4.07 => ( ! [I4: int] :
% 3.82/4.07 ( ( member_int @ I4 @ I6 )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ I4 ) ) )
% 3.82/4.07 => ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( groups4225252721152677374d_enat @ F @ I6 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_pos2
% 3.82/4.07 thf(fact_5350_sum__pos2,axiom,
% 3.82/4.07 ! [I6: set_Extended_enat,I: extended_enat,F: extended_enat > extended_enat] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ I6 )
% 3.82/4.07 => ( ( member_Extended_enat @ I @ I6 )
% 3.82/4.07 => ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( F @ I ) )
% 3.82/4.07 => ( ! [I4: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ I4 @ I6 )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ I4 ) ) )
% 3.82/4.07 => ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( groups2433450451889696826d_enat @ F @ I6 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_pos2
% 3.82/4.07 thf(fact_5351_sum__pos2,axiom,
% 3.82/4.07 ! [I6: set_real,I: real,F: real > real] :
% 3.82/4.07 ( ( finite_finite_real @ I6 )
% 3.82/4.07 => ( ( member_real @ I @ I6 )
% 3.82/4.07 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 3.82/4.07 => ( ! [I4: real] :
% 3.82/4.07 ( ( member_real @ I4 @ I6 )
% 3.82/4.07 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 3.82/4.07 => ( ord_less_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ I6 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_pos2
% 3.82/4.07 thf(fact_5352_sum__pos2,axiom,
% 3.82/4.07 ! [I6: set_complex,I: complex,F: complex > real] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ I6 )
% 3.82/4.07 => ( ( member_complex @ I @ I6 )
% 3.82/4.07 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 3.82/4.07 => ( ! [I4: complex] :
% 3.82/4.07 ( ( member_complex @ I4 @ I6 )
% 3.82/4.07 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 3.82/4.07 => ( ord_less_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ I6 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_pos2
% 3.82/4.07 thf(fact_5353_sum__pos2,axiom,
% 3.82/4.07 ! [I6: set_int,I: int,F: int > real] :
% 3.82/4.07 ( ( finite_finite_int @ I6 )
% 3.82/4.07 => ( ( member_int @ I @ I6 )
% 3.82/4.07 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 3.82/4.07 => ( ! [I4: int] :
% 3.82/4.07 ( ( member_int @ I4 @ I6 )
% 3.82/4.07 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 3.82/4.07 => ( ord_less_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ I6 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_pos2
% 3.82/4.07 thf(fact_5354_sum__pos2,axiom,
% 3.82/4.07 ! [I6: set_Extended_enat,I: extended_enat,F: extended_enat > real] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ I6 )
% 3.82/4.07 => ( ( member_Extended_enat @ I @ I6 )
% 3.82/4.07 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 3.82/4.07 => ( ! [I4: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ I4 @ I6 )
% 3.82/4.07 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 3.82/4.07 => ( ord_less_real @ zero_zero_real @ ( groups4148127829035722712t_real @ F @ I6 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_pos2
% 3.82/4.07 thf(fact_5355_sum__pos2,axiom,
% 3.82/4.07 ! [I6: set_real,I: real,F: real > nat] :
% 3.82/4.07 ( ( finite_finite_real @ I6 )
% 3.82/4.07 => ( ( member_real @ I @ I6 )
% 3.82/4.07 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I ) )
% 3.82/4.07 => ( ! [I4: real] :
% 3.82/4.07 ( ( member_real @ I4 @ I6 )
% 3.82/4.07 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 3.82/4.07 => ( ord_less_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ I6 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_pos2
% 3.82/4.07 thf(fact_5356_sum__pos,axiom,
% 3.82/4.07 ! [I6: set_complex,F: complex > nat] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ I6 )
% 3.82/4.07 => ( ( I6 != bot_bot_set_complex )
% 3.82/4.07 => ( ! [I4: complex] :
% 3.82/4.07 ( ( member_complex @ I4 @ I6 )
% 3.82/4.07 => ( ord_less_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 3.82/4.07 => ( ord_less_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F @ I6 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_pos
% 3.82/4.07 thf(fact_5357_sum__pos,axiom,
% 3.82/4.07 ! [I6: set_Extended_enat,F: extended_enat > nat] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ I6 )
% 3.82/4.07 => ( ( I6 != bot_bo7653980558646680370d_enat )
% 3.82/4.07 => ( ! [I4: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ I4 @ I6 )
% 3.82/4.07 => ( ord_less_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 3.82/4.07 => ( ord_less_nat @ zero_zero_nat @ ( groups2027974829824023292at_nat @ F @ I6 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_pos
% 3.82/4.07 thf(fact_5358_sum__pos,axiom,
% 3.82/4.07 ! [I6: set_real,F: real > nat] :
% 3.82/4.07 ( ( finite_finite_real @ I6 )
% 3.82/4.07 => ( ( I6 != bot_bot_set_real )
% 3.82/4.07 => ( ! [I4: real] :
% 3.82/4.07 ( ( member_real @ I4 @ I6 )
% 3.82/4.07 => ( ord_less_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 3.82/4.07 => ( ord_less_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ I6 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_pos
% 3.82/4.07 thf(fact_5359_sum__pos,axiom,
% 3.82/4.07 ! [I6: set_int,F: int > nat] :
% 3.82/4.07 ( ( finite_finite_int @ I6 )
% 3.82/4.07 => ( ( I6 != bot_bot_set_int )
% 3.82/4.07 => ( ! [I4: int] :
% 3.82/4.07 ( ( member_int @ I4 @ I6 )
% 3.82/4.07 => ( ord_less_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 3.82/4.07 => ( ord_less_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ I6 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_pos
% 3.82/4.07 thf(fact_5360_sum__pos,axiom,
% 3.82/4.07 ! [I6: set_complex,F: complex > extended_enat] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ I6 )
% 3.82/4.07 => ( ( I6 != bot_bot_set_complex )
% 3.82/4.07 => ( ! [I4: complex] :
% 3.82/4.07 ( ( member_complex @ I4 @ I6 )
% 3.82/4.07 => ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( F @ I4 ) ) )
% 3.82/4.07 => ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( groups1752964319039525884d_enat @ F @ I6 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_pos
% 3.82/4.07 thf(fact_5361_sum__pos,axiom,
% 3.82/4.07 ! [I6: set_Extended_enat,F: extended_enat > extended_enat] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ I6 )
% 3.82/4.07 => ( ( I6 != bot_bo7653980558646680370d_enat )
% 3.82/4.07 => ( ! [I4: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ I4 @ I6 )
% 3.82/4.07 => ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( F @ I4 ) ) )
% 3.82/4.07 => ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( groups2433450451889696826d_enat @ F @ I6 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_pos
% 3.82/4.07 thf(fact_5362_sum__pos,axiom,
% 3.82/4.07 ! [I6: set_real,F: real > extended_enat] :
% 3.82/4.07 ( ( finite_finite_real @ I6 )
% 3.82/4.07 => ( ( I6 != bot_bot_set_real )
% 3.82/4.07 => ( ! [I4: real] :
% 3.82/4.07 ( ( member_real @ I4 @ I6 )
% 3.82/4.07 => ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( F @ I4 ) ) )
% 3.82/4.07 => ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( groups2800946370649118462d_enat @ F @ I6 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_pos
% 3.82/4.07 thf(fact_5363_sum__pos,axiom,
% 3.82/4.07 ! [I6: set_nat,F: nat > extended_enat] :
% 3.82/4.07 ( ( finite_finite_nat @ I6 )
% 3.82/4.07 => ( ( I6 != bot_bot_set_nat )
% 3.82/4.07 => ( ! [I4: nat] :
% 3.82/4.07 ( ( member_nat @ I4 @ I6 )
% 3.82/4.07 => ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( F @ I4 ) ) )
% 3.82/4.07 => ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( groups7108830773950497114d_enat @ F @ I6 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_pos
% 3.82/4.07 thf(fact_5364_sum__pos,axiom,
% 3.82/4.07 ! [I6: set_int,F: int > extended_enat] :
% 3.82/4.07 ( ( finite_finite_int @ I6 )
% 3.82/4.07 => ( ( I6 != bot_bot_set_int )
% 3.82/4.07 => ( ! [I4: int] :
% 3.82/4.07 ( ( member_int @ I4 @ I6 )
% 3.82/4.07 => ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( F @ I4 ) ) )
% 3.82/4.07 => ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( groups4225252721152677374d_enat @ F @ I6 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_pos
% 3.82/4.07 thf(fact_5365_sum__pos,axiom,
% 3.82/4.07 ! [I6: set_complex,F: complex > real] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ I6 )
% 3.82/4.07 => ( ( I6 != bot_bot_set_complex )
% 3.82/4.07 => ( ! [I4: complex] :
% 3.82/4.07 ( ( member_complex @ I4 @ I6 )
% 3.82/4.07 => ( ord_less_real @ zero_zero_real @ ( F @ I4 ) ) )
% 3.82/4.07 => ( ord_less_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ I6 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_pos
% 3.82/4.07 thf(fact_5366_sum_Omono__neutral__cong__right,axiom,
% 3.82/4.07 ! [T3: set_real,S2: set_real,G: real > nat,H2: real > nat] :
% 3.82/4.07 ( ( finite_finite_real @ T3 )
% 3.82/4.07 => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 3.82/4.07 => ( ! [X5: real] :
% 3.82/4.07 ( ( member_real @ X5 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 3.82/4.07 => ( ( G @ X5 )
% 3.82/4.07 = zero_zero_nat ) )
% 3.82/4.07 => ( ! [X5: real] :
% 3.82/4.07 ( ( member_real @ X5 @ S2 )
% 3.82/4.07 => ( ( G @ X5 )
% 3.82/4.07 = ( H2 @ X5 ) ) )
% 3.82/4.07 => ( ( groups1935376822645274424al_nat @ G @ T3 )
% 3.82/4.07 = ( groups1935376822645274424al_nat @ H2 @ S2 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.mono_neutral_cong_right
% 3.82/4.07 thf(fact_5367_sum_Omono__neutral__cong__right,axiom,
% 3.82/4.07 ! [T3: set_complex,S2: set_complex,G: complex > nat,H2: complex > nat] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ T3 )
% 3.82/4.07 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 3.82/4.07 => ( ! [X5: complex] :
% 3.82/4.07 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 3.82/4.07 => ( ( G @ X5 )
% 3.82/4.07 = zero_zero_nat ) )
% 3.82/4.07 => ( ! [X5: complex] :
% 3.82/4.07 ( ( member_complex @ X5 @ S2 )
% 3.82/4.07 => ( ( G @ X5 )
% 3.82/4.07 = ( H2 @ X5 ) ) )
% 3.82/4.07 => ( ( groups5693394587270226106ex_nat @ G @ T3 )
% 3.82/4.07 = ( groups5693394587270226106ex_nat @ H2 @ S2 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.mono_neutral_cong_right
% 3.82/4.07 thf(fact_5368_sum_Omono__neutral__cong__right,axiom,
% 3.82/4.07 ! [T3: set_Extended_enat,S2: set_Extended_enat,G: extended_enat > nat,H2: extended_enat > nat] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ T3 )
% 3.82/4.07 => ( ( ord_le7203529160286727270d_enat @ S2 @ T3 )
% 3.82/4.07 => ( ! [X5: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ X5 @ ( minus_925952699566721837d_enat @ T3 @ S2 ) )
% 3.82/4.07 => ( ( G @ X5 )
% 3.82/4.07 = zero_zero_nat ) )
% 3.82/4.07 => ( ! [X5: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ X5 @ S2 )
% 3.82/4.07 => ( ( G @ X5 )
% 3.82/4.07 = ( H2 @ X5 ) ) )
% 3.82/4.07 => ( ( groups2027974829824023292at_nat @ G @ T3 )
% 3.82/4.07 = ( groups2027974829824023292at_nat @ H2 @ S2 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.mono_neutral_cong_right
% 3.82/4.07 thf(fact_5369_sum_Omono__neutral__cong__right,axiom,
% 3.82/4.07 ! [T3: set_real,S2: set_real,G: real > real,H2: real > real] :
% 3.82/4.07 ( ( finite_finite_real @ T3 )
% 3.82/4.07 => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 3.82/4.07 => ( ! [X5: real] :
% 3.82/4.07 ( ( member_real @ X5 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 3.82/4.07 => ( ( G @ X5 )
% 3.82/4.07 = zero_zero_real ) )
% 3.82/4.07 => ( ! [X5: real] :
% 3.82/4.07 ( ( member_real @ X5 @ S2 )
% 3.82/4.07 => ( ( G @ X5 )
% 3.82/4.07 = ( H2 @ X5 ) ) )
% 3.82/4.07 => ( ( groups8097168146408367636l_real @ G @ T3 )
% 3.82/4.07 = ( groups8097168146408367636l_real @ H2 @ S2 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.mono_neutral_cong_right
% 3.82/4.07 thf(fact_5370_sum_Omono__neutral__cong__right,axiom,
% 3.82/4.07 ! [T3: set_complex,S2: set_complex,G: complex > real,H2: complex > real] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ T3 )
% 3.82/4.07 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 3.82/4.07 => ( ! [X5: complex] :
% 3.82/4.07 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 3.82/4.07 => ( ( G @ X5 )
% 3.82/4.07 = zero_zero_real ) )
% 3.82/4.07 => ( ! [X5: complex] :
% 3.82/4.07 ( ( member_complex @ X5 @ S2 )
% 3.82/4.07 => ( ( G @ X5 )
% 3.82/4.07 = ( H2 @ X5 ) ) )
% 3.82/4.07 => ( ( groups5808333547571424918x_real @ G @ T3 )
% 3.82/4.07 = ( groups5808333547571424918x_real @ H2 @ S2 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.mono_neutral_cong_right
% 3.82/4.07 thf(fact_5371_sum_Omono__neutral__cong__right,axiom,
% 3.82/4.07 ! [T3: set_Extended_enat,S2: set_Extended_enat,G: extended_enat > real,H2: extended_enat > real] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ T3 )
% 3.82/4.07 => ( ( ord_le7203529160286727270d_enat @ S2 @ T3 )
% 3.82/4.07 => ( ! [X5: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ X5 @ ( minus_925952699566721837d_enat @ T3 @ S2 ) )
% 3.82/4.07 => ( ( G @ X5 )
% 3.82/4.07 = zero_zero_real ) )
% 3.82/4.07 => ( ! [X5: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ X5 @ S2 )
% 3.82/4.07 => ( ( G @ X5 )
% 3.82/4.07 = ( H2 @ X5 ) ) )
% 3.82/4.07 => ( ( groups4148127829035722712t_real @ G @ T3 )
% 3.82/4.07 = ( groups4148127829035722712t_real @ H2 @ S2 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.mono_neutral_cong_right
% 3.82/4.07 thf(fact_5372_sum_Omono__neutral__cong__right,axiom,
% 3.82/4.07 ! [T3: set_real,S2: set_real,G: real > int,H2: real > int] :
% 3.82/4.07 ( ( finite_finite_real @ T3 )
% 3.82/4.07 => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 3.82/4.07 => ( ! [X5: real] :
% 3.82/4.07 ( ( member_real @ X5 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 3.82/4.07 => ( ( G @ X5 )
% 3.82/4.07 = zero_zero_int ) )
% 3.82/4.07 => ( ! [X5: real] :
% 3.82/4.07 ( ( member_real @ X5 @ S2 )
% 3.82/4.07 => ( ( G @ X5 )
% 3.82/4.07 = ( H2 @ X5 ) ) )
% 3.82/4.07 => ( ( groups1932886352136224148al_int @ G @ T3 )
% 3.82/4.07 = ( groups1932886352136224148al_int @ H2 @ S2 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.mono_neutral_cong_right
% 3.82/4.07 thf(fact_5373_sum_Omono__neutral__cong__right,axiom,
% 3.82/4.07 ! [T3: set_complex,S2: set_complex,G: complex > int,H2: complex > int] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ T3 )
% 3.82/4.07 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 3.82/4.07 => ( ! [X5: complex] :
% 3.82/4.07 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 3.82/4.07 => ( ( G @ X5 )
% 3.82/4.07 = zero_zero_int ) )
% 3.82/4.07 => ( ! [X5: complex] :
% 3.82/4.07 ( ( member_complex @ X5 @ S2 )
% 3.82/4.07 => ( ( G @ X5 )
% 3.82/4.07 = ( H2 @ X5 ) ) )
% 3.82/4.07 => ( ( groups5690904116761175830ex_int @ G @ T3 )
% 3.82/4.07 = ( groups5690904116761175830ex_int @ H2 @ S2 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.mono_neutral_cong_right
% 3.82/4.07 thf(fact_5374_sum_Omono__neutral__cong__right,axiom,
% 3.82/4.07 ! [T3: set_Extended_enat,S2: set_Extended_enat,G: extended_enat > int,H2: extended_enat > int] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ T3 )
% 3.82/4.07 => ( ( ord_le7203529160286727270d_enat @ S2 @ T3 )
% 3.82/4.07 => ( ! [X5: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ X5 @ ( minus_925952699566721837d_enat @ T3 @ S2 ) )
% 3.82/4.07 => ( ( G @ X5 )
% 3.82/4.07 = zero_zero_int ) )
% 3.82/4.07 => ( ! [X5: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ X5 @ S2 )
% 3.82/4.07 => ( ( G @ X5 )
% 3.82/4.07 = ( H2 @ X5 ) ) )
% 3.82/4.07 => ( ( groups2025484359314973016at_int @ G @ T3 )
% 3.82/4.07 = ( groups2025484359314973016at_int @ H2 @ S2 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.mono_neutral_cong_right
% 3.82/4.07 thf(fact_5375_sum_Omono__neutral__cong__right,axiom,
% 3.82/4.07 ! [T3: set_real,S2: set_real,G: real > complex,H2: real > complex] :
% 3.82/4.07 ( ( finite_finite_real @ T3 )
% 3.82/4.07 => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 3.82/4.07 => ( ! [X5: real] :
% 3.82/4.07 ( ( member_real @ X5 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 3.82/4.07 => ( ( G @ X5 )
% 3.82/4.07 = zero_zero_complex ) )
% 3.82/4.07 => ( ! [X5: real] :
% 3.82/4.07 ( ( member_real @ X5 @ S2 )
% 3.82/4.07 => ( ( G @ X5 )
% 3.82/4.07 = ( H2 @ X5 ) ) )
% 3.82/4.07 => ( ( groups5754745047067104278omplex @ G @ T3 )
% 3.82/4.07 = ( groups5754745047067104278omplex @ H2 @ S2 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.mono_neutral_cong_right
% 3.82/4.07 thf(fact_5376_sum_Omono__neutral__cong__left,axiom,
% 3.82/4.07 ! [T3: set_real,S2: set_real,H2: real > nat,G: real > nat] :
% 3.82/4.07 ( ( finite_finite_real @ T3 )
% 3.82/4.07 => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 3.82/4.07 => ( ! [X5: real] :
% 3.82/4.07 ( ( member_real @ X5 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 3.82/4.07 => ( ( H2 @ X5 )
% 3.82/4.07 = zero_zero_nat ) )
% 3.82/4.07 => ( ! [X5: real] :
% 3.82/4.07 ( ( member_real @ X5 @ S2 )
% 3.82/4.07 => ( ( G @ X5 )
% 3.82/4.07 = ( H2 @ X5 ) ) )
% 3.82/4.07 => ( ( groups1935376822645274424al_nat @ G @ S2 )
% 3.82/4.07 = ( groups1935376822645274424al_nat @ H2 @ T3 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.mono_neutral_cong_left
% 3.82/4.07 thf(fact_5377_sum_Omono__neutral__cong__left,axiom,
% 3.82/4.07 ! [T3: set_complex,S2: set_complex,H2: complex > nat,G: complex > nat] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ T3 )
% 3.82/4.07 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 3.82/4.07 => ( ! [X5: complex] :
% 3.82/4.07 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 3.82/4.07 => ( ( H2 @ X5 )
% 3.82/4.07 = zero_zero_nat ) )
% 3.82/4.07 => ( ! [X5: complex] :
% 3.82/4.07 ( ( member_complex @ X5 @ S2 )
% 3.82/4.07 => ( ( G @ X5 )
% 3.82/4.07 = ( H2 @ X5 ) ) )
% 3.82/4.07 => ( ( groups5693394587270226106ex_nat @ G @ S2 )
% 3.82/4.07 = ( groups5693394587270226106ex_nat @ H2 @ T3 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.mono_neutral_cong_left
% 3.82/4.07 thf(fact_5378_sum_Omono__neutral__cong__left,axiom,
% 3.82/4.07 ! [T3: set_Extended_enat,S2: set_Extended_enat,H2: extended_enat > nat,G: extended_enat > nat] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ T3 )
% 3.82/4.07 => ( ( ord_le7203529160286727270d_enat @ S2 @ T3 )
% 3.82/4.07 => ( ! [X5: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ X5 @ ( minus_925952699566721837d_enat @ T3 @ S2 ) )
% 3.82/4.07 => ( ( H2 @ X5 )
% 3.82/4.07 = zero_zero_nat ) )
% 3.82/4.07 => ( ! [X5: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ X5 @ S2 )
% 3.82/4.07 => ( ( G @ X5 )
% 3.82/4.07 = ( H2 @ X5 ) ) )
% 3.82/4.07 => ( ( groups2027974829824023292at_nat @ G @ S2 )
% 3.82/4.07 = ( groups2027974829824023292at_nat @ H2 @ T3 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.mono_neutral_cong_left
% 3.82/4.07 thf(fact_5379_sum_Omono__neutral__cong__left,axiom,
% 3.82/4.07 ! [T3: set_real,S2: set_real,H2: real > real,G: real > real] :
% 3.82/4.07 ( ( finite_finite_real @ T3 )
% 3.82/4.07 => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 3.82/4.07 => ( ! [X5: real] :
% 3.82/4.07 ( ( member_real @ X5 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 3.82/4.07 => ( ( H2 @ X5 )
% 3.82/4.07 = zero_zero_real ) )
% 3.82/4.07 => ( ! [X5: real] :
% 3.82/4.07 ( ( member_real @ X5 @ S2 )
% 3.82/4.07 => ( ( G @ X5 )
% 3.82/4.07 = ( H2 @ X5 ) ) )
% 3.82/4.07 => ( ( groups8097168146408367636l_real @ G @ S2 )
% 3.82/4.07 = ( groups8097168146408367636l_real @ H2 @ T3 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.mono_neutral_cong_left
% 3.82/4.07 thf(fact_5380_sum_Omono__neutral__cong__left,axiom,
% 3.82/4.07 ! [T3: set_complex,S2: set_complex,H2: complex > real,G: complex > real] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ T3 )
% 3.82/4.07 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 3.82/4.07 => ( ! [X5: complex] :
% 3.82/4.07 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 3.82/4.07 => ( ( H2 @ X5 )
% 3.82/4.07 = zero_zero_real ) )
% 3.82/4.07 => ( ! [X5: complex] :
% 3.82/4.07 ( ( member_complex @ X5 @ S2 )
% 3.82/4.07 => ( ( G @ X5 )
% 3.82/4.07 = ( H2 @ X5 ) ) )
% 3.82/4.07 => ( ( groups5808333547571424918x_real @ G @ S2 )
% 3.82/4.07 = ( groups5808333547571424918x_real @ H2 @ T3 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.mono_neutral_cong_left
% 3.82/4.07 thf(fact_5381_sum_Omono__neutral__cong__left,axiom,
% 3.82/4.07 ! [T3: set_Extended_enat,S2: set_Extended_enat,H2: extended_enat > real,G: extended_enat > real] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ T3 )
% 3.82/4.07 => ( ( ord_le7203529160286727270d_enat @ S2 @ T3 )
% 3.82/4.07 => ( ! [X5: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ X5 @ ( minus_925952699566721837d_enat @ T3 @ S2 ) )
% 3.82/4.07 => ( ( H2 @ X5 )
% 3.82/4.07 = zero_zero_real ) )
% 3.82/4.07 => ( ! [X5: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ X5 @ S2 )
% 3.82/4.07 => ( ( G @ X5 )
% 3.82/4.07 = ( H2 @ X5 ) ) )
% 3.82/4.07 => ( ( groups4148127829035722712t_real @ G @ S2 )
% 3.82/4.07 = ( groups4148127829035722712t_real @ H2 @ T3 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.mono_neutral_cong_left
% 3.82/4.07 thf(fact_5382_sum_Omono__neutral__cong__left,axiom,
% 3.82/4.07 ! [T3: set_real,S2: set_real,H2: real > int,G: real > int] :
% 3.82/4.07 ( ( finite_finite_real @ T3 )
% 3.82/4.07 => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 3.82/4.07 => ( ! [X5: real] :
% 3.82/4.07 ( ( member_real @ X5 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 3.82/4.07 => ( ( H2 @ X5 )
% 3.82/4.07 = zero_zero_int ) )
% 3.82/4.07 => ( ! [X5: real] :
% 3.82/4.07 ( ( member_real @ X5 @ S2 )
% 3.82/4.07 => ( ( G @ X5 )
% 3.82/4.07 = ( H2 @ X5 ) ) )
% 3.82/4.07 => ( ( groups1932886352136224148al_int @ G @ S2 )
% 3.82/4.07 = ( groups1932886352136224148al_int @ H2 @ T3 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.mono_neutral_cong_left
% 3.82/4.07 thf(fact_5383_sum_Omono__neutral__cong__left,axiom,
% 3.82/4.07 ! [T3: set_complex,S2: set_complex,H2: complex > int,G: complex > int] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ T3 )
% 3.82/4.07 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 3.82/4.07 => ( ! [X5: complex] :
% 3.82/4.07 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 3.82/4.07 => ( ( H2 @ X5 )
% 3.82/4.07 = zero_zero_int ) )
% 3.82/4.07 => ( ! [X5: complex] :
% 3.82/4.07 ( ( member_complex @ X5 @ S2 )
% 3.82/4.07 => ( ( G @ X5 )
% 3.82/4.07 = ( H2 @ X5 ) ) )
% 3.82/4.07 => ( ( groups5690904116761175830ex_int @ G @ S2 )
% 3.82/4.07 = ( groups5690904116761175830ex_int @ H2 @ T3 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.mono_neutral_cong_left
% 3.82/4.07 thf(fact_5384_sum_Omono__neutral__cong__left,axiom,
% 3.82/4.07 ! [T3: set_Extended_enat,S2: set_Extended_enat,H2: extended_enat > int,G: extended_enat > int] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ T3 )
% 3.82/4.07 => ( ( ord_le7203529160286727270d_enat @ S2 @ T3 )
% 3.82/4.07 => ( ! [X5: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ X5 @ ( minus_925952699566721837d_enat @ T3 @ S2 ) )
% 3.82/4.07 => ( ( H2 @ X5 )
% 3.82/4.07 = zero_zero_int ) )
% 3.82/4.07 => ( ! [X5: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ X5 @ S2 )
% 3.82/4.07 => ( ( G @ X5 )
% 3.82/4.07 = ( H2 @ X5 ) ) )
% 3.82/4.07 => ( ( groups2025484359314973016at_int @ G @ S2 )
% 3.82/4.07 = ( groups2025484359314973016at_int @ H2 @ T3 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.mono_neutral_cong_left
% 3.82/4.07 thf(fact_5385_sum_Omono__neutral__cong__left,axiom,
% 3.82/4.07 ! [T3: set_real,S2: set_real,H2: real > complex,G: real > complex] :
% 3.82/4.07 ( ( finite_finite_real @ T3 )
% 3.82/4.07 => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 3.82/4.07 => ( ! [X5: real] :
% 3.82/4.07 ( ( member_real @ X5 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 3.82/4.07 => ( ( H2 @ X5 )
% 3.82/4.07 = zero_zero_complex ) )
% 3.82/4.07 => ( ! [X5: real] :
% 3.82/4.07 ( ( member_real @ X5 @ S2 )
% 3.82/4.07 => ( ( G @ X5 )
% 3.82/4.07 = ( H2 @ X5 ) ) )
% 3.82/4.07 => ( ( groups5754745047067104278omplex @ G @ S2 )
% 3.82/4.07 = ( groups5754745047067104278omplex @ H2 @ T3 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.mono_neutral_cong_left
% 3.82/4.07 thf(fact_5386_sum_Omono__neutral__right,axiom,
% 3.82/4.07 ! [T3: set_complex,S2: set_complex,G: complex > nat] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ T3 )
% 3.82/4.07 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 3.82/4.07 => ( ! [X5: complex] :
% 3.82/4.07 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 3.82/4.07 => ( ( G @ X5 )
% 3.82/4.07 = zero_zero_nat ) )
% 3.82/4.07 => ( ( groups5693394587270226106ex_nat @ G @ T3 )
% 3.82/4.07 = ( groups5693394587270226106ex_nat @ G @ S2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.mono_neutral_right
% 3.82/4.07 thf(fact_5387_sum_Omono__neutral__right,axiom,
% 3.82/4.07 ! [T3: set_Extended_enat,S2: set_Extended_enat,G: extended_enat > nat] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ T3 )
% 3.82/4.07 => ( ( ord_le7203529160286727270d_enat @ S2 @ T3 )
% 3.82/4.07 => ( ! [X5: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ X5 @ ( minus_925952699566721837d_enat @ T3 @ S2 ) )
% 3.82/4.07 => ( ( G @ X5 )
% 3.82/4.07 = zero_zero_nat ) )
% 3.82/4.07 => ( ( groups2027974829824023292at_nat @ G @ T3 )
% 3.82/4.07 = ( groups2027974829824023292at_nat @ G @ S2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.mono_neutral_right
% 3.82/4.07 thf(fact_5388_sum_Omono__neutral__right,axiom,
% 3.82/4.07 ! [T3: set_complex,S2: set_complex,G: complex > real] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ T3 )
% 3.82/4.07 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 3.82/4.07 => ( ! [X5: complex] :
% 3.82/4.07 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 3.82/4.07 => ( ( G @ X5 )
% 3.82/4.07 = zero_zero_real ) )
% 3.82/4.07 => ( ( groups5808333547571424918x_real @ G @ T3 )
% 3.82/4.07 = ( groups5808333547571424918x_real @ G @ S2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.mono_neutral_right
% 3.82/4.07 thf(fact_5389_sum_Omono__neutral__right,axiom,
% 3.82/4.07 ! [T3: set_Extended_enat,S2: set_Extended_enat,G: extended_enat > real] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ T3 )
% 3.82/4.07 => ( ( ord_le7203529160286727270d_enat @ S2 @ T3 )
% 3.82/4.07 => ( ! [X5: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ X5 @ ( minus_925952699566721837d_enat @ T3 @ S2 ) )
% 3.82/4.07 => ( ( G @ X5 )
% 3.82/4.07 = zero_zero_real ) )
% 3.82/4.07 => ( ( groups4148127829035722712t_real @ G @ T3 )
% 3.82/4.07 = ( groups4148127829035722712t_real @ G @ S2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.mono_neutral_right
% 3.82/4.07 thf(fact_5390_sum_Omono__neutral__right,axiom,
% 3.82/4.07 ! [T3: set_complex,S2: set_complex,G: complex > int] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ T3 )
% 3.82/4.07 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 3.82/4.07 => ( ! [X5: complex] :
% 3.82/4.07 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 3.82/4.07 => ( ( G @ X5 )
% 3.82/4.07 = zero_zero_int ) )
% 3.82/4.07 => ( ( groups5690904116761175830ex_int @ G @ T3 )
% 3.82/4.07 = ( groups5690904116761175830ex_int @ G @ S2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.mono_neutral_right
% 3.82/4.07 thf(fact_5391_sum_Omono__neutral__right,axiom,
% 3.82/4.07 ! [T3: set_Extended_enat,S2: set_Extended_enat,G: extended_enat > int] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ T3 )
% 3.82/4.07 => ( ( ord_le7203529160286727270d_enat @ S2 @ T3 )
% 3.82/4.07 => ( ! [X5: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ X5 @ ( minus_925952699566721837d_enat @ T3 @ S2 ) )
% 3.82/4.07 => ( ( G @ X5 )
% 3.82/4.07 = zero_zero_int ) )
% 3.82/4.07 => ( ( groups2025484359314973016at_int @ G @ T3 )
% 3.82/4.07 = ( groups2025484359314973016at_int @ G @ S2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.mono_neutral_right
% 3.82/4.07 thf(fact_5392_sum_Omono__neutral__right,axiom,
% 3.82/4.07 ! [T3: set_Extended_enat,S2: set_Extended_enat,G: extended_enat > complex] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ T3 )
% 3.82/4.07 => ( ( ord_le7203529160286727270d_enat @ S2 @ T3 )
% 3.82/4.07 => ( ! [X5: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ X5 @ ( minus_925952699566721837d_enat @ T3 @ S2 ) )
% 3.82/4.07 => ( ( G @ X5 )
% 3.82/4.07 = zero_zero_complex ) )
% 3.82/4.07 => ( ( groups6818542070133387226omplex @ G @ T3 )
% 3.82/4.07 = ( groups6818542070133387226omplex @ G @ S2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.mono_neutral_right
% 3.82/4.07 thf(fact_5393_sum_Omono__neutral__right,axiom,
% 3.82/4.07 ! [T3: set_complex,S2: set_complex,G: complex > extended_enat] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ T3 )
% 3.82/4.07 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 3.82/4.07 => ( ! [X5: complex] :
% 3.82/4.07 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 3.82/4.07 => ( ( G @ X5 )
% 3.82/4.07 = zero_z5237406670263579293d_enat ) )
% 3.82/4.07 => ( ( groups1752964319039525884d_enat @ G @ T3 )
% 3.82/4.07 = ( groups1752964319039525884d_enat @ G @ S2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.mono_neutral_right
% 3.82/4.07 thf(fact_5394_sum_Omono__neutral__right,axiom,
% 3.82/4.07 ! [T3: set_Extended_enat,S2: set_Extended_enat,G: extended_enat > extended_enat] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ T3 )
% 3.82/4.07 => ( ( ord_le7203529160286727270d_enat @ S2 @ T3 )
% 3.82/4.07 => ( ! [X5: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ X5 @ ( minus_925952699566721837d_enat @ T3 @ S2 ) )
% 3.82/4.07 => ( ( G @ X5 )
% 3.82/4.07 = zero_z5237406670263579293d_enat ) )
% 3.82/4.07 => ( ( groups2433450451889696826d_enat @ G @ T3 )
% 3.82/4.07 = ( groups2433450451889696826d_enat @ G @ S2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.mono_neutral_right
% 3.82/4.07 thf(fact_5395_sum_Omono__neutral__right,axiom,
% 3.82/4.07 ! [T3: set_nat,S2: set_nat,G: nat > int] :
% 3.82/4.07 ( ( finite_finite_nat @ T3 )
% 3.82/4.07 => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 3.82/4.07 => ( ! [X5: nat] :
% 3.82/4.07 ( ( member_nat @ X5 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 3.82/4.07 => ( ( G @ X5 )
% 3.82/4.07 = zero_zero_int ) )
% 3.82/4.07 => ( ( groups3539618377306564664at_int @ G @ T3 )
% 3.82/4.07 = ( groups3539618377306564664at_int @ G @ S2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.mono_neutral_right
% 3.82/4.07 thf(fact_5396_sum_Omono__neutral__left,axiom,
% 3.82/4.07 ! [T3: set_complex,S2: set_complex,G: complex > nat] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ T3 )
% 3.82/4.07 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 3.82/4.07 => ( ! [X5: complex] :
% 3.82/4.07 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 3.82/4.07 => ( ( G @ X5 )
% 3.82/4.07 = zero_zero_nat ) )
% 3.82/4.07 => ( ( groups5693394587270226106ex_nat @ G @ S2 )
% 3.82/4.07 = ( groups5693394587270226106ex_nat @ G @ T3 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.mono_neutral_left
% 3.82/4.07 thf(fact_5397_sum_Omono__neutral__left,axiom,
% 3.82/4.07 ! [T3: set_Extended_enat,S2: set_Extended_enat,G: extended_enat > nat] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ T3 )
% 3.82/4.07 => ( ( ord_le7203529160286727270d_enat @ S2 @ T3 )
% 3.82/4.07 => ( ! [X5: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ X5 @ ( minus_925952699566721837d_enat @ T3 @ S2 ) )
% 3.82/4.07 => ( ( G @ X5 )
% 3.82/4.07 = zero_zero_nat ) )
% 3.82/4.07 => ( ( groups2027974829824023292at_nat @ G @ S2 )
% 3.82/4.07 = ( groups2027974829824023292at_nat @ G @ T3 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.mono_neutral_left
% 3.82/4.07 thf(fact_5398_sum_Omono__neutral__left,axiom,
% 3.82/4.07 ! [T3: set_complex,S2: set_complex,G: complex > real] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ T3 )
% 3.82/4.07 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 3.82/4.07 => ( ! [X5: complex] :
% 3.82/4.07 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 3.82/4.07 => ( ( G @ X5 )
% 3.82/4.07 = zero_zero_real ) )
% 3.82/4.07 => ( ( groups5808333547571424918x_real @ G @ S2 )
% 3.82/4.07 = ( groups5808333547571424918x_real @ G @ T3 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.mono_neutral_left
% 3.82/4.07 thf(fact_5399_sum_Omono__neutral__left,axiom,
% 3.82/4.07 ! [T3: set_Extended_enat,S2: set_Extended_enat,G: extended_enat > real] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ T3 )
% 3.82/4.07 => ( ( ord_le7203529160286727270d_enat @ S2 @ T3 )
% 3.82/4.07 => ( ! [X5: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ X5 @ ( minus_925952699566721837d_enat @ T3 @ S2 ) )
% 3.82/4.07 => ( ( G @ X5 )
% 3.82/4.07 = zero_zero_real ) )
% 3.82/4.07 => ( ( groups4148127829035722712t_real @ G @ S2 )
% 3.82/4.07 = ( groups4148127829035722712t_real @ G @ T3 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.mono_neutral_left
% 3.82/4.07 thf(fact_5400_sum_Omono__neutral__left,axiom,
% 3.82/4.07 ! [T3: set_complex,S2: set_complex,G: complex > int] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ T3 )
% 3.82/4.07 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 3.82/4.07 => ( ! [X5: complex] :
% 3.82/4.07 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 3.82/4.07 => ( ( G @ X5 )
% 3.82/4.07 = zero_zero_int ) )
% 3.82/4.07 => ( ( groups5690904116761175830ex_int @ G @ S2 )
% 3.82/4.07 = ( groups5690904116761175830ex_int @ G @ T3 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.mono_neutral_left
% 3.82/4.07 thf(fact_5401_sum_Omono__neutral__left,axiom,
% 3.82/4.07 ! [T3: set_Extended_enat,S2: set_Extended_enat,G: extended_enat > int] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ T3 )
% 3.82/4.07 => ( ( ord_le7203529160286727270d_enat @ S2 @ T3 )
% 3.82/4.07 => ( ! [X5: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ X5 @ ( minus_925952699566721837d_enat @ T3 @ S2 ) )
% 3.82/4.07 => ( ( G @ X5 )
% 3.82/4.07 = zero_zero_int ) )
% 3.82/4.07 => ( ( groups2025484359314973016at_int @ G @ S2 )
% 3.82/4.07 = ( groups2025484359314973016at_int @ G @ T3 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.mono_neutral_left
% 3.82/4.07 thf(fact_5402_sum_Omono__neutral__left,axiom,
% 3.82/4.07 ! [T3: set_Extended_enat,S2: set_Extended_enat,G: extended_enat > complex] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ T3 )
% 3.82/4.07 => ( ( ord_le7203529160286727270d_enat @ S2 @ T3 )
% 3.82/4.07 => ( ! [X5: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ X5 @ ( minus_925952699566721837d_enat @ T3 @ S2 ) )
% 3.82/4.07 => ( ( G @ X5 )
% 3.82/4.07 = zero_zero_complex ) )
% 3.82/4.07 => ( ( groups6818542070133387226omplex @ G @ S2 )
% 3.82/4.07 = ( groups6818542070133387226omplex @ G @ T3 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.mono_neutral_left
% 3.82/4.07 thf(fact_5403_sum_Omono__neutral__left,axiom,
% 3.82/4.07 ! [T3: set_complex,S2: set_complex,G: complex > extended_enat] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ T3 )
% 3.82/4.07 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 3.82/4.07 => ( ! [X5: complex] :
% 3.82/4.07 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 3.82/4.07 => ( ( G @ X5 )
% 3.82/4.07 = zero_z5237406670263579293d_enat ) )
% 3.82/4.07 => ( ( groups1752964319039525884d_enat @ G @ S2 )
% 3.82/4.07 = ( groups1752964319039525884d_enat @ G @ T3 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.mono_neutral_left
% 3.82/4.07 thf(fact_5404_sum_Omono__neutral__left,axiom,
% 3.82/4.07 ! [T3: set_Extended_enat,S2: set_Extended_enat,G: extended_enat > extended_enat] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ T3 )
% 3.82/4.07 => ( ( ord_le7203529160286727270d_enat @ S2 @ T3 )
% 3.82/4.07 => ( ! [X5: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ X5 @ ( minus_925952699566721837d_enat @ T3 @ S2 ) )
% 3.82/4.07 => ( ( G @ X5 )
% 3.82/4.07 = zero_z5237406670263579293d_enat ) )
% 3.82/4.07 => ( ( groups2433450451889696826d_enat @ G @ S2 )
% 3.82/4.07 = ( groups2433450451889696826d_enat @ G @ T3 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.mono_neutral_left
% 3.82/4.07 thf(fact_5405_sum_Omono__neutral__left,axiom,
% 3.82/4.07 ! [T3: set_nat,S2: set_nat,G: nat > int] :
% 3.82/4.07 ( ( finite_finite_nat @ T3 )
% 3.82/4.07 => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 3.82/4.07 => ( ! [X5: nat] :
% 3.82/4.07 ( ( member_nat @ X5 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 3.82/4.07 => ( ( G @ X5 )
% 3.82/4.07 = zero_zero_int ) )
% 3.82/4.07 => ( ( groups3539618377306564664at_int @ G @ S2 )
% 3.82/4.07 = ( groups3539618377306564664at_int @ G @ T3 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.mono_neutral_left
% 3.82/4.07 thf(fact_5406_sum_Osame__carrierI,axiom,
% 3.82/4.07 ! [C4: set_real,A2: set_real,B: set_real,G: real > nat,H2: real > nat] :
% 3.82/4.07 ( ( finite_finite_real @ C4 )
% 3.82/4.07 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 3.82/4.07 => ( ( ord_less_eq_set_real @ B @ C4 )
% 3.82/4.07 => ( ! [A4: real] :
% 3.82/4.07 ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 3.82/4.07 => ( ( G @ A4 )
% 3.82/4.07 = zero_zero_nat ) )
% 3.82/4.07 => ( ! [B4: real] :
% 3.82/4.07 ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B ) )
% 3.82/4.07 => ( ( H2 @ B4 )
% 3.82/4.07 = zero_zero_nat ) )
% 3.82/4.07 => ( ( ( groups1935376822645274424al_nat @ G @ C4 )
% 3.82/4.07 = ( groups1935376822645274424al_nat @ H2 @ C4 ) )
% 3.82/4.07 => ( ( groups1935376822645274424al_nat @ G @ A2 )
% 3.82/4.07 = ( groups1935376822645274424al_nat @ H2 @ B ) ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.same_carrierI
% 3.82/4.07 thf(fact_5407_sum_Osame__carrierI,axiom,
% 3.82/4.07 ! [C4: set_complex,A2: set_complex,B: set_complex,G: complex > nat,H2: complex > nat] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ C4 )
% 3.82/4.07 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 3.82/4.07 => ( ( ord_le211207098394363844omplex @ B @ C4 )
% 3.82/4.07 => ( ! [A4: complex] :
% 3.82/4.07 ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 3.82/4.07 => ( ( G @ A4 )
% 3.82/4.07 = zero_zero_nat ) )
% 3.82/4.07 => ( ! [B4: complex] :
% 3.82/4.07 ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ C4 @ B ) )
% 3.82/4.07 => ( ( H2 @ B4 )
% 3.82/4.07 = zero_zero_nat ) )
% 3.82/4.07 => ( ( ( groups5693394587270226106ex_nat @ G @ C4 )
% 3.82/4.07 = ( groups5693394587270226106ex_nat @ H2 @ C4 ) )
% 3.82/4.07 => ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 3.82/4.07 = ( groups5693394587270226106ex_nat @ H2 @ B ) ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.same_carrierI
% 3.82/4.07 thf(fact_5408_sum_Osame__carrierI,axiom,
% 3.82/4.07 ! [C4: set_Extended_enat,A2: set_Extended_enat,B: set_Extended_enat,G: extended_enat > nat,H2: extended_enat > nat] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ C4 )
% 3.82/4.07 => ( ( ord_le7203529160286727270d_enat @ A2 @ C4 )
% 3.82/4.07 => ( ( ord_le7203529160286727270d_enat @ B @ C4 )
% 3.82/4.07 => ( ! [A4: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ A4 @ ( minus_925952699566721837d_enat @ C4 @ A2 ) )
% 3.82/4.07 => ( ( G @ A4 )
% 3.82/4.07 = zero_zero_nat ) )
% 3.82/4.07 => ( ! [B4: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ B4 @ ( minus_925952699566721837d_enat @ C4 @ B ) )
% 3.82/4.07 => ( ( H2 @ B4 )
% 3.82/4.07 = zero_zero_nat ) )
% 3.82/4.07 => ( ( ( groups2027974829824023292at_nat @ G @ C4 )
% 3.82/4.07 = ( groups2027974829824023292at_nat @ H2 @ C4 ) )
% 3.82/4.07 => ( ( groups2027974829824023292at_nat @ G @ A2 )
% 3.82/4.07 = ( groups2027974829824023292at_nat @ H2 @ B ) ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.same_carrierI
% 3.82/4.07 thf(fact_5409_sum_Osame__carrierI,axiom,
% 3.82/4.07 ! [C4: set_real,A2: set_real,B: set_real,G: real > real,H2: real > real] :
% 3.82/4.07 ( ( finite_finite_real @ C4 )
% 3.82/4.07 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 3.82/4.07 => ( ( ord_less_eq_set_real @ B @ C4 )
% 3.82/4.07 => ( ! [A4: real] :
% 3.82/4.07 ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 3.82/4.07 => ( ( G @ A4 )
% 3.82/4.07 = zero_zero_real ) )
% 3.82/4.07 => ( ! [B4: real] :
% 3.82/4.07 ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B ) )
% 3.82/4.07 => ( ( H2 @ B4 )
% 3.82/4.07 = zero_zero_real ) )
% 3.82/4.07 => ( ( ( groups8097168146408367636l_real @ G @ C4 )
% 3.82/4.07 = ( groups8097168146408367636l_real @ H2 @ C4 ) )
% 3.82/4.07 => ( ( groups8097168146408367636l_real @ G @ A2 )
% 3.82/4.07 = ( groups8097168146408367636l_real @ H2 @ B ) ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.same_carrierI
% 3.82/4.07 thf(fact_5410_sum_Osame__carrierI,axiom,
% 3.82/4.07 ! [C4: set_complex,A2: set_complex,B: set_complex,G: complex > real,H2: complex > real] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ C4 )
% 3.82/4.07 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 3.82/4.07 => ( ( ord_le211207098394363844omplex @ B @ C4 )
% 3.82/4.07 => ( ! [A4: complex] :
% 3.82/4.07 ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 3.82/4.07 => ( ( G @ A4 )
% 3.82/4.07 = zero_zero_real ) )
% 3.82/4.07 => ( ! [B4: complex] :
% 3.82/4.07 ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ C4 @ B ) )
% 3.82/4.07 => ( ( H2 @ B4 )
% 3.82/4.07 = zero_zero_real ) )
% 3.82/4.07 => ( ( ( groups5808333547571424918x_real @ G @ C4 )
% 3.82/4.07 = ( groups5808333547571424918x_real @ H2 @ C4 ) )
% 3.82/4.07 => ( ( groups5808333547571424918x_real @ G @ A2 )
% 3.82/4.07 = ( groups5808333547571424918x_real @ H2 @ B ) ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.same_carrierI
% 3.82/4.07 thf(fact_5411_sum_Osame__carrierI,axiom,
% 3.82/4.07 ! [C4: set_Extended_enat,A2: set_Extended_enat,B: set_Extended_enat,G: extended_enat > real,H2: extended_enat > real] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ C4 )
% 3.82/4.07 => ( ( ord_le7203529160286727270d_enat @ A2 @ C4 )
% 3.82/4.07 => ( ( ord_le7203529160286727270d_enat @ B @ C4 )
% 3.82/4.07 => ( ! [A4: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ A4 @ ( minus_925952699566721837d_enat @ C4 @ A2 ) )
% 3.82/4.07 => ( ( G @ A4 )
% 3.82/4.07 = zero_zero_real ) )
% 3.82/4.07 => ( ! [B4: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ B4 @ ( minus_925952699566721837d_enat @ C4 @ B ) )
% 3.82/4.07 => ( ( H2 @ B4 )
% 3.82/4.07 = zero_zero_real ) )
% 3.82/4.07 => ( ( ( groups4148127829035722712t_real @ G @ C4 )
% 3.82/4.07 = ( groups4148127829035722712t_real @ H2 @ C4 ) )
% 3.82/4.07 => ( ( groups4148127829035722712t_real @ G @ A2 )
% 3.82/4.07 = ( groups4148127829035722712t_real @ H2 @ B ) ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.same_carrierI
% 3.82/4.07 thf(fact_5412_sum_Osame__carrierI,axiom,
% 3.82/4.07 ! [C4: set_real,A2: set_real,B: set_real,G: real > int,H2: real > int] :
% 3.82/4.07 ( ( finite_finite_real @ C4 )
% 3.82/4.07 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 3.82/4.07 => ( ( ord_less_eq_set_real @ B @ C4 )
% 3.82/4.07 => ( ! [A4: real] :
% 3.82/4.07 ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 3.82/4.07 => ( ( G @ A4 )
% 3.82/4.07 = zero_zero_int ) )
% 3.82/4.07 => ( ! [B4: real] :
% 3.82/4.07 ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B ) )
% 3.82/4.07 => ( ( H2 @ B4 )
% 3.82/4.07 = zero_zero_int ) )
% 3.82/4.07 => ( ( ( groups1932886352136224148al_int @ G @ C4 )
% 3.82/4.07 = ( groups1932886352136224148al_int @ H2 @ C4 ) )
% 3.82/4.07 => ( ( groups1932886352136224148al_int @ G @ A2 )
% 3.82/4.07 = ( groups1932886352136224148al_int @ H2 @ B ) ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.same_carrierI
% 3.82/4.07 thf(fact_5413_sum_Osame__carrierI,axiom,
% 3.82/4.07 ! [C4: set_complex,A2: set_complex,B: set_complex,G: complex > int,H2: complex > int] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ C4 )
% 3.82/4.07 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 3.82/4.07 => ( ( ord_le211207098394363844omplex @ B @ C4 )
% 3.82/4.07 => ( ! [A4: complex] :
% 3.82/4.07 ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 3.82/4.07 => ( ( G @ A4 )
% 3.82/4.07 = zero_zero_int ) )
% 3.82/4.07 => ( ! [B4: complex] :
% 3.82/4.07 ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ C4 @ B ) )
% 3.82/4.07 => ( ( H2 @ B4 )
% 3.82/4.07 = zero_zero_int ) )
% 3.82/4.07 => ( ( ( groups5690904116761175830ex_int @ G @ C4 )
% 3.82/4.07 = ( groups5690904116761175830ex_int @ H2 @ C4 ) )
% 3.82/4.07 => ( ( groups5690904116761175830ex_int @ G @ A2 )
% 3.82/4.07 = ( groups5690904116761175830ex_int @ H2 @ B ) ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.same_carrierI
% 3.82/4.07 thf(fact_5414_sum_Osame__carrierI,axiom,
% 3.82/4.07 ! [C4: set_Extended_enat,A2: set_Extended_enat,B: set_Extended_enat,G: extended_enat > int,H2: extended_enat > int] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ C4 )
% 3.82/4.07 => ( ( ord_le7203529160286727270d_enat @ A2 @ C4 )
% 3.82/4.07 => ( ( ord_le7203529160286727270d_enat @ B @ C4 )
% 3.82/4.07 => ( ! [A4: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ A4 @ ( minus_925952699566721837d_enat @ C4 @ A2 ) )
% 3.82/4.07 => ( ( G @ A4 )
% 3.82/4.07 = zero_zero_int ) )
% 3.82/4.07 => ( ! [B4: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ B4 @ ( minus_925952699566721837d_enat @ C4 @ B ) )
% 3.82/4.07 => ( ( H2 @ B4 )
% 3.82/4.07 = zero_zero_int ) )
% 3.82/4.07 => ( ( ( groups2025484359314973016at_int @ G @ C4 )
% 3.82/4.07 = ( groups2025484359314973016at_int @ H2 @ C4 ) )
% 3.82/4.07 => ( ( groups2025484359314973016at_int @ G @ A2 )
% 3.82/4.07 = ( groups2025484359314973016at_int @ H2 @ B ) ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.same_carrierI
% 3.82/4.07 thf(fact_5415_sum_Osame__carrierI,axiom,
% 3.82/4.07 ! [C4: set_real,A2: set_real,B: set_real,G: real > complex,H2: real > complex] :
% 3.82/4.07 ( ( finite_finite_real @ C4 )
% 3.82/4.07 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 3.82/4.07 => ( ( ord_less_eq_set_real @ B @ C4 )
% 3.82/4.07 => ( ! [A4: real] :
% 3.82/4.07 ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 3.82/4.07 => ( ( G @ A4 )
% 3.82/4.07 = zero_zero_complex ) )
% 3.82/4.07 => ( ! [B4: real] :
% 3.82/4.07 ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B ) )
% 3.82/4.07 => ( ( H2 @ B4 )
% 3.82/4.07 = zero_zero_complex ) )
% 3.82/4.07 => ( ( ( groups5754745047067104278omplex @ G @ C4 )
% 3.82/4.07 = ( groups5754745047067104278omplex @ H2 @ C4 ) )
% 3.82/4.07 => ( ( groups5754745047067104278omplex @ G @ A2 )
% 3.82/4.07 = ( groups5754745047067104278omplex @ H2 @ B ) ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.same_carrierI
% 3.82/4.07 thf(fact_5416_sum_Osame__carrier,axiom,
% 3.82/4.07 ! [C4: set_real,A2: set_real,B: set_real,G: real > nat,H2: real > nat] :
% 3.82/4.07 ( ( finite_finite_real @ C4 )
% 3.82/4.07 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 3.82/4.07 => ( ( ord_less_eq_set_real @ B @ C4 )
% 3.82/4.07 => ( ! [A4: real] :
% 3.82/4.07 ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 3.82/4.07 => ( ( G @ A4 )
% 3.82/4.07 = zero_zero_nat ) )
% 3.82/4.07 => ( ! [B4: real] :
% 3.82/4.07 ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B ) )
% 3.82/4.07 => ( ( H2 @ B4 )
% 3.82/4.07 = zero_zero_nat ) )
% 3.82/4.07 => ( ( ( groups1935376822645274424al_nat @ G @ A2 )
% 3.82/4.07 = ( groups1935376822645274424al_nat @ H2 @ B ) )
% 3.82/4.07 = ( ( groups1935376822645274424al_nat @ G @ C4 )
% 3.82/4.07 = ( groups1935376822645274424al_nat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.same_carrier
% 3.82/4.07 thf(fact_5417_sum_Osame__carrier,axiom,
% 3.82/4.07 ! [C4: set_complex,A2: set_complex,B: set_complex,G: complex > nat,H2: complex > nat] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ C4 )
% 3.82/4.07 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 3.82/4.07 => ( ( ord_le211207098394363844omplex @ B @ C4 )
% 3.82/4.07 => ( ! [A4: complex] :
% 3.82/4.07 ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 3.82/4.07 => ( ( G @ A4 )
% 3.82/4.07 = zero_zero_nat ) )
% 3.82/4.07 => ( ! [B4: complex] :
% 3.82/4.07 ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ C4 @ B ) )
% 3.82/4.07 => ( ( H2 @ B4 )
% 3.82/4.07 = zero_zero_nat ) )
% 3.82/4.07 => ( ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 3.82/4.07 = ( groups5693394587270226106ex_nat @ H2 @ B ) )
% 3.82/4.07 = ( ( groups5693394587270226106ex_nat @ G @ C4 )
% 3.82/4.07 = ( groups5693394587270226106ex_nat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.same_carrier
% 3.82/4.07 thf(fact_5418_sum_Osame__carrier,axiom,
% 3.82/4.07 ! [C4: set_Extended_enat,A2: set_Extended_enat,B: set_Extended_enat,G: extended_enat > nat,H2: extended_enat > nat] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ C4 )
% 3.82/4.07 => ( ( ord_le7203529160286727270d_enat @ A2 @ C4 )
% 3.82/4.07 => ( ( ord_le7203529160286727270d_enat @ B @ C4 )
% 3.82/4.07 => ( ! [A4: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ A4 @ ( minus_925952699566721837d_enat @ C4 @ A2 ) )
% 3.82/4.07 => ( ( G @ A4 )
% 3.82/4.07 = zero_zero_nat ) )
% 3.82/4.07 => ( ! [B4: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ B4 @ ( minus_925952699566721837d_enat @ C4 @ B ) )
% 3.82/4.07 => ( ( H2 @ B4 )
% 3.82/4.07 = zero_zero_nat ) )
% 3.82/4.07 => ( ( ( groups2027974829824023292at_nat @ G @ A2 )
% 3.82/4.07 = ( groups2027974829824023292at_nat @ H2 @ B ) )
% 3.82/4.07 = ( ( groups2027974829824023292at_nat @ G @ C4 )
% 3.82/4.07 = ( groups2027974829824023292at_nat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.same_carrier
% 3.82/4.07 thf(fact_5419_sum_Osame__carrier,axiom,
% 3.82/4.07 ! [C4: set_real,A2: set_real,B: set_real,G: real > real,H2: real > real] :
% 3.82/4.07 ( ( finite_finite_real @ C4 )
% 3.82/4.07 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 3.82/4.07 => ( ( ord_less_eq_set_real @ B @ C4 )
% 3.82/4.07 => ( ! [A4: real] :
% 3.82/4.07 ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 3.82/4.07 => ( ( G @ A4 )
% 3.82/4.07 = zero_zero_real ) )
% 3.82/4.07 => ( ! [B4: real] :
% 3.82/4.07 ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B ) )
% 3.82/4.07 => ( ( H2 @ B4 )
% 3.82/4.07 = zero_zero_real ) )
% 3.82/4.07 => ( ( ( groups8097168146408367636l_real @ G @ A2 )
% 3.82/4.07 = ( groups8097168146408367636l_real @ H2 @ B ) )
% 3.82/4.07 = ( ( groups8097168146408367636l_real @ G @ C4 )
% 3.82/4.07 = ( groups8097168146408367636l_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.same_carrier
% 3.82/4.07 thf(fact_5420_sum_Osame__carrier,axiom,
% 3.82/4.07 ! [C4: set_complex,A2: set_complex,B: set_complex,G: complex > real,H2: complex > real] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ C4 )
% 3.82/4.07 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 3.82/4.07 => ( ( ord_le211207098394363844omplex @ B @ C4 )
% 3.82/4.07 => ( ! [A4: complex] :
% 3.82/4.07 ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 3.82/4.07 => ( ( G @ A4 )
% 3.82/4.07 = zero_zero_real ) )
% 3.82/4.07 => ( ! [B4: complex] :
% 3.82/4.07 ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ C4 @ B ) )
% 3.82/4.07 => ( ( H2 @ B4 )
% 3.82/4.07 = zero_zero_real ) )
% 3.82/4.07 => ( ( ( groups5808333547571424918x_real @ G @ A2 )
% 3.82/4.07 = ( groups5808333547571424918x_real @ H2 @ B ) )
% 3.82/4.07 = ( ( groups5808333547571424918x_real @ G @ C4 )
% 3.82/4.07 = ( groups5808333547571424918x_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.same_carrier
% 3.82/4.07 thf(fact_5421_sum_Osame__carrier,axiom,
% 3.82/4.07 ! [C4: set_Extended_enat,A2: set_Extended_enat,B: set_Extended_enat,G: extended_enat > real,H2: extended_enat > real] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ C4 )
% 3.82/4.07 => ( ( ord_le7203529160286727270d_enat @ A2 @ C4 )
% 3.82/4.07 => ( ( ord_le7203529160286727270d_enat @ B @ C4 )
% 3.82/4.07 => ( ! [A4: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ A4 @ ( minus_925952699566721837d_enat @ C4 @ A2 ) )
% 3.82/4.07 => ( ( G @ A4 )
% 3.82/4.07 = zero_zero_real ) )
% 3.82/4.07 => ( ! [B4: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ B4 @ ( minus_925952699566721837d_enat @ C4 @ B ) )
% 3.82/4.07 => ( ( H2 @ B4 )
% 3.82/4.07 = zero_zero_real ) )
% 3.82/4.07 => ( ( ( groups4148127829035722712t_real @ G @ A2 )
% 3.82/4.07 = ( groups4148127829035722712t_real @ H2 @ B ) )
% 3.82/4.07 = ( ( groups4148127829035722712t_real @ G @ C4 )
% 3.82/4.07 = ( groups4148127829035722712t_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.same_carrier
% 3.82/4.07 thf(fact_5422_sum_Osame__carrier,axiom,
% 3.82/4.07 ! [C4: set_real,A2: set_real,B: set_real,G: real > int,H2: real > int] :
% 3.82/4.07 ( ( finite_finite_real @ C4 )
% 3.82/4.07 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 3.82/4.07 => ( ( ord_less_eq_set_real @ B @ C4 )
% 3.82/4.07 => ( ! [A4: real] :
% 3.82/4.07 ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 3.82/4.07 => ( ( G @ A4 )
% 3.82/4.07 = zero_zero_int ) )
% 3.82/4.07 => ( ! [B4: real] :
% 3.82/4.07 ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B ) )
% 3.82/4.07 => ( ( H2 @ B4 )
% 3.82/4.07 = zero_zero_int ) )
% 3.82/4.07 => ( ( ( groups1932886352136224148al_int @ G @ A2 )
% 3.82/4.07 = ( groups1932886352136224148al_int @ H2 @ B ) )
% 3.82/4.07 = ( ( groups1932886352136224148al_int @ G @ C4 )
% 3.82/4.07 = ( groups1932886352136224148al_int @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.same_carrier
% 3.82/4.07 thf(fact_5423_sum_Osame__carrier,axiom,
% 3.82/4.07 ! [C4: set_complex,A2: set_complex,B: set_complex,G: complex > int,H2: complex > int] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ C4 )
% 3.82/4.07 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 3.82/4.07 => ( ( ord_le211207098394363844omplex @ B @ C4 )
% 3.82/4.07 => ( ! [A4: complex] :
% 3.82/4.07 ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 3.82/4.07 => ( ( G @ A4 )
% 3.82/4.07 = zero_zero_int ) )
% 3.82/4.07 => ( ! [B4: complex] :
% 3.82/4.07 ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ C4 @ B ) )
% 3.82/4.07 => ( ( H2 @ B4 )
% 3.82/4.07 = zero_zero_int ) )
% 3.82/4.07 => ( ( ( groups5690904116761175830ex_int @ G @ A2 )
% 3.82/4.07 = ( groups5690904116761175830ex_int @ H2 @ B ) )
% 3.82/4.07 = ( ( groups5690904116761175830ex_int @ G @ C4 )
% 3.82/4.07 = ( groups5690904116761175830ex_int @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.same_carrier
% 3.82/4.07 thf(fact_5424_sum_Osame__carrier,axiom,
% 3.82/4.07 ! [C4: set_Extended_enat,A2: set_Extended_enat,B: set_Extended_enat,G: extended_enat > int,H2: extended_enat > int] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ C4 )
% 3.82/4.07 => ( ( ord_le7203529160286727270d_enat @ A2 @ C4 )
% 3.82/4.07 => ( ( ord_le7203529160286727270d_enat @ B @ C4 )
% 3.82/4.07 => ( ! [A4: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ A4 @ ( minus_925952699566721837d_enat @ C4 @ A2 ) )
% 3.82/4.07 => ( ( G @ A4 )
% 3.82/4.07 = zero_zero_int ) )
% 3.82/4.07 => ( ! [B4: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ B4 @ ( minus_925952699566721837d_enat @ C4 @ B ) )
% 3.82/4.07 => ( ( H2 @ B4 )
% 3.82/4.07 = zero_zero_int ) )
% 3.82/4.07 => ( ( ( groups2025484359314973016at_int @ G @ A2 )
% 3.82/4.07 = ( groups2025484359314973016at_int @ H2 @ B ) )
% 3.82/4.07 = ( ( groups2025484359314973016at_int @ G @ C4 )
% 3.82/4.07 = ( groups2025484359314973016at_int @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.same_carrier
% 3.82/4.07 thf(fact_5425_sum_Osame__carrier,axiom,
% 3.82/4.07 ! [C4: set_real,A2: set_real,B: set_real,G: real > complex,H2: real > complex] :
% 3.82/4.07 ( ( finite_finite_real @ C4 )
% 3.82/4.07 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 3.82/4.07 => ( ( ord_less_eq_set_real @ B @ C4 )
% 3.82/4.07 => ( ! [A4: real] :
% 3.82/4.07 ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 3.82/4.07 => ( ( G @ A4 )
% 3.82/4.07 = zero_zero_complex ) )
% 3.82/4.07 => ( ! [B4: real] :
% 3.82/4.07 ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B ) )
% 3.82/4.07 => ( ( H2 @ B4 )
% 3.82/4.07 = zero_zero_complex ) )
% 3.82/4.07 => ( ( ( groups5754745047067104278omplex @ G @ A2 )
% 3.82/4.07 = ( groups5754745047067104278omplex @ H2 @ B ) )
% 3.82/4.07 = ( ( groups5754745047067104278omplex @ G @ C4 )
% 3.82/4.07 = ( groups5754745047067104278omplex @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.same_carrier
% 3.82/4.07 thf(fact_5426_sum_Osubset__diff,axiom,
% 3.82/4.07 ! [B: set_complex,A2: set_complex,G: complex > nat] :
% 3.82/4.07 ( ( ord_le211207098394363844omplex @ B @ A2 )
% 3.82/4.07 => ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.07 => ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 3.82/4.07 = ( plus_plus_nat @ ( groups5693394587270226106ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ B ) ) @ ( groups5693394587270226106ex_nat @ G @ B ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.subset_diff
% 3.82/4.07 thf(fact_5427_sum_Osubset__diff,axiom,
% 3.82/4.07 ! [B: set_Extended_enat,A2: set_Extended_enat,G: extended_enat > nat] :
% 3.82/4.07 ( ( ord_le7203529160286727270d_enat @ B @ A2 )
% 3.82/4.07 => ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.07 => ( ( groups2027974829824023292at_nat @ G @ A2 )
% 3.82/4.07 = ( plus_plus_nat @ ( groups2027974829824023292at_nat @ G @ ( minus_925952699566721837d_enat @ A2 @ B ) ) @ ( groups2027974829824023292at_nat @ G @ B ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.subset_diff
% 3.82/4.07 thf(fact_5428_sum_Osubset__diff,axiom,
% 3.82/4.07 ! [B: set_complex,A2: set_complex,G: complex > int] :
% 3.82/4.07 ( ( ord_le211207098394363844omplex @ B @ A2 )
% 3.82/4.07 => ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.07 => ( ( groups5690904116761175830ex_int @ G @ A2 )
% 3.82/4.07 = ( plus_plus_int @ ( groups5690904116761175830ex_int @ G @ ( minus_811609699411566653omplex @ A2 @ B ) ) @ ( groups5690904116761175830ex_int @ G @ B ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.subset_diff
% 3.82/4.07 thf(fact_5429_sum_Osubset__diff,axiom,
% 3.82/4.07 ! [B: set_Extended_enat,A2: set_Extended_enat,G: extended_enat > int] :
% 3.82/4.07 ( ( ord_le7203529160286727270d_enat @ B @ A2 )
% 3.82/4.07 => ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.07 => ( ( groups2025484359314973016at_int @ G @ A2 )
% 3.82/4.07 = ( plus_plus_int @ ( groups2025484359314973016at_int @ G @ ( minus_925952699566721837d_enat @ A2 @ B ) ) @ ( groups2025484359314973016at_int @ G @ B ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.subset_diff
% 3.82/4.07 thf(fact_5430_sum_Osubset__diff,axiom,
% 3.82/4.07 ! [B: set_complex,A2: set_complex,G: complex > real] :
% 3.82/4.07 ( ( ord_le211207098394363844omplex @ B @ A2 )
% 3.82/4.07 => ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.07 => ( ( groups5808333547571424918x_real @ G @ A2 )
% 3.82/4.07 = ( plus_plus_real @ ( groups5808333547571424918x_real @ G @ ( minus_811609699411566653omplex @ A2 @ B ) ) @ ( groups5808333547571424918x_real @ G @ B ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.subset_diff
% 3.82/4.07 thf(fact_5431_sum_Osubset__diff,axiom,
% 3.82/4.07 ! [B: set_Extended_enat,A2: set_Extended_enat,G: extended_enat > real] :
% 3.82/4.07 ( ( ord_le7203529160286727270d_enat @ B @ A2 )
% 3.82/4.07 => ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.07 => ( ( groups4148127829035722712t_real @ G @ A2 )
% 3.82/4.07 = ( plus_plus_real @ ( groups4148127829035722712t_real @ G @ ( minus_925952699566721837d_enat @ A2 @ B ) ) @ ( groups4148127829035722712t_real @ G @ B ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.subset_diff
% 3.82/4.07 thf(fact_5432_sum_Osubset__diff,axiom,
% 3.82/4.07 ! [B: set_complex,A2: set_complex,G: complex > extended_enat] :
% 3.82/4.07 ( ( ord_le211207098394363844omplex @ B @ A2 )
% 3.82/4.07 => ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.07 => ( ( groups1752964319039525884d_enat @ G @ A2 )
% 3.82/4.07 = ( plus_p3455044024723400733d_enat @ ( groups1752964319039525884d_enat @ G @ ( minus_811609699411566653omplex @ A2 @ B ) ) @ ( groups1752964319039525884d_enat @ G @ B ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.subset_diff
% 3.82/4.07 thf(fact_5433_sum_Osubset__diff,axiom,
% 3.82/4.07 ! [B: set_Extended_enat,A2: set_Extended_enat,G: extended_enat > extended_enat] :
% 3.82/4.07 ( ( ord_le7203529160286727270d_enat @ B @ A2 )
% 3.82/4.07 => ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.07 => ( ( groups2433450451889696826d_enat @ G @ A2 )
% 3.82/4.07 = ( plus_p3455044024723400733d_enat @ ( groups2433450451889696826d_enat @ G @ ( minus_925952699566721837d_enat @ A2 @ B ) ) @ ( groups2433450451889696826d_enat @ G @ B ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.subset_diff
% 3.82/4.07 thf(fact_5434_sum_Osubset__diff,axiom,
% 3.82/4.07 ! [B: set_nat,A2: set_nat,G: nat > int] :
% 3.82/4.07 ( ( ord_less_eq_set_nat @ B @ A2 )
% 3.82/4.07 => ( ( finite_finite_nat @ A2 )
% 3.82/4.07 => ( ( groups3539618377306564664at_int @ G @ A2 )
% 3.82/4.07 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( minus_minus_set_nat @ A2 @ B ) ) @ ( groups3539618377306564664at_int @ G @ B ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.subset_diff
% 3.82/4.07 thf(fact_5435_sum_Osubset__diff,axiom,
% 3.82/4.07 ! [B: set_nat,A2: set_nat,G: nat > extended_enat] :
% 3.82/4.07 ( ( ord_less_eq_set_nat @ B @ A2 )
% 3.82/4.07 => ( ( finite_finite_nat @ A2 )
% 3.82/4.07 => ( ( groups7108830773950497114d_enat @ G @ A2 )
% 3.82/4.07 = ( plus_p3455044024723400733d_enat @ ( groups7108830773950497114d_enat @ G @ ( minus_minus_set_nat @ A2 @ B ) ) @ ( groups7108830773950497114d_enat @ G @ B ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.subset_diff
% 3.82/4.07 thf(fact_5436_sum__diff,axiom,
% 3.82/4.07 ! [A2: set_complex,B: set_complex,F: complex > int] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.07 => ( ( ord_le211207098394363844omplex @ B @ A2 )
% 3.82/4.07 => ( ( groups5690904116761175830ex_int @ F @ ( minus_811609699411566653omplex @ A2 @ B ) )
% 3.82/4.07 = ( minus_minus_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( groups5690904116761175830ex_int @ F @ B ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_diff
% 3.82/4.07 thf(fact_5437_sum__diff,axiom,
% 3.82/4.07 ! [A2: set_Extended_enat,B: set_Extended_enat,F: extended_enat > int] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.07 => ( ( ord_le7203529160286727270d_enat @ B @ A2 )
% 3.82/4.07 => ( ( groups2025484359314973016at_int @ F @ ( minus_925952699566721837d_enat @ A2 @ B ) )
% 3.82/4.07 = ( minus_minus_int @ ( groups2025484359314973016at_int @ F @ A2 ) @ ( groups2025484359314973016at_int @ F @ B ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_diff
% 3.82/4.07 thf(fact_5438_sum__diff,axiom,
% 3.82/4.07 ! [A2: set_complex,B: set_complex,F: complex > real] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.07 => ( ( ord_le211207098394363844omplex @ B @ A2 )
% 3.82/4.07 => ( ( groups5808333547571424918x_real @ F @ ( minus_811609699411566653omplex @ A2 @ B ) )
% 3.82/4.07 = ( minus_minus_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ F @ B ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_diff
% 3.82/4.07 thf(fact_5439_sum__diff,axiom,
% 3.82/4.07 ! [A2: set_Extended_enat,B: set_Extended_enat,F: extended_enat > real] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.07 => ( ( ord_le7203529160286727270d_enat @ B @ A2 )
% 3.82/4.07 => ( ( groups4148127829035722712t_real @ F @ ( minus_925952699566721837d_enat @ A2 @ B ) )
% 3.82/4.07 = ( minus_minus_real @ ( groups4148127829035722712t_real @ F @ A2 ) @ ( groups4148127829035722712t_real @ F @ B ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_diff
% 3.82/4.07 thf(fact_5440_sum__diff,axiom,
% 3.82/4.07 ! [A2: set_nat,B: set_nat,F: nat > int] :
% 3.82/4.07 ( ( finite_finite_nat @ A2 )
% 3.82/4.07 => ( ( ord_less_eq_set_nat @ B @ A2 )
% 3.82/4.07 => ( ( groups3539618377306564664at_int @ F @ ( minus_minus_set_nat @ A2 @ B ) )
% 3.82/4.07 = ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ A2 ) @ ( groups3539618377306564664at_int @ F @ B ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_diff
% 3.82/4.07 thf(fact_5441_sum__diff,axiom,
% 3.82/4.07 ! [A2: set_int,B: set_int,F: int > real] :
% 3.82/4.07 ( ( finite_finite_int @ A2 )
% 3.82/4.07 => ( ( ord_less_eq_set_int @ B @ A2 )
% 3.82/4.07 => ( ( groups8778361861064173332t_real @ F @ ( minus_minus_set_int @ A2 @ B ) )
% 3.82/4.07 = ( minus_minus_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( groups8778361861064173332t_real @ F @ B ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_diff
% 3.82/4.07 thf(fact_5442_sum__diff,axiom,
% 3.82/4.07 ! [A2: set_int,B: set_int,F: int > int] :
% 3.82/4.07 ( ( finite_finite_int @ A2 )
% 3.82/4.07 => ( ( ord_less_eq_set_int @ B @ A2 )
% 3.82/4.07 => ( ( groups4538972089207619220nt_int @ F @ ( minus_minus_set_int @ A2 @ B ) )
% 3.82/4.07 = ( minus_minus_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( groups4538972089207619220nt_int @ F @ B ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_diff
% 3.82/4.07 thf(fact_5443_sum__diff,axiom,
% 3.82/4.07 ! [A2: set_complex,B: set_complex,F: complex > complex] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.07 => ( ( ord_le211207098394363844omplex @ B @ A2 )
% 3.82/4.07 => ( ( groups7754918857620584856omplex @ F @ ( minus_811609699411566653omplex @ A2 @ B ) )
% 3.82/4.07 = ( minus_minus_complex @ ( groups7754918857620584856omplex @ F @ A2 ) @ ( groups7754918857620584856omplex @ F @ B ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_diff
% 3.82/4.07 thf(fact_5444_sum__diff,axiom,
% 3.82/4.07 ! [A2: set_nat,B: set_nat,F: nat > real] :
% 3.82/4.07 ( ( finite_finite_nat @ A2 )
% 3.82/4.07 => ( ( ord_less_eq_set_nat @ B @ A2 )
% 3.82/4.07 => ( ( groups6591440286371151544t_real @ F @ ( minus_minus_set_nat @ A2 @ B ) )
% 3.82/4.07 = ( minus_minus_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ ( groups6591440286371151544t_real @ F @ B ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_diff
% 3.82/4.07 thf(fact_5445_sum__mono2,axiom,
% 3.82/4.07 ! [B: set_real,A2: set_real,F: real > extended_enat] :
% 3.82/4.07 ( ( finite_finite_real @ B )
% 3.82/4.07 => ( ( ord_less_eq_set_real @ A2 @ B )
% 3.82/4.07 => ( ! [B4: real] :
% 3.82/4.07 ( ( member_real @ B4 @ ( minus_minus_set_real @ B @ A2 ) )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ B4 ) ) )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ ( groups2800946370649118462d_enat @ F @ A2 ) @ ( groups2800946370649118462d_enat @ F @ B ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_mono2
% 3.82/4.07 thf(fact_5446_sum__mono2,axiom,
% 3.82/4.07 ! [B: set_complex,A2: set_complex,F: complex > extended_enat] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ B )
% 3.82/4.07 => ( ( ord_le211207098394363844omplex @ A2 @ B )
% 3.82/4.07 => ( ! [B4: complex] :
% 3.82/4.07 ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ B @ A2 ) )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ B4 ) ) )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ ( groups1752964319039525884d_enat @ F @ A2 ) @ ( groups1752964319039525884d_enat @ F @ B ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_mono2
% 3.82/4.07 thf(fact_5447_sum__mono2,axiom,
% 3.82/4.07 ! [B: set_Extended_enat,A2: set_Extended_enat,F: extended_enat > extended_enat] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ B )
% 3.82/4.07 => ( ( ord_le7203529160286727270d_enat @ A2 @ B )
% 3.82/4.07 => ( ! [B4: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ B4 @ ( minus_925952699566721837d_enat @ B @ A2 ) )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ B4 ) ) )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ ( groups2433450451889696826d_enat @ F @ A2 ) @ ( groups2433450451889696826d_enat @ F @ B ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_mono2
% 3.82/4.07 thf(fact_5448_sum__mono2,axiom,
% 3.82/4.07 ! [B: set_real,A2: set_real,F: real > real] :
% 3.82/4.07 ( ( finite_finite_real @ B )
% 3.82/4.07 => ( ( ord_less_eq_set_real @ A2 @ B )
% 3.82/4.07 => ( ! [B4: real] :
% 3.82/4.07 ( ( member_real @ B4 @ ( minus_minus_set_real @ B @ A2 ) )
% 3.82/4.07 => ( ord_less_eq_real @ zero_zero_real @ ( F @ B4 ) ) )
% 3.82/4.07 => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( groups8097168146408367636l_real @ F @ B ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_mono2
% 3.82/4.07 thf(fact_5449_sum__mono2,axiom,
% 3.82/4.07 ! [B: set_complex,A2: set_complex,F: complex > real] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ B )
% 3.82/4.07 => ( ( ord_le211207098394363844omplex @ A2 @ B )
% 3.82/4.07 => ( ! [B4: complex] :
% 3.82/4.07 ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ B @ A2 ) )
% 3.82/4.07 => ( ord_less_eq_real @ zero_zero_real @ ( F @ B4 ) ) )
% 3.82/4.07 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ F @ B ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_mono2
% 3.82/4.07 thf(fact_5450_sum__mono2,axiom,
% 3.82/4.07 ! [B: set_Extended_enat,A2: set_Extended_enat,F: extended_enat > real] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ B )
% 3.82/4.07 => ( ( ord_le7203529160286727270d_enat @ A2 @ B )
% 3.82/4.07 => ( ! [B4: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ B4 @ ( minus_925952699566721837d_enat @ B @ A2 ) )
% 3.82/4.07 => ( ord_less_eq_real @ zero_zero_real @ ( F @ B4 ) ) )
% 3.82/4.07 => ( ord_less_eq_real @ ( groups4148127829035722712t_real @ F @ A2 ) @ ( groups4148127829035722712t_real @ F @ B ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_mono2
% 3.82/4.07 thf(fact_5451_sum__mono2,axiom,
% 3.82/4.07 ! [B: set_real,A2: set_real,F: real > nat] :
% 3.82/4.07 ( ( finite_finite_real @ B )
% 3.82/4.07 => ( ( ord_less_eq_set_real @ A2 @ B )
% 3.82/4.07 => ( ! [B4: real] :
% 3.82/4.07 ( ( member_real @ B4 @ ( minus_minus_set_real @ B @ A2 ) )
% 3.82/4.07 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B4 ) ) )
% 3.82/4.07 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ F @ B ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_mono2
% 3.82/4.07 thf(fact_5452_sum__mono2,axiom,
% 3.82/4.07 ! [B: set_complex,A2: set_complex,F: complex > nat] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ B )
% 3.82/4.07 => ( ( ord_le211207098394363844omplex @ A2 @ B )
% 3.82/4.07 => ( ! [B4: complex] :
% 3.82/4.07 ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ B @ A2 ) )
% 3.82/4.07 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B4 ) ) )
% 3.82/4.07 => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ F @ B ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_mono2
% 3.82/4.07 thf(fact_5453_sum__mono2,axiom,
% 3.82/4.07 ! [B: set_Extended_enat,A2: set_Extended_enat,F: extended_enat > nat] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ B )
% 3.82/4.07 => ( ( ord_le7203529160286727270d_enat @ A2 @ B )
% 3.82/4.07 => ( ! [B4: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ B4 @ ( minus_925952699566721837d_enat @ B @ A2 ) )
% 3.82/4.07 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B4 ) ) )
% 3.82/4.07 => ( ord_less_eq_nat @ ( groups2027974829824023292at_nat @ F @ A2 ) @ ( groups2027974829824023292at_nat @ F @ B ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_mono2
% 3.82/4.07 thf(fact_5454_sum__mono2,axiom,
% 3.82/4.07 ! [B: set_real,A2: set_real,F: real > int] :
% 3.82/4.07 ( ( finite_finite_real @ B )
% 3.82/4.07 => ( ( ord_less_eq_set_real @ A2 @ B )
% 3.82/4.07 => ( ! [B4: real] :
% 3.82/4.07 ( ( member_real @ B4 @ ( minus_minus_set_real @ B @ A2 ) )
% 3.82/4.07 => ( ord_less_eq_int @ zero_zero_int @ ( F @ B4 ) ) )
% 3.82/4.07 => ( ord_less_eq_int @ ( groups1932886352136224148al_int @ F @ A2 ) @ ( groups1932886352136224148al_int @ F @ B ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_mono2
% 3.82/4.07 thf(fact_5455_sum_Oremove,axiom,
% 3.82/4.07 ! [A2: set_complex,X: complex,G: complex > nat] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.07 => ( ( member_complex @ X @ A2 )
% 3.82/4.07 => ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 3.82/4.07 = ( plus_plus_nat @ ( G @ X ) @ ( groups5693394587270226106ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.remove
% 3.82/4.07 thf(fact_5456_sum_Oremove,axiom,
% 3.82/4.07 ! [A2: set_complex,X: complex,G: complex > int] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.07 => ( ( member_complex @ X @ A2 )
% 3.82/4.07 => ( ( groups5690904116761175830ex_int @ G @ A2 )
% 3.82/4.07 = ( plus_plus_int @ ( G @ X ) @ ( groups5690904116761175830ex_int @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.remove
% 3.82/4.07 thf(fact_5457_sum_Oremove,axiom,
% 3.82/4.07 ! [A2: set_complex,X: complex,G: complex > real] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.07 => ( ( member_complex @ X @ A2 )
% 3.82/4.07 => ( ( groups5808333547571424918x_real @ G @ A2 )
% 3.82/4.07 = ( plus_plus_real @ ( G @ X ) @ ( groups5808333547571424918x_real @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.remove
% 3.82/4.07 thf(fact_5458_sum_Oremove,axiom,
% 3.82/4.07 ! [A2: set_complex,X: complex,G: complex > extended_enat] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.07 => ( ( member_complex @ X @ A2 )
% 3.82/4.07 => ( ( groups1752964319039525884d_enat @ G @ A2 )
% 3.82/4.07 = ( plus_p3455044024723400733d_enat @ ( G @ X ) @ ( groups1752964319039525884d_enat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.remove
% 3.82/4.07 thf(fact_5459_sum_Oremove,axiom,
% 3.82/4.07 ! [A2: set_Extended_enat,X: extended_enat,G: extended_enat > nat] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.07 => ( ( member_Extended_enat @ X @ A2 )
% 3.82/4.07 => ( ( groups2027974829824023292at_nat @ G @ A2 )
% 3.82/4.07 = ( plus_plus_nat @ ( G @ X ) @ ( groups2027974829824023292at_nat @ G @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ X @ bot_bo7653980558646680370d_enat ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.remove
% 3.82/4.07 thf(fact_5460_sum_Oremove,axiom,
% 3.82/4.07 ! [A2: set_Extended_enat,X: extended_enat,G: extended_enat > int] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.07 => ( ( member_Extended_enat @ X @ A2 )
% 3.82/4.07 => ( ( groups2025484359314973016at_int @ G @ A2 )
% 3.82/4.07 = ( plus_plus_int @ ( G @ X ) @ ( groups2025484359314973016at_int @ G @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ X @ bot_bo7653980558646680370d_enat ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.remove
% 3.82/4.07 thf(fact_5461_sum_Oremove,axiom,
% 3.82/4.07 ! [A2: set_Extended_enat,X: extended_enat,G: extended_enat > real] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.07 => ( ( member_Extended_enat @ X @ A2 )
% 3.82/4.07 => ( ( groups4148127829035722712t_real @ G @ A2 )
% 3.82/4.07 = ( plus_plus_real @ ( G @ X ) @ ( groups4148127829035722712t_real @ G @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ X @ bot_bo7653980558646680370d_enat ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.remove
% 3.82/4.07 thf(fact_5462_sum_Oremove,axiom,
% 3.82/4.07 ! [A2: set_Extended_enat,X: extended_enat,G: extended_enat > extended_enat] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.07 => ( ( member_Extended_enat @ X @ A2 )
% 3.82/4.07 => ( ( groups2433450451889696826d_enat @ G @ A2 )
% 3.82/4.07 = ( plus_p3455044024723400733d_enat @ ( G @ X ) @ ( groups2433450451889696826d_enat @ G @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ X @ bot_bo7653980558646680370d_enat ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.remove
% 3.82/4.07 thf(fact_5463_sum_Oremove,axiom,
% 3.82/4.07 ! [A2: set_real,X: real,G: real > nat] :
% 3.82/4.07 ( ( finite_finite_real @ A2 )
% 3.82/4.07 => ( ( member_real @ X @ A2 )
% 3.82/4.07 => ( ( groups1935376822645274424al_nat @ G @ A2 )
% 3.82/4.07 = ( plus_plus_nat @ ( G @ X ) @ ( groups1935376822645274424al_nat @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.remove
% 3.82/4.07 thf(fact_5464_sum_Oremove,axiom,
% 3.82/4.07 ! [A2: set_real,X: real,G: real > int] :
% 3.82/4.07 ( ( finite_finite_real @ A2 )
% 3.82/4.07 => ( ( member_real @ X @ A2 )
% 3.82/4.07 => ( ( groups1932886352136224148al_int @ G @ A2 )
% 3.82/4.07 = ( plus_plus_int @ ( G @ X ) @ ( groups1932886352136224148al_int @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.remove
% 3.82/4.07 thf(fact_5465_sum_Oinsert__remove,axiom,
% 3.82/4.07 ! [A2: set_complex,G: complex > nat,X: complex] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.07 => ( ( groups5693394587270226106ex_nat @ G @ ( insert_complex @ X @ A2 ) )
% 3.82/4.07 = ( plus_plus_nat @ ( G @ X ) @ ( groups5693394587270226106ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.insert_remove
% 3.82/4.07 thf(fact_5466_sum_Oinsert__remove,axiom,
% 3.82/4.07 ! [A2: set_complex,G: complex > int,X: complex] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.07 => ( ( groups5690904116761175830ex_int @ G @ ( insert_complex @ X @ A2 ) )
% 3.82/4.07 = ( plus_plus_int @ ( G @ X ) @ ( groups5690904116761175830ex_int @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.insert_remove
% 3.82/4.07 thf(fact_5467_sum_Oinsert__remove,axiom,
% 3.82/4.07 ! [A2: set_complex,G: complex > real,X: complex] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.07 => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X @ A2 ) )
% 3.82/4.07 = ( plus_plus_real @ ( G @ X ) @ ( groups5808333547571424918x_real @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.insert_remove
% 3.82/4.07 thf(fact_5468_sum_Oinsert__remove,axiom,
% 3.82/4.07 ! [A2: set_complex,G: complex > extended_enat,X: complex] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.07 => ( ( groups1752964319039525884d_enat @ G @ ( insert_complex @ X @ A2 ) )
% 3.82/4.07 = ( plus_p3455044024723400733d_enat @ ( G @ X ) @ ( groups1752964319039525884d_enat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.insert_remove
% 3.82/4.07 thf(fact_5469_sum_Oinsert__remove,axiom,
% 3.82/4.07 ! [A2: set_Extended_enat,G: extended_enat > nat,X: extended_enat] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.07 => ( ( groups2027974829824023292at_nat @ G @ ( insert_Extended_enat @ X @ A2 ) )
% 3.82/4.07 = ( plus_plus_nat @ ( G @ X ) @ ( groups2027974829824023292at_nat @ G @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ X @ bot_bo7653980558646680370d_enat ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.insert_remove
% 3.82/4.07 thf(fact_5470_sum_Oinsert__remove,axiom,
% 3.82/4.07 ! [A2: set_Extended_enat,G: extended_enat > int,X: extended_enat] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.07 => ( ( groups2025484359314973016at_int @ G @ ( insert_Extended_enat @ X @ A2 ) )
% 3.82/4.07 = ( plus_plus_int @ ( G @ X ) @ ( groups2025484359314973016at_int @ G @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ X @ bot_bo7653980558646680370d_enat ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.insert_remove
% 3.82/4.07 thf(fact_5471_sum_Oinsert__remove,axiom,
% 3.82/4.07 ! [A2: set_Extended_enat,G: extended_enat > real,X: extended_enat] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.07 => ( ( groups4148127829035722712t_real @ G @ ( insert_Extended_enat @ X @ A2 ) )
% 3.82/4.07 = ( plus_plus_real @ ( G @ X ) @ ( groups4148127829035722712t_real @ G @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ X @ bot_bo7653980558646680370d_enat ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.insert_remove
% 3.82/4.07 thf(fact_5472_sum_Oinsert__remove,axiom,
% 3.82/4.07 ! [A2: set_Extended_enat,G: extended_enat > extended_enat,X: extended_enat] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.07 => ( ( groups2433450451889696826d_enat @ G @ ( insert_Extended_enat @ X @ A2 ) )
% 3.82/4.07 = ( plus_p3455044024723400733d_enat @ ( G @ X ) @ ( groups2433450451889696826d_enat @ G @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ X @ bot_bo7653980558646680370d_enat ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.insert_remove
% 3.82/4.07 thf(fact_5473_sum_Oinsert__remove,axiom,
% 3.82/4.07 ! [A2: set_real,G: real > nat,X: real] :
% 3.82/4.07 ( ( finite_finite_real @ A2 )
% 3.82/4.07 => ( ( groups1935376822645274424al_nat @ G @ ( insert_real @ X @ A2 ) )
% 3.82/4.07 = ( plus_plus_nat @ ( G @ X ) @ ( groups1935376822645274424al_nat @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.insert_remove
% 3.82/4.07 thf(fact_5474_sum_Oinsert__remove,axiom,
% 3.82/4.07 ! [A2: set_real,G: real > int,X: real] :
% 3.82/4.07 ( ( finite_finite_real @ A2 )
% 3.82/4.07 => ( ( groups1932886352136224148al_int @ G @ ( insert_real @ X @ A2 ) )
% 3.82/4.07 = ( plus_plus_int @ ( G @ X ) @ ( groups1932886352136224148al_int @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.insert_remove
% 3.82/4.07 thf(fact_5475_sum__diff1,axiom,
% 3.82/4.07 ! [A2: set_complex,A: complex,F: complex > int] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.07 => ( ( ( member_complex @ A @ A2 )
% 3.82/4.07 => ( ( groups5690904116761175830ex_int @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 3.82/4.07 = ( minus_minus_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( F @ A ) ) ) )
% 3.82/4.07 & ( ~ ( member_complex @ A @ A2 )
% 3.82/4.07 => ( ( groups5690904116761175830ex_int @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 3.82/4.07 = ( groups5690904116761175830ex_int @ F @ A2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_diff1
% 3.82/4.07 thf(fact_5476_sum__diff1,axiom,
% 3.82/4.07 ! [A2: set_Extended_enat,A: extended_enat,F: extended_enat > int] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.07 => ( ( ( member_Extended_enat @ A @ A2 )
% 3.82/4.07 => ( ( groups2025484359314973016at_int @ F @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) )
% 3.82/4.07 = ( minus_minus_int @ ( groups2025484359314973016at_int @ F @ A2 ) @ ( F @ A ) ) ) )
% 3.82/4.07 & ( ~ ( member_Extended_enat @ A @ A2 )
% 3.82/4.07 => ( ( groups2025484359314973016at_int @ F @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) )
% 3.82/4.07 = ( groups2025484359314973016at_int @ F @ A2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_diff1
% 3.82/4.07 thf(fact_5477_sum__diff1,axiom,
% 3.82/4.07 ! [A2: set_real,A: real,F: real > int] :
% 3.82/4.07 ( ( finite_finite_real @ A2 )
% 3.82/4.07 => ( ( ( member_real @ A @ A2 )
% 3.82/4.07 => ( ( groups1932886352136224148al_int @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 3.82/4.07 = ( minus_minus_int @ ( groups1932886352136224148al_int @ F @ A2 ) @ ( F @ A ) ) ) )
% 3.82/4.07 & ( ~ ( member_real @ A @ A2 )
% 3.82/4.07 => ( ( groups1932886352136224148al_int @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 3.82/4.07 = ( groups1932886352136224148al_int @ F @ A2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_diff1
% 3.82/4.07 thf(fact_5478_sum__diff1,axiom,
% 3.82/4.07 ! [A2: set_complex,A: complex,F: complex > real] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.07 => ( ( ( member_complex @ A @ A2 )
% 3.82/4.07 => ( ( groups5808333547571424918x_real @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 3.82/4.07 = ( minus_minus_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( F @ A ) ) ) )
% 3.82/4.07 & ( ~ ( member_complex @ A @ A2 )
% 3.82/4.07 => ( ( groups5808333547571424918x_real @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 3.82/4.07 = ( groups5808333547571424918x_real @ F @ A2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_diff1
% 3.82/4.07 thf(fact_5479_sum__diff1,axiom,
% 3.82/4.07 ! [A2: set_Extended_enat,A: extended_enat,F: extended_enat > real] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.07 => ( ( ( member_Extended_enat @ A @ A2 )
% 3.82/4.07 => ( ( groups4148127829035722712t_real @ F @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) )
% 3.82/4.07 = ( minus_minus_real @ ( groups4148127829035722712t_real @ F @ A2 ) @ ( F @ A ) ) ) )
% 3.82/4.07 & ( ~ ( member_Extended_enat @ A @ A2 )
% 3.82/4.07 => ( ( groups4148127829035722712t_real @ F @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) )
% 3.82/4.07 = ( groups4148127829035722712t_real @ F @ A2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_diff1
% 3.82/4.07 thf(fact_5480_sum__diff1,axiom,
% 3.82/4.07 ! [A2: set_real,A: real,F: real > real] :
% 3.82/4.07 ( ( finite_finite_real @ A2 )
% 3.82/4.07 => ( ( ( member_real @ A @ A2 )
% 3.82/4.07 => ( ( groups8097168146408367636l_real @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 3.82/4.07 = ( minus_minus_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( F @ A ) ) ) )
% 3.82/4.07 & ( ~ ( member_real @ A @ A2 )
% 3.82/4.07 => ( ( groups8097168146408367636l_real @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 3.82/4.07 = ( groups8097168146408367636l_real @ F @ A2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_diff1
% 3.82/4.07 thf(fact_5481_sum__diff1,axiom,
% 3.82/4.07 ! [A2: set_int,A: int,F: int > real] :
% 3.82/4.07 ( ( finite_finite_int @ A2 )
% 3.82/4.07 => ( ( ( member_int @ A @ A2 )
% 3.82/4.07 => ( ( groups8778361861064173332t_real @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 3.82/4.07 = ( minus_minus_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( F @ A ) ) ) )
% 3.82/4.07 & ( ~ ( member_int @ A @ A2 )
% 3.82/4.07 => ( ( groups8778361861064173332t_real @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 3.82/4.07 = ( groups8778361861064173332t_real @ F @ A2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_diff1
% 3.82/4.07 thf(fact_5482_sum__diff1,axiom,
% 3.82/4.07 ! [A2: set_nat,A: nat,F: nat > int] :
% 3.82/4.07 ( ( finite_finite_nat @ A2 )
% 3.82/4.07 => ( ( ( member_nat @ A @ A2 )
% 3.82/4.07 => ( ( groups3539618377306564664at_int @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 3.82/4.07 = ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ A2 ) @ ( F @ A ) ) ) )
% 3.82/4.07 & ( ~ ( member_nat @ A @ A2 )
% 3.82/4.07 => ( ( groups3539618377306564664at_int @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 3.82/4.07 = ( groups3539618377306564664at_int @ F @ A2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_diff1
% 3.82/4.07 thf(fact_5483_sum__diff1,axiom,
% 3.82/4.07 ! [A2: set_int,A: int,F: int > int] :
% 3.82/4.07 ( ( finite_finite_int @ A2 )
% 3.82/4.07 => ( ( ( member_int @ A @ A2 )
% 3.82/4.07 => ( ( groups4538972089207619220nt_int @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 3.82/4.07 = ( minus_minus_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( F @ A ) ) ) )
% 3.82/4.07 & ( ~ ( member_int @ A @ A2 )
% 3.82/4.07 => ( ( groups4538972089207619220nt_int @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 3.82/4.07 = ( groups4538972089207619220nt_int @ F @ A2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_diff1
% 3.82/4.07 thf(fact_5484_sum__diff1,axiom,
% 3.82/4.07 ! [A2: set_complex,A: complex,F: complex > complex] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.07 => ( ( ( member_complex @ A @ A2 )
% 3.82/4.07 => ( ( groups7754918857620584856omplex @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 3.82/4.07 = ( minus_minus_complex @ ( groups7754918857620584856omplex @ F @ A2 ) @ ( F @ A ) ) ) )
% 3.82/4.07 & ( ~ ( member_complex @ A @ A2 )
% 3.82/4.07 => ( ( groups7754918857620584856omplex @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 3.82/4.07 = ( groups7754918857620584856omplex @ F @ A2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_diff1
% 3.82/4.07 thf(fact_5485_sum_Odelta__remove,axiom,
% 3.82/4.07 ! [S2: set_complex,A: complex,B2: complex > nat,C: complex > nat] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ S2 )
% 3.82/4.07 => ( ( ( member_complex @ A @ S2 )
% 3.82/4.07 => ( ( groups5693394587270226106ex_nat
% 3.82/4.07 @ ^ [K2: complex] : ( if_nat @ ( K2 = A ) @ ( B2 @ K2 ) @ ( C @ K2 ) )
% 3.82/4.07 @ S2 )
% 3.82/4.07 = ( plus_plus_nat @ ( B2 @ A ) @ ( groups5693394587270226106ex_nat @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 3.82/4.07 & ( ~ ( member_complex @ A @ S2 )
% 3.82/4.07 => ( ( groups5693394587270226106ex_nat
% 3.82/4.07 @ ^ [K2: complex] : ( if_nat @ ( K2 = A ) @ ( B2 @ K2 ) @ ( C @ K2 ) )
% 3.82/4.07 @ S2 )
% 3.82/4.07 = ( groups5693394587270226106ex_nat @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.delta_remove
% 3.82/4.07 thf(fact_5486_sum_Odelta__remove,axiom,
% 3.82/4.07 ! [S2: set_complex,A: complex,B2: complex > int,C: complex > int] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ S2 )
% 3.82/4.07 => ( ( ( member_complex @ A @ S2 )
% 3.82/4.07 => ( ( groups5690904116761175830ex_int
% 3.82/4.07 @ ^ [K2: complex] : ( if_int @ ( K2 = A ) @ ( B2 @ K2 ) @ ( C @ K2 ) )
% 3.82/4.07 @ S2 )
% 3.82/4.07 = ( plus_plus_int @ ( B2 @ A ) @ ( groups5690904116761175830ex_int @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 3.82/4.07 & ( ~ ( member_complex @ A @ S2 )
% 3.82/4.07 => ( ( groups5690904116761175830ex_int
% 3.82/4.07 @ ^ [K2: complex] : ( if_int @ ( K2 = A ) @ ( B2 @ K2 ) @ ( C @ K2 ) )
% 3.82/4.07 @ S2 )
% 3.82/4.07 = ( groups5690904116761175830ex_int @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.delta_remove
% 3.82/4.07 thf(fact_5487_sum_Odelta__remove,axiom,
% 3.82/4.07 ! [S2: set_complex,A: complex,B2: complex > real,C: complex > real] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ S2 )
% 3.82/4.07 => ( ( ( member_complex @ A @ S2 )
% 3.82/4.07 => ( ( groups5808333547571424918x_real
% 3.82/4.07 @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B2 @ K2 ) @ ( C @ K2 ) )
% 3.82/4.07 @ S2 )
% 3.82/4.07 = ( plus_plus_real @ ( B2 @ A ) @ ( groups5808333547571424918x_real @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 3.82/4.07 & ( ~ ( member_complex @ A @ S2 )
% 3.82/4.07 => ( ( groups5808333547571424918x_real
% 3.82/4.07 @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B2 @ K2 ) @ ( C @ K2 ) )
% 3.82/4.07 @ S2 )
% 3.82/4.07 = ( groups5808333547571424918x_real @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.delta_remove
% 3.82/4.07 thf(fact_5488_sum_Odelta__remove,axiom,
% 3.82/4.07 ! [S2: set_complex,A: complex,B2: complex > extended_enat,C: complex > extended_enat] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ S2 )
% 3.82/4.07 => ( ( ( member_complex @ A @ S2 )
% 3.82/4.07 => ( ( groups1752964319039525884d_enat
% 3.82/4.07 @ ^ [K2: complex] : ( if_Extended_enat @ ( K2 = A ) @ ( B2 @ K2 ) @ ( C @ K2 ) )
% 3.82/4.07 @ S2 )
% 3.82/4.07 = ( plus_p3455044024723400733d_enat @ ( B2 @ A ) @ ( groups1752964319039525884d_enat @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 3.82/4.07 & ( ~ ( member_complex @ A @ S2 )
% 3.82/4.07 => ( ( groups1752964319039525884d_enat
% 3.82/4.07 @ ^ [K2: complex] : ( if_Extended_enat @ ( K2 = A ) @ ( B2 @ K2 ) @ ( C @ K2 ) )
% 3.82/4.07 @ S2 )
% 3.82/4.07 = ( groups1752964319039525884d_enat @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.delta_remove
% 3.82/4.07 thf(fact_5489_sum_Odelta__remove,axiom,
% 3.82/4.07 ! [S2: set_Extended_enat,A: extended_enat,B2: extended_enat > nat,C: extended_enat > nat] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ S2 )
% 3.82/4.07 => ( ( ( member_Extended_enat @ A @ S2 )
% 3.82/4.07 => ( ( groups2027974829824023292at_nat
% 3.82/4.07 @ ^ [K2: extended_enat] : ( if_nat @ ( K2 = A ) @ ( B2 @ K2 ) @ ( C @ K2 ) )
% 3.82/4.07 @ S2 )
% 3.82/4.07 = ( plus_plus_nat @ ( B2 @ A ) @ ( groups2027974829824023292at_nat @ C @ ( minus_925952699566721837d_enat @ S2 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) ) ) ) )
% 3.82/4.07 & ( ~ ( member_Extended_enat @ A @ S2 )
% 3.82/4.07 => ( ( groups2027974829824023292at_nat
% 3.82/4.07 @ ^ [K2: extended_enat] : ( if_nat @ ( K2 = A ) @ ( B2 @ K2 ) @ ( C @ K2 ) )
% 3.82/4.07 @ S2 )
% 3.82/4.07 = ( groups2027974829824023292at_nat @ C @ ( minus_925952699566721837d_enat @ S2 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.delta_remove
% 3.82/4.07 thf(fact_5490_sum_Odelta__remove,axiom,
% 3.82/4.07 ! [S2: set_Extended_enat,A: extended_enat,B2: extended_enat > int,C: extended_enat > int] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ S2 )
% 3.82/4.07 => ( ( ( member_Extended_enat @ A @ S2 )
% 3.82/4.07 => ( ( groups2025484359314973016at_int
% 3.82/4.07 @ ^ [K2: extended_enat] : ( if_int @ ( K2 = A ) @ ( B2 @ K2 ) @ ( C @ K2 ) )
% 3.82/4.07 @ S2 )
% 3.82/4.07 = ( plus_plus_int @ ( B2 @ A ) @ ( groups2025484359314973016at_int @ C @ ( minus_925952699566721837d_enat @ S2 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) ) ) ) )
% 3.82/4.07 & ( ~ ( member_Extended_enat @ A @ S2 )
% 3.82/4.07 => ( ( groups2025484359314973016at_int
% 3.82/4.07 @ ^ [K2: extended_enat] : ( if_int @ ( K2 = A ) @ ( B2 @ K2 ) @ ( C @ K2 ) )
% 3.82/4.07 @ S2 )
% 3.82/4.07 = ( groups2025484359314973016at_int @ C @ ( minus_925952699566721837d_enat @ S2 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.delta_remove
% 3.82/4.07 thf(fact_5491_sum_Odelta__remove,axiom,
% 3.82/4.07 ! [S2: set_Extended_enat,A: extended_enat,B2: extended_enat > real,C: extended_enat > real] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ S2 )
% 3.82/4.07 => ( ( ( member_Extended_enat @ A @ S2 )
% 3.82/4.07 => ( ( groups4148127829035722712t_real
% 3.82/4.07 @ ^ [K2: extended_enat] : ( if_real @ ( K2 = A ) @ ( B2 @ K2 ) @ ( C @ K2 ) )
% 3.82/4.07 @ S2 )
% 3.82/4.07 = ( plus_plus_real @ ( B2 @ A ) @ ( groups4148127829035722712t_real @ C @ ( minus_925952699566721837d_enat @ S2 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) ) ) ) )
% 3.82/4.07 & ( ~ ( member_Extended_enat @ A @ S2 )
% 3.82/4.07 => ( ( groups4148127829035722712t_real
% 3.82/4.07 @ ^ [K2: extended_enat] : ( if_real @ ( K2 = A ) @ ( B2 @ K2 ) @ ( C @ K2 ) )
% 3.82/4.07 @ S2 )
% 3.82/4.07 = ( groups4148127829035722712t_real @ C @ ( minus_925952699566721837d_enat @ S2 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.delta_remove
% 3.82/4.07 thf(fact_5492_sum_Odelta__remove,axiom,
% 3.82/4.07 ! [S2: set_Extended_enat,A: extended_enat,B2: extended_enat > extended_enat,C: extended_enat > extended_enat] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ S2 )
% 3.82/4.07 => ( ( ( member_Extended_enat @ A @ S2 )
% 3.82/4.07 => ( ( groups2433450451889696826d_enat
% 3.82/4.07 @ ^ [K2: extended_enat] : ( if_Extended_enat @ ( K2 = A ) @ ( B2 @ K2 ) @ ( C @ K2 ) )
% 3.82/4.07 @ S2 )
% 3.82/4.07 = ( plus_p3455044024723400733d_enat @ ( B2 @ A ) @ ( groups2433450451889696826d_enat @ C @ ( minus_925952699566721837d_enat @ S2 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) ) ) ) )
% 3.82/4.07 & ( ~ ( member_Extended_enat @ A @ S2 )
% 3.82/4.07 => ( ( groups2433450451889696826d_enat
% 3.82/4.07 @ ^ [K2: extended_enat] : ( if_Extended_enat @ ( K2 = A ) @ ( B2 @ K2 ) @ ( C @ K2 ) )
% 3.82/4.07 @ S2 )
% 3.82/4.07 = ( groups2433450451889696826d_enat @ C @ ( minus_925952699566721837d_enat @ S2 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.delta_remove
% 3.82/4.07 thf(fact_5493_sum_Odelta__remove,axiom,
% 3.82/4.07 ! [S2: set_real,A: real,B2: real > nat,C: real > nat] :
% 3.82/4.07 ( ( finite_finite_real @ S2 )
% 3.82/4.07 => ( ( ( member_real @ A @ S2 )
% 3.82/4.07 => ( ( groups1935376822645274424al_nat
% 3.82/4.07 @ ^ [K2: real] : ( if_nat @ ( K2 = A ) @ ( B2 @ K2 ) @ ( C @ K2 ) )
% 3.82/4.07 @ S2 )
% 3.82/4.07 = ( plus_plus_nat @ ( B2 @ A ) @ ( groups1935376822645274424al_nat @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 3.82/4.07 & ( ~ ( member_real @ A @ S2 )
% 3.82/4.07 => ( ( groups1935376822645274424al_nat
% 3.82/4.07 @ ^ [K2: real] : ( if_nat @ ( K2 = A ) @ ( B2 @ K2 ) @ ( C @ K2 ) )
% 3.82/4.07 @ S2 )
% 3.82/4.07 = ( groups1935376822645274424al_nat @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.delta_remove
% 3.82/4.07 thf(fact_5494_sum_Odelta__remove,axiom,
% 3.82/4.07 ! [S2: set_real,A: real,B2: real > int,C: real > int] :
% 3.82/4.07 ( ( finite_finite_real @ S2 )
% 3.82/4.07 => ( ( ( member_real @ A @ S2 )
% 3.82/4.07 => ( ( groups1932886352136224148al_int
% 3.82/4.07 @ ^ [K2: real] : ( if_int @ ( K2 = A ) @ ( B2 @ K2 ) @ ( C @ K2 ) )
% 3.82/4.07 @ S2 )
% 3.82/4.07 = ( plus_plus_int @ ( B2 @ A ) @ ( groups1932886352136224148al_int @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 3.82/4.07 & ( ~ ( member_real @ A @ S2 )
% 3.82/4.07 => ( ( groups1932886352136224148al_int
% 3.82/4.07 @ ^ [K2: real] : ( if_int @ ( K2 = A ) @ ( B2 @ K2 ) @ ( C @ K2 ) )
% 3.82/4.07 @ S2 )
% 3.82/4.07 = ( groups1932886352136224148al_int @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.delta_remove
% 3.82/4.07 thf(fact_5495_sum__strict__mono2,axiom,
% 3.82/4.07 ! [B: set_real,A2: set_real,B2: real,F: real > real] :
% 3.82/4.07 ( ( finite_finite_real @ B )
% 3.82/4.07 => ( ( ord_less_eq_set_real @ A2 @ B )
% 3.82/4.07 => ( ( member_real @ B2 @ ( minus_minus_set_real @ B @ A2 ) )
% 3.82/4.07 => ( ( ord_less_real @ zero_zero_real @ ( F @ B2 ) )
% 3.82/4.07 => ( ! [X5: real] :
% 3.82/4.07 ( ( member_real @ X5 @ B )
% 3.82/4.07 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 3.82/4.07 => ( ord_less_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( groups8097168146408367636l_real @ F @ B ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_strict_mono2
% 3.82/4.07 thf(fact_5496_sum__strict__mono2,axiom,
% 3.82/4.07 ! [B: set_complex,A2: set_complex,B2: complex,F: complex > real] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ B )
% 3.82/4.07 => ( ( ord_le211207098394363844omplex @ A2 @ B )
% 3.82/4.07 => ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ B @ A2 ) )
% 3.82/4.07 => ( ( ord_less_real @ zero_zero_real @ ( F @ B2 ) )
% 3.82/4.07 => ( ! [X5: complex] :
% 3.82/4.07 ( ( member_complex @ X5 @ B )
% 3.82/4.07 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 3.82/4.07 => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ F @ B ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_strict_mono2
% 3.82/4.07 thf(fact_5497_sum__strict__mono2,axiom,
% 3.82/4.07 ! [B: set_Extended_enat,A2: set_Extended_enat,B2: extended_enat,F: extended_enat > real] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ B )
% 3.82/4.07 => ( ( ord_le7203529160286727270d_enat @ A2 @ B )
% 3.82/4.07 => ( ( member_Extended_enat @ B2 @ ( minus_925952699566721837d_enat @ B @ A2 ) )
% 3.82/4.07 => ( ( ord_less_real @ zero_zero_real @ ( F @ B2 ) )
% 3.82/4.07 => ( ! [X5: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ X5 @ B )
% 3.82/4.07 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 3.82/4.07 => ( ord_less_real @ ( groups4148127829035722712t_real @ F @ A2 ) @ ( groups4148127829035722712t_real @ F @ B ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_strict_mono2
% 3.82/4.07 thf(fact_5498_sum__strict__mono2,axiom,
% 3.82/4.07 ! [B: set_real,A2: set_real,B2: real,F: real > nat] :
% 3.82/4.07 ( ( finite_finite_real @ B )
% 3.82/4.07 => ( ( ord_less_eq_set_real @ A2 @ B )
% 3.82/4.07 => ( ( member_real @ B2 @ ( minus_minus_set_real @ B @ A2 ) )
% 3.82/4.07 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B2 ) )
% 3.82/4.07 => ( ! [X5: real] :
% 3.82/4.07 ( ( member_real @ X5 @ B )
% 3.82/4.07 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) ) )
% 3.82/4.07 => ( ord_less_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ F @ B ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_strict_mono2
% 3.82/4.07 thf(fact_5499_sum__strict__mono2,axiom,
% 3.82/4.07 ! [B: set_complex,A2: set_complex,B2: complex,F: complex > nat] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ B )
% 3.82/4.07 => ( ( ord_le211207098394363844omplex @ A2 @ B )
% 3.82/4.07 => ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ B @ A2 ) )
% 3.82/4.07 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B2 ) )
% 3.82/4.07 => ( ! [X5: complex] :
% 3.82/4.07 ( ( member_complex @ X5 @ B )
% 3.82/4.07 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) ) )
% 3.82/4.07 => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ F @ B ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_strict_mono2
% 3.82/4.07 thf(fact_5500_sum__strict__mono2,axiom,
% 3.82/4.07 ! [B: set_Extended_enat,A2: set_Extended_enat,B2: extended_enat,F: extended_enat > nat] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ B )
% 3.82/4.07 => ( ( ord_le7203529160286727270d_enat @ A2 @ B )
% 3.82/4.07 => ( ( member_Extended_enat @ B2 @ ( minus_925952699566721837d_enat @ B @ A2 ) )
% 3.82/4.07 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B2 ) )
% 3.82/4.07 => ( ! [X5: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ X5 @ B )
% 3.82/4.07 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) ) )
% 3.82/4.07 => ( ord_less_nat @ ( groups2027974829824023292at_nat @ F @ A2 ) @ ( groups2027974829824023292at_nat @ F @ B ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_strict_mono2
% 3.82/4.07 thf(fact_5501_sum__strict__mono2,axiom,
% 3.82/4.07 ! [B: set_real,A2: set_real,B2: real,F: real > int] :
% 3.82/4.07 ( ( finite_finite_real @ B )
% 3.82/4.07 => ( ( ord_less_eq_set_real @ A2 @ B )
% 3.82/4.07 => ( ( member_real @ B2 @ ( minus_minus_set_real @ B @ A2 ) )
% 3.82/4.07 => ( ( ord_less_int @ zero_zero_int @ ( F @ B2 ) )
% 3.82/4.07 => ( ! [X5: real] :
% 3.82/4.07 ( ( member_real @ X5 @ B )
% 3.82/4.07 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X5 ) ) )
% 3.82/4.07 => ( ord_less_int @ ( groups1932886352136224148al_int @ F @ A2 ) @ ( groups1932886352136224148al_int @ F @ B ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_strict_mono2
% 3.82/4.07 thf(fact_5502_sum__strict__mono2,axiom,
% 3.82/4.07 ! [B: set_complex,A2: set_complex,B2: complex,F: complex > int] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ B )
% 3.82/4.07 => ( ( ord_le211207098394363844omplex @ A2 @ B )
% 3.82/4.07 => ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ B @ A2 ) )
% 3.82/4.07 => ( ( ord_less_int @ zero_zero_int @ ( F @ B2 ) )
% 3.82/4.07 => ( ! [X5: complex] :
% 3.82/4.07 ( ( member_complex @ X5 @ B )
% 3.82/4.07 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X5 ) ) )
% 3.82/4.07 => ( ord_less_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( groups5690904116761175830ex_int @ F @ B ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_strict_mono2
% 3.82/4.07 thf(fact_5503_sum__strict__mono2,axiom,
% 3.82/4.07 ! [B: set_Extended_enat,A2: set_Extended_enat,B2: extended_enat,F: extended_enat > int] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ B )
% 3.82/4.07 => ( ( ord_le7203529160286727270d_enat @ A2 @ B )
% 3.82/4.07 => ( ( member_Extended_enat @ B2 @ ( minus_925952699566721837d_enat @ B @ A2 ) )
% 3.82/4.07 => ( ( ord_less_int @ zero_zero_int @ ( F @ B2 ) )
% 3.82/4.07 => ( ! [X5: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ X5 @ B )
% 3.82/4.07 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X5 ) ) )
% 3.82/4.07 => ( ord_less_int @ ( groups2025484359314973016at_int @ F @ A2 ) @ ( groups2025484359314973016at_int @ F @ B ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_strict_mono2
% 3.82/4.07 thf(fact_5504_sum__strict__mono2,axiom,
% 3.82/4.07 ! [B: set_nat,A2: set_nat,B2: nat,F: nat > int] :
% 3.82/4.07 ( ( finite_finite_nat @ B )
% 3.82/4.07 => ( ( ord_less_eq_set_nat @ A2 @ B )
% 3.82/4.07 => ( ( member_nat @ B2 @ ( minus_minus_set_nat @ B @ A2 ) )
% 3.82/4.07 => ( ( ord_less_int @ zero_zero_int @ ( F @ B2 ) )
% 3.82/4.07 => ( ! [X5: nat] :
% 3.82/4.07 ( ( member_nat @ X5 @ B )
% 3.82/4.07 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X5 ) ) )
% 3.82/4.07 => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ A2 ) @ ( groups3539618377306564664at_int @ F @ B ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_strict_mono2
% 3.82/4.07 thf(fact_5505_member__le__sum,axiom,
% 3.82/4.07 ! [I: complex,A2: set_complex,F: complex > extended_enat] :
% 3.82/4.07 ( ( member_complex @ I @ A2 )
% 3.82/4.07 => ( ! [X5: complex] :
% 3.82/4.07 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ I @ bot_bot_set_complex ) ) )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ X5 ) ) )
% 3.82/4.07 => ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ ( F @ I ) @ ( groups1752964319039525884d_enat @ F @ A2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % member_le_sum
% 3.82/4.07 thf(fact_5506_member__le__sum,axiom,
% 3.82/4.07 ! [I: extended_enat,A2: set_Extended_enat,F: extended_enat > extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ I @ A2 )
% 3.82/4.07 => ( ! [X5: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ X5 @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ I @ bot_bo7653980558646680370d_enat ) ) )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ X5 ) ) )
% 3.82/4.07 => ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ ( F @ I ) @ ( groups2433450451889696826d_enat @ F @ A2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % member_le_sum
% 3.82/4.07 thf(fact_5507_member__le__sum,axiom,
% 3.82/4.07 ! [I: real,A2: set_real,F: real > extended_enat] :
% 3.82/4.07 ( ( member_real @ I @ A2 )
% 3.82/4.07 => ( ! [X5: real] :
% 3.82/4.07 ( ( member_real @ X5 @ ( minus_minus_set_real @ A2 @ ( insert_real @ I @ bot_bot_set_real ) ) )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ X5 ) ) )
% 3.82/4.07 => ( ( finite_finite_real @ A2 )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ ( F @ I ) @ ( groups2800946370649118462d_enat @ F @ A2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % member_le_sum
% 3.82/4.07 thf(fact_5508_member__le__sum,axiom,
% 3.82/4.07 ! [I: int,A2: set_int,F: int > extended_enat] :
% 3.82/4.07 ( ( member_int @ I @ A2 )
% 3.82/4.07 => ( ! [X5: int] :
% 3.82/4.07 ( ( member_int @ X5 @ ( minus_minus_set_int @ A2 @ ( insert_int @ I @ bot_bot_set_int ) ) )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ X5 ) ) )
% 3.82/4.07 => ( ( finite_finite_int @ A2 )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ ( F @ I ) @ ( groups4225252721152677374d_enat @ F @ A2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % member_le_sum
% 3.82/4.07 thf(fact_5509_member__le__sum,axiom,
% 3.82/4.07 ! [I: nat,A2: set_nat,F: nat > extended_enat] :
% 3.82/4.07 ( ( member_nat @ I @ A2 )
% 3.82/4.07 => ( ! [X5: nat] :
% 3.82/4.07 ( ( member_nat @ X5 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ I @ bot_bot_set_nat ) ) )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ X5 ) ) )
% 3.82/4.07 => ( ( finite_finite_nat @ A2 )
% 3.82/4.07 => ( ord_le2932123472753598470d_enat @ ( F @ I ) @ ( groups7108830773950497114d_enat @ F @ A2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % member_le_sum
% 3.82/4.07 thf(fact_5510_member__le__sum,axiom,
% 3.82/4.07 ! [I: complex,A2: set_complex,F: complex > real] :
% 3.82/4.07 ( ( member_complex @ I @ A2 )
% 3.82/4.07 => ( ! [X5: complex] :
% 3.82/4.07 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ I @ bot_bot_set_complex ) ) )
% 3.82/4.07 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 3.82/4.07 => ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.07 => ( ord_less_eq_real @ ( F @ I ) @ ( groups5808333547571424918x_real @ F @ A2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % member_le_sum
% 3.82/4.07 thf(fact_5511_member__le__sum,axiom,
% 3.82/4.07 ! [I: extended_enat,A2: set_Extended_enat,F: extended_enat > real] :
% 3.82/4.07 ( ( member_Extended_enat @ I @ A2 )
% 3.82/4.07 => ( ! [X5: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ X5 @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ I @ bot_bo7653980558646680370d_enat ) ) )
% 3.82/4.07 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 3.82/4.07 => ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.07 => ( ord_less_eq_real @ ( F @ I ) @ ( groups4148127829035722712t_real @ F @ A2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % member_le_sum
% 3.82/4.07 thf(fact_5512_member__le__sum,axiom,
% 3.82/4.07 ! [I: real,A2: set_real,F: real > real] :
% 3.82/4.07 ( ( member_real @ I @ A2 )
% 3.82/4.07 => ( ! [X5: real] :
% 3.82/4.07 ( ( member_real @ X5 @ ( minus_minus_set_real @ A2 @ ( insert_real @ I @ bot_bot_set_real ) ) )
% 3.82/4.07 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 3.82/4.07 => ( ( finite_finite_real @ A2 )
% 3.82/4.07 => ( ord_less_eq_real @ ( F @ I ) @ ( groups8097168146408367636l_real @ F @ A2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % member_le_sum
% 3.82/4.07 thf(fact_5513_member__le__sum,axiom,
% 3.82/4.07 ! [I: int,A2: set_int,F: int > real] :
% 3.82/4.07 ( ( member_int @ I @ A2 )
% 3.82/4.07 => ( ! [X5: int] :
% 3.82/4.07 ( ( member_int @ X5 @ ( minus_minus_set_int @ A2 @ ( insert_int @ I @ bot_bot_set_int ) ) )
% 3.82/4.07 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 3.82/4.07 => ( ( finite_finite_int @ A2 )
% 3.82/4.07 => ( ord_less_eq_real @ ( F @ I ) @ ( groups8778361861064173332t_real @ F @ A2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % member_le_sum
% 3.82/4.07 thf(fact_5514_member__le__sum,axiom,
% 3.82/4.07 ! [I: complex,A2: set_complex,F: complex > nat] :
% 3.82/4.07 ( ( member_complex @ I @ A2 )
% 3.82/4.07 => ( ! [X5: complex] :
% 3.82/4.07 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ I @ bot_bot_set_complex ) ) )
% 3.82/4.07 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) ) )
% 3.82/4.07 => ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.07 => ( ord_less_eq_nat @ ( F @ I ) @ ( groups5693394587270226106ex_nat @ F @ A2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % member_le_sum
% 3.82/4.07 thf(fact_5515_and__int_Opelims,axiom,
% 3.82/4.07 ! [X: int,Xa2: int,Y: int] :
% 3.82/4.07 ( ( ( bit_se725231765392027082nd_int @ X @ Xa2 )
% 3.82/4.07 = Y )
% 3.82/4.07 => ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa2 ) )
% 3.82/4.07 => ~ ( ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 3.82/4.07 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 3.82/4.07 => ( Y
% 3.82/4.07 = ( uminus_uminus_int
% 3.82/4.07 @ ( zero_n2684676970156552555ol_int
% 3.82/4.07 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 3.82/4.07 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) ) ) ) )
% 3.82/4.07 & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 3.82/4.07 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 3.82/4.07 => ( Y
% 3.82/4.07 = ( plus_plus_int
% 3.82/4.07 @ ( zero_n2684676970156552555ol_int
% 3.82/4.07 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 3.82/4.07 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) )
% 3.82/4.07 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 3.82/4.07 => ~ ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % and_int.pelims
% 3.82/4.07 thf(fact_5516_and__int_Opsimps,axiom,
% 3.82/4.07 ! [K: int,L: int] :
% 3.82/4.07 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K @ L ) )
% 3.82/4.07 => ( ( ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 3.82/4.07 & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 3.82/4.07 => ( ( bit_se725231765392027082nd_int @ K @ L )
% 3.82/4.07 = ( uminus_uminus_int
% 3.82/4.07 @ ( zero_n2684676970156552555ol_int
% 3.82/4.07 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 3.82/4.07 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) ) ) )
% 3.82/4.07 & ( ~ ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 3.82/4.07 & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 3.82/4.07 => ( ( bit_se725231765392027082nd_int @ K @ L )
% 3.82/4.07 = ( plus_plus_int
% 3.82/4.07 @ ( zero_n2684676970156552555ol_int
% 3.82/4.07 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 3.82/4.07 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 3.82/4.07 @ ( 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 ) ) ) ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % and_int.psimps
% 3.82/4.07 thf(fact_5517_signed__take__bit__eq__take__bit__minus,axiom,
% 3.82/4.07 ( bit_ri631733984087533419it_int
% 3.82/4.07 = ( ^ [N: nat,K2: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N ) @ K2 ) @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K2 @ N ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % signed_take_bit_eq_take_bit_minus
% 3.82/4.07 thf(fact_5518_Sum__Icc__nat,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat] :
% 3.82/4.07 ( ( groups3542108847815614940at_nat
% 3.82/4.07 @ ^ [X4: nat] : X4
% 3.82/4.07 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 3.82/4.07 = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N2 @ ( plus_plus_nat @ N2 @ one_one_nat ) ) @ ( times_times_nat @ M2 @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % Sum_Icc_nat
% 3.82/4.07 thf(fact_5519_neg__numeral__le__ceiling,axiom,
% 3.82/4.07 ! [V: num,X: real] :
% 3.82/4.07 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim7802044766580827645g_real @ X ) )
% 3.82/4.07 = ( ord_less_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) @ X ) ) ).
% 3.82/4.07
% 3.82/4.07 % neg_numeral_le_ceiling
% 3.82/4.07 thf(fact_5520_ceiling__less__neg__numeral,axiom,
% 3.82/4.07 ! [X: real,V: num] :
% 3.82/4.07 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 3.82/4.07 = ( ord_less_eq_real @ X @ ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % ceiling_less_neg_numeral
% 3.82/4.07 thf(fact_5521_arith__series__nat,axiom,
% 3.82/4.07 ! [A: nat,D: nat,N2: nat] :
% 3.82/4.07 ( ( groups3542108847815614940at_nat
% 3.82/4.07 @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ I3 @ D ) )
% 3.82/4.07 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 3.82/4.07 = ( 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 ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % arith_series_nat
% 3.82/4.07 thf(fact_5522_bit__0__eq,axiom,
% 3.82/4.07 ( ( bit_se1146084159140164899it_int @ zero_zero_int )
% 3.82/4.07 = bot_bot_nat_o ) ).
% 3.82/4.07
% 3.82/4.07 % bit_0_eq
% 3.82/4.07 thf(fact_5523_bit__0__eq,axiom,
% 3.82/4.07 ( ( bit_se1148574629649215175it_nat @ zero_zero_nat )
% 3.82/4.07 = bot_bot_nat_o ) ).
% 3.82/4.07
% 3.82/4.07 % bit_0_eq
% 3.82/4.07 thf(fact_5524_ceiling__zero,axiom,
% 3.82/4.07 ( ( archim7802044766580827645g_real @ zero_zero_real )
% 3.82/4.07 = zero_zero_int ) ).
% 3.82/4.07
% 3.82/4.07 % ceiling_zero
% 3.82/4.07 thf(fact_5525_and__nat__numerals_I3_J,axiom,
% 3.82/4.07 ! [X: num] :
% 3.82/4.07 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 3.82/4.07 = zero_zero_nat ) ).
% 3.82/4.07
% 3.82/4.07 % and_nat_numerals(3)
% 3.82/4.07 thf(fact_5526_and__nat__numerals_I1_J,axiom,
% 3.82/4.07 ! [Y: num] :
% 3.82/4.07 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 3.82/4.07 = zero_zero_nat ) ).
% 3.82/4.07
% 3.82/4.07 % and_nat_numerals(1)
% 3.82/4.07 thf(fact_5527_bit__numeral__Bit0__Suc__iff,axiom,
% 3.82/4.07 ! [M2: num,N2: nat] :
% 3.82/4.07 ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit0 @ M2 ) ) @ ( suc @ N2 ) )
% 3.82/4.07 = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ M2 ) @ N2 ) ) ).
% 3.82/4.07
% 3.82/4.07 % bit_numeral_Bit0_Suc_iff
% 3.82/4.07 thf(fact_5528_bit__numeral__Bit0__Suc__iff,axiom,
% 3.82/4.07 ! [M2: num,N2: nat] :
% 3.82/4.07 ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ ( bit0 @ M2 ) ) @ ( suc @ N2 ) )
% 3.82/4.07 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M2 ) @ N2 ) ) ).
% 3.82/4.07
% 3.82/4.07 % bit_numeral_Bit0_Suc_iff
% 3.82/4.07 thf(fact_5529_bit__numeral__Bit1__Suc__iff,axiom,
% 3.82/4.07 ! [M2: num,N2: nat] :
% 3.82/4.07 ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit1 @ M2 ) ) @ ( suc @ N2 ) )
% 3.82/4.07 = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ M2 ) @ N2 ) ) ).
% 3.82/4.07
% 3.82/4.07 % bit_numeral_Bit1_Suc_iff
% 3.82/4.07 thf(fact_5530_bit__numeral__Bit1__Suc__iff,axiom,
% 3.82/4.07 ! [M2: num,N2: nat] :
% 3.82/4.07 ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ ( bit1 @ M2 ) ) @ ( suc @ N2 ) )
% 3.82/4.07 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M2 ) @ N2 ) ) ).
% 3.82/4.07
% 3.82/4.07 % bit_numeral_Bit1_Suc_iff
% 3.82/4.07 thf(fact_5531_ceiling__add__of__int,axiom,
% 3.82/4.07 ! [X: real,Z3: int] :
% 3.82/4.07 ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X @ ( ring_1_of_int_real @ Z3 ) ) )
% 3.82/4.07 = ( plus_plus_int @ ( archim7802044766580827645g_real @ X ) @ Z3 ) ) ).
% 3.82/4.07
% 3.82/4.07 % ceiling_add_of_int
% 3.82/4.07 thf(fact_5532_and__nat__numerals_I2_J,axiom,
% 3.82/4.07 ! [Y: num] :
% 3.82/4.07 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 3.82/4.07 = one_one_nat ) ).
% 3.82/4.07
% 3.82/4.07 % and_nat_numerals(2)
% 3.82/4.07 thf(fact_5533_and__nat__numerals_I4_J,axiom,
% 3.82/4.07 ! [X: num] :
% 3.82/4.07 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 3.82/4.07 = one_one_nat ) ).
% 3.82/4.07
% 3.82/4.07 % and_nat_numerals(4)
% 3.82/4.07 thf(fact_5534_ceiling__le__zero,axiom,
% 3.82/4.07 ! [X: real] :
% 3.82/4.07 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ zero_zero_int )
% 3.82/4.07 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 3.82/4.07
% 3.82/4.07 % ceiling_le_zero
% 3.82/4.07 thf(fact_5535_zero__less__ceiling,axiom,
% 3.82/4.07 ! [X: real] :
% 3.82/4.07 ( ( ord_less_int @ zero_zero_int @ ( archim7802044766580827645g_real @ X ) )
% 3.82/4.07 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 3.82/4.07
% 3.82/4.07 % zero_less_ceiling
% 3.82/4.07 thf(fact_5536_ceiling__le__numeral,axiom,
% 3.82/4.07 ! [X: real,V: num] :
% 3.82/4.07 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ ( numeral_numeral_int @ V ) )
% 3.82/4.07 = ( ord_less_eq_real @ X @ ( numeral_numeral_real @ V ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % ceiling_le_numeral
% 3.82/4.07 thf(fact_5537_ceiling__less__one,axiom,
% 3.82/4.07 ! [X: real] :
% 3.82/4.07 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ one_one_int )
% 3.82/4.07 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 3.82/4.07
% 3.82/4.07 % ceiling_less_one
% 3.82/4.07 thf(fact_5538_one__le__ceiling,axiom,
% 3.82/4.07 ! [X: real] :
% 3.82/4.07 ( ( ord_less_eq_int @ one_one_int @ ( archim7802044766580827645g_real @ X ) )
% 3.82/4.07 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 3.82/4.07
% 3.82/4.07 % one_le_ceiling
% 3.82/4.07 thf(fact_5539_numeral__less__ceiling,axiom,
% 3.82/4.07 ! [V: num,X: real] :
% 3.82/4.07 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim7802044766580827645g_real @ X ) )
% 3.82/4.07 = ( ord_less_real @ ( numeral_numeral_real @ V ) @ X ) ) ).
% 3.82/4.07
% 3.82/4.07 % numeral_less_ceiling
% 3.82/4.07 thf(fact_5540_ceiling__le__one,axiom,
% 3.82/4.07 ! [X: real] :
% 3.82/4.07 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ one_one_int )
% 3.82/4.07 = ( ord_less_eq_real @ X @ one_one_real ) ) ).
% 3.82/4.07
% 3.82/4.07 % ceiling_le_one
% 3.82/4.07 thf(fact_5541_one__less__ceiling,axiom,
% 3.82/4.07 ! [X: real] :
% 3.82/4.07 ( ( ord_less_int @ one_one_int @ ( archim7802044766580827645g_real @ X ) )
% 3.82/4.07 = ( ord_less_real @ one_one_real @ X ) ) ).
% 3.82/4.07
% 3.82/4.07 % one_less_ceiling
% 3.82/4.07 thf(fact_5542_ceiling__add__numeral,axiom,
% 3.82/4.07 ! [X: real,V: num] :
% 3.82/4.07 ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X @ ( numeral_numeral_real @ V ) ) )
% 3.82/4.07 = ( plus_plus_int @ ( archim7802044766580827645g_real @ X ) @ ( numeral_numeral_int @ V ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % ceiling_add_numeral
% 3.82/4.07 thf(fact_5543_ceiling__add__one,axiom,
% 3.82/4.07 ! [X: real] :
% 3.82/4.07 ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X @ one_one_real ) )
% 3.82/4.07 = ( plus_plus_int @ ( archim7802044766580827645g_real @ X ) @ one_one_int ) ) ).
% 3.82/4.07
% 3.82/4.07 % ceiling_add_one
% 3.82/4.07 thf(fact_5544_bit__minus__numeral__Bit0__Suc__iff,axiom,
% 3.82/4.07 ! [W2: num,N2: nat] :
% 3.82/4.07 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W2 ) ) ) @ ( suc @ N2 ) )
% 3.82/4.07 = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W2 ) ) @ N2 ) ) ).
% 3.82/4.07
% 3.82/4.07 % bit_minus_numeral_Bit0_Suc_iff
% 3.82/4.07 thf(fact_5545_bit__minus__numeral__Bit1__Suc__iff,axiom,
% 3.82/4.07 ! [W2: num,N2: nat] :
% 3.82/4.07 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W2 ) ) ) @ ( suc @ N2 ) )
% 3.82/4.07 = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W2 ) @ N2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % bit_minus_numeral_Bit1_Suc_iff
% 3.82/4.07 thf(fact_5546_bit__0,axiom,
% 3.82/4.07 ! [A: int] :
% 3.82/4.07 ( ( bit_se1146084159140164899it_int @ A @ zero_zero_nat )
% 3.82/4.07 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % bit_0
% 3.82/4.07 thf(fact_5547_bit__0,axiom,
% 3.82/4.07 ! [A: nat] :
% 3.82/4.07 ( ( bit_se1148574629649215175it_nat @ A @ zero_zero_nat )
% 3.82/4.07 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % bit_0
% 3.82/4.07 thf(fact_5548_and__Suc__0__eq,axiom,
% 3.82/4.07 ! [N2: nat] :
% 3.82/4.07 ( ( bit_se727722235901077358nd_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 3.82/4.07 = ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % and_Suc_0_eq
% 3.82/4.07 thf(fact_5549_Suc__0__and__eq,axiom,
% 3.82/4.07 ! [N2: nat] :
% 3.82/4.07 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 3.82/4.07 = ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % Suc_0_and_eq
% 3.82/4.07 thf(fact_5550_sum_Ocl__ivl__Suc,axiom,
% 3.82/4.07 ! [N2: nat,M2: nat,G: nat > int] :
% 3.82/4.07 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 3.82/4.07 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 3.82/4.07 = zero_zero_int ) )
% 3.82/4.07 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 3.82/4.07 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 3.82/4.07 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.cl_ivl_Suc
% 3.82/4.07 thf(fact_5551_sum_Ocl__ivl__Suc,axiom,
% 3.82/4.07 ! [N2: nat,M2: nat,G: nat > complex] :
% 3.82/4.07 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 3.82/4.07 => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 3.82/4.07 = zero_zero_complex ) )
% 3.82/4.07 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 3.82/4.07 => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 3.82/4.07 = ( plus_plus_complex @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.cl_ivl_Suc
% 3.82/4.07 thf(fact_5552_sum_Ocl__ivl__Suc,axiom,
% 3.82/4.07 ! [N2: nat,M2: nat,G: nat > extended_enat] :
% 3.82/4.07 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 3.82/4.07 => ( ( groups7108830773950497114d_enat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 3.82/4.07 = zero_z5237406670263579293d_enat ) )
% 3.82/4.07 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 3.82/4.07 => ( ( groups7108830773950497114d_enat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 3.82/4.07 = ( plus_p3455044024723400733d_enat @ ( groups7108830773950497114d_enat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.cl_ivl_Suc
% 3.82/4.07 thf(fact_5553_sum_Ocl__ivl__Suc,axiom,
% 3.82/4.07 ! [N2: nat,M2: nat,G: nat > nat] :
% 3.82/4.07 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 3.82/4.07 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 3.82/4.07 = zero_zero_nat ) )
% 3.82/4.07 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 3.82/4.07 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 3.82/4.07 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.cl_ivl_Suc
% 3.82/4.07 thf(fact_5554_sum_Ocl__ivl__Suc,axiom,
% 3.82/4.07 ! [N2: nat,M2: nat,G: nat > real] :
% 3.82/4.07 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 3.82/4.07 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 3.82/4.07 = zero_zero_real ) )
% 3.82/4.07 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 3.82/4.07 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 3.82/4.07 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.cl_ivl_Suc
% 3.82/4.07 thf(fact_5555_ceiling__less__zero,axiom,
% 3.82/4.07 ! [X: real] :
% 3.82/4.07 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ zero_zero_int )
% 3.82/4.07 = ( ord_less_eq_real @ X @ ( uminus_uminus_real @ one_one_real ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % ceiling_less_zero
% 3.82/4.07 thf(fact_5556_zero__le__ceiling,axiom,
% 3.82/4.07 ! [X: real] :
% 3.82/4.07 ( ( ord_less_eq_int @ zero_zero_int @ ( archim7802044766580827645g_real @ X ) )
% 3.82/4.07 = ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X ) ) ).
% 3.82/4.07
% 3.82/4.07 % zero_le_ceiling
% 3.82/4.07 thf(fact_5557_sum__zero__power,axiom,
% 3.82/4.07 ! [A2: set_nat,C: nat > complex] :
% 3.82/4.07 ( ( ( ( finite_finite_nat @ A2 )
% 3.82/4.07 & ( member_nat @ zero_zero_nat @ A2 ) )
% 3.82/4.07 => ( ( groups2073611262835488442omplex
% 3.82/4.07 @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ zero_zero_complex @ I3 ) )
% 3.82/4.07 @ A2 )
% 3.82/4.07 = ( C @ zero_zero_nat ) ) )
% 3.82/4.07 & ( ~ ( ( finite_finite_nat @ A2 )
% 3.82/4.07 & ( member_nat @ zero_zero_nat @ A2 ) )
% 3.82/4.07 => ( ( groups2073611262835488442omplex
% 3.82/4.07 @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ zero_zero_complex @ I3 ) )
% 3.82/4.07 @ A2 )
% 3.82/4.07 = zero_zero_complex ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_zero_power
% 3.82/4.07 thf(fact_5558_sum__zero__power,axiom,
% 3.82/4.07 ! [A2: set_nat,C: nat > real] :
% 3.82/4.07 ( ( ( ( finite_finite_nat @ A2 )
% 3.82/4.07 & ( member_nat @ zero_zero_nat @ A2 ) )
% 3.82/4.07 => ( ( groups6591440286371151544t_real
% 3.82/4.07 @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ zero_zero_real @ I3 ) )
% 3.82/4.07 @ A2 )
% 3.82/4.07 = ( C @ zero_zero_nat ) ) )
% 3.82/4.07 & ( ~ ( ( finite_finite_nat @ A2 )
% 3.82/4.07 & ( member_nat @ zero_zero_nat @ A2 ) )
% 3.82/4.07 => ( ( groups6591440286371151544t_real
% 3.82/4.07 @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ zero_zero_real @ I3 ) )
% 3.82/4.07 @ A2 )
% 3.82/4.07 = zero_zero_real ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_zero_power
% 3.82/4.07 thf(fact_5559_bit__mod__2__iff,axiom,
% 3.82/4.07 ! [A: int,N2: nat] :
% 3.82/4.07 ( ( bit_se1146084159140164899it_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ N2 )
% 3.82/4.07 = ( ( N2 = zero_zero_nat )
% 3.82/4.07 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % bit_mod_2_iff
% 3.82/4.07 thf(fact_5560_bit__mod__2__iff,axiom,
% 3.82/4.07 ! [A: nat,N2: nat] :
% 3.82/4.07 ( ( bit_se1148574629649215175it_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N2 )
% 3.82/4.07 = ( ( N2 = zero_zero_nat )
% 3.82/4.07 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % bit_mod_2_iff
% 3.82/4.07 thf(fact_5561_ceiling__less__numeral,axiom,
% 3.82/4.07 ! [X: real,V: num] :
% 3.82/4.07 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ ( numeral_numeral_int @ V ) )
% 3.82/4.07 = ( ord_less_eq_real @ X @ ( minus_minus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % ceiling_less_numeral
% 3.82/4.07 thf(fact_5562_numeral__le__ceiling,axiom,
% 3.82/4.07 ! [V: num,X: real] :
% 3.82/4.07 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim7802044766580827645g_real @ X ) )
% 3.82/4.07 = ( ord_less_real @ ( minus_minus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) @ X ) ) ).
% 3.82/4.07
% 3.82/4.07 % numeral_le_ceiling
% 3.82/4.07 thf(fact_5563_ceiling__le__neg__numeral,axiom,
% 3.82/4.07 ! [X: real,V: num] :
% 3.82/4.07 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 3.82/4.07 = ( ord_less_eq_real @ X @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % ceiling_le_neg_numeral
% 3.82/4.07 thf(fact_5564_neg__numeral__less__ceiling,axiom,
% 3.82/4.07 ! [V: num,X: real] :
% 3.82/4.07 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim7802044766580827645g_real @ X ) )
% 3.82/4.07 = ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ X ) ) ).
% 3.82/4.07
% 3.82/4.07 % neg_numeral_less_ceiling
% 3.82/4.07 thf(fact_5565_sum__zero__power_H,axiom,
% 3.82/4.07 ! [A2: set_nat,C: nat > complex,D: nat > complex] :
% 3.82/4.07 ( ( ( ( finite_finite_nat @ A2 )
% 3.82/4.07 & ( member_nat @ zero_zero_nat @ A2 ) )
% 3.82/4.07 => ( ( groups2073611262835488442omplex
% 3.82/4.07 @ ^ [I3: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ zero_zero_complex @ I3 ) ) @ ( D @ I3 ) )
% 3.82/4.07 @ A2 )
% 3.82/4.07 = ( divide1717551699836669952omplex @ ( C @ zero_zero_nat ) @ ( D @ zero_zero_nat ) ) ) )
% 3.82/4.07 & ( ~ ( ( finite_finite_nat @ A2 )
% 3.82/4.07 & ( member_nat @ zero_zero_nat @ A2 ) )
% 3.82/4.07 => ( ( groups2073611262835488442omplex
% 3.82/4.07 @ ^ [I3: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ zero_zero_complex @ I3 ) ) @ ( D @ I3 ) )
% 3.82/4.07 @ A2 )
% 3.82/4.07 = zero_zero_complex ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_zero_power'
% 3.82/4.07 thf(fact_5566_sum__zero__power_H,axiom,
% 3.82/4.07 ! [A2: set_nat,C: nat > real,D: nat > real] :
% 3.82/4.07 ( ( ( ( finite_finite_nat @ A2 )
% 3.82/4.07 & ( member_nat @ zero_zero_nat @ A2 ) )
% 3.82/4.07 => ( ( groups6591440286371151544t_real
% 3.82/4.07 @ ^ [I3: nat] : ( divide_divide_real @ ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ zero_zero_real @ I3 ) ) @ ( D @ I3 ) )
% 3.82/4.07 @ A2 )
% 3.82/4.07 = ( divide_divide_real @ ( C @ zero_zero_nat ) @ ( D @ zero_zero_nat ) ) ) )
% 3.82/4.07 & ( ~ ( ( finite_finite_nat @ A2 )
% 3.82/4.07 & ( member_nat @ zero_zero_nat @ A2 ) )
% 3.82/4.07 => ( ( groups6591440286371151544t_real
% 3.82/4.07 @ ^ [I3: nat] : ( divide_divide_real @ ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ zero_zero_real @ I3 ) ) @ ( D @ I3 ) )
% 3.82/4.07 @ A2 )
% 3.82/4.07 = zero_zero_real ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_zero_power'
% 3.82/4.07 thf(fact_5567_bit__disjunctive__add__iff,axiom,
% 3.82/4.07 ! [A: int,B2: int,N2: nat] :
% 3.82/4.07 ( ! [N3: nat] :
% 3.82/4.07 ( ~ ( bit_se1146084159140164899it_int @ A @ N3 )
% 3.82/4.07 | ~ ( bit_se1146084159140164899it_int @ B2 @ N3 ) )
% 3.82/4.07 => ( ( bit_se1146084159140164899it_int @ ( plus_plus_int @ A @ B2 ) @ N2 )
% 3.82/4.07 = ( ( bit_se1146084159140164899it_int @ A @ N2 )
% 3.82/4.07 | ( bit_se1146084159140164899it_int @ B2 @ N2 ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % bit_disjunctive_add_iff
% 3.82/4.07 thf(fact_5568_bit__disjunctive__add__iff,axiom,
% 3.82/4.07 ! [A: nat,B2: nat,N2: nat] :
% 3.82/4.07 ( ! [N3: nat] :
% 3.82/4.07 ( ~ ( bit_se1148574629649215175it_nat @ A @ N3 )
% 3.82/4.07 | ~ ( bit_se1148574629649215175it_nat @ B2 @ N3 ) )
% 3.82/4.07 => ( ( bit_se1148574629649215175it_nat @ ( plus_plus_nat @ A @ B2 ) @ N2 )
% 3.82/4.07 = ( ( bit_se1148574629649215175it_nat @ A @ N2 )
% 3.82/4.07 | ( bit_se1148574629649215175it_nat @ B2 @ N2 ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % bit_disjunctive_add_iff
% 3.82/4.07 thf(fact_5569_not__bit__1__Suc,axiom,
% 3.82/4.07 ! [N2: nat] :
% 3.82/4.07 ~ ( bit_se1146084159140164899it_int @ one_one_int @ ( suc @ N2 ) ) ).
% 3.82/4.07
% 3.82/4.07 % not_bit_1_Suc
% 3.82/4.07 thf(fact_5570_not__bit__1__Suc,axiom,
% 3.82/4.07 ! [N2: nat] :
% 3.82/4.07 ~ ( bit_se1148574629649215175it_nat @ one_one_nat @ ( suc @ N2 ) ) ).
% 3.82/4.07
% 3.82/4.07 % not_bit_1_Suc
% 3.82/4.07 thf(fact_5571_bit__1__iff,axiom,
% 3.82/4.07 ! [N2: nat] :
% 3.82/4.07 ( ( bit_se1146084159140164899it_int @ one_one_int @ N2 )
% 3.82/4.07 = ( N2 = zero_zero_nat ) ) ).
% 3.82/4.07
% 3.82/4.07 % bit_1_iff
% 3.82/4.07 thf(fact_5572_bit__1__iff,axiom,
% 3.82/4.07 ! [N2: nat] :
% 3.82/4.07 ( ( bit_se1148574629649215175it_nat @ one_one_nat @ N2 )
% 3.82/4.07 = ( N2 = zero_zero_nat ) ) ).
% 3.82/4.07
% 3.82/4.07 % bit_1_iff
% 3.82/4.07 thf(fact_5573_sum__cong__Suc,axiom,
% 3.82/4.07 ! [A2: set_nat,F: nat > nat,G: nat > nat] :
% 3.82/4.07 ( ~ ( member_nat @ zero_zero_nat @ A2 )
% 3.82/4.07 => ( ! [X5: nat] :
% 3.82/4.07 ( ( member_nat @ ( suc @ X5 ) @ A2 )
% 3.82/4.07 => ( ( F @ ( suc @ X5 ) )
% 3.82/4.07 = ( G @ ( suc @ X5 ) ) ) )
% 3.82/4.07 => ( ( groups3542108847815614940at_nat @ F @ A2 )
% 3.82/4.07 = ( groups3542108847815614940at_nat @ G @ A2 ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_cong_Suc
% 3.82/4.07 thf(fact_5574_sum__cong__Suc,axiom,
% 3.82/4.07 ! [A2: set_nat,F: nat > real,G: nat > real] :
% 3.82/4.07 ( ~ ( member_nat @ zero_zero_nat @ A2 )
% 3.82/4.07 => ( ! [X5: nat] :
% 3.82/4.07 ( ( member_nat @ ( suc @ X5 ) @ A2 )
% 3.82/4.07 => ( ( F @ ( suc @ X5 ) )
% 3.82/4.07 = ( G @ ( suc @ X5 ) ) ) )
% 3.82/4.07 => ( ( groups6591440286371151544t_real @ F @ A2 )
% 3.82/4.07 = ( groups6591440286371151544t_real @ G @ A2 ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_cong_Suc
% 3.82/4.07 thf(fact_5575_bit__take__bit__iff,axiom,
% 3.82/4.07 ! [M2: nat,A: nat,N2: nat] :
% 3.82/4.07 ( ( bit_se1148574629649215175it_nat @ ( bit_se2925701944663578781it_nat @ M2 @ A ) @ N2 )
% 3.82/4.07 = ( ( ord_less_nat @ N2 @ M2 )
% 3.82/4.07 & ( bit_se1148574629649215175it_nat @ A @ N2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % bit_take_bit_iff
% 3.82/4.07 thf(fact_5576_bit__take__bit__iff,axiom,
% 3.82/4.07 ! [M2: nat,A: int,N2: nat] :
% 3.82/4.07 ( ( bit_se1146084159140164899it_int @ ( bit_se2923211474154528505it_int @ M2 @ A ) @ N2 )
% 3.82/4.07 = ( ( ord_less_nat @ N2 @ M2 )
% 3.82/4.07 & ( bit_se1146084159140164899it_int @ A @ N2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % bit_take_bit_iff
% 3.82/4.07 thf(fact_5577_ceiling__mono,axiom,
% 3.82/4.07 ! [Y: real,X: real] :
% 3.82/4.07 ( ( ord_less_eq_real @ Y @ X )
% 3.82/4.07 => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ Y ) @ ( archim7802044766580827645g_real @ X ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % ceiling_mono
% 3.82/4.07 thf(fact_5578_le__of__int__ceiling,axiom,
% 3.82/4.07 ! [X: real] : ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % le_of_int_ceiling
% 3.82/4.07 thf(fact_5579_ceiling__less__cancel,axiom,
% 3.82/4.07 ! [X: real,Y: real] :
% 3.82/4.07 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ ( archim7802044766580827645g_real @ Y ) )
% 3.82/4.07 => ( ord_less_real @ X @ Y ) ) ).
% 3.82/4.07
% 3.82/4.07 % ceiling_less_cancel
% 3.82/4.07 thf(fact_5580_bit__of__bool__iff,axiom,
% 3.82/4.07 ! [B2: $o,N2: nat] :
% 3.82/4.07 ( ( bit_se1146084159140164899it_int @ ( zero_n2684676970156552555ol_int @ B2 ) @ N2 )
% 3.82/4.07 = ( B2
% 3.82/4.07 & ( N2 = zero_zero_nat ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % bit_of_bool_iff
% 3.82/4.07 thf(fact_5581_bit__of__bool__iff,axiom,
% 3.82/4.07 ! [B2: $o,N2: nat] :
% 3.82/4.07 ( ( bit_se1148574629649215175it_nat @ ( zero_n2687167440665602831ol_nat @ B2 ) @ N2 )
% 3.82/4.07 = ( B2
% 3.82/4.07 & ( N2 = zero_zero_nat ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % bit_of_bool_iff
% 3.82/4.07 thf(fact_5582_sum__subtractf__nat,axiom,
% 3.82/4.07 ! [A2: set_Extended_enat,G: extended_enat > nat,F: extended_enat > nat] :
% 3.82/4.07 ( ! [X5: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ X5 @ A2 )
% 3.82/4.07 => ( ord_less_eq_nat @ ( G @ X5 ) @ ( F @ X5 ) ) )
% 3.82/4.07 => ( ( groups2027974829824023292at_nat
% 3.82/4.07 @ ^ [X4: extended_enat] : ( minus_minus_nat @ ( F @ X4 ) @ ( G @ X4 ) )
% 3.82/4.07 @ A2 )
% 3.82/4.07 = ( minus_minus_nat @ ( groups2027974829824023292at_nat @ F @ A2 ) @ ( groups2027974829824023292at_nat @ G @ A2 ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_subtractf_nat
% 3.82/4.07 thf(fact_5583_sum__subtractf__nat,axiom,
% 3.82/4.07 ! [A2: set_real,G: real > nat,F: real > nat] :
% 3.82/4.07 ( ! [X5: real] :
% 3.82/4.07 ( ( member_real @ X5 @ A2 )
% 3.82/4.07 => ( ord_less_eq_nat @ ( G @ X5 ) @ ( F @ X5 ) ) )
% 3.82/4.07 => ( ( groups1935376822645274424al_nat
% 3.82/4.07 @ ^ [X4: real] : ( minus_minus_nat @ ( F @ X4 ) @ ( G @ X4 ) )
% 3.82/4.07 @ A2 )
% 3.82/4.07 = ( minus_minus_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ G @ A2 ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_subtractf_nat
% 3.82/4.07 thf(fact_5584_sum__subtractf__nat,axiom,
% 3.82/4.07 ! [A2: set_set_nat,G: set_nat > nat,F: set_nat > nat] :
% 3.82/4.07 ( ! [X5: set_nat] :
% 3.82/4.07 ( ( member_set_nat @ X5 @ A2 )
% 3.82/4.07 => ( ord_less_eq_nat @ ( G @ X5 ) @ ( F @ X5 ) ) )
% 3.82/4.07 => ( ( groups8294997508430121362at_nat
% 3.82/4.07 @ ^ [X4: set_nat] : ( minus_minus_nat @ ( F @ X4 ) @ ( G @ X4 ) )
% 3.82/4.07 @ A2 )
% 3.82/4.07 = ( minus_minus_nat @ ( groups8294997508430121362at_nat @ F @ A2 ) @ ( groups8294997508430121362at_nat @ G @ A2 ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_subtractf_nat
% 3.82/4.07 thf(fact_5585_sum__subtractf__nat,axiom,
% 3.82/4.07 ! [A2: set_int,G: int > nat,F: int > nat] :
% 3.82/4.07 ( ! [X5: int] :
% 3.82/4.07 ( ( member_int @ X5 @ A2 )
% 3.82/4.07 => ( ord_less_eq_nat @ ( G @ X5 ) @ ( F @ X5 ) ) )
% 3.82/4.07 => ( ( groups4541462559716669496nt_nat
% 3.82/4.07 @ ^ [X4: int] : ( minus_minus_nat @ ( F @ X4 ) @ ( G @ X4 ) )
% 3.82/4.07 @ A2 )
% 3.82/4.07 = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_subtractf_nat
% 3.82/4.07 thf(fact_5586_sum__subtractf__nat,axiom,
% 3.82/4.07 ! [A2: set_nat,G: nat > nat,F: nat > nat] :
% 3.82/4.07 ( ! [X5: nat] :
% 3.82/4.07 ( ( member_nat @ X5 @ A2 )
% 3.82/4.07 => ( ord_less_eq_nat @ ( G @ X5 ) @ ( F @ X5 ) ) )
% 3.82/4.07 => ( ( groups3542108847815614940at_nat
% 3.82/4.07 @ ^ [X4: nat] : ( minus_minus_nat @ ( F @ X4 ) @ ( G @ X4 ) )
% 3.82/4.07 @ A2 )
% 3.82/4.07 = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ G @ A2 ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_subtractf_nat
% 3.82/4.07 thf(fact_5587_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 3.82/4.07 ! [G: nat > nat,M2: nat,N2: nat] :
% 3.82/4.07 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( suc @ N2 ) ) )
% 3.82/4.07 = ( groups3542108847815614940at_nat
% 3.82/4.07 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 3.82/4.07 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.shift_bounds_cl_Suc_ivl
% 3.82/4.07 thf(fact_5588_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 3.82/4.07 ! [G: nat > real,M2: nat,N2: nat] :
% 3.82/4.07 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( suc @ N2 ) ) )
% 3.82/4.07 = ( groups6591440286371151544t_real
% 3.82/4.07 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 3.82/4.07 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.shift_bounds_cl_Suc_ivl
% 3.82/4.07 thf(fact_5589_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 3.82/4.07 ! [G: nat > nat,M2: nat,K: nat,N2: nat] :
% 3.82/4.07 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M2 @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 3.82/4.07 = ( groups3542108847815614940at_nat
% 3.82/4.07 @ ^ [I3: nat] : ( G @ ( plus_plus_nat @ I3 @ K ) )
% 3.82/4.07 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.shift_bounds_cl_nat_ivl
% 3.82/4.07 thf(fact_5590_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 3.82/4.07 ! [G: nat > real,M2: nat,K: nat,N2: nat] :
% 3.82/4.07 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M2 @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 3.82/4.07 = ( groups6591440286371151544t_real
% 3.82/4.07 @ ^ [I3: nat] : ( G @ ( plus_plus_nat @ I3 @ K ) )
% 3.82/4.07 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.shift_bounds_cl_nat_ivl
% 3.82/4.07 thf(fact_5591_sum__eq__Suc0__iff,axiom,
% 3.82/4.07 ! [A2: set_complex,F: complex > nat] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.07 => ( ( ( groups5693394587270226106ex_nat @ F @ A2 )
% 3.82/4.07 = ( suc @ zero_zero_nat ) )
% 3.82/4.07 = ( ? [X4: complex] :
% 3.82/4.07 ( ( member_complex @ X4 @ A2 )
% 3.82/4.07 & ( ( F @ X4 )
% 3.82/4.07 = ( suc @ zero_zero_nat ) )
% 3.82/4.07 & ! [Y5: complex] :
% 3.82/4.07 ( ( member_complex @ Y5 @ A2 )
% 3.82/4.07 => ( ( X4 != Y5 )
% 3.82/4.07 => ( ( F @ Y5 )
% 3.82/4.07 = zero_zero_nat ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_eq_Suc0_iff
% 3.82/4.07 thf(fact_5592_sum__eq__Suc0__iff,axiom,
% 3.82/4.07 ! [A2: set_int,F: int > nat] :
% 3.82/4.07 ( ( finite_finite_int @ A2 )
% 3.82/4.07 => ( ( ( groups4541462559716669496nt_nat @ F @ A2 )
% 3.82/4.07 = ( suc @ zero_zero_nat ) )
% 3.82/4.07 = ( ? [X4: int] :
% 3.82/4.07 ( ( member_int @ X4 @ A2 )
% 3.82/4.07 & ( ( F @ X4 )
% 3.82/4.07 = ( suc @ zero_zero_nat ) )
% 3.82/4.07 & ! [Y5: int] :
% 3.82/4.07 ( ( member_int @ Y5 @ A2 )
% 3.82/4.07 => ( ( X4 != Y5 )
% 3.82/4.07 => ( ( F @ Y5 )
% 3.82/4.07 = zero_zero_nat ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_eq_Suc0_iff
% 3.82/4.07 thf(fact_5593_sum__eq__Suc0__iff,axiom,
% 3.82/4.07 ! [A2: set_Extended_enat,F: extended_enat > nat] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.07 => ( ( ( groups2027974829824023292at_nat @ F @ A2 )
% 3.82/4.07 = ( suc @ zero_zero_nat ) )
% 3.82/4.07 = ( ? [X4: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ X4 @ A2 )
% 3.82/4.07 & ( ( F @ X4 )
% 3.82/4.07 = ( suc @ zero_zero_nat ) )
% 3.82/4.07 & ! [Y5: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ Y5 @ A2 )
% 3.82/4.07 => ( ( X4 != Y5 )
% 3.82/4.07 => ( ( F @ Y5 )
% 3.82/4.07 = zero_zero_nat ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_eq_Suc0_iff
% 3.82/4.07 thf(fact_5594_sum__eq__Suc0__iff,axiom,
% 3.82/4.07 ! [A2: set_nat,F: nat > nat] :
% 3.82/4.07 ( ( finite_finite_nat @ A2 )
% 3.82/4.07 => ( ( ( groups3542108847815614940at_nat @ F @ A2 )
% 3.82/4.07 = ( suc @ zero_zero_nat ) )
% 3.82/4.07 = ( ? [X4: nat] :
% 3.82/4.07 ( ( member_nat @ X4 @ A2 )
% 3.82/4.07 & ( ( F @ X4 )
% 3.82/4.07 = ( suc @ zero_zero_nat ) )
% 3.82/4.07 & ! [Y5: nat] :
% 3.82/4.07 ( ( member_nat @ Y5 @ A2 )
% 3.82/4.07 => ( ( X4 != Y5 )
% 3.82/4.07 => ( ( F @ Y5 )
% 3.82/4.07 = zero_zero_nat ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_eq_Suc0_iff
% 3.82/4.07 thf(fact_5595_sum__SucD,axiom,
% 3.82/4.07 ! [F: nat > nat,A2: set_nat,N2: nat] :
% 3.82/4.07 ( ( ( groups3542108847815614940at_nat @ F @ A2 )
% 3.82/4.07 = ( suc @ N2 ) )
% 3.82/4.07 => ? [X5: nat] :
% 3.82/4.07 ( ( member_nat @ X5 @ A2 )
% 3.82/4.07 & ( ord_less_nat @ zero_zero_nat @ ( F @ X5 ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_SucD
% 3.82/4.07 thf(fact_5596_sum__eq__1__iff,axiom,
% 3.82/4.07 ! [A2: set_complex,F: complex > nat] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.07 => ( ( ( groups5693394587270226106ex_nat @ F @ A2 )
% 3.82/4.07 = one_one_nat )
% 3.82/4.07 = ( ? [X4: complex] :
% 3.82/4.07 ( ( member_complex @ X4 @ A2 )
% 3.82/4.07 & ( ( F @ X4 )
% 3.82/4.07 = one_one_nat )
% 3.82/4.07 & ! [Y5: complex] :
% 3.82/4.07 ( ( member_complex @ Y5 @ A2 )
% 3.82/4.07 => ( ( X4 != Y5 )
% 3.82/4.07 => ( ( F @ Y5 )
% 3.82/4.07 = zero_zero_nat ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_eq_1_iff
% 3.82/4.07 thf(fact_5597_sum__eq__1__iff,axiom,
% 3.82/4.07 ! [A2: set_int,F: int > nat] :
% 3.82/4.07 ( ( finite_finite_int @ A2 )
% 3.82/4.07 => ( ( ( groups4541462559716669496nt_nat @ F @ A2 )
% 3.82/4.07 = one_one_nat )
% 3.82/4.07 = ( ? [X4: int] :
% 3.82/4.07 ( ( member_int @ X4 @ A2 )
% 3.82/4.07 & ( ( F @ X4 )
% 3.82/4.07 = one_one_nat )
% 3.82/4.07 & ! [Y5: int] :
% 3.82/4.07 ( ( member_int @ Y5 @ A2 )
% 3.82/4.07 => ( ( X4 != Y5 )
% 3.82/4.07 => ( ( F @ Y5 )
% 3.82/4.07 = zero_zero_nat ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_eq_1_iff
% 3.82/4.07 thf(fact_5598_sum__eq__1__iff,axiom,
% 3.82/4.07 ! [A2: set_Extended_enat,F: extended_enat > nat] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.07 => ( ( ( groups2027974829824023292at_nat @ F @ A2 )
% 3.82/4.07 = one_one_nat )
% 3.82/4.07 = ( ? [X4: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ X4 @ A2 )
% 3.82/4.07 & ( ( F @ X4 )
% 3.82/4.07 = one_one_nat )
% 3.82/4.07 & ! [Y5: extended_enat] :
% 3.82/4.07 ( ( member_Extended_enat @ Y5 @ A2 )
% 3.82/4.07 => ( ( X4 != Y5 )
% 3.82/4.07 => ( ( F @ Y5 )
% 3.82/4.07 = zero_zero_nat ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_eq_1_iff
% 3.82/4.07 thf(fact_5599_sum__eq__1__iff,axiom,
% 3.82/4.07 ! [A2: set_nat,F: nat > nat] :
% 3.82/4.07 ( ( finite_finite_nat @ A2 )
% 3.82/4.07 => ( ( ( groups3542108847815614940at_nat @ F @ A2 )
% 3.82/4.07 = one_one_nat )
% 3.82/4.07 = ( ? [X4: nat] :
% 3.82/4.07 ( ( member_nat @ X4 @ A2 )
% 3.82/4.07 & ( ( F @ X4 )
% 3.82/4.07 = one_one_nat )
% 3.82/4.07 & ! [Y5: nat] :
% 3.82/4.07 ( ( member_nat @ Y5 @ A2 )
% 3.82/4.07 => ( ( X4 != Y5 )
% 3.82/4.07 => ( ( F @ Y5 )
% 3.82/4.07 = zero_zero_nat ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_eq_1_iff
% 3.82/4.07 thf(fact_5600_ceiling__le,axiom,
% 3.82/4.07 ! [X: real,A: int] :
% 3.82/4.07 ( ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ A ) )
% 3.82/4.07 => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ A ) ) ).
% 3.82/4.07
% 3.82/4.07 % ceiling_le
% 3.82/4.07 thf(fact_5601_ceiling__le__iff,axiom,
% 3.82/4.07 ! [X: real,Z3: int] :
% 3.82/4.07 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ Z3 )
% 3.82/4.07 = ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ Z3 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % ceiling_le_iff
% 3.82/4.07 thf(fact_5602_less__ceiling__iff,axiom,
% 3.82/4.07 ! [Z3: int,X: real] :
% 3.82/4.07 ( ( ord_less_int @ Z3 @ ( archim7802044766580827645g_real @ X ) )
% 3.82/4.07 = ( ord_less_real @ ( ring_1_of_int_real @ Z3 ) @ X ) ) ).
% 3.82/4.07
% 3.82/4.07 % less_ceiling_iff
% 3.82/4.07 thf(fact_5603_ceiling__add__le,axiom,
% 3.82/4.07 ! [X: real,Y: real] : ( ord_less_eq_int @ ( archim7802044766580827645g_real @ ( plus_plus_real @ X @ Y ) ) @ ( plus_plus_int @ ( archim7802044766580827645g_real @ X ) @ ( archim7802044766580827645g_real @ Y ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % ceiling_add_le
% 3.82/4.07 thf(fact_5604_sum__power__add,axiom,
% 3.82/4.07 ! [X: int,M2: nat,I6: set_nat] :
% 3.82/4.07 ( ( groups3539618377306564664at_int
% 3.82/4.07 @ ^ [I3: nat] : ( power_power_int @ X @ ( plus_plus_nat @ M2 @ I3 ) )
% 3.82/4.07 @ I6 )
% 3.82/4.07 = ( times_times_int @ ( power_power_int @ X @ M2 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ I6 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_power_add
% 3.82/4.07 thf(fact_5605_sum__power__add,axiom,
% 3.82/4.07 ! [X: complex,M2: nat,I6: set_nat] :
% 3.82/4.07 ( ( groups2073611262835488442omplex
% 3.82/4.07 @ ^ [I3: nat] : ( power_power_complex @ X @ ( plus_plus_nat @ M2 @ I3 ) )
% 3.82/4.07 @ I6 )
% 3.82/4.07 = ( times_times_complex @ ( power_power_complex @ X @ M2 ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ I6 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_power_add
% 3.82/4.07 thf(fact_5606_sum__power__add,axiom,
% 3.82/4.07 ! [X: real,M2: nat,I6: set_nat] :
% 3.82/4.07 ( ( groups6591440286371151544t_real
% 3.82/4.07 @ ^ [I3: nat] : ( power_power_real @ X @ ( plus_plus_nat @ M2 @ I3 ) )
% 3.82/4.07 @ I6 )
% 3.82/4.07 = ( times_times_real @ ( power_power_real @ X @ M2 ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ I6 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_power_add
% 3.82/4.07 thf(fact_5607_sum_OatLeastAtMost__rev,axiom,
% 3.82/4.07 ! [G: nat > nat,N2: nat,M2: nat] :
% 3.82/4.07 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ N2 @ M2 ) )
% 3.82/4.07 = ( groups3542108847815614940at_nat
% 3.82/4.07 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M2 @ N2 ) @ I3 ) )
% 3.82/4.07 @ ( set_or1269000886237332187st_nat @ N2 @ M2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.atLeastAtMost_rev
% 3.82/4.07 thf(fact_5608_sum_OatLeastAtMost__rev,axiom,
% 3.82/4.07 ! [G: nat > real,N2: nat,M2: nat] :
% 3.82/4.07 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ N2 @ M2 ) )
% 3.82/4.07 = ( groups6591440286371151544t_real
% 3.82/4.07 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M2 @ N2 ) @ I3 ) )
% 3.82/4.07 @ ( set_or1269000886237332187st_nat @ N2 @ M2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.atLeastAtMost_rev
% 3.82/4.07 thf(fact_5609_sum__nth__roots,axiom,
% 3.82/4.07 ! [N2: nat,C: complex] :
% 3.82/4.07 ( ( ord_less_nat @ one_one_nat @ N2 )
% 3.82/4.07 => ( ( groups7754918857620584856omplex
% 3.82/4.07 @ ^ [X4: complex] : X4
% 3.82/4.07 @ ( collect_complex
% 3.82/4.07 @ ^ [Z6: complex] :
% 3.82/4.07 ( ( power_power_complex @ Z6 @ N2 )
% 3.82/4.07 = C ) ) )
% 3.82/4.07 = zero_zero_complex ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_nth_roots
% 3.82/4.07 thf(fact_5610_sum__roots__unity,axiom,
% 3.82/4.07 ! [N2: nat] :
% 3.82/4.07 ( ( ord_less_nat @ one_one_nat @ N2 )
% 3.82/4.07 => ( ( groups7754918857620584856omplex
% 3.82/4.07 @ ^ [X4: complex] : X4
% 3.82/4.07 @ ( collect_complex
% 3.82/4.07 @ ^ [Z6: complex] :
% 3.82/4.07 ( ( power_power_complex @ Z6 @ N2 )
% 3.82/4.07 = one_one_complex ) ) )
% 3.82/4.07 = zero_zero_complex ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_roots_unity
% 3.82/4.07 thf(fact_5611_of__int__ceiling__le__add__one,axiom,
% 3.82/4.07 ! [R2: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ R2 ) ) @ ( plus_plus_real @ R2 @ one_one_real ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_int_ceiling_le_add_one
% 3.82/4.07 thf(fact_5612_of__int__ceiling__diff__one__le,axiom,
% 3.82/4.07 ! [R2: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ R2 ) ) @ one_one_real ) @ R2 ) ).
% 3.82/4.07
% 3.82/4.07 % of_int_ceiling_diff_one_le
% 3.82/4.07 thf(fact_5613_sum__diff__nat,axiom,
% 3.82/4.07 ! [B: set_complex,A2: set_complex,F: complex > nat] :
% 3.82/4.07 ( ( finite3207457112153483333omplex @ B )
% 3.82/4.07 => ( ( ord_le211207098394363844omplex @ B @ A2 )
% 3.82/4.07 => ( ( groups5693394587270226106ex_nat @ F @ ( minus_811609699411566653omplex @ A2 @ B ) )
% 3.82/4.07 = ( minus_minus_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ F @ B ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_diff_nat
% 3.82/4.07 thf(fact_5614_sum__diff__nat,axiom,
% 3.82/4.07 ! [B: set_Extended_enat,A2: set_Extended_enat,F: extended_enat > nat] :
% 3.82/4.07 ( ( finite4001608067531595151d_enat @ B )
% 3.82/4.07 => ( ( ord_le7203529160286727270d_enat @ B @ A2 )
% 3.82/4.07 => ( ( groups2027974829824023292at_nat @ F @ ( minus_925952699566721837d_enat @ A2 @ B ) )
% 3.82/4.07 = ( minus_minus_nat @ ( groups2027974829824023292at_nat @ F @ A2 ) @ ( groups2027974829824023292at_nat @ F @ B ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_diff_nat
% 3.82/4.07 thf(fact_5615_sum__diff__nat,axiom,
% 3.82/4.07 ! [B: set_int,A2: set_int,F: int > nat] :
% 3.82/4.07 ( ( finite_finite_int @ B )
% 3.82/4.07 => ( ( ord_less_eq_set_int @ B @ A2 )
% 3.82/4.07 => ( ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ A2 @ B ) )
% 3.82/4.07 = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ F @ B ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_diff_nat
% 3.82/4.07 thf(fact_5616_sum__diff__nat,axiom,
% 3.82/4.07 ! [B: set_nat,A2: set_nat,F: nat > nat] :
% 3.82/4.07 ( ( finite_finite_nat @ B )
% 3.82/4.07 => ( ( ord_less_eq_set_nat @ B @ A2 )
% 3.82/4.07 => ( ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A2 @ B ) )
% 3.82/4.07 = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ F @ B ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_diff_nat
% 3.82/4.07 thf(fact_5617_sum__diff1__nat,axiom,
% 3.82/4.07 ! [A: set_nat,A2: set_set_nat,F: set_nat > nat] :
% 3.82/4.07 ( ( ( member_set_nat @ A @ A2 )
% 3.82/4.07 => ( ( groups8294997508430121362at_nat @ F @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 3.82/4.07 = ( minus_minus_nat @ ( groups8294997508430121362at_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 3.82/4.07 & ( ~ ( member_set_nat @ A @ A2 )
% 3.82/4.07 => ( ( groups8294997508430121362at_nat @ F @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 3.82/4.07 = ( groups8294997508430121362at_nat @ F @ A2 ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_diff1_nat
% 3.82/4.07 thf(fact_5618_sum__diff1__nat,axiom,
% 3.82/4.07 ! [A: extended_enat,A2: set_Extended_enat,F: extended_enat > nat] :
% 3.82/4.07 ( ( ( member_Extended_enat @ A @ A2 )
% 3.82/4.07 => ( ( groups2027974829824023292at_nat @ F @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) )
% 3.82/4.07 = ( minus_minus_nat @ ( groups2027974829824023292at_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 3.82/4.07 & ( ~ ( member_Extended_enat @ A @ A2 )
% 3.82/4.07 => ( ( groups2027974829824023292at_nat @ F @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) )
% 3.82/4.07 = ( groups2027974829824023292at_nat @ F @ A2 ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_diff1_nat
% 3.82/4.07 thf(fact_5619_sum__diff1__nat,axiom,
% 3.82/4.07 ! [A: real,A2: set_real,F: real > nat] :
% 3.82/4.07 ( ( ( member_real @ A @ A2 )
% 3.82/4.07 => ( ( groups1935376822645274424al_nat @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 3.82/4.07 = ( minus_minus_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 3.82/4.07 & ( ~ ( member_real @ A @ A2 )
% 3.82/4.07 => ( ( groups1935376822645274424al_nat @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 3.82/4.07 = ( groups1935376822645274424al_nat @ F @ A2 ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_diff1_nat
% 3.82/4.07 thf(fact_5620_sum__diff1__nat,axiom,
% 3.82/4.07 ! [A: int,A2: set_int,F: int > nat] :
% 3.82/4.07 ( ( ( member_int @ A @ A2 )
% 3.82/4.07 => ( ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 3.82/4.07 = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 3.82/4.07 & ( ~ ( member_int @ A @ A2 )
% 3.82/4.07 => ( ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 3.82/4.07 = ( groups4541462559716669496nt_nat @ F @ A2 ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_diff1_nat
% 3.82/4.07 thf(fact_5621_sum__diff1__nat,axiom,
% 3.82/4.07 ! [A: nat,A2: set_nat,F: nat > nat] :
% 3.82/4.07 ( ( ( member_nat @ A @ A2 )
% 3.82/4.07 => ( ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 3.82/4.07 = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 3.82/4.07 & ( ~ ( member_nat @ A @ A2 )
% 3.82/4.07 => ( ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 3.82/4.07 = ( groups3542108847815614940at_nat @ F @ A2 ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_diff1_nat
% 3.82/4.07 thf(fact_5622_sum__shift__lb__Suc0__0,axiom,
% 3.82/4.07 ! [F: nat > int,K: nat] :
% 3.82/4.07 ( ( ( F @ zero_zero_nat )
% 3.82/4.07 = zero_zero_int )
% 3.82/4.07 => ( ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 3.82/4.07 = ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_shift_lb_Suc0_0
% 3.82/4.07 thf(fact_5623_sum__shift__lb__Suc0__0,axiom,
% 3.82/4.07 ! [F: nat > complex,K: nat] :
% 3.82/4.07 ( ( ( F @ zero_zero_nat )
% 3.82/4.07 = zero_zero_complex )
% 3.82/4.07 => ( ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 3.82/4.07 = ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_shift_lb_Suc0_0
% 3.82/4.07 thf(fact_5624_sum__shift__lb__Suc0__0,axiom,
% 3.82/4.07 ! [F: nat > extended_enat,K: nat] :
% 3.82/4.07 ( ( ( F @ zero_zero_nat )
% 3.82/4.07 = zero_z5237406670263579293d_enat )
% 3.82/4.07 => ( ( groups7108830773950497114d_enat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 3.82/4.07 = ( groups7108830773950497114d_enat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_shift_lb_Suc0_0
% 3.82/4.07 thf(fact_5625_sum__shift__lb__Suc0__0,axiom,
% 3.82/4.07 ! [F: nat > nat,K: nat] :
% 3.82/4.07 ( ( ( F @ zero_zero_nat )
% 3.82/4.07 = zero_zero_nat )
% 3.82/4.07 => ( ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 3.82/4.07 = ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_shift_lb_Suc0_0
% 3.82/4.07 thf(fact_5626_sum__shift__lb__Suc0__0,axiom,
% 3.82/4.07 ! [F: nat > real,K: nat] :
% 3.82/4.07 ( ( ( F @ zero_zero_nat )
% 3.82/4.07 = zero_zero_real )
% 3.82/4.07 => ( ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 3.82/4.07 = ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_shift_lb_Suc0_0
% 3.82/4.07 thf(fact_5627_sum_OatLeast0__atMost__Suc,axiom,
% 3.82/4.07 ! [G: nat > int,N2: nat] :
% 3.82/4.07 ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 3.82/4.07 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.atLeast0_atMost_Suc
% 3.82/4.07 thf(fact_5628_sum_OatLeast0__atMost__Suc,axiom,
% 3.82/4.07 ! [G: nat > extended_enat,N2: nat] :
% 3.82/4.07 ( ( groups7108830773950497114d_enat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 3.82/4.07 = ( plus_p3455044024723400733d_enat @ ( groups7108830773950497114d_enat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.atLeast0_atMost_Suc
% 3.82/4.07 thf(fact_5629_sum_OatLeast0__atMost__Suc,axiom,
% 3.82/4.07 ! [G: nat > nat,N2: nat] :
% 3.82/4.07 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 3.82/4.07 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.atLeast0_atMost_Suc
% 3.82/4.07 thf(fact_5630_sum_OatLeast0__atMost__Suc,axiom,
% 3.82/4.07 ! [G: nat > real,N2: nat] :
% 3.82/4.07 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 3.82/4.07 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.atLeast0_atMost_Suc
% 3.82/4.07 thf(fact_5631_sum_Onat__ivl__Suc_H,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat,G: nat > int] :
% 3.82/4.07 ( ( ord_less_eq_nat @ M2 @ ( suc @ N2 ) )
% 3.82/4.07 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 3.82/4.07 = ( plus_plus_int @ ( G @ ( suc @ N2 ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.nat_ivl_Suc'
% 3.82/4.07 thf(fact_5632_sum_Onat__ivl__Suc_H,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat,G: nat > extended_enat] :
% 3.82/4.07 ( ( ord_less_eq_nat @ M2 @ ( suc @ N2 ) )
% 3.82/4.07 => ( ( groups7108830773950497114d_enat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 3.82/4.07 = ( plus_p3455044024723400733d_enat @ ( G @ ( suc @ N2 ) ) @ ( groups7108830773950497114d_enat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.nat_ivl_Suc'
% 3.82/4.07 thf(fact_5633_sum_Onat__ivl__Suc_H,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat,G: nat > nat] :
% 3.82/4.07 ( ( ord_less_eq_nat @ M2 @ ( suc @ N2 ) )
% 3.82/4.07 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 3.82/4.07 = ( plus_plus_nat @ ( G @ ( suc @ N2 ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.nat_ivl_Suc'
% 3.82/4.07 thf(fact_5634_sum_Onat__ivl__Suc_H,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat,G: nat > real] :
% 3.82/4.07 ( ( ord_less_eq_nat @ M2 @ ( suc @ N2 ) )
% 3.82/4.07 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 3.82/4.07 = ( plus_plus_real @ ( G @ ( suc @ N2 ) ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.nat_ivl_Suc'
% 3.82/4.07 thf(fact_5635_sum_OatLeast__Suc__atMost,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat,G: nat > int] :
% 3.82/4.07 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.07 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 3.82/4.07 = ( plus_plus_int @ ( G @ M2 ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.atLeast_Suc_atMost
% 3.82/4.07 thf(fact_5636_sum_OatLeast__Suc__atMost,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat,G: nat > extended_enat] :
% 3.82/4.07 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.07 => ( ( groups7108830773950497114d_enat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 3.82/4.07 = ( plus_p3455044024723400733d_enat @ ( G @ M2 ) @ ( groups7108830773950497114d_enat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.atLeast_Suc_atMost
% 3.82/4.07 thf(fact_5637_sum_OatLeast__Suc__atMost,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat,G: nat > nat] :
% 3.82/4.07 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.07 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 3.82/4.07 = ( plus_plus_nat @ ( G @ M2 ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.atLeast_Suc_atMost
% 3.82/4.07 thf(fact_5638_sum_OatLeast__Suc__atMost,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat,G: nat > real] :
% 3.82/4.07 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.07 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 3.82/4.07 = ( plus_plus_real @ ( G @ M2 ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.atLeast_Suc_atMost
% 3.82/4.07 thf(fact_5639_bit__imp__take__bit__positive,axiom,
% 3.82/4.07 ! [N2: nat,M2: nat,K: int] :
% 3.82/4.07 ( ( ord_less_nat @ N2 @ M2 )
% 3.82/4.07 => ( ( bit_se1146084159140164899it_int @ K @ N2 )
% 3.82/4.07 => ( ord_less_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ M2 @ K ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % bit_imp_take_bit_positive
% 3.82/4.07 thf(fact_5640_bit__concat__bit__iff,axiom,
% 3.82/4.07 ! [M2: nat,K: int,L: int,N2: nat] :
% 3.82/4.07 ( ( bit_se1146084159140164899it_int @ ( bit_concat_bit @ M2 @ K @ L ) @ N2 )
% 3.82/4.07 = ( ( ( ord_less_nat @ N2 @ M2 )
% 3.82/4.07 & ( bit_se1146084159140164899it_int @ K @ N2 ) )
% 3.82/4.07 | ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.07 & ( bit_se1146084159140164899it_int @ L @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % bit_concat_bit_iff
% 3.82/4.07 thf(fact_5641_sum_OSuc__reindex__ivl,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat,G: nat > int] :
% 3.82/4.07 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.07 => ( ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 3.82/4.07 = ( plus_plus_int @ ( G @ M2 )
% 3.82/4.07 @ ( groups3539618377306564664at_int
% 3.82/4.07 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 3.82/4.07 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.Suc_reindex_ivl
% 3.82/4.07 thf(fact_5642_sum_OSuc__reindex__ivl,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat,G: nat > extended_enat] :
% 3.82/4.07 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.07 => ( ( plus_p3455044024723400733d_enat @ ( groups7108830773950497114d_enat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 3.82/4.07 = ( plus_p3455044024723400733d_enat @ ( G @ M2 )
% 3.82/4.07 @ ( groups7108830773950497114d_enat
% 3.82/4.07 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 3.82/4.07 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.Suc_reindex_ivl
% 3.82/4.07 thf(fact_5643_sum_OSuc__reindex__ivl,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat,G: nat > nat] :
% 3.82/4.07 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.07 => ( ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 3.82/4.07 = ( plus_plus_nat @ ( G @ M2 )
% 3.82/4.07 @ ( groups3542108847815614940at_nat
% 3.82/4.07 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 3.82/4.07 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.Suc_reindex_ivl
% 3.82/4.07 thf(fact_5644_sum_OSuc__reindex__ivl,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat,G: nat > real] :
% 3.82/4.07 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.07 => ( ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 3.82/4.07 = ( plus_plus_real @ ( G @ M2 )
% 3.82/4.07 @ ( groups6591440286371151544t_real
% 3.82/4.07 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 3.82/4.07 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.Suc_reindex_ivl
% 3.82/4.07 thf(fact_5645_sum__Suc__diff,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat,F: nat > int] :
% 3.82/4.07 ( ( ord_less_eq_nat @ M2 @ ( suc @ N2 ) )
% 3.82/4.07 => ( ( groups3539618377306564664at_int
% 3.82/4.07 @ ^ [I3: nat] : ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) )
% 3.82/4.07 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 3.82/4.07 = ( minus_minus_int @ ( F @ ( suc @ N2 ) ) @ ( F @ M2 ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_Suc_diff
% 3.82/4.07 thf(fact_5646_sum__Suc__diff,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat,F: nat > real] :
% 3.82/4.07 ( ( ord_less_eq_nat @ M2 @ ( suc @ N2 ) )
% 3.82/4.07 => ( ( groups6591440286371151544t_real
% 3.82/4.07 @ ^ [I3: nat] : ( minus_minus_real @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) )
% 3.82/4.07 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 3.82/4.07 = ( minus_minus_real @ ( F @ ( suc @ N2 ) ) @ ( F @ M2 ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_Suc_diff
% 3.82/4.07 thf(fact_5647_exp__eq__0__imp__not__bit,axiom,
% 3.82/4.07 ! [N2: nat,A: int] :
% 3.82/4.07 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 3.82/4.07 = zero_zero_int )
% 3.82/4.07 => ~ ( bit_se1146084159140164899it_int @ A @ N2 ) ) ).
% 3.82/4.07
% 3.82/4.07 % exp_eq_0_imp_not_bit
% 3.82/4.07 thf(fact_5648_exp__eq__0__imp__not__bit,axiom,
% 3.82/4.07 ! [N2: nat,A: nat] :
% 3.82/4.07 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 3.82/4.07 = zero_zero_nat )
% 3.82/4.07 => ~ ( bit_se1148574629649215175it_nat @ A @ N2 ) ) ).
% 3.82/4.07
% 3.82/4.07 % exp_eq_0_imp_not_bit
% 3.82/4.07 thf(fact_5649_bit__Suc,axiom,
% 3.82/4.07 ! [A: int,N2: nat] :
% 3.82/4.07 ( ( bit_se1146084159140164899it_int @ A @ ( suc @ N2 ) )
% 3.82/4.07 = ( bit_se1146084159140164899it_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ N2 ) ) ).
% 3.82/4.07
% 3.82/4.07 % bit_Suc
% 3.82/4.07 thf(fact_5650_bit__Suc,axiom,
% 3.82/4.07 ! [A: nat,N2: nat] :
% 3.82/4.07 ( ( bit_se1148574629649215175it_nat @ A @ ( suc @ N2 ) )
% 3.82/4.07 = ( bit_se1148574629649215175it_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N2 ) ) ).
% 3.82/4.07
% 3.82/4.07 % bit_Suc
% 3.82/4.07 thf(fact_5651_ceiling__correct,axiom,
% 3.82/4.07 ! [X: real] :
% 3.82/4.07 ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X ) ) @ one_one_real ) @ X )
% 3.82/4.07 & ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % ceiling_correct
% 3.82/4.07 thf(fact_5652_ceiling__unique,axiom,
% 3.82/4.07 ! [Z3: int,X: real] :
% 3.82/4.07 ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ Z3 ) @ one_one_real ) @ X )
% 3.82/4.07 => ( ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ Z3 ) )
% 3.82/4.07 => ( ( archim7802044766580827645g_real @ X )
% 3.82/4.07 = Z3 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % ceiling_unique
% 3.82/4.07 thf(fact_5653_ceiling__eq__iff,axiom,
% 3.82/4.07 ! [X: real,A: int] :
% 3.82/4.07 ( ( ( archim7802044766580827645g_real @ X )
% 3.82/4.07 = A )
% 3.82/4.07 = ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ A ) @ one_one_real ) @ X )
% 3.82/4.07 & ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ A ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % ceiling_eq_iff
% 3.82/4.07 thf(fact_5654_ceiling__split,axiom,
% 3.82/4.07 ! [P: int > $o,T: real] :
% 3.82/4.07 ( ( P @ ( archim7802044766580827645g_real @ T ) )
% 3.82/4.07 = ( ! [I3: int] :
% 3.82/4.07 ( ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ I3 ) @ one_one_real ) @ T )
% 3.82/4.07 & ( ord_less_eq_real @ T @ ( ring_1_of_int_real @ I3 ) ) )
% 3.82/4.07 => ( P @ I3 ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % ceiling_split
% 3.82/4.07 thf(fact_5655_mult__ceiling__le,axiom,
% 3.82/4.07 ! [A: real,B2: real] :
% 3.82/4.07 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 3.82/4.07 => ( ( ord_less_eq_real @ zero_zero_real @ B2 )
% 3.82/4.07 => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ ( times_times_real @ A @ B2 ) ) @ ( times_times_int @ ( archim7802044766580827645g_real @ A ) @ ( archim7802044766580827645g_real @ B2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % mult_ceiling_le
% 3.82/4.07 thf(fact_5656_ceiling__less__iff,axiom,
% 3.82/4.07 ! [X: real,Z3: int] :
% 3.82/4.07 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ Z3 )
% 3.82/4.07 = ( ord_less_eq_real @ X @ ( minus_minus_real @ ( ring_1_of_int_real @ Z3 ) @ one_one_real ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % ceiling_less_iff
% 3.82/4.07 thf(fact_5657_le__ceiling__iff,axiom,
% 3.82/4.07 ! [Z3: int,X: real] :
% 3.82/4.07 ( ( ord_less_eq_int @ Z3 @ ( archim7802044766580827645g_real @ X ) )
% 3.82/4.07 = ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ Z3 ) @ one_one_real ) @ X ) ) ).
% 3.82/4.07
% 3.82/4.07 % le_ceiling_iff
% 3.82/4.07 thf(fact_5658_int__bit__bound,axiom,
% 3.82/4.07 ! [K: int] :
% 3.82/4.07 ~ ! [N3: nat] :
% 3.82/4.07 ( ! [M5: nat] :
% 3.82/4.07 ( ( ord_less_eq_nat @ N3 @ M5 )
% 3.82/4.07 => ( ( bit_se1146084159140164899it_int @ K @ M5 )
% 3.82/4.07 = ( bit_se1146084159140164899it_int @ K @ N3 ) ) )
% 3.82/4.07 => ~ ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 3.82/4.07 => ( ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N3 @ one_one_nat ) )
% 3.82/4.07 = ( ~ ( bit_se1146084159140164899it_int @ K @ N3 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % int_bit_bound
% 3.82/4.07 thf(fact_5659_sum_Oub__add__nat,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat,G: nat > int,P5: nat] :
% 3.82/4.07 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 3.82/4.07 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N2 @ P5 ) ) )
% 3.82/4.07 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P5 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.ub_add_nat
% 3.82/4.07 thf(fact_5660_sum_Oub__add__nat,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat,G: nat > extended_enat,P5: nat] :
% 3.82/4.07 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 3.82/4.07 => ( ( groups7108830773950497114d_enat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N2 @ P5 ) ) )
% 3.82/4.07 = ( plus_p3455044024723400733d_enat @ ( groups7108830773950497114d_enat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( groups7108830773950497114d_enat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P5 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.ub_add_nat
% 3.82/4.07 thf(fact_5661_sum_Oub__add__nat,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat,G: nat > nat,P5: nat] :
% 3.82/4.07 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 3.82/4.07 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N2 @ P5 ) ) )
% 3.82/4.07 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P5 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.ub_add_nat
% 3.82/4.07 thf(fact_5662_sum_Oub__add__nat,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat,G: nat > real,P5: nat] :
% 3.82/4.07 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 3.82/4.07 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N2 @ P5 ) ) )
% 3.82/4.07 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P5 ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.ub_add_nat
% 3.82/4.07 thf(fact_5663_sum__count__set,axiom,
% 3.82/4.07 ! [Xs: list_complex,X8: set_complex] :
% 3.82/4.07 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ X8 )
% 3.82/4.07 => ( ( finite3207457112153483333omplex @ X8 )
% 3.82/4.07 => ( ( groups5693394587270226106ex_nat @ ( count_list_complex @ Xs ) @ X8 )
% 3.82/4.07 = ( size_s3451745648224563538omplex @ Xs ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_count_set
% 3.82/4.07 thf(fact_5664_sum__count__set,axiom,
% 3.82/4.07 ! [Xs: list_Extended_enat,X8: set_Extended_enat] :
% 3.82/4.07 ( ( ord_le7203529160286727270d_enat @ ( set_Extended_enat2 @ Xs ) @ X8 )
% 3.82/4.07 => ( ( finite4001608067531595151d_enat @ X8 )
% 3.82/4.07 => ( ( groups2027974829824023292at_nat @ ( count_101369445342291426d_enat @ Xs ) @ X8 )
% 3.82/4.07 = ( size_s3941691890525107288d_enat @ Xs ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_count_set
% 3.82/4.07 thf(fact_5665_sum__count__set,axiom,
% 3.82/4.07 ! [Xs: list_VEBT_VEBT,X8: set_VEBT_VEBT] :
% 3.82/4.07 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ X8 )
% 3.82/4.07 => ( ( finite5795047828879050333T_VEBT @ X8 )
% 3.82/4.07 => ( ( groups771621172384141258BT_nat @ ( count_list_VEBT_VEBT @ Xs ) @ X8 )
% 3.82/4.07 = ( size_s6755466524823107622T_VEBT @ Xs ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_count_set
% 3.82/4.07 thf(fact_5666_sum__count__set,axiom,
% 3.82/4.07 ! [Xs: list_int,X8: set_int] :
% 3.82/4.07 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ X8 )
% 3.82/4.07 => ( ( finite_finite_int @ X8 )
% 3.82/4.07 => ( ( groups4541462559716669496nt_nat @ ( count_list_int @ Xs ) @ X8 )
% 3.82/4.07 = ( size_size_list_int @ Xs ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_count_set
% 3.82/4.07 thf(fact_5667_sum__count__set,axiom,
% 3.82/4.07 ! [Xs: list_nat,X8: set_nat] :
% 3.82/4.07 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ X8 )
% 3.82/4.07 => ( ( finite_finite_nat @ X8 )
% 3.82/4.07 => ( ( groups3542108847815614940at_nat @ ( count_list_nat @ Xs ) @ X8 )
% 3.82/4.07 = ( size_size_list_nat @ Xs ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_count_set
% 3.82/4.07 thf(fact_5668_and__exp__eq__0__iff__not__bit,axiom,
% 3.82/4.07 ! [A: int,N2: nat] :
% 3.82/4.07 ( ( ( bit_se725231765392027082nd_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 3.82/4.07 = zero_zero_int )
% 3.82/4.07 = ( ~ ( bit_se1146084159140164899it_int @ A @ N2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % and_exp_eq_0_iff_not_bit
% 3.82/4.07 thf(fact_5669_and__exp__eq__0__iff__not__bit,axiom,
% 3.82/4.07 ! [A: nat,N2: nat] :
% 3.82/4.07 ( ( ( bit_se727722235901077358nd_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 3.82/4.07 = zero_zero_nat )
% 3.82/4.07 = ( ~ ( bit_se1148574629649215175it_nat @ A @ N2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % and_exp_eq_0_iff_not_bit
% 3.82/4.07 thf(fact_5670_ceiling__divide__upper,axiom,
% 3.82/4.07 ! [Q3: real,P5: real] :
% 3.82/4.07 ( ( ord_less_real @ zero_zero_real @ Q3 )
% 3.82/4.07 => ( ord_less_eq_real @ P5 @ ( times_times_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ ( divide_divide_real @ P5 @ Q3 ) ) ) @ Q3 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % ceiling_divide_upper
% 3.82/4.07 thf(fact_5671_sum__natinterval__diff,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat,F: nat > complex] :
% 3.82/4.07 ( ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.07 => ( ( groups2073611262835488442omplex
% 3.82/4.07 @ ^ [K2: nat] : ( minus_minus_complex @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 3.82/4.07 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 3.82/4.07 = ( minus_minus_complex @ ( F @ M2 ) @ ( F @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) )
% 3.82/4.07 & ( ~ ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.07 => ( ( groups2073611262835488442omplex
% 3.82/4.07 @ ^ [K2: nat] : ( minus_minus_complex @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 3.82/4.07 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 3.82/4.07 = zero_zero_complex ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_natinterval_diff
% 3.82/4.07 thf(fact_5672_sum__natinterval__diff,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat,F: nat > int] :
% 3.82/4.07 ( ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.07 => ( ( groups3539618377306564664at_int
% 3.82/4.07 @ ^ [K2: nat] : ( minus_minus_int @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 3.82/4.07 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 3.82/4.07 = ( minus_minus_int @ ( F @ M2 ) @ ( F @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) )
% 3.82/4.07 & ( ~ ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.07 => ( ( groups3539618377306564664at_int
% 3.82/4.07 @ ^ [K2: nat] : ( minus_minus_int @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 3.82/4.07 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 3.82/4.07 = zero_zero_int ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_natinterval_diff
% 3.82/4.07 thf(fact_5673_sum__natinterval__diff,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat,F: nat > real] :
% 3.82/4.07 ( ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.07 => ( ( groups6591440286371151544t_real
% 3.82/4.07 @ ^ [K2: nat] : ( minus_minus_real @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 3.82/4.07 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 3.82/4.07 = ( minus_minus_real @ ( F @ M2 ) @ ( F @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) )
% 3.82/4.07 & ( ~ ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.07 => ( ( groups6591440286371151544t_real
% 3.82/4.07 @ ^ [K2: nat] : ( minus_minus_real @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 3.82/4.07 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 3.82/4.07 = zero_zero_real ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_natinterval_diff
% 3.82/4.07 thf(fact_5674_sum__telescope_H_H,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat,F: nat > int] :
% 3.82/4.07 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.07 => ( ( groups3539618377306564664at_int
% 3.82/4.07 @ ^ [K2: nat] : ( minus_minus_int @ ( F @ K2 ) @ ( F @ ( minus_minus_nat @ K2 @ one_one_nat ) ) )
% 3.82/4.07 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N2 ) )
% 3.82/4.07 = ( minus_minus_int @ ( F @ N2 ) @ ( F @ M2 ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_telescope''
% 3.82/4.07 thf(fact_5675_sum__telescope_H_H,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat,F: nat > real] :
% 3.82/4.07 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.07 => ( ( groups6591440286371151544t_real
% 3.82/4.07 @ ^ [K2: nat] : ( minus_minus_real @ ( F @ K2 ) @ ( F @ ( minus_minus_nat @ K2 @ one_one_nat ) ) )
% 3.82/4.07 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N2 ) )
% 3.82/4.07 = ( minus_minus_real @ ( F @ N2 ) @ ( F @ M2 ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_telescope''
% 3.82/4.07 thf(fact_5676_even__bit__succ__iff,axiom,
% 3.82/4.07 ! [A: int,N2: nat] :
% 3.82/4.07 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 3.82/4.07 => ( ( bit_se1146084159140164899it_int @ ( plus_plus_int @ one_one_int @ A ) @ N2 )
% 3.82/4.07 = ( ( bit_se1146084159140164899it_int @ A @ N2 )
% 3.82/4.07 | ( N2 = zero_zero_nat ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % even_bit_succ_iff
% 3.82/4.07 thf(fact_5677_even__bit__succ__iff,axiom,
% 3.82/4.07 ! [A: nat,N2: nat] :
% 3.82/4.07 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 3.82/4.07 => ( ( bit_se1148574629649215175it_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ N2 )
% 3.82/4.07 = ( ( bit_se1148574629649215175it_nat @ A @ N2 )
% 3.82/4.07 | ( N2 = zero_zero_nat ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % even_bit_succ_iff
% 3.82/4.07 thf(fact_5678_odd__bit__iff__bit__pred,axiom,
% 3.82/4.07 ! [A: int,N2: nat] :
% 3.82/4.07 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 3.82/4.07 => ( ( bit_se1146084159140164899it_int @ A @ N2 )
% 3.82/4.07 = ( ( bit_se1146084159140164899it_int @ ( minus_minus_int @ A @ one_one_int ) @ N2 )
% 3.82/4.07 | ( N2 = zero_zero_nat ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % odd_bit_iff_bit_pred
% 3.82/4.07 thf(fact_5679_odd__bit__iff__bit__pred,axiom,
% 3.82/4.07 ! [A: nat,N2: nat] :
% 3.82/4.07 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 3.82/4.07 => ( ( bit_se1148574629649215175it_nat @ A @ N2 )
% 3.82/4.07 = ( ( bit_se1148574629649215175it_nat @ ( minus_minus_nat @ A @ one_one_nat ) @ N2 )
% 3.82/4.07 | ( N2 = zero_zero_nat ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % odd_bit_iff_bit_pred
% 3.82/4.07 thf(fact_5680_ceiling__divide__lower,axiom,
% 3.82/4.07 ! [Q3: real,P5: real] :
% 3.82/4.07 ( ( ord_less_real @ zero_zero_real @ Q3 )
% 3.82/4.07 => ( ord_less_real @ ( times_times_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ ( divide_divide_real @ P5 @ Q3 ) ) ) @ one_one_real ) @ Q3 ) @ P5 ) ) ).
% 3.82/4.07
% 3.82/4.07 % ceiling_divide_lower
% 3.82/4.07 thf(fact_5681_ceiling__eq,axiom,
% 3.82/4.07 ! [N2: int,X: real] :
% 3.82/4.07 ( ( ord_less_real @ ( ring_1_of_int_real @ N2 ) @ X )
% 3.82/4.07 => ( ( ord_less_eq_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ N2 ) @ one_one_real ) )
% 3.82/4.07 => ( ( archim7802044766580827645g_real @ X )
% 3.82/4.07 = ( plus_plus_int @ N2 @ one_one_int ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % ceiling_eq
% 3.82/4.07 thf(fact_5682_mask__eq__sum__exp,axiom,
% 3.82/4.07 ! [N2: nat] :
% 3.82/4.07 ( ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int )
% 3.82/4.07 = ( groups3539618377306564664at_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 3.82/4.07 @ ( collect_nat
% 3.82/4.07 @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N2 ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % mask_eq_sum_exp
% 3.82/4.07 thf(fact_5683_mask__eq__sum__exp,axiom,
% 3.82/4.07 ! [N2: nat] :
% 3.82/4.07 ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat )
% 3.82/4.07 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.07 @ ( collect_nat
% 3.82/4.07 @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N2 ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % mask_eq_sum_exp
% 3.82/4.07 thf(fact_5684_sum__gp__multiplied,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat,X: int] :
% 3.82/4.07 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.07 => ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) )
% 3.82/4.07 = ( minus_minus_int @ ( power_power_int @ X @ M2 ) @ ( power_power_int @ X @ ( suc @ N2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_gp_multiplied
% 3.82/4.07 thf(fact_5685_sum__gp__multiplied,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat,X: complex] :
% 3.82/4.07 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.07 => ( ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) )
% 3.82/4.07 = ( minus_minus_complex @ ( power_power_complex @ X @ M2 ) @ ( power_power_complex @ X @ ( suc @ N2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_gp_multiplied
% 3.82/4.07 thf(fact_5686_sum__gp__multiplied,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat,X: real] :
% 3.82/4.07 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.07 => ( ( times_times_real @ ( minus_minus_real @ one_one_real @ X ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) )
% 3.82/4.07 = ( minus_minus_real @ ( power_power_real @ X @ M2 ) @ ( power_power_real @ X @ ( suc @ N2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_gp_multiplied
% 3.82/4.07 thf(fact_5687_sum_Oin__pairs,axiom,
% 3.82/4.07 ! [G: nat > int,M2: nat,N2: nat] :
% 3.82/4.07 ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 3.82/4.07 = ( groups3539618377306564664at_int
% 3.82/4.07 @ ^ [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 ) ) ) )
% 3.82/4.07 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.in_pairs
% 3.82/4.07 thf(fact_5688_sum_Oin__pairs,axiom,
% 3.82/4.07 ! [G: nat > extended_enat,M2: nat,N2: nat] :
% 3.82/4.07 ( ( groups7108830773950497114d_enat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 3.82/4.07 = ( groups7108830773950497114d_enat
% 3.82/4.07 @ ^ [I3: nat] : ( plus_p3455044024723400733d_enat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 3.82/4.07 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.in_pairs
% 3.82/4.07 thf(fact_5689_sum_Oin__pairs,axiom,
% 3.82/4.07 ! [G: nat > nat,M2: nat,N2: nat] :
% 3.82/4.07 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 3.82/4.07 = ( groups3542108847815614940at_nat
% 3.82/4.07 @ ^ [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 ) ) ) )
% 3.82/4.07 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.in_pairs
% 3.82/4.07 thf(fact_5690_sum_Oin__pairs,axiom,
% 3.82/4.07 ! [G: nat > real,M2: nat,N2: nat] :
% 3.82/4.07 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 3.82/4.07 = ( groups6591440286371151544t_real
% 3.82/4.07 @ ^ [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 ) ) ) )
% 3.82/4.07 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum.in_pairs
% 3.82/4.07 thf(fact_5691_and__int_Opinduct,axiom,
% 3.82/4.07 ! [A0: int,A1: int,P: int > int > $o] :
% 3.82/4.07 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ A0 @ A1 ) )
% 3.82/4.07 => ( ! [K3: int,L4: int] :
% 3.82/4.07 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K3 @ L4 ) )
% 3.82/4.07 => ( ( ~ ( ( member_int @ K3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 3.82/4.07 & ( member_int @ L4 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 3.82/4.07 => ( P @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 3.82/4.07 => ( P @ K3 @ L4 ) ) )
% 3.82/4.07 => ( P @ A0 @ A1 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % and_int.pinduct
% 3.82/4.07 thf(fact_5692_bit__sum__mult__2__cases,axiom,
% 3.82/4.07 ! [A: int,B2: int,N2: nat] :
% 3.82/4.07 ( ! [J3: nat] :
% 3.82/4.07 ~ ( bit_se1146084159140164899it_int @ A @ ( suc @ J3 ) )
% 3.82/4.07 => ( ( bit_se1146084159140164899it_int @ ( plus_plus_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) ) @ N2 )
% 3.82/4.07 = ( ( ( N2 = zero_zero_nat )
% 3.82/4.07 => ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 3.82/4.07 & ( ( N2 != zero_zero_nat )
% 3.82/4.07 => ( bit_se1146084159140164899it_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) @ N2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % bit_sum_mult_2_cases
% 3.82/4.07 thf(fact_5693_bit__sum__mult__2__cases,axiom,
% 3.82/4.07 ! [A: nat,B2: nat,N2: nat] :
% 3.82/4.07 ( ! [J3: nat] :
% 3.82/4.07 ~ ( bit_se1148574629649215175it_nat @ A @ ( suc @ J3 ) )
% 3.82/4.07 => ( ( bit_se1148574629649215175it_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) ) @ N2 )
% 3.82/4.07 = ( ( ( N2 = zero_zero_nat )
% 3.82/4.07 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 3.82/4.07 & ( ( N2 != zero_zero_nat )
% 3.82/4.07 => ( bit_se1148574629649215175it_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) @ N2 ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % bit_sum_mult_2_cases
% 3.82/4.07 thf(fact_5694_bit__rec,axiom,
% 3.82/4.07 ( bit_se1146084159140164899it_int
% 3.82/4.07 = ( ^ [A3: int,N: nat] :
% 3.82/4.07 ( ( ( N = zero_zero_nat )
% 3.82/4.07 => ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A3 ) )
% 3.82/4.07 & ( ( N != zero_zero_nat )
% 3.82/4.07 => ( bit_se1146084159140164899it_int @ ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % bit_rec
% 3.82/4.07 thf(fact_5695_bit__rec,axiom,
% 3.82/4.07 ( bit_se1148574629649215175it_nat
% 3.82/4.07 = ( ^ [A3: nat,N: nat] :
% 3.82/4.07 ( ( ( N = zero_zero_nat )
% 3.82/4.07 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A3 ) )
% 3.82/4.07 & ( ( N != zero_zero_nat )
% 3.82/4.07 => ( bit_se1148574629649215175it_nat @ ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % bit_rec
% 3.82/4.07 thf(fact_5696_and__nat__unfold,axiom,
% 3.82/4.07 ( bit_se727722235901077358nd_nat
% 3.82/4.07 = ( ^ [M: nat,N: nat] :
% 3.82/4.07 ( if_nat
% 3.82/4.07 @ ( ( M = zero_zero_nat )
% 3.82/4.07 | ( N = zero_zero_nat ) )
% 3.82/4.07 @ zero_zero_nat
% 3.82/4.07 @ ( plus_plus_nat @ ( times_times_nat @ ( modulo_modulo_nat @ M @ ( 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 @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % and_nat_unfold
% 3.82/4.07 thf(fact_5697_and__nat__rec,axiom,
% 3.82/4.07 ( bit_se727722235901077358nd_nat
% 3.82/4.07 = ( ^ [M: nat,N: nat] :
% 3.82/4.07 ( plus_plus_nat
% 3.82/4.07 @ ( zero_n2687167440665602831ol_nat
% 3.82/4.07 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 3.82/4.07 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 3.82/4.07 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % and_nat_rec
% 3.82/4.07 thf(fact_5698_mask__eq__sum__exp__nat,axiom,
% 3.82/4.07 ! [N2: nat] :
% 3.82/4.07 ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ ( suc @ zero_zero_nat ) )
% 3.82/4.07 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 3.82/4.07 @ ( collect_nat
% 3.82/4.07 @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N2 ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % mask_eq_sum_exp_nat
% 3.82/4.07 thf(fact_5699_gauss__sum__nat,axiom,
% 3.82/4.07 ! [N2: nat] :
% 3.82/4.07 ( ( groups3542108847815614940at_nat
% 3.82/4.07 @ ^ [X4: nat] : X4
% 3.82/4.07 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 3.82/4.07 = ( divide_divide_nat @ ( times_times_nat @ N2 @ ( suc @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % gauss_sum_nat
% 3.82/4.07 thf(fact_5700_take__bit__Suc__from__most,axiom,
% 3.82/4.07 ! [N2: nat,K: int] :
% 3.82/4.07 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ K )
% 3.82/4.07 = ( 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 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % take_bit_Suc_from_most
% 3.82/4.07 thf(fact_5701_upto_Opinduct,axiom,
% 3.82/4.07 ! [A0: int,A1: int,P: int > int > $o] :
% 3.82/4.07 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ A0 @ A1 ) )
% 3.82/4.07 => ( ! [I4: int,J3: int] :
% 3.82/4.07 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I4 @ J3 ) )
% 3.82/4.07 => ( ( ( ord_less_eq_int @ I4 @ J3 )
% 3.82/4.07 => ( P @ ( plus_plus_int @ I4 @ one_one_int ) @ J3 ) )
% 3.82/4.07 => ( P @ I4 @ J3 ) ) )
% 3.82/4.07 => ( P @ A0 @ A1 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % upto.pinduct
% 3.82/4.07 thf(fact_5702_sum__gp,axiom,
% 3.82/4.07 ! [N2: nat,M2: nat,X: complex] :
% 3.82/4.07 ( ( ( ord_less_nat @ N2 @ M2 )
% 3.82/4.07 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 3.82/4.07 = zero_zero_complex ) )
% 3.82/4.07 & ( ~ ( ord_less_nat @ N2 @ M2 )
% 3.82/4.07 => ( ( ( X = one_one_complex )
% 3.82/4.07 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 3.82/4.07 = ( semiri8010041392384452111omplex @ ( minus_minus_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ M2 ) ) ) )
% 3.82/4.07 & ( ( X != one_one_complex )
% 3.82/4.07 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 3.82/4.07 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X @ M2 ) @ ( power_power_complex @ X @ ( suc @ N2 ) ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_gp
% 3.82/4.07 thf(fact_5703_sum__gp,axiom,
% 3.82/4.07 ! [N2: nat,M2: nat,X: real] :
% 3.82/4.07 ( ( ( ord_less_nat @ N2 @ M2 )
% 3.82/4.07 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 3.82/4.07 = zero_zero_real ) )
% 3.82/4.07 & ( ~ ( ord_less_nat @ N2 @ M2 )
% 3.82/4.07 => ( ( ( X = one_one_real )
% 3.82/4.07 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 3.82/4.07 = ( semiri5074537144036343181t_real @ ( minus_minus_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ M2 ) ) ) )
% 3.82/4.07 & ( ( X != one_one_real )
% 3.82/4.07 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 3.82/4.07 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X @ M2 ) @ ( power_power_real @ X @ ( suc @ N2 ) ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_gp
% 3.82/4.07 thf(fact_5704_gauss__sum__from__Suc__0,axiom,
% 3.82/4.07 ! [N2: nat] :
% 3.82/4.07 ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 3.82/4.07 = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % gauss_sum_from_Suc_0
% 3.82/4.07 thf(fact_5705_gauss__sum__from__Suc__0,axiom,
% 3.82/4.07 ! [N2: nat] :
% 3.82/4.07 ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 3.82/4.07 = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % gauss_sum_from_Suc_0
% 3.82/4.07 thf(fact_5706_sum__gp__offset,axiom,
% 3.82/4.07 ! [X: complex,M2: nat,N2: nat] :
% 3.82/4.07 ( ( ( X = one_one_complex )
% 3.82/4.07 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ M2 @ N2 ) ) )
% 3.82/4.07 = ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N2 ) @ one_one_complex ) ) )
% 3.82/4.07 & ( ( X != one_one_complex )
% 3.82/4.07 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ M2 @ N2 ) ) )
% 3.82/4.07 = ( divide1717551699836669952omplex @ ( times_times_complex @ ( power_power_complex @ X @ M2 ) @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ ( suc @ N2 ) ) ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_gp_offset
% 3.82/4.07 thf(fact_5707_sum__gp__offset,axiom,
% 3.82/4.07 ! [X: real,M2: nat,N2: nat] :
% 3.82/4.07 ( ( ( X = one_one_real )
% 3.82/4.07 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ M2 @ N2 ) ) )
% 3.82/4.07 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) ) )
% 3.82/4.07 & ( ( X != one_one_real )
% 3.82/4.07 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ M2 @ N2 ) ) )
% 3.82/4.07 = ( divide_divide_real @ ( times_times_real @ ( power_power_real @ X @ M2 ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( suc @ N2 ) ) ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % sum_gp_offset
% 3.82/4.07 thf(fact_5708_double__gauss__sum__from__Suc__0,axiom,
% 3.82/4.07 ! [N2: nat] :
% 3.82/4.07 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 3.82/4.07 = ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N2 ) @ one_one_complex ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % double_gauss_sum_from_Suc_0
% 3.82/4.07 thf(fact_5709_double__gauss__sum__from__Suc__0,axiom,
% 3.82/4.07 ! [N2: nat] :
% 3.82/4.07 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ ( groups7108830773950497114d_enat @ semiri4216267220026989637d_enat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 3.82/4.07 = ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ N2 ) @ ( plus_p3455044024723400733d_enat @ ( semiri4216267220026989637d_enat @ N2 ) @ one_on7984719198319812577d_enat ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % double_gauss_sum_from_Suc_0
% 3.82/4.07 thf(fact_5710_double__gauss__sum__from__Suc__0,axiom,
% 3.82/4.07 ! [N2: nat] :
% 3.82/4.07 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 3.82/4.07 = ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % double_gauss_sum_from_Suc_0
% 3.82/4.07 thf(fact_5711_double__gauss__sum__from__Suc__0,axiom,
% 3.82/4.07 ! [N2: nat] :
% 3.82/4.07 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 3.82/4.07 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % double_gauss_sum_from_Suc_0
% 3.82/4.07 thf(fact_5712_double__gauss__sum__from__Suc__0,axiom,
% 3.82/4.07 ! [N2: nat] :
% 3.82/4.07 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 3.82/4.07 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % double_gauss_sum_from_Suc_0
% 3.82/4.07 thf(fact_5713_arith__series,axiom,
% 3.82/4.07 ! [A: int,D: int,N2: nat] :
% 3.82/4.07 ( ( groups3539618377306564664at_int
% 3.82/4.07 @ ^ [I3: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I3 ) @ D ) )
% 3.82/4.07 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 3.82/4.07 = ( 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 ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % arith_series
% 3.82/4.07 thf(fact_5714_arith__series,axiom,
% 3.82/4.07 ! [A: nat,D: nat,N2: nat] :
% 3.82/4.07 ( ( groups3542108847815614940at_nat
% 3.82/4.07 @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I3 ) @ D ) )
% 3.82/4.07 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 3.82/4.07 = ( 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 ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % arith_series
% 3.82/4.07 thf(fact_5715_of__nat__eq__iff,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat] :
% 3.82/4.07 ( ( ( semiri5074537144036343181t_real @ M2 )
% 3.82/4.07 = ( semiri5074537144036343181t_real @ N2 ) )
% 3.82/4.07 = ( M2 = N2 ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_eq_iff
% 3.82/4.07 thf(fact_5716_of__nat__eq__iff,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat] :
% 3.82/4.07 ( ( ( semiri1314217659103216013at_int @ M2 )
% 3.82/4.07 = ( semiri1314217659103216013at_int @ N2 ) )
% 3.82/4.07 = ( M2 = N2 ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_eq_iff
% 3.82/4.07 thf(fact_5717_of__nat__eq__iff,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat] :
% 3.82/4.07 ( ( ( semiri1316708129612266289at_nat @ M2 )
% 3.82/4.07 = ( semiri1316708129612266289at_nat @ N2 ) )
% 3.82/4.07 = ( M2 = N2 ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_eq_iff
% 3.82/4.07 thf(fact_5718_numeral__le__real__of__nat__iff,axiom,
% 3.82/4.07 ! [N2: num,M2: nat] :
% 3.82/4.07 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N2 ) @ ( semiri5074537144036343181t_real @ M2 ) )
% 3.82/4.07 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ N2 ) @ M2 ) ) ).
% 3.82/4.07
% 3.82/4.07 % numeral_le_real_of_nat_iff
% 3.82/4.07 thf(fact_5719_int__eq__iff__numeral,axiom,
% 3.82/4.07 ! [M2: nat,V: num] :
% 3.82/4.07 ( ( ( semiri1314217659103216013at_int @ M2 )
% 3.82/4.07 = ( numeral_numeral_int @ V ) )
% 3.82/4.07 = ( M2
% 3.82/4.07 = ( numeral_numeral_nat @ V ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % int_eq_iff_numeral
% 3.82/4.07 thf(fact_5720_negative__eq__positive,axiom,
% 3.82/4.07 ! [N2: nat,M2: nat] :
% 3.82/4.07 ( ( ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) )
% 3.82/4.07 = ( semiri1314217659103216013at_int @ M2 ) )
% 3.82/4.07 = ( ( N2 = zero_zero_nat )
% 3.82/4.07 & ( M2 = zero_zero_nat ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % negative_eq_positive
% 3.82/4.07 thf(fact_5721_of__int__of__nat__eq,axiom,
% 3.82/4.07 ! [N2: nat] :
% 3.82/4.07 ( ( ring_1_of_int_real @ ( semiri1314217659103216013at_int @ N2 ) )
% 3.82/4.07 = ( semiri5074537144036343181t_real @ N2 ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_int_of_nat_eq
% 3.82/4.07 thf(fact_5722_of__int__of__nat__eq,axiom,
% 3.82/4.07 ! [N2: nat] :
% 3.82/4.07 ( ( ring_1_of_int_int @ ( semiri1314217659103216013at_int @ N2 ) )
% 3.82/4.07 = ( semiri1314217659103216013at_int @ N2 ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_int_of_nat_eq
% 3.82/4.07 thf(fact_5723_negative__zle,axiom,
% 3.82/4.07 ! [N2: nat,M2: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ ( semiri1314217659103216013at_int @ M2 ) ) ).
% 3.82/4.07
% 3.82/4.07 % negative_zle
% 3.82/4.07 thf(fact_5724_int__dvd__int__iff,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat] :
% 3.82/4.07 ( ( dvd_dvd_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 3.82/4.07 = ( dvd_dvd_nat @ M2 @ N2 ) ) ).
% 3.82/4.07
% 3.82/4.07 % int_dvd_int_iff
% 3.82/4.07 thf(fact_5725_of__nat__0,axiom,
% 3.82/4.07 ( ( semiri8010041392384452111omplex @ zero_zero_nat )
% 3.82/4.07 = zero_zero_complex ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_0
% 3.82/4.07 thf(fact_5726_of__nat__0,axiom,
% 3.82/4.07 ( ( semiri4216267220026989637d_enat @ zero_zero_nat )
% 3.82/4.07 = zero_z5237406670263579293d_enat ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_0
% 3.82/4.07 thf(fact_5727_of__nat__0,axiom,
% 3.82/4.07 ( ( semiri5074537144036343181t_real @ zero_zero_nat )
% 3.82/4.07 = zero_zero_real ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_0
% 3.82/4.07 thf(fact_5728_of__nat__0,axiom,
% 3.82/4.07 ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 3.82/4.07 = zero_zero_int ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_0
% 3.82/4.07 thf(fact_5729_of__nat__0,axiom,
% 3.82/4.07 ( ( semiri1316708129612266289at_nat @ zero_zero_nat )
% 3.82/4.07 = zero_zero_nat ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_0
% 3.82/4.07 thf(fact_5730_of__nat__0__eq__iff,axiom,
% 3.82/4.07 ! [N2: nat] :
% 3.82/4.07 ( ( zero_zero_complex
% 3.82/4.07 = ( semiri8010041392384452111omplex @ N2 ) )
% 3.82/4.07 = ( zero_zero_nat = N2 ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_0_eq_iff
% 3.82/4.07 thf(fact_5731_of__nat__0__eq__iff,axiom,
% 3.82/4.07 ! [N2: nat] :
% 3.82/4.07 ( ( zero_z5237406670263579293d_enat
% 3.82/4.07 = ( semiri4216267220026989637d_enat @ N2 ) )
% 3.82/4.07 = ( zero_zero_nat = N2 ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_0_eq_iff
% 3.82/4.07 thf(fact_5732_of__nat__0__eq__iff,axiom,
% 3.82/4.07 ! [N2: nat] :
% 3.82/4.07 ( ( zero_zero_real
% 3.82/4.07 = ( semiri5074537144036343181t_real @ N2 ) )
% 3.82/4.07 = ( zero_zero_nat = N2 ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_0_eq_iff
% 3.82/4.07 thf(fact_5733_of__nat__0__eq__iff,axiom,
% 3.82/4.07 ! [N2: nat] :
% 3.82/4.07 ( ( zero_zero_int
% 3.82/4.07 = ( semiri1314217659103216013at_int @ N2 ) )
% 3.82/4.07 = ( zero_zero_nat = N2 ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_0_eq_iff
% 3.82/4.07 thf(fact_5734_of__nat__0__eq__iff,axiom,
% 3.82/4.07 ! [N2: nat] :
% 3.82/4.07 ( ( zero_zero_nat
% 3.82/4.07 = ( semiri1316708129612266289at_nat @ N2 ) )
% 3.82/4.07 = ( zero_zero_nat = N2 ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_0_eq_iff
% 3.82/4.07 thf(fact_5735_of__nat__eq__0__iff,axiom,
% 3.82/4.07 ! [M2: nat] :
% 3.82/4.07 ( ( ( semiri8010041392384452111omplex @ M2 )
% 3.82/4.07 = zero_zero_complex )
% 3.82/4.07 = ( M2 = zero_zero_nat ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_eq_0_iff
% 3.82/4.07 thf(fact_5736_of__nat__eq__0__iff,axiom,
% 3.82/4.07 ! [M2: nat] :
% 3.82/4.07 ( ( ( semiri4216267220026989637d_enat @ M2 )
% 3.82/4.07 = zero_z5237406670263579293d_enat )
% 3.82/4.07 = ( M2 = zero_zero_nat ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_eq_0_iff
% 3.82/4.07 thf(fact_5737_of__nat__eq__0__iff,axiom,
% 3.82/4.07 ! [M2: nat] :
% 3.82/4.07 ( ( ( semiri5074537144036343181t_real @ M2 )
% 3.82/4.07 = zero_zero_real )
% 3.82/4.07 = ( M2 = zero_zero_nat ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_eq_0_iff
% 3.82/4.07 thf(fact_5738_of__nat__eq__0__iff,axiom,
% 3.82/4.07 ! [M2: nat] :
% 3.82/4.07 ( ( ( semiri1314217659103216013at_int @ M2 )
% 3.82/4.07 = zero_zero_int )
% 3.82/4.07 = ( M2 = zero_zero_nat ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_eq_0_iff
% 3.82/4.07 thf(fact_5739_of__nat__eq__0__iff,axiom,
% 3.82/4.07 ! [M2: nat] :
% 3.82/4.07 ( ( ( semiri1316708129612266289at_nat @ M2 )
% 3.82/4.07 = zero_zero_nat )
% 3.82/4.07 = ( M2 = zero_zero_nat ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_eq_0_iff
% 3.82/4.07 thf(fact_5740_of__nat__less__iff,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat] :
% 3.82/4.07 ( ( ord_le72135733267957522d_enat @ ( semiri4216267220026989637d_enat @ M2 ) @ ( semiri4216267220026989637d_enat @ N2 ) )
% 3.82/4.07 = ( ord_less_nat @ M2 @ N2 ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_less_iff
% 3.82/4.07 thf(fact_5741_of__nat__less__iff,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat] :
% 3.82/4.07 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( semiri5074537144036343181t_real @ N2 ) )
% 3.82/4.07 = ( ord_less_nat @ M2 @ N2 ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_less_iff
% 3.82/4.07 thf(fact_5742_of__nat__less__iff,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat] :
% 3.82/4.07 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 3.82/4.07 = ( ord_less_nat @ M2 @ N2 ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_less_iff
% 3.82/4.07 thf(fact_5743_of__nat__less__iff,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat] :
% 3.82/4.07 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N2 ) )
% 3.82/4.07 = ( ord_less_nat @ M2 @ N2 ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_less_iff
% 3.82/4.07 thf(fact_5744_of__nat__le__iff,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat] :
% 3.82/4.07 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( semiri5074537144036343181t_real @ N2 ) )
% 3.82/4.07 = ( ord_less_eq_nat @ M2 @ N2 ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_le_iff
% 3.82/4.07 thf(fact_5745_of__nat__le__iff,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat] :
% 3.82/4.07 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N2 ) )
% 3.82/4.07 = ( ord_less_eq_nat @ M2 @ N2 ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_le_iff
% 3.82/4.07 thf(fact_5746_of__nat__le__iff,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat] :
% 3.82/4.07 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 3.82/4.07 = ( ord_less_eq_nat @ M2 @ N2 ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_le_iff
% 3.82/4.07 thf(fact_5747_numeral__less__real__of__nat__iff,axiom,
% 3.82/4.07 ! [W2: num,N2: nat] :
% 3.82/4.07 ( ( ord_less_real @ ( numeral_numeral_real @ W2 ) @ ( semiri5074537144036343181t_real @ N2 ) )
% 3.82/4.07 = ( ord_less_nat @ ( numeral_numeral_nat @ W2 ) @ N2 ) ) ).
% 3.82/4.07
% 3.82/4.07 % numeral_less_real_of_nat_iff
% 3.82/4.07 thf(fact_5748_real__of__nat__less__numeral__iff,axiom,
% 3.82/4.07 ! [N2: nat,W2: num] :
% 3.82/4.07 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( numeral_numeral_real @ W2 ) )
% 3.82/4.07 = ( ord_less_nat @ N2 @ ( numeral_numeral_nat @ W2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % real_of_nat_less_numeral_iff
% 3.82/4.07 thf(fact_5749_of__nat__add,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat] :
% 3.82/4.07 ( ( semiri4216267220026989637d_enat @ ( plus_plus_nat @ M2 @ N2 ) )
% 3.82/4.07 = ( plus_p3455044024723400733d_enat @ ( semiri4216267220026989637d_enat @ M2 ) @ ( semiri4216267220026989637d_enat @ N2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_add
% 3.82/4.07 thf(fact_5750_of__nat__add,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat] :
% 3.82/4.07 ( ( semiri5074537144036343181t_real @ ( plus_plus_nat @ M2 @ N2 ) )
% 3.82/4.07 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_add
% 3.82/4.07 thf(fact_5751_of__nat__add,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat] :
% 3.82/4.07 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M2 @ N2 ) )
% 3.82/4.07 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_add
% 3.82/4.07 thf(fact_5752_of__nat__add,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat] :
% 3.82/4.07 ( ( semiri1316708129612266289at_nat @ ( plus_plus_nat @ M2 @ N2 ) )
% 3.82/4.07 = ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_add
% 3.82/4.07 thf(fact_5753_of__nat__mult,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat] :
% 3.82/4.07 ( ( semiri8010041392384452111omplex @ ( times_times_nat @ M2 @ N2 ) )
% 3.82/4.07 = ( times_times_complex @ ( semiri8010041392384452111omplex @ M2 ) @ ( semiri8010041392384452111omplex @ N2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_mult
% 3.82/4.07 thf(fact_5754_of__nat__mult,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat] :
% 3.82/4.07 ( ( semiri4216267220026989637d_enat @ ( times_times_nat @ M2 @ N2 ) )
% 3.82/4.07 = ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ M2 ) @ ( semiri4216267220026989637d_enat @ N2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_mult
% 3.82/4.07 thf(fact_5755_of__nat__mult,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat] :
% 3.82/4.07 ( ( semiri5074537144036343181t_real @ ( times_times_nat @ M2 @ N2 ) )
% 3.82/4.07 = ( times_times_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_mult
% 3.82/4.07 thf(fact_5756_of__nat__mult,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat] :
% 3.82/4.07 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ M2 @ N2 ) )
% 3.82/4.07 = ( times_times_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_mult
% 3.82/4.07 thf(fact_5757_of__nat__mult,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat] :
% 3.82/4.07 ( ( semiri1316708129612266289at_nat @ ( times_times_nat @ M2 @ N2 ) )
% 3.82/4.07 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_mult
% 3.82/4.07 thf(fact_5758_of__nat__eq__1__iff,axiom,
% 3.82/4.07 ! [N2: nat] :
% 3.82/4.07 ( ( ( semiri8010041392384452111omplex @ N2 )
% 3.82/4.07 = one_one_complex )
% 3.82/4.07 = ( N2 = one_one_nat ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_eq_1_iff
% 3.82/4.07 thf(fact_5759_of__nat__eq__1__iff,axiom,
% 3.82/4.07 ! [N2: nat] :
% 3.82/4.07 ( ( ( semiri5074537144036343181t_real @ N2 )
% 3.82/4.07 = one_one_real )
% 3.82/4.07 = ( N2 = one_one_nat ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_eq_1_iff
% 3.82/4.07 thf(fact_5760_of__nat__eq__1__iff,axiom,
% 3.82/4.07 ! [N2: nat] :
% 3.82/4.07 ( ( ( semiri1314217659103216013at_int @ N2 )
% 3.82/4.07 = one_one_int )
% 3.82/4.07 = ( N2 = one_one_nat ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_eq_1_iff
% 3.82/4.07 thf(fact_5761_of__nat__eq__1__iff,axiom,
% 3.82/4.07 ! [N2: nat] :
% 3.82/4.07 ( ( ( semiri1316708129612266289at_nat @ N2 )
% 3.82/4.07 = one_one_nat )
% 3.82/4.07 = ( N2 = one_one_nat ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_eq_1_iff
% 3.82/4.07 thf(fact_5762_of__nat__1__eq__iff,axiom,
% 3.82/4.07 ! [N2: nat] :
% 3.82/4.07 ( ( one_one_complex
% 3.82/4.07 = ( semiri8010041392384452111omplex @ N2 ) )
% 3.82/4.07 = ( N2 = one_one_nat ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_1_eq_iff
% 3.82/4.07 thf(fact_5763_of__nat__1__eq__iff,axiom,
% 3.82/4.07 ! [N2: nat] :
% 3.82/4.07 ( ( one_one_real
% 3.82/4.07 = ( semiri5074537144036343181t_real @ N2 ) )
% 3.82/4.07 = ( N2 = one_one_nat ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_1_eq_iff
% 3.82/4.07 thf(fact_5764_of__nat__1__eq__iff,axiom,
% 3.82/4.07 ! [N2: nat] :
% 3.82/4.07 ( ( one_one_int
% 3.82/4.07 = ( semiri1314217659103216013at_int @ N2 ) )
% 3.82/4.07 = ( N2 = one_one_nat ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_1_eq_iff
% 3.82/4.07 thf(fact_5765_of__nat__1__eq__iff,axiom,
% 3.82/4.07 ! [N2: nat] :
% 3.82/4.07 ( ( one_one_nat
% 3.82/4.07 = ( semiri1316708129612266289at_nat @ N2 ) )
% 3.82/4.07 = ( N2 = one_one_nat ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_1_eq_iff
% 3.82/4.07 thf(fact_5766_of__nat__1,axiom,
% 3.82/4.07 ( ( semiri8010041392384452111omplex @ one_one_nat )
% 3.82/4.07 = one_one_complex ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_1
% 3.82/4.07 thf(fact_5767_of__nat__1,axiom,
% 3.82/4.07 ( ( semiri5074537144036343181t_real @ one_one_nat )
% 3.82/4.07 = one_one_real ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_1
% 3.82/4.07 thf(fact_5768_of__nat__1,axiom,
% 3.82/4.07 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 3.82/4.07 = one_one_int ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_1
% 3.82/4.07 thf(fact_5769_of__nat__1,axiom,
% 3.82/4.07 ( ( semiri1316708129612266289at_nat @ one_one_nat )
% 3.82/4.07 = one_one_nat ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_1
% 3.82/4.07 thf(fact_5770_negative__zless,axiom,
% 3.82/4.07 ! [N2: nat,M2: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) @ ( semiri1314217659103216013at_int @ M2 ) ) ).
% 3.82/4.07
% 3.82/4.07 % negative_zless
% 3.82/4.07 thf(fact_5771_of__nat__of__bool,axiom,
% 3.82/4.07 ! [P: $o] :
% 3.82/4.07 ( ( semiri5074537144036343181t_real @ ( zero_n2687167440665602831ol_nat @ P ) )
% 3.82/4.07 = ( zero_n3304061248610475627l_real @ P ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_of_bool
% 3.82/4.07 thf(fact_5772_of__nat__of__bool,axiom,
% 3.82/4.07 ! [P: $o] :
% 3.82/4.07 ( ( semiri1316708129612266289at_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 3.82/4.07 = ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_of_bool
% 3.82/4.07 thf(fact_5773_of__nat__of__bool,axiom,
% 3.82/4.07 ! [P: $o] :
% 3.82/4.07 ( ( semiri1314217659103216013at_int @ ( zero_n2687167440665602831ol_nat @ P ) )
% 3.82/4.07 = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_of_bool
% 3.82/4.07 thf(fact_5774_of__nat__sum,axiom,
% 3.82/4.07 ! [F: int > nat,A2: set_int] :
% 3.82/4.07 ( ( semiri1314217659103216013at_int @ ( groups4541462559716669496nt_nat @ F @ A2 ) )
% 3.82/4.07 = ( groups4538972089207619220nt_int
% 3.82/4.07 @ ^ [X4: int] : ( semiri1314217659103216013at_int @ ( F @ X4 ) )
% 3.82/4.07 @ A2 ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_sum
% 3.82/4.07 thf(fact_5775_of__nat__sum,axiom,
% 3.82/4.07 ! [F: complex > nat,A2: set_complex] :
% 3.82/4.07 ( ( semiri8010041392384452111omplex @ ( groups5693394587270226106ex_nat @ F @ A2 ) )
% 3.82/4.07 = ( groups7754918857620584856omplex
% 3.82/4.07 @ ^ [X4: complex] : ( semiri8010041392384452111omplex @ ( F @ X4 ) )
% 3.82/4.07 @ A2 ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_sum
% 3.82/4.07 thf(fact_5776_of__nat__sum,axiom,
% 3.82/4.07 ! [F: nat > nat,A2: set_nat] :
% 3.82/4.07 ( ( semiri1314217659103216013at_int @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 3.82/4.07 = ( groups3539618377306564664at_int
% 3.82/4.07 @ ^ [X4: nat] : ( semiri1314217659103216013at_int @ ( F @ X4 ) )
% 3.82/4.07 @ A2 ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_sum
% 3.82/4.07 thf(fact_5777_of__nat__sum,axiom,
% 3.82/4.07 ! [F: nat > nat,A2: set_nat] :
% 3.82/4.07 ( ( semiri1316708129612266289at_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 3.82/4.07 = ( groups3542108847815614940at_nat
% 3.82/4.07 @ ^ [X4: nat] : ( semiri1316708129612266289at_nat @ ( F @ X4 ) )
% 3.82/4.07 @ A2 ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_sum
% 3.82/4.07 thf(fact_5778_of__nat__sum,axiom,
% 3.82/4.07 ! [F: nat > nat,A2: set_nat] :
% 3.82/4.07 ( ( semiri5074537144036343181t_real @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 3.82/4.07 = ( groups6591440286371151544t_real
% 3.82/4.07 @ ^ [X4: nat] : ( semiri5074537144036343181t_real @ ( F @ X4 ) )
% 3.82/4.07 @ A2 ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_sum
% 3.82/4.07 thf(fact_5779_of__nat__le__0__iff,axiom,
% 3.82/4.07 ! [M2: nat] :
% 3.82/4.07 ( ( ord_le2932123472753598470d_enat @ ( semiri4216267220026989637d_enat @ M2 ) @ zero_z5237406670263579293d_enat )
% 3.82/4.07 = ( M2 = zero_zero_nat ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_le_0_iff
% 3.82/4.07 thf(fact_5780_of__nat__le__0__iff,axiom,
% 3.82/4.07 ! [M2: nat] :
% 3.82/4.07 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M2 ) @ zero_zero_real )
% 3.82/4.07 = ( M2 = zero_zero_nat ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_le_0_iff
% 3.82/4.07 thf(fact_5781_of__nat__le__0__iff,axiom,
% 3.82/4.07 ! [M2: nat] :
% 3.82/4.07 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ zero_zero_nat )
% 3.82/4.07 = ( M2 = zero_zero_nat ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_le_0_iff
% 3.82/4.07 thf(fact_5782_of__nat__le__0__iff,axiom,
% 3.82/4.07 ! [M2: nat] :
% 3.82/4.07 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M2 ) @ zero_zero_int )
% 3.82/4.07 = ( M2 = zero_zero_nat ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_le_0_iff
% 3.82/4.07 thf(fact_5783_of__nat__Suc,axiom,
% 3.82/4.07 ! [M2: nat] :
% 3.82/4.07 ( ( semiri8010041392384452111omplex @ ( suc @ M2 ) )
% 3.82/4.07 = ( plus_plus_complex @ one_one_complex @ ( semiri8010041392384452111omplex @ M2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_Suc
% 3.82/4.07 thf(fact_5784_of__nat__Suc,axiom,
% 3.82/4.07 ! [M2: nat] :
% 3.82/4.07 ( ( semiri4216267220026989637d_enat @ ( suc @ M2 ) )
% 3.82/4.07 = ( plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ ( semiri4216267220026989637d_enat @ M2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_Suc
% 3.82/4.07 thf(fact_5785_of__nat__Suc,axiom,
% 3.82/4.07 ! [M2: nat] :
% 3.82/4.07 ( ( semiri5074537144036343181t_real @ ( suc @ M2 ) )
% 3.82/4.07 = ( plus_plus_real @ one_one_real @ ( semiri5074537144036343181t_real @ M2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_Suc
% 3.82/4.07 thf(fact_5786_of__nat__Suc,axiom,
% 3.82/4.07 ! [M2: nat] :
% 3.82/4.07 ( ( semiri1314217659103216013at_int @ ( suc @ M2 ) )
% 3.82/4.07 = ( plus_plus_int @ one_one_int @ ( semiri1314217659103216013at_int @ M2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_Suc
% 3.82/4.07 thf(fact_5787_of__nat__Suc,axiom,
% 3.82/4.07 ! [M2: nat] :
% 3.82/4.07 ( ( semiri1316708129612266289at_nat @ ( suc @ M2 ) )
% 3.82/4.07 = ( plus_plus_nat @ one_one_nat @ ( semiri1316708129612266289at_nat @ M2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_Suc
% 3.82/4.07 thf(fact_5788_of__nat__0__less__iff,axiom,
% 3.82/4.07 ! [N2: nat] :
% 3.82/4.07 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( semiri4216267220026989637d_enat @ N2 ) )
% 3.82/4.07 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_0_less_iff
% 3.82/4.07 thf(fact_5789_of__nat__0__less__iff,axiom,
% 3.82/4.07 ! [N2: nat] :
% 3.82/4.07 ( ( ord_less_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N2 ) )
% 3.82/4.07 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_0_less_iff
% 3.82/4.07 thf(fact_5790_of__nat__0__less__iff,axiom,
% 3.82/4.07 ! [N2: nat] :
% 3.82/4.07 ( ( ord_less_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N2 ) )
% 3.82/4.07 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_0_less_iff
% 3.82/4.07 thf(fact_5791_of__nat__0__less__iff,axiom,
% 3.82/4.07 ! [N2: nat] :
% 3.82/4.07 ( ( ord_less_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N2 ) )
% 3.82/4.07 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_0_less_iff
% 3.82/4.07 thf(fact_5792_of__nat__less__of__nat__power__cancel__iff,axiom,
% 3.82/4.07 ! [B2: nat,W2: nat,X: nat] :
% 3.82/4.07 ( ( ord_less_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B2 ) @ W2 ) @ ( semiri5074537144036343181t_real @ X ) )
% 3.82/4.07 = ( ord_less_nat @ ( power_power_nat @ B2 @ W2 ) @ X ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_less_of_nat_power_cancel_iff
% 3.82/4.07 thf(fact_5793_of__nat__less__of__nat__power__cancel__iff,axiom,
% 3.82/4.07 ! [B2: nat,W2: nat,X: nat] :
% 3.82/4.07 ( ( ord_less_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B2 ) @ W2 ) @ ( semiri1314217659103216013at_int @ X ) )
% 3.82/4.07 = ( ord_less_nat @ ( power_power_nat @ B2 @ W2 ) @ X ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_less_of_nat_power_cancel_iff
% 3.82/4.07 thf(fact_5794_of__nat__less__of__nat__power__cancel__iff,axiom,
% 3.82/4.07 ! [B2: nat,W2: nat,X: nat] :
% 3.82/4.07 ( ( ord_less_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B2 ) @ W2 ) @ ( semiri1316708129612266289at_nat @ X ) )
% 3.82/4.07 = ( ord_less_nat @ ( power_power_nat @ B2 @ W2 ) @ X ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_less_of_nat_power_cancel_iff
% 3.82/4.07 thf(fact_5795_of__nat__power__less__of__nat__cancel__iff,axiom,
% 3.82/4.07 ! [X: nat,B2: nat,W2: nat] :
% 3.82/4.07 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B2 ) @ W2 ) )
% 3.82/4.07 = ( ord_less_nat @ X @ ( power_power_nat @ B2 @ W2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_power_less_of_nat_cancel_iff
% 3.82/4.07 thf(fact_5796_of__nat__power__less__of__nat__cancel__iff,axiom,
% 3.82/4.07 ! [X: nat,B2: nat,W2: nat] :
% 3.82/4.07 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B2 ) @ W2 ) )
% 3.82/4.07 = ( ord_less_nat @ X @ ( power_power_nat @ B2 @ W2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_power_less_of_nat_cancel_iff
% 3.82/4.07 thf(fact_5797_of__nat__power__less__of__nat__cancel__iff,axiom,
% 3.82/4.07 ! [X: nat,B2: nat,W2: nat] :
% 3.82/4.07 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B2 ) @ W2 ) )
% 3.82/4.07 = ( ord_less_nat @ X @ ( power_power_nat @ B2 @ W2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_power_less_of_nat_cancel_iff
% 3.82/4.07 thf(fact_5798_of__nat__power__le__of__nat__cancel__iff,axiom,
% 3.82/4.07 ! [X: nat,B2: nat,W2: nat] :
% 3.82/4.07 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B2 ) @ W2 ) )
% 3.82/4.07 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B2 @ W2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_power_le_of_nat_cancel_iff
% 3.82/4.07 thf(fact_5799_of__nat__power__le__of__nat__cancel__iff,axiom,
% 3.82/4.07 ! [X: nat,B2: nat,W2: nat] :
% 3.82/4.07 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B2 ) @ W2 ) )
% 3.82/4.07 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B2 @ W2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_power_le_of_nat_cancel_iff
% 3.82/4.07 thf(fact_5800_of__nat__power__le__of__nat__cancel__iff,axiom,
% 3.82/4.07 ! [X: nat,B2: nat,W2: nat] :
% 3.82/4.07 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B2 ) @ W2 ) )
% 3.82/4.07 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B2 @ W2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_power_le_of_nat_cancel_iff
% 3.82/4.07 thf(fact_5801_of__nat__le__of__nat__power__cancel__iff,axiom,
% 3.82/4.07 ! [B2: nat,W2: nat,X: nat] :
% 3.82/4.07 ( ( ord_less_eq_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B2 ) @ W2 ) @ ( semiri5074537144036343181t_real @ X ) )
% 3.82/4.07 = ( ord_less_eq_nat @ ( power_power_nat @ B2 @ W2 ) @ X ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_le_of_nat_power_cancel_iff
% 3.82/4.07 thf(fact_5802_of__nat__le__of__nat__power__cancel__iff,axiom,
% 3.82/4.07 ! [B2: nat,W2: nat,X: nat] :
% 3.82/4.07 ( ( ord_less_eq_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B2 ) @ W2 ) @ ( semiri1316708129612266289at_nat @ X ) )
% 3.82/4.07 = ( ord_less_eq_nat @ ( power_power_nat @ B2 @ W2 ) @ X ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_le_of_nat_power_cancel_iff
% 3.82/4.07 thf(fact_5803_of__nat__le__of__nat__power__cancel__iff,axiom,
% 3.82/4.07 ! [B2: nat,W2: nat,X: nat] :
% 3.82/4.07 ( ( ord_less_eq_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B2 ) @ W2 ) @ ( semiri1314217659103216013at_int @ X ) )
% 3.82/4.07 = ( ord_less_eq_nat @ ( power_power_nat @ B2 @ W2 ) @ X ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_le_of_nat_power_cancel_iff
% 3.82/4.07 thf(fact_5804_of__nat__zero__less__power__iff,axiom,
% 3.82/4.07 ! [X: nat,N2: nat] :
% 3.82/4.07 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ X ) @ N2 ) )
% 3.82/4.07 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 3.82/4.07 | ( N2 = zero_zero_nat ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_zero_less_power_iff
% 3.82/4.07 thf(fact_5805_of__nat__zero__less__power__iff,axiom,
% 3.82/4.07 ! [X: nat,N2: nat] :
% 3.82/4.07 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ X ) @ N2 ) )
% 3.82/4.07 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 3.82/4.07 | ( N2 = zero_zero_nat ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_zero_less_power_iff
% 3.82/4.07 thf(fact_5806_of__nat__zero__less__power__iff,axiom,
% 3.82/4.07 ! [X: nat,N2: nat] :
% 3.82/4.07 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ X ) @ N2 ) )
% 3.82/4.07 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 3.82/4.07 | ( N2 = zero_zero_nat ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_zero_less_power_iff
% 3.82/4.07 thf(fact_5807_of__nat__less__numeral__power__cancel__iff,axiom,
% 3.82/4.07 ! [X: nat,I: num,N2: nat] :
% 3.82/4.07 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N2 ) )
% 3.82/4.07 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_less_numeral_power_cancel_iff
% 3.82/4.07 thf(fact_5808_of__nat__less__numeral__power__cancel__iff,axiom,
% 3.82/4.07 ! [X: nat,I: num,N2: nat] :
% 3.82/4.07 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N2 ) )
% 3.82/4.07 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_less_numeral_power_cancel_iff
% 3.82/4.07 thf(fact_5809_of__nat__less__numeral__power__cancel__iff,axiom,
% 3.82/4.07 ! [X: nat,I: num,N2: nat] :
% 3.82/4.07 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) )
% 3.82/4.07 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_less_numeral_power_cancel_iff
% 3.82/4.07 thf(fact_5810_numeral__power__less__of__nat__cancel__iff,axiom,
% 3.82/4.07 ! [I: num,N2: nat,X: nat] :
% 3.82/4.07 ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N2 ) @ ( semiri5074537144036343181t_real @ X ) )
% 3.82/4.07 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) @ X ) ) ).
% 3.82/4.07
% 3.82/4.07 % numeral_power_less_of_nat_cancel_iff
% 3.82/4.07 thf(fact_5811_numeral__power__less__of__nat__cancel__iff,axiom,
% 3.82/4.07 ! [I: num,N2: nat,X: nat] :
% 3.82/4.07 ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N2 ) @ ( semiri1314217659103216013at_int @ X ) )
% 3.82/4.07 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) @ X ) ) ).
% 3.82/4.07
% 3.82/4.07 % numeral_power_less_of_nat_cancel_iff
% 3.82/4.07 thf(fact_5812_numeral__power__less__of__nat__cancel__iff,axiom,
% 3.82/4.07 ! [I: num,N2: nat,X: nat] :
% 3.82/4.07 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) @ ( semiri1316708129612266289at_nat @ X ) )
% 3.82/4.07 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) @ X ) ) ).
% 3.82/4.07
% 3.82/4.07 % numeral_power_less_of_nat_cancel_iff
% 3.82/4.07 thf(fact_5813_of__nat__le__numeral__power__cancel__iff,axiom,
% 3.82/4.07 ! [X: nat,I: num,N2: nat] :
% 3.82/4.07 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N2 ) )
% 3.82/4.07 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_le_numeral_power_cancel_iff
% 3.82/4.07 thf(fact_5814_of__nat__le__numeral__power__cancel__iff,axiom,
% 3.82/4.07 ! [X: nat,I: num,N2: nat] :
% 3.82/4.07 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) )
% 3.82/4.07 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_le_numeral_power_cancel_iff
% 3.82/4.07 thf(fact_5815_of__nat__le__numeral__power__cancel__iff,axiom,
% 3.82/4.07 ! [X: nat,I: num,N2: nat] :
% 3.82/4.07 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N2 ) )
% 3.82/4.07 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_le_numeral_power_cancel_iff
% 3.82/4.07 thf(fact_5816_numeral__power__le__of__nat__cancel__iff,axiom,
% 3.82/4.07 ! [I: num,N2: nat,X: nat] :
% 3.82/4.07 ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N2 ) @ ( semiri5074537144036343181t_real @ X ) )
% 3.82/4.07 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) @ X ) ) ).
% 3.82/4.07
% 3.82/4.07 % numeral_power_le_of_nat_cancel_iff
% 3.82/4.07 thf(fact_5817_numeral__power__le__of__nat__cancel__iff,axiom,
% 3.82/4.07 ! [I: num,N2: nat,X: nat] :
% 3.82/4.07 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) @ ( semiri1316708129612266289at_nat @ X ) )
% 3.82/4.07 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) @ X ) ) ).
% 3.82/4.07
% 3.82/4.07 % numeral_power_le_of_nat_cancel_iff
% 3.82/4.07 thf(fact_5818_numeral__power__le__of__nat__cancel__iff,axiom,
% 3.82/4.07 ! [I: num,N2: nat,X: nat] :
% 3.82/4.07 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N2 ) @ ( semiri1314217659103216013at_int @ X ) )
% 3.82/4.07 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) @ X ) ) ).
% 3.82/4.07
% 3.82/4.07 % numeral_power_le_of_nat_cancel_iff
% 3.82/4.07 thf(fact_5819_real__arch__simple,axiom,
% 3.82/4.07 ! [X: real] :
% 3.82/4.07 ? [N3: nat] : ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ N3 ) ) ).
% 3.82/4.07
% 3.82/4.07 % real_arch_simple
% 3.82/4.07 thf(fact_5820_reals__Archimedean2,axiom,
% 3.82/4.07 ! [X: real] :
% 3.82/4.07 ? [N3: nat] : ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ N3 ) ) ).
% 3.82/4.07
% 3.82/4.07 % reals_Archimedean2
% 3.82/4.07 thf(fact_5821_mult__of__nat__commute,axiom,
% 3.82/4.07 ! [X: nat,Y: complex] :
% 3.82/4.07 ( ( times_times_complex @ ( semiri8010041392384452111omplex @ X ) @ Y )
% 3.82/4.07 = ( times_times_complex @ Y @ ( semiri8010041392384452111omplex @ X ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % mult_of_nat_commute
% 3.82/4.07 thf(fact_5822_mult__of__nat__commute,axiom,
% 3.82/4.07 ! [X: nat,Y: extended_enat] :
% 3.82/4.07 ( ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ X ) @ Y )
% 3.82/4.07 = ( times_7803423173614009249d_enat @ Y @ ( semiri4216267220026989637d_enat @ X ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % mult_of_nat_commute
% 3.82/4.07 thf(fact_5823_mult__of__nat__commute,axiom,
% 3.82/4.07 ! [X: nat,Y: real] :
% 3.82/4.07 ( ( times_times_real @ ( semiri5074537144036343181t_real @ X ) @ Y )
% 3.82/4.07 = ( times_times_real @ Y @ ( semiri5074537144036343181t_real @ X ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % mult_of_nat_commute
% 3.82/4.07 thf(fact_5824_mult__of__nat__commute,axiom,
% 3.82/4.07 ! [X: nat,Y: int] :
% 3.82/4.07 ( ( times_times_int @ ( semiri1314217659103216013at_int @ X ) @ Y )
% 3.82/4.07 = ( times_times_int @ Y @ ( semiri1314217659103216013at_int @ X ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % mult_of_nat_commute
% 3.82/4.07 thf(fact_5825_mult__of__nat__commute,axiom,
% 3.82/4.07 ! [X: nat,Y: nat] :
% 3.82/4.07 ( ( times_times_nat @ ( semiri1316708129612266289at_nat @ X ) @ Y )
% 3.82/4.07 = ( times_times_nat @ Y @ ( semiri1316708129612266289at_nat @ X ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % mult_of_nat_commute
% 3.82/4.07 thf(fact_5826_nat__less__real__le,axiom,
% 3.82/4.07 ( ord_less_nat
% 3.82/4.07 = ( ^ [N: nat,M: nat] : ( ord_less_eq_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % nat_less_real_le
% 3.82/4.07 thf(fact_5827_int__cases2,axiom,
% 3.82/4.07 ! [Z3: int] :
% 3.82/4.07 ( ! [N3: nat] :
% 3.82/4.07 ( Z3
% 3.82/4.07 != ( semiri1314217659103216013at_int @ N3 ) )
% 3.82/4.07 => ~ ! [N3: nat] :
% 3.82/4.07 ( Z3
% 3.82/4.07 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % int_cases2
% 3.82/4.07 thf(fact_5828_int__diff__cases,axiom,
% 3.82/4.07 ! [Z3: int] :
% 3.82/4.07 ~ ! [M3: nat,N3: nat] :
% 3.82/4.07 ( Z3
% 3.82/4.07 != ( minus_minus_int @ ( semiri1314217659103216013at_int @ M3 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % int_diff_cases
% 3.82/4.07 thf(fact_5829_of__nat__less__of__int__iff,axiom,
% 3.82/4.07 ! [N2: nat,X: int] :
% 3.82/4.07 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( ring_1_of_int_real @ X ) )
% 3.82/4.07 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ X ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_less_of_int_iff
% 3.82/4.07 thf(fact_5830_of__nat__less__of__int__iff,axiom,
% 3.82/4.07 ! [N2: nat,X: int] :
% 3.82/4.07 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( ring_1_of_int_int @ X ) )
% 3.82/4.07 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ X ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_less_of_int_iff
% 3.82/4.07 thf(fact_5831_bit__Suc__0__iff,axiom,
% 3.82/4.07 ! [N2: nat] :
% 3.82/4.07 ( ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 3.82/4.07 = ( N2 = zero_zero_nat ) ) ).
% 3.82/4.07
% 3.82/4.07 % bit_Suc_0_iff
% 3.82/4.07 thf(fact_5832_not__bit__Suc__0__Suc,axiom,
% 3.82/4.07 ! [N2: nat] :
% 3.82/4.07 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( suc @ N2 ) ) ).
% 3.82/4.07
% 3.82/4.07 % not_bit_Suc_0_Suc
% 3.82/4.07 thf(fact_5833_of__nat__0__le__iff,axiom,
% 3.82/4.07 ! [N2: nat] : ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( semiri4216267220026989637d_enat @ N2 ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_0_le_iff
% 3.82/4.07 thf(fact_5834_of__nat__0__le__iff,axiom,
% 3.82/4.07 ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N2 ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_0_le_iff
% 3.82/4.07 thf(fact_5835_of__nat__0__le__iff,axiom,
% 3.82/4.07 ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N2 ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_0_le_iff
% 3.82/4.07 thf(fact_5836_of__nat__0__le__iff,axiom,
% 3.82/4.07 ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N2 ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_0_le_iff
% 3.82/4.07 thf(fact_5837_of__nat__less__0__iff,axiom,
% 3.82/4.07 ! [M2: nat] :
% 3.82/4.07 ~ ( ord_le72135733267957522d_enat @ ( semiri4216267220026989637d_enat @ M2 ) @ zero_z5237406670263579293d_enat ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_less_0_iff
% 3.82/4.07 thf(fact_5838_of__nat__less__0__iff,axiom,
% 3.82/4.07 ! [M2: nat] :
% 3.82/4.07 ~ ( ord_less_real @ ( semiri5074537144036343181t_real @ M2 ) @ zero_zero_real ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_less_0_iff
% 3.82/4.07 thf(fact_5839_of__nat__less__0__iff,axiom,
% 3.82/4.07 ! [M2: nat] :
% 3.82/4.07 ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ M2 ) @ zero_zero_int ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_less_0_iff
% 3.82/4.07 thf(fact_5840_of__nat__less__0__iff,axiom,
% 3.82/4.07 ! [M2: nat] :
% 3.82/4.07 ~ ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ zero_zero_nat ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_less_0_iff
% 3.82/4.07 thf(fact_5841_of__nat__neq__0,axiom,
% 3.82/4.07 ! [N2: nat] :
% 3.82/4.07 ( ( semiri8010041392384452111omplex @ ( suc @ N2 ) )
% 3.82/4.07 != zero_zero_complex ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_neq_0
% 3.82/4.07 thf(fact_5842_of__nat__neq__0,axiom,
% 3.82/4.07 ! [N2: nat] :
% 3.82/4.07 ( ( semiri4216267220026989637d_enat @ ( suc @ N2 ) )
% 3.82/4.07 != zero_z5237406670263579293d_enat ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_neq_0
% 3.82/4.07 thf(fact_5843_of__nat__neq__0,axiom,
% 3.82/4.07 ! [N2: nat] :
% 3.82/4.07 ( ( semiri5074537144036343181t_real @ ( suc @ N2 ) )
% 3.82/4.07 != zero_zero_real ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_neq_0
% 3.82/4.07 thf(fact_5844_of__nat__neq__0,axiom,
% 3.82/4.07 ! [N2: nat] :
% 3.82/4.07 ( ( semiri1314217659103216013at_int @ ( suc @ N2 ) )
% 3.82/4.07 != zero_zero_int ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_neq_0
% 3.82/4.07 thf(fact_5845_of__nat__neq__0,axiom,
% 3.82/4.07 ! [N2: nat] :
% 3.82/4.07 ( ( semiri1316708129612266289at_nat @ ( suc @ N2 ) )
% 3.82/4.07 != zero_zero_nat ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_neq_0
% 3.82/4.07 thf(fact_5846_less__imp__of__nat__less,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat] :
% 3.82/4.07 ( ( ord_less_nat @ M2 @ N2 )
% 3.82/4.07 => ( ord_le72135733267957522d_enat @ ( semiri4216267220026989637d_enat @ M2 ) @ ( semiri4216267220026989637d_enat @ N2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % less_imp_of_nat_less
% 3.82/4.07 thf(fact_5847_less__imp__of__nat__less,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat] :
% 3.82/4.07 ( ( ord_less_nat @ M2 @ N2 )
% 3.82/4.07 => ( ord_less_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % less_imp_of_nat_less
% 3.82/4.07 thf(fact_5848_less__imp__of__nat__less,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat] :
% 3.82/4.07 ( ( ord_less_nat @ M2 @ N2 )
% 3.82/4.07 => ( ord_less_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % less_imp_of_nat_less
% 3.82/4.07 thf(fact_5849_less__imp__of__nat__less,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat] :
% 3.82/4.07 ( ( ord_less_nat @ M2 @ N2 )
% 3.82/4.07 => ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % less_imp_of_nat_less
% 3.82/4.07 thf(fact_5850_of__nat__less__imp__less,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat] :
% 3.82/4.07 ( ( ord_le72135733267957522d_enat @ ( semiri4216267220026989637d_enat @ M2 ) @ ( semiri4216267220026989637d_enat @ N2 ) )
% 3.82/4.07 => ( ord_less_nat @ M2 @ N2 ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_less_imp_less
% 3.82/4.07 thf(fact_5851_of__nat__less__imp__less,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat] :
% 3.82/4.07 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( semiri5074537144036343181t_real @ N2 ) )
% 3.82/4.07 => ( ord_less_nat @ M2 @ N2 ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_less_imp_less
% 3.82/4.07 thf(fact_5852_of__nat__less__imp__less,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat] :
% 3.82/4.07 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 3.82/4.07 => ( ord_less_nat @ M2 @ N2 ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_less_imp_less
% 3.82/4.07 thf(fact_5853_of__nat__less__imp__less,axiom,
% 3.82/4.07 ! [M2: nat,N2: nat] :
% 3.82/4.07 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N2 ) )
% 3.82/4.07 => ( ord_less_nat @ M2 @ N2 ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_less_imp_less
% 3.82/4.07 thf(fact_5854_of__nat__mono,axiom,
% 3.82/4.07 ! [I: nat,J: nat] :
% 3.82/4.07 ( ( ord_less_eq_nat @ I @ J )
% 3.82/4.07 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ I ) @ ( semiri5074537144036343181t_real @ J ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_mono
% 3.82/4.07 thf(fact_5855_of__nat__mono,axiom,
% 3.82/4.07 ! [I: nat,J: nat] :
% 3.82/4.07 ( ( ord_less_eq_nat @ I @ J )
% 3.82/4.07 => ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ I ) @ ( semiri1316708129612266289at_nat @ J ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_mono
% 3.82/4.07 thf(fact_5856_of__nat__mono,axiom,
% 3.82/4.07 ! [I: nat,J: nat] :
% 3.82/4.07 ( ( ord_less_eq_nat @ I @ J )
% 3.82/4.07 => ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ J ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % of_nat_mono
% 3.82/4.07 thf(fact_5857_nat__le__real__less,axiom,
% 3.82/4.07 ( ord_less_eq_nat
% 3.82/4.07 = ( ^ [N: nat,M: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ one_one_real ) ) ) ) ).
% 3.82/4.07
% 3.82/4.07 % nat_le_real_less
% 3.82/4.07 thf(fact_5858_int__ops_I1_J,axiom,
% 3.82/4.07 ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 3.82/4.07 = zero_zero_int ) ).
% 3.82/4.07
% 3.82/4.07 % int_ops(1)
% 3.82/4.08 thf(fact_5859_nat__int__comparison_I2_J,axiom,
% 3.82/4.08 ( ord_less_nat
% 3.82/4.08 = ( ^ [A3: nat,B3: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % nat_int_comparison(2)
% 3.82/4.08 thf(fact_5860_int__cases,axiom,
% 3.82/4.08 ! [Z3: int] :
% 3.82/4.08 ( ! [N3: nat] :
% 3.82/4.08 ( Z3
% 3.82/4.08 != ( semiri1314217659103216013at_int @ N3 ) )
% 3.82/4.08 => ~ ! [N3: nat] :
% 3.82/4.08 ( Z3
% 3.82/4.08 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % int_cases
% 3.82/4.08 thf(fact_5861_int__of__nat__induct,axiom,
% 3.82/4.08 ! [P: int > $o,Z3: int] :
% 3.82/4.08 ( ! [N3: nat] : ( P @ ( semiri1314217659103216013at_int @ N3 ) )
% 3.82/4.08 => ( ! [N3: nat] : ( P @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) )
% 3.82/4.08 => ( P @ Z3 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % int_of_nat_induct
% 3.82/4.08 thf(fact_5862_zle__int,axiom,
% 3.82/4.08 ! [M2: nat,N2: nat] :
% 3.82/4.08 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 3.82/4.08 = ( ord_less_eq_nat @ M2 @ N2 ) ) ).
% 3.82/4.08
% 3.82/4.08 % zle_int
% 3.82/4.08 thf(fact_5863_nat__int__comparison_I3_J,axiom,
% 3.82/4.08 ( ord_less_eq_nat
% 3.82/4.08 = ( ^ [A3: nat,B3: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % nat_int_comparison(3)
% 3.82/4.08 thf(fact_5864_nonneg__int__cases,axiom,
% 3.82/4.08 ! [K: int] :
% 3.82/4.08 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 3.82/4.08 => ~ ! [N3: nat] :
% 3.82/4.08 ( K
% 3.82/4.08 != ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % nonneg_int_cases
% 3.82/4.08 thf(fact_5865_zero__le__imp__eq__int,axiom,
% 3.82/4.08 ! [K: int] :
% 3.82/4.08 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 3.82/4.08 => ? [N3: nat] :
% 3.82/4.08 ( K
% 3.82/4.08 = ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % zero_le_imp_eq_int
% 3.82/4.08 thf(fact_5866_zadd__int__left,axiom,
% 3.82/4.08 ! [M2: nat,N2: nat,Z3: int] :
% 3.82/4.08 ( ( plus_plus_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ Z3 ) )
% 3.82/4.08 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M2 @ N2 ) ) @ Z3 ) ) ).
% 3.82/4.08
% 3.82/4.08 % zadd_int_left
% 3.82/4.08 thf(fact_5867_int__plus,axiom,
% 3.82/4.08 ! [N2: nat,M2: nat] :
% 3.82/4.08 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ N2 @ M2 ) )
% 3.82/4.08 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( semiri1314217659103216013at_int @ M2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % int_plus
% 3.82/4.08 thf(fact_5868_int__ops_I5_J,axiom,
% 3.82/4.08 ! [A: nat,B2: nat] :
% 3.82/4.08 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ A @ B2 ) )
% 3.82/4.08 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % int_ops(5)
% 3.82/4.08 thf(fact_5869_zle__iff__zadd,axiom,
% 3.82/4.08 ( ord_less_eq_int
% 3.82/4.08 = ( ^ [W3: int,Z6: int] :
% 3.82/4.08 ? [N: nat] :
% 3.82/4.08 ( Z6
% 3.82/4.08 = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % zle_iff_zadd
% 3.82/4.08 thf(fact_5870_not__int__zless__negative,axiom,
% 3.82/4.08 ! [N2: nat,M2: nat] :
% 3.82/4.08 ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % not_int_zless_negative
% 3.82/4.08 thf(fact_5871_of__nat__max,axiom,
% 3.82/4.08 ! [X: nat,Y: nat] :
% 3.82/4.08 ( ( semiri5074537144036343181t_real @ ( ord_max_nat @ X @ Y ) )
% 3.82/4.08 = ( ord_max_real @ ( semiri5074537144036343181t_real @ X ) @ ( semiri5074537144036343181t_real @ Y ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % of_nat_max
% 3.82/4.08 thf(fact_5872_of__nat__max,axiom,
% 3.82/4.08 ! [X: nat,Y: nat] :
% 3.82/4.08 ( ( semiri1314217659103216013at_int @ ( ord_max_nat @ X @ Y ) )
% 3.82/4.08 = ( ord_max_int @ ( semiri1314217659103216013at_int @ X ) @ ( semiri1314217659103216013at_int @ Y ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % of_nat_max
% 3.82/4.08 thf(fact_5873_of__nat__max,axiom,
% 3.82/4.08 ! [X: nat,Y: nat] :
% 3.82/4.08 ( ( semiri1316708129612266289at_nat @ ( ord_max_nat @ X @ Y ) )
% 3.82/4.08 = ( ord_max_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( semiri1316708129612266289at_nat @ Y ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % of_nat_max
% 3.82/4.08 thf(fact_5874_nat__less__as__int,axiom,
% 3.82/4.08 ( ord_less_nat
% 3.82/4.08 = ( ^ [A3: nat,B3: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % nat_less_as_int
% 3.82/4.08 thf(fact_5875_nat__leq__as__int,axiom,
% 3.82/4.08 ( ord_less_eq_nat
% 3.82/4.08 = ( ^ [A3: nat,B3: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % nat_leq_as_int
% 3.82/4.08 thf(fact_5876_not__bit__Suc__0__numeral,axiom,
% 3.82/4.08 ! [N2: num] :
% 3.82/4.08 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ N2 ) ) ).
% 3.82/4.08
% 3.82/4.08 % not_bit_Suc_0_numeral
% 3.82/4.08 thf(fact_5877_ex__less__of__nat__mult,axiom,
% 3.82/4.08 ! [X: real,Y: real] :
% 3.82/4.08 ( ( ord_less_real @ zero_zero_real @ X )
% 3.82/4.08 => ? [N3: nat] : ( ord_less_real @ Y @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ X ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % ex_less_of_nat_mult
% 3.82/4.08 thf(fact_5878_of__nat__diff,axiom,
% 3.82/4.08 ! [N2: nat,M2: nat] :
% 3.82/4.08 ( ( ord_less_eq_nat @ N2 @ M2 )
% 3.82/4.08 => ( ( semiri5074537144036343181t_real @ ( minus_minus_nat @ M2 @ N2 ) )
% 3.82/4.08 = ( minus_minus_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % of_nat_diff
% 3.82/4.08 thf(fact_5879_of__nat__diff,axiom,
% 3.82/4.08 ! [N2: nat,M2: nat] :
% 3.82/4.08 ( ( ord_less_eq_nat @ N2 @ M2 )
% 3.82/4.08 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ M2 @ N2 ) )
% 3.82/4.08 = ( minus_minus_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % of_nat_diff
% 3.82/4.08 thf(fact_5880_of__nat__diff,axiom,
% 3.82/4.08 ! [N2: nat,M2: nat] :
% 3.82/4.08 ( ( ord_less_eq_nat @ N2 @ M2 )
% 3.82/4.08 => ( ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ M2 @ N2 ) )
% 3.82/4.08 = ( minus_minus_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % of_nat_diff
% 3.82/4.08 thf(fact_5881_real__archimedian__rdiv__eq__0,axiom,
% 3.82/4.08 ! [X: real,C: real] :
% 3.82/4.08 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 3.82/4.08 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 3.82/4.08 => ( ! [M3: nat] :
% 3.82/4.08 ( ( ord_less_nat @ zero_zero_nat @ M3 )
% 3.82/4.08 => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M3 ) @ X ) @ C ) )
% 3.82/4.08 => ( X = zero_zero_real ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % real_archimedian_rdiv_eq_0
% 3.82/4.08 thf(fact_5882_int__cases4,axiom,
% 3.82/4.08 ! [M2: int] :
% 3.82/4.08 ( ! [N3: nat] :
% 3.82/4.08 ( M2
% 3.82/4.08 != ( semiri1314217659103216013at_int @ N3 ) )
% 3.82/4.08 => ~ ! [N3: nat] :
% 3.82/4.08 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 3.82/4.08 => ( M2
% 3.82/4.08 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % int_cases4
% 3.82/4.08 thf(fact_5883_int__zle__neg,axiom,
% 3.82/4.08 ! [N2: nat,M2: nat] :
% 3.82/4.08 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M2 ) ) )
% 3.82/4.08 = ( ( N2 = zero_zero_nat )
% 3.82/4.08 & ( M2 = zero_zero_nat ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % int_zle_neg
% 3.82/4.08 thf(fact_5884_int__ops_I4_J,axiom,
% 3.82/4.08 ! [A: nat] :
% 3.82/4.08 ( ( semiri1314217659103216013at_int @ ( suc @ A ) )
% 3.82/4.08 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ one_one_int ) ) ).
% 3.82/4.08
% 3.82/4.08 % int_ops(4)
% 3.82/4.08 thf(fact_5885_int__Suc,axiom,
% 3.82/4.08 ! [N2: nat] :
% 3.82/4.08 ( ( semiri1314217659103216013at_int @ ( suc @ N2 ) )
% 3.82/4.08 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) ).
% 3.82/4.08
% 3.82/4.08 % int_Suc
% 3.82/4.08 thf(fact_5886_zless__iff__Suc__zadd,axiom,
% 3.82/4.08 ( ord_less_int
% 3.82/4.08 = ( ^ [W3: int,Z6: int] :
% 3.82/4.08 ? [N: nat] :
% 3.82/4.08 ( Z6
% 3.82/4.08 = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % zless_iff_Suc_zadd
% 3.82/4.08 thf(fact_5887_negative__zle__0,axiom,
% 3.82/4.08 ! [N2: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ zero_zero_int ) ).
% 3.82/4.08
% 3.82/4.08 % negative_zle_0
% 3.82/4.08 thf(fact_5888_nonpos__int__cases,axiom,
% 3.82/4.08 ! [K: int] :
% 3.82/4.08 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 3.82/4.08 => ~ ! [N3: nat] :
% 3.82/4.08 ( K
% 3.82/4.08 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % nonpos_int_cases
% 3.82/4.08 thf(fact_5889_int__sum,axiom,
% 3.82/4.08 ! [F: int > nat,A2: set_int] :
% 3.82/4.08 ( ( semiri1314217659103216013at_int @ ( groups4541462559716669496nt_nat @ F @ A2 ) )
% 3.82/4.08 = ( groups4538972089207619220nt_int
% 3.82/4.08 @ ^ [X4: int] : ( semiri1314217659103216013at_int @ ( F @ X4 ) )
% 3.82/4.08 @ A2 ) ) ).
% 3.82/4.08
% 3.82/4.08 % int_sum
% 3.82/4.08 thf(fact_5890_int__sum,axiom,
% 3.82/4.08 ! [F: nat > nat,A2: set_nat] :
% 3.82/4.08 ( ( semiri1314217659103216013at_int @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 3.82/4.08 = ( groups3539618377306564664at_int
% 3.82/4.08 @ ^ [X4: nat] : ( semiri1314217659103216013at_int @ ( F @ X4 ) )
% 3.82/4.08 @ A2 ) ) ).
% 3.82/4.08
% 3.82/4.08 % int_sum
% 3.82/4.08 thf(fact_5891_mod__mult2__eq_H,axiom,
% 3.82/4.08 ! [A: int,M2: nat,N2: nat] :
% 3.82/4.08 ( ( modulo_modulo_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 3.82/4.08 = ( plus_plus_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( modulo_modulo_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) @ ( modulo_modulo_int @ A @ ( semiri1314217659103216013at_int @ M2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % mod_mult2_eq'
% 3.82/4.08 thf(fact_5892_mod__mult2__eq_H,axiom,
% 3.82/4.08 ! [A: nat,M2: nat,N2: nat] :
% 3.82/4.08 ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N2 ) ) )
% 3.82/4.08 = ( plus_plus_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M2 ) ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) @ ( modulo_modulo_nat @ A @ ( semiri1316708129612266289at_nat @ M2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % mod_mult2_eq'
% 3.82/4.08 thf(fact_5893_zero__less__imp__eq__int,axiom,
% 3.82/4.08 ! [K: int] :
% 3.82/4.08 ( ( ord_less_int @ zero_zero_int @ K )
% 3.82/4.08 => ? [N3: nat] :
% 3.82/4.08 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 3.82/4.08 & ( K
% 3.82/4.08 = ( semiri1314217659103216013at_int @ N3 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % zero_less_imp_eq_int
% 3.82/4.08 thf(fact_5894_pos__int__cases,axiom,
% 3.82/4.08 ! [K: int] :
% 3.82/4.08 ( ( ord_less_int @ zero_zero_int @ K )
% 3.82/4.08 => ~ ! [N3: nat] :
% 3.82/4.08 ( ( K
% 3.82/4.08 = ( semiri1314217659103216013at_int @ N3 ) )
% 3.82/4.08 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pos_int_cases
% 3.82/4.08 thf(fact_5895_int__cases3,axiom,
% 3.82/4.08 ! [K: int] :
% 3.82/4.08 ( ( K != zero_zero_int )
% 3.82/4.08 => ( ! [N3: nat] :
% 3.82/4.08 ( ( K
% 3.82/4.08 = ( semiri1314217659103216013at_int @ N3 ) )
% 3.82/4.08 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) )
% 3.82/4.08 => ~ ! [N3: nat] :
% 3.82/4.08 ( ( K
% 3.82/4.08 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
% 3.82/4.08 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % int_cases3
% 3.82/4.08 thf(fact_5896_zmult__zless__mono2__lemma,axiom,
% 3.82/4.08 ! [I: int,J: int,K: nat] :
% 3.82/4.08 ( ( ord_less_int @ I @ J )
% 3.82/4.08 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 3.82/4.08 => ( ord_less_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ I ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ J ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % zmult_zless_mono2_lemma
% 3.82/4.08 thf(fact_5897_not__zle__0__negative,axiom,
% 3.82/4.08 ! [N2: nat] :
% 3.82/4.08 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % not_zle_0_negative
% 3.82/4.08 thf(fact_5898_negD,axiom,
% 3.82/4.08 ! [X: int] :
% 3.82/4.08 ( ( ord_less_int @ X @ zero_zero_int )
% 3.82/4.08 => ? [N3: nat] :
% 3.82/4.08 ( X
% 3.82/4.08 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % negD
% 3.82/4.08 thf(fact_5899_negative__zless__0,axiom,
% 3.82/4.08 ! [N2: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) @ zero_zero_int ) ).
% 3.82/4.08
% 3.82/4.08 % negative_zless_0
% 3.82/4.08 thf(fact_5900_nat__approx__posE,axiom,
% 3.82/4.08 ! [E2: real] :
% 3.82/4.08 ( ( ord_less_real @ zero_zero_real @ E2 )
% 3.82/4.08 => ~ ! [N3: nat] :
% 3.82/4.08 ~ ( ord_less_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) @ E2 ) ) ).
% 3.82/4.08
% 3.82/4.08 % nat_approx_posE
% 3.82/4.08 thf(fact_5901_of__nat__less__two__power,axiom,
% 3.82/4.08 ! [N2: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N2 ) ) ).
% 3.82/4.08
% 3.82/4.08 % of_nat_less_two_power
% 3.82/4.08 thf(fact_5902_of__nat__less__two__power,axiom,
% 3.82/4.08 ! [N2: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ).
% 3.82/4.08
% 3.82/4.08 % of_nat_less_two_power
% 3.82/4.08 thf(fact_5903_inverse__of__nat__le,axiom,
% 3.82/4.08 ! [N2: nat,M2: nat] :
% 3.82/4.08 ( ( ord_less_eq_nat @ N2 @ M2 )
% 3.82/4.08 => ( ( N2 != zero_zero_nat )
% 3.82/4.08 => ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ M2 ) ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % inverse_of_nat_le
% 3.82/4.08 thf(fact_5904_neg__int__cases,axiom,
% 3.82/4.08 ! [K: int] :
% 3.82/4.08 ( ( ord_less_int @ K @ zero_zero_int )
% 3.82/4.08 => ~ ! [N3: nat] :
% 3.82/4.08 ( ( K
% 3.82/4.08 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
% 3.82/4.08 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % neg_int_cases
% 3.82/4.08 thf(fact_5905_zdiff__int__split,axiom,
% 3.82/4.08 ! [P: int > $o,X: nat,Y: nat] :
% 3.82/4.08 ( ( P @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ X @ Y ) ) )
% 3.82/4.08 = ( ( ( ord_less_eq_nat @ Y @ X )
% 3.82/4.08 => ( P @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ X ) @ ( semiri1314217659103216013at_int @ Y ) ) ) )
% 3.82/4.08 & ( ( ord_less_nat @ X @ Y )
% 3.82/4.08 => ( P @ zero_zero_int ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % zdiff_int_split
% 3.82/4.08 thf(fact_5906_double__arith__series,axiom,
% 3.82/4.08 ! [A: complex,D: complex,N2: nat] :
% 3.82/4.08 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 3.82/4.08 @ ( groups2073611262835488442omplex
% 3.82/4.08 @ ^ [I3: nat] : ( plus_plus_complex @ A @ ( times_times_complex @ ( semiri8010041392384452111omplex @ I3 ) @ D ) )
% 3.82/4.08 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 3.82/4.08 = ( 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 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % double_arith_series
% 3.82/4.08 thf(fact_5907_double__arith__series,axiom,
% 3.82/4.08 ! [A: extended_enat,D: extended_enat,N2: nat] :
% 3.82/4.08 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) )
% 3.82/4.08 @ ( groups7108830773950497114d_enat
% 3.82/4.08 @ ^ [I3: nat] : ( plus_p3455044024723400733d_enat @ A @ ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ I3 ) @ D ) )
% 3.82/4.08 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 3.82/4.08 = ( 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 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % double_arith_series
% 3.82/4.08 thf(fact_5908_double__arith__series,axiom,
% 3.82/4.08 ! [A: int,D: int,N2: nat] :
% 3.82/4.08 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 3.82/4.08 @ ( groups3539618377306564664at_int
% 3.82/4.08 @ ^ [I3: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I3 ) @ D ) )
% 3.82/4.08 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 3.82/4.08 = ( 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 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % double_arith_series
% 3.82/4.08 thf(fact_5909_double__arith__series,axiom,
% 3.82/4.08 ! [A: nat,D: nat,N2: nat] :
% 3.82/4.08 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 3.82/4.08 @ ( groups3542108847815614940at_nat
% 3.82/4.08 @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I3 ) @ D ) )
% 3.82/4.08 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 3.82/4.08 = ( 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 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % double_arith_series
% 3.82/4.08 thf(fact_5910_double__arith__series,axiom,
% 3.82/4.08 ! [A: real,D: real,N2: nat] :
% 3.82/4.08 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 3.82/4.08 @ ( groups6591440286371151544t_real
% 3.82/4.08 @ ^ [I3: nat] : ( plus_plus_real @ A @ ( times_times_real @ ( semiri5074537144036343181t_real @ I3 ) @ D ) )
% 3.82/4.08 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 3.82/4.08 = ( 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 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % double_arith_series
% 3.82/4.08 thf(fact_5911_double__gauss__sum,axiom,
% 3.82/4.08 ! [N2: nat] :
% 3.82/4.08 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 3.82/4.08 = ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N2 ) @ one_one_complex ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % double_gauss_sum
% 3.82/4.08 thf(fact_5912_double__gauss__sum,axiom,
% 3.82/4.08 ! [N2: nat] :
% 3.82/4.08 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ ( groups7108830773950497114d_enat @ semiri4216267220026989637d_enat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 3.82/4.08 = ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ N2 ) @ ( plus_p3455044024723400733d_enat @ ( semiri4216267220026989637d_enat @ N2 ) @ one_on7984719198319812577d_enat ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % double_gauss_sum
% 3.82/4.08 thf(fact_5913_double__gauss__sum,axiom,
% 3.82/4.08 ! [N2: nat] :
% 3.82/4.08 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 3.82/4.08 = ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % double_gauss_sum
% 3.82/4.08 thf(fact_5914_double__gauss__sum,axiom,
% 3.82/4.08 ! [N2: nat] :
% 3.82/4.08 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 3.82/4.08 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % double_gauss_sum
% 3.82/4.08 thf(fact_5915_double__gauss__sum,axiom,
% 3.82/4.08 ! [N2: nat] :
% 3.82/4.08 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 3.82/4.08 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % double_gauss_sum
% 3.82/4.08 thf(fact_5916_gauss__sum,axiom,
% 3.82/4.08 ! [N2: nat] :
% 3.82/4.08 ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 3.82/4.08 = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % gauss_sum
% 3.82/4.08 thf(fact_5917_gauss__sum,axiom,
% 3.82/4.08 ! [N2: nat] :
% 3.82/4.08 ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 3.82/4.08 = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % gauss_sum
% 3.82/4.08 thf(fact_5918_of__nat__code__if,axiom,
% 3.82/4.08 ( semiri8010041392384452111omplex
% 3.82/4.08 = ( ^ [N: nat] :
% 3.82/4.08 ( if_complex @ ( N = zero_zero_nat ) @ zero_zero_complex
% 3.82/4.08 @ ( produc1917071388513777916omplex
% 3.82/4.08 @ ^ [M: nat,Q5: nat] : ( if_complex @ ( Q5 = zero_zero_nat ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M ) ) @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M ) ) @ one_one_complex ) )
% 3.82/4.08 @ ( divmod_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % of_nat_code_if
% 3.82/4.08 thf(fact_5919_of__nat__code__if,axiom,
% 3.82/4.08 ( semiri4216267220026989637d_enat
% 3.82/4.08 = ( ^ [N: nat] :
% 3.82/4.08 ( if_Extended_enat @ ( N = zero_zero_nat ) @ zero_z5237406670263579293d_enat
% 3.82/4.08 @ ( produc2676513652042109336d_enat
% 3.82/4.08 @ ^ [M: nat,Q5: nat] : ( if_Extended_enat @ ( Q5 = zero_zero_nat ) @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ ( semiri4216267220026989637d_enat @ M ) ) @ ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ ( semiri4216267220026989637d_enat @ M ) ) @ one_on7984719198319812577d_enat ) )
% 3.82/4.08 @ ( divmod_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % of_nat_code_if
% 3.82/4.08 thf(fact_5920_of__nat__code__if,axiom,
% 3.82/4.08 ( semiri5074537144036343181t_real
% 3.82/4.08 = ( ^ [N: nat] :
% 3.82/4.08 ( if_real @ ( N = zero_zero_nat ) @ zero_zero_real
% 3.82/4.08 @ ( produc1703576794950452218t_real
% 3.82/4.08 @ ^ [M: nat,Q5: nat] : ( if_real @ ( Q5 = zero_zero_nat ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ one_one_real ) )
% 3.82/4.08 @ ( divmod_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % of_nat_code_if
% 3.82/4.08 thf(fact_5921_of__nat__code__if,axiom,
% 3.82/4.08 ( semiri1314217659103216013at_int
% 3.82/4.08 = ( ^ [N: nat] :
% 3.82/4.08 ( if_int @ ( N = zero_zero_nat ) @ zero_zero_int
% 3.82/4.08 @ ( produc6840382203811409530at_int
% 3.82/4.08 @ ^ [M: nat,Q5: nat] : ( if_int @ ( Q5 = zero_zero_nat ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ M ) ) @ one_one_int ) )
% 3.82/4.08 @ ( divmod_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % of_nat_code_if
% 3.82/4.08 thf(fact_5922_of__nat__code__if,axiom,
% 3.82/4.08 ( semiri1316708129612266289at_nat
% 3.82/4.08 = ( ^ [N: nat] :
% 3.82/4.08 ( if_nat @ ( N = zero_zero_nat ) @ zero_zero_nat
% 3.82/4.08 @ ( produc6842872674320459806at_nat
% 3.82/4.08 @ ^ [M: nat,Q5: nat] : ( if_nat @ ( Q5 = zero_zero_nat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ M ) ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ M ) ) @ one_one_nat ) )
% 3.82/4.08 @ ( divmod_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % of_nat_code_if
% 3.82/4.08 thf(fact_5923_lemma__termdiff2,axiom,
% 3.82/4.08 ! [H2: complex,Z3: complex,N2: nat] :
% 3.82/4.08 ( ( H2 != zero_zero_complex )
% 3.82/4.08 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z3 @ H2 ) @ N2 ) @ ( power_power_complex @ Z3 @ N2 ) ) @ H2 ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( power_power_complex @ Z3 @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 3.82/4.08 = ( times_times_complex @ H2
% 3.82/4.08 @ ( groups2073611262835488442omplex
% 3.82/4.08 @ ^ [P6: nat] :
% 3.82/4.08 ( groups2073611262835488442omplex
% 3.82/4.08 @ ^ [Q5: nat] : ( times_times_complex @ ( power_power_complex @ ( plus_plus_complex @ Z3 @ H2 ) @ Q5 ) @ ( power_power_complex @ Z3 @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q5 ) ) )
% 3.82/4.08 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ P6 ) ) )
% 3.82/4.08 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % lemma_termdiff2
% 3.82/4.08 thf(fact_5924_lemma__termdiff2,axiom,
% 3.82/4.08 ! [H2: real,Z3: real,N2: nat] :
% 3.82/4.08 ( ( H2 != zero_zero_real )
% 3.82/4.08 => ( ( minus_minus_real @ ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z3 @ H2 ) @ N2 ) @ ( power_power_real @ Z3 @ N2 ) ) @ H2 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ Z3 @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 3.82/4.08 = ( times_times_real @ H2
% 3.82/4.08 @ ( groups6591440286371151544t_real
% 3.82/4.08 @ ^ [P6: nat] :
% 3.82/4.08 ( groups6591440286371151544t_real
% 3.82/4.08 @ ^ [Q5: nat] : ( times_times_real @ ( power_power_real @ ( plus_plus_real @ Z3 @ H2 ) @ Q5 ) @ ( power_power_real @ Z3 @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q5 ) ) )
% 3.82/4.08 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ P6 ) ) )
% 3.82/4.08 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % lemma_termdiff2
% 3.82/4.08 thf(fact_5925_lemma__termdiff3,axiom,
% 3.82/4.08 ! [H2: real,Z3: real,K5: real,N2: nat] :
% 3.82/4.08 ( ( H2 != zero_zero_real )
% 3.82/4.08 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z3 ) @ K5 )
% 3.82/4.08 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ Z3 @ H2 ) ) @ K5 )
% 3.82/4.08 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z3 @ H2 ) @ N2 ) @ ( power_power_real @ Z3 @ N2 ) ) @ H2 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ Z3 @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) @ ( power_power_real @ K5 @ ( minus_minus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( real_V7735802525324610683m_real @ H2 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % lemma_termdiff3
% 3.82/4.08 thf(fact_5926_lemma__termdiff3,axiom,
% 3.82/4.08 ! [H2: complex,Z3: complex,K5: real,N2: nat] :
% 3.82/4.08 ( ( H2 != zero_zero_complex )
% 3.82/4.08 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z3 ) @ K5 )
% 3.82/4.08 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ Z3 @ H2 ) ) @ K5 )
% 3.82/4.08 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z3 @ H2 ) @ N2 ) @ ( power_power_complex @ Z3 @ N2 ) ) @ H2 ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( power_power_complex @ Z3 @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) @ ( power_power_real @ K5 @ ( minus_minus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( real_V1022390504157884413omplex @ H2 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % lemma_termdiff3
% 3.82/4.08 thf(fact_5927_pochhammer__double,axiom,
% 3.82/4.08 ! [Z3: complex,N2: nat] :
% 3.82/4.08 ( ( comm_s2602460028002588243omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z3 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 3.82/4.08 = ( 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 @ Z3 @ N2 ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z3 @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ N2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_double
% 3.82/4.08 thf(fact_5928_pochhammer__double,axiom,
% 3.82/4.08 ! [Z3: real,N2: nat] :
% 3.82/4.08 ( ( comm_s7457072308508201937r_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z3 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 3.82/4.08 = ( 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 @ Z3 @ N2 ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z3 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ N2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_double
% 3.82/4.08 thf(fact_5929_of__nat__code,axiom,
% 3.82/4.08 ( semiri8010041392384452111omplex
% 3.82/4.08 = ( ^ [N: nat] :
% 3.82/4.08 ( semiri2816024913162550771omplex
% 3.82/4.08 @ ^ [I3: complex] : ( plus_plus_complex @ I3 @ one_one_complex )
% 3.82/4.08 @ N
% 3.82/4.08 @ zero_zero_complex ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % of_nat_code
% 3.82/4.08 thf(fact_5930_of__nat__code,axiom,
% 3.82/4.08 ( semiri4216267220026989637d_enat
% 3.82/4.08 = ( ^ [N: nat] :
% 3.82/4.08 ( semiri8563196900006977889d_enat
% 3.82/4.08 @ ^ [I3: extended_enat] : ( plus_p3455044024723400733d_enat @ I3 @ one_on7984719198319812577d_enat )
% 3.82/4.08 @ N
% 3.82/4.08 @ zero_z5237406670263579293d_enat ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % of_nat_code
% 3.82/4.08 thf(fact_5931_of__nat__code,axiom,
% 3.82/4.08 ( semiri5074537144036343181t_real
% 3.82/4.08 = ( ^ [N: nat] :
% 3.82/4.08 ( semiri7260567687927622513x_real
% 3.82/4.08 @ ^ [I3: real] : ( plus_plus_real @ I3 @ one_one_real )
% 3.82/4.08 @ N
% 3.82/4.08 @ zero_zero_real ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % of_nat_code
% 3.82/4.08 thf(fact_5932_of__nat__code,axiom,
% 3.82/4.08 ( semiri1314217659103216013at_int
% 3.82/4.08 = ( ^ [N: nat] :
% 3.82/4.08 ( semiri8420488043553186161ux_int
% 3.82/4.08 @ ^ [I3: int] : ( plus_plus_int @ I3 @ one_one_int )
% 3.82/4.08 @ N
% 3.82/4.08 @ zero_zero_int ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % of_nat_code
% 3.82/4.08 thf(fact_5933_of__nat__code,axiom,
% 3.82/4.08 ( semiri1316708129612266289at_nat
% 3.82/4.08 = ( ^ [N: nat] :
% 3.82/4.08 ( semiri8422978514062236437ux_nat
% 3.82/4.08 @ ^ [I3: nat] : ( plus_plus_nat @ I3 @ one_one_nat )
% 3.82/4.08 @ N
% 3.82/4.08 @ zero_zero_nat ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % of_nat_code
% 3.82/4.08 thf(fact_5934_ceiling__log__nat__eq__powr__iff,axiom,
% 3.82/4.08 ! [B2: nat,K: nat,N2: nat] :
% 3.82/4.08 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 )
% 3.82/4.08 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 3.82/4.08 => ( ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B2 ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 3.82/4.08 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) )
% 3.82/4.08 = ( ( ord_less_nat @ ( power_power_nat @ B2 @ N2 ) @ K )
% 3.82/4.08 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B2 @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % ceiling_log_nat_eq_powr_iff
% 3.82/4.08 thf(fact_5935_lessThan__eq__iff,axiom,
% 3.82/4.08 ! [X: nat,Y: nat] :
% 3.82/4.08 ( ( ( set_ord_lessThan_nat @ X )
% 3.82/4.08 = ( set_ord_lessThan_nat @ Y ) )
% 3.82/4.08 = ( X = Y ) ) ).
% 3.82/4.08
% 3.82/4.08 % lessThan_eq_iff
% 3.82/4.08 thf(fact_5936_lessThan__eq__iff,axiom,
% 3.82/4.08 ! [X: int,Y: int] :
% 3.82/4.08 ( ( ( set_ord_lessThan_int @ X )
% 3.82/4.08 = ( set_ord_lessThan_int @ Y ) )
% 3.82/4.08 = ( X = Y ) ) ).
% 3.82/4.08
% 3.82/4.08 % lessThan_eq_iff
% 3.82/4.08 thf(fact_5937_lessThan__iff,axiom,
% 3.82/4.08 ! [I: set_nat,K: set_nat] :
% 3.82/4.08 ( ( member_set_nat @ I @ ( set_or890127255671739683et_nat @ K ) )
% 3.82/4.08 = ( ord_less_set_nat @ I @ K ) ) ).
% 3.82/4.08
% 3.82/4.08 % lessThan_iff
% 3.82/4.08 thf(fact_5938_lessThan__iff,axiom,
% 3.82/4.08 ! [I: extended_enat,K: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ I @ ( set_or8419480210114673929d_enat @ K ) )
% 3.82/4.08 = ( ord_le72135733267957522d_enat @ I @ K ) ) ).
% 3.82/4.08
% 3.82/4.08 % lessThan_iff
% 3.82/4.08 thf(fact_5939_lessThan__iff,axiom,
% 3.82/4.08 ! [I: real,K: real] :
% 3.82/4.08 ( ( member_real @ I @ ( set_or5984915006950818249n_real @ K ) )
% 3.82/4.08 = ( ord_less_real @ I @ K ) ) ).
% 3.82/4.08
% 3.82/4.08 % lessThan_iff
% 3.82/4.08 thf(fact_5940_lessThan__iff,axiom,
% 3.82/4.08 ! [I: nat,K: nat] :
% 3.82/4.08 ( ( member_nat @ I @ ( set_ord_lessThan_nat @ K ) )
% 3.82/4.08 = ( ord_less_nat @ I @ K ) ) ).
% 3.82/4.08
% 3.82/4.08 % lessThan_iff
% 3.82/4.08 thf(fact_5941_lessThan__iff,axiom,
% 3.82/4.08 ! [I: int,K: int] :
% 3.82/4.08 ( ( member_int @ I @ ( set_ord_lessThan_int @ K ) )
% 3.82/4.08 = ( ord_less_int @ I @ K ) ) ).
% 3.82/4.08
% 3.82/4.08 % lessThan_iff
% 3.82/4.08 thf(fact_5942_finite__lessThan,axiom,
% 3.82/4.08 ! [K: nat] : ( finite_finite_nat @ ( set_ord_lessThan_nat @ K ) ) ).
% 3.82/4.08
% 3.82/4.08 % finite_lessThan
% 3.82/4.08 thf(fact_5943_lessThan__subset__iff,axiom,
% 3.82/4.08 ! [X: real,Y: real] :
% 3.82/4.08 ( ( ord_less_eq_set_real @ ( set_or5984915006950818249n_real @ X ) @ ( set_or5984915006950818249n_real @ Y ) )
% 3.82/4.08 = ( ord_less_eq_real @ X @ Y ) ) ).
% 3.82/4.08
% 3.82/4.08 % lessThan_subset_iff
% 3.82/4.08 thf(fact_5944_lessThan__subset__iff,axiom,
% 3.82/4.08 ! [X: nat,Y: nat] :
% 3.82/4.08 ( ( ord_less_eq_set_nat @ ( set_ord_lessThan_nat @ X ) @ ( set_ord_lessThan_nat @ Y ) )
% 3.82/4.08 = ( ord_less_eq_nat @ X @ Y ) ) ).
% 3.82/4.08
% 3.82/4.08 % lessThan_subset_iff
% 3.82/4.08 thf(fact_5945_lessThan__subset__iff,axiom,
% 3.82/4.08 ! [X: int,Y: int] :
% 3.82/4.08 ( ( ord_less_eq_set_int @ ( set_ord_lessThan_int @ X ) @ ( set_ord_lessThan_int @ Y ) )
% 3.82/4.08 = ( ord_less_eq_int @ X @ Y ) ) ).
% 3.82/4.08
% 3.82/4.08 % lessThan_subset_iff
% 3.82/4.08 thf(fact_5946_pochhammer__0,axiom,
% 3.82/4.08 ! [A: nat] :
% 3.82/4.08 ( ( comm_s4663373288045622133er_nat @ A @ zero_zero_nat )
% 3.82/4.08 = one_one_nat ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_0
% 3.82/4.08 thf(fact_5947_pochhammer__0,axiom,
% 3.82/4.08 ! [A: int] :
% 3.82/4.08 ( ( comm_s4660882817536571857er_int @ A @ zero_zero_nat )
% 3.82/4.08 = one_one_int ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_0
% 3.82/4.08 thf(fact_5948_pochhammer__0,axiom,
% 3.82/4.08 ! [A: complex] :
% 3.82/4.08 ( ( comm_s2602460028002588243omplex @ A @ zero_zero_nat )
% 3.82/4.08 = one_one_complex ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_0
% 3.82/4.08 thf(fact_5949_pochhammer__0,axiom,
% 3.82/4.08 ! [A: real] :
% 3.82/4.08 ( ( comm_s7457072308508201937r_real @ A @ zero_zero_nat )
% 3.82/4.08 = one_one_real ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_0
% 3.82/4.08 thf(fact_5950_lessThan__0,axiom,
% 3.82/4.08 ( ( set_ord_lessThan_nat @ zero_zero_nat )
% 3.82/4.08 = bot_bot_set_nat ) ).
% 3.82/4.08
% 3.82/4.08 % lessThan_0
% 3.82/4.08 thf(fact_5951_single__Diff__lessThan,axiom,
% 3.82/4.08 ! [K: extended_enat] :
% 3.82/4.08 ( ( minus_925952699566721837d_enat @ ( insert_Extended_enat @ K @ bot_bo7653980558646680370d_enat ) @ ( set_or8419480210114673929d_enat @ K ) )
% 3.82/4.08 = ( insert_Extended_enat @ K @ bot_bo7653980558646680370d_enat ) ) ).
% 3.82/4.08
% 3.82/4.08 % single_Diff_lessThan
% 3.82/4.08 thf(fact_5952_single__Diff__lessThan,axiom,
% 3.82/4.08 ! [K: real] :
% 3.82/4.08 ( ( minus_minus_set_real @ ( insert_real @ K @ bot_bot_set_real ) @ ( set_or5984915006950818249n_real @ K ) )
% 3.82/4.08 = ( insert_real @ K @ bot_bot_set_real ) ) ).
% 3.82/4.08
% 3.82/4.08 % single_Diff_lessThan
% 3.82/4.08 thf(fact_5953_single__Diff__lessThan,axiom,
% 3.82/4.08 ! [K: nat] :
% 3.82/4.08 ( ( minus_minus_set_nat @ ( insert_nat @ K @ bot_bot_set_nat ) @ ( set_ord_lessThan_nat @ K ) )
% 3.82/4.08 = ( insert_nat @ K @ bot_bot_set_nat ) ) ).
% 3.82/4.08
% 3.82/4.08 % single_Diff_lessThan
% 3.82/4.08 thf(fact_5954_single__Diff__lessThan,axiom,
% 3.82/4.08 ! [K: int] :
% 3.82/4.08 ( ( minus_minus_set_int @ ( insert_int @ K @ bot_bot_set_int ) @ ( set_ord_lessThan_int @ K ) )
% 3.82/4.08 = ( insert_int @ K @ bot_bot_set_int ) ) ).
% 3.82/4.08
% 3.82/4.08 % single_Diff_lessThan
% 3.82/4.08 thf(fact_5955_sum_OlessThan__Suc,axiom,
% 3.82/4.08 ! [G: nat > int,N2: nat] :
% 3.82/4.08 ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 3.82/4.08 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % sum.lessThan_Suc
% 3.82/4.08 thf(fact_5956_sum_OlessThan__Suc,axiom,
% 3.82/4.08 ! [G: nat > extended_enat,N2: nat] :
% 3.82/4.08 ( ( groups7108830773950497114d_enat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 3.82/4.08 = ( plus_p3455044024723400733d_enat @ ( groups7108830773950497114d_enat @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % sum.lessThan_Suc
% 3.82/4.08 thf(fact_5957_sum_OlessThan__Suc,axiom,
% 3.82/4.08 ! [G: nat > nat,N2: nat] :
% 3.82/4.08 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 3.82/4.08 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % sum.lessThan_Suc
% 3.82/4.08 thf(fact_5958_sum_OlessThan__Suc,axiom,
% 3.82/4.08 ! [G: nat > real,N2: nat] :
% 3.82/4.08 ( ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 3.82/4.08 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % sum.lessThan_Suc
% 3.82/4.08 thf(fact_5959_int__int__eq,axiom,
% 3.82/4.08 ! [M2: nat,N2: nat] :
% 3.82/4.08 ( ( ( semiri1314217659103216013at_int @ M2 )
% 3.82/4.08 = ( semiri1314217659103216013at_int @ N2 ) )
% 3.82/4.08 = ( M2 = N2 ) ) ).
% 3.82/4.08
% 3.82/4.08 % int_int_eq
% 3.82/4.08 thf(fact_5960_lessThan__non__empty,axiom,
% 3.82/4.08 ! [X: real] :
% 3.82/4.08 ( ( set_or5984915006950818249n_real @ X )
% 3.82/4.08 != bot_bot_set_real ) ).
% 3.82/4.08
% 3.82/4.08 % lessThan_non_empty
% 3.82/4.08 thf(fact_5961_lessThan__non__empty,axiom,
% 3.82/4.08 ! [X: int] :
% 3.82/4.08 ( ( set_ord_lessThan_int @ X )
% 3.82/4.08 != bot_bot_set_int ) ).
% 3.82/4.08
% 3.82/4.08 % lessThan_non_empty
% 3.82/4.08 thf(fact_5962_infinite__Iio,axiom,
% 3.82/4.08 ! [A: int] :
% 3.82/4.08 ~ ( finite_finite_int @ ( set_ord_lessThan_int @ A ) ) ).
% 3.82/4.08
% 3.82/4.08 % infinite_Iio
% 3.82/4.08 thf(fact_5963_lessThan__def,axiom,
% 3.82/4.08 ( set_or890127255671739683et_nat
% 3.82/4.08 = ( ^ [U2: set_nat] :
% 3.82/4.08 ( collect_set_nat
% 3.82/4.08 @ ^ [X4: set_nat] : ( ord_less_set_nat @ X4 @ U2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % lessThan_def
% 3.82/4.08 thf(fact_5964_lessThan__def,axiom,
% 3.82/4.08 ( set_or8419480210114673929d_enat
% 3.82/4.08 = ( ^ [U2: extended_enat] :
% 3.82/4.08 ( collec4429806609662206161d_enat
% 3.82/4.08 @ ^ [X4: extended_enat] : ( ord_le72135733267957522d_enat @ X4 @ U2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % lessThan_def
% 3.82/4.08 thf(fact_5965_lessThan__def,axiom,
% 3.82/4.08 ( set_or5984915006950818249n_real
% 3.82/4.08 = ( ^ [U2: real] :
% 3.82/4.08 ( collect_real
% 3.82/4.08 @ ^ [X4: real] : ( ord_less_real @ X4 @ U2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % lessThan_def
% 3.82/4.08 thf(fact_5966_lessThan__def,axiom,
% 3.82/4.08 ( set_ord_lessThan_nat
% 3.82/4.08 = ( ^ [U2: nat] :
% 3.82/4.08 ( collect_nat
% 3.82/4.08 @ ^ [X4: nat] : ( ord_less_nat @ X4 @ U2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % lessThan_def
% 3.82/4.08 thf(fact_5967_lessThan__def,axiom,
% 3.82/4.08 ( set_ord_lessThan_int
% 3.82/4.08 = ( ^ [U2: int] :
% 3.82/4.08 ( collect_int
% 3.82/4.08 @ ^ [X4: int] : ( ord_less_int @ X4 @ U2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % lessThan_def
% 3.82/4.08 thf(fact_5968_Iio__eq__empty__iff,axiom,
% 3.82/4.08 ! [N2: extended_enat] :
% 3.82/4.08 ( ( ( set_or8419480210114673929d_enat @ N2 )
% 3.82/4.08 = bot_bo7653980558646680370d_enat )
% 3.82/4.08 = ( N2 = bot_bo4199563552545308370d_enat ) ) ).
% 3.82/4.08
% 3.82/4.08 % Iio_eq_empty_iff
% 3.82/4.08 thf(fact_5969_Iio__eq__empty__iff,axiom,
% 3.82/4.08 ! [N2: nat] :
% 3.82/4.08 ( ( ( set_ord_lessThan_nat @ N2 )
% 3.82/4.08 = bot_bot_set_nat )
% 3.82/4.08 = ( N2 = bot_bot_nat ) ) ).
% 3.82/4.08
% 3.82/4.08 % Iio_eq_empty_iff
% 3.82/4.08 thf(fact_5970_lessThan__strict__subset__iff,axiom,
% 3.82/4.08 ! [M2: extended_enat,N2: extended_enat] :
% 3.82/4.08 ( ( ord_le2529575680413868914d_enat @ ( set_or8419480210114673929d_enat @ M2 ) @ ( set_or8419480210114673929d_enat @ N2 ) )
% 3.82/4.08 = ( ord_le72135733267957522d_enat @ M2 @ N2 ) ) ).
% 3.82/4.08
% 3.82/4.08 % lessThan_strict_subset_iff
% 3.82/4.08 thf(fact_5971_lessThan__strict__subset__iff,axiom,
% 3.82/4.08 ! [M2: real,N2: real] :
% 3.82/4.08 ( ( ord_less_set_real @ ( set_or5984915006950818249n_real @ M2 ) @ ( set_or5984915006950818249n_real @ N2 ) )
% 3.82/4.08 = ( ord_less_real @ M2 @ N2 ) ) ).
% 3.82/4.08
% 3.82/4.08 % lessThan_strict_subset_iff
% 3.82/4.08 thf(fact_5972_lessThan__strict__subset__iff,axiom,
% 3.82/4.08 ! [M2: nat,N2: nat] :
% 3.82/4.08 ( ( ord_less_set_nat @ ( set_ord_lessThan_nat @ M2 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 3.82/4.08 = ( ord_less_nat @ M2 @ N2 ) ) ).
% 3.82/4.08
% 3.82/4.08 % lessThan_strict_subset_iff
% 3.82/4.08 thf(fact_5973_lessThan__strict__subset__iff,axiom,
% 3.82/4.08 ! [M2: int,N2: int] :
% 3.82/4.08 ( ( ord_less_set_int @ ( set_ord_lessThan_int @ M2 ) @ ( set_ord_lessThan_int @ N2 ) )
% 3.82/4.08 = ( ord_less_int @ M2 @ N2 ) ) ).
% 3.82/4.08
% 3.82/4.08 % lessThan_strict_subset_iff
% 3.82/4.08 thf(fact_5974_pochhammer__pos,axiom,
% 3.82/4.08 ! [X: nat,N2: nat] :
% 3.82/4.08 ( ( ord_less_nat @ zero_zero_nat @ X )
% 3.82/4.08 => ( ord_less_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X @ N2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_pos
% 3.82/4.08 thf(fact_5975_pochhammer__pos,axiom,
% 3.82/4.08 ! [X: real,N2: nat] :
% 3.82/4.08 ( ( ord_less_real @ zero_zero_real @ X )
% 3.82/4.08 => ( ord_less_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X @ N2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_pos
% 3.82/4.08 thf(fact_5976_pochhammer__pos,axiom,
% 3.82/4.08 ! [X: int,N2: nat] :
% 3.82/4.08 ( ( ord_less_int @ zero_zero_int @ X )
% 3.82/4.08 => ( ord_less_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X @ N2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_pos
% 3.82/4.08 thf(fact_5977_pochhammer__eq__0__mono,axiom,
% 3.82/4.08 ! [A: real,N2: nat,M2: nat] :
% 3.82/4.08 ( ( ( comm_s7457072308508201937r_real @ A @ N2 )
% 3.82/4.08 = zero_zero_real )
% 3.82/4.08 => ( ( ord_less_eq_nat @ N2 @ M2 )
% 3.82/4.08 => ( ( comm_s7457072308508201937r_real @ A @ M2 )
% 3.82/4.08 = zero_zero_real ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_eq_0_mono
% 3.82/4.08 thf(fact_5978_pochhammer__eq__0__mono,axiom,
% 3.82/4.08 ! [A: complex,N2: nat,M2: nat] :
% 3.82/4.08 ( ( ( comm_s2602460028002588243omplex @ A @ N2 )
% 3.82/4.08 = zero_zero_complex )
% 3.82/4.08 => ( ( ord_less_eq_nat @ N2 @ M2 )
% 3.82/4.08 => ( ( comm_s2602460028002588243omplex @ A @ M2 )
% 3.82/4.08 = zero_zero_complex ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_eq_0_mono
% 3.82/4.08 thf(fact_5979_pochhammer__neq__0__mono,axiom,
% 3.82/4.08 ! [A: real,M2: nat,N2: nat] :
% 3.82/4.08 ( ( ( comm_s7457072308508201937r_real @ A @ M2 )
% 3.82/4.08 != zero_zero_real )
% 3.82/4.08 => ( ( ord_less_eq_nat @ N2 @ M2 )
% 3.82/4.08 => ( ( comm_s7457072308508201937r_real @ A @ N2 )
% 3.82/4.08 != zero_zero_real ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_neq_0_mono
% 3.82/4.08 thf(fact_5980_pochhammer__neq__0__mono,axiom,
% 3.82/4.08 ! [A: complex,M2: nat,N2: nat] :
% 3.82/4.08 ( ( ( comm_s2602460028002588243omplex @ A @ M2 )
% 3.82/4.08 != zero_zero_complex )
% 3.82/4.08 => ( ( ord_less_eq_nat @ N2 @ M2 )
% 3.82/4.08 => ( ( comm_s2602460028002588243omplex @ A @ N2 )
% 3.82/4.08 != zero_zero_complex ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_neq_0_mono
% 3.82/4.08 thf(fact_5981_lessThan__Suc,axiom,
% 3.82/4.08 ! [K: nat] :
% 3.82/4.08 ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 3.82/4.08 = ( insert_nat @ K @ ( set_ord_lessThan_nat @ K ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % lessThan_Suc
% 3.82/4.08 thf(fact_5982_lessThan__empty__iff,axiom,
% 3.82/4.08 ! [N2: nat] :
% 3.82/4.08 ( ( ( set_ord_lessThan_nat @ N2 )
% 3.82/4.08 = bot_bot_set_nat )
% 3.82/4.08 = ( N2 = zero_zero_nat ) ) ).
% 3.82/4.08
% 3.82/4.08 % lessThan_empty_iff
% 3.82/4.08 thf(fact_5983_finite__nat__bounded,axiom,
% 3.82/4.08 ! [S2: set_nat] :
% 3.82/4.08 ( ( finite_finite_nat @ S2 )
% 3.82/4.08 => ? [K3: nat] : ( ord_less_eq_set_nat @ S2 @ ( set_ord_lessThan_nat @ K3 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % finite_nat_bounded
% 3.82/4.08 thf(fact_5984_finite__nat__iff__bounded,axiom,
% 3.82/4.08 ( finite_finite_nat
% 3.82/4.08 = ( ^ [S6: set_nat] :
% 3.82/4.08 ? [K2: nat] : ( ord_less_eq_set_nat @ S6 @ ( set_ord_lessThan_nat @ K2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % finite_nat_iff_bounded
% 3.82/4.08 thf(fact_5985_pochhammer__nonneg,axiom,
% 3.82/4.08 ! [X: real,N2: nat] :
% 3.82/4.08 ( ( ord_less_real @ zero_zero_real @ X )
% 3.82/4.08 => ( ord_less_eq_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X @ N2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_nonneg
% 3.82/4.08 thf(fact_5986_pochhammer__nonneg,axiom,
% 3.82/4.08 ! [X: nat,N2: nat] :
% 3.82/4.08 ( ( ord_less_nat @ zero_zero_nat @ X )
% 3.82/4.08 => ( ord_less_eq_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X @ N2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_nonneg
% 3.82/4.08 thf(fact_5987_pochhammer__nonneg,axiom,
% 3.82/4.08 ! [X: int,N2: nat] :
% 3.82/4.08 ( ( ord_less_int @ zero_zero_int @ X )
% 3.82/4.08 => ( ord_less_eq_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X @ N2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_nonneg
% 3.82/4.08 thf(fact_5988_pochhammer__0__left,axiom,
% 3.82/4.08 ! [N2: nat] :
% 3.82/4.08 ( ( ( N2 = zero_zero_nat )
% 3.82/4.08 => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N2 )
% 3.82/4.08 = one_one_nat ) )
% 3.82/4.08 & ( ( N2 != zero_zero_nat )
% 3.82/4.08 => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N2 )
% 3.82/4.08 = zero_zero_nat ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_0_left
% 3.82/4.08 thf(fact_5989_pochhammer__0__left,axiom,
% 3.82/4.08 ! [N2: nat] :
% 3.82/4.08 ( ( ( N2 = zero_zero_nat )
% 3.82/4.08 => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N2 )
% 3.82/4.08 = one_one_real ) )
% 3.82/4.08 & ( ( N2 != zero_zero_nat )
% 3.82/4.08 => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N2 )
% 3.82/4.08 = zero_zero_real ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_0_left
% 3.82/4.08 thf(fact_5990_pochhammer__0__left,axiom,
% 3.82/4.08 ! [N2: nat] :
% 3.82/4.08 ( ( ( N2 = zero_zero_nat )
% 3.82/4.08 => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N2 )
% 3.82/4.08 = one_one_int ) )
% 3.82/4.08 & ( ( N2 != zero_zero_nat )
% 3.82/4.08 => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N2 )
% 3.82/4.08 = zero_zero_int ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_0_left
% 3.82/4.08 thf(fact_5991_pochhammer__0__left,axiom,
% 3.82/4.08 ! [N2: nat] :
% 3.82/4.08 ( ( ( N2 = zero_zero_nat )
% 3.82/4.08 => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N2 )
% 3.82/4.08 = one_one_complex ) )
% 3.82/4.08 & ( ( N2 != zero_zero_nat )
% 3.82/4.08 => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N2 )
% 3.82/4.08 = zero_zero_complex ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_0_left
% 3.82/4.08 thf(fact_5992_pochhammer__0__left,axiom,
% 3.82/4.08 ! [N2: nat] :
% 3.82/4.08 ( ( ( N2 = zero_zero_nat )
% 3.82/4.08 => ( ( comm_s3181272606743183617d_enat @ zero_z5237406670263579293d_enat @ N2 )
% 3.82/4.08 = one_on7984719198319812577d_enat ) )
% 3.82/4.08 & ( ( N2 != zero_zero_nat )
% 3.82/4.08 => ( ( comm_s3181272606743183617d_enat @ zero_z5237406670263579293d_enat @ N2 )
% 3.82/4.08 = zero_z5237406670263579293d_enat ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_0_left
% 3.82/4.08 thf(fact_5993_lessThan__nat__numeral,axiom,
% 3.82/4.08 ! [K: num] :
% 3.82/4.08 ( ( set_ord_lessThan_nat @ ( numeral_numeral_nat @ K ) )
% 3.82/4.08 = ( insert_nat @ ( pred_numeral @ K ) @ ( set_ord_lessThan_nat @ ( pred_numeral @ K ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % lessThan_nat_numeral
% 3.82/4.08 thf(fact_5994_sum_Onat__diff__reindex,axiom,
% 3.82/4.08 ! [G: nat > nat,N2: nat] :
% 3.82/4.08 ( ( groups3542108847815614940at_nat
% 3.82/4.08 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) )
% 3.82/4.08 @ ( set_ord_lessThan_nat @ N2 ) )
% 3.82/4.08 = ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % sum.nat_diff_reindex
% 3.82/4.08 thf(fact_5995_sum_Onat__diff__reindex,axiom,
% 3.82/4.08 ! [G: nat > real,N2: nat] :
% 3.82/4.08 ( ( groups6591440286371151544t_real
% 3.82/4.08 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) )
% 3.82/4.08 @ ( set_ord_lessThan_nat @ N2 ) )
% 3.82/4.08 = ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % sum.nat_diff_reindex
% 3.82/4.08 thf(fact_5996_sum__diff__distrib,axiom,
% 3.82/4.08 ! [Q: int > nat,P: int > nat,N2: int] :
% 3.82/4.08 ( ! [X5: int] : ( ord_less_eq_nat @ ( Q @ X5 ) @ ( P @ X5 ) )
% 3.82/4.08 => ( ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ P @ ( set_ord_lessThan_int @ N2 ) ) @ ( groups4541462559716669496nt_nat @ Q @ ( set_ord_lessThan_int @ N2 ) ) )
% 3.82/4.08 = ( groups4541462559716669496nt_nat
% 3.82/4.08 @ ^ [X4: int] : ( minus_minus_nat @ ( P @ X4 ) @ ( Q @ X4 ) )
% 3.82/4.08 @ ( set_ord_lessThan_int @ N2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % sum_diff_distrib
% 3.82/4.08 thf(fact_5997_sum__diff__distrib,axiom,
% 3.82/4.08 ! [Q: nat > nat,P: nat > nat,N2: nat] :
% 3.82/4.08 ( ! [X5: nat] : ( ord_less_eq_nat @ ( Q @ X5 ) @ ( P @ X5 ) )
% 3.82/4.08 => ( ( minus_minus_nat @ ( groups3542108847815614940at_nat @ P @ ( set_ord_lessThan_nat @ N2 ) ) @ ( groups3542108847815614940at_nat @ Q @ ( set_ord_lessThan_nat @ N2 ) ) )
% 3.82/4.08 = ( groups3542108847815614940at_nat
% 3.82/4.08 @ ^ [X4: nat] : ( minus_minus_nat @ ( P @ X4 ) @ ( Q @ X4 ) )
% 3.82/4.08 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % sum_diff_distrib
% 3.82/4.08 thf(fact_5998_log__of__power__le,axiom,
% 3.82/4.08 ! [M2: nat,B2: real,N2: nat] :
% 3.82/4.08 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( power_power_real @ B2 @ N2 ) )
% 3.82/4.08 => ( ( ord_less_real @ one_one_real @ B2 )
% 3.82/4.08 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 3.82/4.08 => ( ord_less_eq_real @ ( log @ B2 @ ( semiri5074537144036343181t_real @ M2 ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % log_of_power_le
% 3.82/4.08 thf(fact_5999_log__of__power__less,axiom,
% 3.82/4.08 ! [M2: nat,B2: real,N2: nat] :
% 3.82/4.08 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( power_power_real @ B2 @ N2 ) )
% 3.82/4.08 => ( ( ord_less_real @ one_one_real @ B2 )
% 3.82/4.08 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 3.82/4.08 => ( ord_less_real @ ( log @ B2 @ ( semiri5074537144036343181t_real @ M2 ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % log_of_power_less
% 3.82/4.08 thf(fact_6000_pochhammer__rec,axiom,
% 3.82/4.08 ! [A: nat,N2: nat] :
% 3.82/4.08 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N2 ) )
% 3.82/4.08 = ( times_times_nat @ A @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ N2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_rec
% 3.82/4.08 thf(fact_6001_pochhammer__rec,axiom,
% 3.82/4.08 ! [A: int,N2: nat] :
% 3.82/4.08 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N2 ) )
% 3.82/4.08 = ( times_times_int @ A @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ one_one_int ) @ N2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_rec
% 3.82/4.08 thf(fact_6002_pochhammer__rec,axiom,
% 3.82/4.08 ! [A: real,N2: nat] :
% 3.82/4.08 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N2 ) )
% 3.82/4.08 = ( times_times_real @ A @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ A @ one_one_real ) @ N2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_rec
% 3.82/4.08 thf(fact_6003_pochhammer__rec,axiom,
% 3.82/4.08 ! [A: complex,N2: nat] :
% 3.82/4.08 ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N2 ) )
% 3.82/4.08 = ( times_times_complex @ A @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ N2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_rec
% 3.82/4.08 thf(fact_6004_pochhammer__rec,axiom,
% 3.82/4.08 ! [A: extended_enat,N2: nat] :
% 3.82/4.08 ( ( comm_s3181272606743183617d_enat @ A @ ( suc @ N2 ) )
% 3.82/4.08 = ( times_7803423173614009249d_enat @ A @ ( comm_s3181272606743183617d_enat @ ( plus_p3455044024723400733d_enat @ A @ one_on7984719198319812577d_enat ) @ N2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_rec
% 3.82/4.08 thf(fact_6005_pochhammer__rec_H,axiom,
% 3.82/4.08 ! [Z3: complex,N2: nat] :
% 3.82/4.08 ( ( comm_s2602460028002588243omplex @ Z3 @ ( suc @ N2 ) )
% 3.82/4.08 = ( times_times_complex @ ( plus_plus_complex @ Z3 @ ( semiri8010041392384452111omplex @ N2 ) ) @ ( comm_s2602460028002588243omplex @ Z3 @ N2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_rec'
% 3.82/4.08 thf(fact_6006_pochhammer__rec_H,axiom,
% 3.82/4.08 ! [Z3: extended_enat,N2: nat] :
% 3.82/4.08 ( ( comm_s3181272606743183617d_enat @ Z3 @ ( suc @ N2 ) )
% 3.82/4.08 = ( times_7803423173614009249d_enat @ ( plus_p3455044024723400733d_enat @ Z3 @ ( semiri4216267220026989637d_enat @ N2 ) ) @ ( comm_s3181272606743183617d_enat @ Z3 @ N2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_rec'
% 3.82/4.08 thf(fact_6007_pochhammer__rec_H,axiom,
% 3.82/4.08 ! [Z3: real,N2: nat] :
% 3.82/4.08 ( ( comm_s7457072308508201937r_real @ Z3 @ ( suc @ N2 ) )
% 3.82/4.08 = ( times_times_real @ ( plus_plus_real @ Z3 @ ( semiri5074537144036343181t_real @ N2 ) ) @ ( comm_s7457072308508201937r_real @ Z3 @ N2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_rec'
% 3.82/4.08 thf(fact_6008_pochhammer__rec_H,axiom,
% 3.82/4.08 ! [Z3: int,N2: nat] :
% 3.82/4.08 ( ( comm_s4660882817536571857er_int @ Z3 @ ( suc @ N2 ) )
% 3.82/4.08 = ( times_times_int @ ( plus_plus_int @ Z3 @ ( semiri1314217659103216013at_int @ N2 ) ) @ ( comm_s4660882817536571857er_int @ Z3 @ N2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_rec'
% 3.82/4.08 thf(fact_6009_pochhammer__rec_H,axiom,
% 3.82/4.08 ! [Z3: nat,N2: nat] :
% 3.82/4.08 ( ( comm_s4663373288045622133er_nat @ Z3 @ ( suc @ N2 ) )
% 3.82/4.08 = ( times_times_nat @ ( plus_plus_nat @ Z3 @ ( semiri1316708129612266289at_nat @ N2 ) ) @ ( comm_s4663373288045622133er_nat @ Z3 @ N2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_rec'
% 3.82/4.08 thf(fact_6010_pochhammer__Suc,axiom,
% 3.82/4.08 ! [A: complex,N2: nat] :
% 3.82/4.08 ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N2 ) )
% 3.82/4.08 = ( times_times_complex @ ( comm_s2602460028002588243omplex @ A @ N2 ) @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ N2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_Suc
% 3.82/4.08 thf(fact_6011_pochhammer__Suc,axiom,
% 3.82/4.08 ! [A: extended_enat,N2: nat] :
% 3.82/4.08 ( ( comm_s3181272606743183617d_enat @ A @ ( suc @ N2 ) )
% 3.82/4.08 = ( times_7803423173614009249d_enat @ ( comm_s3181272606743183617d_enat @ A @ N2 ) @ ( plus_p3455044024723400733d_enat @ A @ ( semiri4216267220026989637d_enat @ N2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_Suc
% 3.82/4.08 thf(fact_6012_pochhammer__Suc,axiom,
% 3.82/4.08 ! [A: real,N2: nat] :
% 3.82/4.08 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N2 ) )
% 3.82/4.08 = ( times_times_real @ ( comm_s7457072308508201937r_real @ A @ N2 ) @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_Suc
% 3.82/4.08 thf(fact_6013_pochhammer__Suc,axiom,
% 3.82/4.08 ! [A: int,N2: nat] :
% 3.82/4.08 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N2 ) )
% 3.82/4.08 = ( times_times_int @ ( comm_s4660882817536571857er_int @ A @ N2 ) @ ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_Suc
% 3.82/4.08 thf(fact_6014_pochhammer__Suc,axiom,
% 3.82/4.08 ! [A: nat,N2: nat] :
% 3.82/4.08 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N2 ) )
% 3.82/4.08 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ A @ N2 ) @ ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_Suc
% 3.82/4.08 thf(fact_6015_pochhammer__of__nat__eq__0__lemma,axiom,
% 3.82/4.08 ! [N2: nat,K: nat] :
% 3.82/4.08 ( ( ord_less_nat @ N2 @ K )
% 3.82/4.08 => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N2 ) ) @ K )
% 3.82/4.08 = zero_zero_complex ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_of_nat_eq_0_lemma
% 3.82/4.08 thf(fact_6016_pochhammer__of__nat__eq__0__lemma,axiom,
% 3.82/4.08 ! [N2: nat,K: nat] :
% 3.82/4.08 ( ( ord_less_nat @ N2 @ K )
% 3.82/4.08 => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ K )
% 3.82/4.08 = zero_zero_real ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_of_nat_eq_0_lemma
% 3.82/4.08 thf(fact_6017_pochhammer__of__nat__eq__0__lemma,axiom,
% 3.82/4.08 ! [N2: nat,K: nat] :
% 3.82/4.08 ( ( ord_less_nat @ N2 @ K )
% 3.82/4.08 => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ K )
% 3.82/4.08 = zero_zero_int ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_of_nat_eq_0_lemma
% 3.82/4.08 thf(fact_6018_pochhammer__of__nat__eq__0__iff,axiom,
% 3.82/4.08 ! [N2: nat,K: nat] :
% 3.82/4.08 ( ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N2 ) ) @ K )
% 3.82/4.08 = zero_zero_complex )
% 3.82/4.08 = ( ord_less_nat @ N2 @ K ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_of_nat_eq_0_iff
% 3.82/4.08 thf(fact_6019_pochhammer__of__nat__eq__0__iff,axiom,
% 3.82/4.08 ! [N2: nat,K: nat] :
% 3.82/4.08 ( ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ K )
% 3.82/4.08 = zero_zero_real )
% 3.82/4.08 = ( ord_less_nat @ N2 @ K ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_of_nat_eq_0_iff
% 3.82/4.08 thf(fact_6020_pochhammer__of__nat__eq__0__iff,axiom,
% 3.82/4.08 ! [N2: nat,K: nat] :
% 3.82/4.08 ( ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ K )
% 3.82/4.08 = zero_zero_int )
% 3.82/4.08 = ( ord_less_nat @ N2 @ K ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_of_nat_eq_0_iff
% 3.82/4.08 thf(fact_6021_pochhammer__eq__0__iff,axiom,
% 3.82/4.08 ! [A: complex,N2: nat] :
% 3.82/4.08 ( ( ( comm_s2602460028002588243omplex @ A @ N2 )
% 3.82/4.08 = zero_zero_complex )
% 3.82/4.08 = ( ? [K2: nat] :
% 3.82/4.08 ( ( ord_less_nat @ K2 @ N2 )
% 3.82/4.08 & ( A
% 3.82/4.08 = ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ K2 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_eq_0_iff
% 3.82/4.08 thf(fact_6022_pochhammer__eq__0__iff,axiom,
% 3.82/4.08 ! [A: real,N2: nat] :
% 3.82/4.08 ( ( ( comm_s7457072308508201937r_real @ A @ N2 )
% 3.82/4.08 = zero_zero_real )
% 3.82/4.08 = ( ? [K2: nat] :
% 3.82/4.08 ( ( ord_less_nat @ K2 @ N2 )
% 3.82/4.08 & ( A
% 3.82/4.08 = ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ K2 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_eq_0_iff
% 3.82/4.08 thf(fact_6023_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 3.82/4.08 ! [K: nat,N2: nat] :
% 3.82/4.08 ( ( ord_less_eq_nat @ K @ N2 )
% 3.82/4.08 => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N2 ) ) @ K )
% 3.82/4.08 != zero_zero_complex ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_of_nat_eq_0_lemma'
% 3.82/4.08 thf(fact_6024_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 3.82/4.08 ! [K: nat,N2: nat] :
% 3.82/4.08 ( ( ord_less_eq_nat @ K @ N2 )
% 3.82/4.08 => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ K )
% 3.82/4.08 != zero_zero_real ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_of_nat_eq_0_lemma'
% 3.82/4.08 thf(fact_6025_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 3.82/4.08 ! [K: nat,N2: nat] :
% 3.82/4.08 ( ( ord_less_eq_nat @ K @ N2 )
% 3.82/4.08 => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ K )
% 3.82/4.08 != zero_zero_int ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_of_nat_eq_0_lemma'
% 3.82/4.08 thf(fact_6026_pochhammer__product_H,axiom,
% 3.82/4.08 ! [Z3: complex,N2: nat,M2: nat] :
% 3.82/4.08 ( ( comm_s2602460028002588243omplex @ Z3 @ ( plus_plus_nat @ N2 @ M2 ) )
% 3.82/4.08 = ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z3 @ N2 ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z3 @ ( semiri8010041392384452111omplex @ N2 ) ) @ M2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_product'
% 3.82/4.08 thf(fact_6027_pochhammer__product_H,axiom,
% 3.82/4.08 ! [Z3: extended_enat,N2: nat,M2: nat] :
% 3.82/4.08 ( ( comm_s3181272606743183617d_enat @ Z3 @ ( plus_plus_nat @ N2 @ M2 ) )
% 3.82/4.08 = ( times_7803423173614009249d_enat @ ( comm_s3181272606743183617d_enat @ Z3 @ N2 ) @ ( comm_s3181272606743183617d_enat @ ( plus_p3455044024723400733d_enat @ Z3 @ ( semiri4216267220026989637d_enat @ N2 ) ) @ M2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_product'
% 3.82/4.08 thf(fact_6028_pochhammer__product_H,axiom,
% 3.82/4.08 ! [Z3: real,N2: nat,M2: nat] :
% 3.82/4.08 ( ( comm_s7457072308508201937r_real @ Z3 @ ( plus_plus_nat @ N2 @ M2 ) )
% 3.82/4.08 = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z3 @ N2 ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z3 @ ( semiri5074537144036343181t_real @ N2 ) ) @ M2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_product'
% 3.82/4.08 thf(fact_6029_pochhammer__product_H,axiom,
% 3.82/4.08 ! [Z3: int,N2: nat,M2: nat] :
% 3.82/4.08 ( ( comm_s4660882817536571857er_int @ Z3 @ ( plus_plus_nat @ N2 @ M2 ) )
% 3.82/4.08 = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z3 @ N2 ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z3 @ ( semiri1314217659103216013at_int @ N2 ) ) @ M2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_product'
% 3.82/4.08 thf(fact_6030_pochhammer__product_H,axiom,
% 3.82/4.08 ! [Z3: nat,N2: nat,M2: nat] :
% 3.82/4.08 ( ( comm_s4663373288045622133er_nat @ Z3 @ ( plus_plus_nat @ N2 @ M2 ) )
% 3.82/4.08 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z3 @ N2 ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z3 @ ( semiri1316708129612266289at_nat @ N2 ) ) @ M2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_product'
% 3.82/4.08 thf(fact_6031_sum_OlessThan__Suc__shift,axiom,
% 3.82/4.08 ! [G: nat > int,N2: nat] :
% 3.82/4.08 ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 3.82/4.08 = ( plus_plus_int @ ( G @ zero_zero_nat )
% 3.82/4.08 @ ( groups3539618377306564664at_int
% 3.82/4.08 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 3.82/4.08 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % sum.lessThan_Suc_shift
% 3.82/4.08 thf(fact_6032_sum_OlessThan__Suc__shift,axiom,
% 3.82/4.08 ! [G: nat > extended_enat,N2: nat] :
% 3.82/4.08 ( ( groups7108830773950497114d_enat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 3.82/4.08 = ( plus_p3455044024723400733d_enat @ ( G @ zero_zero_nat )
% 3.82/4.08 @ ( groups7108830773950497114d_enat
% 3.82/4.08 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 3.82/4.08 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % sum.lessThan_Suc_shift
% 3.82/4.08 thf(fact_6033_sum_OlessThan__Suc__shift,axiom,
% 3.82/4.08 ! [G: nat > nat,N2: nat] :
% 3.82/4.08 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 3.82/4.08 = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 3.82/4.08 @ ( groups3542108847815614940at_nat
% 3.82/4.08 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 3.82/4.08 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % sum.lessThan_Suc_shift
% 3.82/4.08 thf(fact_6034_sum_OlessThan__Suc__shift,axiom,
% 3.82/4.08 ! [G: nat > real,N2: nat] :
% 3.82/4.08 ( ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 3.82/4.08 = ( plus_plus_real @ ( G @ zero_zero_nat )
% 3.82/4.08 @ ( groups6591440286371151544t_real
% 3.82/4.08 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 3.82/4.08 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % sum.lessThan_Suc_shift
% 3.82/4.08 thf(fact_6035_sum__lessThan__telescope,axiom,
% 3.82/4.08 ! [F: nat > int,M2: nat] :
% 3.82/4.08 ( ( groups3539618377306564664at_int
% 3.82/4.08 @ ^ [N: nat] : ( minus_minus_int @ ( F @ ( suc @ N ) ) @ ( F @ N ) )
% 3.82/4.08 @ ( set_ord_lessThan_nat @ M2 ) )
% 3.82/4.08 = ( minus_minus_int @ ( F @ M2 ) @ ( F @ zero_zero_nat ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % sum_lessThan_telescope
% 3.82/4.08 thf(fact_6036_sum__lessThan__telescope,axiom,
% 3.82/4.08 ! [F: nat > real,M2: nat] :
% 3.82/4.08 ( ( groups6591440286371151544t_real
% 3.82/4.08 @ ^ [N: nat] : ( minus_minus_real @ ( F @ ( suc @ N ) ) @ ( F @ N ) )
% 3.82/4.08 @ ( set_ord_lessThan_nat @ M2 ) )
% 3.82/4.08 = ( minus_minus_real @ ( F @ M2 ) @ ( F @ zero_zero_nat ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % sum_lessThan_telescope
% 3.82/4.08 thf(fact_6037_sum__lessThan__telescope_H,axiom,
% 3.82/4.08 ! [F: nat > int,M2: nat] :
% 3.82/4.08 ( ( groups3539618377306564664at_int
% 3.82/4.08 @ ^ [N: nat] : ( minus_minus_int @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 3.82/4.08 @ ( set_ord_lessThan_nat @ M2 ) )
% 3.82/4.08 = ( minus_minus_int @ ( F @ zero_zero_nat ) @ ( F @ M2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % sum_lessThan_telescope'
% 3.82/4.08 thf(fact_6038_sum__lessThan__telescope_H,axiom,
% 3.82/4.08 ! [F: nat > real,M2: nat] :
% 3.82/4.08 ( ( groups6591440286371151544t_real
% 3.82/4.08 @ ^ [N: nat] : ( minus_minus_real @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 3.82/4.08 @ ( set_ord_lessThan_nat @ M2 ) )
% 3.82/4.08 = ( minus_minus_real @ ( F @ zero_zero_nat ) @ ( F @ M2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % sum_lessThan_telescope'
% 3.82/4.08 thf(fact_6039_sum_OatLeast1__atMost__eq,axiom,
% 3.82/4.08 ! [G: nat > nat,N2: nat] :
% 3.82/4.08 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 3.82/4.08 = ( groups3542108847815614940at_nat
% 3.82/4.08 @ ^ [K2: nat] : ( G @ ( suc @ K2 ) )
% 3.82/4.08 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % sum.atLeast1_atMost_eq
% 3.82/4.08 thf(fact_6040_sum_OatLeast1__atMost__eq,axiom,
% 3.82/4.08 ! [G: nat > real,N2: nat] :
% 3.82/4.08 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 3.82/4.08 = ( groups6591440286371151544t_real
% 3.82/4.08 @ ^ [K2: nat] : ( G @ ( suc @ K2 ) )
% 3.82/4.08 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % sum.atLeast1_atMost_eq
% 3.82/4.08 thf(fact_6041_le__log2__of__power,axiom,
% 3.82/4.08 ! [N2: nat,M2: nat] :
% 3.82/4.08 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ M2 )
% 3.82/4.08 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % le_log2_of_power
% 3.82/4.08 thf(fact_6042_one__diff__power__eq,axiom,
% 3.82/4.08 ! [X: int,N2: nat] :
% 3.82/4.08 ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ N2 ) )
% 3.82/4.08 = ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % one_diff_power_eq
% 3.82/4.08 thf(fact_6043_one__diff__power__eq,axiom,
% 3.82/4.08 ! [X: complex,N2: nat] :
% 3.82/4.08 ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ N2 ) )
% 3.82/4.08 = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % one_diff_power_eq
% 3.82/4.08 thf(fact_6044_one__diff__power__eq,axiom,
% 3.82/4.08 ! [X: real,N2: nat] :
% 3.82/4.08 ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ N2 ) )
% 3.82/4.08 = ( times_times_real @ ( minus_minus_real @ one_one_real @ X ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % one_diff_power_eq
% 3.82/4.08 thf(fact_6045_power__diff__1__eq,axiom,
% 3.82/4.08 ! [X: int,N2: nat] :
% 3.82/4.08 ( ( minus_minus_int @ ( power_power_int @ X @ N2 ) @ one_one_int )
% 3.82/4.08 = ( times_times_int @ ( minus_minus_int @ X @ one_one_int ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % power_diff_1_eq
% 3.82/4.08 thf(fact_6046_power__diff__1__eq,axiom,
% 3.82/4.08 ! [X: complex,N2: nat] :
% 3.82/4.08 ( ( minus_minus_complex @ ( power_power_complex @ X @ N2 ) @ one_one_complex )
% 3.82/4.08 = ( times_times_complex @ ( minus_minus_complex @ X @ one_one_complex ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % power_diff_1_eq
% 3.82/4.08 thf(fact_6047_power__diff__1__eq,axiom,
% 3.82/4.08 ! [X: real,N2: nat] :
% 3.82/4.08 ( ( minus_minus_real @ ( power_power_real @ X @ N2 ) @ one_one_real )
% 3.82/4.08 = ( times_times_real @ ( minus_minus_real @ X @ one_one_real ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % power_diff_1_eq
% 3.82/4.08 thf(fact_6048_geometric__sum,axiom,
% 3.82/4.08 ! [X: complex,N2: nat] :
% 3.82/4.08 ( ( X != one_one_complex )
% 3.82/4.08 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N2 ) )
% 3.82/4.08 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X @ N2 ) @ one_one_complex ) @ ( minus_minus_complex @ X @ one_one_complex ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % geometric_sum
% 3.82/4.08 thf(fact_6049_geometric__sum,axiom,
% 3.82/4.08 ! [X: real,N2: nat] :
% 3.82/4.08 ( ( X != one_one_real )
% 3.82/4.08 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N2 ) )
% 3.82/4.08 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X @ N2 ) @ one_one_real ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % geometric_sum
% 3.82/4.08 thf(fact_6050_pochhammer__product,axiom,
% 3.82/4.08 ! [M2: nat,N2: nat,Z3: complex] :
% 3.82/4.08 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.08 => ( ( comm_s2602460028002588243omplex @ Z3 @ N2 )
% 3.82/4.08 = ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z3 @ M2 ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z3 @ ( semiri8010041392384452111omplex @ M2 ) ) @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_product
% 3.82/4.08 thf(fact_6051_pochhammer__product,axiom,
% 3.82/4.08 ! [M2: nat,N2: nat,Z3: extended_enat] :
% 3.82/4.08 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.08 => ( ( comm_s3181272606743183617d_enat @ Z3 @ N2 )
% 3.82/4.08 = ( times_7803423173614009249d_enat @ ( comm_s3181272606743183617d_enat @ Z3 @ M2 ) @ ( comm_s3181272606743183617d_enat @ ( plus_p3455044024723400733d_enat @ Z3 @ ( semiri4216267220026989637d_enat @ M2 ) ) @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_product
% 3.82/4.08 thf(fact_6052_pochhammer__product,axiom,
% 3.82/4.08 ! [M2: nat,N2: nat,Z3: real] :
% 3.82/4.08 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.08 => ( ( comm_s7457072308508201937r_real @ Z3 @ N2 )
% 3.82/4.08 = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z3 @ M2 ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z3 @ ( semiri5074537144036343181t_real @ M2 ) ) @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_product
% 3.82/4.08 thf(fact_6053_pochhammer__product,axiom,
% 3.82/4.08 ! [M2: nat,N2: nat,Z3: int] :
% 3.82/4.08 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.08 => ( ( comm_s4660882817536571857er_int @ Z3 @ N2 )
% 3.82/4.08 = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z3 @ M2 ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z3 @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_product
% 3.82/4.08 thf(fact_6054_pochhammer__product,axiom,
% 3.82/4.08 ! [M2: nat,N2: nat,Z3: nat] :
% 3.82/4.08 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.08 => ( ( comm_s4663373288045622133er_nat @ Z3 @ N2 )
% 3.82/4.08 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z3 @ M2 ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z3 @ ( semiri1316708129612266289at_nat @ M2 ) ) @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_product
% 3.82/4.08 thf(fact_6055_less__log2__of__power,axiom,
% 3.82/4.08 ! [N2: nat,M2: nat] :
% 3.82/4.08 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ M2 )
% 3.82/4.08 => ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % less_log2_of_power
% 3.82/4.08 thf(fact_6056_sum__gp__strict,axiom,
% 3.82/4.08 ! [X: complex,N2: nat] :
% 3.82/4.08 ( ( ( X = one_one_complex )
% 3.82/4.08 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N2 ) )
% 3.82/4.08 = ( semiri8010041392384452111omplex @ N2 ) ) )
% 3.82/4.08 & ( ( X != one_one_complex )
% 3.82/4.08 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N2 ) )
% 3.82/4.08 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ N2 ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % sum_gp_strict
% 3.82/4.08 thf(fact_6057_sum__gp__strict,axiom,
% 3.82/4.08 ! [X: real,N2: nat] :
% 3.82/4.08 ( ( ( X = one_one_real )
% 3.82/4.08 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N2 ) )
% 3.82/4.08 = ( semiri5074537144036343181t_real @ N2 ) ) )
% 3.82/4.08 & ( ( X != one_one_real )
% 3.82/4.08 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N2 ) )
% 3.82/4.08 = ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ N2 ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % sum_gp_strict
% 3.82/4.08 thf(fact_6058_lemma__termdiff1,axiom,
% 3.82/4.08 ! [Z3: int,H2: int,M2: nat] :
% 3.82/4.08 ( ( groups3539618377306564664at_int
% 3.82/4.08 @ ^ [P6: nat] : ( minus_minus_int @ ( times_times_int @ ( power_power_int @ ( plus_plus_int @ Z3 @ H2 ) @ ( minus_minus_nat @ M2 @ P6 ) ) @ ( power_power_int @ Z3 @ P6 ) ) @ ( power_power_int @ Z3 @ M2 ) )
% 3.82/4.08 @ ( set_ord_lessThan_nat @ M2 ) )
% 3.82/4.08 = ( groups3539618377306564664at_int
% 3.82/4.08 @ ^ [P6: nat] : ( times_times_int @ ( power_power_int @ Z3 @ P6 ) @ ( minus_minus_int @ ( power_power_int @ ( plus_plus_int @ Z3 @ H2 ) @ ( minus_minus_nat @ M2 @ P6 ) ) @ ( power_power_int @ Z3 @ ( minus_minus_nat @ M2 @ P6 ) ) ) )
% 3.82/4.08 @ ( set_ord_lessThan_nat @ M2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % lemma_termdiff1
% 3.82/4.08 thf(fact_6059_lemma__termdiff1,axiom,
% 3.82/4.08 ! [Z3: complex,H2: complex,M2: nat] :
% 3.82/4.08 ( ( groups2073611262835488442omplex
% 3.82/4.08 @ ^ [P6: nat] : ( minus_minus_complex @ ( times_times_complex @ ( power_power_complex @ ( plus_plus_complex @ Z3 @ H2 ) @ ( minus_minus_nat @ M2 @ P6 ) ) @ ( power_power_complex @ Z3 @ P6 ) ) @ ( power_power_complex @ Z3 @ M2 ) )
% 3.82/4.08 @ ( set_ord_lessThan_nat @ M2 ) )
% 3.82/4.08 = ( groups2073611262835488442omplex
% 3.82/4.08 @ ^ [P6: nat] : ( times_times_complex @ ( power_power_complex @ Z3 @ P6 ) @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z3 @ H2 ) @ ( minus_minus_nat @ M2 @ P6 ) ) @ ( power_power_complex @ Z3 @ ( minus_minus_nat @ M2 @ P6 ) ) ) )
% 3.82/4.08 @ ( set_ord_lessThan_nat @ M2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % lemma_termdiff1
% 3.82/4.08 thf(fact_6060_lemma__termdiff1,axiom,
% 3.82/4.08 ! [Z3: real,H2: real,M2: nat] :
% 3.82/4.08 ( ( groups6591440286371151544t_real
% 3.82/4.08 @ ^ [P6: nat] : ( minus_minus_real @ ( times_times_real @ ( power_power_real @ ( plus_plus_real @ Z3 @ H2 ) @ ( minus_minus_nat @ M2 @ P6 ) ) @ ( power_power_real @ Z3 @ P6 ) ) @ ( power_power_real @ Z3 @ M2 ) )
% 3.82/4.08 @ ( set_ord_lessThan_nat @ M2 ) )
% 3.82/4.08 = ( groups6591440286371151544t_real
% 3.82/4.08 @ ^ [P6: nat] : ( times_times_real @ ( power_power_real @ Z3 @ P6 ) @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z3 @ H2 ) @ ( minus_minus_nat @ M2 @ P6 ) ) @ ( power_power_real @ Z3 @ ( minus_minus_nat @ M2 @ P6 ) ) ) )
% 3.82/4.08 @ ( set_ord_lessThan_nat @ M2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % lemma_termdiff1
% 3.82/4.08 thf(fact_6061_diff__power__eq__sum,axiom,
% 3.82/4.08 ! [X: int,N2: nat,Y: int] :
% 3.82/4.08 ( ( minus_minus_int @ ( power_power_int @ X @ ( suc @ N2 ) ) @ ( power_power_int @ Y @ ( suc @ N2 ) ) )
% 3.82/4.08 = ( times_times_int @ ( minus_minus_int @ X @ Y )
% 3.82/4.08 @ ( groups3539618377306564664at_int
% 3.82/4.08 @ ^ [P6: nat] : ( times_times_int @ ( power_power_int @ X @ P6 ) @ ( power_power_int @ Y @ ( minus_minus_nat @ N2 @ P6 ) ) )
% 3.82/4.08 @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % diff_power_eq_sum
% 3.82/4.08 thf(fact_6062_diff__power__eq__sum,axiom,
% 3.82/4.08 ! [X: complex,N2: nat,Y: complex] :
% 3.82/4.08 ( ( minus_minus_complex @ ( power_power_complex @ X @ ( suc @ N2 ) ) @ ( power_power_complex @ Y @ ( suc @ N2 ) ) )
% 3.82/4.08 = ( times_times_complex @ ( minus_minus_complex @ X @ Y )
% 3.82/4.08 @ ( groups2073611262835488442omplex
% 3.82/4.08 @ ^ [P6: nat] : ( times_times_complex @ ( power_power_complex @ X @ P6 ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ N2 @ P6 ) ) )
% 3.82/4.08 @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % diff_power_eq_sum
% 3.82/4.08 thf(fact_6063_diff__power__eq__sum,axiom,
% 3.82/4.08 ! [X: real,N2: nat,Y: real] :
% 3.82/4.08 ( ( minus_minus_real @ ( power_power_real @ X @ ( suc @ N2 ) ) @ ( power_power_real @ Y @ ( suc @ N2 ) ) )
% 3.82/4.08 = ( times_times_real @ ( minus_minus_real @ X @ Y )
% 3.82/4.08 @ ( groups6591440286371151544t_real
% 3.82/4.08 @ ^ [P6: nat] : ( times_times_real @ ( power_power_real @ X @ P6 ) @ ( power_power_real @ Y @ ( minus_minus_nat @ N2 @ P6 ) ) )
% 3.82/4.08 @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % diff_power_eq_sum
% 3.82/4.08 thf(fact_6064_power__diff__sumr2,axiom,
% 3.82/4.08 ! [X: int,N2: nat,Y: int] :
% 3.82/4.08 ( ( minus_minus_int @ ( power_power_int @ X @ N2 ) @ ( power_power_int @ Y @ N2 ) )
% 3.82/4.08 = ( times_times_int @ ( minus_minus_int @ X @ Y )
% 3.82/4.08 @ ( groups3539618377306564664at_int
% 3.82/4.08 @ ^ [I3: nat] : ( times_times_int @ ( power_power_int @ Y @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) ) @ ( power_power_int @ X @ I3 ) )
% 3.82/4.08 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % power_diff_sumr2
% 3.82/4.08 thf(fact_6065_power__diff__sumr2,axiom,
% 3.82/4.08 ! [X: complex,N2: nat,Y: complex] :
% 3.82/4.08 ( ( minus_minus_complex @ ( power_power_complex @ X @ N2 ) @ ( power_power_complex @ Y @ N2 ) )
% 3.82/4.08 = ( times_times_complex @ ( minus_minus_complex @ X @ Y )
% 3.82/4.08 @ ( groups2073611262835488442omplex
% 3.82/4.08 @ ^ [I3: nat] : ( times_times_complex @ ( power_power_complex @ Y @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) ) @ ( power_power_complex @ X @ I3 ) )
% 3.82/4.08 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % power_diff_sumr2
% 3.82/4.08 thf(fact_6066_power__diff__sumr2,axiom,
% 3.82/4.08 ! [X: real,N2: nat,Y: real] :
% 3.82/4.08 ( ( minus_minus_real @ ( power_power_real @ X @ N2 ) @ ( power_power_real @ Y @ N2 ) )
% 3.82/4.08 = ( times_times_real @ ( minus_minus_real @ X @ Y )
% 3.82/4.08 @ ( groups6591440286371151544t_real
% 3.82/4.08 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ Y @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) ) @ ( power_power_real @ X @ I3 ) )
% 3.82/4.08 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % power_diff_sumr2
% 3.82/4.08 thf(fact_6067_pochhammer__absorb__comp,axiom,
% 3.82/4.08 ! [R2: complex,K: nat] :
% 3.82/4.08 ( ( times_times_complex @ ( minus_minus_complex @ R2 @ ( semiri8010041392384452111omplex @ K ) ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ R2 ) @ K ) )
% 3.82/4.08 = ( times_times_complex @ R2 @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ R2 ) @ one_one_complex ) @ K ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_absorb_comp
% 3.82/4.08 thf(fact_6068_pochhammer__absorb__comp,axiom,
% 3.82/4.08 ! [R2: real,K: nat] :
% 3.82/4.08 ( ( times_times_real @ ( minus_minus_real @ R2 @ ( semiri5074537144036343181t_real @ K ) ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ R2 ) @ K ) )
% 3.82/4.08 = ( times_times_real @ R2 @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( uminus_uminus_real @ R2 ) @ one_one_real ) @ K ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_absorb_comp
% 3.82/4.08 thf(fact_6069_pochhammer__absorb__comp,axiom,
% 3.82/4.08 ! [R2: int,K: nat] :
% 3.82/4.08 ( ( times_times_int @ ( minus_minus_int @ R2 @ ( semiri1314217659103216013at_int @ K ) ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ R2 ) @ K ) )
% 3.82/4.08 = ( times_times_int @ R2 @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( uminus_uminus_int @ R2 ) @ one_one_int ) @ K ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_absorb_comp
% 3.82/4.08 thf(fact_6070_log2__of__power__less,axiom,
% 3.82/4.08 ! [M2: nat,N2: nat] :
% 3.82/4.08 ( ( ord_less_nat @ M2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 3.82/4.08 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 3.82/4.08 => ( ord_less_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M2 ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % log2_of_power_less
% 3.82/4.08 thf(fact_6071_log2__of__power__le,axiom,
% 3.82/4.08 ! [M2: nat,N2: nat] :
% 3.82/4.08 ( ( ord_less_eq_nat @ M2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 3.82/4.08 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 3.82/4.08 => ( ord_less_eq_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M2 ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % log2_of_power_le
% 3.82/4.08 thf(fact_6072_real__sum__nat__ivl__bounded2,axiom,
% 3.82/4.08 ! [N2: nat,F: nat > int,K5: int,K: nat] :
% 3.82/4.08 ( ! [P7: nat] :
% 3.82/4.08 ( ( ord_less_nat @ P7 @ N2 )
% 3.82/4.08 => ( ord_less_eq_int @ ( F @ P7 ) @ K5 ) )
% 3.82/4.08 => ( ( ord_less_eq_int @ zero_zero_int @ K5 )
% 3.82/4.08 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ K5 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % real_sum_nat_ivl_bounded2
% 3.82/4.08 thf(fact_6073_real__sum__nat__ivl__bounded2,axiom,
% 3.82/4.08 ! [N2: nat,F: nat > nat,K5: nat,K: nat] :
% 3.82/4.08 ( ! [P7: nat] :
% 3.82/4.08 ( ( ord_less_nat @ P7 @ N2 )
% 3.82/4.08 => ( ord_less_eq_nat @ ( F @ P7 ) @ K5 ) )
% 3.82/4.08 => ( ( ord_less_eq_nat @ zero_zero_nat @ K5 )
% 3.82/4.08 => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ K5 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % real_sum_nat_ivl_bounded2
% 3.82/4.08 thf(fact_6074_real__sum__nat__ivl__bounded2,axiom,
% 3.82/4.08 ! [N2: nat,F: nat > real,K5: real,K: nat] :
% 3.82/4.08 ( ! [P7: nat] :
% 3.82/4.08 ( ( ord_less_nat @ P7 @ N2 )
% 3.82/4.08 => ( ord_less_eq_real @ ( F @ P7 ) @ K5 ) )
% 3.82/4.08 => ( ( ord_less_eq_real @ zero_zero_real @ K5 )
% 3.82/4.08 => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ K5 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % real_sum_nat_ivl_bounded2
% 3.82/4.08 thf(fact_6075_one__diff__power__eq_H,axiom,
% 3.82/4.08 ! [X: int,N2: nat] :
% 3.82/4.08 ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ N2 ) )
% 3.82/4.08 = ( times_times_int @ ( minus_minus_int @ one_one_int @ X )
% 3.82/4.08 @ ( groups3539618377306564664at_int
% 3.82/4.08 @ ^ [I3: nat] : ( power_power_int @ X @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) )
% 3.82/4.08 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % one_diff_power_eq'
% 3.82/4.08 thf(fact_6076_one__diff__power__eq_H,axiom,
% 3.82/4.08 ! [X: complex,N2: nat] :
% 3.82/4.08 ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ N2 ) )
% 3.82/4.08 = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X )
% 3.82/4.08 @ ( groups2073611262835488442omplex
% 3.82/4.08 @ ^ [I3: nat] : ( power_power_complex @ X @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) )
% 3.82/4.08 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % one_diff_power_eq'
% 3.82/4.08 thf(fact_6077_one__diff__power__eq_H,axiom,
% 3.82/4.08 ! [X: real,N2: nat] :
% 3.82/4.08 ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ N2 ) )
% 3.82/4.08 = ( times_times_real @ ( minus_minus_real @ one_one_real @ X )
% 3.82/4.08 @ ( groups6591440286371151544t_real
% 3.82/4.08 @ ^ [I3: nat] : ( power_power_real @ X @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) )
% 3.82/4.08 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % one_diff_power_eq'
% 3.82/4.08 thf(fact_6078_sum__split__even__odd,axiom,
% 3.82/4.08 ! [F: nat > real,G: nat > real,N2: nat] :
% 3.82/4.08 ( ( groups6591440286371151544t_real
% 3.82/4.08 @ ^ [I3: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) @ ( F @ I3 ) @ ( G @ I3 ) )
% 3.82/4.08 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 3.82/4.08 = ( plus_plus_real
% 3.82/4.08 @ ( groups6591440286371151544t_real
% 3.82/4.08 @ ^ [I3: nat] : ( F @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) )
% 3.82/4.08 @ ( set_ord_lessThan_nat @ N2 ) )
% 3.82/4.08 @ ( groups6591440286371151544t_real
% 3.82/4.08 @ ^ [I3: nat] : ( G @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) @ one_one_nat ) )
% 3.82/4.08 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % sum_split_even_odd
% 3.82/4.08 thf(fact_6079_pochhammer__minus,axiom,
% 3.82/4.08 ! [B2: complex,K: nat] :
% 3.82/4.08 ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B2 ) @ K )
% 3.82/4.08 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ B2 @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ K ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_minus
% 3.82/4.08 thf(fact_6080_pochhammer__minus,axiom,
% 3.82/4.08 ! [B2: real,K: nat] :
% 3.82/4.08 ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B2 ) @ K )
% 3.82/4.08 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ B2 @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ K ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_minus
% 3.82/4.08 thf(fact_6081_pochhammer__minus,axiom,
% 3.82/4.08 ! [B2: int,K: nat] :
% 3.82/4.08 ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B2 ) @ K )
% 3.82/4.08 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B2 @ ( semiri1314217659103216013at_int @ K ) ) @ one_one_int ) @ K ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_minus
% 3.82/4.08 thf(fact_6082_pochhammer__minus_H,axiom,
% 3.82/4.08 ! [B2: complex,K: nat] :
% 3.82/4.08 ( ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ B2 @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ K )
% 3.82/4.08 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B2 ) @ K ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_minus'
% 3.82/4.08 thf(fact_6083_pochhammer__minus_H,axiom,
% 3.82/4.08 ! [B2: real,K: nat] :
% 3.82/4.08 ( ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ B2 @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ K )
% 3.82/4.08 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B2 ) @ K ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_minus'
% 3.82/4.08 thf(fact_6084_pochhammer__minus_H,axiom,
% 3.82/4.08 ! [B2: int,K: nat] :
% 3.82/4.08 ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B2 @ ( semiri1314217659103216013at_int @ K ) ) @ one_one_int ) @ K )
% 3.82/4.08 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B2 ) @ K ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_minus'
% 3.82/4.08 thf(fact_6085_ceiling__log__nat__eq__if,axiom,
% 3.82/4.08 ! [B2: nat,N2: nat,K: nat] :
% 3.82/4.08 ( ( ord_less_nat @ ( power_power_nat @ B2 @ N2 ) @ K )
% 3.82/4.08 => ( ( ord_less_eq_nat @ K @ ( power_power_nat @ B2 @ ( plus_plus_nat @ N2 @ one_one_nat ) ) )
% 3.82/4.08 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 )
% 3.82/4.08 => ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B2 ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 3.82/4.08 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % ceiling_log_nat_eq_if
% 3.82/4.08 thf(fact_6086_ceiling__log2__div2,axiom,
% 3.82/4.08 ! [N2: nat] :
% 3.82/4.08 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 3.82/4.08 => ( ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 3.82/4.08 = ( 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 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % ceiling_log2_div2
% 3.82/4.08 thf(fact_6087_norm__le__zero__iff,axiom,
% 3.82/4.08 ! [X: real] :
% 3.82/4.08 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ X ) @ zero_zero_real )
% 3.82/4.08 = ( X = zero_zero_real ) ) ).
% 3.82/4.08
% 3.82/4.08 % norm_le_zero_iff
% 3.82/4.08 thf(fact_6088_norm__le__zero__iff,axiom,
% 3.82/4.08 ! [X: complex] :
% 3.82/4.08 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ zero_zero_real )
% 3.82/4.08 = ( X = zero_zero_complex ) ) ).
% 3.82/4.08
% 3.82/4.08 % norm_le_zero_iff
% 3.82/4.08 thf(fact_6089_zero__less__norm__iff,axiom,
% 3.82/4.08 ! [X: real] :
% 3.82/4.08 ( ( ord_less_real @ zero_zero_real @ ( real_V7735802525324610683m_real @ X ) )
% 3.82/4.08 = ( X != zero_zero_real ) ) ).
% 3.82/4.08
% 3.82/4.08 % zero_less_norm_iff
% 3.82/4.08 thf(fact_6090_zero__less__norm__iff,axiom,
% 3.82/4.08 ! [X: complex] :
% 3.82/4.08 ( ( ord_less_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X ) )
% 3.82/4.08 = ( X != zero_zero_complex ) ) ).
% 3.82/4.08
% 3.82/4.08 % zero_less_norm_iff
% 3.82/4.08 thf(fact_6091_norm__eq__zero,axiom,
% 3.82/4.08 ! [X: real] :
% 3.82/4.08 ( ( ( real_V7735802525324610683m_real @ X )
% 3.82/4.08 = zero_zero_real )
% 3.82/4.08 = ( X = zero_zero_real ) ) ).
% 3.82/4.08
% 3.82/4.08 % norm_eq_zero
% 3.82/4.08 thf(fact_6092_norm__eq__zero,axiom,
% 3.82/4.08 ! [X: complex] :
% 3.82/4.08 ( ( ( real_V1022390504157884413omplex @ X )
% 3.82/4.08 = zero_zero_real )
% 3.82/4.08 = ( X = zero_zero_complex ) ) ).
% 3.82/4.08
% 3.82/4.08 % norm_eq_zero
% 3.82/4.08 thf(fact_6093_norm__zero,axiom,
% 3.82/4.08 ( ( real_V7735802525324610683m_real @ zero_zero_real )
% 3.82/4.08 = zero_zero_real ) ).
% 3.82/4.08
% 3.82/4.08 % norm_zero
% 3.82/4.08 thf(fact_6094_norm__zero,axiom,
% 3.82/4.08 ( ( real_V1022390504157884413omplex @ zero_zero_complex )
% 3.82/4.08 = zero_zero_real ) ).
% 3.82/4.08
% 3.82/4.08 % norm_zero
% 3.82/4.08 thf(fact_6095_nonzero__norm__divide,axiom,
% 3.82/4.08 ! [B2: real,A: real] :
% 3.82/4.08 ( ( B2 != zero_zero_real )
% 3.82/4.08 => ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B2 ) )
% 3.82/4.08 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % nonzero_norm_divide
% 3.82/4.08 thf(fact_6096_nonzero__norm__divide,axiom,
% 3.82/4.08 ! [B2: complex,A: complex] :
% 3.82/4.08 ( ( B2 != zero_zero_complex )
% 3.82/4.08 => ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B2 ) )
% 3.82/4.08 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % nonzero_norm_divide
% 3.82/4.08 thf(fact_6097_norm__diff__ineq,axiom,
% 3.82/4.08 ! [A: real,B2: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B2 ) ) @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % norm_diff_ineq
% 3.82/4.08 thf(fact_6098_norm__diff__ineq,axiom,
% 3.82/4.08 ! [A: complex,B2: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B2 ) ) @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % norm_diff_ineq
% 3.82/4.08 thf(fact_6099_norm__uminus__minus,axiom,
% 3.82/4.08 ! [X: real,Y: real] :
% 3.82/4.08 ( ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( uminus_uminus_real @ X ) @ Y ) )
% 3.82/4.08 = ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % norm_uminus_minus
% 3.82/4.08 thf(fact_6100_norm__uminus__minus,axiom,
% 3.82/4.08 ! [X: complex,Y: complex] :
% 3.82/4.08 ( ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X ) @ Y ) )
% 3.82/4.08 = ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % norm_uminus_minus
% 3.82/4.08 thf(fact_6101_power__eq__imp__eq__norm,axiom,
% 3.82/4.08 ! [W2: real,N2: nat,Z3: real] :
% 3.82/4.08 ( ( ( power_power_real @ W2 @ N2 )
% 3.82/4.08 = ( power_power_real @ Z3 @ N2 ) )
% 3.82/4.08 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.08 => ( ( real_V7735802525324610683m_real @ W2 )
% 3.82/4.08 = ( real_V7735802525324610683m_real @ Z3 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % power_eq_imp_eq_norm
% 3.82/4.08 thf(fact_6102_power__eq__imp__eq__norm,axiom,
% 3.82/4.08 ! [W2: complex,N2: nat,Z3: complex] :
% 3.82/4.08 ( ( ( power_power_complex @ W2 @ N2 )
% 3.82/4.08 = ( power_power_complex @ Z3 @ N2 ) )
% 3.82/4.08 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.08 => ( ( real_V1022390504157884413omplex @ W2 )
% 3.82/4.08 = ( real_V1022390504157884413omplex @ Z3 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % power_eq_imp_eq_norm
% 3.82/4.08 thf(fact_6103_norm__triangle__lt,axiom,
% 3.82/4.08 ! [X: real,Y: real,E2: real] :
% 3.82/4.08 ( ( ord_less_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y ) ) @ E2 )
% 3.82/4.08 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y ) ) @ E2 ) ) ).
% 3.82/4.08
% 3.82/4.08 % norm_triangle_lt
% 3.82/4.08 thf(fact_6104_norm__triangle__lt,axiom,
% 3.82/4.08 ! [X: complex,Y: complex,E2: real] :
% 3.82/4.08 ( ( ord_less_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) @ E2 )
% 3.82/4.08 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y ) ) @ E2 ) ) ).
% 3.82/4.08
% 3.82/4.08 % norm_triangle_lt
% 3.82/4.08 thf(fact_6105_norm__add__less,axiom,
% 3.82/4.08 ! [X: real,R2: real,Y: real,S: real] :
% 3.82/4.08 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X ) @ R2 )
% 3.82/4.08 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y ) @ S )
% 3.82/4.08 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y ) ) @ ( plus_plus_real @ R2 @ S ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % norm_add_less
% 3.82/4.08 thf(fact_6106_norm__add__less,axiom,
% 3.82/4.08 ! [X: complex,R2: real,Y: complex,S: real] :
% 3.82/4.08 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ R2 )
% 3.82/4.08 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y ) @ S )
% 3.82/4.08 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y ) ) @ ( plus_plus_real @ R2 @ S ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % norm_add_less
% 3.82/4.08 thf(fact_6107_norm__add__leD,axiom,
% 3.82/4.08 ! [A: real,B2: real,C: real] :
% 3.82/4.08 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B2 ) ) @ C )
% 3.82/4.08 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B2 ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ A ) @ C ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % norm_add_leD
% 3.82/4.08 thf(fact_6108_norm__add__leD,axiom,
% 3.82/4.08 ! [A: complex,B2: complex,C: real] :
% 3.82/4.08 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B2 ) ) @ C )
% 3.82/4.08 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B2 ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A ) @ C ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % norm_add_leD
% 3.82/4.08 thf(fact_6109_norm__triangle__le,axiom,
% 3.82/4.08 ! [X: real,Y: real,E2: real] :
% 3.82/4.08 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y ) ) @ E2 )
% 3.82/4.08 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y ) ) @ E2 ) ) ).
% 3.82/4.08
% 3.82/4.08 % norm_triangle_le
% 3.82/4.08 thf(fact_6110_norm__triangle__le,axiom,
% 3.82/4.08 ! [X: complex,Y: complex,E2: real] :
% 3.82/4.08 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) @ E2 )
% 3.82/4.08 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y ) ) @ E2 ) ) ).
% 3.82/4.08
% 3.82/4.08 % norm_triangle_le
% 3.82/4.08 thf(fact_6111_norm__triangle__ineq,axiom,
% 3.82/4.08 ! [X: real,Y: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % norm_triangle_ineq
% 3.82/4.08 thf(fact_6112_norm__triangle__ineq,axiom,
% 3.82/4.08 ! [X: complex,Y: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % norm_triangle_ineq
% 3.82/4.08 thf(fact_6113_norm__triangle__mono,axiom,
% 3.82/4.08 ! [A: real,R2: real,B2: real,S: real] :
% 3.82/4.08 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ A ) @ R2 )
% 3.82/4.08 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B2 ) @ S )
% 3.82/4.08 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B2 ) ) @ ( plus_plus_real @ R2 @ S ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % norm_triangle_mono
% 3.82/4.08 thf(fact_6114_norm__triangle__mono,axiom,
% 3.82/4.08 ! [A: complex,R2: real,B2: complex,S: real] :
% 3.82/4.08 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ A ) @ R2 )
% 3.82/4.08 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B2 ) @ S )
% 3.82/4.08 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B2 ) ) @ ( plus_plus_real @ R2 @ S ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % norm_triangle_mono
% 3.82/4.08 thf(fact_6115_power__eq__1__iff,axiom,
% 3.82/4.08 ! [W2: real,N2: nat] :
% 3.82/4.08 ( ( ( power_power_real @ W2 @ N2 )
% 3.82/4.08 = one_one_real )
% 3.82/4.08 => ( ( ( real_V7735802525324610683m_real @ W2 )
% 3.82/4.08 = one_one_real )
% 3.82/4.08 | ( N2 = zero_zero_nat ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % power_eq_1_iff
% 3.82/4.08 thf(fact_6116_power__eq__1__iff,axiom,
% 3.82/4.08 ! [W2: complex,N2: nat] :
% 3.82/4.08 ( ( ( power_power_complex @ W2 @ N2 )
% 3.82/4.08 = one_one_complex )
% 3.82/4.08 => ( ( ( real_V1022390504157884413omplex @ W2 )
% 3.82/4.08 = one_one_real )
% 3.82/4.08 | ( N2 = zero_zero_nat ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % power_eq_1_iff
% 3.82/4.08 thf(fact_6117_norm__diff__triangle__ineq,axiom,
% 3.82/4.08 ! [A: real,B2: real,C: real,D: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B2 ) @ ( plus_plus_real @ C @ D ) ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ C ) ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ B2 @ D ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % norm_diff_triangle_ineq
% 3.82/4.08 thf(fact_6118_norm__diff__triangle__ineq,axiom,
% 3.82/4.08 ! [A: complex,B2: complex,C: complex,D: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( plus_plus_complex @ A @ B2 ) @ ( plus_plus_complex @ C @ D ) ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ C ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ B2 @ D ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % norm_diff_triangle_ineq
% 3.82/4.08 thf(fact_6119_sum__bounds__lt__plus1,axiom,
% 3.82/4.08 ! [F: nat > nat,Mm: nat] :
% 3.82/4.08 ( ( groups3542108847815614940at_nat
% 3.82/4.08 @ ^ [K2: nat] : ( F @ ( suc @ K2 ) )
% 3.82/4.08 @ ( set_ord_lessThan_nat @ Mm ) )
% 3.82/4.08 = ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ one_one_nat @ Mm ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % sum_bounds_lt_plus1
% 3.82/4.08 thf(fact_6120_sum__bounds__lt__plus1,axiom,
% 3.82/4.08 ! [F: nat > real,Mm: nat] :
% 3.82/4.08 ( ( groups6591440286371151544t_real
% 3.82/4.08 @ ^ [K2: nat] : ( F @ ( suc @ K2 ) )
% 3.82/4.08 @ ( set_ord_lessThan_nat @ Mm ) )
% 3.82/4.08 = ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ one_one_nat @ Mm ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % sum_bounds_lt_plus1
% 3.82/4.08 thf(fact_6121_sumr__cos__zero__one,axiom,
% 3.82/4.08 ! [N2: nat] :
% 3.82/4.08 ( ( groups6591440286371151544t_real
% 3.82/4.08 @ ^ [M: nat] : ( times_times_real @ ( cos_coeff @ M ) @ ( power_power_real @ zero_zero_real @ M ) )
% 3.82/4.08 @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 3.82/4.08 = one_one_real ) ).
% 3.82/4.08
% 3.82/4.08 % sumr_cos_zero_one
% 3.82/4.08 thf(fact_6122_pochhammer__times__pochhammer__half,axiom,
% 3.82/4.08 ! [Z3: complex,N2: nat] :
% 3.82/4.08 ( ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z3 @ ( suc @ N2 ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z3 @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ ( suc @ N2 ) ) )
% 3.82/4.08 = ( groups6464643781859351333omplex
% 3.82/4.08 @ ^ [K2: nat] : ( plus_plus_complex @ Z3 @ ( divide1717551699836669952omplex @ ( semiri8010041392384452111omplex @ K2 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 3.82/4.08 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_times_pochhammer_half
% 3.82/4.08 thf(fact_6123_pochhammer__times__pochhammer__half,axiom,
% 3.82/4.08 ! [Z3: real,N2: nat] :
% 3.82/4.08 ( ( times_times_real @ ( comm_s7457072308508201937r_real @ Z3 @ ( suc @ N2 ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z3 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( suc @ N2 ) ) )
% 3.82/4.08 = ( groups129246275422532515t_real
% 3.82/4.08 @ ^ [K2: nat] : ( plus_plus_real @ Z3 @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ K2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 3.82/4.08 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_times_pochhammer_half
% 3.82/4.08 thf(fact_6124_pochhammer__code,axiom,
% 3.82/4.08 ( comm_s2602460028002588243omplex
% 3.82/4.08 = ( ^ [A3: complex,N: nat] :
% 3.82/4.08 ( if_complex @ ( N = zero_zero_nat ) @ one_one_complex
% 3.82/4.08 @ ( set_fo1517530859248394432omplex
% 3.82/4.08 @ ^ [O: nat] : ( times_times_complex @ ( plus_plus_complex @ A3 @ ( semiri8010041392384452111omplex @ O ) ) )
% 3.82/4.08 @ zero_zero_nat
% 3.82/4.08 @ ( minus_minus_nat @ N @ one_one_nat )
% 3.82/4.08 @ one_one_complex ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_code
% 3.82/4.08 thf(fact_6125_pochhammer__code,axiom,
% 3.82/4.08 ( comm_s3181272606743183617d_enat
% 3.82/4.08 = ( ^ [A3: extended_enat,N: nat] :
% 3.82/4.08 ( if_Extended_enat @ ( N = zero_zero_nat ) @ one_on7984719198319812577d_enat
% 3.82/4.08 @ ( set_fo2538466533108834004d_enat
% 3.82/4.08 @ ^ [O: nat] : ( times_7803423173614009249d_enat @ ( plus_p3455044024723400733d_enat @ A3 @ ( semiri4216267220026989637d_enat @ O ) ) )
% 3.82/4.08 @ zero_zero_nat
% 3.82/4.08 @ ( minus_minus_nat @ N @ one_one_nat )
% 3.82/4.08 @ one_on7984719198319812577d_enat ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_code
% 3.82/4.08 thf(fact_6126_pochhammer__code,axiom,
% 3.82/4.08 ( comm_s7457072308508201937r_real
% 3.82/4.08 = ( ^ [A3: real,N: nat] :
% 3.82/4.08 ( if_real @ ( N = zero_zero_nat ) @ one_one_real
% 3.82/4.08 @ ( set_fo3111899725591712190t_real
% 3.82/4.08 @ ^ [O: nat] : ( times_times_real @ ( plus_plus_real @ A3 @ ( semiri5074537144036343181t_real @ O ) ) )
% 3.82/4.08 @ zero_zero_nat
% 3.82/4.08 @ ( minus_minus_nat @ N @ one_one_nat )
% 3.82/4.08 @ one_one_real ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_code
% 3.82/4.08 thf(fact_6127_pochhammer__code,axiom,
% 3.82/4.08 ( comm_s4660882817536571857er_int
% 3.82/4.08 = ( ^ [A3: int,N: nat] :
% 3.82/4.08 ( if_int @ ( N = zero_zero_nat ) @ one_one_int
% 3.82/4.08 @ ( set_fo2581907887559384638at_int
% 3.82/4.08 @ ^ [O: nat] : ( times_times_int @ ( plus_plus_int @ A3 @ ( semiri1314217659103216013at_int @ O ) ) )
% 3.82/4.08 @ zero_zero_nat
% 3.82/4.08 @ ( minus_minus_nat @ N @ one_one_nat )
% 3.82/4.08 @ one_one_int ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_code
% 3.82/4.08 thf(fact_6128_pochhammer__code,axiom,
% 3.82/4.08 ( comm_s4663373288045622133er_nat
% 3.82/4.08 = ( ^ [A3: nat,N: nat] :
% 3.82/4.08 ( if_nat @ ( N = zero_zero_nat ) @ one_one_nat
% 3.82/4.08 @ ( set_fo2584398358068434914at_nat
% 3.82/4.08 @ ^ [O: nat] : ( times_times_nat @ ( plus_plus_nat @ A3 @ ( semiri1316708129612266289at_nat @ O ) ) )
% 3.82/4.08 @ zero_zero_nat
% 3.82/4.08 @ ( minus_minus_nat @ N @ one_one_nat )
% 3.82/4.08 @ one_one_nat ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % pochhammer_code
% 3.82/4.08 thf(fact_6129_ceiling__log__eq__powr__iff,axiom,
% 3.82/4.08 ! [X: real,B2: real,K: nat] :
% 3.82/4.08 ( ( ord_less_real @ zero_zero_real @ X )
% 3.82/4.08 => ( ( ord_less_real @ one_one_real @ B2 )
% 3.82/4.08 => ( ( ( archim7802044766580827645g_real @ ( log @ B2 @ X ) )
% 3.82/4.08 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ K ) @ one_one_int ) )
% 3.82/4.08 = ( ( ord_less_real @ ( powr_real @ B2 @ ( semiri5074537144036343181t_real @ K ) ) @ X )
% 3.82/4.08 & ( ord_less_eq_real @ X @ ( powr_real @ B2 @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % ceiling_log_eq_powr_iff
% 3.82/4.08 thf(fact_6130_geometric__deriv__sums,axiom,
% 3.82/4.08 ! [Z3: real] :
% 3.82/4.08 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z3 ) @ one_one_real )
% 3.82/4.08 => ( sums_real
% 3.82/4.08 @ ^ [N: nat] : ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) @ ( power_power_real @ Z3 @ N ) )
% 3.82/4.08 @ ( divide_divide_real @ one_one_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ Z3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % geometric_deriv_sums
% 3.82/4.08 thf(fact_6131_geometric__deriv__sums,axiom,
% 3.82/4.08 ! [Z3: complex] :
% 3.82/4.08 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z3 ) @ one_one_real )
% 3.82/4.08 => ( sums_complex
% 3.82/4.08 @ ^ [N: nat] : ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ N ) ) @ ( power_power_complex @ Z3 @ N ) )
% 3.82/4.08 @ ( divide1717551699836669952omplex @ one_one_complex @ ( power_power_complex @ ( minus_minus_complex @ one_one_complex @ Z3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % geometric_deriv_sums
% 3.82/4.08 thf(fact_6132_powr__eq__0__iff,axiom,
% 3.82/4.08 ! [W2: real,Z3: real] :
% 3.82/4.08 ( ( ( powr_real @ W2 @ Z3 )
% 3.82/4.08 = zero_zero_real )
% 3.82/4.08 = ( W2 = zero_zero_real ) ) ).
% 3.82/4.08
% 3.82/4.08 % powr_eq_0_iff
% 3.82/4.08 thf(fact_6133_powr__0,axiom,
% 3.82/4.08 ! [Z3: real] :
% 3.82/4.08 ( ( powr_real @ zero_zero_real @ Z3 )
% 3.82/4.08 = zero_zero_real ) ).
% 3.82/4.08
% 3.82/4.08 % powr_0
% 3.82/4.08 thf(fact_6134_of__nat__prod,axiom,
% 3.82/4.08 ! [F: int > nat,A2: set_int] :
% 3.82/4.08 ( ( semiri1314217659103216013at_int @ ( groups1707563613775114915nt_nat @ F @ A2 ) )
% 3.82/4.08 = ( groups1705073143266064639nt_int
% 3.82/4.08 @ ^ [X4: int] : ( semiri1314217659103216013at_int @ ( F @ X4 ) )
% 3.82/4.08 @ A2 ) ) ).
% 3.82/4.08
% 3.82/4.08 % of_nat_prod
% 3.82/4.08 thf(fact_6135_of__nat__prod,axiom,
% 3.82/4.08 ! [F: nat > nat,A2: set_nat] :
% 3.82/4.08 ( ( semiri5074537144036343181t_real @ ( groups708209901874060359at_nat @ F @ A2 ) )
% 3.82/4.08 = ( groups129246275422532515t_real
% 3.82/4.08 @ ^ [X4: nat] : ( semiri5074537144036343181t_real @ ( F @ X4 ) )
% 3.82/4.08 @ A2 ) ) ).
% 3.82/4.08
% 3.82/4.08 % of_nat_prod
% 3.82/4.08 thf(fact_6136_of__nat__prod,axiom,
% 3.82/4.08 ! [F: nat > nat,A2: set_nat] :
% 3.82/4.08 ( ( semiri1314217659103216013at_int @ ( groups708209901874060359at_nat @ F @ A2 ) )
% 3.82/4.08 = ( groups705719431365010083at_int
% 3.82/4.08 @ ^ [X4: nat] : ( semiri1314217659103216013at_int @ ( F @ X4 ) )
% 3.82/4.08 @ A2 ) ) ).
% 3.82/4.08
% 3.82/4.08 % of_nat_prod
% 3.82/4.08 thf(fact_6137_of__nat__prod,axiom,
% 3.82/4.08 ! [F: nat > nat,A2: set_nat] :
% 3.82/4.08 ( ( semiri1316708129612266289at_nat @ ( groups708209901874060359at_nat @ F @ A2 ) )
% 3.82/4.08 = ( groups708209901874060359at_nat
% 3.82/4.08 @ ^ [X4: nat] : ( semiri1316708129612266289at_nat @ ( F @ X4 ) )
% 3.82/4.08 @ A2 ) ) ).
% 3.82/4.08
% 3.82/4.08 % of_nat_prod
% 3.82/4.08 thf(fact_6138_of__int__prod,axiom,
% 3.82/4.08 ! [F: nat > int,A2: set_nat] :
% 3.82/4.08 ( ( ring_1_of_int_real @ ( groups705719431365010083at_int @ F @ A2 ) )
% 3.82/4.08 = ( groups129246275422532515t_real
% 3.82/4.08 @ ^ [X4: nat] : ( ring_1_of_int_real @ ( F @ X4 ) )
% 3.82/4.08 @ A2 ) ) ).
% 3.82/4.08
% 3.82/4.08 % of_int_prod
% 3.82/4.08 thf(fact_6139_of__int__prod,axiom,
% 3.82/4.08 ! [F: nat > int,A2: set_nat] :
% 3.82/4.08 ( ( ring_1_of_int_int @ ( groups705719431365010083at_int @ F @ A2 ) )
% 3.82/4.08 = ( groups705719431365010083at_int
% 3.82/4.08 @ ^ [X4: nat] : ( ring_1_of_int_int @ ( F @ X4 ) )
% 3.82/4.08 @ A2 ) ) ).
% 3.82/4.08
% 3.82/4.08 % of_int_prod
% 3.82/4.08 thf(fact_6140_of__int__prod,axiom,
% 3.82/4.08 ! [F: int > int,A2: set_int] :
% 3.82/4.08 ( ( ring_1_of_int_real @ ( groups1705073143266064639nt_int @ F @ A2 ) )
% 3.82/4.08 = ( groups2316167850115554303t_real
% 3.82/4.08 @ ^ [X4: int] : ( ring_1_of_int_real @ ( F @ X4 ) )
% 3.82/4.08 @ A2 ) ) ).
% 3.82/4.08
% 3.82/4.08 % of_int_prod
% 3.82/4.08 thf(fact_6141_of__int__prod,axiom,
% 3.82/4.08 ! [F: int > int,A2: set_int] :
% 3.82/4.08 ( ( ring_1_of_int_int @ ( groups1705073143266064639nt_int @ F @ A2 ) )
% 3.82/4.08 = ( groups1705073143266064639nt_int
% 3.82/4.08 @ ^ [X4: int] : ( ring_1_of_int_int @ ( F @ X4 ) )
% 3.82/4.08 @ A2 ) ) ).
% 3.82/4.08
% 3.82/4.08 % of_int_prod
% 3.82/4.08 thf(fact_6142_prod__zero__iff,axiom,
% 3.82/4.08 ! [A2: set_complex,F: complex > nat] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.08 => ( ( ( groups861055069439313189ex_nat @ F @ A2 )
% 3.82/4.08 = zero_zero_nat )
% 3.82/4.08 = ( ? [X4: complex] :
% 3.82/4.08 ( ( member_complex @ X4 @ A2 )
% 3.82/4.08 & ( ( F @ X4 )
% 3.82/4.08 = zero_zero_nat ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_zero_iff
% 3.82/4.08 thf(fact_6143_prod__zero__iff,axiom,
% 3.82/4.08 ! [A2: set_int,F: int > nat] :
% 3.82/4.08 ( ( finite_finite_int @ A2 )
% 3.82/4.08 => ( ( ( groups1707563613775114915nt_nat @ F @ A2 )
% 3.82/4.08 = zero_zero_nat )
% 3.82/4.08 = ( ? [X4: int] :
% 3.82/4.08 ( ( member_int @ X4 @ A2 )
% 3.82/4.08 & ( ( F @ X4 )
% 3.82/4.08 = zero_zero_nat ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_zero_iff
% 3.82/4.08 thf(fact_6144_prod__zero__iff,axiom,
% 3.82/4.08 ! [A2: set_Extended_enat,F: extended_enat > nat] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.08 => ( ( ( groups2880970938130013265at_nat @ F @ A2 )
% 3.82/4.08 = zero_zero_nat )
% 3.82/4.08 = ( ? [X4: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ X4 @ A2 )
% 3.82/4.08 & ( ( F @ X4 )
% 3.82/4.08 = zero_zero_nat ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_zero_iff
% 3.82/4.08 thf(fact_6145_prod__zero__iff,axiom,
% 3.82/4.08 ! [A2: set_nat,F: nat > real] :
% 3.82/4.08 ( ( finite_finite_nat @ A2 )
% 3.82/4.08 => ( ( ( groups129246275422532515t_real @ F @ A2 )
% 3.82/4.08 = zero_zero_real )
% 3.82/4.08 = ( ? [X4: nat] :
% 3.82/4.08 ( ( member_nat @ X4 @ A2 )
% 3.82/4.08 & ( ( F @ X4 )
% 3.82/4.08 = zero_zero_real ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_zero_iff
% 3.82/4.08 thf(fact_6146_prod__zero__iff,axiom,
% 3.82/4.08 ! [A2: set_complex,F: complex > real] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.08 => ( ( ( groups766887009212190081x_real @ F @ A2 )
% 3.82/4.08 = zero_zero_real )
% 3.82/4.08 = ( ? [X4: complex] :
% 3.82/4.08 ( ( member_complex @ X4 @ A2 )
% 3.82/4.08 & ( ( F @ X4 )
% 3.82/4.08 = zero_zero_real ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_zero_iff
% 3.82/4.08 thf(fact_6147_prod__zero__iff,axiom,
% 3.82/4.08 ! [A2: set_int,F: int > real] :
% 3.82/4.08 ( ( finite_finite_int @ A2 )
% 3.82/4.08 => ( ( ( groups2316167850115554303t_real @ F @ A2 )
% 3.82/4.08 = zero_zero_real )
% 3.82/4.08 = ( ? [X4: int] :
% 3.82/4.08 ( ( member_int @ X4 @ A2 )
% 3.82/4.08 & ( ( F @ X4 )
% 3.82/4.08 = zero_zero_real ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_zero_iff
% 3.82/4.08 thf(fact_6148_prod__zero__iff,axiom,
% 3.82/4.08 ! [A2: set_Extended_enat,F: extended_enat > real] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.08 => ( ( ( groups97031904164794029t_real @ F @ A2 )
% 3.82/4.08 = zero_zero_real )
% 3.82/4.08 = ( ? [X4: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ X4 @ A2 )
% 3.82/4.08 & ( ( F @ X4 )
% 3.82/4.08 = zero_zero_real ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_zero_iff
% 3.82/4.08 thf(fact_6149_prod__zero__iff,axiom,
% 3.82/4.08 ! [A2: set_complex,F: complex > int] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.08 => ( ( ( groups858564598930262913ex_int @ F @ A2 )
% 3.82/4.08 = zero_zero_int )
% 3.82/4.08 = ( ? [X4: complex] :
% 3.82/4.08 ( ( member_complex @ X4 @ A2 )
% 3.82/4.08 & ( ( F @ X4 )
% 3.82/4.08 = zero_zero_int ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_zero_iff
% 3.82/4.08 thf(fact_6150_prod__zero__iff,axiom,
% 3.82/4.08 ! [A2: set_Extended_enat,F: extended_enat > int] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.08 => ( ( ( groups2878480467620962989at_int @ F @ A2 )
% 3.82/4.08 = zero_zero_int )
% 3.82/4.08 = ( ? [X4: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ X4 @ A2 )
% 3.82/4.08 & ( ( F @ X4 )
% 3.82/4.08 = zero_zero_int ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_zero_iff
% 3.82/4.08 thf(fact_6151_prod__zero__iff,axiom,
% 3.82/4.08 ! [A2: set_nat,F: nat > complex] :
% 3.82/4.08 ( ( finite_finite_nat @ A2 )
% 3.82/4.08 => ( ( ( groups6464643781859351333omplex @ F @ A2 )
% 3.82/4.08 = zero_zero_complex )
% 3.82/4.08 = ( ? [X4: nat] :
% 3.82/4.08 ( ( member_nat @ X4 @ A2 )
% 3.82/4.08 & ( ( F @ X4 )
% 3.82/4.08 = zero_zero_complex ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_zero_iff
% 3.82/4.08 thf(fact_6152_prod_Oempty,axiom,
% 3.82/4.08 ! [G: extended_enat > nat] :
% 3.82/4.08 ( ( groups2880970938130013265at_nat @ G @ bot_bo7653980558646680370d_enat )
% 3.82/4.08 = one_one_nat ) ).
% 3.82/4.08
% 3.82/4.08 % prod.empty
% 3.82/4.08 thf(fact_6153_prod_Oempty,axiom,
% 3.82/4.08 ! [G: extended_enat > int] :
% 3.82/4.08 ( ( groups2878480467620962989at_int @ G @ bot_bo7653980558646680370d_enat )
% 3.82/4.08 = one_one_int ) ).
% 3.82/4.08
% 3.82/4.08 % prod.empty
% 3.82/4.08 thf(fact_6154_prod_Oempty,axiom,
% 3.82/4.08 ! [G: extended_enat > complex] :
% 3.82/4.08 ( ( groups4622424608036095791omplex @ G @ bot_bo7653980558646680370d_enat )
% 3.82/4.08 = one_one_complex ) ).
% 3.82/4.08
% 3.82/4.08 % prod.empty
% 3.82/4.08 thf(fact_6155_prod_Oempty,axiom,
% 3.82/4.08 ! [G: extended_enat > real] :
% 3.82/4.08 ( ( groups97031904164794029t_real @ G @ bot_bo7653980558646680370d_enat )
% 3.82/4.08 = one_one_real ) ).
% 3.82/4.08
% 3.82/4.08 % prod.empty
% 3.82/4.08 thf(fact_6156_prod_Oempty,axiom,
% 3.82/4.08 ! [G: real > nat] :
% 3.82/4.08 ( ( groups4696554848551431203al_nat @ G @ bot_bot_set_real )
% 3.82/4.08 = one_one_nat ) ).
% 3.82/4.08
% 3.82/4.08 % prod.empty
% 3.82/4.08 thf(fact_6157_prod_Oempty,axiom,
% 3.82/4.08 ! [G: real > int] :
% 3.82/4.08 ( ( groups4694064378042380927al_int @ G @ bot_bot_set_real )
% 3.82/4.08 = one_one_int ) ).
% 3.82/4.08
% 3.82/4.08 % prod.empty
% 3.82/4.08 thf(fact_6158_prod_Oempty,axiom,
% 3.82/4.08 ! [G: real > complex] :
% 3.82/4.08 ( ( groups713298508707869441omplex @ G @ bot_bot_set_real )
% 3.82/4.08 = one_one_complex ) ).
% 3.82/4.08
% 3.82/4.08 % prod.empty
% 3.82/4.08 thf(fact_6159_prod_Oempty,axiom,
% 3.82/4.08 ! [G: real > real] :
% 3.82/4.08 ( ( groups1681761925125756287l_real @ G @ bot_bot_set_real )
% 3.82/4.08 = one_one_real ) ).
% 3.82/4.08
% 3.82/4.08 % prod.empty
% 3.82/4.08 thf(fact_6160_prod_Oempty,axiom,
% 3.82/4.08 ! [G: nat > complex] :
% 3.82/4.08 ( ( groups6464643781859351333omplex @ G @ bot_bot_set_nat )
% 3.82/4.08 = one_one_complex ) ).
% 3.82/4.08
% 3.82/4.08 % prod.empty
% 3.82/4.08 thf(fact_6161_prod_Oempty,axiom,
% 3.82/4.08 ! [G: nat > real] :
% 3.82/4.08 ( ( groups129246275422532515t_real @ G @ bot_bot_set_nat )
% 3.82/4.08 = one_one_real ) ).
% 3.82/4.08
% 3.82/4.08 % prod.empty
% 3.82/4.08 thf(fact_6162_prod_Oinfinite,axiom,
% 3.82/4.08 ! [A2: set_complex,G: complex > nat] :
% 3.82/4.08 ( ~ ( finite3207457112153483333omplex @ A2 )
% 3.82/4.08 => ( ( groups861055069439313189ex_nat @ G @ A2 )
% 3.82/4.08 = one_one_nat ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.infinite
% 3.82/4.08 thf(fact_6163_prod_Oinfinite,axiom,
% 3.82/4.08 ! [A2: set_int,G: int > nat] :
% 3.82/4.08 ( ~ ( finite_finite_int @ A2 )
% 3.82/4.08 => ( ( groups1707563613775114915nt_nat @ G @ A2 )
% 3.82/4.08 = one_one_nat ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.infinite
% 3.82/4.08 thf(fact_6164_prod_Oinfinite,axiom,
% 3.82/4.08 ! [A2: set_Extended_enat,G: extended_enat > nat] :
% 3.82/4.08 ( ~ ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.08 => ( ( groups2880970938130013265at_nat @ G @ A2 )
% 3.82/4.08 = one_one_nat ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.infinite
% 3.82/4.08 thf(fact_6165_prod_Oinfinite,axiom,
% 3.82/4.08 ! [A2: set_complex,G: complex > int] :
% 3.82/4.08 ( ~ ( finite3207457112153483333omplex @ A2 )
% 3.82/4.08 => ( ( groups858564598930262913ex_int @ G @ A2 )
% 3.82/4.08 = one_one_int ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.infinite
% 3.82/4.08 thf(fact_6166_prod_Oinfinite,axiom,
% 3.82/4.08 ! [A2: set_Extended_enat,G: extended_enat > int] :
% 3.82/4.08 ( ~ ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.08 => ( ( groups2878480467620962989at_int @ G @ A2 )
% 3.82/4.08 = one_one_int ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.infinite
% 3.82/4.08 thf(fact_6167_prod_Oinfinite,axiom,
% 3.82/4.08 ! [A2: set_nat,G: nat > complex] :
% 3.82/4.08 ( ~ ( finite_finite_nat @ A2 )
% 3.82/4.08 => ( ( groups6464643781859351333omplex @ G @ A2 )
% 3.82/4.08 = one_one_complex ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.infinite
% 3.82/4.08 thf(fact_6168_prod_Oinfinite,axiom,
% 3.82/4.08 ! [A2: set_complex,G: complex > complex] :
% 3.82/4.08 ( ~ ( finite3207457112153483333omplex @ A2 )
% 3.82/4.08 => ( ( groups3708469109370488835omplex @ G @ A2 )
% 3.82/4.08 = one_one_complex ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.infinite
% 3.82/4.08 thf(fact_6169_prod_Oinfinite,axiom,
% 3.82/4.08 ! [A2: set_int,G: int > complex] :
% 3.82/4.08 ( ~ ( finite_finite_int @ A2 )
% 3.82/4.08 => ( ( groups7440179247065528705omplex @ G @ A2 )
% 3.82/4.08 = one_one_complex ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.infinite
% 3.82/4.08 thf(fact_6170_prod_Oinfinite,axiom,
% 3.82/4.08 ! [A2: set_Extended_enat,G: extended_enat > complex] :
% 3.82/4.08 ( ~ ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.08 => ( ( groups4622424608036095791omplex @ G @ A2 )
% 3.82/4.08 = one_one_complex ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.infinite
% 3.82/4.08 thf(fact_6171_prod_Oinfinite,axiom,
% 3.82/4.08 ! [A2: set_nat,G: nat > real] :
% 3.82/4.08 ( ~ ( finite_finite_nat @ A2 )
% 3.82/4.08 => ( ( groups129246275422532515t_real @ G @ A2 )
% 3.82/4.08 = one_one_real ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.infinite
% 3.82/4.08 thf(fact_6172_powr__zero__eq__one,axiom,
% 3.82/4.08 ! [X: real] :
% 3.82/4.08 ( ( ( X = zero_zero_real )
% 3.82/4.08 => ( ( powr_real @ X @ zero_zero_real )
% 3.82/4.08 = zero_zero_real ) )
% 3.82/4.08 & ( ( X != zero_zero_real )
% 3.82/4.08 => ( ( powr_real @ X @ zero_zero_real )
% 3.82/4.08 = one_one_real ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % powr_zero_eq_one
% 3.82/4.08 thf(fact_6173_dvd__prodI,axiom,
% 3.82/4.08 ! [A2: set_real,A: real,F: real > nat] :
% 3.82/4.08 ( ( finite_finite_real @ A2 )
% 3.82/4.08 => ( ( member_real @ A @ A2 )
% 3.82/4.08 => ( dvd_dvd_nat @ ( F @ A ) @ ( groups4696554848551431203al_nat @ F @ A2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % dvd_prodI
% 3.82/4.08 thf(fact_6174_dvd__prodI,axiom,
% 3.82/4.08 ! [A2: set_complex,A: complex,F: complex > nat] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.08 => ( ( member_complex @ A @ A2 )
% 3.82/4.08 => ( dvd_dvd_nat @ ( F @ A ) @ ( groups861055069439313189ex_nat @ F @ A2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % dvd_prodI
% 3.82/4.08 thf(fact_6175_dvd__prodI,axiom,
% 3.82/4.08 ! [A2: set_int,A: int,F: int > nat] :
% 3.82/4.08 ( ( finite_finite_int @ A2 )
% 3.82/4.08 => ( ( member_int @ A @ A2 )
% 3.82/4.08 => ( dvd_dvd_nat @ ( F @ A ) @ ( groups1707563613775114915nt_nat @ F @ A2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % dvd_prodI
% 3.82/4.08 thf(fact_6176_dvd__prodI,axiom,
% 3.82/4.08 ! [A2: set_Extended_enat,A: extended_enat,F: extended_enat > nat] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.08 => ( ( member_Extended_enat @ A @ A2 )
% 3.82/4.08 => ( dvd_dvd_nat @ ( F @ A ) @ ( groups2880970938130013265at_nat @ F @ A2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % dvd_prodI
% 3.82/4.08 thf(fact_6177_dvd__prodI,axiom,
% 3.82/4.08 ! [A2: set_real,A: real,F: real > int] :
% 3.82/4.08 ( ( finite_finite_real @ A2 )
% 3.82/4.08 => ( ( member_real @ A @ A2 )
% 3.82/4.08 => ( dvd_dvd_int @ ( F @ A ) @ ( groups4694064378042380927al_int @ F @ A2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % dvd_prodI
% 3.82/4.08 thf(fact_6178_dvd__prodI,axiom,
% 3.82/4.08 ! [A2: set_complex,A: complex,F: complex > int] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.08 => ( ( member_complex @ A @ A2 )
% 3.82/4.08 => ( dvd_dvd_int @ ( F @ A ) @ ( groups858564598930262913ex_int @ F @ A2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % dvd_prodI
% 3.82/4.08 thf(fact_6179_dvd__prodI,axiom,
% 3.82/4.08 ! [A2: set_Extended_enat,A: extended_enat,F: extended_enat > int] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.08 => ( ( member_Extended_enat @ A @ A2 )
% 3.82/4.08 => ( dvd_dvd_int @ ( F @ A ) @ ( groups2878480467620962989at_int @ F @ A2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % dvd_prodI
% 3.82/4.08 thf(fact_6180_dvd__prodI,axiom,
% 3.82/4.08 ! [A2: set_nat,A: nat,F: nat > int] :
% 3.82/4.08 ( ( finite_finite_nat @ A2 )
% 3.82/4.08 => ( ( member_nat @ A @ A2 )
% 3.82/4.08 => ( dvd_dvd_int @ ( F @ A ) @ ( groups705719431365010083at_int @ F @ A2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % dvd_prodI
% 3.82/4.08 thf(fact_6181_dvd__prodI,axiom,
% 3.82/4.08 ! [A2: set_int,A: int,F: int > int] :
% 3.82/4.08 ( ( finite_finite_int @ A2 )
% 3.82/4.08 => ( ( member_int @ A @ A2 )
% 3.82/4.08 => ( dvd_dvd_int @ ( F @ A ) @ ( groups1705073143266064639nt_int @ F @ A2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % dvd_prodI
% 3.82/4.08 thf(fact_6182_dvd__prodI,axiom,
% 3.82/4.08 ! [A2: set_nat,A: nat,F: nat > nat] :
% 3.82/4.08 ( ( finite_finite_nat @ A2 )
% 3.82/4.08 => ( ( member_nat @ A @ A2 )
% 3.82/4.08 => ( dvd_dvd_nat @ ( F @ A ) @ ( groups708209901874060359at_nat @ F @ A2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % dvd_prodI
% 3.82/4.08 thf(fact_6183_dvd__prod__eqI,axiom,
% 3.82/4.08 ! [A2: set_real,A: real,B2: nat,F: real > nat] :
% 3.82/4.08 ( ( finite_finite_real @ A2 )
% 3.82/4.08 => ( ( member_real @ A @ A2 )
% 3.82/4.08 => ( ( B2
% 3.82/4.08 = ( F @ A ) )
% 3.82/4.08 => ( dvd_dvd_nat @ B2 @ ( groups4696554848551431203al_nat @ F @ A2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % dvd_prod_eqI
% 3.82/4.08 thf(fact_6184_dvd__prod__eqI,axiom,
% 3.82/4.08 ! [A2: set_complex,A: complex,B2: nat,F: complex > nat] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.08 => ( ( member_complex @ A @ A2 )
% 3.82/4.08 => ( ( B2
% 3.82/4.08 = ( F @ A ) )
% 3.82/4.08 => ( dvd_dvd_nat @ B2 @ ( groups861055069439313189ex_nat @ F @ A2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % dvd_prod_eqI
% 3.82/4.08 thf(fact_6185_dvd__prod__eqI,axiom,
% 3.82/4.08 ! [A2: set_int,A: int,B2: nat,F: int > nat] :
% 3.82/4.08 ( ( finite_finite_int @ A2 )
% 3.82/4.08 => ( ( member_int @ A @ A2 )
% 3.82/4.08 => ( ( B2
% 3.82/4.08 = ( F @ A ) )
% 3.82/4.08 => ( dvd_dvd_nat @ B2 @ ( groups1707563613775114915nt_nat @ F @ A2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % dvd_prod_eqI
% 3.82/4.08 thf(fact_6186_dvd__prod__eqI,axiom,
% 3.82/4.08 ! [A2: set_Extended_enat,A: extended_enat,B2: nat,F: extended_enat > nat] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.08 => ( ( member_Extended_enat @ A @ A2 )
% 3.82/4.08 => ( ( B2
% 3.82/4.08 = ( F @ A ) )
% 3.82/4.08 => ( dvd_dvd_nat @ B2 @ ( groups2880970938130013265at_nat @ F @ A2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % dvd_prod_eqI
% 3.82/4.08 thf(fact_6187_dvd__prod__eqI,axiom,
% 3.82/4.08 ! [A2: set_real,A: real,B2: int,F: real > int] :
% 3.82/4.08 ( ( finite_finite_real @ A2 )
% 3.82/4.08 => ( ( member_real @ A @ A2 )
% 3.82/4.08 => ( ( B2
% 3.82/4.08 = ( F @ A ) )
% 3.82/4.08 => ( dvd_dvd_int @ B2 @ ( groups4694064378042380927al_int @ F @ A2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % dvd_prod_eqI
% 3.82/4.08 thf(fact_6188_dvd__prod__eqI,axiom,
% 3.82/4.08 ! [A2: set_complex,A: complex,B2: int,F: complex > int] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.08 => ( ( member_complex @ A @ A2 )
% 3.82/4.08 => ( ( B2
% 3.82/4.08 = ( F @ A ) )
% 3.82/4.08 => ( dvd_dvd_int @ B2 @ ( groups858564598930262913ex_int @ F @ A2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % dvd_prod_eqI
% 3.82/4.08 thf(fact_6189_dvd__prod__eqI,axiom,
% 3.82/4.08 ! [A2: set_Extended_enat,A: extended_enat,B2: int,F: extended_enat > int] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.08 => ( ( member_Extended_enat @ A @ A2 )
% 3.82/4.08 => ( ( B2
% 3.82/4.08 = ( F @ A ) )
% 3.82/4.08 => ( dvd_dvd_int @ B2 @ ( groups2878480467620962989at_int @ F @ A2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % dvd_prod_eqI
% 3.82/4.08 thf(fact_6190_dvd__prod__eqI,axiom,
% 3.82/4.08 ! [A2: set_nat,A: nat,B2: int,F: nat > int] :
% 3.82/4.08 ( ( finite_finite_nat @ A2 )
% 3.82/4.08 => ( ( member_nat @ A @ A2 )
% 3.82/4.08 => ( ( B2
% 3.82/4.08 = ( F @ A ) )
% 3.82/4.08 => ( dvd_dvd_int @ B2 @ ( groups705719431365010083at_int @ F @ A2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % dvd_prod_eqI
% 3.82/4.08 thf(fact_6191_dvd__prod__eqI,axiom,
% 3.82/4.08 ! [A2: set_int,A: int,B2: int,F: int > int] :
% 3.82/4.08 ( ( finite_finite_int @ A2 )
% 3.82/4.08 => ( ( member_int @ A @ A2 )
% 3.82/4.08 => ( ( B2
% 3.82/4.08 = ( F @ A ) )
% 3.82/4.08 => ( dvd_dvd_int @ B2 @ ( groups1705073143266064639nt_int @ F @ A2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % dvd_prod_eqI
% 3.82/4.08 thf(fact_6192_dvd__prod__eqI,axiom,
% 3.82/4.08 ! [A2: set_nat,A: nat,B2: nat,F: nat > nat] :
% 3.82/4.08 ( ( finite_finite_nat @ A2 )
% 3.82/4.08 => ( ( member_nat @ A @ A2 )
% 3.82/4.08 => ( ( B2
% 3.82/4.08 = ( F @ A ) )
% 3.82/4.08 => ( dvd_dvd_nat @ B2 @ ( groups708209901874060359at_nat @ F @ A2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % dvd_prod_eqI
% 3.82/4.08 thf(fact_6193_cos__coeff__0,axiom,
% 3.82/4.08 ( ( cos_coeff @ zero_zero_nat )
% 3.82/4.08 = one_one_real ) ).
% 3.82/4.08
% 3.82/4.08 % cos_coeff_0
% 3.82/4.08 thf(fact_6194_prod_Odelta,axiom,
% 3.82/4.08 ! [S2: set_real,A: real,B2: real > nat] :
% 3.82/4.08 ( ( finite_finite_real @ S2 )
% 3.82/4.08 => ( ( ( member_real @ A @ S2 )
% 3.82/4.08 => ( ( groups4696554848551431203al_nat
% 3.82/4.08 @ ^ [K2: real] : ( if_nat @ ( K2 = A ) @ ( B2 @ K2 ) @ one_one_nat )
% 3.82/4.08 @ S2 )
% 3.82/4.08 = ( B2 @ A ) ) )
% 3.82/4.08 & ( ~ ( member_real @ A @ S2 )
% 3.82/4.08 => ( ( groups4696554848551431203al_nat
% 3.82/4.08 @ ^ [K2: real] : ( if_nat @ ( K2 = A ) @ ( B2 @ K2 ) @ one_one_nat )
% 3.82/4.08 @ S2 )
% 3.82/4.08 = one_one_nat ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.delta
% 3.82/4.08 thf(fact_6195_prod_Odelta,axiom,
% 3.82/4.08 ! [S2: set_complex,A: complex,B2: complex > nat] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ S2 )
% 3.82/4.08 => ( ( ( member_complex @ A @ S2 )
% 3.82/4.08 => ( ( groups861055069439313189ex_nat
% 3.82/4.08 @ ^ [K2: complex] : ( if_nat @ ( K2 = A ) @ ( B2 @ K2 ) @ one_one_nat )
% 3.82/4.08 @ S2 )
% 3.82/4.08 = ( B2 @ A ) ) )
% 3.82/4.08 & ( ~ ( member_complex @ A @ S2 )
% 3.82/4.08 => ( ( groups861055069439313189ex_nat
% 3.82/4.08 @ ^ [K2: complex] : ( if_nat @ ( K2 = A ) @ ( B2 @ K2 ) @ one_one_nat )
% 3.82/4.08 @ S2 )
% 3.82/4.08 = one_one_nat ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.delta
% 3.82/4.08 thf(fact_6196_prod_Odelta,axiom,
% 3.82/4.08 ! [S2: set_int,A: int,B2: int > nat] :
% 3.82/4.08 ( ( finite_finite_int @ S2 )
% 3.82/4.08 => ( ( ( member_int @ A @ S2 )
% 3.82/4.08 => ( ( groups1707563613775114915nt_nat
% 3.82/4.08 @ ^ [K2: int] : ( if_nat @ ( K2 = A ) @ ( B2 @ K2 ) @ one_one_nat )
% 3.82/4.08 @ S2 )
% 3.82/4.08 = ( B2 @ A ) ) )
% 3.82/4.08 & ( ~ ( member_int @ A @ S2 )
% 3.82/4.08 => ( ( groups1707563613775114915nt_nat
% 3.82/4.08 @ ^ [K2: int] : ( if_nat @ ( K2 = A ) @ ( B2 @ K2 ) @ one_one_nat )
% 3.82/4.08 @ S2 )
% 3.82/4.08 = one_one_nat ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.delta
% 3.82/4.08 thf(fact_6197_prod_Odelta,axiom,
% 3.82/4.08 ! [S2: set_Extended_enat,A: extended_enat,B2: extended_enat > nat] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ S2 )
% 3.82/4.08 => ( ( ( member_Extended_enat @ A @ S2 )
% 3.82/4.08 => ( ( groups2880970938130013265at_nat
% 3.82/4.08 @ ^ [K2: extended_enat] : ( if_nat @ ( K2 = A ) @ ( B2 @ K2 ) @ one_one_nat )
% 3.82/4.08 @ S2 )
% 3.82/4.08 = ( B2 @ A ) ) )
% 3.82/4.08 & ( ~ ( member_Extended_enat @ A @ S2 )
% 3.82/4.08 => ( ( groups2880970938130013265at_nat
% 3.82/4.08 @ ^ [K2: extended_enat] : ( if_nat @ ( K2 = A ) @ ( B2 @ K2 ) @ one_one_nat )
% 3.82/4.08 @ S2 )
% 3.82/4.08 = one_one_nat ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.delta
% 3.82/4.08 thf(fact_6198_prod_Odelta,axiom,
% 3.82/4.08 ! [S2: set_real,A: real,B2: real > int] :
% 3.82/4.08 ( ( finite_finite_real @ S2 )
% 3.82/4.08 => ( ( ( member_real @ A @ S2 )
% 3.82/4.08 => ( ( groups4694064378042380927al_int
% 3.82/4.08 @ ^ [K2: real] : ( if_int @ ( K2 = A ) @ ( B2 @ K2 ) @ one_one_int )
% 3.82/4.08 @ S2 )
% 3.82/4.08 = ( B2 @ A ) ) )
% 3.82/4.08 & ( ~ ( member_real @ A @ S2 )
% 3.82/4.08 => ( ( groups4694064378042380927al_int
% 3.82/4.08 @ ^ [K2: real] : ( if_int @ ( K2 = A ) @ ( B2 @ K2 ) @ one_one_int )
% 3.82/4.08 @ S2 )
% 3.82/4.08 = one_one_int ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.delta
% 3.82/4.08 thf(fact_6199_prod_Odelta,axiom,
% 3.82/4.08 ! [S2: set_complex,A: complex,B2: complex > int] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ S2 )
% 3.82/4.08 => ( ( ( member_complex @ A @ S2 )
% 3.82/4.08 => ( ( groups858564598930262913ex_int
% 3.82/4.08 @ ^ [K2: complex] : ( if_int @ ( K2 = A ) @ ( B2 @ K2 ) @ one_one_int )
% 3.82/4.08 @ S2 )
% 3.82/4.08 = ( B2 @ A ) ) )
% 3.82/4.08 & ( ~ ( member_complex @ A @ S2 )
% 3.82/4.08 => ( ( groups858564598930262913ex_int
% 3.82/4.08 @ ^ [K2: complex] : ( if_int @ ( K2 = A ) @ ( B2 @ K2 ) @ one_one_int )
% 3.82/4.08 @ S2 )
% 3.82/4.08 = one_one_int ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.delta
% 3.82/4.08 thf(fact_6200_prod_Odelta,axiom,
% 3.82/4.08 ! [S2: set_Extended_enat,A: extended_enat,B2: extended_enat > int] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ S2 )
% 3.82/4.08 => ( ( ( member_Extended_enat @ A @ S2 )
% 3.82/4.08 => ( ( groups2878480467620962989at_int
% 3.82/4.08 @ ^ [K2: extended_enat] : ( if_int @ ( K2 = A ) @ ( B2 @ K2 ) @ one_one_int )
% 3.82/4.08 @ S2 )
% 3.82/4.08 = ( B2 @ A ) ) )
% 3.82/4.08 & ( ~ ( member_Extended_enat @ A @ S2 )
% 3.82/4.08 => ( ( groups2878480467620962989at_int
% 3.82/4.08 @ ^ [K2: extended_enat] : ( if_int @ ( K2 = A ) @ ( B2 @ K2 ) @ one_one_int )
% 3.82/4.08 @ S2 )
% 3.82/4.08 = one_one_int ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.delta
% 3.82/4.08 thf(fact_6201_prod_Odelta,axiom,
% 3.82/4.08 ! [S2: set_real,A: real,B2: real > complex] :
% 3.82/4.08 ( ( finite_finite_real @ S2 )
% 3.82/4.08 => ( ( ( member_real @ A @ S2 )
% 3.82/4.08 => ( ( groups713298508707869441omplex
% 3.82/4.08 @ ^ [K2: real] : ( if_complex @ ( K2 = A ) @ ( B2 @ K2 ) @ one_one_complex )
% 3.82/4.08 @ S2 )
% 3.82/4.08 = ( B2 @ A ) ) )
% 3.82/4.08 & ( ~ ( member_real @ A @ S2 )
% 3.82/4.08 => ( ( groups713298508707869441omplex
% 3.82/4.08 @ ^ [K2: real] : ( if_complex @ ( K2 = A ) @ ( B2 @ K2 ) @ one_one_complex )
% 3.82/4.08 @ S2 )
% 3.82/4.08 = one_one_complex ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.delta
% 3.82/4.08 thf(fact_6202_prod_Odelta,axiom,
% 3.82/4.08 ! [S2: set_nat,A: nat,B2: nat > complex] :
% 3.82/4.08 ( ( finite_finite_nat @ S2 )
% 3.82/4.08 => ( ( ( member_nat @ A @ S2 )
% 3.82/4.08 => ( ( groups6464643781859351333omplex
% 3.82/4.08 @ ^ [K2: nat] : ( if_complex @ ( K2 = A ) @ ( B2 @ K2 ) @ one_one_complex )
% 3.82/4.08 @ S2 )
% 3.82/4.08 = ( B2 @ A ) ) )
% 3.82/4.08 & ( ~ ( member_nat @ A @ S2 )
% 3.82/4.08 => ( ( groups6464643781859351333omplex
% 3.82/4.08 @ ^ [K2: nat] : ( if_complex @ ( K2 = A ) @ ( B2 @ K2 ) @ one_one_complex )
% 3.82/4.08 @ S2 )
% 3.82/4.08 = one_one_complex ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.delta
% 3.82/4.08 thf(fact_6203_prod_Odelta,axiom,
% 3.82/4.08 ! [S2: set_complex,A: complex,B2: complex > complex] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ S2 )
% 3.82/4.08 => ( ( ( member_complex @ A @ S2 )
% 3.82/4.08 => ( ( groups3708469109370488835omplex
% 3.82/4.08 @ ^ [K2: complex] : ( if_complex @ ( K2 = A ) @ ( B2 @ K2 ) @ one_one_complex )
% 3.82/4.08 @ S2 )
% 3.82/4.08 = ( B2 @ A ) ) )
% 3.82/4.08 & ( ~ ( member_complex @ A @ S2 )
% 3.82/4.08 => ( ( groups3708469109370488835omplex
% 3.82/4.08 @ ^ [K2: complex] : ( if_complex @ ( K2 = A ) @ ( B2 @ K2 ) @ one_one_complex )
% 3.82/4.08 @ S2 )
% 3.82/4.08 = one_one_complex ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.delta
% 3.82/4.08 thf(fact_6204_prod_Odelta_H,axiom,
% 3.82/4.08 ! [S2: set_real,A: real,B2: real > nat] :
% 3.82/4.08 ( ( finite_finite_real @ S2 )
% 3.82/4.08 => ( ( ( member_real @ A @ S2 )
% 3.82/4.08 => ( ( groups4696554848551431203al_nat
% 3.82/4.08 @ ^ [K2: real] : ( if_nat @ ( A = K2 ) @ ( B2 @ K2 ) @ one_one_nat )
% 3.82/4.08 @ S2 )
% 3.82/4.08 = ( B2 @ A ) ) )
% 3.82/4.08 & ( ~ ( member_real @ A @ S2 )
% 3.82/4.08 => ( ( groups4696554848551431203al_nat
% 3.82/4.08 @ ^ [K2: real] : ( if_nat @ ( A = K2 ) @ ( B2 @ K2 ) @ one_one_nat )
% 3.82/4.08 @ S2 )
% 3.82/4.08 = one_one_nat ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.delta'
% 3.82/4.08 thf(fact_6205_prod_Odelta_H,axiom,
% 3.82/4.08 ! [S2: set_complex,A: complex,B2: complex > nat] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ S2 )
% 3.82/4.08 => ( ( ( member_complex @ A @ S2 )
% 3.82/4.08 => ( ( groups861055069439313189ex_nat
% 3.82/4.08 @ ^ [K2: complex] : ( if_nat @ ( A = K2 ) @ ( B2 @ K2 ) @ one_one_nat )
% 3.82/4.08 @ S2 )
% 3.82/4.08 = ( B2 @ A ) ) )
% 3.82/4.08 & ( ~ ( member_complex @ A @ S2 )
% 3.82/4.08 => ( ( groups861055069439313189ex_nat
% 3.82/4.08 @ ^ [K2: complex] : ( if_nat @ ( A = K2 ) @ ( B2 @ K2 ) @ one_one_nat )
% 3.82/4.08 @ S2 )
% 3.82/4.08 = one_one_nat ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.delta'
% 3.82/4.08 thf(fact_6206_prod_Odelta_H,axiom,
% 3.82/4.08 ! [S2: set_int,A: int,B2: int > nat] :
% 3.82/4.08 ( ( finite_finite_int @ S2 )
% 3.82/4.08 => ( ( ( member_int @ A @ S2 )
% 3.82/4.08 => ( ( groups1707563613775114915nt_nat
% 3.82/4.08 @ ^ [K2: int] : ( if_nat @ ( A = K2 ) @ ( B2 @ K2 ) @ one_one_nat )
% 3.82/4.08 @ S2 )
% 3.82/4.08 = ( B2 @ A ) ) )
% 3.82/4.08 & ( ~ ( member_int @ A @ S2 )
% 3.82/4.08 => ( ( groups1707563613775114915nt_nat
% 3.82/4.08 @ ^ [K2: int] : ( if_nat @ ( A = K2 ) @ ( B2 @ K2 ) @ one_one_nat )
% 3.82/4.08 @ S2 )
% 3.82/4.08 = one_one_nat ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.delta'
% 3.82/4.08 thf(fact_6207_prod_Odelta_H,axiom,
% 3.82/4.08 ! [S2: set_Extended_enat,A: extended_enat,B2: extended_enat > nat] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ S2 )
% 3.82/4.08 => ( ( ( member_Extended_enat @ A @ S2 )
% 3.82/4.08 => ( ( groups2880970938130013265at_nat
% 3.82/4.08 @ ^ [K2: extended_enat] : ( if_nat @ ( A = K2 ) @ ( B2 @ K2 ) @ one_one_nat )
% 3.82/4.08 @ S2 )
% 3.82/4.08 = ( B2 @ A ) ) )
% 3.82/4.08 & ( ~ ( member_Extended_enat @ A @ S2 )
% 3.82/4.08 => ( ( groups2880970938130013265at_nat
% 3.82/4.08 @ ^ [K2: extended_enat] : ( if_nat @ ( A = K2 ) @ ( B2 @ K2 ) @ one_one_nat )
% 3.82/4.08 @ S2 )
% 3.82/4.08 = one_one_nat ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.delta'
% 3.82/4.08 thf(fact_6208_prod_Odelta_H,axiom,
% 3.82/4.08 ! [S2: set_real,A: real,B2: real > int] :
% 3.82/4.08 ( ( finite_finite_real @ S2 )
% 3.82/4.08 => ( ( ( member_real @ A @ S2 )
% 3.82/4.08 => ( ( groups4694064378042380927al_int
% 3.82/4.08 @ ^ [K2: real] : ( if_int @ ( A = K2 ) @ ( B2 @ K2 ) @ one_one_int )
% 3.82/4.08 @ S2 )
% 3.82/4.08 = ( B2 @ A ) ) )
% 3.82/4.08 & ( ~ ( member_real @ A @ S2 )
% 3.82/4.08 => ( ( groups4694064378042380927al_int
% 3.82/4.08 @ ^ [K2: real] : ( if_int @ ( A = K2 ) @ ( B2 @ K2 ) @ one_one_int )
% 3.82/4.08 @ S2 )
% 3.82/4.08 = one_one_int ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.delta'
% 3.82/4.08 thf(fact_6209_prod_Odelta_H,axiom,
% 3.82/4.08 ! [S2: set_complex,A: complex,B2: complex > int] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ S2 )
% 3.82/4.08 => ( ( ( member_complex @ A @ S2 )
% 3.82/4.08 => ( ( groups858564598930262913ex_int
% 3.82/4.08 @ ^ [K2: complex] : ( if_int @ ( A = K2 ) @ ( B2 @ K2 ) @ one_one_int )
% 3.82/4.08 @ S2 )
% 3.82/4.08 = ( B2 @ A ) ) )
% 3.82/4.08 & ( ~ ( member_complex @ A @ S2 )
% 3.82/4.08 => ( ( groups858564598930262913ex_int
% 3.82/4.08 @ ^ [K2: complex] : ( if_int @ ( A = K2 ) @ ( B2 @ K2 ) @ one_one_int )
% 3.82/4.08 @ S2 )
% 3.82/4.08 = one_one_int ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.delta'
% 3.82/4.08 thf(fact_6210_prod_Odelta_H,axiom,
% 3.82/4.08 ! [S2: set_Extended_enat,A: extended_enat,B2: extended_enat > int] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ S2 )
% 3.82/4.08 => ( ( ( member_Extended_enat @ A @ S2 )
% 3.82/4.08 => ( ( groups2878480467620962989at_int
% 3.82/4.08 @ ^ [K2: extended_enat] : ( if_int @ ( A = K2 ) @ ( B2 @ K2 ) @ one_one_int )
% 3.82/4.08 @ S2 )
% 3.82/4.08 = ( B2 @ A ) ) )
% 3.82/4.08 & ( ~ ( member_Extended_enat @ A @ S2 )
% 3.82/4.08 => ( ( groups2878480467620962989at_int
% 3.82/4.08 @ ^ [K2: extended_enat] : ( if_int @ ( A = K2 ) @ ( B2 @ K2 ) @ one_one_int )
% 3.82/4.08 @ S2 )
% 3.82/4.08 = one_one_int ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.delta'
% 3.82/4.08 thf(fact_6211_prod_Odelta_H,axiom,
% 3.82/4.08 ! [S2: set_real,A: real,B2: real > complex] :
% 3.82/4.08 ( ( finite_finite_real @ S2 )
% 3.82/4.08 => ( ( ( member_real @ A @ S2 )
% 3.82/4.08 => ( ( groups713298508707869441omplex
% 3.82/4.08 @ ^ [K2: real] : ( if_complex @ ( A = K2 ) @ ( B2 @ K2 ) @ one_one_complex )
% 3.82/4.08 @ S2 )
% 3.82/4.08 = ( B2 @ A ) ) )
% 3.82/4.08 & ( ~ ( member_real @ A @ S2 )
% 3.82/4.08 => ( ( groups713298508707869441omplex
% 3.82/4.08 @ ^ [K2: real] : ( if_complex @ ( A = K2 ) @ ( B2 @ K2 ) @ one_one_complex )
% 3.82/4.08 @ S2 )
% 3.82/4.08 = one_one_complex ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.delta'
% 3.82/4.08 thf(fact_6212_prod_Odelta_H,axiom,
% 3.82/4.08 ! [S2: set_nat,A: nat,B2: nat > complex] :
% 3.82/4.08 ( ( finite_finite_nat @ S2 )
% 3.82/4.08 => ( ( ( member_nat @ A @ S2 )
% 3.82/4.08 => ( ( groups6464643781859351333omplex
% 3.82/4.08 @ ^ [K2: nat] : ( if_complex @ ( A = K2 ) @ ( B2 @ K2 ) @ one_one_complex )
% 3.82/4.08 @ S2 )
% 3.82/4.08 = ( B2 @ A ) ) )
% 3.82/4.08 & ( ~ ( member_nat @ A @ S2 )
% 3.82/4.08 => ( ( groups6464643781859351333omplex
% 3.82/4.08 @ ^ [K2: nat] : ( if_complex @ ( A = K2 ) @ ( B2 @ K2 ) @ one_one_complex )
% 3.82/4.08 @ S2 )
% 3.82/4.08 = one_one_complex ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.delta'
% 3.82/4.08 thf(fact_6213_prod_Odelta_H,axiom,
% 3.82/4.08 ! [S2: set_complex,A: complex,B2: complex > complex] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ S2 )
% 3.82/4.08 => ( ( ( member_complex @ A @ S2 )
% 3.82/4.08 => ( ( groups3708469109370488835omplex
% 3.82/4.08 @ ^ [K2: complex] : ( if_complex @ ( A = K2 ) @ ( B2 @ K2 ) @ one_one_complex )
% 3.82/4.08 @ S2 )
% 3.82/4.08 = ( B2 @ A ) ) )
% 3.82/4.08 & ( ~ ( member_complex @ A @ S2 )
% 3.82/4.08 => ( ( groups3708469109370488835omplex
% 3.82/4.08 @ ^ [K2: complex] : ( if_complex @ ( A = K2 ) @ ( B2 @ K2 ) @ one_one_complex )
% 3.82/4.08 @ S2 )
% 3.82/4.08 = one_one_complex ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.delta'
% 3.82/4.08 thf(fact_6214_prod_Oinsert,axiom,
% 3.82/4.08 ! [A2: set_real,X: real,G: real > nat] :
% 3.82/4.08 ( ( finite_finite_real @ A2 )
% 3.82/4.08 => ( ~ ( member_real @ X @ A2 )
% 3.82/4.08 => ( ( groups4696554848551431203al_nat @ G @ ( insert_real @ X @ A2 ) )
% 3.82/4.08 = ( times_times_nat @ ( G @ X ) @ ( groups4696554848551431203al_nat @ G @ A2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.insert
% 3.82/4.08 thf(fact_6215_prod_Oinsert,axiom,
% 3.82/4.08 ! [A2: set_complex,X: complex,G: complex > nat] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.08 => ( ~ ( member_complex @ X @ A2 )
% 3.82/4.08 => ( ( groups861055069439313189ex_nat @ G @ ( insert_complex @ X @ A2 ) )
% 3.82/4.08 = ( times_times_nat @ ( G @ X ) @ ( groups861055069439313189ex_nat @ G @ A2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.insert
% 3.82/4.08 thf(fact_6216_prod_Oinsert,axiom,
% 3.82/4.08 ! [A2: set_int,X: int,G: int > nat] :
% 3.82/4.08 ( ( finite_finite_int @ A2 )
% 3.82/4.08 => ( ~ ( member_int @ X @ A2 )
% 3.82/4.08 => ( ( groups1707563613775114915nt_nat @ G @ ( insert_int @ X @ A2 ) )
% 3.82/4.08 = ( times_times_nat @ ( G @ X ) @ ( groups1707563613775114915nt_nat @ G @ A2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.insert
% 3.82/4.08 thf(fact_6217_prod_Oinsert,axiom,
% 3.82/4.08 ! [A2: set_Extended_enat,X: extended_enat,G: extended_enat > nat] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.08 => ( ~ ( member_Extended_enat @ X @ A2 )
% 3.82/4.08 => ( ( groups2880970938130013265at_nat @ G @ ( insert_Extended_enat @ X @ A2 ) )
% 3.82/4.08 = ( times_times_nat @ ( G @ X ) @ ( groups2880970938130013265at_nat @ G @ A2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.insert
% 3.82/4.08 thf(fact_6218_prod_Oinsert,axiom,
% 3.82/4.08 ! [A2: set_real,X: real,G: real > int] :
% 3.82/4.08 ( ( finite_finite_real @ A2 )
% 3.82/4.08 => ( ~ ( member_real @ X @ A2 )
% 3.82/4.08 => ( ( groups4694064378042380927al_int @ G @ ( insert_real @ X @ A2 ) )
% 3.82/4.08 = ( times_times_int @ ( G @ X ) @ ( groups4694064378042380927al_int @ G @ A2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.insert
% 3.82/4.08 thf(fact_6219_prod_Oinsert,axiom,
% 3.82/4.08 ! [A2: set_complex,X: complex,G: complex > int] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.08 => ( ~ ( member_complex @ X @ A2 )
% 3.82/4.08 => ( ( groups858564598930262913ex_int @ G @ ( insert_complex @ X @ A2 ) )
% 3.82/4.08 = ( times_times_int @ ( G @ X ) @ ( groups858564598930262913ex_int @ G @ A2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.insert
% 3.82/4.08 thf(fact_6220_prod_Oinsert,axiom,
% 3.82/4.08 ! [A2: set_Extended_enat,X: extended_enat,G: extended_enat > int] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.08 => ( ~ ( member_Extended_enat @ X @ A2 )
% 3.82/4.08 => ( ( groups2878480467620962989at_int @ G @ ( insert_Extended_enat @ X @ A2 ) )
% 3.82/4.08 = ( times_times_int @ ( G @ X ) @ ( groups2878480467620962989at_int @ G @ A2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.insert
% 3.82/4.08 thf(fact_6221_prod_Oinsert,axiom,
% 3.82/4.08 ! [A2: set_real,X: real,G: real > real] :
% 3.82/4.08 ( ( finite_finite_real @ A2 )
% 3.82/4.08 => ( ~ ( member_real @ X @ A2 )
% 3.82/4.08 => ( ( groups1681761925125756287l_real @ G @ ( insert_real @ X @ A2 ) )
% 3.82/4.08 = ( times_times_real @ ( G @ X ) @ ( groups1681761925125756287l_real @ G @ A2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.insert
% 3.82/4.08 thf(fact_6222_prod_Oinsert,axiom,
% 3.82/4.08 ! [A2: set_nat,X: nat,G: nat > real] :
% 3.82/4.08 ( ( finite_finite_nat @ A2 )
% 3.82/4.08 => ( ~ ( member_nat @ X @ A2 )
% 3.82/4.08 => ( ( groups129246275422532515t_real @ G @ ( insert_nat @ X @ A2 ) )
% 3.82/4.08 = ( times_times_real @ ( G @ X ) @ ( groups129246275422532515t_real @ G @ A2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.insert
% 3.82/4.08 thf(fact_6223_prod_Oinsert,axiom,
% 3.82/4.08 ! [A2: set_complex,X: complex,G: complex > real] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.08 => ( ~ ( member_complex @ X @ A2 )
% 3.82/4.08 => ( ( groups766887009212190081x_real @ G @ ( insert_complex @ X @ A2 ) )
% 3.82/4.08 = ( times_times_real @ ( G @ X ) @ ( groups766887009212190081x_real @ G @ A2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.insert
% 3.82/4.08 thf(fact_6224_prod_OlessThan__Suc,axiom,
% 3.82/4.08 ! [G: nat > real,N2: nat] :
% 3.82/4.08 ( ( groups129246275422532515t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 3.82/4.08 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.lessThan_Suc
% 3.82/4.08 thf(fact_6225_prod_OlessThan__Suc,axiom,
% 3.82/4.08 ! [G: nat > complex,N2: nat] :
% 3.82/4.08 ( ( groups6464643781859351333omplex @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 3.82/4.08 = ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.lessThan_Suc
% 3.82/4.08 thf(fact_6226_prod_OlessThan__Suc,axiom,
% 3.82/4.08 ! [G: nat > extended_enat,N2: nat] :
% 3.82/4.08 ( ( groups7961826882256487087d_enat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 3.82/4.08 = ( times_7803423173614009249d_enat @ ( groups7961826882256487087d_enat @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.lessThan_Suc
% 3.82/4.08 thf(fact_6227_prod_OlessThan__Suc,axiom,
% 3.82/4.08 ! [G: nat > int,N2: nat] :
% 3.82/4.08 ( ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 3.82/4.08 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.lessThan_Suc
% 3.82/4.08 thf(fact_6228_prod_OlessThan__Suc,axiom,
% 3.82/4.08 ! [G: nat > nat,N2: nat] :
% 3.82/4.08 ( ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 3.82/4.08 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.lessThan_Suc
% 3.82/4.08 thf(fact_6229_powser__sums__zero__iff,axiom,
% 3.82/4.08 ! [A: nat > real,X: real] :
% 3.82/4.08 ( ( sums_real
% 3.82/4.08 @ ^ [N: nat] : ( times_times_real @ ( A @ N ) @ ( power_power_real @ zero_zero_real @ N ) )
% 3.82/4.08 @ X )
% 3.82/4.08 = ( ( A @ zero_zero_nat )
% 3.82/4.08 = X ) ) ).
% 3.82/4.08
% 3.82/4.08 % powser_sums_zero_iff
% 3.82/4.08 thf(fact_6230_powser__sums__zero__iff,axiom,
% 3.82/4.08 ! [A: nat > complex,X: complex] :
% 3.82/4.08 ( ( sums_complex
% 3.82/4.08 @ ^ [N: nat] : ( times_times_complex @ ( A @ N ) @ ( power_power_complex @ zero_zero_complex @ N ) )
% 3.82/4.08 @ X )
% 3.82/4.08 = ( ( A @ zero_zero_nat )
% 3.82/4.08 = X ) ) ).
% 3.82/4.08
% 3.82/4.08 % powser_sums_zero_iff
% 3.82/4.08 thf(fact_6231_prod_Ocl__ivl__Suc,axiom,
% 3.82/4.08 ! [N2: nat,M2: nat,G: nat > real] :
% 3.82/4.08 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 3.82/4.08 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 3.82/4.08 = one_one_real ) )
% 3.82/4.08 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 3.82/4.08 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 3.82/4.08 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.cl_ivl_Suc
% 3.82/4.08 thf(fact_6232_prod_Ocl__ivl__Suc,axiom,
% 3.82/4.08 ! [N2: nat,M2: nat,G: nat > complex] :
% 3.82/4.08 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 3.82/4.08 => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 3.82/4.08 = one_one_complex ) )
% 3.82/4.08 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 3.82/4.08 => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 3.82/4.08 = ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.cl_ivl_Suc
% 3.82/4.08 thf(fact_6233_prod_Ocl__ivl__Suc,axiom,
% 3.82/4.08 ! [N2: nat,M2: nat,G: nat > extended_enat] :
% 3.82/4.08 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 3.82/4.08 => ( ( groups7961826882256487087d_enat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 3.82/4.08 = one_on7984719198319812577d_enat ) )
% 3.82/4.08 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 3.82/4.08 => ( ( groups7961826882256487087d_enat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 3.82/4.08 = ( times_7803423173614009249d_enat @ ( groups7961826882256487087d_enat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.cl_ivl_Suc
% 3.82/4.08 thf(fact_6234_prod_Ocl__ivl__Suc,axiom,
% 3.82/4.08 ! [N2: nat,M2: nat,G: nat > int] :
% 3.82/4.08 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 3.82/4.08 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 3.82/4.08 = one_one_int ) )
% 3.82/4.08 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 3.82/4.08 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 3.82/4.08 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.cl_ivl_Suc
% 3.82/4.08 thf(fact_6235_prod_Ocl__ivl__Suc,axiom,
% 3.82/4.08 ! [N2: nat,M2: nat,G: nat > nat] :
% 3.82/4.08 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 3.82/4.08 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 3.82/4.08 = one_one_nat ) )
% 3.82/4.08 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 3.82/4.08 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 3.82/4.08 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.cl_ivl_Suc
% 3.82/4.08 thf(fact_6236_prod_Oswap__restrict,axiom,
% 3.82/4.08 ! [A2: set_real,B: set_nat,G: real > nat > int,R: real > nat > $o] :
% 3.82/4.08 ( ( finite_finite_real @ A2 )
% 3.82/4.08 => ( ( finite_finite_nat @ B )
% 3.82/4.08 => ( ( groups4694064378042380927al_int
% 3.82/4.08 @ ^ [X4: real] :
% 3.82/4.08 ( groups705719431365010083at_int @ ( G @ X4 )
% 3.82/4.08 @ ( collect_nat
% 3.82/4.08 @ ^ [Y5: nat] :
% 3.82/4.08 ( ( member_nat @ Y5 @ B )
% 3.82/4.08 & ( R @ X4 @ Y5 ) ) ) )
% 3.82/4.08 @ A2 )
% 3.82/4.08 = ( groups705719431365010083at_int
% 3.82/4.08 @ ^ [Y5: nat] :
% 3.82/4.08 ( groups4694064378042380927al_int
% 3.82/4.08 @ ^ [X4: real] : ( G @ X4 @ Y5 )
% 3.82/4.08 @ ( collect_real
% 3.82/4.08 @ ^ [X4: real] :
% 3.82/4.08 ( ( member_real @ X4 @ A2 )
% 3.82/4.08 & ( R @ X4 @ Y5 ) ) ) )
% 3.82/4.08 @ B ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.swap_restrict
% 3.82/4.08 thf(fact_6237_prod_Oswap__restrict,axiom,
% 3.82/4.08 ! [A2: set_complex,B: set_nat,G: complex > nat > int,R: complex > nat > $o] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.08 => ( ( finite_finite_nat @ B )
% 3.82/4.08 => ( ( groups858564598930262913ex_int
% 3.82/4.08 @ ^ [X4: complex] :
% 3.82/4.08 ( groups705719431365010083at_int @ ( G @ X4 )
% 3.82/4.08 @ ( collect_nat
% 3.82/4.08 @ ^ [Y5: nat] :
% 3.82/4.08 ( ( member_nat @ Y5 @ B )
% 3.82/4.08 & ( R @ X4 @ Y5 ) ) ) )
% 3.82/4.08 @ A2 )
% 3.82/4.08 = ( groups705719431365010083at_int
% 3.82/4.08 @ ^ [Y5: nat] :
% 3.82/4.08 ( groups858564598930262913ex_int
% 3.82/4.08 @ ^ [X4: complex] : ( G @ X4 @ Y5 )
% 3.82/4.08 @ ( collect_complex
% 3.82/4.08 @ ^ [X4: complex] :
% 3.82/4.08 ( ( member_complex @ X4 @ A2 )
% 3.82/4.08 & ( R @ X4 @ Y5 ) ) ) )
% 3.82/4.08 @ B ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.swap_restrict
% 3.82/4.08 thf(fact_6238_prod_Oswap__restrict,axiom,
% 3.82/4.08 ! [A2: set_Extended_enat,B: set_nat,G: extended_enat > nat > int,R: extended_enat > nat > $o] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.08 => ( ( finite_finite_nat @ B )
% 3.82/4.08 => ( ( groups2878480467620962989at_int
% 3.82/4.08 @ ^ [X4: extended_enat] :
% 3.82/4.08 ( groups705719431365010083at_int @ ( G @ X4 )
% 3.82/4.08 @ ( collect_nat
% 3.82/4.08 @ ^ [Y5: nat] :
% 3.82/4.08 ( ( member_nat @ Y5 @ B )
% 3.82/4.08 & ( R @ X4 @ Y5 ) ) ) )
% 3.82/4.08 @ A2 )
% 3.82/4.08 = ( groups705719431365010083at_int
% 3.82/4.08 @ ^ [Y5: nat] :
% 3.82/4.08 ( groups2878480467620962989at_int
% 3.82/4.08 @ ^ [X4: extended_enat] : ( G @ X4 @ Y5 )
% 3.82/4.08 @ ( collec4429806609662206161d_enat
% 3.82/4.08 @ ^ [X4: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ X4 @ A2 )
% 3.82/4.08 & ( R @ X4 @ Y5 ) ) ) )
% 3.82/4.08 @ B ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.swap_restrict
% 3.82/4.08 thf(fact_6239_prod_Oswap__restrict,axiom,
% 3.82/4.08 ! [A2: set_real,B: set_int,G: real > int > int,R: real > int > $o] :
% 3.82/4.08 ( ( finite_finite_real @ A2 )
% 3.82/4.08 => ( ( finite_finite_int @ B )
% 3.82/4.08 => ( ( groups4694064378042380927al_int
% 3.82/4.08 @ ^ [X4: real] :
% 3.82/4.08 ( groups1705073143266064639nt_int @ ( G @ X4 )
% 3.82/4.08 @ ( collect_int
% 3.82/4.08 @ ^ [Y5: int] :
% 3.82/4.08 ( ( member_int @ Y5 @ B )
% 3.82/4.08 & ( R @ X4 @ Y5 ) ) ) )
% 3.82/4.08 @ A2 )
% 3.82/4.08 = ( groups1705073143266064639nt_int
% 3.82/4.08 @ ^ [Y5: int] :
% 3.82/4.08 ( groups4694064378042380927al_int
% 3.82/4.08 @ ^ [X4: real] : ( G @ X4 @ Y5 )
% 3.82/4.08 @ ( collect_real
% 3.82/4.08 @ ^ [X4: real] :
% 3.82/4.08 ( ( member_real @ X4 @ A2 )
% 3.82/4.08 & ( R @ X4 @ Y5 ) ) ) )
% 3.82/4.08 @ B ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.swap_restrict
% 3.82/4.08 thf(fact_6240_prod_Oswap__restrict,axiom,
% 3.82/4.08 ! [A2: set_complex,B: set_int,G: complex > int > int,R: complex > int > $o] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.08 => ( ( finite_finite_int @ B )
% 3.82/4.08 => ( ( groups858564598930262913ex_int
% 3.82/4.08 @ ^ [X4: complex] :
% 3.82/4.08 ( groups1705073143266064639nt_int @ ( G @ X4 )
% 3.82/4.08 @ ( collect_int
% 3.82/4.08 @ ^ [Y5: int] :
% 3.82/4.08 ( ( member_int @ Y5 @ B )
% 3.82/4.08 & ( R @ X4 @ Y5 ) ) ) )
% 3.82/4.08 @ A2 )
% 3.82/4.08 = ( groups1705073143266064639nt_int
% 3.82/4.08 @ ^ [Y5: int] :
% 3.82/4.08 ( groups858564598930262913ex_int
% 3.82/4.08 @ ^ [X4: complex] : ( G @ X4 @ Y5 )
% 3.82/4.08 @ ( collect_complex
% 3.82/4.08 @ ^ [X4: complex] :
% 3.82/4.08 ( ( member_complex @ X4 @ A2 )
% 3.82/4.08 & ( R @ X4 @ Y5 ) ) ) )
% 3.82/4.08 @ B ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.swap_restrict
% 3.82/4.08 thf(fact_6241_prod_Oswap__restrict,axiom,
% 3.82/4.08 ! [A2: set_Extended_enat,B: set_int,G: extended_enat > int > int,R: extended_enat > int > $o] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.08 => ( ( finite_finite_int @ B )
% 3.82/4.08 => ( ( groups2878480467620962989at_int
% 3.82/4.08 @ ^ [X4: extended_enat] :
% 3.82/4.08 ( groups1705073143266064639nt_int @ ( G @ X4 )
% 3.82/4.08 @ ( collect_int
% 3.82/4.08 @ ^ [Y5: int] :
% 3.82/4.08 ( ( member_int @ Y5 @ B )
% 3.82/4.08 & ( R @ X4 @ Y5 ) ) ) )
% 3.82/4.08 @ A2 )
% 3.82/4.08 = ( groups1705073143266064639nt_int
% 3.82/4.08 @ ^ [Y5: int] :
% 3.82/4.08 ( groups2878480467620962989at_int
% 3.82/4.08 @ ^ [X4: extended_enat] : ( G @ X4 @ Y5 )
% 3.82/4.08 @ ( collec4429806609662206161d_enat
% 3.82/4.08 @ ^ [X4: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ X4 @ A2 )
% 3.82/4.08 & ( R @ X4 @ Y5 ) ) ) )
% 3.82/4.08 @ B ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.swap_restrict
% 3.82/4.08 thf(fact_6242_prod_Oswap__restrict,axiom,
% 3.82/4.08 ! [A2: set_real,B: set_nat,G: real > nat > nat,R: real > nat > $o] :
% 3.82/4.08 ( ( finite_finite_real @ A2 )
% 3.82/4.08 => ( ( finite_finite_nat @ B )
% 3.82/4.08 => ( ( groups4696554848551431203al_nat
% 3.82/4.08 @ ^ [X4: real] :
% 3.82/4.08 ( groups708209901874060359at_nat @ ( G @ X4 )
% 3.82/4.08 @ ( collect_nat
% 3.82/4.08 @ ^ [Y5: nat] :
% 3.82/4.08 ( ( member_nat @ Y5 @ B )
% 3.82/4.08 & ( R @ X4 @ Y5 ) ) ) )
% 3.82/4.08 @ A2 )
% 3.82/4.08 = ( groups708209901874060359at_nat
% 3.82/4.08 @ ^ [Y5: nat] :
% 3.82/4.08 ( groups4696554848551431203al_nat
% 3.82/4.08 @ ^ [X4: real] : ( G @ X4 @ Y5 )
% 3.82/4.08 @ ( collect_real
% 3.82/4.08 @ ^ [X4: real] :
% 3.82/4.08 ( ( member_real @ X4 @ A2 )
% 3.82/4.08 & ( R @ X4 @ Y5 ) ) ) )
% 3.82/4.08 @ B ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.swap_restrict
% 3.82/4.08 thf(fact_6243_prod_Oswap__restrict,axiom,
% 3.82/4.08 ! [A2: set_complex,B: set_nat,G: complex > nat > nat,R: complex > nat > $o] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.08 => ( ( finite_finite_nat @ B )
% 3.82/4.08 => ( ( groups861055069439313189ex_nat
% 3.82/4.08 @ ^ [X4: complex] :
% 3.82/4.08 ( groups708209901874060359at_nat @ ( G @ X4 )
% 3.82/4.08 @ ( collect_nat
% 3.82/4.08 @ ^ [Y5: nat] :
% 3.82/4.08 ( ( member_nat @ Y5 @ B )
% 3.82/4.08 & ( R @ X4 @ Y5 ) ) ) )
% 3.82/4.08 @ A2 )
% 3.82/4.08 = ( groups708209901874060359at_nat
% 3.82/4.08 @ ^ [Y5: nat] :
% 3.82/4.08 ( groups861055069439313189ex_nat
% 3.82/4.08 @ ^ [X4: complex] : ( G @ X4 @ Y5 )
% 3.82/4.08 @ ( collect_complex
% 3.82/4.08 @ ^ [X4: complex] :
% 3.82/4.08 ( ( member_complex @ X4 @ A2 )
% 3.82/4.08 & ( R @ X4 @ Y5 ) ) ) )
% 3.82/4.08 @ B ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.swap_restrict
% 3.82/4.08 thf(fact_6244_prod_Oswap__restrict,axiom,
% 3.82/4.08 ! [A2: set_int,B: set_nat,G: int > nat > nat,R: int > nat > $o] :
% 3.82/4.08 ( ( finite_finite_int @ A2 )
% 3.82/4.08 => ( ( finite_finite_nat @ B )
% 3.82/4.08 => ( ( groups1707563613775114915nt_nat
% 3.82/4.08 @ ^ [X4: int] :
% 3.82/4.08 ( groups708209901874060359at_nat @ ( G @ X4 )
% 3.82/4.08 @ ( collect_nat
% 3.82/4.08 @ ^ [Y5: nat] :
% 3.82/4.08 ( ( member_nat @ Y5 @ B )
% 3.82/4.08 & ( R @ X4 @ Y5 ) ) ) )
% 3.82/4.08 @ A2 )
% 3.82/4.08 = ( groups708209901874060359at_nat
% 3.82/4.08 @ ^ [Y5: nat] :
% 3.82/4.08 ( groups1707563613775114915nt_nat
% 3.82/4.08 @ ^ [X4: int] : ( G @ X4 @ Y5 )
% 3.82/4.08 @ ( collect_int
% 3.82/4.08 @ ^ [X4: int] :
% 3.82/4.08 ( ( member_int @ X4 @ A2 )
% 3.82/4.08 & ( R @ X4 @ Y5 ) ) ) )
% 3.82/4.08 @ B ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.swap_restrict
% 3.82/4.08 thf(fact_6245_prod_Oswap__restrict,axiom,
% 3.82/4.08 ! [A2: set_Extended_enat,B: set_nat,G: extended_enat > nat > nat,R: extended_enat > nat > $o] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.08 => ( ( finite_finite_nat @ B )
% 3.82/4.08 => ( ( groups2880970938130013265at_nat
% 3.82/4.08 @ ^ [X4: extended_enat] :
% 3.82/4.08 ( groups708209901874060359at_nat @ ( G @ X4 )
% 3.82/4.08 @ ( collect_nat
% 3.82/4.08 @ ^ [Y5: nat] :
% 3.82/4.08 ( ( member_nat @ Y5 @ B )
% 3.82/4.08 & ( R @ X4 @ Y5 ) ) ) )
% 3.82/4.08 @ A2 )
% 3.82/4.08 = ( groups708209901874060359at_nat
% 3.82/4.08 @ ^ [Y5: nat] :
% 3.82/4.08 ( groups2880970938130013265at_nat
% 3.82/4.08 @ ^ [X4: extended_enat] : ( G @ X4 @ Y5 )
% 3.82/4.08 @ ( collec4429806609662206161d_enat
% 3.82/4.08 @ ^ [X4: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ X4 @ A2 )
% 3.82/4.08 & ( R @ X4 @ Y5 ) ) ) )
% 3.82/4.08 @ B ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.swap_restrict
% 3.82/4.08 thf(fact_6246_prod__mono,axiom,
% 3.82/4.08 ! [A2: set_Extended_enat,F: extended_enat > real,G: extended_enat > real] :
% 3.82/4.08 ( ! [I4: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ I4 @ A2 )
% 3.82/4.08 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 3.82/4.08 & ( ord_less_eq_real @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 3.82/4.08 => ( ord_less_eq_real @ ( groups97031904164794029t_real @ F @ A2 ) @ ( groups97031904164794029t_real @ G @ A2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_mono
% 3.82/4.08 thf(fact_6247_prod__mono,axiom,
% 3.82/4.08 ! [A2: set_real,F: real > real,G: real > real] :
% 3.82/4.08 ( ! [I4: real] :
% 3.82/4.08 ( ( member_real @ I4 @ A2 )
% 3.82/4.08 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 3.82/4.08 & ( ord_less_eq_real @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 3.82/4.08 => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ ( groups1681761925125756287l_real @ G @ A2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_mono
% 3.82/4.08 thf(fact_6248_prod__mono,axiom,
% 3.82/4.08 ! [A2: set_nat,F: nat > real,G: nat > real] :
% 3.82/4.08 ( ! [I4: nat] :
% 3.82/4.08 ( ( member_nat @ I4 @ A2 )
% 3.82/4.08 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 3.82/4.08 & ( ord_less_eq_real @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 3.82/4.08 => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F @ A2 ) @ ( groups129246275422532515t_real @ G @ A2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_mono
% 3.82/4.08 thf(fact_6249_prod__mono,axiom,
% 3.82/4.08 ! [A2: set_int,F: int > real,G: int > real] :
% 3.82/4.08 ( ! [I4: int] :
% 3.82/4.08 ( ( member_int @ I4 @ A2 )
% 3.82/4.08 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 3.82/4.08 & ( ord_less_eq_real @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 3.82/4.08 => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ ( groups2316167850115554303t_real @ G @ A2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_mono
% 3.82/4.08 thf(fact_6250_prod__mono,axiom,
% 3.82/4.08 ! [A2: set_Extended_enat,F: extended_enat > nat,G: extended_enat > nat] :
% 3.82/4.08 ( ! [I4: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ I4 @ A2 )
% 3.82/4.08 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) )
% 3.82/4.08 & ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 3.82/4.08 => ( ord_less_eq_nat @ ( groups2880970938130013265at_nat @ F @ A2 ) @ ( groups2880970938130013265at_nat @ G @ A2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_mono
% 3.82/4.08 thf(fact_6251_prod__mono,axiom,
% 3.82/4.08 ! [A2: set_real,F: real > nat,G: real > nat] :
% 3.82/4.08 ( ! [I4: real] :
% 3.82/4.08 ( ( member_real @ I4 @ A2 )
% 3.82/4.08 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) )
% 3.82/4.08 & ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 3.82/4.08 => ( ord_less_eq_nat @ ( groups4696554848551431203al_nat @ F @ A2 ) @ ( groups4696554848551431203al_nat @ G @ A2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_mono
% 3.82/4.08 thf(fact_6252_prod__mono,axiom,
% 3.82/4.08 ! [A2: set_int,F: int > nat,G: int > nat] :
% 3.82/4.08 ( ! [I4: int] :
% 3.82/4.08 ( ( member_int @ I4 @ A2 )
% 3.82/4.08 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) )
% 3.82/4.08 & ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 3.82/4.08 => ( ord_less_eq_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) @ ( groups1707563613775114915nt_nat @ G @ A2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_mono
% 3.82/4.08 thf(fact_6253_prod__mono,axiom,
% 3.82/4.08 ! [A2: set_Extended_enat,F: extended_enat > int,G: extended_enat > int] :
% 3.82/4.08 ( ! [I4: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ I4 @ A2 )
% 3.82/4.08 => ( ( ord_less_eq_int @ zero_zero_int @ ( F @ I4 ) )
% 3.82/4.08 & ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 3.82/4.08 => ( ord_less_eq_int @ ( groups2878480467620962989at_int @ F @ A2 ) @ ( groups2878480467620962989at_int @ G @ A2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_mono
% 3.82/4.08 thf(fact_6254_prod__mono,axiom,
% 3.82/4.08 ! [A2: set_real,F: real > int,G: real > int] :
% 3.82/4.08 ( ! [I4: real] :
% 3.82/4.08 ( ( member_real @ I4 @ A2 )
% 3.82/4.08 => ( ( ord_less_eq_int @ zero_zero_int @ ( F @ I4 ) )
% 3.82/4.08 & ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 3.82/4.08 => ( ord_less_eq_int @ ( groups4694064378042380927al_int @ F @ A2 ) @ ( groups4694064378042380927al_int @ G @ A2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_mono
% 3.82/4.08 thf(fact_6255_prod__mono,axiom,
% 3.82/4.08 ! [A2: set_nat,F: nat > int,G: nat > int] :
% 3.82/4.08 ( ! [I4: nat] :
% 3.82/4.08 ( ( member_nat @ I4 @ A2 )
% 3.82/4.08 => ( ( ord_less_eq_int @ zero_zero_int @ ( F @ I4 ) )
% 3.82/4.08 & ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 3.82/4.08 => ( ord_less_eq_int @ ( groups705719431365010083at_int @ F @ A2 ) @ ( groups705719431365010083at_int @ G @ A2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_mono
% 3.82/4.08 thf(fact_6256_prod__nonneg,axiom,
% 3.82/4.08 ! [A2: set_nat,F: nat > int] :
% 3.82/4.08 ( ! [X5: nat] :
% 3.82/4.08 ( ( member_nat @ X5 @ A2 )
% 3.82/4.08 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X5 ) ) )
% 3.82/4.08 => ( ord_less_eq_int @ zero_zero_int @ ( groups705719431365010083at_int @ F @ A2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_nonneg
% 3.82/4.08 thf(fact_6257_prod__nonneg,axiom,
% 3.82/4.08 ! [A2: set_int,F: int > int] :
% 3.82/4.08 ( ! [X5: int] :
% 3.82/4.08 ( ( member_int @ X5 @ A2 )
% 3.82/4.08 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X5 ) ) )
% 3.82/4.08 => ( ord_less_eq_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F @ A2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_nonneg
% 3.82/4.08 thf(fact_6258_prod__nonneg,axiom,
% 3.82/4.08 ! [A2: set_nat,F: nat > nat] :
% 3.82/4.08 ( ! [X5: nat] :
% 3.82/4.08 ( ( member_nat @ X5 @ A2 )
% 3.82/4.08 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) ) )
% 3.82/4.08 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_nonneg
% 3.82/4.08 thf(fact_6259_prod__pos,axiom,
% 3.82/4.08 ! [A2: set_nat,F: nat > int] :
% 3.82/4.08 ( ! [X5: nat] :
% 3.82/4.08 ( ( member_nat @ X5 @ A2 )
% 3.82/4.08 => ( ord_less_int @ zero_zero_int @ ( F @ X5 ) ) )
% 3.82/4.08 => ( ord_less_int @ zero_zero_int @ ( groups705719431365010083at_int @ F @ A2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_pos
% 3.82/4.08 thf(fact_6260_prod__pos,axiom,
% 3.82/4.08 ! [A2: set_int,F: int > int] :
% 3.82/4.08 ( ! [X5: int] :
% 3.82/4.08 ( ( member_int @ X5 @ A2 )
% 3.82/4.08 => ( ord_less_int @ zero_zero_int @ ( F @ X5 ) ) )
% 3.82/4.08 => ( ord_less_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F @ A2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_pos
% 3.82/4.08 thf(fact_6261_prod__pos,axiom,
% 3.82/4.08 ! [A2: set_nat,F: nat > nat] :
% 3.82/4.08 ( ! [X5: nat] :
% 3.82/4.08 ( ( member_nat @ X5 @ A2 )
% 3.82/4.08 => ( ord_less_nat @ zero_zero_nat @ ( F @ X5 ) ) )
% 3.82/4.08 => ( ord_less_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_pos
% 3.82/4.08 thf(fact_6262_prod__ge__1,axiom,
% 3.82/4.08 ! [A2: set_Extended_enat,F: extended_enat > real] :
% 3.82/4.08 ( ! [X5: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ X5 @ A2 )
% 3.82/4.08 => ( ord_less_eq_real @ one_one_real @ ( F @ X5 ) ) )
% 3.82/4.08 => ( ord_less_eq_real @ one_one_real @ ( groups97031904164794029t_real @ F @ A2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_ge_1
% 3.82/4.08 thf(fact_6263_prod__ge__1,axiom,
% 3.82/4.08 ! [A2: set_real,F: real > real] :
% 3.82/4.08 ( ! [X5: real] :
% 3.82/4.08 ( ( member_real @ X5 @ A2 )
% 3.82/4.08 => ( ord_less_eq_real @ one_one_real @ ( F @ X5 ) ) )
% 3.82/4.08 => ( ord_less_eq_real @ one_one_real @ ( groups1681761925125756287l_real @ F @ A2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_ge_1
% 3.82/4.08 thf(fact_6264_prod__ge__1,axiom,
% 3.82/4.08 ! [A2: set_nat,F: nat > real] :
% 3.82/4.08 ( ! [X5: nat] :
% 3.82/4.08 ( ( member_nat @ X5 @ A2 )
% 3.82/4.08 => ( ord_less_eq_real @ one_one_real @ ( F @ X5 ) ) )
% 3.82/4.08 => ( ord_less_eq_real @ one_one_real @ ( groups129246275422532515t_real @ F @ A2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_ge_1
% 3.82/4.08 thf(fact_6265_prod__ge__1,axiom,
% 3.82/4.08 ! [A2: set_int,F: int > real] :
% 3.82/4.08 ( ! [X5: int] :
% 3.82/4.08 ( ( member_int @ X5 @ A2 )
% 3.82/4.08 => ( ord_less_eq_real @ one_one_real @ ( F @ X5 ) ) )
% 3.82/4.08 => ( ord_less_eq_real @ one_one_real @ ( groups2316167850115554303t_real @ F @ A2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_ge_1
% 3.82/4.08 thf(fact_6266_prod__ge__1,axiom,
% 3.82/4.08 ! [A2: set_Extended_enat,F: extended_enat > nat] :
% 3.82/4.08 ( ! [X5: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ X5 @ A2 )
% 3.82/4.08 => ( ord_less_eq_nat @ one_one_nat @ ( F @ X5 ) ) )
% 3.82/4.08 => ( ord_less_eq_nat @ one_one_nat @ ( groups2880970938130013265at_nat @ F @ A2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_ge_1
% 3.82/4.08 thf(fact_6267_prod__ge__1,axiom,
% 3.82/4.08 ! [A2: set_real,F: real > nat] :
% 3.82/4.08 ( ! [X5: real] :
% 3.82/4.08 ( ( member_real @ X5 @ A2 )
% 3.82/4.08 => ( ord_less_eq_nat @ one_one_nat @ ( F @ X5 ) ) )
% 3.82/4.08 => ( ord_less_eq_nat @ one_one_nat @ ( groups4696554848551431203al_nat @ F @ A2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_ge_1
% 3.82/4.08 thf(fact_6268_prod__ge__1,axiom,
% 3.82/4.08 ! [A2: set_int,F: int > nat] :
% 3.82/4.08 ( ! [X5: int] :
% 3.82/4.08 ( ( member_int @ X5 @ A2 )
% 3.82/4.08 => ( ord_less_eq_nat @ one_one_nat @ ( F @ X5 ) ) )
% 3.82/4.08 => ( ord_less_eq_nat @ one_one_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_ge_1
% 3.82/4.08 thf(fact_6269_prod__ge__1,axiom,
% 3.82/4.08 ! [A2: set_Extended_enat,F: extended_enat > int] :
% 3.82/4.08 ( ! [X5: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ X5 @ A2 )
% 3.82/4.08 => ( ord_less_eq_int @ one_one_int @ ( F @ X5 ) ) )
% 3.82/4.08 => ( ord_less_eq_int @ one_one_int @ ( groups2878480467620962989at_int @ F @ A2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_ge_1
% 3.82/4.08 thf(fact_6270_prod__ge__1,axiom,
% 3.82/4.08 ! [A2: set_real,F: real > int] :
% 3.82/4.08 ( ! [X5: real] :
% 3.82/4.08 ( ( member_real @ X5 @ A2 )
% 3.82/4.08 => ( ord_less_eq_int @ one_one_int @ ( F @ X5 ) ) )
% 3.82/4.08 => ( ord_less_eq_int @ one_one_int @ ( groups4694064378042380927al_int @ F @ A2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_ge_1
% 3.82/4.08 thf(fact_6271_prod__ge__1,axiom,
% 3.82/4.08 ! [A2: set_nat,F: nat > int] :
% 3.82/4.08 ( ! [X5: nat] :
% 3.82/4.08 ( ( member_nat @ X5 @ A2 )
% 3.82/4.08 => ( ord_less_eq_int @ one_one_int @ ( F @ X5 ) ) )
% 3.82/4.08 => ( ord_less_eq_int @ one_one_int @ ( groups705719431365010083at_int @ F @ A2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_ge_1
% 3.82/4.08 thf(fact_6272_prod__zero,axiom,
% 3.82/4.08 ! [A2: set_complex,F: complex > nat] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.08 => ( ? [X2: complex] :
% 3.82/4.08 ( ( member_complex @ X2 @ A2 )
% 3.82/4.08 & ( ( F @ X2 )
% 3.82/4.08 = zero_zero_nat ) )
% 3.82/4.08 => ( ( groups861055069439313189ex_nat @ F @ A2 )
% 3.82/4.08 = zero_zero_nat ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_zero
% 3.82/4.08 thf(fact_6273_prod__zero,axiom,
% 3.82/4.08 ! [A2: set_int,F: int > nat] :
% 3.82/4.08 ( ( finite_finite_int @ A2 )
% 3.82/4.08 => ( ? [X2: int] :
% 3.82/4.08 ( ( member_int @ X2 @ A2 )
% 3.82/4.08 & ( ( F @ X2 )
% 3.82/4.08 = zero_zero_nat ) )
% 3.82/4.08 => ( ( groups1707563613775114915nt_nat @ F @ A2 )
% 3.82/4.08 = zero_zero_nat ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_zero
% 3.82/4.08 thf(fact_6274_prod__zero,axiom,
% 3.82/4.08 ! [A2: set_Extended_enat,F: extended_enat > nat] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.08 => ( ? [X2: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ X2 @ A2 )
% 3.82/4.08 & ( ( F @ X2 )
% 3.82/4.08 = zero_zero_nat ) )
% 3.82/4.08 => ( ( groups2880970938130013265at_nat @ F @ A2 )
% 3.82/4.08 = zero_zero_nat ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_zero
% 3.82/4.08 thf(fact_6275_prod__zero,axiom,
% 3.82/4.08 ! [A2: set_nat,F: nat > real] :
% 3.82/4.08 ( ( finite_finite_nat @ A2 )
% 3.82/4.08 => ( ? [X2: nat] :
% 3.82/4.08 ( ( member_nat @ X2 @ A2 )
% 3.82/4.08 & ( ( F @ X2 )
% 3.82/4.08 = zero_zero_real ) )
% 3.82/4.08 => ( ( groups129246275422532515t_real @ F @ A2 )
% 3.82/4.08 = zero_zero_real ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_zero
% 3.82/4.08 thf(fact_6276_prod__zero,axiom,
% 3.82/4.08 ! [A2: set_complex,F: complex > real] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.08 => ( ? [X2: complex] :
% 3.82/4.08 ( ( member_complex @ X2 @ A2 )
% 3.82/4.08 & ( ( F @ X2 )
% 3.82/4.08 = zero_zero_real ) )
% 3.82/4.08 => ( ( groups766887009212190081x_real @ F @ A2 )
% 3.82/4.08 = zero_zero_real ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_zero
% 3.82/4.08 thf(fact_6277_prod__zero,axiom,
% 3.82/4.08 ! [A2: set_int,F: int > real] :
% 3.82/4.08 ( ( finite_finite_int @ A2 )
% 3.82/4.08 => ( ? [X2: int] :
% 3.82/4.08 ( ( member_int @ X2 @ A2 )
% 3.82/4.08 & ( ( F @ X2 )
% 3.82/4.08 = zero_zero_real ) )
% 3.82/4.08 => ( ( groups2316167850115554303t_real @ F @ A2 )
% 3.82/4.08 = zero_zero_real ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_zero
% 3.82/4.08 thf(fact_6278_prod__zero,axiom,
% 3.82/4.08 ! [A2: set_Extended_enat,F: extended_enat > real] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.08 => ( ? [X2: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ X2 @ A2 )
% 3.82/4.08 & ( ( F @ X2 )
% 3.82/4.08 = zero_zero_real ) )
% 3.82/4.08 => ( ( groups97031904164794029t_real @ F @ A2 )
% 3.82/4.08 = zero_zero_real ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_zero
% 3.82/4.08 thf(fact_6279_prod__zero,axiom,
% 3.82/4.08 ! [A2: set_complex,F: complex > int] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.08 => ( ? [X2: complex] :
% 3.82/4.08 ( ( member_complex @ X2 @ A2 )
% 3.82/4.08 & ( ( F @ X2 )
% 3.82/4.08 = zero_zero_int ) )
% 3.82/4.08 => ( ( groups858564598930262913ex_int @ F @ A2 )
% 3.82/4.08 = zero_zero_int ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_zero
% 3.82/4.08 thf(fact_6280_prod__zero,axiom,
% 3.82/4.08 ! [A2: set_Extended_enat,F: extended_enat > int] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.08 => ( ? [X2: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ X2 @ A2 )
% 3.82/4.08 & ( ( F @ X2 )
% 3.82/4.08 = zero_zero_int ) )
% 3.82/4.08 => ( ( groups2878480467620962989at_int @ F @ A2 )
% 3.82/4.08 = zero_zero_int ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_zero
% 3.82/4.08 thf(fact_6281_prod__zero,axiom,
% 3.82/4.08 ! [A2: set_nat,F: nat > complex] :
% 3.82/4.08 ( ( finite_finite_nat @ A2 )
% 3.82/4.08 => ( ? [X2: nat] :
% 3.82/4.08 ( ( member_nat @ X2 @ A2 )
% 3.82/4.08 & ( ( F @ X2 )
% 3.82/4.08 = zero_zero_complex ) )
% 3.82/4.08 => ( ( groups6464643781859351333omplex @ F @ A2 )
% 3.82/4.08 = zero_zero_complex ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_zero
% 3.82/4.08 thf(fact_6282_prod__atLeastAtMost__code,axiom,
% 3.82/4.08 ! [F: nat > real,A: nat,B2: nat] :
% 3.82/4.08 ( ( groups129246275422532515t_real @ F @ ( set_or1269000886237332187st_nat @ A @ B2 ) )
% 3.82/4.08 = ( set_fo3111899725591712190t_real
% 3.82/4.08 @ ^ [A3: nat] : ( times_times_real @ ( F @ A3 ) )
% 3.82/4.08 @ A
% 3.82/4.08 @ B2
% 3.82/4.08 @ one_one_real ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_atLeastAtMost_code
% 3.82/4.08 thf(fact_6283_prod__atLeastAtMost__code,axiom,
% 3.82/4.08 ! [F: nat > complex,A: nat,B2: nat] :
% 3.82/4.08 ( ( groups6464643781859351333omplex @ F @ ( set_or1269000886237332187st_nat @ A @ B2 ) )
% 3.82/4.08 = ( set_fo1517530859248394432omplex
% 3.82/4.08 @ ^ [A3: nat] : ( times_times_complex @ ( F @ A3 ) )
% 3.82/4.08 @ A
% 3.82/4.08 @ B2
% 3.82/4.08 @ one_one_complex ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_atLeastAtMost_code
% 3.82/4.08 thf(fact_6284_prod__atLeastAtMost__code,axiom,
% 3.82/4.08 ! [F: nat > extended_enat,A: nat,B2: nat] :
% 3.82/4.08 ( ( groups7961826882256487087d_enat @ F @ ( set_or1269000886237332187st_nat @ A @ B2 ) )
% 3.82/4.08 = ( set_fo2538466533108834004d_enat
% 3.82/4.08 @ ^ [A3: nat] : ( times_7803423173614009249d_enat @ ( F @ A3 ) )
% 3.82/4.08 @ A
% 3.82/4.08 @ B2
% 3.82/4.08 @ one_on7984719198319812577d_enat ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_atLeastAtMost_code
% 3.82/4.08 thf(fact_6285_prod__atLeastAtMost__code,axiom,
% 3.82/4.08 ! [F: nat > int,A: nat,B2: nat] :
% 3.82/4.08 ( ( groups705719431365010083at_int @ F @ ( set_or1269000886237332187st_nat @ A @ B2 ) )
% 3.82/4.08 = ( set_fo2581907887559384638at_int
% 3.82/4.08 @ ^ [A3: nat] : ( times_times_int @ ( F @ A3 ) )
% 3.82/4.08 @ A
% 3.82/4.08 @ B2
% 3.82/4.08 @ one_one_int ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_atLeastAtMost_code
% 3.82/4.08 thf(fact_6286_prod__atLeastAtMost__code,axiom,
% 3.82/4.08 ! [F: nat > nat,A: nat,B2: nat] :
% 3.82/4.08 ( ( groups708209901874060359at_nat @ F @ ( set_or1269000886237332187st_nat @ A @ B2 ) )
% 3.82/4.08 = ( set_fo2584398358068434914at_nat
% 3.82/4.08 @ ^ [A3: nat] : ( times_times_nat @ ( F @ A3 ) )
% 3.82/4.08 @ A
% 3.82/4.08 @ B2
% 3.82/4.08 @ one_one_nat ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_atLeastAtMost_code
% 3.82/4.08 thf(fact_6287_prod_Ointer__filter,axiom,
% 3.82/4.08 ! [A2: set_real,G: real > nat,P: real > $o] :
% 3.82/4.08 ( ( finite_finite_real @ A2 )
% 3.82/4.08 => ( ( groups4696554848551431203al_nat @ G
% 3.82/4.08 @ ( collect_real
% 3.82/4.08 @ ^ [X4: real] :
% 3.82/4.08 ( ( member_real @ X4 @ A2 )
% 3.82/4.08 & ( P @ X4 ) ) ) )
% 3.82/4.08 = ( groups4696554848551431203al_nat
% 3.82/4.08 @ ^ [X4: real] : ( if_nat @ ( P @ X4 ) @ ( G @ X4 ) @ one_one_nat )
% 3.82/4.08 @ A2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.inter_filter
% 3.82/4.08 thf(fact_6288_prod_Ointer__filter,axiom,
% 3.82/4.08 ! [A2: set_complex,G: complex > nat,P: complex > $o] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.08 => ( ( groups861055069439313189ex_nat @ G
% 3.82/4.08 @ ( collect_complex
% 3.82/4.08 @ ^ [X4: complex] :
% 3.82/4.08 ( ( member_complex @ X4 @ A2 )
% 3.82/4.08 & ( P @ X4 ) ) ) )
% 3.82/4.08 = ( groups861055069439313189ex_nat
% 3.82/4.08 @ ^ [X4: complex] : ( if_nat @ ( P @ X4 ) @ ( G @ X4 ) @ one_one_nat )
% 3.82/4.08 @ A2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.inter_filter
% 3.82/4.08 thf(fact_6289_prod_Ointer__filter,axiom,
% 3.82/4.08 ! [A2: set_int,G: int > nat,P: int > $o] :
% 3.82/4.08 ( ( finite_finite_int @ A2 )
% 3.82/4.08 => ( ( groups1707563613775114915nt_nat @ G
% 3.82/4.08 @ ( collect_int
% 3.82/4.08 @ ^ [X4: int] :
% 3.82/4.08 ( ( member_int @ X4 @ A2 )
% 3.82/4.08 & ( P @ X4 ) ) ) )
% 3.82/4.08 = ( groups1707563613775114915nt_nat
% 3.82/4.08 @ ^ [X4: int] : ( if_nat @ ( P @ X4 ) @ ( G @ X4 ) @ one_one_nat )
% 3.82/4.08 @ A2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.inter_filter
% 3.82/4.08 thf(fact_6290_prod_Ointer__filter,axiom,
% 3.82/4.08 ! [A2: set_Extended_enat,G: extended_enat > nat,P: extended_enat > $o] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.08 => ( ( groups2880970938130013265at_nat @ G
% 3.82/4.08 @ ( collec4429806609662206161d_enat
% 3.82/4.08 @ ^ [X4: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ X4 @ A2 )
% 3.82/4.08 & ( P @ X4 ) ) ) )
% 3.82/4.08 = ( groups2880970938130013265at_nat
% 3.82/4.08 @ ^ [X4: extended_enat] : ( if_nat @ ( P @ X4 ) @ ( G @ X4 ) @ one_one_nat )
% 3.82/4.08 @ A2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.inter_filter
% 3.82/4.08 thf(fact_6291_prod_Ointer__filter,axiom,
% 3.82/4.08 ! [A2: set_real,G: real > int,P: real > $o] :
% 3.82/4.08 ( ( finite_finite_real @ A2 )
% 3.82/4.08 => ( ( groups4694064378042380927al_int @ G
% 3.82/4.08 @ ( collect_real
% 3.82/4.08 @ ^ [X4: real] :
% 3.82/4.08 ( ( member_real @ X4 @ A2 )
% 3.82/4.08 & ( P @ X4 ) ) ) )
% 3.82/4.08 = ( groups4694064378042380927al_int
% 3.82/4.08 @ ^ [X4: real] : ( if_int @ ( P @ X4 ) @ ( G @ X4 ) @ one_one_int )
% 3.82/4.08 @ A2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.inter_filter
% 3.82/4.08 thf(fact_6292_prod_Ointer__filter,axiom,
% 3.82/4.08 ! [A2: set_complex,G: complex > int,P: complex > $o] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.08 => ( ( groups858564598930262913ex_int @ G
% 3.82/4.08 @ ( collect_complex
% 3.82/4.08 @ ^ [X4: complex] :
% 3.82/4.08 ( ( member_complex @ X4 @ A2 )
% 3.82/4.08 & ( P @ X4 ) ) ) )
% 3.82/4.08 = ( groups858564598930262913ex_int
% 3.82/4.08 @ ^ [X4: complex] : ( if_int @ ( P @ X4 ) @ ( G @ X4 ) @ one_one_int )
% 3.82/4.08 @ A2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.inter_filter
% 3.82/4.08 thf(fact_6293_prod_Ointer__filter,axiom,
% 3.82/4.08 ! [A2: set_Extended_enat,G: extended_enat > int,P: extended_enat > $o] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.08 => ( ( groups2878480467620962989at_int @ G
% 3.82/4.08 @ ( collec4429806609662206161d_enat
% 3.82/4.08 @ ^ [X4: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ X4 @ A2 )
% 3.82/4.08 & ( P @ X4 ) ) ) )
% 3.82/4.08 = ( groups2878480467620962989at_int
% 3.82/4.08 @ ^ [X4: extended_enat] : ( if_int @ ( P @ X4 ) @ ( G @ X4 ) @ one_one_int )
% 3.82/4.08 @ A2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.inter_filter
% 3.82/4.08 thf(fact_6294_prod_Ointer__filter,axiom,
% 3.82/4.08 ! [A2: set_real,G: real > complex,P: real > $o] :
% 3.82/4.08 ( ( finite_finite_real @ A2 )
% 3.82/4.08 => ( ( groups713298508707869441omplex @ G
% 3.82/4.08 @ ( collect_real
% 3.82/4.08 @ ^ [X4: real] :
% 3.82/4.08 ( ( member_real @ X4 @ A2 )
% 3.82/4.08 & ( P @ X4 ) ) ) )
% 3.82/4.08 = ( groups713298508707869441omplex
% 3.82/4.08 @ ^ [X4: real] : ( if_complex @ ( P @ X4 ) @ ( G @ X4 ) @ one_one_complex )
% 3.82/4.08 @ A2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.inter_filter
% 3.82/4.08 thf(fact_6295_prod_Ointer__filter,axiom,
% 3.82/4.08 ! [A2: set_nat,G: nat > complex,P: nat > $o] :
% 3.82/4.08 ( ( finite_finite_nat @ A2 )
% 3.82/4.08 => ( ( groups6464643781859351333omplex @ G
% 3.82/4.08 @ ( collect_nat
% 3.82/4.08 @ ^ [X4: nat] :
% 3.82/4.08 ( ( member_nat @ X4 @ A2 )
% 3.82/4.08 & ( P @ X4 ) ) ) )
% 3.82/4.08 = ( groups6464643781859351333omplex
% 3.82/4.08 @ ^ [X4: nat] : ( if_complex @ ( P @ X4 ) @ ( G @ X4 ) @ one_one_complex )
% 3.82/4.08 @ A2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.inter_filter
% 3.82/4.08 thf(fact_6296_prod_Ointer__filter,axiom,
% 3.82/4.08 ! [A2: set_complex,G: complex > complex,P: complex > $o] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.08 => ( ( groups3708469109370488835omplex @ G
% 3.82/4.08 @ ( collect_complex
% 3.82/4.08 @ ^ [X4: complex] :
% 3.82/4.08 ( ( member_complex @ X4 @ A2 )
% 3.82/4.08 & ( P @ X4 ) ) ) )
% 3.82/4.08 = ( groups3708469109370488835omplex
% 3.82/4.08 @ ^ [X4: complex] : ( if_complex @ ( P @ X4 ) @ ( G @ X4 ) @ one_one_complex )
% 3.82/4.08 @ A2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.inter_filter
% 3.82/4.08 thf(fact_6297_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 3.82/4.08 ! [G: nat > int,M2: nat,N2: nat] :
% 3.82/4.08 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( suc @ N2 ) ) )
% 3.82/4.08 = ( groups705719431365010083at_int
% 3.82/4.08 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 3.82/4.08 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.shift_bounds_cl_Suc_ivl
% 3.82/4.08 thf(fact_6298_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 3.82/4.08 ! [G: nat > nat,M2: nat,N2: nat] :
% 3.82/4.08 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( suc @ N2 ) ) )
% 3.82/4.08 = ( groups708209901874060359at_nat
% 3.82/4.08 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 3.82/4.08 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.shift_bounds_cl_Suc_ivl
% 3.82/4.08 thf(fact_6299_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 3.82/4.08 ! [G: nat > int,M2: nat,K: nat,N2: nat] :
% 3.82/4.08 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M2 @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 3.82/4.08 = ( groups705719431365010083at_int
% 3.82/4.08 @ ^ [I3: nat] : ( G @ ( plus_plus_nat @ I3 @ K ) )
% 3.82/4.08 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.shift_bounds_cl_nat_ivl
% 3.82/4.08 thf(fact_6300_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 3.82/4.08 ! [G: nat > nat,M2: nat,K: nat,N2: nat] :
% 3.82/4.08 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M2 @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 3.82/4.08 = ( groups708209901874060359at_nat
% 3.82/4.08 @ ^ [I3: nat] : ( G @ ( plus_plus_nat @ I3 @ K ) )
% 3.82/4.08 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.shift_bounds_cl_nat_ivl
% 3.82/4.08 thf(fact_6301_prod__le__1,axiom,
% 3.82/4.08 ! [A2: set_Extended_enat,F: extended_enat > extended_enat] :
% 3.82/4.08 ( ! [X5: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ X5 @ A2 )
% 3.82/4.08 => ( ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ X5 ) )
% 3.82/4.08 & ( ord_le2932123472753598470d_enat @ ( F @ X5 ) @ one_on7984719198319812577d_enat ) ) )
% 3.82/4.08 => ( ord_le2932123472753598470d_enat @ ( groups8932437906259616549d_enat @ F @ A2 ) @ one_on7984719198319812577d_enat ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_le_1
% 3.82/4.08 thf(fact_6302_prod__le__1,axiom,
% 3.82/4.08 ! [A2: set_real,F: real > extended_enat] :
% 3.82/4.08 ( ! [X5: real] :
% 3.82/4.08 ( ( member_real @ X5 @ A2 )
% 3.82/4.08 => ( ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ X5 ) )
% 3.82/4.08 & ( ord_le2932123472753598470d_enat @ ( F @ X5 ) @ one_on7984719198319812577d_enat ) ) )
% 3.82/4.08 => ( ord_le2932123472753598470d_enat @ ( groups7973222482632965587d_enat @ F @ A2 ) @ one_on7984719198319812577d_enat ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_le_1
% 3.82/4.08 thf(fact_6303_prod__le__1,axiom,
% 3.82/4.08 ! [A2: set_nat,F: nat > extended_enat] :
% 3.82/4.08 ( ! [X5: nat] :
% 3.82/4.08 ( ( member_nat @ X5 @ A2 )
% 3.82/4.08 => ( ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ X5 ) )
% 3.82/4.08 & ( ord_le2932123472753598470d_enat @ ( F @ X5 ) @ one_on7984719198319812577d_enat ) ) )
% 3.82/4.08 => ( ord_le2932123472753598470d_enat @ ( groups7961826882256487087d_enat @ F @ A2 ) @ one_on7984719198319812577d_enat ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_le_1
% 3.82/4.08 thf(fact_6304_prod__le__1,axiom,
% 3.82/4.08 ! [A2: set_int,F: int > extended_enat] :
% 3.82/4.08 ( ! [X5: int] :
% 3.82/4.08 ( ( member_int @ X5 @ A2 )
% 3.82/4.08 => ( ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ X5 ) )
% 3.82/4.08 & ( ord_le2932123472753598470d_enat @ ( F @ X5 ) @ one_on7984719198319812577d_enat ) ) )
% 3.82/4.08 => ( ord_le2932123472753598470d_enat @ ( groups5078248829458667347d_enat @ F @ A2 ) @ one_on7984719198319812577d_enat ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_le_1
% 3.82/4.08 thf(fact_6305_prod__le__1,axiom,
% 3.82/4.08 ! [A2: set_Extended_enat,F: extended_enat > real] :
% 3.82/4.08 ( ! [X5: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ X5 @ A2 )
% 3.82/4.08 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) )
% 3.82/4.08 & ( ord_less_eq_real @ ( F @ X5 ) @ one_one_real ) ) )
% 3.82/4.08 => ( ord_less_eq_real @ ( groups97031904164794029t_real @ F @ A2 ) @ one_one_real ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_le_1
% 3.82/4.08 thf(fact_6306_prod__le__1,axiom,
% 3.82/4.08 ! [A2: set_real,F: real > real] :
% 3.82/4.08 ( ! [X5: real] :
% 3.82/4.08 ( ( member_real @ X5 @ A2 )
% 3.82/4.08 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) )
% 3.82/4.08 & ( ord_less_eq_real @ ( F @ X5 ) @ one_one_real ) ) )
% 3.82/4.08 => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ one_one_real ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_le_1
% 3.82/4.08 thf(fact_6307_prod__le__1,axiom,
% 3.82/4.08 ! [A2: set_nat,F: nat > real] :
% 3.82/4.08 ( ! [X5: nat] :
% 3.82/4.08 ( ( member_nat @ X5 @ A2 )
% 3.82/4.08 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) )
% 3.82/4.08 & ( ord_less_eq_real @ ( F @ X5 ) @ one_one_real ) ) )
% 3.82/4.08 => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F @ A2 ) @ one_one_real ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_le_1
% 3.82/4.08 thf(fact_6308_prod__le__1,axiom,
% 3.82/4.08 ! [A2: set_int,F: int > real] :
% 3.82/4.08 ( ! [X5: int] :
% 3.82/4.08 ( ( member_int @ X5 @ A2 )
% 3.82/4.08 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) )
% 3.82/4.08 & ( ord_less_eq_real @ ( F @ X5 ) @ one_one_real ) ) )
% 3.82/4.08 => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ one_one_real ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_le_1
% 3.82/4.08 thf(fact_6309_prod__le__1,axiom,
% 3.82/4.08 ! [A2: set_Extended_enat,F: extended_enat > nat] :
% 3.82/4.08 ( ! [X5: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ X5 @ A2 )
% 3.82/4.08 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) )
% 3.82/4.08 & ( ord_less_eq_nat @ ( F @ X5 ) @ one_one_nat ) ) )
% 3.82/4.08 => ( ord_less_eq_nat @ ( groups2880970938130013265at_nat @ F @ A2 ) @ one_one_nat ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_le_1
% 3.82/4.08 thf(fact_6310_prod__le__1,axiom,
% 3.82/4.08 ! [A2: set_real,F: real > nat] :
% 3.82/4.08 ( ! [X5: real] :
% 3.82/4.08 ( ( member_real @ X5 @ A2 )
% 3.82/4.08 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) )
% 3.82/4.08 & ( ord_less_eq_nat @ ( F @ X5 ) @ one_one_nat ) ) )
% 3.82/4.08 => ( ord_less_eq_nat @ ( groups4696554848551431203al_nat @ F @ A2 ) @ one_one_nat ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_le_1
% 3.82/4.08 thf(fact_6311_prod_Orelated,axiom,
% 3.82/4.08 ! [R: nat > nat > $o,S2: set_complex,H2: complex > nat,G: complex > nat] :
% 3.82/4.08 ( ( R @ one_one_nat @ one_one_nat )
% 3.82/4.08 => ( ! [X1: nat,Y1: nat,X23: nat,Y22: nat] :
% 3.82/4.08 ( ( ( R @ X1 @ X23 )
% 3.82/4.08 & ( R @ Y1 @ Y22 ) )
% 3.82/4.08 => ( R @ ( times_times_nat @ X1 @ Y1 ) @ ( times_times_nat @ X23 @ Y22 ) ) )
% 3.82/4.08 => ( ( finite3207457112153483333omplex @ S2 )
% 3.82/4.08 => ( ! [X5: complex] :
% 3.82/4.08 ( ( member_complex @ X5 @ S2 )
% 3.82/4.08 => ( R @ ( H2 @ X5 ) @ ( G @ X5 ) ) )
% 3.82/4.08 => ( R @ ( groups861055069439313189ex_nat @ H2 @ S2 ) @ ( groups861055069439313189ex_nat @ G @ S2 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.related
% 3.82/4.08 thf(fact_6312_prod_Orelated,axiom,
% 3.82/4.08 ! [R: nat > nat > $o,S2: set_int,H2: int > nat,G: int > nat] :
% 3.82/4.08 ( ( R @ one_one_nat @ one_one_nat )
% 3.82/4.08 => ( ! [X1: nat,Y1: nat,X23: nat,Y22: nat] :
% 3.82/4.08 ( ( ( R @ X1 @ X23 )
% 3.82/4.08 & ( R @ Y1 @ Y22 ) )
% 3.82/4.08 => ( R @ ( times_times_nat @ X1 @ Y1 ) @ ( times_times_nat @ X23 @ Y22 ) ) )
% 3.82/4.08 => ( ( finite_finite_int @ S2 )
% 3.82/4.08 => ( ! [X5: int] :
% 3.82/4.08 ( ( member_int @ X5 @ S2 )
% 3.82/4.08 => ( R @ ( H2 @ X5 ) @ ( G @ X5 ) ) )
% 3.82/4.08 => ( R @ ( groups1707563613775114915nt_nat @ H2 @ S2 ) @ ( groups1707563613775114915nt_nat @ G @ S2 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.related
% 3.82/4.08 thf(fact_6313_prod_Orelated,axiom,
% 3.82/4.08 ! [R: nat > nat > $o,S2: set_Extended_enat,H2: extended_enat > nat,G: extended_enat > nat] :
% 3.82/4.08 ( ( R @ one_one_nat @ one_one_nat )
% 3.82/4.08 => ( ! [X1: nat,Y1: nat,X23: nat,Y22: nat] :
% 3.82/4.08 ( ( ( R @ X1 @ X23 )
% 3.82/4.08 & ( R @ Y1 @ Y22 ) )
% 3.82/4.08 => ( R @ ( times_times_nat @ X1 @ Y1 ) @ ( times_times_nat @ X23 @ Y22 ) ) )
% 3.82/4.08 => ( ( finite4001608067531595151d_enat @ S2 )
% 3.82/4.08 => ( ! [X5: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ X5 @ S2 )
% 3.82/4.08 => ( R @ ( H2 @ X5 ) @ ( G @ X5 ) ) )
% 3.82/4.08 => ( R @ ( groups2880970938130013265at_nat @ H2 @ S2 ) @ ( groups2880970938130013265at_nat @ G @ S2 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.related
% 3.82/4.08 thf(fact_6314_prod_Orelated,axiom,
% 3.82/4.08 ! [R: int > int > $o,S2: set_complex,H2: complex > int,G: complex > int] :
% 3.82/4.08 ( ( R @ one_one_int @ one_one_int )
% 3.82/4.08 => ( ! [X1: int,Y1: int,X23: int,Y22: int] :
% 3.82/4.08 ( ( ( R @ X1 @ X23 )
% 3.82/4.08 & ( R @ Y1 @ Y22 ) )
% 3.82/4.08 => ( R @ ( times_times_int @ X1 @ Y1 ) @ ( times_times_int @ X23 @ Y22 ) ) )
% 3.82/4.08 => ( ( finite3207457112153483333omplex @ S2 )
% 3.82/4.08 => ( ! [X5: complex] :
% 3.82/4.08 ( ( member_complex @ X5 @ S2 )
% 3.82/4.08 => ( R @ ( H2 @ X5 ) @ ( G @ X5 ) ) )
% 3.82/4.08 => ( R @ ( groups858564598930262913ex_int @ H2 @ S2 ) @ ( groups858564598930262913ex_int @ G @ S2 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.related
% 3.82/4.08 thf(fact_6315_prod_Orelated,axiom,
% 3.82/4.08 ! [R: int > int > $o,S2: set_Extended_enat,H2: extended_enat > int,G: extended_enat > int] :
% 3.82/4.08 ( ( R @ one_one_int @ one_one_int )
% 3.82/4.08 => ( ! [X1: int,Y1: int,X23: int,Y22: int] :
% 3.82/4.08 ( ( ( R @ X1 @ X23 )
% 3.82/4.08 & ( R @ Y1 @ Y22 ) )
% 3.82/4.08 => ( R @ ( times_times_int @ X1 @ Y1 ) @ ( times_times_int @ X23 @ Y22 ) ) )
% 3.82/4.08 => ( ( finite4001608067531595151d_enat @ S2 )
% 3.82/4.08 => ( ! [X5: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ X5 @ S2 )
% 3.82/4.08 => ( R @ ( H2 @ X5 ) @ ( G @ X5 ) ) )
% 3.82/4.08 => ( R @ ( groups2878480467620962989at_int @ H2 @ S2 ) @ ( groups2878480467620962989at_int @ G @ S2 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.related
% 3.82/4.08 thf(fact_6316_prod_Orelated,axiom,
% 3.82/4.08 ! [R: real > real > $o,S2: set_nat,H2: nat > real,G: nat > real] :
% 3.82/4.08 ( ( R @ one_one_real @ one_one_real )
% 3.82/4.08 => ( ! [X1: real,Y1: real,X23: real,Y22: real] :
% 3.82/4.08 ( ( ( R @ X1 @ X23 )
% 3.82/4.08 & ( R @ Y1 @ Y22 ) )
% 3.82/4.08 => ( R @ ( times_times_real @ X1 @ Y1 ) @ ( times_times_real @ X23 @ Y22 ) ) )
% 3.82/4.08 => ( ( finite_finite_nat @ S2 )
% 3.82/4.08 => ( ! [X5: nat] :
% 3.82/4.08 ( ( member_nat @ X5 @ S2 )
% 3.82/4.08 => ( R @ ( H2 @ X5 ) @ ( G @ X5 ) ) )
% 3.82/4.08 => ( R @ ( groups129246275422532515t_real @ H2 @ S2 ) @ ( groups129246275422532515t_real @ G @ S2 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.related
% 3.82/4.08 thf(fact_6317_prod_Orelated,axiom,
% 3.82/4.08 ! [R: real > real > $o,S2: set_complex,H2: complex > real,G: complex > real] :
% 3.82/4.08 ( ( R @ one_one_real @ one_one_real )
% 3.82/4.08 => ( ! [X1: real,Y1: real,X23: real,Y22: real] :
% 3.82/4.08 ( ( ( R @ X1 @ X23 )
% 3.82/4.08 & ( R @ Y1 @ Y22 ) )
% 3.82/4.08 => ( R @ ( times_times_real @ X1 @ Y1 ) @ ( times_times_real @ X23 @ Y22 ) ) )
% 3.82/4.08 => ( ( finite3207457112153483333omplex @ S2 )
% 3.82/4.08 => ( ! [X5: complex] :
% 3.82/4.08 ( ( member_complex @ X5 @ S2 )
% 3.82/4.08 => ( R @ ( H2 @ X5 ) @ ( G @ X5 ) ) )
% 3.82/4.08 => ( R @ ( groups766887009212190081x_real @ H2 @ S2 ) @ ( groups766887009212190081x_real @ G @ S2 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.related
% 3.82/4.08 thf(fact_6318_prod_Orelated,axiom,
% 3.82/4.08 ! [R: real > real > $o,S2: set_int,H2: int > real,G: int > real] :
% 3.82/4.08 ( ( R @ one_one_real @ one_one_real )
% 3.82/4.08 => ( ! [X1: real,Y1: real,X23: real,Y22: real] :
% 3.82/4.08 ( ( ( R @ X1 @ X23 )
% 3.82/4.08 & ( R @ Y1 @ Y22 ) )
% 3.82/4.08 => ( R @ ( times_times_real @ X1 @ Y1 ) @ ( times_times_real @ X23 @ Y22 ) ) )
% 3.82/4.08 => ( ( finite_finite_int @ S2 )
% 3.82/4.08 => ( ! [X5: int] :
% 3.82/4.08 ( ( member_int @ X5 @ S2 )
% 3.82/4.08 => ( R @ ( H2 @ X5 ) @ ( G @ X5 ) ) )
% 3.82/4.08 => ( R @ ( groups2316167850115554303t_real @ H2 @ S2 ) @ ( groups2316167850115554303t_real @ G @ S2 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.related
% 3.82/4.08 thf(fact_6319_prod_Orelated,axiom,
% 3.82/4.08 ! [R: real > real > $o,S2: set_Extended_enat,H2: extended_enat > real,G: extended_enat > real] :
% 3.82/4.08 ( ( R @ one_one_real @ one_one_real )
% 3.82/4.08 => ( ! [X1: real,Y1: real,X23: real,Y22: real] :
% 3.82/4.08 ( ( ( R @ X1 @ X23 )
% 3.82/4.08 & ( R @ Y1 @ Y22 ) )
% 3.82/4.08 => ( R @ ( times_times_real @ X1 @ Y1 ) @ ( times_times_real @ X23 @ Y22 ) ) )
% 3.82/4.08 => ( ( finite4001608067531595151d_enat @ S2 )
% 3.82/4.08 => ( ! [X5: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ X5 @ S2 )
% 3.82/4.08 => ( R @ ( H2 @ X5 ) @ ( G @ X5 ) ) )
% 3.82/4.08 => ( R @ ( groups97031904164794029t_real @ H2 @ S2 ) @ ( groups97031904164794029t_real @ G @ S2 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.related
% 3.82/4.08 thf(fact_6320_prod_Orelated,axiom,
% 3.82/4.08 ! [R: complex > complex > $o,S2: set_nat,H2: nat > complex,G: nat > complex] :
% 3.82/4.08 ( ( R @ one_one_complex @ one_one_complex )
% 3.82/4.08 => ( ! [X1: complex,Y1: complex,X23: complex,Y22: complex] :
% 3.82/4.08 ( ( ( R @ X1 @ X23 )
% 3.82/4.08 & ( R @ Y1 @ Y22 ) )
% 3.82/4.08 => ( R @ ( times_times_complex @ X1 @ Y1 ) @ ( times_times_complex @ X23 @ Y22 ) ) )
% 3.82/4.08 => ( ( finite_finite_nat @ S2 )
% 3.82/4.08 => ( ! [X5: nat] :
% 3.82/4.08 ( ( member_nat @ X5 @ S2 )
% 3.82/4.08 => ( R @ ( H2 @ X5 ) @ ( G @ X5 ) ) )
% 3.82/4.08 => ( R @ ( groups6464643781859351333omplex @ H2 @ S2 ) @ ( groups6464643781859351333omplex @ G @ S2 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.related
% 3.82/4.08 thf(fact_6321_prod_Oinsert__if,axiom,
% 3.82/4.08 ! [A2: set_real,X: real,G: real > nat] :
% 3.82/4.08 ( ( finite_finite_real @ A2 )
% 3.82/4.08 => ( ( ( member_real @ X @ A2 )
% 3.82/4.08 => ( ( groups4696554848551431203al_nat @ G @ ( insert_real @ X @ A2 ) )
% 3.82/4.08 = ( groups4696554848551431203al_nat @ G @ A2 ) ) )
% 3.82/4.08 & ( ~ ( member_real @ X @ A2 )
% 3.82/4.08 => ( ( groups4696554848551431203al_nat @ G @ ( insert_real @ X @ A2 ) )
% 3.82/4.08 = ( times_times_nat @ ( G @ X ) @ ( groups4696554848551431203al_nat @ G @ A2 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.insert_if
% 3.82/4.08 thf(fact_6322_prod_Oinsert__if,axiom,
% 3.82/4.08 ! [A2: set_complex,X: complex,G: complex > nat] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.08 => ( ( ( member_complex @ X @ A2 )
% 3.82/4.08 => ( ( groups861055069439313189ex_nat @ G @ ( insert_complex @ X @ A2 ) )
% 3.82/4.08 = ( groups861055069439313189ex_nat @ G @ A2 ) ) )
% 3.82/4.08 & ( ~ ( member_complex @ X @ A2 )
% 3.82/4.08 => ( ( groups861055069439313189ex_nat @ G @ ( insert_complex @ X @ A2 ) )
% 3.82/4.08 = ( times_times_nat @ ( G @ X ) @ ( groups861055069439313189ex_nat @ G @ A2 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.insert_if
% 3.82/4.08 thf(fact_6323_prod_Oinsert__if,axiom,
% 3.82/4.08 ! [A2: set_int,X: int,G: int > nat] :
% 3.82/4.08 ( ( finite_finite_int @ A2 )
% 3.82/4.08 => ( ( ( member_int @ X @ A2 )
% 3.82/4.08 => ( ( groups1707563613775114915nt_nat @ G @ ( insert_int @ X @ A2 ) )
% 3.82/4.08 = ( groups1707563613775114915nt_nat @ G @ A2 ) ) )
% 3.82/4.08 & ( ~ ( member_int @ X @ A2 )
% 3.82/4.08 => ( ( groups1707563613775114915nt_nat @ G @ ( insert_int @ X @ A2 ) )
% 3.82/4.08 = ( times_times_nat @ ( G @ X ) @ ( groups1707563613775114915nt_nat @ G @ A2 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.insert_if
% 3.82/4.08 thf(fact_6324_prod_Oinsert__if,axiom,
% 3.82/4.08 ! [A2: set_Extended_enat,X: extended_enat,G: extended_enat > nat] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.08 => ( ( ( member_Extended_enat @ X @ A2 )
% 3.82/4.08 => ( ( groups2880970938130013265at_nat @ G @ ( insert_Extended_enat @ X @ A2 ) )
% 3.82/4.08 = ( groups2880970938130013265at_nat @ G @ A2 ) ) )
% 3.82/4.08 & ( ~ ( member_Extended_enat @ X @ A2 )
% 3.82/4.08 => ( ( groups2880970938130013265at_nat @ G @ ( insert_Extended_enat @ X @ A2 ) )
% 3.82/4.08 = ( times_times_nat @ ( G @ X ) @ ( groups2880970938130013265at_nat @ G @ A2 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.insert_if
% 3.82/4.08 thf(fact_6325_prod_Oinsert__if,axiom,
% 3.82/4.08 ! [A2: set_real,X: real,G: real > int] :
% 3.82/4.08 ( ( finite_finite_real @ A2 )
% 3.82/4.08 => ( ( ( member_real @ X @ A2 )
% 3.82/4.08 => ( ( groups4694064378042380927al_int @ G @ ( insert_real @ X @ A2 ) )
% 3.82/4.08 = ( groups4694064378042380927al_int @ G @ A2 ) ) )
% 3.82/4.08 & ( ~ ( member_real @ X @ A2 )
% 3.82/4.08 => ( ( groups4694064378042380927al_int @ G @ ( insert_real @ X @ A2 ) )
% 3.82/4.08 = ( times_times_int @ ( G @ X ) @ ( groups4694064378042380927al_int @ G @ A2 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.insert_if
% 3.82/4.08 thf(fact_6326_prod_Oinsert__if,axiom,
% 3.82/4.08 ! [A2: set_complex,X: complex,G: complex > int] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.08 => ( ( ( member_complex @ X @ A2 )
% 3.82/4.08 => ( ( groups858564598930262913ex_int @ G @ ( insert_complex @ X @ A2 ) )
% 3.82/4.08 = ( groups858564598930262913ex_int @ G @ A2 ) ) )
% 3.82/4.08 & ( ~ ( member_complex @ X @ A2 )
% 3.82/4.08 => ( ( groups858564598930262913ex_int @ G @ ( insert_complex @ X @ A2 ) )
% 3.82/4.08 = ( times_times_int @ ( G @ X ) @ ( groups858564598930262913ex_int @ G @ A2 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.insert_if
% 3.82/4.08 thf(fact_6327_prod_Oinsert__if,axiom,
% 3.82/4.08 ! [A2: set_Extended_enat,X: extended_enat,G: extended_enat > int] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.08 => ( ( ( member_Extended_enat @ X @ A2 )
% 3.82/4.08 => ( ( groups2878480467620962989at_int @ G @ ( insert_Extended_enat @ X @ A2 ) )
% 3.82/4.08 = ( groups2878480467620962989at_int @ G @ A2 ) ) )
% 3.82/4.08 & ( ~ ( member_Extended_enat @ X @ A2 )
% 3.82/4.08 => ( ( groups2878480467620962989at_int @ G @ ( insert_Extended_enat @ X @ A2 ) )
% 3.82/4.08 = ( times_times_int @ ( G @ X ) @ ( groups2878480467620962989at_int @ G @ A2 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.insert_if
% 3.82/4.08 thf(fact_6328_prod_Oinsert__if,axiom,
% 3.82/4.08 ! [A2: set_real,X: real,G: real > real] :
% 3.82/4.08 ( ( finite_finite_real @ A2 )
% 3.82/4.08 => ( ( ( member_real @ X @ A2 )
% 3.82/4.08 => ( ( groups1681761925125756287l_real @ G @ ( insert_real @ X @ A2 ) )
% 3.82/4.08 = ( groups1681761925125756287l_real @ G @ A2 ) ) )
% 3.82/4.08 & ( ~ ( member_real @ X @ A2 )
% 3.82/4.08 => ( ( groups1681761925125756287l_real @ G @ ( insert_real @ X @ A2 ) )
% 3.82/4.08 = ( times_times_real @ ( G @ X ) @ ( groups1681761925125756287l_real @ G @ A2 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.insert_if
% 3.82/4.08 thf(fact_6329_prod_Oinsert__if,axiom,
% 3.82/4.08 ! [A2: set_nat,X: nat,G: nat > real] :
% 3.82/4.08 ( ( finite_finite_nat @ A2 )
% 3.82/4.08 => ( ( ( member_nat @ X @ A2 )
% 3.82/4.08 => ( ( groups129246275422532515t_real @ G @ ( insert_nat @ X @ A2 ) )
% 3.82/4.08 = ( groups129246275422532515t_real @ G @ A2 ) ) )
% 3.82/4.08 & ( ~ ( member_nat @ X @ A2 )
% 3.82/4.08 => ( ( groups129246275422532515t_real @ G @ ( insert_nat @ X @ A2 ) )
% 3.82/4.08 = ( times_times_real @ ( G @ X ) @ ( groups129246275422532515t_real @ G @ A2 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.insert_if
% 3.82/4.08 thf(fact_6330_prod_Oinsert__if,axiom,
% 3.82/4.08 ! [A2: set_complex,X: complex,G: complex > real] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.08 => ( ( ( member_complex @ X @ A2 )
% 3.82/4.08 => ( ( groups766887009212190081x_real @ G @ ( insert_complex @ X @ A2 ) )
% 3.82/4.08 = ( groups766887009212190081x_real @ G @ A2 ) ) )
% 3.82/4.08 & ( ~ ( member_complex @ X @ A2 )
% 3.82/4.08 => ( ( groups766887009212190081x_real @ G @ ( insert_complex @ X @ A2 ) )
% 3.82/4.08 = ( times_times_real @ ( G @ X ) @ ( groups766887009212190081x_real @ G @ A2 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.insert_if
% 3.82/4.08 thf(fact_6331_prod__dvd__prod__subset,axiom,
% 3.82/4.08 ! [B: set_complex,A2: set_complex,F: complex > nat] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ B )
% 3.82/4.08 => ( ( ord_le211207098394363844omplex @ A2 @ B )
% 3.82/4.08 => ( dvd_dvd_nat @ ( groups861055069439313189ex_nat @ F @ A2 ) @ ( groups861055069439313189ex_nat @ F @ B ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_dvd_prod_subset
% 3.82/4.08 thf(fact_6332_prod__dvd__prod__subset,axiom,
% 3.82/4.08 ! [B: set_Extended_enat,A2: set_Extended_enat,F: extended_enat > nat] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ B )
% 3.82/4.08 => ( ( ord_le7203529160286727270d_enat @ A2 @ B )
% 3.82/4.08 => ( dvd_dvd_nat @ ( groups2880970938130013265at_nat @ F @ A2 ) @ ( groups2880970938130013265at_nat @ F @ B ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_dvd_prod_subset
% 3.82/4.08 thf(fact_6333_prod__dvd__prod__subset,axiom,
% 3.82/4.08 ! [B: set_complex,A2: set_complex,F: complex > int] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ B )
% 3.82/4.08 => ( ( ord_le211207098394363844omplex @ A2 @ B )
% 3.82/4.08 => ( dvd_dvd_int @ ( groups858564598930262913ex_int @ F @ A2 ) @ ( groups858564598930262913ex_int @ F @ B ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_dvd_prod_subset
% 3.82/4.08 thf(fact_6334_prod__dvd__prod__subset,axiom,
% 3.82/4.08 ! [B: set_Extended_enat,A2: set_Extended_enat,F: extended_enat > int] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ B )
% 3.82/4.08 => ( ( ord_le7203529160286727270d_enat @ A2 @ B )
% 3.82/4.08 => ( dvd_dvd_int @ ( groups2878480467620962989at_int @ F @ A2 ) @ ( groups2878480467620962989at_int @ F @ B ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_dvd_prod_subset
% 3.82/4.08 thf(fact_6335_prod__dvd__prod__subset,axiom,
% 3.82/4.08 ! [B: set_int,A2: set_int,F: int > nat] :
% 3.82/4.08 ( ( finite_finite_int @ B )
% 3.82/4.08 => ( ( ord_less_eq_set_int @ A2 @ B )
% 3.82/4.08 => ( dvd_dvd_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) @ ( groups1707563613775114915nt_nat @ F @ B ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_dvd_prod_subset
% 3.82/4.08 thf(fact_6336_prod__dvd__prod__subset,axiom,
% 3.82/4.08 ! [B: set_nat,A2: set_nat,F: nat > int] :
% 3.82/4.08 ( ( finite_finite_nat @ B )
% 3.82/4.08 => ( ( ord_less_eq_set_nat @ A2 @ B )
% 3.82/4.08 => ( dvd_dvd_int @ ( groups705719431365010083at_int @ F @ A2 ) @ ( groups705719431365010083at_int @ F @ B ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_dvd_prod_subset
% 3.82/4.08 thf(fact_6337_prod__dvd__prod__subset,axiom,
% 3.82/4.08 ! [B: set_int,A2: set_int,F: int > int] :
% 3.82/4.08 ( ( finite_finite_int @ B )
% 3.82/4.08 => ( ( ord_less_eq_set_int @ A2 @ B )
% 3.82/4.08 => ( dvd_dvd_int @ ( groups1705073143266064639nt_int @ F @ A2 ) @ ( groups1705073143266064639nt_int @ F @ B ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_dvd_prod_subset
% 3.82/4.08 thf(fact_6338_prod__dvd__prod__subset,axiom,
% 3.82/4.08 ! [B: set_nat,A2: set_nat,F: nat > nat] :
% 3.82/4.08 ( ( finite_finite_nat @ B )
% 3.82/4.08 => ( ( ord_less_eq_set_nat @ A2 @ B )
% 3.82/4.08 => ( dvd_dvd_nat @ ( groups708209901874060359at_nat @ F @ A2 ) @ ( groups708209901874060359at_nat @ F @ B ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_dvd_prod_subset
% 3.82/4.08 thf(fact_6339_prod__dvd__prod__subset2,axiom,
% 3.82/4.08 ! [B: set_real,A2: set_real,F: real > nat,G: real > nat] :
% 3.82/4.08 ( ( finite_finite_real @ B )
% 3.82/4.08 => ( ( ord_less_eq_set_real @ A2 @ B )
% 3.82/4.08 => ( ! [A4: real] :
% 3.82/4.08 ( ( member_real @ A4 @ A2 )
% 3.82/4.08 => ( dvd_dvd_nat @ ( F @ A4 ) @ ( G @ A4 ) ) )
% 3.82/4.08 => ( dvd_dvd_nat @ ( groups4696554848551431203al_nat @ F @ A2 ) @ ( groups4696554848551431203al_nat @ G @ B ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_dvd_prod_subset2
% 3.82/4.08 thf(fact_6340_prod__dvd__prod__subset2,axiom,
% 3.82/4.08 ! [B: set_complex,A2: set_complex,F: complex > nat,G: complex > nat] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ B )
% 3.82/4.08 => ( ( ord_le211207098394363844omplex @ A2 @ B )
% 3.82/4.08 => ( ! [A4: complex] :
% 3.82/4.08 ( ( member_complex @ A4 @ A2 )
% 3.82/4.08 => ( dvd_dvd_nat @ ( F @ A4 ) @ ( G @ A4 ) ) )
% 3.82/4.08 => ( dvd_dvd_nat @ ( groups861055069439313189ex_nat @ F @ A2 ) @ ( groups861055069439313189ex_nat @ G @ B ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_dvd_prod_subset2
% 3.82/4.08 thf(fact_6341_prod__dvd__prod__subset2,axiom,
% 3.82/4.08 ! [B: set_Extended_enat,A2: set_Extended_enat,F: extended_enat > nat,G: extended_enat > nat] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ B )
% 3.82/4.08 => ( ( ord_le7203529160286727270d_enat @ A2 @ B )
% 3.82/4.08 => ( ! [A4: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ A4 @ A2 )
% 3.82/4.08 => ( dvd_dvd_nat @ ( F @ A4 ) @ ( G @ A4 ) ) )
% 3.82/4.08 => ( dvd_dvd_nat @ ( groups2880970938130013265at_nat @ F @ A2 ) @ ( groups2880970938130013265at_nat @ G @ B ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_dvd_prod_subset2
% 3.82/4.08 thf(fact_6342_prod__dvd__prod__subset2,axiom,
% 3.82/4.08 ! [B: set_real,A2: set_real,F: real > int,G: real > int] :
% 3.82/4.08 ( ( finite_finite_real @ B )
% 3.82/4.08 => ( ( ord_less_eq_set_real @ A2 @ B )
% 3.82/4.08 => ( ! [A4: real] :
% 3.82/4.08 ( ( member_real @ A4 @ A2 )
% 3.82/4.08 => ( dvd_dvd_int @ ( F @ A4 ) @ ( G @ A4 ) ) )
% 3.82/4.08 => ( dvd_dvd_int @ ( groups4694064378042380927al_int @ F @ A2 ) @ ( groups4694064378042380927al_int @ G @ B ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_dvd_prod_subset2
% 3.82/4.08 thf(fact_6343_prod__dvd__prod__subset2,axiom,
% 3.82/4.08 ! [B: set_complex,A2: set_complex,F: complex > int,G: complex > int] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ B )
% 3.82/4.08 => ( ( ord_le211207098394363844omplex @ A2 @ B )
% 3.82/4.08 => ( ! [A4: complex] :
% 3.82/4.08 ( ( member_complex @ A4 @ A2 )
% 3.82/4.08 => ( dvd_dvd_int @ ( F @ A4 ) @ ( G @ A4 ) ) )
% 3.82/4.08 => ( dvd_dvd_int @ ( groups858564598930262913ex_int @ F @ A2 ) @ ( groups858564598930262913ex_int @ G @ B ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_dvd_prod_subset2
% 3.82/4.08 thf(fact_6344_prod__dvd__prod__subset2,axiom,
% 3.82/4.08 ! [B: set_Extended_enat,A2: set_Extended_enat,F: extended_enat > int,G: extended_enat > int] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ B )
% 3.82/4.08 => ( ( ord_le7203529160286727270d_enat @ A2 @ B )
% 3.82/4.08 => ( ! [A4: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ A4 @ A2 )
% 3.82/4.08 => ( dvd_dvd_int @ ( F @ A4 ) @ ( G @ A4 ) ) )
% 3.82/4.08 => ( dvd_dvd_int @ ( groups2878480467620962989at_int @ F @ A2 ) @ ( groups2878480467620962989at_int @ G @ B ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_dvd_prod_subset2
% 3.82/4.08 thf(fact_6345_prod__dvd__prod__subset2,axiom,
% 3.82/4.08 ! [B: set_int,A2: set_int,F: int > nat,G: int > nat] :
% 3.82/4.08 ( ( finite_finite_int @ B )
% 3.82/4.08 => ( ( ord_less_eq_set_int @ A2 @ B )
% 3.82/4.08 => ( ! [A4: int] :
% 3.82/4.08 ( ( member_int @ A4 @ A2 )
% 3.82/4.08 => ( dvd_dvd_nat @ ( F @ A4 ) @ ( G @ A4 ) ) )
% 3.82/4.08 => ( dvd_dvd_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) @ ( groups1707563613775114915nt_nat @ G @ B ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_dvd_prod_subset2
% 3.82/4.08 thf(fact_6346_prod__dvd__prod__subset2,axiom,
% 3.82/4.08 ! [B: set_nat,A2: set_nat,F: nat > int,G: nat > int] :
% 3.82/4.08 ( ( finite_finite_nat @ B )
% 3.82/4.08 => ( ( ord_less_eq_set_nat @ A2 @ B )
% 3.82/4.08 => ( ! [A4: nat] :
% 3.82/4.08 ( ( member_nat @ A4 @ A2 )
% 3.82/4.08 => ( dvd_dvd_int @ ( F @ A4 ) @ ( G @ A4 ) ) )
% 3.82/4.08 => ( dvd_dvd_int @ ( groups705719431365010083at_int @ F @ A2 ) @ ( groups705719431365010083at_int @ G @ B ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_dvd_prod_subset2
% 3.82/4.08 thf(fact_6347_prod__dvd__prod__subset2,axiom,
% 3.82/4.08 ! [B: set_int,A2: set_int,F: int > int,G: int > int] :
% 3.82/4.08 ( ( finite_finite_int @ B )
% 3.82/4.08 => ( ( ord_less_eq_set_int @ A2 @ B )
% 3.82/4.08 => ( ! [A4: int] :
% 3.82/4.08 ( ( member_int @ A4 @ A2 )
% 3.82/4.08 => ( dvd_dvd_int @ ( F @ A4 ) @ ( G @ A4 ) ) )
% 3.82/4.08 => ( dvd_dvd_int @ ( groups1705073143266064639nt_int @ F @ A2 ) @ ( groups1705073143266064639nt_int @ G @ B ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_dvd_prod_subset2
% 3.82/4.08 thf(fact_6348_prod__dvd__prod__subset2,axiom,
% 3.82/4.08 ! [B: set_nat,A2: set_nat,F: nat > nat,G: nat > nat] :
% 3.82/4.08 ( ( finite_finite_nat @ B )
% 3.82/4.08 => ( ( ord_less_eq_set_nat @ A2 @ B )
% 3.82/4.08 => ( ! [A4: nat] :
% 3.82/4.08 ( ( member_nat @ A4 @ A2 )
% 3.82/4.08 => ( dvd_dvd_nat @ ( F @ A4 ) @ ( G @ A4 ) ) )
% 3.82/4.08 => ( dvd_dvd_nat @ ( groups708209901874060359at_nat @ F @ A2 ) @ ( groups708209901874060359at_nat @ G @ B ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_dvd_prod_subset2
% 3.82/4.08 thf(fact_6349_prod_Oreindex__bij__witness__not__neutral,axiom,
% 3.82/4.08 ! [S5: set_real,T5: set_real,S2: set_real,I: real > real,J: real > real,T3: set_real,G: real > nat,H2: real > nat] :
% 3.82/4.08 ( ( finite_finite_real @ S5 )
% 3.82/4.08 => ( ( finite_finite_real @ T5 )
% 3.82/4.08 => ( ! [A4: real] :
% 3.82/4.08 ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 3.82/4.08 => ( ( I @ ( J @ A4 ) )
% 3.82/4.08 = A4 ) )
% 3.82/4.08 => ( ! [A4: real] :
% 3.82/4.08 ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 3.82/4.08 => ( member_real @ ( J @ A4 ) @ ( minus_minus_set_real @ T3 @ T5 ) ) )
% 3.82/4.08 => ( ! [B4: real] :
% 3.82/4.08 ( ( member_real @ B4 @ ( minus_minus_set_real @ T3 @ T5 ) )
% 3.82/4.08 => ( ( J @ ( I @ B4 ) )
% 3.82/4.08 = B4 ) )
% 3.82/4.08 => ( ! [B4: real] :
% 3.82/4.08 ( ( member_real @ B4 @ ( minus_minus_set_real @ T3 @ T5 ) )
% 3.82/4.08 => ( member_real @ ( I @ B4 ) @ ( minus_minus_set_real @ S2 @ S5 ) ) )
% 3.82/4.08 => ( ! [A4: real] :
% 3.82/4.08 ( ( member_real @ A4 @ S5 )
% 3.82/4.08 => ( ( G @ A4 )
% 3.82/4.08 = one_one_nat ) )
% 3.82/4.08 => ( ! [B4: real] :
% 3.82/4.08 ( ( member_real @ B4 @ T5 )
% 3.82/4.08 => ( ( H2 @ B4 )
% 3.82/4.08 = one_one_nat ) )
% 3.82/4.08 => ( ! [A4: real] :
% 3.82/4.08 ( ( member_real @ A4 @ S2 )
% 3.82/4.08 => ( ( H2 @ ( J @ A4 ) )
% 3.82/4.08 = ( G @ A4 ) ) )
% 3.82/4.08 => ( ( groups4696554848551431203al_nat @ G @ S2 )
% 3.82/4.08 = ( groups4696554848551431203al_nat @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.reindex_bij_witness_not_neutral
% 3.82/4.08 thf(fact_6350_prod_Oreindex__bij__witness__not__neutral,axiom,
% 3.82/4.08 ! [S5: set_real,T5: set_complex,S2: set_real,I: complex > real,J: real > complex,T3: set_complex,G: real > nat,H2: complex > nat] :
% 3.82/4.08 ( ( finite_finite_real @ S5 )
% 3.82/4.08 => ( ( finite3207457112153483333omplex @ T5 )
% 3.82/4.08 => ( ! [A4: real] :
% 3.82/4.08 ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 3.82/4.08 => ( ( I @ ( J @ A4 ) )
% 3.82/4.08 = A4 ) )
% 3.82/4.08 => ( ! [A4: real] :
% 3.82/4.08 ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 3.82/4.08 => ( member_complex @ ( J @ A4 ) @ ( minus_811609699411566653omplex @ T3 @ T5 ) ) )
% 3.82/4.08 => ( ! [B4: complex] :
% 3.82/4.08 ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ T3 @ T5 ) )
% 3.82/4.08 => ( ( J @ ( I @ B4 ) )
% 3.82/4.08 = B4 ) )
% 3.82/4.08 => ( ! [B4: complex] :
% 3.82/4.08 ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ T3 @ T5 ) )
% 3.82/4.08 => ( member_real @ ( I @ B4 ) @ ( minus_minus_set_real @ S2 @ S5 ) ) )
% 3.82/4.08 => ( ! [A4: real] :
% 3.82/4.08 ( ( member_real @ A4 @ S5 )
% 3.82/4.08 => ( ( G @ A4 )
% 3.82/4.08 = one_one_nat ) )
% 3.82/4.08 => ( ! [B4: complex] :
% 3.82/4.08 ( ( member_complex @ B4 @ T5 )
% 3.82/4.08 => ( ( H2 @ B4 )
% 3.82/4.08 = one_one_nat ) )
% 3.82/4.08 => ( ! [A4: real] :
% 3.82/4.08 ( ( member_real @ A4 @ S2 )
% 3.82/4.08 => ( ( H2 @ ( J @ A4 ) )
% 3.82/4.08 = ( G @ A4 ) ) )
% 3.82/4.08 => ( ( groups4696554848551431203al_nat @ G @ S2 )
% 3.82/4.08 = ( groups861055069439313189ex_nat @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.reindex_bij_witness_not_neutral
% 3.82/4.08 thf(fact_6351_prod_Oreindex__bij__witness__not__neutral,axiom,
% 3.82/4.08 ! [S5: set_real,T5: set_int,S2: set_real,I: int > real,J: real > int,T3: set_int,G: real > nat,H2: int > nat] :
% 3.82/4.08 ( ( finite_finite_real @ S5 )
% 3.82/4.08 => ( ( finite_finite_int @ T5 )
% 3.82/4.08 => ( ! [A4: real] :
% 3.82/4.08 ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 3.82/4.08 => ( ( I @ ( J @ A4 ) )
% 3.82/4.08 = A4 ) )
% 3.82/4.08 => ( ! [A4: real] :
% 3.82/4.08 ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 3.82/4.08 => ( member_int @ ( J @ A4 ) @ ( minus_minus_set_int @ T3 @ T5 ) ) )
% 3.82/4.08 => ( ! [B4: int] :
% 3.82/4.08 ( ( member_int @ B4 @ ( minus_minus_set_int @ T3 @ T5 ) )
% 3.82/4.08 => ( ( J @ ( I @ B4 ) )
% 3.82/4.08 = B4 ) )
% 3.82/4.08 => ( ! [B4: int] :
% 3.82/4.08 ( ( member_int @ B4 @ ( minus_minus_set_int @ T3 @ T5 ) )
% 3.82/4.08 => ( member_real @ ( I @ B4 ) @ ( minus_minus_set_real @ S2 @ S5 ) ) )
% 3.82/4.08 => ( ! [A4: real] :
% 3.82/4.08 ( ( member_real @ A4 @ S5 )
% 3.82/4.08 => ( ( G @ A4 )
% 3.82/4.08 = one_one_nat ) )
% 3.82/4.08 => ( ! [B4: int] :
% 3.82/4.08 ( ( member_int @ B4 @ T5 )
% 3.82/4.08 => ( ( H2 @ B4 )
% 3.82/4.08 = one_one_nat ) )
% 3.82/4.08 => ( ! [A4: real] :
% 3.82/4.08 ( ( member_real @ A4 @ S2 )
% 3.82/4.08 => ( ( H2 @ ( J @ A4 ) )
% 3.82/4.08 = ( G @ A4 ) ) )
% 3.82/4.08 => ( ( groups4696554848551431203al_nat @ G @ S2 )
% 3.82/4.08 = ( groups1707563613775114915nt_nat @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.reindex_bij_witness_not_neutral
% 3.82/4.08 thf(fact_6352_prod_Oreindex__bij__witness__not__neutral,axiom,
% 3.82/4.08 ! [S5: set_real,T5: set_Extended_enat,S2: set_real,I: extended_enat > real,J: real > extended_enat,T3: set_Extended_enat,G: real > nat,H2: extended_enat > nat] :
% 3.82/4.08 ( ( finite_finite_real @ S5 )
% 3.82/4.08 => ( ( finite4001608067531595151d_enat @ T5 )
% 3.82/4.08 => ( ! [A4: real] :
% 3.82/4.08 ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 3.82/4.08 => ( ( I @ ( J @ A4 ) )
% 3.82/4.08 = A4 ) )
% 3.82/4.08 => ( ! [A4: real] :
% 3.82/4.08 ( ( member_real @ A4 @ ( minus_minus_set_real @ S2 @ S5 ) )
% 3.82/4.08 => ( member_Extended_enat @ ( J @ A4 ) @ ( minus_925952699566721837d_enat @ T3 @ T5 ) ) )
% 3.82/4.08 => ( ! [B4: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ B4 @ ( minus_925952699566721837d_enat @ T3 @ T5 ) )
% 3.82/4.08 => ( ( J @ ( I @ B4 ) )
% 3.82/4.08 = B4 ) )
% 3.82/4.08 => ( ! [B4: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ B4 @ ( minus_925952699566721837d_enat @ T3 @ T5 ) )
% 3.82/4.08 => ( member_real @ ( I @ B4 ) @ ( minus_minus_set_real @ S2 @ S5 ) ) )
% 3.82/4.08 => ( ! [A4: real] :
% 3.82/4.08 ( ( member_real @ A4 @ S5 )
% 3.82/4.08 => ( ( G @ A4 )
% 3.82/4.08 = one_one_nat ) )
% 3.82/4.08 => ( ! [B4: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ B4 @ T5 )
% 3.82/4.08 => ( ( H2 @ B4 )
% 3.82/4.08 = one_one_nat ) )
% 3.82/4.08 => ( ! [A4: real] :
% 3.82/4.08 ( ( member_real @ A4 @ S2 )
% 3.82/4.08 => ( ( H2 @ ( J @ A4 ) )
% 3.82/4.08 = ( G @ A4 ) ) )
% 3.82/4.08 => ( ( groups4696554848551431203al_nat @ G @ S2 )
% 3.82/4.08 = ( groups2880970938130013265at_nat @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.reindex_bij_witness_not_neutral
% 3.82/4.08 thf(fact_6353_prod_Oreindex__bij__witness__not__neutral,axiom,
% 3.82/4.08 ! [S5: set_complex,T5: set_real,S2: set_complex,I: real > complex,J: complex > real,T3: set_real,G: complex > nat,H2: real > nat] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ S5 )
% 3.82/4.08 => ( ( finite_finite_real @ T5 )
% 3.82/4.08 => ( ! [A4: complex] :
% 3.82/4.08 ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ S2 @ S5 ) )
% 3.82/4.08 => ( ( I @ ( J @ A4 ) )
% 3.82/4.08 = A4 ) )
% 3.82/4.08 => ( ! [A4: complex] :
% 3.82/4.08 ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ S2 @ S5 ) )
% 3.82/4.08 => ( member_real @ ( J @ A4 ) @ ( minus_minus_set_real @ T3 @ T5 ) ) )
% 3.82/4.08 => ( ! [B4: real] :
% 3.82/4.08 ( ( member_real @ B4 @ ( minus_minus_set_real @ T3 @ T5 ) )
% 3.82/4.08 => ( ( J @ ( I @ B4 ) )
% 3.82/4.08 = B4 ) )
% 3.82/4.08 => ( ! [B4: real] :
% 3.82/4.08 ( ( member_real @ B4 @ ( minus_minus_set_real @ T3 @ T5 ) )
% 3.82/4.08 => ( member_complex @ ( I @ B4 ) @ ( minus_811609699411566653omplex @ S2 @ S5 ) ) )
% 3.82/4.08 => ( ! [A4: complex] :
% 3.82/4.08 ( ( member_complex @ A4 @ S5 )
% 3.82/4.08 => ( ( G @ A4 )
% 3.82/4.08 = one_one_nat ) )
% 3.82/4.08 => ( ! [B4: real] :
% 3.82/4.08 ( ( member_real @ B4 @ T5 )
% 3.82/4.08 => ( ( H2 @ B4 )
% 3.82/4.08 = one_one_nat ) )
% 3.82/4.08 => ( ! [A4: complex] :
% 3.82/4.08 ( ( member_complex @ A4 @ S2 )
% 3.82/4.08 => ( ( H2 @ ( J @ A4 ) )
% 3.82/4.08 = ( G @ A4 ) ) )
% 3.82/4.08 => ( ( groups861055069439313189ex_nat @ G @ S2 )
% 3.82/4.08 = ( groups4696554848551431203al_nat @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.reindex_bij_witness_not_neutral
% 3.82/4.08 thf(fact_6354_prod_Oreindex__bij__witness__not__neutral,axiom,
% 3.82/4.08 ! [S5: set_complex,T5: set_complex,S2: set_complex,I: complex > complex,J: complex > complex,T3: set_complex,G: complex > nat,H2: complex > nat] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ S5 )
% 3.82/4.08 => ( ( finite3207457112153483333omplex @ T5 )
% 3.82/4.08 => ( ! [A4: complex] :
% 3.82/4.08 ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ S2 @ S5 ) )
% 3.82/4.08 => ( ( I @ ( J @ A4 ) )
% 3.82/4.08 = A4 ) )
% 3.82/4.08 => ( ! [A4: complex] :
% 3.82/4.08 ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ S2 @ S5 ) )
% 3.82/4.08 => ( member_complex @ ( J @ A4 ) @ ( minus_811609699411566653omplex @ T3 @ T5 ) ) )
% 3.82/4.08 => ( ! [B4: complex] :
% 3.82/4.08 ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ T3 @ T5 ) )
% 3.82/4.08 => ( ( J @ ( I @ B4 ) )
% 3.82/4.08 = B4 ) )
% 3.82/4.08 => ( ! [B4: complex] :
% 3.82/4.08 ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ T3 @ T5 ) )
% 3.82/4.08 => ( member_complex @ ( I @ B4 ) @ ( minus_811609699411566653omplex @ S2 @ S5 ) ) )
% 3.82/4.08 => ( ! [A4: complex] :
% 3.82/4.08 ( ( member_complex @ A4 @ S5 )
% 3.82/4.08 => ( ( G @ A4 )
% 3.82/4.08 = one_one_nat ) )
% 3.82/4.08 => ( ! [B4: complex] :
% 3.82/4.08 ( ( member_complex @ B4 @ T5 )
% 3.82/4.08 => ( ( H2 @ B4 )
% 3.82/4.08 = one_one_nat ) )
% 3.82/4.08 => ( ! [A4: complex] :
% 3.82/4.08 ( ( member_complex @ A4 @ S2 )
% 3.82/4.08 => ( ( H2 @ ( J @ A4 ) )
% 3.82/4.08 = ( G @ A4 ) ) )
% 3.82/4.08 => ( ( groups861055069439313189ex_nat @ G @ S2 )
% 3.82/4.08 = ( groups861055069439313189ex_nat @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.reindex_bij_witness_not_neutral
% 3.82/4.08 thf(fact_6355_prod_Oreindex__bij__witness__not__neutral,axiom,
% 3.82/4.08 ! [S5: set_complex,T5: set_int,S2: set_complex,I: int > complex,J: complex > int,T3: set_int,G: complex > nat,H2: int > nat] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ S5 )
% 3.82/4.08 => ( ( finite_finite_int @ T5 )
% 3.82/4.08 => ( ! [A4: complex] :
% 3.82/4.08 ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ S2 @ S5 ) )
% 3.82/4.08 => ( ( I @ ( J @ A4 ) )
% 3.82/4.08 = A4 ) )
% 3.82/4.08 => ( ! [A4: complex] :
% 3.82/4.08 ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ S2 @ S5 ) )
% 3.82/4.08 => ( member_int @ ( J @ A4 ) @ ( minus_minus_set_int @ T3 @ T5 ) ) )
% 3.82/4.08 => ( ! [B4: int] :
% 3.82/4.08 ( ( member_int @ B4 @ ( minus_minus_set_int @ T3 @ T5 ) )
% 3.82/4.08 => ( ( J @ ( I @ B4 ) )
% 3.82/4.08 = B4 ) )
% 3.82/4.08 => ( ! [B4: int] :
% 3.82/4.08 ( ( member_int @ B4 @ ( minus_minus_set_int @ T3 @ T5 ) )
% 3.82/4.08 => ( member_complex @ ( I @ B4 ) @ ( minus_811609699411566653omplex @ S2 @ S5 ) ) )
% 3.82/4.08 => ( ! [A4: complex] :
% 3.82/4.08 ( ( member_complex @ A4 @ S5 )
% 3.82/4.08 => ( ( G @ A4 )
% 3.82/4.08 = one_one_nat ) )
% 3.82/4.08 => ( ! [B4: int] :
% 3.82/4.08 ( ( member_int @ B4 @ T5 )
% 3.82/4.08 => ( ( H2 @ B4 )
% 3.82/4.08 = one_one_nat ) )
% 3.82/4.08 => ( ! [A4: complex] :
% 3.82/4.08 ( ( member_complex @ A4 @ S2 )
% 3.82/4.08 => ( ( H2 @ ( J @ A4 ) )
% 3.82/4.08 = ( G @ A4 ) ) )
% 3.82/4.08 => ( ( groups861055069439313189ex_nat @ G @ S2 )
% 3.82/4.08 = ( groups1707563613775114915nt_nat @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.reindex_bij_witness_not_neutral
% 3.82/4.08 thf(fact_6356_prod_Oreindex__bij__witness__not__neutral,axiom,
% 3.82/4.08 ! [S5: set_complex,T5: set_Extended_enat,S2: set_complex,I: extended_enat > complex,J: complex > extended_enat,T3: set_Extended_enat,G: complex > nat,H2: extended_enat > nat] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ S5 )
% 3.82/4.08 => ( ( finite4001608067531595151d_enat @ T5 )
% 3.82/4.08 => ( ! [A4: complex] :
% 3.82/4.08 ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ S2 @ S5 ) )
% 3.82/4.08 => ( ( I @ ( J @ A4 ) )
% 3.82/4.08 = A4 ) )
% 3.82/4.08 => ( ! [A4: complex] :
% 3.82/4.08 ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ S2 @ S5 ) )
% 3.82/4.08 => ( member_Extended_enat @ ( J @ A4 ) @ ( minus_925952699566721837d_enat @ T3 @ T5 ) ) )
% 3.82/4.08 => ( ! [B4: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ B4 @ ( minus_925952699566721837d_enat @ T3 @ T5 ) )
% 3.82/4.08 => ( ( J @ ( I @ B4 ) )
% 3.82/4.08 = B4 ) )
% 3.82/4.08 => ( ! [B4: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ B4 @ ( minus_925952699566721837d_enat @ T3 @ T5 ) )
% 3.82/4.08 => ( member_complex @ ( I @ B4 ) @ ( minus_811609699411566653omplex @ S2 @ S5 ) ) )
% 3.82/4.08 => ( ! [A4: complex] :
% 3.82/4.08 ( ( member_complex @ A4 @ S5 )
% 3.82/4.08 => ( ( G @ A4 )
% 3.82/4.08 = one_one_nat ) )
% 3.82/4.08 => ( ! [B4: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ B4 @ T5 )
% 3.82/4.08 => ( ( H2 @ B4 )
% 3.82/4.08 = one_one_nat ) )
% 3.82/4.08 => ( ! [A4: complex] :
% 3.82/4.08 ( ( member_complex @ A4 @ S2 )
% 3.82/4.08 => ( ( H2 @ ( J @ A4 ) )
% 3.82/4.08 = ( G @ A4 ) ) )
% 3.82/4.08 => ( ( groups861055069439313189ex_nat @ G @ S2 )
% 3.82/4.08 = ( groups2880970938130013265at_nat @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.reindex_bij_witness_not_neutral
% 3.82/4.08 thf(fact_6357_prod_Oreindex__bij__witness__not__neutral,axiom,
% 3.82/4.08 ! [S5: set_int,T5: set_real,S2: set_int,I: real > int,J: int > real,T3: set_real,G: int > nat,H2: real > nat] :
% 3.82/4.08 ( ( finite_finite_int @ S5 )
% 3.82/4.08 => ( ( finite_finite_real @ T5 )
% 3.82/4.08 => ( ! [A4: int] :
% 3.82/4.08 ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 3.82/4.08 => ( ( I @ ( J @ A4 ) )
% 3.82/4.08 = A4 ) )
% 3.82/4.08 => ( ! [A4: int] :
% 3.82/4.08 ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 3.82/4.08 => ( member_real @ ( J @ A4 ) @ ( minus_minus_set_real @ T3 @ T5 ) ) )
% 3.82/4.08 => ( ! [B4: real] :
% 3.82/4.08 ( ( member_real @ B4 @ ( minus_minus_set_real @ T3 @ T5 ) )
% 3.82/4.08 => ( ( J @ ( I @ B4 ) )
% 3.82/4.08 = B4 ) )
% 3.82/4.08 => ( ! [B4: real] :
% 3.82/4.08 ( ( member_real @ B4 @ ( minus_minus_set_real @ T3 @ T5 ) )
% 3.82/4.08 => ( member_int @ ( I @ B4 ) @ ( minus_minus_set_int @ S2 @ S5 ) ) )
% 3.82/4.08 => ( ! [A4: int] :
% 3.82/4.08 ( ( member_int @ A4 @ S5 )
% 3.82/4.08 => ( ( G @ A4 )
% 3.82/4.08 = one_one_nat ) )
% 3.82/4.08 => ( ! [B4: real] :
% 3.82/4.08 ( ( member_real @ B4 @ T5 )
% 3.82/4.08 => ( ( H2 @ B4 )
% 3.82/4.08 = one_one_nat ) )
% 3.82/4.08 => ( ! [A4: int] :
% 3.82/4.08 ( ( member_int @ A4 @ S2 )
% 3.82/4.08 => ( ( H2 @ ( J @ A4 ) )
% 3.82/4.08 = ( G @ A4 ) ) )
% 3.82/4.08 => ( ( groups1707563613775114915nt_nat @ G @ S2 )
% 3.82/4.08 = ( groups4696554848551431203al_nat @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.reindex_bij_witness_not_neutral
% 3.82/4.08 thf(fact_6358_prod_Oreindex__bij__witness__not__neutral,axiom,
% 3.82/4.08 ! [S5: set_int,T5: set_complex,S2: set_int,I: complex > int,J: int > complex,T3: set_complex,G: int > nat,H2: complex > nat] :
% 3.82/4.08 ( ( finite_finite_int @ S5 )
% 3.82/4.08 => ( ( finite3207457112153483333omplex @ T5 )
% 3.82/4.08 => ( ! [A4: int] :
% 3.82/4.08 ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 3.82/4.08 => ( ( I @ ( J @ A4 ) )
% 3.82/4.08 = A4 ) )
% 3.82/4.08 => ( ! [A4: int] :
% 3.82/4.08 ( ( member_int @ A4 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 3.82/4.08 => ( member_complex @ ( J @ A4 ) @ ( minus_811609699411566653omplex @ T3 @ T5 ) ) )
% 3.82/4.08 => ( ! [B4: complex] :
% 3.82/4.08 ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ T3 @ T5 ) )
% 3.82/4.08 => ( ( J @ ( I @ B4 ) )
% 3.82/4.08 = B4 ) )
% 3.82/4.08 => ( ! [B4: complex] :
% 3.82/4.08 ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ T3 @ T5 ) )
% 3.82/4.08 => ( member_int @ ( I @ B4 ) @ ( minus_minus_set_int @ S2 @ S5 ) ) )
% 3.82/4.08 => ( ! [A4: int] :
% 3.82/4.08 ( ( member_int @ A4 @ S5 )
% 3.82/4.08 => ( ( G @ A4 )
% 3.82/4.08 = one_one_nat ) )
% 3.82/4.08 => ( ! [B4: complex] :
% 3.82/4.08 ( ( member_complex @ B4 @ T5 )
% 3.82/4.08 => ( ( H2 @ B4 )
% 3.82/4.08 = one_one_nat ) )
% 3.82/4.08 => ( ! [A4: int] :
% 3.82/4.08 ( ( member_int @ A4 @ S2 )
% 3.82/4.08 => ( ( H2 @ ( J @ A4 ) )
% 3.82/4.08 = ( G @ A4 ) ) )
% 3.82/4.08 => ( ( groups1707563613775114915nt_nat @ G @ S2 )
% 3.82/4.08 = ( groups861055069439313189ex_nat @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.reindex_bij_witness_not_neutral
% 3.82/4.08 thf(fact_6359_powr__add,axiom,
% 3.82/4.08 ! [X: real,A: real,B2: real] :
% 3.82/4.08 ( ( powr_real @ X @ ( plus_plus_real @ A @ B2 ) )
% 3.82/4.08 = ( times_times_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % powr_add
% 3.82/4.08 thf(fact_6360_prod_Osetdiff__irrelevant,axiom,
% 3.82/4.08 ! [A2: set_real,G: real > nat] :
% 3.82/4.08 ( ( finite_finite_real @ A2 )
% 3.82/4.08 => ( ( groups4696554848551431203al_nat @ G
% 3.82/4.08 @ ( minus_minus_set_real @ A2
% 3.82/4.08 @ ( collect_real
% 3.82/4.08 @ ^ [X4: real] :
% 3.82/4.08 ( ( G @ X4 )
% 3.82/4.08 = one_one_nat ) ) ) )
% 3.82/4.08 = ( groups4696554848551431203al_nat @ G @ A2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.setdiff_irrelevant
% 3.82/4.08 thf(fact_6361_prod_Osetdiff__irrelevant,axiom,
% 3.82/4.08 ! [A2: set_complex,G: complex > nat] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.08 => ( ( groups861055069439313189ex_nat @ G
% 3.82/4.08 @ ( minus_811609699411566653omplex @ A2
% 3.82/4.08 @ ( collect_complex
% 3.82/4.08 @ ^ [X4: complex] :
% 3.82/4.08 ( ( G @ X4 )
% 3.82/4.08 = one_one_nat ) ) ) )
% 3.82/4.08 = ( groups861055069439313189ex_nat @ G @ A2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.setdiff_irrelevant
% 3.82/4.08 thf(fact_6362_prod_Osetdiff__irrelevant,axiom,
% 3.82/4.08 ! [A2: set_int,G: int > nat] :
% 3.82/4.08 ( ( finite_finite_int @ A2 )
% 3.82/4.08 => ( ( groups1707563613775114915nt_nat @ G
% 3.82/4.08 @ ( minus_minus_set_int @ A2
% 3.82/4.08 @ ( collect_int
% 3.82/4.08 @ ^ [X4: int] :
% 3.82/4.08 ( ( G @ X4 )
% 3.82/4.08 = one_one_nat ) ) ) )
% 3.82/4.08 = ( groups1707563613775114915nt_nat @ G @ A2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.setdiff_irrelevant
% 3.82/4.08 thf(fact_6363_prod_Osetdiff__irrelevant,axiom,
% 3.82/4.08 ! [A2: set_Extended_enat,G: extended_enat > nat] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.08 => ( ( groups2880970938130013265at_nat @ G
% 3.82/4.08 @ ( minus_925952699566721837d_enat @ A2
% 3.82/4.08 @ ( collec4429806609662206161d_enat
% 3.82/4.08 @ ^ [X4: extended_enat] :
% 3.82/4.08 ( ( G @ X4 )
% 3.82/4.08 = one_one_nat ) ) ) )
% 3.82/4.08 = ( groups2880970938130013265at_nat @ G @ A2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.setdiff_irrelevant
% 3.82/4.08 thf(fact_6364_prod_Osetdiff__irrelevant,axiom,
% 3.82/4.08 ! [A2: set_real,G: real > int] :
% 3.82/4.08 ( ( finite_finite_real @ A2 )
% 3.82/4.08 => ( ( groups4694064378042380927al_int @ G
% 3.82/4.08 @ ( minus_minus_set_real @ A2
% 3.82/4.08 @ ( collect_real
% 3.82/4.08 @ ^ [X4: real] :
% 3.82/4.08 ( ( G @ X4 )
% 3.82/4.08 = one_one_int ) ) ) )
% 3.82/4.08 = ( groups4694064378042380927al_int @ G @ A2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.setdiff_irrelevant
% 3.82/4.08 thf(fact_6365_prod_Osetdiff__irrelevant,axiom,
% 3.82/4.08 ! [A2: set_complex,G: complex > int] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.08 => ( ( groups858564598930262913ex_int @ G
% 3.82/4.08 @ ( minus_811609699411566653omplex @ A2
% 3.82/4.08 @ ( collect_complex
% 3.82/4.08 @ ^ [X4: complex] :
% 3.82/4.08 ( ( G @ X4 )
% 3.82/4.08 = one_one_int ) ) ) )
% 3.82/4.08 = ( groups858564598930262913ex_int @ G @ A2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.setdiff_irrelevant
% 3.82/4.08 thf(fact_6366_prod_Osetdiff__irrelevant,axiom,
% 3.82/4.08 ! [A2: set_Extended_enat,G: extended_enat > int] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.08 => ( ( groups2878480467620962989at_int @ G
% 3.82/4.08 @ ( minus_925952699566721837d_enat @ A2
% 3.82/4.08 @ ( collec4429806609662206161d_enat
% 3.82/4.08 @ ^ [X4: extended_enat] :
% 3.82/4.08 ( ( G @ X4 )
% 3.82/4.08 = one_one_int ) ) ) )
% 3.82/4.08 = ( groups2878480467620962989at_int @ G @ A2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.setdiff_irrelevant
% 3.82/4.08 thf(fact_6367_prod_Osetdiff__irrelevant,axiom,
% 3.82/4.08 ! [A2: set_real,G: real > complex] :
% 3.82/4.08 ( ( finite_finite_real @ A2 )
% 3.82/4.08 => ( ( groups713298508707869441omplex @ G
% 3.82/4.08 @ ( minus_minus_set_real @ A2
% 3.82/4.08 @ ( collect_real
% 3.82/4.08 @ ^ [X4: real] :
% 3.82/4.08 ( ( G @ X4 )
% 3.82/4.08 = one_one_complex ) ) ) )
% 3.82/4.08 = ( groups713298508707869441omplex @ G @ A2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.setdiff_irrelevant
% 3.82/4.08 thf(fact_6368_prod_Osetdiff__irrelevant,axiom,
% 3.82/4.08 ! [A2: set_complex,G: complex > complex] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.08 => ( ( groups3708469109370488835omplex @ G
% 3.82/4.08 @ ( minus_811609699411566653omplex @ A2
% 3.82/4.08 @ ( collect_complex
% 3.82/4.08 @ ^ [X4: complex] :
% 3.82/4.08 ( ( G @ X4 )
% 3.82/4.08 = one_one_complex ) ) ) )
% 3.82/4.08 = ( groups3708469109370488835omplex @ G @ A2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.setdiff_irrelevant
% 3.82/4.08 thf(fact_6369_prod_Osetdiff__irrelevant,axiom,
% 3.82/4.08 ! [A2: set_int,G: int > complex] :
% 3.82/4.08 ( ( finite_finite_int @ A2 )
% 3.82/4.08 => ( ( groups7440179247065528705omplex @ G
% 3.82/4.08 @ ( minus_minus_set_int @ A2
% 3.82/4.08 @ ( collect_int
% 3.82/4.08 @ ^ [X4: int] :
% 3.82/4.08 ( ( G @ X4 )
% 3.82/4.08 = one_one_complex ) ) ) )
% 3.82/4.08 = ( groups7440179247065528705omplex @ G @ A2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.setdiff_irrelevant
% 3.82/4.08 thf(fact_6370_prod_Onat__diff__reindex,axiom,
% 3.82/4.08 ! [G: nat > int,N2: nat] :
% 3.82/4.08 ( ( groups705719431365010083at_int
% 3.82/4.08 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) )
% 3.82/4.08 @ ( set_ord_lessThan_nat @ N2 ) )
% 3.82/4.08 = ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.nat_diff_reindex
% 3.82/4.08 thf(fact_6371_prod_Onat__diff__reindex,axiom,
% 3.82/4.08 ! [G: nat > nat,N2: nat] :
% 3.82/4.08 ( ( groups708209901874060359at_nat
% 3.82/4.08 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) )
% 3.82/4.08 @ ( set_ord_lessThan_nat @ N2 ) )
% 3.82/4.08 = ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.nat_diff_reindex
% 3.82/4.08 thf(fact_6372_prod_OatLeastAtMost__rev,axiom,
% 3.82/4.08 ! [G: nat > int,N2: nat,M2: nat] :
% 3.82/4.08 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ N2 @ M2 ) )
% 3.82/4.08 = ( groups705719431365010083at_int
% 3.82/4.08 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M2 @ N2 ) @ I3 ) )
% 3.82/4.08 @ ( set_or1269000886237332187st_nat @ N2 @ M2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.atLeastAtMost_rev
% 3.82/4.08 thf(fact_6373_prod_OatLeastAtMost__rev,axiom,
% 3.82/4.08 ! [G: nat > nat,N2: nat,M2: nat] :
% 3.82/4.08 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ N2 @ M2 ) )
% 3.82/4.08 = ( groups708209901874060359at_nat
% 3.82/4.08 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M2 @ N2 ) @ I3 ) )
% 3.82/4.08 @ ( set_or1269000886237332187st_nat @ N2 @ M2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.atLeastAtMost_rev
% 3.82/4.08 thf(fact_6374_less__1__prod2,axiom,
% 3.82/4.08 ! [I6: set_real,I: real,F: real > real] :
% 3.82/4.08 ( ( finite_finite_real @ I6 )
% 3.82/4.08 => ( ( member_real @ I @ I6 )
% 3.82/4.08 => ( ( ord_less_real @ one_one_real @ ( F @ I ) )
% 3.82/4.08 => ( ! [I4: real] :
% 3.82/4.08 ( ( member_real @ I4 @ I6 )
% 3.82/4.08 => ( ord_less_eq_real @ one_one_real @ ( F @ I4 ) ) )
% 3.82/4.08 => ( ord_less_real @ one_one_real @ ( groups1681761925125756287l_real @ F @ I6 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % less_1_prod2
% 3.82/4.08 thf(fact_6375_less__1__prod2,axiom,
% 3.82/4.08 ! [I6: set_nat,I: nat,F: nat > real] :
% 3.82/4.08 ( ( finite_finite_nat @ I6 )
% 3.82/4.08 => ( ( member_nat @ I @ I6 )
% 3.82/4.08 => ( ( ord_less_real @ one_one_real @ ( F @ I ) )
% 3.82/4.08 => ( ! [I4: nat] :
% 3.82/4.08 ( ( member_nat @ I4 @ I6 )
% 3.82/4.08 => ( ord_less_eq_real @ one_one_real @ ( F @ I4 ) ) )
% 3.82/4.08 => ( ord_less_real @ one_one_real @ ( groups129246275422532515t_real @ F @ I6 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % less_1_prod2
% 3.82/4.08 thf(fact_6376_less__1__prod2,axiom,
% 3.82/4.08 ! [I6: set_complex,I: complex,F: complex > real] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ I6 )
% 3.82/4.08 => ( ( member_complex @ I @ I6 )
% 3.82/4.08 => ( ( ord_less_real @ one_one_real @ ( F @ I ) )
% 3.82/4.08 => ( ! [I4: complex] :
% 3.82/4.08 ( ( member_complex @ I4 @ I6 )
% 3.82/4.08 => ( ord_less_eq_real @ one_one_real @ ( F @ I4 ) ) )
% 3.82/4.08 => ( ord_less_real @ one_one_real @ ( groups766887009212190081x_real @ F @ I6 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % less_1_prod2
% 3.82/4.08 thf(fact_6377_less__1__prod2,axiom,
% 3.82/4.08 ! [I6: set_int,I: int,F: int > real] :
% 3.82/4.08 ( ( finite_finite_int @ I6 )
% 3.82/4.08 => ( ( member_int @ I @ I6 )
% 3.82/4.08 => ( ( ord_less_real @ one_one_real @ ( F @ I ) )
% 3.82/4.08 => ( ! [I4: int] :
% 3.82/4.08 ( ( member_int @ I4 @ I6 )
% 3.82/4.08 => ( ord_less_eq_real @ one_one_real @ ( F @ I4 ) ) )
% 3.82/4.08 => ( ord_less_real @ one_one_real @ ( groups2316167850115554303t_real @ F @ I6 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % less_1_prod2
% 3.82/4.08 thf(fact_6378_less__1__prod2,axiom,
% 3.82/4.08 ! [I6: set_Extended_enat,I: extended_enat,F: extended_enat > real] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ I6 )
% 3.82/4.08 => ( ( member_Extended_enat @ I @ I6 )
% 3.82/4.08 => ( ( ord_less_real @ one_one_real @ ( F @ I ) )
% 3.82/4.08 => ( ! [I4: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ I4 @ I6 )
% 3.82/4.08 => ( ord_less_eq_real @ one_one_real @ ( F @ I4 ) ) )
% 3.82/4.08 => ( ord_less_real @ one_one_real @ ( groups97031904164794029t_real @ F @ I6 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % less_1_prod2
% 3.82/4.08 thf(fact_6379_less__1__prod2,axiom,
% 3.82/4.08 ! [I6: set_real,I: real,F: real > int] :
% 3.82/4.08 ( ( finite_finite_real @ I6 )
% 3.82/4.08 => ( ( member_real @ I @ I6 )
% 3.82/4.08 => ( ( ord_less_int @ one_one_int @ ( F @ I ) )
% 3.82/4.08 => ( ! [I4: real] :
% 3.82/4.08 ( ( member_real @ I4 @ I6 )
% 3.82/4.08 => ( ord_less_eq_int @ one_one_int @ ( F @ I4 ) ) )
% 3.82/4.08 => ( ord_less_int @ one_one_int @ ( groups4694064378042380927al_int @ F @ I6 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % less_1_prod2
% 3.82/4.08 thf(fact_6380_less__1__prod2,axiom,
% 3.82/4.08 ! [I6: set_complex,I: complex,F: complex > int] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ I6 )
% 3.82/4.08 => ( ( member_complex @ I @ I6 )
% 3.82/4.08 => ( ( ord_less_int @ one_one_int @ ( F @ I ) )
% 3.82/4.08 => ( ! [I4: complex] :
% 3.82/4.08 ( ( member_complex @ I4 @ I6 )
% 3.82/4.08 => ( ord_less_eq_int @ one_one_int @ ( F @ I4 ) ) )
% 3.82/4.08 => ( ord_less_int @ one_one_int @ ( groups858564598930262913ex_int @ F @ I6 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % less_1_prod2
% 3.82/4.08 thf(fact_6381_less__1__prod2,axiom,
% 3.82/4.08 ! [I6: set_Extended_enat,I: extended_enat,F: extended_enat > int] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ I6 )
% 3.82/4.08 => ( ( member_Extended_enat @ I @ I6 )
% 3.82/4.08 => ( ( ord_less_int @ one_one_int @ ( F @ I ) )
% 3.82/4.08 => ( ! [I4: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ I4 @ I6 )
% 3.82/4.08 => ( ord_less_eq_int @ one_one_int @ ( F @ I4 ) ) )
% 3.82/4.08 => ( ord_less_int @ one_one_int @ ( groups2878480467620962989at_int @ F @ I6 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % less_1_prod2
% 3.82/4.08 thf(fact_6382_less__1__prod2,axiom,
% 3.82/4.08 ! [I6: set_nat,I: nat,F: nat > int] :
% 3.82/4.08 ( ( finite_finite_nat @ I6 )
% 3.82/4.08 => ( ( member_nat @ I @ I6 )
% 3.82/4.08 => ( ( ord_less_int @ one_one_int @ ( F @ I ) )
% 3.82/4.08 => ( ! [I4: nat] :
% 3.82/4.08 ( ( member_nat @ I4 @ I6 )
% 3.82/4.08 => ( ord_less_eq_int @ one_one_int @ ( F @ I4 ) ) )
% 3.82/4.08 => ( ord_less_int @ one_one_int @ ( groups705719431365010083at_int @ F @ I6 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % less_1_prod2
% 3.82/4.08 thf(fact_6383_less__1__prod2,axiom,
% 3.82/4.08 ! [I6: set_int,I: int,F: int > int] :
% 3.82/4.08 ( ( finite_finite_int @ I6 )
% 3.82/4.08 => ( ( member_int @ I @ I6 )
% 3.82/4.08 => ( ( ord_less_int @ one_one_int @ ( F @ I ) )
% 3.82/4.08 => ( ! [I4: int] :
% 3.82/4.08 ( ( member_int @ I4 @ I6 )
% 3.82/4.08 => ( ord_less_eq_int @ one_one_int @ ( F @ I4 ) ) )
% 3.82/4.08 => ( ord_less_int @ one_one_int @ ( groups1705073143266064639nt_int @ F @ I6 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % less_1_prod2
% 3.82/4.08 thf(fact_6384_less__1__prod,axiom,
% 3.82/4.08 ! [I6: set_complex,F: complex > real] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ I6 )
% 3.82/4.08 => ( ( I6 != bot_bot_set_complex )
% 3.82/4.08 => ( ! [I4: complex] :
% 3.82/4.08 ( ( member_complex @ I4 @ I6 )
% 3.82/4.08 => ( ord_less_real @ one_one_real @ ( F @ I4 ) ) )
% 3.82/4.08 => ( ord_less_real @ one_one_real @ ( groups766887009212190081x_real @ F @ I6 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % less_1_prod
% 3.82/4.08 thf(fact_6385_less__1__prod,axiom,
% 3.82/4.08 ! [I6: set_Extended_enat,F: extended_enat > real] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ I6 )
% 3.82/4.08 => ( ( I6 != bot_bo7653980558646680370d_enat )
% 3.82/4.08 => ( ! [I4: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ I4 @ I6 )
% 3.82/4.08 => ( ord_less_real @ one_one_real @ ( F @ I4 ) ) )
% 3.82/4.08 => ( ord_less_real @ one_one_real @ ( groups97031904164794029t_real @ F @ I6 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % less_1_prod
% 3.82/4.08 thf(fact_6386_less__1__prod,axiom,
% 3.82/4.08 ! [I6: set_real,F: real > real] :
% 3.82/4.08 ( ( finite_finite_real @ I6 )
% 3.82/4.08 => ( ( I6 != bot_bot_set_real )
% 3.82/4.08 => ( ! [I4: real] :
% 3.82/4.08 ( ( member_real @ I4 @ I6 )
% 3.82/4.08 => ( ord_less_real @ one_one_real @ ( F @ I4 ) ) )
% 3.82/4.08 => ( ord_less_real @ one_one_real @ ( groups1681761925125756287l_real @ F @ I6 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % less_1_prod
% 3.82/4.08 thf(fact_6387_less__1__prod,axiom,
% 3.82/4.08 ! [I6: set_nat,F: nat > real] :
% 3.82/4.08 ( ( finite_finite_nat @ I6 )
% 3.82/4.08 => ( ( I6 != bot_bot_set_nat )
% 3.82/4.08 => ( ! [I4: nat] :
% 3.82/4.08 ( ( member_nat @ I4 @ I6 )
% 3.82/4.08 => ( ord_less_real @ one_one_real @ ( F @ I4 ) ) )
% 3.82/4.08 => ( ord_less_real @ one_one_real @ ( groups129246275422532515t_real @ F @ I6 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % less_1_prod
% 3.82/4.08 thf(fact_6388_less__1__prod,axiom,
% 3.82/4.08 ! [I6: set_int,F: int > real] :
% 3.82/4.08 ( ( finite_finite_int @ I6 )
% 3.82/4.08 => ( ( I6 != bot_bot_set_int )
% 3.82/4.08 => ( ! [I4: int] :
% 3.82/4.08 ( ( member_int @ I4 @ I6 )
% 3.82/4.08 => ( ord_less_real @ one_one_real @ ( F @ I4 ) ) )
% 3.82/4.08 => ( ord_less_real @ one_one_real @ ( groups2316167850115554303t_real @ F @ I6 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % less_1_prod
% 3.82/4.08 thf(fact_6389_less__1__prod,axiom,
% 3.82/4.08 ! [I6: set_complex,F: complex > int] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ I6 )
% 3.82/4.08 => ( ( I6 != bot_bot_set_complex )
% 3.82/4.08 => ( ! [I4: complex] :
% 3.82/4.08 ( ( member_complex @ I4 @ I6 )
% 3.82/4.08 => ( ord_less_int @ one_one_int @ ( F @ I4 ) ) )
% 3.82/4.08 => ( ord_less_int @ one_one_int @ ( groups858564598930262913ex_int @ F @ I6 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % less_1_prod
% 3.82/4.08 thf(fact_6390_less__1__prod,axiom,
% 3.82/4.08 ! [I6: set_Extended_enat,F: extended_enat > int] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ I6 )
% 3.82/4.08 => ( ( I6 != bot_bo7653980558646680370d_enat )
% 3.82/4.08 => ( ! [I4: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ I4 @ I6 )
% 3.82/4.08 => ( ord_less_int @ one_one_int @ ( F @ I4 ) ) )
% 3.82/4.08 => ( ord_less_int @ one_one_int @ ( groups2878480467620962989at_int @ F @ I6 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % less_1_prod
% 3.82/4.08 thf(fact_6391_less__1__prod,axiom,
% 3.82/4.08 ! [I6: set_real,F: real > int] :
% 3.82/4.08 ( ( finite_finite_real @ I6 )
% 3.82/4.08 => ( ( I6 != bot_bot_set_real )
% 3.82/4.08 => ( ! [I4: real] :
% 3.82/4.08 ( ( member_real @ I4 @ I6 )
% 3.82/4.08 => ( ord_less_int @ one_one_int @ ( F @ I4 ) ) )
% 3.82/4.08 => ( ord_less_int @ one_one_int @ ( groups4694064378042380927al_int @ F @ I6 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % less_1_prod
% 3.82/4.08 thf(fact_6392_less__1__prod,axiom,
% 3.82/4.08 ! [I6: set_nat,F: nat > int] :
% 3.82/4.08 ( ( finite_finite_nat @ I6 )
% 3.82/4.08 => ( ( I6 != bot_bot_set_nat )
% 3.82/4.08 => ( ! [I4: nat] :
% 3.82/4.08 ( ( member_nat @ I4 @ I6 )
% 3.82/4.08 => ( ord_less_int @ one_one_int @ ( F @ I4 ) ) )
% 3.82/4.08 => ( ord_less_int @ one_one_int @ ( groups705719431365010083at_int @ F @ I6 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % less_1_prod
% 3.82/4.08 thf(fact_6393_less__1__prod,axiom,
% 3.82/4.08 ! [I6: set_int,F: int > int] :
% 3.82/4.08 ( ( finite_finite_int @ I6 )
% 3.82/4.08 => ( ( I6 != bot_bot_set_int )
% 3.82/4.08 => ( ! [I4: int] :
% 3.82/4.08 ( ( member_int @ I4 @ I6 )
% 3.82/4.08 => ( ord_less_int @ one_one_int @ ( F @ I4 ) ) )
% 3.82/4.08 => ( ord_less_int @ one_one_int @ ( groups1705073143266064639nt_int @ F @ I6 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % less_1_prod
% 3.82/4.08 thf(fact_6394_prod_Osubset__diff,axiom,
% 3.82/4.08 ! [B: set_complex,A2: set_complex,G: complex > nat] :
% 3.82/4.08 ( ( ord_le211207098394363844omplex @ B @ A2 )
% 3.82/4.08 => ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.08 => ( ( groups861055069439313189ex_nat @ G @ A2 )
% 3.82/4.08 = ( times_times_nat @ ( groups861055069439313189ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ B ) ) @ ( groups861055069439313189ex_nat @ G @ B ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.subset_diff
% 3.82/4.08 thf(fact_6395_prod_Osubset__diff,axiom,
% 3.82/4.08 ! [B: set_Extended_enat,A2: set_Extended_enat,G: extended_enat > nat] :
% 3.82/4.08 ( ( ord_le7203529160286727270d_enat @ B @ A2 )
% 3.82/4.08 => ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.08 => ( ( groups2880970938130013265at_nat @ G @ A2 )
% 3.82/4.08 = ( times_times_nat @ ( groups2880970938130013265at_nat @ G @ ( minus_925952699566721837d_enat @ A2 @ B ) ) @ ( groups2880970938130013265at_nat @ G @ B ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.subset_diff
% 3.82/4.08 thf(fact_6396_prod_Osubset__diff,axiom,
% 3.82/4.08 ! [B: set_complex,A2: set_complex,G: complex > int] :
% 3.82/4.08 ( ( ord_le211207098394363844omplex @ B @ A2 )
% 3.82/4.08 => ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.08 => ( ( groups858564598930262913ex_int @ G @ A2 )
% 3.82/4.08 = ( times_times_int @ ( groups858564598930262913ex_int @ G @ ( minus_811609699411566653omplex @ A2 @ B ) ) @ ( groups858564598930262913ex_int @ G @ B ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.subset_diff
% 3.82/4.08 thf(fact_6397_prod_Osubset__diff,axiom,
% 3.82/4.08 ! [B: set_Extended_enat,A2: set_Extended_enat,G: extended_enat > int] :
% 3.82/4.08 ( ( ord_le7203529160286727270d_enat @ B @ A2 )
% 3.82/4.08 => ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.08 => ( ( groups2878480467620962989at_int @ G @ A2 )
% 3.82/4.08 = ( times_times_int @ ( groups2878480467620962989at_int @ G @ ( minus_925952699566721837d_enat @ A2 @ B ) ) @ ( groups2878480467620962989at_int @ G @ B ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.subset_diff
% 3.82/4.08 thf(fact_6398_prod_Osubset__diff,axiom,
% 3.82/4.08 ! [B: set_complex,A2: set_complex,G: complex > real] :
% 3.82/4.08 ( ( ord_le211207098394363844omplex @ B @ A2 )
% 3.82/4.08 => ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.08 => ( ( groups766887009212190081x_real @ G @ A2 )
% 3.82/4.08 = ( times_times_real @ ( groups766887009212190081x_real @ G @ ( minus_811609699411566653omplex @ A2 @ B ) ) @ ( groups766887009212190081x_real @ G @ B ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.subset_diff
% 3.82/4.08 thf(fact_6399_prod_Osubset__diff,axiom,
% 3.82/4.08 ! [B: set_Extended_enat,A2: set_Extended_enat,G: extended_enat > real] :
% 3.82/4.08 ( ( ord_le7203529160286727270d_enat @ B @ A2 )
% 3.82/4.08 => ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.08 => ( ( groups97031904164794029t_real @ G @ A2 )
% 3.82/4.08 = ( times_times_real @ ( groups97031904164794029t_real @ G @ ( minus_925952699566721837d_enat @ A2 @ B ) ) @ ( groups97031904164794029t_real @ G @ B ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.subset_diff
% 3.82/4.08 thf(fact_6400_prod_Osubset__diff,axiom,
% 3.82/4.08 ! [B: set_complex,A2: set_complex,G: complex > complex] :
% 3.82/4.08 ( ( ord_le211207098394363844omplex @ B @ A2 )
% 3.82/4.08 => ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.08 => ( ( groups3708469109370488835omplex @ G @ A2 )
% 3.82/4.08 = ( times_times_complex @ ( groups3708469109370488835omplex @ G @ ( minus_811609699411566653omplex @ A2 @ B ) ) @ ( groups3708469109370488835omplex @ G @ B ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.subset_diff
% 3.82/4.08 thf(fact_6401_prod_Osubset__diff,axiom,
% 3.82/4.08 ! [B: set_Extended_enat,A2: set_Extended_enat,G: extended_enat > complex] :
% 3.82/4.08 ( ( ord_le7203529160286727270d_enat @ B @ A2 )
% 3.82/4.08 => ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.08 => ( ( groups4622424608036095791omplex @ G @ A2 )
% 3.82/4.08 = ( times_times_complex @ ( groups4622424608036095791omplex @ G @ ( minus_925952699566721837d_enat @ A2 @ B ) ) @ ( groups4622424608036095791omplex @ G @ B ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.subset_diff
% 3.82/4.08 thf(fact_6402_prod_Osubset__diff,axiom,
% 3.82/4.08 ! [B: set_complex,A2: set_complex,G: complex > extended_enat] :
% 3.82/4.08 ( ( ord_le211207098394363844omplex @ B @ A2 )
% 3.82/4.08 => ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.08 => ( ( groups8780218893797010257d_enat @ G @ A2 )
% 3.82/4.08 = ( times_7803423173614009249d_enat @ ( groups8780218893797010257d_enat @ G @ ( minus_811609699411566653omplex @ A2 @ B ) ) @ ( groups8780218893797010257d_enat @ G @ B ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.subset_diff
% 3.82/4.08 thf(fact_6403_prod_Osubset__diff,axiom,
% 3.82/4.08 ! [B: set_Extended_enat,A2: set_Extended_enat,G: extended_enat > extended_enat] :
% 3.82/4.08 ( ( ord_le7203529160286727270d_enat @ B @ A2 )
% 3.82/4.08 => ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.08 => ( ( groups8932437906259616549d_enat @ G @ A2 )
% 3.82/4.08 = ( times_7803423173614009249d_enat @ ( groups8932437906259616549d_enat @ G @ ( minus_925952699566721837d_enat @ A2 @ B ) ) @ ( groups8932437906259616549d_enat @ G @ B ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.subset_diff
% 3.82/4.08 thf(fact_6404_prod_Osame__carrier,axiom,
% 3.82/4.08 ! [C4: set_real,A2: set_real,B: set_real,G: real > nat,H2: real > nat] :
% 3.82/4.08 ( ( finite_finite_real @ C4 )
% 3.82/4.08 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 3.82/4.08 => ( ( ord_less_eq_set_real @ B @ C4 )
% 3.82/4.08 => ( ! [A4: real] :
% 3.82/4.08 ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 3.82/4.08 => ( ( G @ A4 )
% 3.82/4.08 = one_one_nat ) )
% 3.82/4.08 => ( ! [B4: real] :
% 3.82/4.08 ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B ) )
% 3.82/4.08 => ( ( H2 @ B4 )
% 3.82/4.08 = one_one_nat ) )
% 3.82/4.08 => ( ( ( groups4696554848551431203al_nat @ G @ A2 )
% 3.82/4.08 = ( groups4696554848551431203al_nat @ H2 @ B ) )
% 3.82/4.08 = ( ( groups4696554848551431203al_nat @ G @ C4 )
% 3.82/4.08 = ( groups4696554848551431203al_nat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.same_carrier
% 3.82/4.08 thf(fact_6405_prod_Osame__carrier,axiom,
% 3.82/4.08 ! [C4: set_complex,A2: set_complex,B: set_complex,G: complex > nat,H2: complex > nat] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ C4 )
% 3.82/4.08 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 3.82/4.08 => ( ( ord_le211207098394363844omplex @ B @ C4 )
% 3.82/4.08 => ( ! [A4: complex] :
% 3.82/4.08 ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 3.82/4.08 => ( ( G @ A4 )
% 3.82/4.08 = one_one_nat ) )
% 3.82/4.08 => ( ! [B4: complex] :
% 3.82/4.08 ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ C4 @ B ) )
% 3.82/4.08 => ( ( H2 @ B4 )
% 3.82/4.08 = one_one_nat ) )
% 3.82/4.08 => ( ( ( groups861055069439313189ex_nat @ G @ A2 )
% 3.82/4.08 = ( groups861055069439313189ex_nat @ H2 @ B ) )
% 3.82/4.08 = ( ( groups861055069439313189ex_nat @ G @ C4 )
% 3.82/4.08 = ( groups861055069439313189ex_nat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.same_carrier
% 3.82/4.08 thf(fact_6406_prod_Osame__carrier,axiom,
% 3.82/4.08 ! [C4: set_Extended_enat,A2: set_Extended_enat,B: set_Extended_enat,G: extended_enat > nat,H2: extended_enat > nat] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ C4 )
% 3.82/4.08 => ( ( ord_le7203529160286727270d_enat @ A2 @ C4 )
% 3.82/4.08 => ( ( ord_le7203529160286727270d_enat @ B @ C4 )
% 3.82/4.08 => ( ! [A4: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ A4 @ ( minus_925952699566721837d_enat @ C4 @ A2 ) )
% 3.82/4.08 => ( ( G @ A4 )
% 3.82/4.08 = one_one_nat ) )
% 3.82/4.08 => ( ! [B4: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ B4 @ ( minus_925952699566721837d_enat @ C4 @ B ) )
% 3.82/4.08 => ( ( H2 @ B4 )
% 3.82/4.08 = one_one_nat ) )
% 3.82/4.08 => ( ( ( groups2880970938130013265at_nat @ G @ A2 )
% 3.82/4.08 = ( groups2880970938130013265at_nat @ H2 @ B ) )
% 3.82/4.08 = ( ( groups2880970938130013265at_nat @ G @ C4 )
% 3.82/4.08 = ( groups2880970938130013265at_nat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.same_carrier
% 3.82/4.08 thf(fact_6407_prod_Osame__carrier,axiom,
% 3.82/4.08 ! [C4: set_real,A2: set_real,B: set_real,G: real > int,H2: real > int] :
% 3.82/4.08 ( ( finite_finite_real @ C4 )
% 3.82/4.08 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 3.82/4.08 => ( ( ord_less_eq_set_real @ B @ C4 )
% 3.82/4.08 => ( ! [A4: real] :
% 3.82/4.08 ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 3.82/4.08 => ( ( G @ A4 )
% 3.82/4.08 = one_one_int ) )
% 3.82/4.08 => ( ! [B4: real] :
% 3.82/4.08 ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B ) )
% 3.82/4.08 => ( ( H2 @ B4 )
% 3.82/4.08 = one_one_int ) )
% 3.82/4.08 => ( ( ( groups4694064378042380927al_int @ G @ A2 )
% 3.82/4.08 = ( groups4694064378042380927al_int @ H2 @ B ) )
% 3.82/4.08 = ( ( groups4694064378042380927al_int @ G @ C4 )
% 3.82/4.08 = ( groups4694064378042380927al_int @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.same_carrier
% 3.82/4.08 thf(fact_6408_prod_Osame__carrier,axiom,
% 3.82/4.08 ! [C4: set_complex,A2: set_complex,B: set_complex,G: complex > int,H2: complex > int] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ C4 )
% 3.82/4.08 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 3.82/4.08 => ( ( ord_le211207098394363844omplex @ B @ C4 )
% 3.82/4.08 => ( ! [A4: complex] :
% 3.82/4.08 ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 3.82/4.08 => ( ( G @ A4 )
% 3.82/4.08 = one_one_int ) )
% 3.82/4.08 => ( ! [B4: complex] :
% 3.82/4.08 ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ C4 @ B ) )
% 3.82/4.08 => ( ( H2 @ B4 )
% 3.82/4.08 = one_one_int ) )
% 3.82/4.08 => ( ( ( groups858564598930262913ex_int @ G @ A2 )
% 3.82/4.08 = ( groups858564598930262913ex_int @ H2 @ B ) )
% 3.82/4.08 = ( ( groups858564598930262913ex_int @ G @ C4 )
% 3.82/4.08 = ( groups858564598930262913ex_int @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.same_carrier
% 3.82/4.08 thf(fact_6409_prod_Osame__carrier,axiom,
% 3.82/4.08 ! [C4: set_Extended_enat,A2: set_Extended_enat,B: set_Extended_enat,G: extended_enat > int,H2: extended_enat > int] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ C4 )
% 3.82/4.08 => ( ( ord_le7203529160286727270d_enat @ A2 @ C4 )
% 3.82/4.08 => ( ( ord_le7203529160286727270d_enat @ B @ C4 )
% 3.82/4.08 => ( ! [A4: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ A4 @ ( minus_925952699566721837d_enat @ C4 @ A2 ) )
% 3.82/4.08 => ( ( G @ A4 )
% 3.82/4.08 = one_one_int ) )
% 3.82/4.08 => ( ! [B4: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ B4 @ ( minus_925952699566721837d_enat @ C4 @ B ) )
% 3.82/4.08 => ( ( H2 @ B4 )
% 3.82/4.08 = one_one_int ) )
% 3.82/4.08 => ( ( ( groups2878480467620962989at_int @ G @ A2 )
% 3.82/4.08 = ( groups2878480467620962989at_int @ H2 @ B ) )
% 3.82/4.08 = ( ( groups2878480467620962989at_int @ G @ C4 )
% 3.82/4.08 = ( groups2878480467620962989at_int @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.same_carrier
% 3.82/4.08 thf(fact_6410_prod_Osame__carrier,axiom,
% 3.82/4.08 ! [C4: set_real,A2: set_real,B: set_real,G: real > complex,H2: real > complex] :
% 3.82/4.08 ( ( finite_finite_real @ C4 )
% 3.82/4.08 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 3.82/4.08 => ( ( ord_less_eq_set_real @ B @ C4 )
% 3.82/4.08 => ( ! [A4: real] :
% 3.82/4.08 ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 3.82/4.08 => ( ( G @ A4 )
% 3.82/4.08 = one_one_complex ) )
% 3.82/4.08 => ( ! [B4: real] :
% 3.82/4.08 ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B ) )
% 3.82/4.08 => ( ( H2 @ B4 )
% 3.82/4.08 = one_one_complex ) )
% 3.82/4.08 => ( ( ( groups713298508707869441omplex @ G @ A2 )
% 3.82/4.08 = ( groups713298508707869441omplex @ H2 @ B ) )
% 3.82/4.08 = ( ( groups713298508707869441omplex @ G @ C4 )
% 3.82/4.08 = ( groups713298508707869441omplex @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.same_carrier
% 3.82/4.08 thf(fact_6411_prod_Osame__carrier,axiom,
% 3.82/4.08 ! [C4: set_complex,A2: set_complex,B: set_complex,G: complex > complex,H2: complex > complex] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ C4 )
% 3.82/4.08 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 3.82/4.08 => ( ( ord_le211207098394363844omplex @ B @ C4 )
% 3.82/4.08 => ( ! [A4: complex] :
% 3.82/4.08 ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 3.82/4.08 => ( ( G @ A4 )
% 3.82/4.08 = one_one_complex ) )
% 3.82/4.08 => ( ! [B4: complex] :
% 3.82/4.08 ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ C4 @ B ) )
% 3.82/4.08 => ( ( H2 @ B4 )
% 3.82/4.08 = one_one_complex ) )
% 3.82/4.08 => ( ( ( groups3708469109370488835omplex @ G @ A2 )
% 3.82/4.08 = ( groups3708469109370488835omplex @ H2 @ B ) )
% 3.82/4.08 = ( ( groups3708469109370488835omplex @ G @ C4 )
% 3.82/4.08 = ( groups3708469109370488835omplex @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.same_carrier
% 3.82/4.08 thf(fact_6412_prod_Osame__carrier,axiom,
% 3.82/4.08 ! [C4: set_Extended_enat,A2: set_Extended_enat,B: set_Extended_enat,G: extended_enat > complex,H2: extended_enat > complex] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ C4 )
% 3.82/4.08 => ( ( ord_le7203529160286727270d_enat @ A2 @ C4 )
% 3.82/4.08 => ( ( ord_le7203529160286727270d_enat @ B @ C4 )
% 3.82/4.08 => ( ! [A4: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ A4 @ ( minus_925952699566721837d_enat @ C4 @ A2 ) )
% 3.82/4.08 => ( ( G @ A4 )
% 3.82/4.08 = one_one_complex ) )
% 3.82/4.08 => ( ! [B4: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ B4 @ ( minus_925952699566721837d_enat @ C4 @ B ) )
% 3.82/4.08 => ( ( H2 @ B4 )
% 3.82/4.08 = one_one_complex ) )
% 3.82/4.08 => ( ( ( groups4622424608036095791omplex @ G @ A2 )
% 3.82/4.08 = ( groups4622424608036095791omplex @ H2 @ B ) )
% 3.82/4.08 = ( ( groups4622424608036095791omplex @ G @ C4 )
% 3.82/4.08 = ( groups4622424608036095791omplex @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.same_carrier
% 3.82/4.08 thf(fact_6413_prod_Osame__carrier,axiom,
% 3.82/4.08 ! [C4: set_real,A2: set_real,B: set_real,G: real > real,H2: real > real] :
% 3.82/4.08 ( ( finite_finite_real @ C4 )
% 3.82/4.08 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 3.82/4.08 => ( ( ord_less_eq_set_real @ B @ C4 )
% 3.82/4.08 => ( ! [A4: real] :
% 3.82/4.08 ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 3.82/4.08 => ( ( G @ A4 )
% 3.82/4.08 = one_one_real ) )
% 3.82/4.08 => ( ! [B4: real] :
% 3.82/4.08 ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B ) )
% 3.82/4.08 => ( ( H2 @ B4 )
% 3.82/4.08 = one_one_real ) )
% 3.82/4.08 => ( ( ( groups1681761925125756287l_real @ G @ A2 )
% 3.82/4.08 = ( groups1681761925125756287l_real @ H2 @ B ) )
% 3.82/4.08 = ( ( groups1681761925125756287l_real @ G @ C4 )
% 3.82/4.08 = ( groups1681761925125756287l_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.same_carrier
% 3.82/4.08 thf(fact_6414_prod_Osame__carrierI,axiom,
% 3.82/4.08 ! [C4: set_real,A2: set_real,B: set_real,G: real > nat,H2: real > nat] :
% 3.82/4.08 ( ( finite_finite_real @ C4 )
% 3.82/4.08 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 3.82/4.08 => ( ( ord_less_eq_set_real @ B @ C4 )
% 3.82/4.08 => ( ! [A4: real] :
% 3.82/4.08 ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 3.82/4.08 => ( ( G @ A4 )
% 3.82/4.08 = one_one_nat ) )
% 3.82/4.08 => ( ! [B4: real] :
% 3.82/4.08 ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B ) )
% 3.82/4.08 => ( ( H2 @ B4 )
% 3.82/4.08 = one_one_nat ) )
% 3.82/4.08 => ( ( ( groups4696554848551431203al_nat @ G @ C4 )
% 3.82/4.08 = ( groups4696554848551431203al_nat @ H2 @ C4 ) )
% 3.82/4.08 => ( ( groups4696554848551431203al_nat @ G @ A2 )
% 3.82/4.08 = ( groups4696554848551431203al_nat @ H2 @ B ) ) ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.same_carrierI
% 3.82/4.08 thf(fact_6415_prod_Osame__carrierI,axiom,
% 3.82/4.08 ! [C4: set_complex,A2: set_complex,B: set_complex,G: complex > nat,H2: complex > nat] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ C4 )
% 3.82/4.08 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 3.82/4.08 => ( ( ord_le211207098394363844omplex @ B @ C4 )
% 3.82/4.08 => ( ! [A4: complex] :
% 3.82/4.08 ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 3.82/4.08 => ( ( G @ A4 )
% 3.82/4.08 = one_one_nat ) )
% 3.82/4.08 => ( ! [B4: complex] :
% 3.82/4.08 ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ C4 @ B ) )
% 3.82/4.08 => ( ( H2 @ B4 )
% 3.82/4.08 = one_one_nat ) )
% 3.82/4.08 => ( ( ( groups861055069439313189ex_nat @ G @ C4 )
% 3.82/4.08 = ( groups861055069439313189ex_nat @ H2 @ C4 ) )
% 3.82/4.08 => ( ( groups861055069439313189ex_nat @ G @ A2 )
% 3.82/4.08 = ( groups861055069439313189ex_nat @ H2 @ B ) ) ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.same_carrierI
% 3.82/4.08 thf(fact_6416_prod_Osame__carrierI,axiom,
% 3.82/4.08 ! [C4: set_Extended_enat,A2: set_Extended_enat,B: set_Extended_enat,G: extended_enat > nat,H2: extended_enat > nat] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ C4 )
% 3.82/4.08 => ( ( ord_le7203529160286727270d_enat @ A2 @ C4 )
% 3.82/4.08 => ( ( ord_le7203529160286727270d_enat @ B @ C4 )
% 3.82/4.08 => ( ! [A4: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ A4 @ ( minus_925952699566721837d_enat @ C4 @ A2 ) )
% 3.82/4.08 => ( ( G @ A4 )
% 3.82/4.08 = one_one_nat ) )
% 3.82/4.08 => ( ! [B4: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ B4 @ ( minus_925952699566721837d_enat @ C4 @ B ) )
% 3.82/4.08 => ( ( H2 @ B4 )
% 3.82/4.08 = one_one_nat ) )
% 3.82/4.08 => ( ( ( groups2880970938130013265at_nat @ G @ C4 )
% 3.82/4.08 = ( groups2880970938130013265at_nat @ H2 @ C4 ) )
% 3.82/4.08 => ( ( groups2880970938130013265at_nat @ G @ A2 )
% 3.82/4.08 = ( groups2880970938130013265at_nat @ H2 @ B ) ) ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.same_carrierI
% 3.82/4.08 thf(fact_6417_prod_Osame__carrierI,axiom,
% 3.82/4.08 ! [C4: set_real,A2: set_real,B: set_real,G: real > int,H2: real > int] :
% 3.82/4.08 ( ( finite_finite_real @ C4 )
% 3.82/4.08 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 3.82/4.08 => ( ( ord_less_eq_set_real @ B @ C4 )
% 3.82/4.08 => ( ! [A4: real] :
% 3.82/4.08 ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 3.82/4.08 => ( ( G @ A4 )
% 3.82/4.08 = one_one_int ) )
% 3.82/4.08 => ( ! [B4: real] :
% 3.82/4.08 ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B ) )
% 3.82/4.08 => ( ( H2 @ B4 )
% 3.82/4.08 = one_one_int ) )
% 3.82/4.08 => ( ( ( groups4694064378042380927al_int @ G @ C4 )
% 3.82/4.08 = ( groups4694064378042380927al_int @ H2 @ C4 ) )
% 3.82/4.08 => ( ( groups4694064378042380927al_int @ G @ A2 )
% 3.82/4.08 = ( groups4694064378042380927al_int @ H2 @ B ) ) ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.same_carrierI
% 3.82/4.08 thf(fact_6418_prod_Osame__carrierI,axiom,
% 3.82/4.08 ! [C4: set_complex,A2: set_complex,B: set_complex,G: complex > int,H2: complex > int] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ C4 )
% 3.82/4.08 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 3.82/4.08 => ( ( ord_le211207098394363844omplex @ B @ C4 )
% 3.82/4.08 => ( ! [A4: complex] :
% 3.82/4.08 ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 3.82/4.08 => ( ( G @ A4 )
% 3.82/4.08 = one_one_int ) )
% 3.82/4.08 => ( ! [B4: complex] :
% 3.82/4.08 ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ C4 @ B ) )
% 3.82/4.08 => ( ( H2 @ B4 )
% 3.82/4.08 = one_one_int ) )
% 3.82/4.08 => ( ( ( groups858564598930262913ex_int @ G @ C4 )
% 3.82/4.08 = ( groups858564598930262913ex_int @ H2 @ C4 ) )
% 3.82/4.08 => ( ( groups858564598930262913ex_int @ G @ A2 )
% 3.82/4.08 = ( groups858564598930262913ex_int @ H2 @ B ) ) ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.same_carrierI
% 3.82/4.08 thf(fact_6419_prod_Osame__carrierI,axiom,
% 3.82/4.08 ! [C4: set_Extended_enat,A2: set_Extended_enat,B: set_Extended_enat,G: extended_enat > int,H2: extended_enat > int] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ C4 )
% 3.82/4.08 => ( ( ord_le7203529160286727270d_enat @ A2 @ C4 )
% 3.82/4.08 => ( ( ord_le7203529160286727270d_enat @ B @ C4 )
% 3.82/4.08 => ( ! [A4: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ A4 @ ( minus_925952699566721837d_enat @ C4 @ A2 ) )
% 3.82/4.08 => ( ( G @ A4 )
% 3.82/4.08 = one_one_int ) )
% 3.82/4.08 => ( ! [B4: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ B4 @ ( minus_925952699566721837d_enat @ C4 @ B ) )
% 3.82/4.08 => ( ( H2 @ B4 )
% 3.82/4.08 = one_one_int ) )
% 3.82/4.08 => ( ( ( groups2878480467620962989at_int @ G @ C4 )
% 3.82/4.08 = ( groups2878480467620962989at_int @ H2 @ C4 ) )
% 3.82/4.08 => ( ( groups2878480467620962989at_int @ G @ A2 )
% 3.82/4.08 = ( groups2878480467620962989at_int @ H2 @ B ) ) ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.same_carrierI
% 3.82/4.08 thf(fact_6420_prod_Osame__carrierI,axiom,
% 3.82/4.08 ! [C4: set_real,A2: set_real,B: set_real,G: real > complex,H2: real > complex] :
% 3.82/4.08 ( ( finite_finite_real @ C4 )
% 3.82/4.08 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 3.82/4.08 => ( ( ord_less_eq_set_real @ B @ C4 )
% 3.82/4.08 => ( ! [A4: real] :
% 3.82/4.08 ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 3.82/4.08 => ( ( G @ A4 )
% 3.82/4.08 = one_one_complex ) )
% 3.82/4.08 => ( ! [B4: real] :
% 3.82/4.08 ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B ) )
% 3.82/4.08 => ( ( H2 @ B4 )
% 3.82/4.08 = one_one_complex ) )
% 3.82/4.08 => ( ( ( groups713298508707869441omplex @ G @ C4 )
% 3.82/4.08 = ( groups713298508707869441omplex @ H2 @ C4 ) )
% 3.82/4.08 => ( ( groups713298508707869441omplex @ G @ A2 )
% 3.82/4.08 = ( groups713298508707869441omplex @ H2 @ B ) ) ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.same_carrierI
% 3.82/4.08 thf(fact_6421_prod_Osame__carrierI,axiom,
% 3.82/4.08 ! [C4: set_complex,A2: set_complex,B: set_complex,G: complex > complex,H2: complex > complex] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ C4 )
% 3.82/4.08 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 3.82/4.08 => ( ( ord_le211207098394363844omplex @ B @ C4 )
% 3.82/4.08 => ( ! [A4: complex] :
% 3.82/4.08 ( ( member_complex @ A4 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 3.82/4.08 => ( ( G @ A4 )
% 3.82/4.08 = one_one_complex ) )
% 3.82/4.08 => ( ! [B4: complex] :
% 3.82/4.08 ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ C4 @ B ) )
% 3.82/4.08 => ( ( H2 @ B4 )
% 3.82/4.08 = one_one_complex ) )
% 3.82/4.08 => ( ( ( groups3708469109370488835omplex @ G @ C4 )
% 3.82/4.08 = ( groups3708469109370488835omplex @ H2 @ C4 ) )
% 3.82/4.08 => ( ( groups3708469109370488835omplex @ G @ A2 )
% 3.82/4.08 = ( groups3708469109370488835omplex @ H2 @ B ) ) ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.same_carrierI
% 3.82/4.08 thf(fact_6422_prod_Osame__carrierI,axiom,
% 3.82/4.08 ! [C4: set_Extended_enat,A2: set_Extended_enat,B: set_Extended_enat,G: extended_enat > complex,H2: extended_enat > complex] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ C4 )
% 3.82/4.08 => ( ( ord_le7203529160286727270d_enat @ A2 @ C4 )
% 3.82/4.08 => ( ( ord_le7203529160286727270d_enat @ B @ C4 )
% 3.82/4.08 => ( ! [A4: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ A4 @ ( minus_925952699566721837d_enat @ C4 @ A2 ) )
% 3.82/4.08 => ( ( G @ A4 )
% 3.82/4.08 = one_one_complex ) )
% 3.82/4.08 => ( ! [B4: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ B4 @ ( minus_925952699566721837d_enat @ C4 @ B ) )
% 3.82/4.08 => ( ( H2 @ B4 )
% 3.82/4.08 = one_one_complex ) )
% 3.82/4.08 => ( ( ( groups4622424608036095791omplex @ G @ C4 )
% 3.82/4.08 = ( groups4622424608036095791omplex @ H2 @ C4 ) )
% 3.82/4.08 => ( ( groups4622424608036095791omplex @ G @ A2 )
% 3.82/4.08 = ( groups4622424608036095791omplex @ H2 @ B ) ) ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.same_carrierI
% 3.82/4.08 thf(fact_6423_prod_Osame__carrierI,axiom,
% 3.82/4.08 ! [C4: set_real,A2: set_real,B: set_real,G: real > real,H2: real > real] :
% 3.82/4.08 ( ( finite_finite_real @ C4 )
% 3.82/4.08 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 3.82/4.08 => ( ( ord_less_eq_set_real @ B @ C4 )
% 3.82/4.08 => ( ! [A4: real] :
% 3.82/4.08 ( ( member_real @ A4 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 3.82/4.08 => ( ( G @ A4 )
% 3.82/4.08 = one_one_real ) )
% 3.82/4.08 => ( ! [B4: real] :
% 3.82/4.08 ( ( member_real @ B4 @ ( minus_minus_set_real @ C4 @ B ) )
% 3.82/4.08 => ( ( H2 @ B4 )
% 3.82/4.08 = one_one_real ) )
% 3.82/4.08 => ( ( ( groups1681761925125756287l_real @ G @ C4 )
% 3.82/4.08 = ( groups1681761925125756287l_real @ H2 @ C4 ) )
% 3.82/4.08 => ( ( groups1681761925125756287l_real @ G @ A2 )
% 3.82/4.08 = ( groups1681761925125756287l_real @ H2 @ B ) ) ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.same_carrierI
% 3.82/4.08 thf(fact_6424_prod_Omono__neutral__left,axiom,
% 3.82/4.08 ! [T3: set_complex,S2: set_complex,G: complex > nat] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ T3 )
% 3.82/4.08 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 3.82/4.08 => ( ! [X5: complex] :
% 3.82/4.08 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 3.82/4.08 => ( ( G @ X5 )
% 3.82/4.08 = one_one_nat ) )
% 3.82/4.08 => ( ( groups861055069439313189ex_nat @ G @ S2 )
% 3.82/4.08 = ( groups861055069439313189ex_nat @ G @ T3 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.mono_neutral_left
% 3.82/4.08 thf(fact_6425_prod_Omono__neutral__left,axiom,
% 3.82/4.08 ! [T3: set_Extended_enat,S2: set_Extended_enat,G: extended_enat > nat] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ T3 )
% 3.82/4.08 => ( ( ord_le7203529160286727270d_enat @ S2 @ T3 )
% 3.82/4.08 => ( ! [X5: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ X5 @ ( minus_925952699566721837d_enat @ T3 @ S2 ) )
% 3.82/4.08 => ( ( G @ X5 )
% 3.82/4.08 = one_one_nat ) )
% 3.82/4.08 => ( ( groups2880970938130013265at_nat @ G @ S2 )
% 3.82/4.08 = ( groups2880970938130013265at_nat @ G @ T3 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.mono_neutral_left
% 3.82/4.08 thf(fact_6426_prod_Omono__neutral__left,axiom,
% 3.82/4.08 ! [T3: set_complex,S2: set_complex,G: complex > int] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ T3 )
% 3.82/4.08 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 3.82/4.08 => ( ! [X5: complex] :
% 3.82/4.08 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 3.82/4.08 => ( ( G @ X5 )
% 3.82/4.08 = one_one_int ) )
% 3.82/4.08 => ( ( groups858564598930262913ex_int @ G @ S2 )
% 3.82/4.08 = ( groups858564598930262913ex_int @ G @ T3 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.mono_neutral_left
% 3.82/4.08 thf(fact_6427_prod_Omono__neutral__left,axiom,
% 3.82/4.08 ! [T3: set_Extended_enat,S2: set_Extended_enat,G: extended_enat > int] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ T3 )
% 3.82/4.08 => ( ( ord_le7203529160286727270d_enat @ S2 @ T3 )
% 3.82/4.08 => ( ! [X5: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ X5 @ ( minus_925952699566721837d_enat @ T3 @ S2 ) )
% 3.82/4.08 => ( ( G @ X5 )
% 3.82/4.08 = one_one_int ) )
% 3.82/4.08 => ( ( groups2878480467620962989at_int @ G @ S2 )
% 3.82/4.08 = ( groups2878480467620962989at_int @ G @ T3 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.mono_neutral_left
% 3.82/4.08 thf(fact_6428_prod_Omono__neutral__left,axiom,
% 3.82/4.08 ! [T3: set_complex,S2: set_complex,G: complex > complex] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ T3 )
% 3.82/4.08 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 3.82/4.08 => ( ! [X5: complex] :
% 3.82/4.08 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 3.82/4.08 => ( ( G @ X5 )
% 3.82/4.08 = one_one_complex ) )
% 3.82/4.08 => ( ( groups3708469109370488835omplex @ G @ S2 )
% 3.82/4.08 = ( groups3708469109370488835omplex @ G @ T3 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.mono_neutral_left
% 3.82/4.08 thf(fact_6429_prod_Omono__neutral__left,axiom,
% 3.82/4.08 ! [T3: set_Extended_enat,S2: set_Extended_enat,G: extended_enat > complex] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ T3 )
% 3.82/4.08 => ( ( ord_le7203529160286727270d_enat @ S2 @ T3 )
% 3.82/4.08 => ( ! [X5: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ X5 @ ( minus_925952699566721837d_enat @ T3 @ S2 ) )
% 3.82/4.08 => ( ( G @ X5 )
% 3.82/4.08 = one_one_complex ) )
% 3.82/4.08 => ( ( groups4622424608036095791omplex @ G @ S2 )
% 3.82/4.08 = ( groups4622424608036095791omplex @ G @ T3 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.mono_neutral_left
% 3.82/4.08 thf(fact_6430_prod_Omono__neutral__left,axiom,
% 3.82/4.08 ! [T3: set_complex,S2: set_complex,G: complex > real] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ T3 )
% 3.82/4.08 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 3.82/4.08 => ( ! [X5: complex] :
% 3.82/4.08 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 3.82/4.08 => ( ( G @ X5 )
% 3.82/4.08 = one_one_real ) )
% 3.82/4.08 => ( ( groups766887009212190081x_real @ G @ S2 )
% 3.82/4.08 = ( groups766887009212190081x_real @ G @ T3 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.mono_neutral_left
% 3.82/4.08 thf(fact_6431_prod_Omono__neutral__left,axiom,
% 3.82/4.08 ! [T3: set_Extended_enat,S2: set_Extended_enat,G: extended_enat > real] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ T3 )
% 3.82/4.08 => ( ( ord_le7203529160286727270d_enat @ S2 @ T3 )
% 3.82/4.08 => ( ! [X5: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ X5 @ ( minus_925952699566721837d_enat @ T3 @ S2 ) )
% 3.82/4.08 => ( ( G @ X5 )
% 3.82/4.08 = one_one_real ) )
% 3.82/4.08 => ( ( groups97031904164794029t_real @ G @ S2 )
% 3.82/4.08 = ( groups97031904164794029t_real @ G @ T3 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.mono_neutral_left
% 3.82/4.08 thf(fact_6432_prod_Omono__neutral__left,axiom,
% 3.82/4.08 ! [T3: set_nat,S2: set_nat,G: nat > complex] :
% 3.82/4.08 ( ( finite_finite_nat @ T3 )
% 3.82/4.08 => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 3.82/4.08 => ( ! [X5: nat] :
% 3.82/4.08 ( ( member_nat @ X5 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 3.82/4.08 => ( ( G @ X5 )
% 3.82/4.08 = one_one_complex ) )
% 3.82/4.08 => ( ( groups6464643781859351333omplex @ G @ S2 )
% 3.82/4.08 = ( groups6464643781859351333omplex @ G @ T3 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.mono_neutral_left
% 3.82/4.08 thf(fact_6433_prod_Omono__neutral__left,axiom,
% 3.82/4.08 ! [T3: set_nat,S2: set_nat,G: nat > real] :
% 3.82/4.08 ( ( finite_finite_nat @ T3 )
% 3.82/4.08 => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 3.82/4.08 => ( ! [X5: nat] :
% 3.82/4.08 ( ( member_nat @ X5 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 3.82/4.08 => ( ( G @ X5 )
% 3.82/4.08 = one_one_real ) )
% 3.82/4.08 => ( ( groups129246275422532515t_real @ G @ S2 )
% 3.82/4.08 = ( groups129246275422532515t_real @ G @ T3 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.mono_neutral_left
% 3.82/4.08 thf(fact_6434_prod_Omono__neutral__right,axiom,
% 3.82/4.08 ! [T3: set_complex,S2: set_complex,G: complex > nat] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ T3 )
% 3.82/4.08 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 3.82/4.08 => ( ! [X5: complex] :
% 3.82/4.08 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 3.82/4.08 => ( ( G @ X5 )
% 3.82/4.08 = one_one_nat ) )
% 3.82/4.08 => ( ( groups861055069439313189ex_nat @ G @ T3 )
% 3.82/4.08 = ( groups861055069439313189ex_nat @ G @ S2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.mono_neutral_right
% 3.82/4.08 thf(fact_6435_prod_Omono__neutral__right,axiom,
% 3.82/4.08 ! [T3: set_Extended_enat,S2: set_Extended_enat,G: extended_enat > nat] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ T3 )
% 3.82/4.08 => ( ( ord_le7203529160286727270d_enat @ S2 @ T3 )
% 3.82/4.08 => ( ! [X5: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ X5 @ ( minus_925952699566721837d_enat @ T3 @ S2 ) )
% 3.82/4.08 => ( ( G @ X5 )
% 3.82/4.08 = one_one_nat ) )
% 3.82/4.08 => ( ( groups2880970938130013265at_nat @ G @ T3 )
% 3.82/4.08 = ( groups2880970938130013265at_nat @ G @ S2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.mono_neutral_right
% 3.82/4.08 thf(fact_6436_prod_Omono__neutral__right,axiom,
% 3.82/4.08 ! [T3: set_complex,S2: set_complex,G: complex > int] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ T3 )
% 3.82/4.08 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 3.82/4.08 => ( ! [X5: complex] :
% 3.82/4.08 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 3.82/4.08 => ( ( G @ X5 )
% 3.82/4.08 = one_one_int ) )
% 3.82/4.08 => ( ( groups858564598930262913ex_int @ G @ T3 )
% 3.82/4.08 = ( groups858564598930262913ex_int @ G @ S2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.mono_neutral_right
% 3.82/4.08 thf(fact_6437_prod_Omono__neutral__right,axiom,
% 3.82/4.08 ! [T3: set_Extended_enat,S2: set_Extended_enat,G: extended_enat > int] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ T3 )
% 3.82/4.08 => ( ( ord_le7203529160286727270d_enat @ S2 @ T3 )
% 3.82/4.08 => ( ! [X5: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ X5 @ ( minus_925952699566721837d_enat @ T3 @ S2 ) )
% 3.82/4.08 => ( ( G @ X5 )
% 3.82/4.08 = one_one_int ) )
% 3.82/4.08 => ( ( groups2878480467620962989at_int @ G @ T3 )
% 3.82/4.08 = ( groups2878480467620962989at_int @ G @ S2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.mono_neutral_right
% 3.82/4.08 thf(fact_6438_prod_Omono__neutral__right,axiom,
% 3.82/4.08 ! [T3: set_complex,S2: set_complex,G: complex > complex] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ T3 )
% 3.82/4.08 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 3.82/4.08 => ( ! [X5: complex] :
% 3.82/4.08 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 3.82/4.08 => ( ( G @ X5 )
% 3.82/4.08 = one_one_complex ) )
% 3.82/4.08 => ( ( groups3708469109370488835omplex @ G @ T3 )
% 3.82/4.08 = ( groups3708469109370488835omplex @ G @ S2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.mono_neutral_right
% 3.82/4.08 thf(fact_6439_prod_Omono__neutral__right,axiom,
% 3.82/4.08 ! [T3: set_Extended_enat,S2: set_Extended_enat,G: extended_enat > complex] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ T3 )
% 3.82/4.08 => ( ( ord_le7203529160286727270d_enat @ S2 @ T3 )
% 3.82/4.08 => ( ! [X5: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ X5 @ ( minus_925952699566721837d_enat @ T3 @ S2 ) )
% 3.82/4.08 => ( ( G @ X5 )
% 3.82/4.08 = one_one_complex ) )
% 3.82/4.08 => ( ( groups4622424608036095791omplex @ G @ T3 )
% 3.82/4.08 = ( groups4622424608036095791omplex @ G @ S2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.mono_neutral_right
% 3.82/4.08 thf(fact_6440_prod_Omono__neutral__right,axiom,
% 3.82/4.08 ! [T3: set_complex,S2: set_complex,G: complex > real] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ T3 )
% 3.82/4.08 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 3.82/4.08 => ( ! [X5: complex] :
% 3.82/4.08 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 3.82/4.08 => ( ( G @ X5 )
% 3.82/4.08 = one_one_real ) )
% 3.82/4.08 => ( ( groups766887009212190081x_real @ G @ T3 )
% 3.82/4.08 = ( groups766887009212190081x_real @ G @ S2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.mono_neutral_right
% 3.82/4.08 thf(fact_6441_prod_Omono__neutral__right,axiom,
% 3.82/4.08 ! [T3: set_Extended_enat,S2: set_Extended_enat,G: extended_enat > real] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ T3 )
% 3.82/4.08 => ( ( ord_le7203529160286727270d_enat @ S2 @ T3 )
% 3.82/4.08 => ( ! [X5: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ X5 @ ( minus_925952699566721837d_enat @ T3 @ S2 ) )
% 3.82/4.08 => ( ( G @ X5 )
% 3.82/4.08 = one_one_real ) )
% 3.82/4.08 => ( ( groups97031904164794029t_real @ G @ T3 )
% 3.82/4.08 = ( groups97031904164794029t_real @ G @ S2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.mono_neutral_right
% 3.82/4.08 thf(fact_6442_prod_Omono__neutral__right,axiom,
% 3.82/4.08 ! [T3: set_nat,S2: set_nat,G: nat > complex] :
% 3.82/4.08 ( ( finite_finite_nat @ T3 )
% 3.82/4.08 => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 3.82/4.08 => ( ! [X5: nat] :
% 3.82/4.08 ( ( member_nat @ X5 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 3.82/4.08 => ( ( G @ X5 )
% 3.82/4.08 = one_one_complex ) )
% 3.82/4.08 => ( ( groups6464643781859351333omplex @ G @ T3 )
% 3.82/4.08 = ( groups6464643781859351333omplex @ G @ S2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.mono_neutral_right
% 3.82/4.08 thf(fact_6443_prod_Omono__neutral__right,axiom,
% 3.82/4.08 ! [T3: set_nat,S2: set_nat,G: nat > real] :
% 3.82/4.08 ( ( finite_finite_nat @ T3 )
% 3.82/4.08 => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 3.82/4.08 => ( ! [X5: nat] :
% 3.82/4.08 ( ( member_nat @ X5 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 3.82/4.08 => ( ( G @ X5 )
% 3.82/4.08 = one_one_real ) )
% 3.82/4.08 => ( ( groups129246275422532515t_real @ G @ T3 )
% 3.82/4.08 = ( groups129246275422532515t_real @ G @ S2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.mono_neutral_right
% 3.82/4.08 thf(fact_6444_prod_Omono__neutral__cong__left,axiom,
% 3.82/4.08 ! [T3: set_real,S2: set_real,H2: real > nat,G: real > nat] :
% 3.82/4.08 ( ( finite_finite_real @ T3 )
% 3.82/4.08 => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 3.82/4.08 => ( ! [X5: real] :
% 3.82/4.08 ( ( member_real @ X5 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 3.82/4.08 => ( ( H2 @ X5 )
% 3.82/4.08 = one_one_nat ) )
% 3.82/4.08 => ( ! [X5: real] :
% 3.82/4.08 ( ( member_real @ X5 @ S2 )
% 3.82/4.08 => ( ( G @ X5 )
% 3.82/4.08 = ( H2 @ X5 ) ) )
% 3.82/4.08 => ( ( groups4696554848551431203al_nat @ G @ S2 )
% 3.82/4.08 = ( groups4696554848551431203al_nat @ H2 @ T3 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.mono_neutral_cong_left
% 3.82/4.08 thf(fact_6445_prod_Omono__neutral__cong__left,axiom,
% 3.82/4.08 ! [T3: set_complex,S2: set_complex,H2: complex > nat,G: complex > nat] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ T3 )
% 3.82/4.08 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 3.82/4.08 => ( ! [X5: complex] :
% 3.82/4.08 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 3.82/4.08 => ( ( H2 @ X5 )
% 3.82/4.08 = one_one_nat ) )
% 3.82/4.08 => ( ! [X5: complex] :
% 3.82/4.08 ( ( member_complex @ X5 @ S2 )
% 3.82/4.08 => ( ( G @ X5 )
% 3.82/4.08 = ( H2 @ X5 ) ) )
% 3.82/4.08 => ( ( groups861055069439313189ex_nat @ G @ S2 )
% 3.82/4.08 = ( groups861055069439313189ex_nat @ H2 @ T3 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.mono_neutral_cong_left
% 3.82/4.08 thf(fact_6446_prod_Omono__neutral__cong__left,axiom,
% 3.82/4.08 ! [T3: set_Extended_enat,S2: set_Extended_enat,H2: extended_enat > nat,G: extended_enat > nat] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ T3 )
% 3.82/4.08 => ( ( ord_le7203529160286727270d_enat @ S2 @ T3 )
% 3.82/4.08 => ( ! [X5: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ X5 @ ( minus_925952699566721837d_enat @ T3 @ S2 ) )
% 3.82/4.08 => ( ( H2 @ X5 )
% 3.82/4.08 = one_one_nat ) )
% 3.82/4.08 => ( ! [X5: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ X5 @ S2 )
% 3.82/4.08 => ( ( G @ X5 )
% 3.82/4.08 = ( H2 @ X5 ) ) )
% 3.82/4.08 => ( ( groups2880970938130013265at_nat @ G @ S2 )
% 3.82/4.08 = ( groups2880970938130013265at_nat @ H2 @ T3 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.mono_neutral_cong_left
% 3.82/4.08 thf(fact_6447_prod_Omono__neutral__cong__left,axiom,
% 3.82/4.08 ! [T3: set_real,S2: set_real,H2: real > int,G: real > int] :
% 3.82/4.08 ( ( finite_finite_real @ T3 )
% 3.82/4.08 => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 3.82/4.08 => ( ! [X5: real] :
% 3.82/4.08 ( ( member_real @ X5 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 3.82/4.08 => ( ( H2 @ X5 )
% 3.82/4.08 = one_one_int ) )
% 3.82/4.08 => ( ! [X5: real] :
% 3.82/4.08 ( ( member_real @ X5 @ S2 )
% 3.82/4.08 => ( ( G @ X5 )
% 3.82/4.08 = ( H2 @ X5 ) ) )
% 3.82/4.08 => ( ( groups4694064378042380927al_int @ G @ S2 )
% 3.82/4.08 = ( groups4694064378042380927al_int @ H2 @ T3 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.mono_neutral_cong_left
% 3.82/4.08 thf(fact_6448_prod_Omono__neutral__cong__left,axiom,
% 3.82/4.08 ! [T3: set_complex,S2: set_complex,H2: complex > int,G: complex > int] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ T3 )
% 3.82/4.08 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 3.82/4.08 => ( ! [X5: complex] :
% 3.82/4.08 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 3.82/4.08 => ( ( H2 @ X5 )
% 3.82/4.08 = one_one_int ) )
% 3.82/4.08 => ( ! [X5: complex] :
% 3.82/4.08 ( ( member_complex @ X5 @ S2 )
% 3.82/4.08 => ( ( G @ X5 )
% 3.82/4.08 = ( H2 @ X5 ) ) )
% 3.82/4.08 => ( ( groups858564598930262913ex_int @ G @ S2 )
% 3.82/4.08 = ( groups858564598930262913ex_int @ H2 @ T3 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.mono_neutral_cong_left
% 3.82/4.08 thf(fact_6449_prod_Omono__neutral__cong__left,axiom,
% 3.82/4.08 ! [T3: set_Extended_enat,S2: set_Extended_enat,H2: extended_enat > int,G: extended_enat > int] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ T3 )
% 3.82/4.08 => ( ( ord_le7203529160286727270d_enat @ S2 @ T3 )
% 3.82/4.08 => ( ! [X5: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ X5 @ ( minus_925952699566721837d_enat @ T3 @ S2 ) )
% 3.82/4.08 => ( ( H2 @ X5 )
% 3.82/4.08 = one_one_int ) )
% 3.82/4.08 => ( ! [X5: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ X5 @ S2 )
% 3.82/4.08 => ( ( G @ X5 )
% 3.82/4.08 = ( H2 @ X5 ) ) )
% 3.82/4.08 => ( ( groups2878480467620962989at_int @ G @ S2 )
% 3.82/4.08 = ( groups2878480467620962989at_int @ H2 @ T3 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.mono_neutral_cong_left
% 3.82/4.08 thf(fact_6450_prod_Omono__neutral__cong__left,axiom,
% 3.82/4.08 ! [T3: set_real,S2: set_real,H2: real > complex,G: real > complex] :
% 3.82/4.08 ( ( finite_finite_real @ T3 )
% 3.82/4.08 => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 3.82/4.08 => ( ! [X5: real] :
% 3.82/4.08 ( ( member_real @ X5 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 3.82/4.08 => ( ( H2 @ X5 )
% 3.82/4.08 = one_one_complex ) )
% 3.82/4.08 => ( ! [X5: real] :
% 3.82/4.08 ( ( member_real @ X5 @ S2 )
% 3.82/4.08 => ( ( G @ X5 )
% 3.82/4.08 = ( H2 @ X5 ) ) )
% 3.82/4.08 => ( ( groups713298508707869441omplex @ G @ S2 )
% 3.82/4.08 = ( groups713298508707869441omplex @ H2 @ T3 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.mono_neutral_cong_left
% 3.82/4.08 thf(fact_6451_prod_Omono__neutral__cong__left,axiom,
% 3.82/4.08 ! [T3: set_complex,S2: set_complex,H2: complex > complex,G: complex > complex] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ T3 )
% 3.82/4.08 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 3.82/4.08 => ( ! [X5: complex] :
% 3.82/4.08 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 3.82/4.08 => ( ( H2 @ X5 )
% 3.82/4.08 = one_one_complex ) )
% 3.82/4.08 => ( ! [X5: complex] :
% 3.82/4.08 ( ( member_complex @ X5 @ S2 )
% 3.82/4.08 => ( ( G @ X5 )
% 3.82/4.08 = ( H2 @ X5 ) ) )
% 3.82/4.08 => ( ( groups3708469109370488835omplex @ G @ S2 )
% 3.82/4.08 = ( groups3708469109370488835omplex @ H2 @ T3 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.mono_neutral_cong_left
% 3.82/4.08 thf(fact_6452_prod_Omono__neutral__cong__left,axiom,
% 3.82/4.08 ! [T3: set_Extended_enat,S2: set_Extended_enat,H2: extended_enat > complex,G: extended_enat > complex] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ T3 )
% 3.82/4.08 => ( ( ord_le7203529160286727270d_enat @ S2 @ T3 )
% 3.82/4.08 => ( ! [X5: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ X5 @ ( minus_925952699566721837d_enat @ T3 @ S2 ) )
% 3.82/4.08 => ( ( H2 @ X5 )
% 3.82/4.08 = one_one_complex ) )
% 3.82/4.08 => ( ! [X5: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ X5 @ S2 )
% 3.82/4.08 => ( ( G @ X5 )
% 3.82/4.08 = ( H2 @ X5 ) ) )
% 3.82/4.08 => ( ( groups4622424608036095791omplex @ G @ S2 )
% 3.82/4.08 = ( groups4622424608036095791omplex @ H2 @ T3 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.mono_neutral_cong_left
% 3.82/4.08 thf(fact_6453_prod_Omono__neutral__cong__left,axiom,
% 3.82/4.08 ! [T3: set_real,S2: set_real,H2: real > real,G: real > real] :
% 3.82/4.08 ( ( finite_finite_real @ T3 )
% 3.82/4.08 => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 3.82/4.08 => ( ! [X5: real] :
% 3.82/4.08 ( ( member_real @ X5 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 3.82/4.08 => ( ( H2 @ X5 )
% 3.82/4.08 = one_one_real ) )
% 3.82/4.08 => ( ! [X5: real] :
% 3.82/4.08 ( ( member_real @ X5 @ S2 )
% 3.82/4.08 => ( ( G @ X5 )
% 3.82/4.08 = ( H2 @ X5 ) ) )
% 3.82/4.08 => ( ( groups1681761925125756287l_real @ G @ S2 )
% 3.82/4.08 = ( groups1681761925125756287l_real @ H2 @ T3 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.mono_neutral_cong_left
% 3.82/4.08 thf(fact_6454_prod_Omono__neutral__cong__right,axiom,
% 3.82/4.08 ! [T3: set_real,S2: set_real,G: real > nat,H2: real > nat] :
% 3.82/4.08 ( ( finite_finite_real @ T3 )
% 3.82/4.08 => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 3.82/4.08 => ( ! [X5: real] :
% 3.82/4.08 ( ( member_real @ X5 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 3.82/4.08 => ( ( G @ X5 )
% 3.82/4.08 = one_one_nat ) )
% 3.82/4.08 => ( ! [X5: real] :
% 3.82/4.08 ( ( member_real @ X5 @ S2 )
% 3.82/4.08 => ( ( G @ X5 )
% 3.82/4.08 = ( H2 @ X5 ) ) )
% 3.82/4.08 => ( ( groups4696554848551431203al_nat @ G @ T3 )
% 3.82/4.08 = ( groups4696554848551431203al_nat @ H2 @ S2 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.mono_neutral_cong_right
% 3.82/4.08 thf(fact_6455_prod_Omono__neutral__cong__right,axiom,
% 3.82/4.08 ! [T3: set_complex,S2: set_complex,G: complex > nat,H2: complex > nat] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ T3 )
% 3.82/4.08 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 3.82/4.08 => ( ! [X5: complex] :
% 3.82/4.08 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 3.82/4.08 => ( ( G @ X5 )
% 3.82/4.08 = one_one_nat ) )
% 3.82/4.08 => ( ! [X5: complex] :
% 3.82/4.08 ( ( member_complex @ X5 @ S2 )
% 3.82/4.08 => ( ( G @ X5 )
% 3.82/4.08 = ( H2 @ X5 ) ) )
% 3.82/4.08 => ( ( groups861055069439313189ex_nat @ G @ T3 )
% 3.82/4.08 = ( groups861055069439313189ex_nat @ H2 @ S2 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.mono_neutral_cong_right
% 3.82/4.08 thf(fact_6456_prod_Omono__neutral__cong__right,axiom,
% 3.82/4.08 ! [T3: set_Extended_enat,S2: set_Extended_enat,G: extended_enat > nat,H2: extended_enat > nat] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ T3 )
% 3.82/4.08 => ( ( ord_le7203529160286727270d_enat @ S2 @ T3 )
% 3.82/4.08 => ( ! [X5: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ X5 @ ( minus_925952699566721837d_enat @ T3 @ S2 ) )
% 3.82/4.08 => ( ( G @ X5 )
% 3.82/4.08 = one_one_nat ) )
% 3.82/4.08 => ( ! [X5: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ X5 @ S2 )
% 3.82/4.08 => ( ( G @ X5 )
% 3.82/4.08 = ( H2 @ X5 ) ) )
% 3.82/4.08 => ( ( groups2880970938130013265at_nat @ G @ T3 )
% 3.82/4.08 = ( groups2880970938130013265at_nat @ H2 @ S2 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.mono_neutral_cong_right
% 3.82/4.08 thf(fact_6457_prod_Omono__neutral__cong__right,axiom,
% 3.82/4.08 ! [T3: set_real,S2: set_real,G: real > int,H2: real > int] :
% 3.82/4.08 ( ( finite_finite_real @ T3 )
% 3.82/4.08 => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 3.82/4.08 => ( ! [X5: real] :
% 3.82/4.08 ( ( member_real @ X5 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 3.82/4.08 => ( ( G @ X5 )
% 3.82/4.08 = one_one_int ) )
% 3.82/4.08 => ( ! [X5: real] :
% 3.82/4.08 ( ( member_real @ X5 @ S2 )
% 3.82/4.08 => ( ( G @ X5 )
% 3.82/4.08 = ( H2 @ X5 ) ) )
% 3.82/4.08 => ( ( groups4694064378042380927al_int @ G @ T3 )
% 3.82/4.08 = ( groups4694064378042380927al_int @ H2 @ S2 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.mono_neutral_cong_right
% 3.82/4.08 thf(fact_6458_prod_Omono__neutral__cong__right,axiom,
% 3.82/4.08 ! [T3: set_complex,S2: set_complex,G: complex > int,H2: complex > int] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ T3 )
% 3.82/4.08 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 3.82/4.08 => ( ! [X5: complex] :
% 3.82/4.08 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 3.82/4.08 => ( ( G @ X5 )
% 3.82/4.08 = one_one_int ) )
% 3.82/4.08 => ( ! [X5: complex] :
% 3.82/4.08 ( ( member_complex @ X5 @ S2 )
% 3.82/4.08 => ( ( G @ X5 )
% 3.82/4.08 = ( H2 @ X5 ) ) )
% 3.82/4.08 => ( ( groups858564598930262913ex_int @ G @ T3 )
% 3.82/4.08 = ( groups858564598930262913ex_int @ H2 @ S2 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.mono_neutral_cong_right
% 3.82/4.08 thf(fact_6459_prod_Omono__neutral__cong__right,axiom,
% 3.82/4.08 ! [T3: set_Extended_enat,S2: set_Extended_enat,G: extended_enat > int,H2: extended_enat > int] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ T3 )
% 3.82/4.08 => ( ( ord_le7203529160286727270d_enat @ S2 @ T3 )
% 3.82/4.08 => ( ! [X5: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ X5 @ ( minus_925952699566721837d_enat @ T3 @ S2 ) )
% 3.82/4.08 => ( ( G @ X5 )
% 3.82/4.08 = one_one_int ) )
% 3.82/4.08 => ( ! [X5: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ X5 @ S2 )
% 3.82/4.08 => ( ( G @ X5 )
% 3.82/4.08 = ( H2 @ X5 ) ) )
% 3.82/4.08 => ( ( groups2878480467620962989at_int @ G @ T3 )
% 3.82/4.08 = ( groups2878480467620962989at_int @ H2 @ S2 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.mono_neutral_cong_right
% 3.82/4.08 thf(fact_6460_prod_Omono__neutral__cong__right,axiom,
% 3.82/4.08 ! [T3: set_real,S2: set_real,G: real > complex,H2: real > complex] :
% 3.82/4.08 ( ( finite_finite_real @ T3 )
% 3.82/4.08 => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 3.82/4.08 => ( ! [X5: real] :
% 3.82/4.08 ( ( member_real @ X5 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 3.82/4.08 => ( ( G @ X5 )
% 3.82/4.08 = one_one_complex ) )
% 3.82/4.08 => ( ! [X5: real] :
% 3.82/4.08 ( ( member_real @ X5 @ S2 )
% 3.82/4.08 => ( ( G @ X5 )
% 3.82/4.08 = ( H2 @ X5 ) ) )
% 3.82/4.08 => ( ( groups713298508707869441omplex @ G @ T3 )
% 3.82/4.08 = ( groups713298508707869441omplex @ H2 @ S2 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.mono_neutral_cong_right
% 3.82/4.08 thf(fact_6461_prod_Omono__neutral__cong__right,axiom,
% 3.82/4.08 ! [T3: set_complex,S2: set_complex,G: complex > complex,H2: complex > complex] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ T3 )
% 3.82/4.08 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 3.82/4.08 => ( ! [X5: complex] :
% 3.82/4.08 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 3.82/4.08 => ( ( G @ X5 )
% 3.82/4.08 = one_one_complex ) )
% 3.82/4.08 => ( ! [X5: complex] :
% 3.82/4.08 ( ( member_complex @ X5 @ S2 )
% 3.82/4.08 => ( ( G @ X5 )
% 3.82/4.08 = ( H2 @ X5 ) ) )
% 3.82/4.08 => ( ( groups3708469109370488835omplex @ G @ T3 )
% 3.82/4.08 = ( groups3708469109370488835omplex @ H2 @ S2 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.mono_neutral_cong_right
% 3.82/4.08 thf(fact_6462_prod_Omono__neutral__cong__right,axiom,
% 3.82/4.08 ! [T3: set_Extended_enat,S2: set_Extended_enat,G: extended_enat > complex,H2: extended_enat > complex] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ T3 )
% 3.82/4.08 => ( ( ord_le7203529160286727270d_enat @ S2 @ T3 )
% 3.82/4.08 => ( ! [X5: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ X5 @ ( minus_925952699566721837d_enat @ T3 @ S2 ) )
% 3.82/4.08 => ( ( G @ X5 )
% 3.82/4.08 = one_one_complex ) )
% 3.82/4.08 => ( ! [X5: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ X5 @ S2 )
% 3.82/4.08 => ( ( G @ X5 )
% 3.82/4.08 = ( H2 @ X5 ) ) )
% 3.82/4.08 => ( ( groups4622424608036095791omplex @ G @ T3 )
% 3.82/4.08 = ( groups4622424608036095791omplex @ H2 @ S2 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.mono_neutral_cong_right
% 3.82/4.08 thf(fact_6463_prod_Omono__neutral__cong__right,axiom,
% 3.82/4.08 ! [T3: set_real,S2: set_real,G: real > real,H2: real > real] :
% 3.82/4.08 ( ( finite_finite_real @ T3 )
% 3.82/4.08 => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 3.82/4.08 => ( ! [X5: real] :
% 3.82/4.08 ( ( member_real @ X5 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 3.82/4.08 => ( ( G @ X5 )
% 3.82/4.08 = one_one_real ) )
% 3.82/4.08 => ( ! [X5: real] :
% 3.82/4.08 ( ( member_real @ X5 @ S2 )
% 3.82/4.08 => ( ( G @ X5 )
% 3.82/4.08 = ( H2 @ X5 ) ) )
% 3.82/4.08 => ( ( groups1681761925125756287l_real @ G @ T3 )
% 3.82/4.08 = ( groups1681761925125756287l_real @ H2 @ S2 ) ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.mono_neutral_cong_right
% 3.82/4.08 thf(fact_6464_prod_OatLeast0__atMost__Suc,axiom,
% 3.82/4.08 ! [G: nat > real,N2: nat] :
% 3.82/4.08 ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 3.82/4.08 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.atLeast0_atMost_Suc
% 3.82/4.08 thf(fact_6465_prod_OatLeast0__atMost__Suc,axiom,
% 3.82/4.08 ! [G: nat > complex,N2: nat] :
% 3.82/4.08 ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 3.82/4.08 = ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.atLeast0_atMost_Suc
% 3.82/4.08 thf(fact_6466_prod_OatLeast0__atMost__Suc,axiom,
% 3.82/4.08 ! [G: nat > extended_enat,N2: nat] :
% 3.82/4.08 ( ( groups7961826882256487087d_enat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 3.82/4.08 = ( times_7803423173614009249d_enat @ ( groups7961826882256487087d_enat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.atLeast0_atMost_Suc
% 3.82/4.08 thf(fact_6467_prod_OatLeast0__atMost__Suc,axiom,
% 3.82/4.08 ! [G: nat > int,N2: nat] :
% 3.82/4.08 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 3.82/4.08 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.atLeast0_atMost_Suc
% 3.82/4.08 thf(fact_6468_prod_OatLeast0__atMost__Suc,axiom,
% 3.82/4.08 ! [G: nat > nat,N2: nat] :
% 3.82/4.08 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 3.82/4.08 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.atLeast0_atMost_Suc
% 3.82/4.08 thf(fact_6469_powser__sums__zero,axiom,
% 3.82/4.08 ! [A: nat > real] :
% 3.82/4.08 ( sums_real
% 3.82/4.08 @ ^ [N: nat] : ( times_times_real @ ( A @ N ) @ ( power_power_real @ zero_zero_real @ N ) )
% 3.82/4.08 @ ( A @ zero_zero_nat ) ) ).
% 3.82/4.08
% 3.82/4.08 % powser_sums_zero
% 3.82/4.08 thf(fact_6470_powser__sums__zero,axiom,
% 3.82/4.08 ! [A: nat > complex] :
% 3.82/4.08 ( sums_complex
% 3.82/4.08 @ ^ [N: nat] : ( times_times_complex @ ( A @ N ) @ ( power_power_complex @ zero_zero_complex @ N ) )
% 3.82/4.08 @ ( A @ zero_zero_nat ) ) ).
% 3.82/4.08
% 3.82/4.08 % powser_sums_zero
% 3.82/4.08 thf(fact_6471_prod_OatLeast__Suc__atMost,axiom,
% 3.82/4.08 ! [M2: nat,N2: nat,G: nat > real] :
% 3.82/4.08 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.08 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 3.82/4.08 = ( times_times_real @ ( G @ M2 ) @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.atLeast_Suc_atMost
% 3.82/4.08 thf(fact_6472_prod_OatLeast__Suc__atMost,axiom,
% 3.82/4.08 ! [M2: nat,N2: nat,G: nat > complex] :
% 3.82/4.08 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.08 => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 3.82/4.08 = ( times_times_complex @ ( G @ M2 ) @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.atLeast_Suc_atMost
% 3.82/4.08 thf(fact_6473_prod_OatLeast__Suc__atMost,axiom,
% 3.82/4.08 ! [M2: nat,N2: nat,G: nat > extended_enat] :
% 3.82/4.08 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.08 => ( ( groups7961826882256487087d_enat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 3.82/4.08 = ( times_7803423173614009249d_enat @ ( G @ M2 ) @ ( groups7961826882256487087d_enat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.atLeast_Suc_atMost
% 3.82/4.08 thf(fact_6474_prod_OatLeast__Suc__atMost,axiom,
% 3.82/4.08 ! [M2: nat,N2: nat,G: nat > int] :
% 3.82/4.08 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.08 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 3.82/4.08 = ( times_times_int @ ( G @ M2 ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.atLeast_Suc_atMost
% 3.82/4.08 thf(fact_6475_prod_OatLeast__Suc__atMost,axiom,
% 3.82/4.08 ! [M2: nat,N2: nat,G: nat > nat] :
% 3.82/4.08 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.08 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 3.82/4.08 = ( times_times_nat @ ( G @ M2 ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.atLeast_Suc_atMost
% 3.82/4.08 thf(fact_6476_prod_Onat__ivl__Suc_H,axiom,
% 3.82/4.08 ! [M2: nat,N2: nat,G: nat > real] :
% 3.82/4.08 ( ( ord_less_eq_nat @ M2 @ ( suc @ N2 ) )
% 3.82/4.08 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 3.82/4.08 = ( times_times_real @ ( G @ ( suc @ N2 ) ) @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.nat_ivl_Suc'
% 3.82/4.08 thf(fact_6477_prod_Onat__ivl__Suc_H,axiom,
% 3.82/4.08 ! [M2: nat,N2: nat,G: nat > complex] :
% 3.82/4.08 ( ( ord_less_eq_nat @ M2 @ ( suc @ N2 ) )
% 3.82/4.08 => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 3.82/4.08 = ( times_times_complex @ ( G @ ( suc @ N2 ) ) @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.nat_ivl_Suc'
% 3.82/4.08 thf(fact_6478_prod_Onat__ivl__Suc_H,axiom,
% 3.82/4.08 ! [M2: nat,N2: nat,G: nat > extended_enat] :
% 3.82/4.08 ( ( ord_less_eq_nat @ M2 @ ( suc @ N2 ) )
% 3.82/4.08 => ( ( groups7961826882256487087d_enat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 3.82/4.08 = ( times_7803423173614009249d_enat @ ( G @ ( suc @ N2 ) ) @ ( groups7961826882256487087d_enat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.nat_ivl_Suc'
% 3.82/4.08 thf(fact_6479_prod_Onat__ivl__Suc_H,axiom,
% 3.82/4.08 ! [M2: nat,N2: nat,G: nat > int] :
% 3.82/4.08 ( ( ord_less_eq_nat @ M2 @ ( suc @ N2 ) )
% 3.82/4.08 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 3.82/4.08 = ( times_times_int @ ( G @ ( suc @ N2 ) ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.nat_ivl_Suc'
% 3.82/4.08 thf(fact_6480_prod_Onat__ivl__Suc_H,axiom,
% 3.82/4.08 ! [M2: nat,N2: nat,G: nat > nat] :
% 3.82/4.08 ( ( ord_less_eq_nat @ M2 @ ( suc @ N2 ) )
% 3.82/4.08 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N2 ) ) )
% 3.82/4.08 = ( times_times_nat @ ( G @ ( suc @ N2 ) ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.nat_ivl_Suc'
% 3.82/4.08 thf(fact_6481_prod_OlessThan__Suc__shift,axiom,
% 3.82/4.08 ! [G: nat > real,N2: nat] :
% 3.82/4.08 ( ( groups129246275422532515t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 3.82/4.08 = ( times_times_real @ ( G @ zero_zero_nat )
% 3.82/4.08 @ ( groups129246275422532515t_real
% 3.82/4.08 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 3.82/4.08 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.lessThan_Suc_shift
% 3.82/4.08 thf(fact_6482_prod_OlessThan__Suc__shift,axiom,
% 3.82/4.08 ! [G: nat > complex,N2: nat] :
% 3.82/4.08 ( ( groups6464643781859351333omplex @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 3.82/4.08 = ( times_times_complex @ ( G @ zero_zero_nat )
% 3.82/4.08 @ ( groups6464643781859351333omplex
% 3.82/4.08 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 3.82/4.08 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.lessThan_Suc_shift
% 3.82/4.08 thf(fact_6483_prod_OlessThan__Suc__shift,axiom,
% 3.82/4.08 ! [G: nat > extended_enat,N2: nat] :
% 3.82/4.08 ( ( groups7961826882256487087d_enat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 3.82/4.08 = ( times_7803423173614009249d_enat @ ( G @ zero_zero_nat )
% 3.82/4.08 @ ( groups7961826882256487087d_enat
% 3.82/4.08 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 3.82/4.08 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.lessThan_Suc_shift
% 3.82/4.08 thf(fact_6484_prod_OlessThan__Suc__shift,axiom,
% 3.82/4.08 ! [G: nat > int,N2: nat] :
% 3.82/4.08 ( ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 3.82/4.08 = ( times_times_int @ ( G @ zero_zero_nat )
% 3.82/4.08 @ ( groups705719431365010083at_int
% 3.82/4.08 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 3.82/4.08 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.lessThan_Suc_shift
% 3.82/4.08 thf(fact_6485_prod_OlessThan__Suc__shift,axiom,
% 3.82/4.08 ! [G: nat > nat,N2: nat] :
% 3.82/4.08 ( ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 3.82/4.08 = ( times_times_nat @ ( G @ zero_zero_nat )
% 3.82/4.08 @ ( groups708209901874060359at_nat
% 3.82/4.08 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 3.82/4.08 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.lessThan_Suc_shift
% 3.82/4.08 thf(fact_6486_prod_OSuc__reindex__ivl,axiom,
% 3.82/4.08 ! [M2: nat,N2: nat,G: nat > real] :
% 3.82/4.08 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.08 => ( ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 3.82/4.08 = ( times_times_real @ ( G @ M2 )
% 3.82/4.08 @ ( groups129246275422532515t_real
% 3.82/4.08 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 3.82/4.08 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.Suc_reindex_ivl
% 3.82/4.08 thf(fact_6487_prod_OSuc__reindex__ivl,axiom,
% 3.82/4.08 ! [M2: nat,N2: nat,G: nat > complex] :
% 3.82/4.08 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.08 => ( ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 3.82/4.08 = ( times_times_complex @ ( G @ M2 )
% 3.82/4.08 @ ( groups6464643781859351333omplex
% 3.82/4.08 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 3.82/4.08 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.Suc_reindex_ivl
% 3.82/4.08 thf(fact_6488_prod_OSuc__reindex__ivl,axiom,
% 3.82/4.08 ! [M2: nat,N2: nat,G: nat > extended_enat] :
% 3.82/4.08 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.08 => ( ( times_7803423173614009249d_enat @ ( groups7961826882256487087d_enat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 3.82/4.08 = ( times_7803423173614009249d_enat @ ( G @ M2 )
% 3.82/4.08 @ ( groups7961826882256487087d_enat
% 3.82/4.08 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 3.82/4.08 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.Suc_reindex_ivl
% 3.82/4.08 thf(fact_6489_prod_OSuc__reindex__ivl,axiom,
% 3.82/4.08 ! [M2: nat,N2: nat,G: nat > int] :
% 3.82/4.08 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.08 => ( ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 3.82/4.08 = ( times_times_int @ ( G @ M2 )
% 3.82/4.08 @ ( groups705719431365010083at_int
% 3.82/4.08 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 3.82/4.08 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.Suc_reindex_ivl
% 3.82/4.08 thf(fact_6490_prod_OSuc__reindex__ivl,axiom,
% 3.82/4.08 ! [M2: nat,N2: nat,G: nat > nat] :
% 3.82/4.08 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.08 => ( ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 3.82/4.08 = ( times_times_nat @ ( G @ M2 )
% 3.82/4.08 @ ( groups708209901874060359at_nat
% 3.82/4.08 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 3.82/4.08 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.Suc_reindex_ivl
% 3.82/4.08 thf(fact_6491_prod_OatLeast1__atMost__eq,axiom,
% 3.82/4.08 ! [G: nat > int,N2: nat] :
% 3.82/4.08 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 3.82/4.08 = ( groups705719431365010083at_int
% 3.82/4.08 @ ^ [K2: nat] : ( G @ ( suc @ K2 ) )
% 3.82/4.08 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.atLeast1_atMost_eq
% 3.82/4.08 thf(fact_6492_prod_OatLeast1__atMost__eq,axiom,
% 3.82/4.08 ! [G: nat > nat,N2: nat] :
% 3.82/4.08 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 3.82/4.08 = ( groups708209901874060359at_nat
% 3.82/4.08 @ ^ [K2: nat] : ( G @ ( suc @ K2 ) )
% 3.82/4.08 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod.atLeast1_atMost_eq
% 3.82/4.08 thf(fact_6493_prod__mono__strict,axiom,
% 3.82/4.08 ! [A2: set_complex,F: complex > real,G: complex > real] :
% 3.82/4.08 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.08 => ( ! [I4: complex] :
% 3.82/4.08 ( ( member_complex @ I4 @ A2 )
% 3.82/4.08 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 3.82/4.08 & ( ord_less_real @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 3.82/4.08 => ( ( A2 != bot_bot_set_complex )
% 3.82/4.08 => ( ord_less_real @ ( groups766887009212190081x_real @ F @ A2 ) @ ( groups766887009212190081x_real @ G @ A2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_mono_strict
% 3.82/4.08 thf(fact_6494_prod__mono__strict,axiom,
% 3.82/4.08 ! [A2: set_Extended_enat,F: extended_enat > real,G: extended_enat > real] :
% 3.82/4.08 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.08 => ( ! [I4: extended_enat] :
% 3.82/4.08 ( ( member_Extended_enat @ I4 @ A2 )
% 3.82/4.08 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 3.82/4.08 & ( ord_less_real @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 3.82/4.08 => ( ( A2 != bot_bo7653980558646680370d_enat )
% 3.82/4.08 => ( ord_less_real @ ( groups97031904164794029t_real @ F @ A2 ) @ ( groups97031904164794029t_real @ G @ A2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_mono_strict
% 3.82/4.08 thf(fact_6495_prod__mono__strict,axiom,
% 3.82/4.08 ! [A2: set_real,F: real > real,G: real > real] :
% 3.82/4.08 ( ( finite_finite_real @ A2 )
% 3.82/4.08 => ( ! [I4: real] :
% 3.82/4.08 ( ( member_real @ I4 @ A2 )
% 3.82/4.08 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 3.82/4.08 & ( ord_less_real @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 3.82/4.08 => ( ( A2 != bot_bot_set_real )
% 3.82/4.08 => ( ord_less_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ ( groups1681761925125756287l_real @ G @ A2 ) ) ) ) ) ).
% 3.82/4.08
% 3.82/4.08 % prod_mono_strict
% 3.82/4.09 thf(fact_6496_prod__mono__strict,axiom,
% 3.82/4.09 ! [A2: set_nat,F: nat > real,G: nat > real] :
% 3.82/4.09 ( ( finite_finite_nat @ A2 )
% 3.82/4.09 => ( ! [I4: nat] :
% 3.82/4.09 ( ( member_nat @ I4 @ A2 )
% 3.82/4.09 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 3.82/4.09 & ( ord_less_real @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 3.82/4.09 => ( ( A2 != bot_bot_set_nat )
% 3.82/4.09 => ( ord_less_real @ ( groups129246275422532515t_real @ F @ A2 ) @ ( groups129246275422532515t_real @ G @ A2 ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod_mono_strict
% 3.82/4.09 thf(fact_6497_prod__mono__strict,axiom,
% 3.82/4.09 ! [A2: set_int,F: int > real,G: int > real] :
% 3.82/4.09 ( ( finite_finite_int @ A2 )
% 3.82/4.09 => ( ! [I4: int] :
% 3.82/4.09 ( ( member_int @ I4 @ A2 )
% 3.82/4.09 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 3.82/4.09 & ( ord_less_real @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 3.82/4.09 => ( ( A2 != bot_bot_set_int )
% 3.82/4.09 => ( ord_less_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ ( groups2316167850115554303t_real @ G @ A2 ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod_mono_strict
% 3.82/4.09 thf(fact_6498_prod__mono__strict,axiom,
% 3.82/4.09 ! [A2: set_complex,F: complex > nat,G: complex > nat] :
% 3.82/4.09 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.09 => ( ! [I4: complex] :
% 3.82/4.09 ( ( member_complex @ I4 @ A2 )
% 3.82/4.09 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) )
% 3.82/4.09 & ( ord_less_nat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 3.82/4.09 => ( ( A2 != bot_bot_set_complex )
% 3.82/4.09 => ( ord_less_nat @ ( groups861055069439313189ex_nat @ F @ A2 ) @ ( groups861055069439313189ex_nat @ G @ A2 ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod_mono_strict
% 3.82/4.09 thf(fact_6499_prod__mono__strict,axiom,
% 3.82/4.09 ! [A2: set_Extended_enat,F: extended_enat > nat,G: extended_enat > nat] :
% 3.82/4.09 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.09 => ( ! [I4: extended_enat] :
% 3.82/4.09 ( ( member_Extended_enat @ I4 @ A2 )
% 3.82/4.09 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) )
% 3.82/4.09 & ( ord_less_nat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 3.82/4.09 => ( ( A2 != bot_bo7653980558646680370d_enat )
% 3.82/4.09 => ( ord_less_nat @ ( groups2880970938130013265at_nat @ F @ A2 ) @ ( groups2880970938130013265at_nat @ G @ A2 ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod_mono_strict
% 3.82/4.09 thf(fact_6500_prod__mono__strict,axiom,
% 3.82/4.09 ! [A2: set_real,F: real > nat,G: real > nat] :
% 3.82/4.09 ( ( finite_finite_real @ A2 )
% 3.82/4.09 => ( ! [I4: real] :
% 3.82/4.09 ( ( member_real @ I4 @ A2 )
% 3.82/4.09 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) )
% 3.82/4.09 & ( ord_less_nat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 3.82/4.09 => ( ( A2 != bot_bot_set_real )
% 3.82/4.09 => ( ord_less_nat @ ( groups4696554848551431203al_nat @ F @ A2 ) @ ( groups4696554848551431203al_nat @ G @ A2 ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod_mono_strict
% 3.82/4.09 thf(fact_6501_prod__mono__strict,axiom,
% 3.82/4.09 ! [A2: set_int,F: int > nat,G: int > nat] :
% 3.82/4.09 ( ( finite_finite_int @ A2 )
% 3.82/4.09 => ( ! [I4: int] :
% 3.82/4.09 ( ( member_int @ I4 @ A2 )
% 3.82/4.09 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) )
% 3.82/4.09 & ( ord_less_nat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 3.82/4.09 => ( ( A2 != bot_bot_set_int )
% 3.82/4.09 => ( ord_less_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) @ ( groups1707563613775114915nt_nat @ G @ A2 ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod_mono_strict
% 3.82/4.09 thf(fact_6502_prod__mono__strict,axiom,
% 3.82/4.09 ! [A2: set_complex,F: complex > int,G: complex > int] :
% 3.82/4.09 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.09 => ( ! [I4: complex] :
% 3.82/4.09 ( ( member_complex @ I4 @ A2 )
% 3.82/4.09 => ( ( ord_less_eq_int @ zero_zero_int @ ( F @ I4 ) )
% 3.82/4.09 & ( ord_less_int @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 3.82/4.09 => ( ( A2 != bot_bot_set_complex )
% 3.82/4.09 => ( ord_less_int @ ( groups858564598930262913ex_int @ F @ A2 ) @ ( groups858564598930262913ex_int @ G @ A2 ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod_mono_strict
% 3.82/4.09 thf(fact_6503_even__prod__iff,axiom,
% 3.82/4.09 ! [A2: set_complex,F: complex > nat] :
% 3.82/4.09 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.09 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups861055069439313189ex_nat @ F @ A2 ) )
% 3.82/4.09 = ( ? [X4: complex] :
% 3.82/4.09 ( ( member_complex @ X4 @ A2 )
% 3.82/4.09 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( F @ X4 ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % even_prod_iff
% 3.82/4.09 thf(fact_6504_even__prod__iff,axiom,
% 3.82/4.09 ! [A2: set_int,F: int > nat] :
% 3.82/4.09 ( ( finite_finite_int @ A2 )
% 3.82/4.09 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups1707563613775114915nt_nat @ F @ A2 ) )
% 3.82/4.09 = ( ? [X4: int] :
% 3.82/4.09 ( ( member_int @ X4 @ A2 )
% 3.82/4.09 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( F @ X4 ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % even_prod_iff
% 3.82/4.09 thf(fact_6505_even__prod__iff,axiom,
% 3.82/4.09 ! [A2: set_Extended_enat,F: extended_enat > nat] :
% 3.82/4.09 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.09 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups2880970938130013265at_nat @ F @ A2 ) )
% 3.82/4.09 = ( ? [X4: extended_enat] :
% 3.82/4.09 ( ( member_Extended_enat @ X4 @ A2 )
% 3.82/4.09 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( F @ X4 ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % even_prod_iff
% 3.82/4.09 thf(fact_6506_even__prod__iff,axiom,
% 3.82/4.09 ! [A2: set_complex,F: complex > int] :
% 3.82/4.09 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.09 => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups858564598930262913ex_int @ F @ A2 ) )
% 3.82/4.09 = ( ? [X4: complex] :
% 3.82/4.09 ( ( member_complex @ X4 @ A2 )
% 3.82/4.09 & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( F @ X4 ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % even_prod_iff
% 3.82/4.09 thf(fact_6507_even__prod__iff,axiom,
% 3.82/4.09 ! [A2: set_Extended_enat,F: extended_enat > int] :
% 3.82/4.09 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.09 => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups2878480467620962989at_int @ F @ A2 ) )
% 3.82/4.09 = ( ? [X4: extended_enat] :
% 3.82/4.09 ( ( member_Extended_enat @ X4 @ A2 )
% 3.82/4.09 & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( F @ X4 ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % even_prod_iff
% 3.82/4.09 thf(fact_6508_even__prod__iff,axiom,
% 3.82/4.09 ! [A2: set_nat,F: nat > int] :
% 3.82/4.09 ( ( finite_finite_nat @ A2 )
% 3.82/4.09 => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups705719431365010083at_int @ F @ A2 ) )
% 3.82/4.09 = ( ? [X4: nat] :
% 3.82/4.09 ( ( member_nat @ X4 @ A2 )
% 3.82/4.09 & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( F @ X4 ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % even_prod_iff
% 3.82/4.09 thf(fact_6509_even__prod__iff,axiom,
% 3.82/4.09 ! [A2: set_int,F: int > int] :
% 3.82/4.09 ( ( finite_finite_int @ A2 )
% 3.82/4.09 => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups1705073143266064639nt_int @ F @ A2 ) )
% 3.82/4.09 = ( ? [X4: int] :
% 3.82/4.09 ( ( member_int @ X4 @ A2 )
% 3.82/4.09 & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( F @ X4 ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % even_prod_iff
% 3.82/4.09 thf(fact_6510_even__prod__iff,axiom,
% 3.82/4.09 ! [A2: set_nat,F: nat > nat] :
% 3.82/4.09 ( ( finite_finite_nat @ A2 )
% 3.82/4.09 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups708209901874060359at_nat @ F @ A2 ) )
% 3.82/4.09 = ( ? [X4: nat] :
% 3.82/4.09 ( ( member_nat @ X4 @ A2 )
% 3.82/4.09 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( F @ X4 ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % even_prod_iff
% 3.82/4.09 thf(fact_6511_prod_Oinsert__remove,axiom,
% 3.82/4.09 ! [A2: set_complex,G: complex > nat,X: complex] :
% 3.82/4.09 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.09 => ( ( groups861055069439313189ex_nat @ G @ ( insert_complex @ X @ A2 ) )
% 3.82/4.09 = ( times_times_nat @ ( G @ X ) @ ( groups861055069439313189ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.insert_remove
% 3.82/4.09 thf(fact_6512_prod_Oinsert__remove,axiom,
% 3.82/4.09 ! [A2: set_Extended_enat,G: extended_enat > nat,X: extended_enat] :
% 3.82/4.09 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.09 => ( ( groups2880970938130013265at_nat @ G @ ( insert_Extended_enat @ X @ A2 ) )
% 3.82/4.09 = ( times_times_nat @ ( G @ X ) @ ( groups2880970938130013265at_nat @ G @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ X @ bot_bo7653980558646680370d_enat ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.insert_remove
% 3.82/4.09 thf(fact_6513_prod_Oinsert__remove,axiom,
% 3.82/4.09 ! [A2: set_real,G: real > nat,X: real] :
% 3.82/4.09 ( ( finite_finite_real @ A2 )
% 3.82/4.09 => ( ( groups4696554848551431203al_nat @ G @ ( insert_real @ X @ A2 ) )
% 3.82/4.09 = ( times_times_nat @ ( G @ X ) @ ( groups4696554848551431203al_nat @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.insert_remove
% 3.82/4.09 thf(fact_6514_prod_Oinsert__remove,axiom,
% 3.82/4.09 ! [A2: set_int,G: int > nat,X: int] :
% 3.82/4.09 ( ( finite_finite_int @ A2 )
% 3.82/4.09 => ( ( groups1707563613775114915nt_nat @ G @ ( insert_int @ X @ A2 ) )
% 3.82/4.09 = ( times_times_nat @ ( G @ X ) @ ( groups1707563613775114915nt_nat @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.insert_remove
% 3.82/4.09 thf(fact_6515_prod_Oinsert__remove,axiom,
% 3.82/4.09 ! [A2: set_complex,G: complex > int,X: complex] :
% 3.82/4.09 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.09 => ( ( groups858564598930262913ex_int @ G @ ( insert_complex @ X @ A2 ) )
% 3.82/4.09 = ( times_times_int @ ( G @ X ) @ ( groups858564598930262913ex_int @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.insert_remove
% 3.82/4.09 thf(fact_6516_prod_Oinsert__remove,axiom,
% 3.82/4.09 ! [A2: set_Extended_enat,G: extended_enat > int,X: extended_enat] :
% 3.82/4.09 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.09 => ( ( groups2878480467620962989at_int @ G @ ( insert_Extended_enat @ X @ A2 ) )
% 3.82/4.09 = ( times_times_int @ ( G @ X ) @ ( groups2878480467620962989at_int @ G @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ X @ bot_bo7653980558646680370d_enat ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.insert_remove
% 3.82/4.09 thf(fact_6517_prod_Oinsert__remove,axiom,
% 3.82/4.09 ! [A2: set_real,G: real > int,X: real] :
% 3.82/4.09 ( ( finite_finite_real @ A2 )
% 3.82/4.09 => ( ( groups4694064378042380927al_int @ G @ ( insert_real @ X @ A2 ) )
% 3.82/4.09 = ( times_times_int @ ( G @ X ) @ ( groups4694064378042380927al_int @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.insert_remove
% 3.82/4.09 thf(fact_6518_prod_Oinsert__remove,axiom,
% 3.82/4.09 ! [A2: set_complex,G: complex > real,X: complex] :
% 3.82/4.09 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.09 => ( ( groups766887009212190081x_real @ G @ ( insert_complex @ X @ A2 ) )
% 3.82/4.09 = ( times_times_real @ ( G @ X ) @ ( groups766887009212190081x_real @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.insert_remove
% 3.82/4.09 thf(fact_6519_prod_Oinsert__remove,axiom,
% 3.82/4.09 ! [A2: set_Extended_enat,G: extended_enat > real,X: extended_enat] :
% 3.82/4.09 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.09 => ( ( groups97031904164794029t_real @ G @ ( insert_Extended_enat @ X @ A2 ) )
% 3.82/4.09 = ( times_times_real @ ( G @ X ) @ ( groups97031904164794029t_real @ G @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ X @ bot_bo7653980558646680370d_enat ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.insert_remove
% 3.82/4.09 thf(fact_6520_prod_Oinsert__remove,axiom,
% 3.82/4.09 ! [A2: set_real,G: real > real,X: real] :
% 3.82/4.09 ( ( finite_finite_real @ A2 )
% 3.82/4.09 => ( ( groups1681761925125756287l_real @ G @ ( insert_real @ X @ A2 ) )
% 3.82/4.09 = ( times_times_real @ ( G @ X ) @ ( groups1681761925125756287l_real @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.insert_remove
% 3.82/4.09 thf(fact_6521_prod_Oremove,axiom,
% 3.82/4.09 ! [A2: set_complex,X: complex,G: complex > nat] :
% 3.82/4.09 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.09 => ( ( member_complex @ X @ A2 )
% 3.82/4.09 => ( ( groups861055069439313189ex_nat @ G @ A2 )
% 3.82/4.09 = ( times_times_nat @ ( G @ X ) @ ( groups861055069439313189ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.remove
% 3.82/4.09 thf(fact_6522_prod_Oremove,axiom,
% 3.82/4.09 ! [A2: set_Extended_enat,X: extended_enat,G: extended_enat > nat] :
% 3.82/4.09 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.09 => ( ( member_Extended_enat @ X @ A2 )
% 3.82/4.09 => ( ( groups2880970938130013265at_nat @ G @ A2 )
% 3.82/4.09 = ( times_times_nat @ ( G @ X ) @ ( groups2880970938130013265at_nat @ G @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ X @ bot_bo7653980558646680370d_enat ) ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.remove
% 3.82/4.09 thf(fact_6523_prod_Oremove,axiom,
% 3.82/4.09 ! [A2: set_real,X: real,G: real > nat] :
% 3.82/4.09 ( ( finite_finite_real @ A2 )
% 3.82/4.09 => ( ( member_real @ X @ A2 )
% 3.82/4.09 => ( ( groups4696554848551431203al_nat @ G @ A2 )
% 3.82/4.09 = ( times_times_nat @ ( G @ X ) @ ( groups4696554848551431203al_nat @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.remove
% 3.82/4.09 thf(fact_6524_prod_Oremove,axiom,
% 3.82/4.09 ! [A2: set_int,X: int,G: int > nat] :
% 3.82/4.09 ( ( finite_finite_int @ A2 )
% 3.82/4.09 => ( ( member_int @ X @ A2 )
% 3.82/4.09 => ( ( groups1707563613775114915nt_nat @ G @ A2 )
% 3.82/4.09 = ( times_times_nat @ ( G @ X ) @ ( groups1707563613775114915nt_nat @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.remove
% 3.82/4.09 thf(fact_6525_prod_Oremove,axiom,
% 3.82/4.09 ! [A2: set_complex,X: complex,G: complex > int] :
% 3.82/4.09 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.09 => ( ( member_complex @ X @ A2 )
% 3.82/4.09 => ( ( groups858564598930262913ex_int @ G @ A2 )
% 3.82/4.09 = ( times_times_int @ ( G @ X ) @ ( groups858564598930262913ex_int @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.remove
% 3.82/4.09 thf(fact_6526_prod_Oremove,axiom,
% 3.82/4.09 ! [A2: set_Extended_enat,X: extended_enat,G: extended_enat > int] :
% 3.82/4.09 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.09 => ( ( member_Extended_enat @ X @ A2 )
% 3.82/4.09 => ( ( groups2878480467620962989at_int @ G @ A2 )
% 3.82/4.09 = ( times_times_int @ ( G @ X ) @ ( groups2878480467620962989at_int @ G @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ X @ bot_bo7653980558646680370d_enat ) ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.remove
% 3.82/4.09 thf(fact_6527_prod_Oremove,axiom,
% 3.82/4.09 ! [A2: set_real,X: real,G: real > int] :
% 3.82/4.09 ( ( finite_finite_real @ A2 )
% 3.82/4.09 => ( ( member_real @ X @ A2 )
% 3.82/4.09 => ( ( groups4694064378042380927al_int @ G @ A2 )
% 3.82/4.09 = ( times_times_int @ ( G @ X ) @ ( groups4694064378042380927al_int @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.remove
% 3.82/4.09 thf(fact_6528_prod_Oremove,axiom,
% 3.82/4.09 ! [A2: set_complex,X: complex,G: complex > real] :
% 3.82/4.09 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.09 => ( ( member_complex @ X @ A2 )
% 3.82/4.09 => ( ( groups766887009212190081x_real @ G @ A2 )
% 3.82/4.09 = ( times_times_real @ ( G @ X ) @ ( groups766887009212190081x_real @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.remove
% 3.82/4.09 thf(fact_6529_prod_Oremove,axiom,
% 3.82/4.09 ! [A2: set_Extended_enat,X: extended_enat,G: extended_enat > real] :
% 3.82/4.09 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.09 => ( ( member_Extended_enat @ X @ A2 )
% 3.82/4.09 => ( ( groups97031904164794029t_real @ G @ A2 )
% 3.82/4.09 = ( times_times_real @ ( G @ X ) @ ( groups97031904164794029t_real @ G @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ X @ bot_bo7653980558646680370d_enat ) ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.remove
% 3.82/4.09 thf(fact_6530_prod_Oremove,axiom,
% 3.82/4.09 ! [A2: set_real,X: real,G: real > real] :
% 3.82/4.09 ( ( finite_finite_real @ A2 )
% 3.82/4.09 => ( ( member_real @ X @ A2 )
% 3.82/4.09 => ( ( groups1681761925125756287l_real @ G @ A2 )
% 3.82/4.09 = ( times_times_real @ ( G @ X ) @ ( groups1681761925125756287l_real @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.remove
% 3.82/4.09 thf(fact_6531_prod_Oub__add__nat,axiom,
% 3.82/4.09 ! [M2: nat,N2: nat,G: nat > real,P5: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 3.82/4.09 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N2 @ P5 ) ) )
% 3.82/4.09 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P5 ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.ub_add_nat
% 3.82/4.09 thf(fact_6532_prod_Oub__add__nat,axiom,
% 3.82/4.09 ! [M2: nat,N2: nat,G: nat > complex,P5: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 3.82/4.09 => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N2 @ P5 ) ) )
% 3.82/4.09 = ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P5 ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.ub_add_nat
% 3.82/4.09 thf(fact_6533_prod_Oub__add__nat,axiom,
% 3.82/4.09 ! [M2: nat,N2: nat,G: nat > extended_enat,P5: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 3.82/4.09 => ( ( groups7961826882256487087d_enat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N2 @ P5 ) ) )
% 3.82/4.09 = ( times_7803423173614009249d_enat @ ( groups7961826882256487087d_enat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( groups7961826882256487087d_enat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P5 ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.ub_add_nat
% 3.82/4.09 thf(fact_6534_prod_Oub__add__nat,axiom,
% 3.82/4.09 ! [M2: nat,N2: nat,G: nat > int,P5: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 3.82/4.09 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N2 @ P5 ) ) )
% 3.82/4.09 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P5 ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.ub_add_nat
% 3.82/4.09 thf(fact_6535_prod_Oub__add__nat,axiom,
% 3.82/4.09 ! [M2: nat,N2: nat,G: nat > nat,P5: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 3.82/4.09 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N2 @ P5 ) ) )
% 3.82/4.09 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P5 ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.ub_add_nat
% 3.82/4.09 thf(fact_6536_prod_Odelta__remove,axiom,
% 3.82/4.09 ! [S2: set_complex,A: complex,B2: complex > nat,C: complex > nat] :
% 3.82/4.09 ( ( finite3207457112153483333omplex @ S2 )
% 3.82/4.09 => ( ( ( member_complex @ A @ S2 )
% 3.82/4.09 => ( ( groups861055069439313189ex_nat
% 3.82/4.09 @ ^ [K2: complex] : ( if_nat @ ( K2 = A ) @ ( B2 @ K2 ) @ ( C @ K2 ) )
% 3.82/4.09 @ S2 )
% 3.82/4.09 = ( times_times_nat @ ( B2 @ A ) @ ( groups861055069439313189ex_nat @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 3.82/4.09 & ( ~ ( member_complex @ A @ S2 )
% 3.82/4.09 => ( ( groups861055069439313189ex_nat
% 3.82/4.09 @ ^ [K2: complex] : ( if_nat @ ( K2 = A ) @ ( B2 @ K2 ) @ ( C @ K2 ) )
% 3.82/4.09 @ S2 )
% 3.82/4.09 = ( groups861055069439313189ex_nat @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.delta_remove
% 3.82/4.09 thf(fact_6537_prod_Odelta__remove,axiom,
% 3.82/4.09 ! [S2: set_Extended_enat,A: extended_enat,B2: extended_enat > nat,C: extended_enat > nat] :
% 3.82/4.09 ( ( finite4001608067531595151d_enat @ S2 )
% 3.82/4.09 => ( ( ( member_Extended_enat @ A @ S2 )
% 3.82/4.09 => ( ( groups2880970938130013265at_nat
% 3.82/4.09 @ ^ [K2: extended_enat] : ( if_nat @ ( K2 = A ) @ ( B2 @ K2 ) @ ( C @ K2 ) )
% 3.82/4.09 @ S2 )
% 3.82/4.09 = ( times_times_nat @ ( B2 @ A ) @ ( groups2880970938130013265at_nat @ C @ ( minus_925952699566721837d_enat @ S2 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) ) ) ) )
% 3.82/4.09 & ( ~ ( member_Extended_enat @ A @ S2 )
% 3.82/4.09 => ( ( groups2880970938130013265at_nat
% 3.82/4.09 @ ^ [K2: extended_enat] : ( if_nat @ ( K2 = A ) @ ( B2 @ K2 ) @ ( C @ K2 ) )
% 3.82/4.09 @ S2 )
% 3.82/4.09 = ( groups2880970938130013265at_nat @ C @ ( minus_925952699566721837d_enat @ S2 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.delta_remove
% 3.82/4.09 thf(fact_6538_prod_Odelta__remove,axiom,
% 3.82/4.09 ! [S2: set_real,A: real,B2: real > nat,C: real > nat] :
% 3.82/4.09 ( ( finite_finite_real @ S2 )
% 3.82/4.09 => ( ( ( member_real @ A @ S2 )
% 3.82/4.09 => ( ( groups4696554848551431203al_nat
% 3.82/4.09 @ ^ [K2: real] : ( if_nat @ ( K2 = A ) @ ( B2 @ K2 ) @ ( C @ K2 ) )
% 3.82/4.09 @ S2 )
% 3.82/4.09 = ( times_times_nat @ ( B2 @ A ) @ ( groups4696554848551431203al_nat @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 3.82/4.09 & ( ~ ( member_real @ A @ S2 )
% 3.82/4.09 => ( ( groups4696554848551431203al_nat
% 3.82/4.09 @ ^ [K2: real] : ( if_nat @ ( K2 = A ) @ ( B2 @ K2 ) @ ( C @ K2 ) )
% 3.82/4.09 @ S2 )
% 3.82/4.09 = ( groups4696554848551431203al_nat @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.delta_remove
% 3.82/4.09 thf(fact_6539_prod_Odelta__remove,axiom,
% 3.82/4.09 ! [S2: set_int,A: int,B2: int > nat,C: int > nat] :
% 3.82/4.09 ( ( finite_finite_int @ S2 )
% 3.82/4.09 => ( ( ( member_int @ A @ S2 )
% 3.82/4.09 => ( ( groups1707563613775114915nt_nat
% 3.82/4.09 @ ^ [K2: int] : ( if_nat @ ( K2 = A ) @ ( B2 @ K2 ) @ ( C @ K2 ) )
% 3.82/4.09 @ S2 )
% 3.82/4.09 = ( times_times_nat @ ( B2 @ A ) @ ( groups1707563613775114915nt_nat @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 3.82/4.09 & ( ~ ( member_int @ A @ S2 )
% 3.82/4.09 => ( ( groups1707563613775114915nt_nat
% 3.82/4.09 @ ^ [K2: int] : ( if_nat @ ( K2 = A ) @ ( B2 @ K2 ) @ ( C @ K2 ) )
% 3.82/4.09 @ S2 )
% 3.82/4.09 = ( groups1707563613775114915nt_nat @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.delta_remove
% 3.82/4.09 thf(fact_6540_prod_Odelta__remove,axiom,
% 3.82/4.09 ! [S2: set_complex,A: complex,B2: complex > int,C: complex > int] :
% 3.82/4.09 ( ( finite3207457112153483333omplex @ S2 )
% 3.82/4.09 => ( ( ( member_complex @ A @ S2 )
% 3.82/4.09 => ( ( groups858564598930262913ex_int
% 3.82/4.09 @ ^ [K2: complex] : ( if_int @ ( K2 = A ) @ ( B2 @ K2 ) @ ( C @ K2 ) )
% 3.82/4.09 @ S2 )
% 3.82/4.09 = ( times_times_int @ ( B2 @ A ) @ ( groups858564598930262913ex_int @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 3.82/4.09 & ( ~ ( member_complex @ A @ S2 )
% 3.82/4.09 => ( ( groups858564598930262913ex_int
% 3.82/4.09 @ ^ [K2: complex] : ( if_int @ ( K2 = A ) @ ( B2 @ K2 ) @ ( C @ K2 ) )
% 3.82/4.09 @ S2 )
% 3.82/4.09 = ( groups858564598930262913ex_int @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.delta_remove
% 3.82/4.09 thf(fact_6541_prod_Odelta__remove,axiom,
% 3.82/4.09 ! [S2: set_Extended_enat,A: extended_enat,B2: extended_enat > int,C: extended_enat > int] :
% 3.82/4.09 ( ( finite4001608067531595151d_enat @ S2 )
% 3.82/4.09 => ( ( ( member_Extended_enat @ A @ S2 )
% 3.82/4.09 => ( ( groups2878480467620962989at_int
% 3.82/4.09 @ ^ [K2: extended_enat] : ( if_int @ ( K2 = A ) @ ( B2 @ K2 ) @ ( C @ K2 ) )
% 3.82/4.09 @ S2 )
% 3.82/4.09 = ( times_times_int @ ( B2 @ A ) @ ( groups2878480467620962989at_int @ C @ ( minus_925952699566721837d_enat @ S2 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) ) ) ) )
% 3.82/4.09 & ( ~ ( member_Extended_enat @ A @ S2 )
% 3.82/4.09 => ( ( groups2878480467620962989at_int
% 3.82/4.09 @ ^ [K2: extended_enat] : ( if_int @ ( K2 = A ) @ ( B2 @ K2 ) @ ( C @ K2 ) )
% 3.82/4.09 @ S2 )
% 3.82/4.09 = ( groups2878480467620962989at_int @ C @ ( minus_925952699566721837d_enat @ S2 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.delta_remove
% 3.82/4.09 thf(fact_6542_prod_Odelta__remove,axiom,
% 3.82/4.09 ! [S2: set_real,A: real,B2: real > int,C: real > int] :
% 3.82/4.09 ( ( finite_finite_real @ S2 )
% 3.82/4.09 => ( ( ( member_real @ A @ S2 )
% 3.82/4.09 => ( ( groups4694064378042380927al_int
% 3.82/4.09 @ ^ [K2: real] : ( if_int @ ( K2 = A ) @ ( B2 @ K2 ) @ ( C @ K2 ) )
% 3.82/4.09 @ S2 )
% 3.82/4.09 = ( times_times_int @ ( B2 @ A ) @ ( groups4694064378042380927al_int @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 3.82/4.09 & ( ~ ( member_real @ A @ S2 )
% 3.82/4.09 => ( ( groups4694064378042380927al_int
% 3.82/4.09 @ ^ [K2: real] : ( if_int @ ( K2 = A ) @ ( B2 @ K2 ) @ ( C @ K2 ) )
% 3.82/4.09 @ S2 )
% 3.82/4.09 = ( groups4694064378042380927al_int @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.delta_remove
% 3.82/4.09 thf(fact_6543_prod_Odelta__remove,axiom,
% 3.82/4.09 ! [S2: set_complex,A: complex,B2: complex > real,C: complex > real] :
% 3.82/4.09 ( ( finite3207457112153483333omplex @ S2 )
% 3.82/4.09 => ( ( ( member_complex @ A @ S2 )
% 3.82/4.09 => ( ( groups766887009212190081x_real
% 3.82/4.09 @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B2 @ K2 ) @ ( C @ K2 ) )
% 3.82/4.09 @ S2 )
% 3.82/4.09 = ( times_times_real @ ( B2 @ A ) @ ( groups766887009212190081x_real @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 3.82/4.09 & ( ~ ( member_complex @ A @ S2 )
% 3.82/4.09 => ( ( groups766887009212190081x_real
% 3.82/4.09 @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B2 @ K2 ) @ ( C @ K2 ) )
% 3.82/4.09 @ S2 )
% 3.82/4.09 = ( groups766887009212190081x_real @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.delta_remove
% 3.82/4.09 thf(fact_6544_prod_Odelta__remove,axiom,
% 3.82/4.09 ! [S2: set_Extended_enat,A: extended_enat,B2: extended_enat > real,C: extended_enat > real] :
% 3.82/4.09 ( ( finite4001608067531595151d_enat @ S2 )
% 3.82/4.09 => ( ( ( member_Extended_enat @ A @ S2 )
% 3.82/4.09 => ( ( groups97031904164794029t_real
% 3.82/4.09 @ ^ [K2: extended_enat] : ( if_real @ ( K2 = A ) @ ( B2 @ K2 ) @ ( C @ K2 ) )
% 3.82/4.09 @ S2 )
% 3.82/4.09 = ( times_times_real @ ( B2 @ A ) @ ( groups97031904164794029t_real @ C @ ( minus_925952699566721837d_enat @ S2 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) ) ) ) )
% 3.82/4.09 & ( ~ ( member_Extended_enat @ A @ S2 )
% 3.82/4.09 => ( ( groups97031904164794029t_real
% 3.82/4.09 @ ^ [K2: extended_enat] : ( if_real @ ( K2 = A ) @ ( B2 @ K2 ) @ ( C @ K2 ) )
% 3.82/4.09 @ S2 )
% 3.82/4.09 = ( groups97031904164794029t_real @ C @ ( minus_925952699566721837d_enat @ S2 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.delta_remove
% 3.82/4.09 thf(fact_6545_prod_Odelta__remove,axiom,
% 3.82/4.09 ! [S2: set_real,A: real,B2: real > real,C: real > real] :
% 3.82/4.09 ( ( finite_finite_real @ S2 )
% 3.82/4.09 => ( ( ( member_real @ A @ S2 )
% 3.82/4.09 => ( ( groups1681761925125756287l_real
% 3.82/4.09 @ ^ [K2: real] : ( if_real @ ( K2 = A ) @ ( B2 @ K2 ) @ ( C @ K2 ) )
% 3.82/4.09 @ S2 )
% 3.82/4.09 = ( times_times_real @ ( B2 @ A ) @ ( groups1681761925125756287l_real @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 3.82/4.09 & ( ~ ( member_real @ A @ S2 )
% 3.82/4.09 => ( ( groups1681761925125756287l_real
% 3.82/4.09 @ ^ [K2: real] : ( if_real @ ( K2 = A ) @ ( B2 @ K2 ) @ ( C @ K2 ) )
% 3.82/4.09 @ S2 )
% 3.82/4.09 = ( groups1681761925125756287l_real @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.delta_remove
% 3.82/4.09 thf(fact_6546_fold__atLeastAtMost__nat_Oelims,axiom,
% 3.82/4.09 ! [X: nat > nat > nat,Xa2: nat,Xb: nat,Xc: nat,Y: nat] :
% 3.82/4.09 ( ( ( set_fo2584398358068434914at_nat @ X @ Xa2 @ Xb @ Xc )
% 3.82/4.09 = Y )
% 3.82/4.09 => ( ( ( ord_less_nat @ Xb @ Xa2 )
% 3.82/4.09 => ( Y = Xc ) )
% 3.82/4.09 & ( ~ ( ord_less_nat @ Xb @ Xa2 )
% 3.82/4.09 => ( Y
% 3.82/4.09 = ( set_fo2584398358068434914at_nat @ X @ ( plus_plus_nat @ Xa2 @ one_one_nat ) @ Xb @ ( X @ Xa2 @ Xc ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % fold_atLeastAtMost_nat.elims
% 3.82/4.09 thf(fact_6547_fold__atLeastAtMost__nat_Osimps,axiom,
% 3.82/4.09 ( set_fo2584398358068434914at_nat
% 3.82/4.09 = ( ^ [F5: nat > nat > nat,A3: nat,B3: nat,Acc2: nat] : ( if_nat @ ( ord_less_nat @ B3 @ A3 ) @ Acc2 @ ( set_fo2584398358068434914at_nat @ F5 @ ( plus_plus_nat @ A3 @ one_one_nat ) @ B3 @ ( F5 @ A3 @ Acc2 ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % fold_atLeastAtMost_nat.simps
% 3.82/4.09 thf(fact_6548_prod__mono2,axiom,
% 3.82/4.09 ! [B: set_real,A2: set_real,F: real > real] :
% 3.82/4.09 ( ( finite_finite_real @ B )
% 3.82/4.09 => ( ( ord_less_eq_set_real @ A2 @ B )
% 3.82/4.09 => ( ! [B4: real] :
% 3.82/4.09 ( ( member_real @ B4 @ ( minus_minus_set_real @ B @ A2 ) )
% 3.82/4.09 => ( ord_less_eq_real @ one_one_real @ ( F @ B4 ) ) )
% 3.82/4.09 => ( ! [A4: real] :
% 3.82/4.09 ( ( member_real @ A4 @ A2 )
% 3.82/4.09 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A4 ) ) )
% 3.82/4.09 => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ ( groups1681761925125756287l_real @ F @ B ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod_mono2
% 3.82/4.09 thf(fact_6549_prod__mono2,axiom,
% 3.82/4.09 ! [B: set_complex,A2: set_complex,F: complex > real] :
% 3.82/4.09 ( ( finite3207457112153483333omplex @ B )
% 3.82/4.09 => ( ( ord_le211207098394363844omplex @ A2 @ B )
% 3.82/4.09 => ( ! [B4: complex] :
% 3.82/4.09 ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ B @ A2 ) )
% 3.82/4.09 => ( ord_less_eq_real @ one_one_real @ ( F @ B4 ) ) )
% 3.82/4.09 => ( ! [A4: complex] :
% 3.82/4.09 ( ( member_complex @ A4 @ A2 )
% 3.82/4.09 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A4 ) ) )
% 3.82/4.09 => ( ord_less_eq_real @ ( groups766887009212190081x_real @ F @ A2 ) @ ( groups766887009212190081x_real @ F @ B ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod_mono2
% 3.82/4.09 thf(fact_6550_prod__mono2,axiom,
% 3.82/4.09 ! [B: set_Extended_enat,A2: set_Extended_enat,F: extended_enat > real] :
% 3.82/4.09 ( ( finite4001608067531595151d_enat @ B )
% 3.82/4.09 => ( ( ord_le7203529160286727270d_enat @ A2 @ B )
% 3.82/4.09 => ( ! [B4: extended_enat] :
% 3.82/4.09 ( ( member_Extended_enat @ B4 @ ( minus_925952699566721837d_enat @ B @ A2 ) )
% 3.82/4.09 => ( ord_less_eq_real @ one_one_real @ ( F @ B4 ) ) )
% 3.82/4.09 => ( ! [A4: extended_enat] :
% 3.82/4.09 ( ( member_Extended_enat @ A4 @ A2 )
% 3.82/4.09 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A4 ) ) )
% 3.82/4.09 => ( ord_less_eq_real @ ( groups97031904164794029t_real @ F @ A2 ) @ ( groups97031904164794029t_real @ F @ B ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod_mono2
% 3.82/4.09 thf(fact_6551_prod__mono2,axiom,
% 3.82/4.09 ! [B: set_real,A2: set_real,F: real > int] :
% 3.82/4.09 ( ( finite_finite_real @ B )
% 3.82/4.09 => ( ( ord_less_eq_set_real @ A2 @ B )
% 3.82/4.09 => ( ! [B4: real] :
% 3.82/4.09 ( ( member_real @ B4 @ ( minus_minus_set_real @ B @ A2 ) )
% 3.82/4.09 => ( ord_less_eq_int @ one_one_int @ ( F @ B4 ) ) )
% 3.82/4.09 => ( ! [A4: real] :
% 3.82/4.09 ( ( member_real @ A4 @ A2 )
% 3.82/4.09 => ( ord_less_eq_int @ zero_zero_int @ ( F @ A4 ) ) )
% 3.82/4.09 => ( ord_less_eq_int @ ( groups4694064378042380927al_int @ F @ A2 ) @ ( groups4694064378042380927al_int @ F @ B ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod_mono2
% 3.82/4.09 thf(fact_6552_prod__mono2,axiom,
% 3.82/4.09 ! [B: set_complex,A2: set_complex,F: complex > int] :
% 3.82/4.09 ( ( finite3207457112153483333omplex @ B )
% 3.82/4.09 => ( ( ord_le211207098394363844omplex @ A2 @ B )
% 3.82/4.09 => ( ! [B4: complex] :
% 3.82/4.09 ( ( member_complex @ B4 @ ( minus_811609699411566653omplex @ B @ A2 ) )
% 3.82/4.09 => ( ord_less_eq_int @ one_one_int @ ( F @ B4 ) ) )
% 3.82/4.09 => ( ! [A4: complex] :
% 3.82/4.09 ( ( member_complex @ A4 @ A2 )
% 3.82/4.09 => ( ord_less_eq_int @ zero_zero_int @ ( F @ A4 ) ) )
% 3.82/4.09 => ( ord_less_eq_int @ ( groups858564598930262913ex_int @ F @ A2 ) @ ( groups858564598930262913ex_int @ F @ B ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod_mono2
% 3.82/4.09 thf(fact_6553_prod__mono2,axiom,
% 3.82/4.09 ! [B: set_Extended_enat,A2: set_Extended_enat,F: extended_enat > int] :
% 3.82/4.09 ( ( finite4001608067531595151d_enat @ B )
% 3.82/4.09 => ( ( ord_le7203529160286727270d_enat @ A2 @ B )
% 3.82/4.09 => ( ! [B4: extended_enat] :
% 3.82/4.09 ( ( member_Extended_enat @ B4 @ ( minus_925952699566721837d_enat @ B @ A2 ) )
% 3.82/4.09 => ( ord_less_eq_int @ one_one_int @ ( F @ B4 ) ) )
% 3.82/4.09 => ( ! [A4: extended_enat] :
% 3.82/4.09 ( ( member_Extended_enat @ A4 @ A2 )
% 3.82/4.09 => ( ord_less_eq_int @ zero_zero_int @ ( F @ A4 ) ) )
% 3.82/4.09 => ( ord_less_eq_int @ ( groups2878480467620962989at_int @ F @ A2 ) @ ( groups2878480467620962989at_int @ F @ B ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod_mono2
% 3.82/4.09 thf(fact_6554_prod__mono2,axiom,
% 3.82/4.09 ! [B: set_nat,A2: set_nat,F: nat > real] :
% 3.82/4.09 ( ( finite_finite_nat @ B )
% 3.82/4.09 => ( ( ord_less_eq_set_nat @ A2 @ B )
% 3.82/4.09 => ( ! [B4: nat] :
% 3.82/4.09 ( ( member_nat @ B4 @ ( minus_minus_set_nat @ B @ A2 ) )
% 3.82/4.09 => ( ord_less_eq_real @ one_one_real @ ( F @ B4 ) ) )
% 3.82/4.09 => ( ! [A4: nat] :
% 3.82/4.09 ( ( member_nat @ A4 @ A2 )
% 3.82/4.09 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A4 ) ) )
% 3.82/4.09 => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F @ A2 ) @ ( groups129246275422532515t_real @ F @ B ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod_mono2
% 3.82/4.09 thf(fact_6555_prod__mono2,axiom,
% 3.82/4.09 ! [B: set_int,A2: set_int,F: int > real] :
% 3.82/4.09 ( ( finite_finite_int @ B )
% 3.82/4.09 => ( ( ord_less_eq_set_int @ A2 @ B )
% 3.82/4.09 => ( ! [B4: int] :
% 3.82/4.09 ( ( member_int @ B4 @ ( minus_minus_set_int @ B @ A2 ) )
% 3.82/4.09 => ( ord_less_eq_real @ one_one_real @ ( F @ B4 ) ) )
% 3.82/4.09 => ( ! [A4: int] :
% 3.82/4.09 ( ( member_int @ A4 @ A2 )
% 3.82/4.09 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A4 ) ) )
% 3.82/4.09 => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ ( groups2316167850115554303t_real @ F @ B ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod_mono2
% 3.82/4.09 thf(fact_6556_prod__mono2,axiom,
% 3.82/4.09 ! [B: set_nat,A2: set_nat,F: nat > int] :
% 3.82/4.09 ( ( finite_finite_nat @ B )
% 3.82/4.09 => ( ( ord_less_eq_set_nat @ A2 @ B )
% 3.82/4.09 => ( ! [B4: nat] :
% 3.82/4.09 ( ( member_nat @ B4 @ ( minus_minus_set_nat @ B @ A2 ) )
% 3.82/4.09 => ( ord_less_eq_int @ one_one_int @ ( F @ B4 ) ) )
% 3.82/4.09 => ( ! [A4: nat] :
% 3.82/4.09 ( ( member_nat @ A4 @ A2 )
% 3.82/4.09 => ( ord_less_eq_int @ zero_zero_int @ ( F @ A4 ) ) )
% 3.82/4.09 => ( ord_less_eq_int @ ( groups705719431365010083at_int @ F @ A2 ) @ ( groups705719431365010083at_int @ F @ B ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod_mono2
% 3.82/4.09 thf(fact_6557_prod__mono2,axiom,
% 3.82/4.09 ! [B: set_int,A2: set_int,F: int > int] :
% 3.82/4.09 ( ( finite_finite_int @ B )
% 3.82/4.09 => ( ( ord_less_eq_set_int @ A2 @ B )
% 3.82/4.09 => ( ! [B4: int] :
% 3.82/4.09 ( ( member_int @ B4 @ ( minus_minus_set_int @ B @ A2 ) )
% 3.82/4.09 => ( ord_less_eq_int @ one_one_int @ ( F @ B4 ) ) )
% 3.82/4.09 => ( ! [A4: int] :
% 3.82/4.09 ( ( member_int @ A4 @ A2 )
% 3.82/4.09 => ( ord_less_eq_int @ zero_zero_int @ ( F @ A4 ) ) )
% 3.82/4.09 => ( ord_less_eq_int @ ( groups1705073143266064639nt_int @ F @ A2 ) @ ( groups1705073143266064639nt_int @ F @ B ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod_mono2
% 3.82/4.09 thf(fact_6558_prod__diff1,axiom,
% 3.82/4.09 ! [A2: set_complex,F: complex > complex,A: complex] :
% 3.82/4.09 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.09 => ( ( ( F @ A )
% 3.82/4.09 != zero_zero_complex )
% 3.82/4.09 => ( ( ( member_complex @ A @ A2 )
% 3.82/4.09 => ( ( groups3708469109370488835omplex @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 3.82/4.09 = ( divide1717551699836669952omplex @ ( groups3708469109370488835omplex @ F @ A2 ) @ ( F @ A ) ) ) )
% 3.82/4.09 & ( ~ ( member_complex @ A @ A2 )
% 3.82/4.09 => ( ( groups3708469109370488835omplex @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 3.82/4.09 = ( groups3708469109370488835omplex @ F @ A2 ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod_diff1
% 3.82/4.09 thf(fact_6559_prod__diff1,axiom,
% 3.82/4.09 ! [A2: set_Extended_enat,F: extended_enat > complex,A: extended_enat] :
% 3.82/4.09 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.09 => ( ( ( F @ A )
% 3.82/4.09 != zero_zero_complex )
% 3.82/4.09 => ( ( ( member_Extended_enat @ A @ A2 )
% 3.82/4.09 => ( ( groups4622424608036095791omplex @ F @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) )
% 3.82/4.09 = ( divide1717551699836669952omplex @ ( groups4622424608036095791omplex @ F @ A2 ) @ ( F @ A ) ) ) )
% 3.82/4.09 & ( ~ ( member_Extended_enat @ A @ A2 )
% 3.82/4.09 => ( ( groups4622424608036095791omplex @ F @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) )
% 3.82/4.09 = ( groups4622424608036095791omplex @ F @ A2 ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod_diff1
% 3.82/4.09 thf(fact_6560_prod__diff1,axiom,
% 3.82/4.09 ! [A2: set_real,F: real > complex,A: real] :
% 3.82/4.09 ( ( finite_finite_real @ A2 )
% 3.82/4.09 => ( ( ( F @ A )
% 3.82/4.09 != zero_zero_complex )
% 3.82/4.09 => ( ( ( member_real @ A @ A2 )
% 3.82/4.09 => ( ( groups713298508707869441omplex @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 3.82/4.09 = ( divide1717551699836669952omplex @ ( groups713298508707869441omplex @ F @ A2 ) @ ( F @ A ) ) ) )
% 3.82/4.09 & ( ~ ( member_real @ A @ A2 )
% 3.82/4.09 => ( ( groups713298508707869441omplex @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 3.82/4.09 = ( groups713298508707869441omplex @ F @ A2 ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod_diff1
% 3.82/4.09 thf(fact_6561_prod__diff1,axiom,
% 3.82/4.09 ! [A2: set_int,F: int > complex,A: int] :
% 3.82/4.09 ( ( finite_finite_int @ A2 )
% 3.82/4.09 => ( ( ( F @ A )
% 3.82/4.09 != zero_zero_complex )
% 3.82/4.09 => ( ( ( member_int @ A @ A2 )
% 3.82/4.09 => ( ( groups7440179247065528705omplex @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 3.82/4.09 = ( divide1717551699836669952omplex @ ( groups7440179247065528705omplex @ F @ A2 ) @ ( F @ A ) ) ) )
% 3.82/4.09 & ( ~ ( member_int @ A @ A2 )
% 3.82/4.09 => ( ( groups7440179247065528705omplex @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 3.82/4.09 = ( groups7440179247065528705omplex @ F @ A2 ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod_diff1
% 3.82/4.09 thf(fact_6562_prod__diff1,axiom,
% 3.82/4.09 ! [A2: set_nat,F: nat > complex,A: nat] :
% 3.82/4.09 ( ( finite_finite_nat @ A2 )
% 3.82/4.09 => ( ( ( F @ A )
% 3.82/4.09 != zero_zero_complex )
% 3.82/4.09 => ( ( ( member_nat @ A @ A2 )
% 3.82/4.09 => ( ( groups6464643781859351333omplex @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 3.82/4.09 = ( divide1717551699836669952omplex @ ( groups6464643781859351333omplex @ F @ A2 ) @ ( F @ A ) ) ) )
% 3.82/4.09 & ( ~ ( member_nat @ A @ A2 )
% 3.82/4.09 => ( ( groups6464643781859351333omplex @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 3.82/4.09 = ( groups6464643781859351333omplex @ F @ A2 ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod_diff1
% 3.82/4.09 thf(fact_6563_prod__diff1,axiom,
% 3.82/4.09 ! [A2: set_complex,F: complex > nat,A: complex] :
% 3.82/4.09 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.09 => ( ( ( F @ A )
% 3.82/4.09 != zero_zero_nat )
% 3.82/4.09 => ( ( ( member_complex @ A @ A2 )
% 3.82/4.09 => ( ( groups861055069439313189ex_nat @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 3.82/4.09 = ( divide_divide_nat @ ( groups861055069439313189ex_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 3.82/4.09 & ( ~ ( member_complex @ A @ A2 )
% 3.82/4.09 => ( ( groups861055069439313189ex_nat @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 3.82/4.09 = ( groups861055069439313189ex_nat @ F @ A2 ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod_diff1
% 3.82/4.09 thf(fact_6564_prod__diff1,axiom,
% 3.82/4.09 ! [A2: set_Extended_enat,F: extended_enat > nat,A: extended_enat] :
% 3.82/4.09 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.09 => ( ( ( F @ A )
% 3.82/4.09 != zero_zero_nat )
% 3.82/4.09 => ( ( ( member_Extended_enat @ A @ A2 )
% 3.82/4.09 => ( ( groups2880970938130013265at_nat @ F @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) )
% 3.82/4.09 = ( divide_divide_nat @ ( groups2880970938130013265at_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 3.82/4.09 & ( ~ ( member_Extended_enat @ A @ A2 )
% 3.82/4.09 => ( ( groups2880970938130013265at_nat @ F @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) )
% 3.82/4.09 = ( groups2880970938130013265at_nat @ F @ A2 ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod_diff1
% 3.82/4.09 thf(fact_6565_prod__diff1,axiom,
% 3.82/4.09 ! [A2: set_real,F: real > nat,A: real] :
% 3.82/4.09 ( ( finite_finite_real @ A2 )
% 3.82/4.09 => ( ( ( F @ A )
% 3.82/4.09 != zero_zero_nat )
% 3.82/4.09 => ( ( ( member_real @ A @ A2 )
% 3.82/4.09 => ( ( groups4696554848551431203al_nat @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 3.82/4.09 = ( divide_divide_nat @ ( groups4696554848551431203al_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 3.82/4.09 & ( ~ ( member_real @ A @ A2 )
% 3.82/4.09 => ( ( groups4696554848551431203al_nat @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 3.82/4.09 = ( groups4696554848551431203al_nat @ F @ A2 ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod_diff1
% 3.82/4.09 thf(fact_6566_prod__diff1,axiom,
% 3.82/4.09 ! [A2: set_int,F: int > nat,A: int] :
% 3.82/4.09 ( ( finite_finite_int @ A2 )
% 3.82/4.09 => ( ( ( F @ A )
% 3.82/4.09 != zero_zero_nat )
% 3.82/4.09 => ( ( ( member_int @ A @ A2 )
% 3.82/4.09 => ( ( groups1707563613775114915nt_nat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 3.82/4.09 = ( divide_divide_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 3.82/4.09 & ( ~ ( member_int @ A @ A2 )
% 3.82/4.09 => ( ( groups1707563613775114915nt_nat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 3.82/4.09 = ( groups1707563613775114915nt_nat @ F @ A2 ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod_diff1
% 3.82/4.09 thf(fact_6567_prod__diff1,axiom,
% 3.82/4.09 ! [A2: set_complex,F: complex > int,A: complex] :
% 3.82/4.09 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.09 => ( ( ( F @ A )
% 3.82/4.09 != zero_zero_int )
% 3.82/4.09 => ( ( ( member_complex @ A @ A2 )
% 3.82/4.09 => ( ( groups858564598930262913ex_int @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 3.82/4.09 = ( divide_divide_int @ ( groups858564598930262913ex_int @ F @ A2 ) @ ( F @ A ) ) ) )
% 3.82/4.09 & ( ~ ( member_complex @ A @ A2 )
% 3.82/4.09 => ( ( groups858564598930262913ex_int @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 3.82/4.09 = ( groups858564598930262913ex_int @ F @ A2 ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod_diff1
% 3.82/4.09 thf(fact_6568_pochhammer__Suc__prod,axiom,
% 3.82/4.09 ! [A: extended_enat,N2: nat] :
% 3.82/4.09 ( ( comm_s3181272606743183617d_enat @ A @ ( suc @ N2 ) )
% 3.82/4.09 = ( groups7961826882256487087d_enat
% 3.82/4.09 @ ^ [I3: nat] : ( plus_p3455044024723400733d_enat @ A @ ( semiri4216267220026989637d_enat @ I3 ) )
% 3.82/4.09 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % pochhammer_Suc_prod
% 3.82/4.09 thf(fact_6569_pochhammer__Suc__prod,axiom,
% 3.82/4.09 ! [A: real,N2: nat] :
% 3.82/4.09 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N2 ) )
% 3.82/4.09 = ( groups129246275422532515t_real
% 3.82/4.09 @ ^ [I3: nat] : ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ I3 ) )
% 3.82/4.09 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % pochhammer_Suc_prod
% 3.82/4.09 thf(fact_6570_pochhammer__Suc__prod,axiom,
% 3.82/4.09 ! [A: int,N2: nat] :
% 3.82/4.09 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N2 ) )
% 3.82/4.09 = ( groups705719431365010083at_int
% 3.82/4.09 @ ^ [I3: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ I3 ) )
% 3.82/4.09 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % pochhammer_Suc_prod
% 3.82/4.09 thf(fact_6571_pochhammer__Suc__prod,axiom,
% 3.82/4.09 ! [A: nat,N2: nat] :
% 3.82/4.09 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N2 ) )
% 3.82/4.09 = ( groups708209901874060359at_nat
% 3.82/4.09 @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ I3 ) )
% 3.82/4.09 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % pochhammer_Suc_prod
% 3.82/4.09 thf(fact_6572_pochhammer__prod__rev,axiom,
% 3.82/4.09 ( comm_s3181272606743183617d_enat
% 3.82/4.09 = ( ^ [A3: extended_enat,N: nat] :
% 3.82/4.09 ( groups7961826882256487087d_enat
% 3.82/4.09 @ ^ [I3: nat] : ( plus_p3455044024723400733d_enat @ A3 @ ( semiri4216267220026989637d_enat @ ( minus_minus_nat @ N @ I3 ) ) )
% 3.82/4.09 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % pochhammer_prod_rev
% 3.82/4.09 thf(fact_6573_pochhammer__prod__rev,axiom,
% 3.82/4.09 ( comm_s7457072308508201937r_real
% 3.82/4.09 = ( ^ [A3: real,N: nat] :
% 3.82/4.09 ( groups129246275422532515t_real
% 3.82/4.09 @ ^ [I3: nat] : ( plus_plus_real @ A3 @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N @ I3 ) ) )
% 3.82/4.09 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % pochhammer_prod_rev
% 3.82/4.09 thf(fact_6574_pochhammer__prod__rev,axiom,
% 3.82/4.09 ( comm_s4660882817536571857er_int
% 3.82/4.09 = ( ^ [A3: int,N: nat] :
% 3.82/4.09 ( groups705719431365010083at_int
% 3.82/4.09 @ ^ [I3: nat] : ( plus_plus_int @ A3 @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N @ I3 ) ) )
% 3.82/4.09 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % pochhammer_prod_rev
% 3.82/4.09 thf(fact_6575_pochhammer__prod__rev,axiom,
% 3.82/4.09 ( comm_s4663373288045622133er_nat
% 3.82/4.09 = ( ^ [A3: nat,N: nat] :
% 3.82/4.09 ( groups708209901874060359at_nat
% 3.82/4.09 @ ^ [I3: nat] : ( plus_plus_nat @ A3 @ ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ N @ I3 ) ) )
% 3.82/4.09 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % pochhammer_prod_rev
% 3.82/4.09 thf(fact_6576_prod_Oin__pairs,axiom,
% 3.82/4.09 ! [G: nat > real,M2: nat,N2: nat] :
% 3.82/4.09 ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 3.82/4.09 = ( groups129246275422532515t_real
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 3.82/4.09 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.in_pairs
% 3.82/4.09 thf(fact_6577_prod_Oin__pairs,axiom,
% 3.82/4.09 ! [G: nat > complex,M2: nat,N2: nat] :
% 3.82/4.09 ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 3.82/4.09 = ( groups6464643781859351333omplex
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_complex @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 3.82/4.09 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.in_pairs
% 3.82/4.09 thf(fact_6578_prod_Oin__pairs,axiom,
% 3.82/4.09 ! [G: nat > extended_enat,M2: nat,N2: nat] :
% 3.82/4.09 ( ( groups7961826882256487087d_enat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 3.82/4.09 = ( groups7961826882256487087d_enat
% 3.82/4.09 @ ^ [I3: nat] : ( times_7803423173614009249d_enat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 3.82/4.09 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.in_pairs
% 3.82/4.09 thf(fact_6579_prod_Oin__pairs,axiom,
% 3.82/4.09 ! [G: nat > int,M2: nat,N2: nat] :
% 3.82/4.09 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 3.82/4.09 = ( groups705719431365010083at_int
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 3.82/4.09 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.in_pairs
% 3.82/4.09 thf(fact_6580_prod_Oin__pairs,axiom,
% 3.82/4.09 ! [G: nat > nat,M2: nat,N2: nat] :
% 3.82/4.09 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 3.82/4.09 = ( groups708209901874060359at_nat
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 3.82/4.09 @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.in_pairs
% 3.82/4.09 thf(fact_6581_sum__atLeastAtMost__code,axiom,
% 3.82/4.09 ! [F: nat > int,A: nat,B2: nat] :
% 3.82/4.09 ( ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ A @ B2 ) )
% 3.82/4.09 = ( set_fo2581907887559384638at_int
% 3.82/4.09 @ ^ [A3: nat] : ( plus_plus_int @ ( F @ A3 ) )
% 3.82/4.09 @ A
% 3.82/4.09 @ B2
% 3.82/4.09 @ zero_zero_int ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum_atLeastAtMost_code
% 3.82/4.09 thf(fact_6582_sum__atLeastAtMost__code,axiom,
% 3.82/4.09 ! [F: nat > complex,A: nat,B2: nat] :
% 3.82/4.09 ( ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ A @ B2 ) )
% 3.82/4.09 = ( set_fo1517530859248394432omplex
% 3.82/4.09 @ ^ [A3: nat] : ( plus_plus_complex @ ( F @ A3 ) )
% 3.82/4.09 @ A
% 3.82/4.09 @ B2
% 3.82/4.09 @ zero_zero_complex ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum_atLeastAtMost_code
% 3.82/4.09 thf(fact_6583_sum__atLeastAtMost__code,axiom,
% 3.82/4.09 ! [F: nat > extended_enat,A: nat,B2: nat] :
% 3.82/4.09 ( ( groups7108830773950497114d_enat @ F @ ( set_or1269000886237332187st_nat @ A @ B2 ) )
% 3.82/4.09 = ( set_fo2538466533108834004d_enat
% 3.82/4.09 @ ^ [A3: nat] : ( plus_p3455044024723400733d_enat @ ( F @ A3 ) )
% 3.82/4.09 @ A
% 3.82/4.09 @ B2
% 3.82/4.09 @ zero_z5237406670263579293d_enat ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum_atLeastAtMost_code
% 3.82/4.09 thf(fact_6584_sum__atLeastAtMost__code,axiom,
% 3.82/4.09 ! [F: nat > nat,A: nat,B2: nat] :
% 3.82/4.09 ( ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ A @ B2 ) )
% 3.82/4.09 = ( set_fo2584398358068434914at_nat
% 3.82/4.09 @ ^ [A3: nat] : ( plus_plus_nat @ ( F @ A3 ) )
% 3.82/4.09 @ A
% 3.82/4.09 @ B2
% 3.82/4.09 @ zero_zero_nat ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum_atLeastAtMost_code
% 3.82/4.09 thf(fact_6585_sum__atLeastAtMost__code,axiom,
% 3.82/4.09 ! [F: nat > real,A: nat,B2: nat] :
% 3.82/4.09 ( ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ A @ B2 ) )
% 3.82/4.09 = ( set_fo3111899725591712190t_real
% 3.82/4.09 @ ^ [A3: nat] : ( plus_plus_real @ ( F @ A3 ) )
% 3.82/4.09 @ A
% 3.82/4.09 @ B2
% 3.82/4.09 @ zero_zero_real ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum_atLeastAtMost_code
% 3.82/4.09 thf(fact_6586_pochhammer__Suc__prod__rev,axiom,
% 3.82/4.09 ! [A: extended_enat,N2: nat] :
% 3.82/4.09 ( ( comm_s3181272606743183617d_enat @ A @ ( suc @ N2 ) )
% 3.82/4.09 = ( groups7961826882256487087d_enat
% 3.82/4.09 @ ^ [I3: nat] : ( plus_p3455044024723400733d_enat @ A @ ( semiri4216267220026989637d_enat @ ( minus_minus_nat @ N2 @ I3 ) ) )
% 3.82/4.09 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % pochhammer_Suc_prod_rev
% 3.82/4.09 thf(fact_6587_pochhammer__Suc__prod__rev,axiom,
% 3.82/4.09 ! [A: real,N2: nat] :
% 3.82/4.09 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N2 ) )
% 3.82/4.09 = ( groups129246275422532515t_real
% 3.82/4.09 @ ^ [I3: nat] : ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N2 @ I3 ) ) )
% 3.82/4.09 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % pochhammer_Suc_prod_rev
% 3.82/4.09 thf(fact_6588_pochhammer__Suc__prod__rev,axiom,
% 3.82/4.09 ! [A: int,N2: nat] :
% 3.82/4.09 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N2 ) )
% 3.82/4.09 = ( groups705719431365010083at_int
% 3.82/4.09 @ ^ [I3: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N2 @ I3 ) ) )
% 3.82/4.09 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % pochhammer_Suc_prod_rev
% 3.82/4.09 thf(fact_6589_pochhammer__Suc__prod__rev,axiom,
% 3.82/4.09 ! [A: nat,N2: nat] :
% 3.82/4.09 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N2 ) )
% 3.82/4.09 = ( groups708209901874060359at_nat
% 3.82/4.09 @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ N2 @ I3 ) ) )
% 3.82/4.09 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % pochhammer_Suc_prod_rev
% 3.82/4.09 thf(fact_6590_power__half__series,axiom,
% 3.82/4.09 ( sums_real
% 3.82/4.09 @ ^ [N: nat] : ( power_power_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( suc @ N ) )
% 3.82/4.09 @ one_one_real ) ).
% 3.82/4.09
% 3.82/4.09 % power_half_series
% 3.82/4.09 thf(fact_6591_sums__zero,axiom,
% 3.82/4.09 ( sums_nat
% 3.82/4.09 @ ^ [N: nat] : zero_zero_nat
% 3.82/4.09 @ zero_zero_nat ) ).
% 3.82/4.09
% 3.82/4.09 % sums_zero
% 3.82/4.09 thf(fact_6592_sums__zero,axiom,
% 3.82/4.09 ( sums_real
% 3.82/4.09 @ ^ [N: nat] : zero_zero_real
% 3.82/4.09 @ zero_zero_real ) ).
% 3.82/4.09
% 3.82/4.09 % sums_zero
% 3.82/4.09 thf(fact_6593_sums__zero,axiom,
% 3.82/4.09 ( sums_int
% 3.82/4.09 @ ^ [N: nat] : zero_zero_int
% 3.82/4.09 @ zero_zero_int ) ).
% 3.82/4.09
% 3.82/4.09 % sums_zero
% 3.82/4.09 thf(fact_6594_sums__zero,axiom,
% 3.82/4.09 ( sums_complex
% 3.82/4.09 @ ^ [N: nat] : zero_zero_complex
% 3.82/4.09 @ zero_zero_complex ) ).
% 3.82/4.09
% 3.82/4.09 % sums_zero
% 3.82/4.09 thf(fact_6595_sums__If__finite__set_H,axiom,
% 3.82/4.09 ! [G: nat > real,S2: real,A2: set_nat,S5: real,F: nat > real] :
% 3.82/4.09 ( ( sums_real @ G @ S2 )
% 3.82/4.09 => ( ( finite_finite_nat @ A2 )
% 3.82/4.09 => ( ( S5
% 3.82/4.09 = ( plus_plus_real @ S2
% 3.82/4.09 @ ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [N: nat] : ( minus_minus_real @ ( F @ N ) @ ( G @ N ) )
% 3.82/4.09 @ A2 ) ) )
% 3.82/4.09 => ( sums_real
% 3.82/4.09 @ ^ [N: nat] : ( if_real @ ( member_nat @ N @ A2 ) @ ( F @ N ) @ ( G @ N ) )
% 3.82/4.09 @ S5 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sums_If_finite_set'
% 3.82/4.09 thf(fact_6596_sums__iff__shift_H,axiom,
% 3.82/4.09 ! [F: nat > real,N2: nat,S: real] :
% 3.82/4.09 ( ( sums_real
% 3.82/4.09 @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N2 ) )
% 3.82/4.09 @ ( minus_minus_real @ S @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) ) )
% 3.82/4.09 = ( sums_real @ F @ S ) ) ).
% 3.82/4.09
% 3.82/4.09 % sums_iff_shift'
% 3.82/4.09 thf(fact_6597_sums__split__initial__segment,axiom,
% 3.82/4.09 ! [F: nat > real,S: real,N2: nat] :
% 3.82/4.09 ( ( sums_real @ F @ S )
% 3.82/4.09 => ( sums_real
% 3.82/4.09 @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N2 ) )
% 3.82/4.09 @ ( minus_minus_real @ S @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sums_split_initial_segment
% 3.82/4.09 thf(fact_6598_sums__iff__shift,axiom,
% 3.82/4.09 ! [F: nat > real,N2: nat,S: real] :
% 3.82/4.09 ( ( sums_real
% 3.82/4.09 @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N2 ) )
% 3.82/4.09 @ S )
% 3.82/4.09 = ( sums_real @ F @ ( plus_plus_real @ S @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sums_iff_shift
% 3.82/4.09 thf(fact_6599_prod__eq__1__iff,axiom,
% 3.82/4.09 ! [A2: set_complex,F: complex > nat] :
% 3.82/4.09 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.09 => ( ( ( groups861055069439313189ex_nat @ F @ A2 )
% 3.82/4.09 = one_one_nat )
% 3.82/4.09 = ( ! [X4: complex] :
% 3.82/4.09 ( ( member_complex @ X4 @ A2 )
% 3.82/4.09 => ( ( F @ X4 )
% 3.82/4.09 = one_one_nat ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod_eq_1_iff
% 3.82/4.09 thf(fact_6600_prod__eq__1__iff,axiom,
% 3.82/4.09 ! [A2: set_int,F: int > nat] :
% 3.82/4.09 ( ( finite_finite_int @ A2 )
% 3.82/4.09 => ( ( ( groups1707563613775114915nt_nat @ F @ A2 )
% 3.82/4.09 = one_one_nat )
% 3.82/4.09 = ( ! [X4: int] :
% 3.82/4.09 ( ( member_int @ X4 @ A2 )
% 3.82/4.09 => ( ( F @ X4 )
% 3.82/4.09 = one_one_nat ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod_eq_1_iff
% 3.82/4.09 thf(fact_6601_prod__eq__1__iff,axiom,
% 3.82/4.09 ! [A2: set_Extended_enat,F: extended_enat > nat] :
% 3.82/4.09 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.09 => ( ( ( groups2880970938130013265at_nat @ F @ A2 )
% 3.82/4.09 = one_one_nat )
% 3.82/4.09 = ( ! [X4: extended_enat] :
% 3.82/4.09 ( ( member_Extended_enat @ X4 @ A2 )
% 3.82/4.09 => ( ( F @ X4 )
% 3.82/4.09 = one_one_nat ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod_eq_1_iff
% 3.82/4.09 thf(fact_6602_prod__eq__1__iff,axiom,
% 3.82/4.09 ! [A2: set_nat,F: nat > nat] :
% 3.82/4.09 ( ( finite_finite_nat @ A2 )
% 3.82/4.09 => ( ( ( groups708209901874060359at_nat @ F @ A2 )
% 3.82/4.09 = one_one_nat )
% 3.82/4.09 = ( ! [X4: nat] :
% 3.82/4.09 ( ( member_nat @ X4 @ A2 )
% 3.82/4.09 => ( ( F @ X4 )
% 3.82/4.09 = one_one_nat ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod_eq_1_iff
% 3.82/4.09 thf(fact_6603_prod__pos__nat__iff,axiom,
% 3.82/4.09 ! [A2: set_complex,F: complex > nat] :
% 3.82/4.09 ( ( finite3207457112153483333omplex @ A2 )
% 3.82/4.09 => ( ( ord_less_nat @ zero_zero_nat @ ( groups861055069439313189ex_nat @ F @ A2 ) )
% 3.82/4.09 = ( ! [X4: complex] :
% 3.82/4.09 ( ( member_complex @ X4 @ A2 )
% 3.82/4.09 => ( ord_less_nat @ zero_zero_nat @ ( F @ X4 ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod_pos_nat_iff
% 3.82/4.09 thf(fact_6604_prod__pos__nat__iff,axiom,
% 3.82/4.09 ! [A2: set_int,F: int > nat] :
% 3.82/4.09 ( ( finite_finite_int @ A2 )
% 3.82/4.09 => ( ( ord_less_nat @ zero_zero_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) )
% 3.82/4.09 = ( ! [X4: int] :
% 3.82/4.09 ( ( member_int @ X4 @ A2 )
% 3.82/4.09 => ( ord_less_nat @ zero_zero_nat @ ( F @ X4 ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod_pos_nat_iff
% 3.82/4.09 thf(fact_6605_prod__pos__nat__iff,axiom,
% 3.82/4.09 ! [A2: set_Extended_enat,F: extended_enat > nat] :
% 3.82/4.09 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.09 => ( ( ord_less_nat @ zero_zero_nat @ ( groups2880970938130013265at_nat @ F @ A2 ) )
% 3.82/4.09 = ( ! [X4: extended_enat] :
% 3.82/4.09 ( ( member_Extended_enat @ X4 @ A2 )
% 3.82/4.09 => ( ord_less_nat @ zero_zero_nat @ ( F @ X4 ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod_pos_nat_iff
% 3.82/4.09 thf(fact_6606_prod__pos__nat__iff,axiom,
% 3.82/4.09 ! [A2: set_nat,F: nat > nat] :
% 3.82/4.09 ( ( finite_finite_nat @ A2 )
% 3.82/4.09 => ( ( ord_less_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A2 ) )
% 3.82/4.09 = ( ! [X4: nat] :
% 3.82/4.09 ( ( member_nat @ X4 @ A2 )
% 3.82/4.09 => ( ord_less_nat @ zero_zero_nat @ ( F @ X4 ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod_pos_nat_iff
% 3.82/4.09 thf(fact_6607_int__prod,axiom,
% 3.82/4.09 ! [F: int > nat,A2: set_int] :
% 3.82/4.09 ( ( semiri1314217659103216013at_int @ ( groups1707563613775114915nt_nat @ F @ A2 ) )
% 3.82/4.09 = ( groups1705073143266064639nt_int
% 3.82/4.09 @ ^ [X4: int] : ( semiri1314217659103216013at_int @ ( F @ X4 ) )
% 3.82/4.09 @ A2 ) ) ).
% 3.82/4.09
% 3.82/4.09 % int_prod
% 3.82/4.09 thf(fact_6608_int__prod,axiom,
% 3.82/4.09 ! [F: nat > nat,A2: set_nat] :
% 3.82/4.09 ( ( semiri1314217659103216013at_int @ ( groups708209901874060359at_nat @ F @ A2 ) )
% 3.82/4.09 = ( groups705719431365010083at_int
% 3.82/4.09 @ ^ [X4: nat] : ( semiri1314217659103216013at_int @ ( F @ X4 ) )
% 3.82/4.09 @ A2 ) ) ).
% 3.82/4.09
% 3.82/4.09 % int_prod
% 3.82/4.09 thf(fact_6609_prod__int__eq,axiom,
% 3.82/4.09 ! [I: nat,J: nat] :
% 3.82/4.09 ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I @ J ) )
% 3.82/4.09 = ( groups1705073143266064639nt_int
% 3.82/4.09 @ ^ [X4: int] : X4
% 3.82/4.09 @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ J ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod_int_eq
% 3.82/4.09 thf(fact_6610_ln__prod,axiom,
% 3.82/4.09 ! [I6: set_real,F: real > real] :
% 3.82/4.09 ( ( finite_finite_real @ I6 )
% 3.82/4.09 => ( ! [I4: real] :
% 3.82/4.09 ( ( member_real @ I4 @ I6 )
% 3.82/4.09 => ( ord_less_real @ zero_zero_real @ ( F @ I4 ) ) )
% 3.82/4.09 => ( ( ln_ln_real @ ( groups1681761925125756287l_real @ F @ I6 ) )
% 3.82/4.09 = ( groups8097168146408367636l_real
% 3.82/4.09 @ ^ [X4: real] : ( ln_ln_real @ ( F @ X4 ) )
% 3.82/4.09 @ I6 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % ln_prod
% 3.82/4.09 thf(fact_6611_ln__prod,axiom,
% 3.82/4.09 ! [I6: set_set_nat,F: set_nat > real] :
% 3.82/4.09 ( ( finite1152437895449049373et_nat @ I6 )
% 3.82/4.09 => ( ! [I4: set_nat] :
% 3.82/4.09 ( ( member_set_nat @ I4 @ I6 )
% 3.82/4.09 => ( ord_less_real @ zero_zero_real @ ( F @ I4 ) ) )
% 3.82/4.09 => ( ( ln_ln_real @ ( groups3619160379726066777t_real @ F @ I6 ) )
% 3.82/4.09 = ( groups5107569545109728110t_real
% 3.82/4.09 @ ^ [X4: set_nat] : ( ln_ln_real @ ( F @ X4 ) )
% 3.82/4.09 @ I6 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % ln_prod
% 3.82/4.09 thf(fact_6612_ln__prod,axiom,
% 3.82/4.09 ! [I6: set_complex,F: complex > real] :
% 3.82/4.09 ( ( finite3207457112153483333omplex @ I6 )
% 3.82/4.09 => ( ! [I4: complex] :
% 3.82/4.09 ( ( member_complex @ I4 @ I6 )
% 3.82/4.09 => ( ord_less_real @ zero_zero_real @ ( F @ I4 ) ) )
% 3.82/4.09 => ( ( ln_ln_real @ ( groups766887009212190081x_real @ F @ I6 ) )
% 3.82/4.09 = ( groups5808333547571424918x_real
% 3.82/4.09 @ ^ [X4: complex] : ( ln_ln_real @ ( F @ X4 ) )
% 3.82/4.09 @ I6 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % ln_prod
% 3.82/4.09 thf(fact_6613_ln__prod,axiom,
% 3.82/4.09 ! [I6: set_int,F: int > real] :
% 3.82/4.09 ( ( finite_finite_int @ I6 )
% 3.82/4.09 => ( ! [I4: int] :
% 3.82/4.09 ( ( member_int @ I4 @ I6 )
% 3.82/4.09 => ( ord_less_real @ zero_zero_real @ ( F @ I4 ) ) )
% 3.82/4.09 => ( ( ln_ln_real @ ( groups2316167850115554303t_real @ F @ I6 ) )
% 3.82/4.09 = ( groups8778361861064173332t_real
% 3.82/4.09 @ ^ [X4: int] : ( ln_ln_real @ ( F @ X4 ) )
% 3.82/4.09 @ I6 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % ln_prod
% 3.82/4.09 thf(fact_6614_ln__prod,axiom,
% 3.82/4.09 ! [I6: set_Extended_enat,F: extended_enat > real] :
% 3.82/4.09 ( ( finite4001608067531595151d_enat @ I6 )
% 3.82/4.09 => ( ! [I4: extended_enat] :
% 3.82/4.09 ( ( member_Extended_enat @ I4 @ I6 )
% 3.82/4.09 => ( ord_less_real @ zero_zero_real @ ( F @ I4 ) ) )
% 3.82/4.09 => ( ( ln_ln_real @ ( groups97031904164794029t_real @ F @ I6 ) )
% 3.82/4.09 = ( groups4148127829035722712t_real
% 3.82/4.09 @ ^ [X4: extended_enat] : ( ln_ln_real @ ( F @ X4 ) )
% 3.82/4.09 @ I6 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % ln_prod
% 3.82/4.09 thf(fact_6615_ln__prod,axiom,
% 3.82/4.09 ! [I6: set_nat,F: nat > real] :
% 3.82/4.09 ( ( finite_finite_nat @ I6 )
% 3.82/4.09 => ( ! [I4: nat] :
% 3.82/4.09 ( ( member_nat @ I4 @ I6 )
% 3.82/4.09 => ( ord_less_real @ zero_zero_real @ ( F @ I4 ) ) )
% 3.82/4.09 => ( ( ln_ln_real @ ( groups129246275422532515t_real @ F @ I6 ) )
% 3.82/4.09 = ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [X4: nat] : ( ln_ln_real @ ( F @ X4 ) )
% 3.82/4.09 @ I6 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % ln_prod
% 3.82/4.09 thf(fact_6616_prod__int__plus__eq,axiom,
% 3.82/4.09 ! [I: nat,J: nat] :
% 3.82/4.09 ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I @ ( plus_plus_nat @ I @ J ) ) )
% 3.82/4.09 = ( groups1705073143266064639nt_int
% 3.82/4.09 @ ^ [X4: int] : X4
% 3.82/4.09 @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ I @ J ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod_int_plus_eq
% 3.82/4.09 thf(fact_6617_sums__le,axiom,
% 3.82/4.09 ! [F: nat > real,G: nat > real,S: real,T: real] :
% 3.82/4.09 ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 3.82/4.09 => ( ( sums_real @ F @ S )
% 3.82/4.09 => ( ( sums_real @ G @ T )
% 3.82/4.09 => ( ord_less_eq_real @ S @ T ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sums_le
% 3.82/4.09 thf(fact_6618_sums__le,axiom,
% 3.82/4.09 ! [F: nat > nat,G: nat > nat,S: nat,T: nat] :
% 3.82/4.09 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( G @ N3 ) )
% 3.82/4.09 => ( ( sums_nat @ F @ S )
% 3.82/4.09 => ( ( sums_nat @ G @ T )
% 3.82/4.09 => ( ord_less_eq_nat @ S @ T ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sums_le
% 3.82/4.09 thf(fact_6619_sums__le,axiom,
% 3.82/4.09 ! [F: nat > int,G: nat > int,S: int,T: int] :
% 3.82/4.09 ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( G @ N3 ) )
% 3.82/4.09 => ( ( sums_int @ F @ S )
% 3.82/4.09 => ( ( sums_int @ G @ T )
% 3.82/4.09 => ( ord_less_eq_int @ S @ T ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sums_le
% 3.82/4.09 thf(fact_6620_sums__0,axiom,
% 3.82/4.09 ! [F: nat > nat] :
% 3.82/4.09 ( ! [N3: nat] :
% 3.82/4.09 ( ( F @ N3 )
% 3.82/4.09 = zero_zero_nat )
% 3.82/4.09 => ( sums_nat @ F @ zero_zero_nat ) ) ).
% 3.82/4.09
% 3.82/4.09 % sums_0
% 3.82/4.09 thf(fact_6621_sums__0,axiom,
% 3.82/4.09 ! [F: nat > real] :
% 3.82/4.09 ( ! [N3: nat] :
% 3.82/4.09 ( ( F @ N3 )
% 3.82/4.09 = zero_zero_real )
% 3.82/4.09 => ( sums_real @ F @ zero_zero_real ) ) ).
% 3.82/4.09
% 3.82/4.09 % sums_0
% 3.82/4.09 thf(fact_6622_sums__0,axiom,
% 3.82/4.09 ! [F: nat > int] :
% 3.82/4.09 ( ! [N3: nat] :
% 3.82/4.09 ( ( F @ N3 )
% 3.82/4.09 = zero_zero_int )
% 3.82/4.09 => ( sums_int @ F @ zero_zero_int ) ) ).
% 3.82/4.09
% 3.82/4.09 % sums_0
% 3.82/4.09 thf(fact_6623_sums__0,axiom,
% 3.82/4.09 ! [F: nat > complex] :
% 3.82/4.09 ( ! [N3: nat] :
% 3.82/4.09 ( ( F @ N3 )
% 3.82/4.09 = zero_zero_complex )
% 3.82/4.09 => ( sums_complex @ F @ zero_zero_complex ) ) ).
% 3.82/4.09
% 3.82/4.09 % sums_0
% 3.82/4.09 thf(fact_6624_sums__single,axiom,
% 3.82/4.09 ! [I: nat,F: nat > nat] :
% 3.82/4.09 ( sums_nat
% 3.82/4.09 @ ^ [R4: nat] : ( if_nat @ ( R4 = I ) @ ( F @ R4 ) @ zero_zero_nat )
% 3.82/4.09 @ ( F @ I ) ) ).
% 3.82/4.09
% 3.82/4.09 % sums_single
% 3.82/4.09 thf(fact_6625_sums__single,axiom,
% 3.82/4.09 ! [I: nat,F: nat > real] :
% 3.82/4.09 ( sums_real
% 3.82/4.09 @ ^ [R4: nat] : ( if_real @ ( R4 = I ) @ ( F @ R4 ) @ zero_zero_real )
% 3.82/4.09 @ ( F @ I ) ) ).
% 3.82/4.09
% 3.82/4.09 % sums_single
% 3.82/4.09 thf(fact_6626_sums__single,axiom,
% 3.82/4.09 ! [I: nat,F: nat > int] :
% 3.82/4.09 ( sums_int
% 3.82/4.09 @ ^ [R4: nat] : ( if_int @ ( R4 = I ) @ ( F @ R4 ) @ zero_zero_int )
% 3.82/4.09 @ ( F @ I ) ) ).
% 3.82/4.09
% 3.82/4.09 % sums_single
% 3.82/4.09 thf(fact_6627_sums__single,axiom,
% 3.82/4.09 ! [I: nat,F: nat > complex] :
% 3.82/4.09 ( sums_complex
% 3.82/4.09 @ ^ [R4: nat] : ( if_complex @ ( R4 = I ) @ ( F @ R4 ) @ zero_zero_complex )
% 3.82/4.09 @ ( F @ I ) ) ).
% 3.82/4.09
% 3.82/4.09 % sums_single
% 3.82/4.09 thf(fact_6628_sums__add,axiom,
% 3.82/4.09 ! [F: nat > nat,A: nat,G: nat > nat,B2: nat] :
% 3.82/4.09 ( ( sums_nat @ F @ A )
% 3.82/4.09 => ( ( sums_nat @ G @ B2 )
% 3.82/4.09 => ( sums_nat
% 3.82/4.09 @ ^ [N: nat] : ( plus_plus_nat @ ( F @ N ) @ ( G @ N ) )
% 3.82/4.09 @ ( plus_plus_nat @ A @ B2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sums_add
% 3.82/4.09 thf(fact_6629_sums__add,axiom,
% 3.82/4.09 ! [F: nat > int,A: int,G: nat > int,B2: int] :
% 3.82/4.09 ( ( sums_int @ F @ A )
% 3.82/4.09 => ( ( sums_int @ G @ B2 )
% 3.82/4.09 => ( sums_int
% 3.82/4.09 @ ^ [N: nat] : ( plus_plus_int @ ( F @ N ) @ ( G @ N ) )
% 3.82/4.09 @ ( plus_plus_int @ A @ B2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sums_add
% 3.82/4.09 thf(fact_6630_sums__add,axiom,
% 3.82/4.09 ! [F: nat > real,A: real,G: nat > real,B2: real] :
% 3.82/4.09 ( ( sums_real @ F @ A )
% 3.82/4.09 => ( ( sums_real @ G @ B2 )
% 3.82/4.09 => ( sums_real
% 3.82/4.09 @ ^ [N: nat] : ( plus_plus_real @ ( F @ N ) @ ( G @ N ) )
% 3.82/4.09 @ ( plus_plus_real @ A @ B2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sums_add
% 3.82/4.09 thf(fact_6631_sums__mult__iff,axiom,
% 3.82/4.09 ! [C: real,F: nat > real,D: real] :
% 3.82/4.09 ( ( C != zero_zero_real )
% 3.82/4.09 => ( ( sums_real
% 3.82/4.09 @ ^ [N: nat] : ( times_times_real @ C @ ( F @ N ) )
% 3.82/4.09 @ ( times_times_real @ C @ D ) )
% 3.82/4.09 = ( sums_real @ F @ D ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sums_mult_iff
% 3.82/4.09 thf(fact_6632_sums__mult__iff,axiom,
% 3.82/4.09 ! [C: complex,F: nat > complex,D: complex] :
% 3.82/4.09 ( ( C != zero_zero_complex )
% 3.82/4.09 => ( ( sums_complex
% 3.82/4.09 @ ^ [N: nat] : ( times_times_complex @ C @ ( F @ N ) )
% 3.82/4.09 @ ( times_times_complex @ C @ D ) )
% 3.82/4.09 = ( sums_complex @ F @ D ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sums_mult_iff
% 3.82/4.09 thf(fact_6633_sums__mult2__iff,axiom,
% 3.82/4.09 ! [C: real,F: nat > real,D: real] :
% 3.82/4.09 ( ( C != zero_zero_real )
% 3.82/4.09 => ( ( sums_real
% 3.82/4.09 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ C )
% 3.82/4.09 @ ( times_times_real @ D @ C ) )
% 3.82/4.09 = ( sums_real @ F @ D ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sums_mult2_iff
% 3.82/4.09 thf(fact_6634_sums__mult2__iff,axiom,
% 3.82/4.09 ! [C: complex,F: nat > complex,D: complex] :
% 3.82/4.09 ( ( C != zero_zero_complex )
% 3.82/4.09 => ( ( sums_complex
% 3.82/4.09 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ C )
% 3.82/4.09 @ ( times_times_complex @ D @ C ) )
% 3.82/4.09 = ( sums_complex @ F @ D ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sums_mult2_iff
% 3.82/4.09 thf(fact_6635_sums__mult__D,axiom,
% 3.82/4.09 ! [C: complex,F: nat > complex,A: complex] :
% 3.82/4.09 ( ( sums_complex
% 3.82/4.09 @ ^ [N: nat] : ( times_times_complex @ C @ ( F @ N ) )
% 3.82/4.09 @ A )
% 3.82/4.09 => ( ( C != zero_zero_complex )
% 3.82/4.09 => ( sums_complex @ F @ ( divide1717551699836669952omplex @ A @ C ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sums_mult_D
% 3.82/4.09 thf(fact_6636_sums__mult__D,axiom,
% 3.82/4.09 ! [C: real,F: nat > real,A: real] :
% 3.82/4.09 ( ( sums_real
% 3.82/4.09 @ ^ [N: nat] : ( times_times_real @ C @ ( F @ N ) )
% 3.82/4.09 @ A )
% 3.82/4.09 => ( ( C != zero_zero_real )
% 3.82/4.09 => ( sums_real @ F @ ( divide_divide_real @ A @ C ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sums_mult_D
% 3.82/4.09 thf(fact_6637_sums__Suc__imp,axiom,
% 3.82/4.09 ! [F: nat > real,S: real] :
% 3.82/4.09 ( ( ( F @ zero_zero_nat )
% 3.82/4.09 = zero_zero_real )
% 3.82/4.09 => ( ( sums_real
% 3.82/4.09 @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 3.82/4.09 @ S )
% 3.82/4.09 => ( sums_real @ F @ S ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sums_Suc_imp
% 3.82/4.09 thf(fact_6638_sums__Suc__imp,axiom,
% 3.82/4.09 ! [F: nat > complex,S: complex] :
% 3.82/4.09 ( ( ( F @ zero_zero_nat )
% 3.82/4.09 = zero_zero_complex )
% 3.82/4.09 => ( ( sums_complex
% 3.82/4.09 @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 3.82/4.09 @ S )
% 3.82/4.09 => ( sums_complex @ F @ S ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sums_Suc_imp
% 3.82/4.09 thf(fact_6639_sums__Suc__iff,axiom,
% 3.82/4.09 ! [F: nat > real,S: real] :
% 3.82/4.09 ( ( sums_real
% 3.82/4.09 @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 3.82/4.09 @ S )
% 3.82/4.09 = ( sums_real @ F @ ( plus_plus_real @ S @ ( F @ zero_zero_nat ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sums_Suc_iff
% 3.82/4.09 thf(fact_6640_sums__Suc,axiom,
% 3.82/4.09 ! [F: nat > nat,L: nat] :
% 3.82/4.09 ( ( sums_nat
% 3.82/4.09 @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 3.82/4.09 @ L )
% 3.82/4.09 => ( sums_nat @ F @ ( plus_plus_nat @ L @ ( F @ zero_zero_nat ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sums_Suc
% 3.82/4.09 thf(fact_6641_sums__Suc,axiom,
% 3.82/4.09 ! [F: nat > int,L: int] :
% 3.82/4.09 ( ( sums_int
% 3.82/4.09 @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 3.82/4.09 @ L )
% 3.82/4.09 => ( sums_int @ F @ ( plus_plus_int @ L @ ( F @ zero_zero_nat ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sums_Suc
% 3.82/4.09 thf(fact_6642_sums__Suc,axiom,
% 3.82/4.09 ! [F: nat > real,L: real] :
% 3.82/4.09 ( ( sums_real
% 3.82/4.09 @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 3.82/4.09 @ L )
% 3.82/4.09 => ( sums_real @ F @ ( plus_plus_real @ L @ ( F @ zero_zero_nat ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sums_Suc
% 3.82/4.09 thf(fact_6643_sums__zero__iff__shift,axiom,
% 3.82/4.09 ! [N2: nat,F: nat > real,S: real] :
% 3.82/4.09 ( ! [I4: nat] :
% 3.82/4.09 ( ( ord_less_nat @ I4 @ N2 )
% 3.82/4.09 => ( ( F @ I4 )
% 3.82/4.09 = zero_zero_real ) )
% 3.82/4.09 => ( ( sums_real
% 3.82/4.09 @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N2 ) )
% 3.82/4.09 @ S )
% 3.82/4.09 = ( sums_real @ F @ S ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sums_zero_iff_shift
% 3.82/4.09 thf(fact_6644_sums__zero__iff__shift,axiom,
% 3.82/4.09 ! [N2: nat,F: nat > complex,S: complex] :
% 3.82/4.09 ( ! [I4: nat] :
% 3.82/4.09 ( ( ord_less_nat @ I4 @ N2 )
% 3.82/4.09 => ( ( F @ I4 )
% 3.82/4.09 = zero_zero_complex ) )
% 3.82/4.09 => ( ( sums_complex
% 3.82/4.09 @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N2 ) )
% 3.82/4.09 @ S )
% 3.82/4.09 = ( sums_complex @ F @ S ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sums_zero_iff_shift
% 3.82/4.09 thf(fact_6645_sums__finite,axiom,
% 3.82/4.09 ! [N6: set_nat,F: nat > int] :
% 3.82/4.09 ( ( finite_finite_nat @ N6 )
% 3.82/4.09 => ( ! [N3: nat] :
% 3.82/4.09 ( ~ ( member_nat @ N3 @ N6 )
% 3.82/4.09 => ( ( F @ N3 )
% 3.82/4.09 = zero_zero_int ) )
% 3.82/4.09 => ( sums_int @ F @ ( groups3539618377306564664at_int @ F @ N6 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sums_finite
% 3.82/4.09 thf(fact_6646_sums__finite,axiom,
% 3.82/4.09 ! [N6: set_nat,F: nat > complex] :
% 3.82/4.09 ( ( finite_finite_nat @ N6 )
% 3.82/4.09 => ( ! [N3: nat] :
% 3.82/4.09 ( ~ ( member_nat @ N3 @ N6 )
% 3.82/4.09 => ( ( F @ N3 )
% 3.82/4.09 = zero_zero_complex ) )
% 3.82/4.09 => ( sums_complex @ F @ ( groups2073611262835488442omplex @ F @ N6 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sums_finite
% 3.82/4.09 thf(fact_6647_sums__finite,axiom,
% 3.82/4.09 ! [N6: set_nat,F: nat > nat] :
% 3.82/4.09 ( ( finite_finite_nat @ N6 )
% 3.82/4.09 => ( ! [N3: nat] :
% 3.82/4.09 ( ~ ( member_nat @ N3 @ N6 )
% 3.82/4.09 => ( ( F @ N3 )
% 3.82/4.09 = zero_zero_nat ) )
% 3.82/4.09 => ( sums_nat @ F @ ( groups3542108847815614940at_nat @ F @ N6 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sums_finite
% 3.82/4.09 thf(fact_6648_sums__finite,axiom,
% 3.82/4.09 ! [N6: set_nat,F: nat > real] :
% 3.82/4.09 ( ( finite_finite_nat @ N6 )
% 3.82/4.09 => ( ! [N3: nat] :
% 3.82/4.09 ( ~ ( member_nat @ N3 @ N6 )
% 3.82/4.09 => ( ( F @ N3 )
% 3.82/4.09 = zero_zero_real ) )
% 3.82/4.09 => ( sums_real @ F @ ( groups6591440286371151544t_real @ F @ N6 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sums_finite
% 3.82/4.09 thf(fact_6649_sums__If__finite,axiom,
% 3.82/4.09 ! [P: nat > $o,F: nat > int] :
% 3.82/4.09 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 3.82/4.09 => ( sums_int
% 3.82/4.09 @ ^ [R4: nat] : ( if_int @ ( P @ R4 ) @ ( F @ R4 ) @ zero_zero_int )
% 3.82/4.09 @ ( groups3539618377306564664at_int @ F @ ( collect_nat @ P ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sums_If_finite
% 3.82/4.09 thf(fact_6650_sums__If__finite,axiom,
% 3.82/4.09 ! [P: nat > $o,F: nat > complex] :
% 3.82/4.09 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 3.82/4.09 => ( sums_complex
% 3.82/4.09 @ ^ [R4: nat] : ( if_complex @ ( P @ R4 ) @ ( F @ R4 ) @ zero_zero_complex )
% 3.82/4.09 @ ( groups2073611262835488442omplex @ F @ ( collect_nat @ P ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sums_If_finite
% 3.82/4.09 thf(fact_6651_sums__If__finite,axiom,
% 3.82/4.09 ! [P: nat > $o,F: nat > nat] :
% 3.82/4.09 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 3.82/4.09 => ( sums_nat
% 3.82/4.09 @ ^ [R4: nat] : ( if_nat @ ( P @ R4 ) @ ( F @ R4 ) @ zero_zero_nat )
% 3.82/4.09 @ ( groups3542108847815614940at_nat @ F @ ( collect_nat @ P ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sums_If_finite
% 3.82/4.09 thf(fact_6652_sums__If__finite,axiom,
% 3.82/4.09 ! [P: nat > $o,F: nat > real] :
% 3.82/4.09 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 3.82/4.09 => ( sums_real
% 3.82/4.09 @ ^ [R4: nat] : ( if_real @ ( P @ R4 ) @ ( F @ R4 ) @ zero_zero_real )
% 3.82/4.09 @ ( groups6591440286371151544t_real @ F @ ( collect_nat @ P ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sums_If_finite
% 3.82/4.09 thf(fact_6653_sums__If__finite__set,axiom,
% 3.82/4.09 ! [A2: set_nat,F: nat > int] :
% 3.82/4.09 ( ( finite_finite_nat @ A2 )
% 3.82/4.09 => ( sums_int
% 3.82/4.09 @ ^ [R4: nat] : ( if_int @ ( member_nat @ R4 @ A2 ) @ ( F @ R4 ) @ zero_zero_int )
% 3.82/4.09 @ ( groups3539618377306564664at_int @ F @ A2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sums_If_finite_set
% 3.82/4.09 thf(fact_6654_sums__If__finite__set,axiom,
% 3.82/4.09 ! [A2: set_nat,F: nat > complex] :
% 3.82/4.09 ( ( finite_finite_nat @ A2 )
% 3.82/4.09 => ( sums_complex
% 3.82/4.09 @ ^ [R4: nat] : ( if_complex @ ( member_nat @ R4 @ A2 ) @ ( F @ R4 ) @ zero_zero_complex )
% 3.82/4.09 @ ( groups2073611262835488442omplex @ F @ A2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sums_If_finite_set
% 3.82/4.09 thf(fact_6655_sums__If__finite__set,axiom,
% 3.82/4.09 ! [A2: set_nat,F: nat > nat] :
% 3.82/4.09 ( ( finite_finite_nat @ A2 )
% 3.82/4.09 => ( sums_nat
% 3.82/4.09 @ ^ [R4: nat] : ( if_nat @ ( member_nat @ R4 @ A2 ) @ ( F @ R4 ) @ zero_zero_nat )
% 3.82/4.09 @ ( groups3542108847815614940at_nat @ F @ A2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sums_If_finite_set
% 3.82/4.09 thf(fact_6656_sums__If__finite__set,axiom,
% 3.82/4.09 ! [A2: set_nat,F: nat > real] :
% 3.82/4.09 ( ( finite_finite_nat @ A2 )
% 3.82/4.09 => ( sums_real
% 3.82/4.09 @ ^ [R4: nat] : ( if_real @ ( member_nat @ R4 @ A2 ) @ ( F @ R4 ) @ zero_zero_real )
% 3.82/4.09 @ ( groups6591440286371151544t_real @ F @ A2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sums_If_finite_set
% 3.82/4.09 thf(fact_6657_powser__sums__if,axiom,
% 3.82/4.09 ! [M2: nat,Z3: int] :
% 3.82/4.09 ( sums_int
% 3.82/4.09 @ ^ [N: nat] : ( times_times_int @ ( if_int @ ( N = M2 ) @ one_one_int @ zero_zero_int ) @ ( power_power_int @ Z3 @ N ) )
% 3.82/4.09 @ ( power_power_int @ Z3 @ M2 ) ) ).
% 3.82/4.09
% 3.82/4.09 % powser_sums_if
% 3.82/4.09 thf(fact_6658_powser__sums__if,axiom,
% 3.82/4.09 ! [M2: nat,Z3: real] :
% 3.82/4.09 ( sums_real
% 3.82/4.09 @ ^ [N: nat] : ( times_times_real @ ( if_real @ ( N = M2 ) @ one_one_real @ zero_zero_real ) @ ( power_power_real @ Z3 @ N ) )
% 3.82/4.09 @ ( power_power_real @ Z3 @ M2 ) ) ).
% 3.82/4.09
% 3.82/4.09 % powser_sums_if
% 3.82/4.09 thf(fact_6659_powser__sums__if,axiom,
% 3.82/4.09 ! [M2: nat,Z3: complex] :
% 3.82/4.09 ( sums_complex
% 3.82/4.09 @ ^ [N: nat] : ( times_times_complex @ ( if_complex @ ( N = M2 ) @ one_one_complex @ zero_zero_complex ) @ ( power_power_complex @ Z3 @ N ) )
% 3.82/4.09 @ ( power_power_complex @ Z3 @ M2 ) ) ).
% 3.82/4.09
% 3.82/4.09 % powser_sums_if
% 3.82/4.09 thf(fact_6660_ln__series,axiom,
% 3.82/4.09 ! [X: real] :
% 3.82/4.09 ( ( ord_less_real @ zero_zero_real @ X )
% 3.82/4.09 => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 3.82/4.09 => ( ( ln_ln_real @ X )
% 3.82/4.09 = ( suminf_real
% 3.82/4.09 @ ^ [N: nat] : ( times_times_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) @ ( power_power_real @ ( minus_minus_real @ X @ one_one_real ) @ ( suc @ N ) ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % ln_series
% 3.82/4.09 thf(fact_6661_arcosh__def,axiom,
% 3.82/4.09 ( arcosh_real
% 3.82/4.09 = ( ^ [X4: real] : ( ln_ln_real @ ( plus_plus_real @ X4 @ ( powr_real @ ( minus_minus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( real_V1803761363581548252l_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % arcosh_def
% 3.82/4.09 thf(fact_6662_arsinh__def,axiom,
% 3.82/4.09 ( arsinh_real
% 3.82/4.09 = ( ^ [X4: real] : ( ln_ln_real @ ( plus_plus_real @ X4 @ ( powr_real @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( real_V1803761363581548252l_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % arsinh_def
% 3.82/4.09 thf(fact_6663_floor__log__nat__eq__powr__iff,axiom,
% 3.82/4.09 ! [B2: nat,K: nat,N2: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 )
% 3.82/4.09 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 3.82/4.09 => ( ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B2 ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 3.82/4.09 = ( semiri1314217659103216013at_int @ N2 ) )
% 3.82/4.09 = ( ( ord_less_eq_nat @ ( power_power_nat @ B2 @ N2 ) @ K )
% 3.82/4.09 & ( ord_less_nat @ K @ ( power_power_nat @ B2 @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % floor_log_nat_eq_powr_iff
% 3.82/4.09 thf(fact_6664_gchoose__row__sum__weighted,axiom,
% 3.82/4.09 ! [R2: complex,M2: nat] :
% 3.82/4.09 ( ( groups2073611262835488442omplex
% 3.82/4.09 @ ^ [K2: nat] : ( times_times_complex @ ( gbinomial_complex @ R2 @ K2 ) @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ R2 @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( semiri8010041392384452111omplex @ K2 ) ) )
% 3.82/4.09 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M2 ) )
% 3.82/4.09 = ( times_times_complex @ ( divide1717551699836669952omplex @ ( semiri8010041392384452111omplex @ ( suc @ M2 ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( gbinomial_complex @ R2 @ ( suc @ M2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % gchoose_row_sum_weighted
% 3.82/4.09 thf(fact_6665_gchoose__row__sum__weighted,axiom,
% 3.82/4.09 ! [R2: real,M2: nat] :
% 3.82/4.09 ( ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [K2: nat] : ( times_times_real @ ( gbinomial_real @ R2 @ K2 ) @ ( minus_minus_real @ ( divide_divide_real @ R2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ K2 ) ) )
% 3.82/4.09 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M2 ) )
% 3.82/4.09 = ( times_times_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ ( suc @ M2 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( gbinomial_real @ R2 @ ( suc @ M2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % gchoose_row_sum_weighted
% 3.82/4.09 thf(fact_6666_central__binomial__lower__bound,axiom,
% 3.82/4.09 ! [N2: nat] :
% 3.82/4.09 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.09 => ( 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 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % central_binomial_lower_bound
% 3.82/4.09 thf(fact_6667_binomial__Suc__n,axiom,
% 3.82/4.09 ! [N2: nat] :
% 3.82/4.09 ( ( binomial @ ( suc @ N2 ) @ N2 )
% 3.82/4.09 = ( suc @ N2 ) ) ).
% 3.82/4.09
% 3.82/4.09 % binomial_Suc_n
% 3.82/4.09 thf(fact_6668_suminf__zero,axiom,
% 3.82/4.09 ( ( suminf_nat
% 3.82/4.09 @ ^ [N: nat] : zero_zero_nat )
% 3.82/4.09 = zero_zero_nat ) ).
% 3.82/4.09
% 3.82/4.09 % suminf_zero
% 3.82/4.09 thf(fact_6669_suminf__zero,axiom,
% 3.82/4.09 ( ( suminf_real
% 3.82/4.09 @ ^ [N: nat] : zero_zero_real )
% 3.82/4.09 = zero_zero_real ) ).
% 3.82/4.09
% 3.82/4.09 % suminf_zero
% 3.82/4.09 thf(fact_6670_suminf__zero,axiom,
% 3.82/4.09 ( ( suminf_int
% 3.82/4.09 @ ^ [N: nat] : zero_zero_int )
% 3.82/4.09 = zero_zero_int ) ).
% 3.82/4.09
% 3.82/4.09 % suminf_zero
% 3.82/4.09 thf(fact_6671_suminf__zero,axiom,
% 3.82/4.09 ( ( suminf_complex
% 3.82/4.09 @ ^ [N: nat] : zero_zero_complex )
% 3.82/4.09 = zero_zero_complex ) ).
% 3.82/4.09
% 3.82/4.09 % suminf_zero
% 3.82/4.09 thf(fact_6672_of__real__eq__0__iff,axiom,
% 3.82/4.09 ! [X: real] :
% 3.82/4.09 ( ( ( real_V1803761363581548252l_real @ X )
% 3.82/4.09 = zero_zero_real )
% 3.82/4.09 = ( X = zero_zero_real ) ) ).
% 3.82/4.09
% 3.82/4.09 % of_real_eq_0_iff
% 3.82/4.09 thf(fact_6673_of__real__eq__0__iff,axiom,
% 3.82/4.09 ! [X: real] :
% 3.82/4.09 ( ( ( real_V4546457046886955230omplex @ X )
% 3.82/4.09 = zero_zero_complex )
% 3.82/4.09 = ( X = zero_zero_real ) ) ).
% 3.82/4.09
% 3.82/4.09 % of_real_eq_0_iff
% 3.82/4.09 thf(fact_6674_of__real__0,axiom,
% 3.82/4.09 ( ( real_V1803761363581548252l_real @ zero_zero_real )
% 3.82/4.09 = zero_zero_real ) ).
% 3.82/4.09
% 3.82/4.09 % of_real_0
% 3.82/4.09 thf(fact_6675_of__real__0,axiom,
% 3.82/4.09 ( ( real_V4546457046886955230omplex @ zero_zero_real )
% 3.82/4.09 = zero_zero_complex ) ).
% 3.82/4.09
% 3.82/4.09 % of_real_0
% 3.82/4.09 thf(fact_6676_floor__zero,axiom,
% 3.82/4.09 ( ( archim6058952711729229775r_real @ zero_zero_real )
% 3.82/4.09 = zero_zero_int ) ).
% 3.82/4.09
% 3.82/4.09 % floor_zero
% 3.82/4.09 thf(fact_6677_gbinomial__0_I2_J,axiom,
% 3.82/4.09 ! [K: nat] :
% 3.82/4.09 ( ( gbinomial_nat @ zero_zero_nat @ ( suc @ K ) )
% 3.82/4.09 = zero_zero_nat ) ).
% 3.82/4.09
% 3.82/4.09 % gbinomial_0(2)
% 3.82/4.09 thf(fact_6678_gbinomial__0_I2_J,axiom,
% 3.82/4.09 ! [K: nat] :
% 3.82/4.09 ( ( gbinomial_real @ zero_zero_real @ ( suc @ K ) )
% 3.82/4.09 = zero_zero_real ) ).
% 3.82/4.09
% 3.82/4.09 % gbinomial_0(2)
% 3.82/4.09 thf(fact_6679_gbinomial__0_I2_J,axiom,
% 3.82/4.09 ! [K: nat] :
% 3.82/4.09 ( ( gbinomial_int @ zero_zero_int @ ( suc @ K ) )
% 3.82/4.09 = zero_zero_int ) ).
% 3.82/4.09
% 3.82/4.09 % gbinomial_0(2)
% 3.82/4.09 thf(fact_6680_gbinomial__0_I2_J,axiom,
% 3.82/4.09 ! [K: nat] :
% 3.82/4.09 ( ( gbinomial_complex @ zero_zero_complex @ ( suc @ K ) )
% 3.82/4.09 = zero_zero_complex ) ).
% 3.82/4.09
% 3.82/4.09 % gbinomial_0(2)
% 3.82/4.09 thf(fact_6681_binomial__0__Suc,axiom,
% 3.82/4.09 ! [K: nat] :
% 3.82/4.09 ( ( binomial @ zero_zero_nat @ ( suc @ K ) )
% 3.82/4.09 = zero_zero_nat ) ).
% 3.82/4.09
% 3.82/4.09 % binomial_0_Suc
% 3.82/4.09 thf(fact_6682_binomial__1,axiom,
% 3.82/4.09 ! [N2: nat] :
% 3.82/4.09 ( ( binomial @ N2 @ ( suc @ zero_zero_nat ) )
% 3.82/4.09 = N2 ) ).
% 3.82/4.09
% 3.82/4.09 % binomial_1
% 3.82/4.09 thf(fact_6683_binomial__eq__0__iff,axiom,
% 3.82/4.09 ! [N2: nat,K: nat] :
% 3.82/4.09 ( ( ( binomial @ N2 @ K )
% 3.82/4.09 = zero_zero_nat )
% 3.82/4.09 = ( ord_less_nat @ N2 @ K ) ) ).
% 3.82/4.09
% 3.82/4.09 % binomial_eq_0_iff
% 3.82/4.09 thf(fact_6684_gbinomial__0_I1_J,axiom,
% 3.82/4.09 ! [A: nat] :
% 3.82/4.09 ( ( gbinomial_nat @ A @ zero_zero_nat )
% 3.82/4.09 = one_one_nat ) ).
% 3.82/4.09
% 3.82/4.09 % gbinomial_0(1)
% 3.82/4.09 thf(fact_6685_gbinomial__0_I1_J,axiom,
% 3.82/4.09 ! [A: int] :
% 3.82/4.09 ( ( gbinomial_int @ A @ zero_zero_nat )
% 3.82/4.09 = one_one_int ) ).
% 3.82/4.09
% 3.82/4.09 % gbinomial_0(1)
% 3.82/4.09 thf(fact_6686_gbinomial__0_I1_J,axiom,
% 3.82/4.09 ! [A: complex] :
% 3.82/4.09 ( ( gbinomial_complex @ A @ zero_zero_nat )
% 3.82/4.09 = one_one_complex ) ).
% 3.82/4.09
% 3.82/4.09 % gbinomial_0(1)
% 3.82/4.09 thf(fact_6687_gbinomial__0_I1_J,axiom,
% 3.82/4.09 ! [A: real] :
% 3.82/4.09 ( ( gbinomial_real @ A @ zero_zero_nat )
% 3.82/4.09 = one_one_real ) ).
% 3.82/4.09
% 3.82/4.09 % gbinomial_0(1)
% 3.82/4.09 thf(fact_6688_of__real__add,axiom,
% 3.82/4.09 ! [X: real,Y: real] :
% 3.82/4.09 ( ( real_V1803761363581548252l_real @ ( plus_plus_real @ X @ Y ) )
% 3.82/4.09 = ( plus_plus_real @ ( real_V1803761363581548252l_real @ X ) @ ( real_V1803761363581548252l_real @ Y ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % of_real_add
% 3.82/4.09 thf(fact_6689_of__real__add,axiom,
% 3.82/4.09 ! [X: real,Y: real] :
% 3.82/4.09 ( ( real_V4546457046886955230omplex @ ( plus_plus_real @ X @ Y ) )
% 3.82/4.09 = ( plus_plus_complex @ ( real_V4546457046886955230omplex @ X ) @ ( real_V4546457046886955230omplex @ Y ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % of_real_add
% 3.82/4.09 thf(fact_6690_binomial__Suc__Suc,axiom,
% 3.82/4.09 ! [N2: nat,K: nat] :
% 3.82/4.09 ( ( binomial @ ( suc @ N2 ) @ ( suc @ K ) )
% 3.82/4.09 = ( plus_plus_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ ( suc @ K ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % binomial_Suc_Suc
% 3.82/4.09 thf(fact_6691_binomial__n__0,axiom,
% 3.82/4.09 ! [N2: nat] :
% 3.82/4.09 ( ( binomial @ N2 @ zero_zero_nat )
% 3.82/4.09 = one_one_nat ) ).
% 3.82/4.09
% 3.82/4.09 % binomial_n_0
% 3.82/4.09 thf(fact_6692_zero__less__binomial__iff,axiom,
% 3.82/4.09 ! [N2: nat,K: nat] :
% 3.82/4.09 ( ( ord_less_nat @ zero_zero_nat @ ( binomial @ N2 @ K ) )
% 3.82/4.09 = ( ord_less_eq_nat @ K @ N2 ) ) ).
% 3.82/4.09
% 3.82/4.09 % zero_less_binomial_iff
% 3.82/4.09 thf(fact_6693_zero__le__floor,axiom,
% 3.82/4.09 ! [X: real] :
% 3.82/4.09 ( ( ord_less_eq_int @ zero_zero_int @ ( archim6058952711729229775r_real @ X ) )
% 3.82/4.09 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 3.82/4.09
% 3.82/4.09 % zero_le_floor
% 3.82/4.09 thf(fact_6694_floor__less__zero,axiom,
% 3.82/4.09 ! [X: real] :
% 3.82/4.09 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X ) @ zero_zero_int )
% 3.82/4.09 = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 3.82/4.09
% 3.82/4.09 % floor_less_zero
% 3.82/4.09 thf(fact_6695_numeral__le__floor,axiom,
% 3.82/4.09 ! [V: num,X: real] :
% 3.82/4.09 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim6058952711729229775r_real @ X ) )
% 3.82/4.09 = ( ord_less_eq_real @ ( numeral_numeral_real @ V ) @ X ) ) ).
% 3.82/4.09
% 3.82/4.09 % numeral_le_floor
% 3.82/4.09 thf(fact_6696_zero__less__floor,axiom,
% 3.82/4.09 ! [X: real] :
% 3.82/4.09 ( ( ord_less_int @ zero_zero_int @ ( archim6058952711729229775r_real @ X ) )
% 3.82/4.09 = ( ord_less_eq_real @ one_one_real @ X ) ) ).
% 3.82/4.09
% 3.82/4.09 % zero_less_floor
% 3.82/4.09 thf(fact_6697_floor__le__zero,axiom,
% 3.82/4.09 ! [X: real] :
% 3.82/4.09 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ zero_zero_int )
% 3.82/4.09 = ( ord_less_real @ X @ one_one_real ) ) ).
% 3.82/4.09
% 3.82/4.09 % floor_le_zero
% 3.82/4.09 thf(fact_6698_floor__less__numeral,axiom,
% 3.82/4.09 ! [X: real,V: num] :
% 3.82/4.09 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X ) @ ( numeral_numeral_int @ V ) )
% 3.82/4.09 = ( ord_less_real @ X @ ( numeral_numeral_real @ V ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % floor_less_numeral
% 3.82/4.09 thf(fact_6699_one__le__floor,axiom,
% 3.82/4.09 ! [X: real] :
% 3.82/4.09 ( ( ord_less_eq_int @ one_one_int @ ( archim6058952711729229775r_real @ X ) )
% 3.82/4.09 = ( ord_less_eq_real @ one_one_real @ X ) ) ).
% 3.82/4.09
% 3.82/4.09 % one_le_floor
% 3.82/4.09 thf(fact_6700_floor__less__one,axiom,
% 3.82/4.09 ! [X: real] :
% 3.82/4.09 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X ) @ one_one_int )
% 3.82/4.09 = ( ord_less_real @ X @ one_one_real ) ) ).
% 3.82/4.09
% 3.82/4.09 % floor_less_one
% 3.82/4.09 thf(fact_6701_powser__zero,axiom,
% 3.82/4.09 ! [F: nat > real] :
% 3.82/4.09 ( ( suminf_real
% 3.82/4.09 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ zero_zero_real @ N ) ) )
% 3.82/4.09 = ( F @ zero_zero_nat ) ) ).
% 3.82/4.09
% 3.82/4.09 % powser_zero
% 3.82/4.09 thf(fact_6702_powser__zero,axiom,
% 3.82/4.09 ! [F: nat > complex] :
% 3.82/4.09 ( ( suminf_complex
% 3.82/4.09 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ zero_zero_complex @ N ) ) )
% 3.82/4.09 = ( F @ zero_zero_nat ) ) ).
% 3.82/4.09
% 3.82/4.09 % powser_zero
% 3.82/4.09 thf(fact_6703_numeral__less__floor,axiom,
% 3.82/4.09 ! [V: num,X: real] :
% 3.82/4.09 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim6058952711729229775r_real @ X ) )
% 3.82/4.09 = ( ord_less_eq_real @ ( plus_plus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) @ X ) ) ).
% 3.82/4.09
% 3.82/4.09 % numeral_less_floor
% 3.82/4.09 thf(fact_6704_floor__le__numeral,axiom,
% 3.82/4.09 ! [X: real,V: num] :
% 3.82/4.09 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ ( numeral_numeral_int @ V ) )
% 3.82/4.09 = ( ord_less_real @ X @ ( plus_plus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % floor_le_numeral
% 3.82/4.09 thf(fact_6705_one__less__floor,axiom,
% 3.82/4.09 ! [X: real] :
% 3.82/4.09 ( ( ord_less_int @ one_one_int @ ( archim6058952711729229775r_real @ X ) )
% 3.82/4.09 = ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) ).
% 3.82/4.09
% 3.82/4.09 % one_less_floor
% 3.82/4.09 thf(fact_6706_floor__le__one,axiom,
% 3.82/4.09 ! [X: real] :
% 3.82/4.09 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ one_one_int )
% 3.82/4.09 = ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % floor_le_one
% 3.82/4.09 thf(fact_6707_neg__numeral__le__floor,axiom,
% 3.82/4.09 ! [V: num,X: real] :
% 3.82/4.09 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim6058952711729229775r_real @ X ) )
% 3.82/4.09 = ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ X ) ) ).
% 3.82/4.09
% 3.82/4.09 % neg_numeral_le_floor
% 3.82/4.09 thf(fact_6708_floor__less__neg__numeral,axiom,
% 3.82/4.09 ! [X: real,V: num] :
% 3.82/4.09 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 3.82/4.09 = ( ord_less_real @ X @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % floor_less_neg_numeral
% 3.82/4.09 thf(fact_6709_neg__numeral__less__floor,axiom,
% 3.82/4.09 ! [V: num,X: real] :
% 3.82/4.09 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim6058952711729229775r_real @ X ) )
% 3.82/4.09 = ( ord_less_eq_real @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) @ X ) ) ).
% 3.82/4.09
% 3.82/4.09 % neg_numeral_less_floor
% 3.82/4.09 thf(fact_6710_floor__le__neg__numeral,axiom,
% 3.82/4.09 ! [X: real,V: num] :
% 3.82/4.09 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 3.82/4.09 = ( ord_less_real @ X @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % floor_le_neg_numeral
% 3.82/4.09 thf(fact_6711_floor__mono,axiom,
% 3.82/4.09 ! [X: real,Y: real] :
% 3.82/4.09 ( ( ord_less_eq_real @ X @ Y )
% 3.82/4.09 => ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ ( archim6058952711729229775r_real @ Y ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % floor_mono
% 3.82/4.09 thf(fact_6712_binomial__eq__0,axiom,
% 3.82/4.09 ! [N2: nat,K: nat] :
% 3.82/4.09 ( ( ord_less_nat @ N2 @ K )
% 3.82/4.09 => ( ( binomial @ N2 @ K )
% 3.82/4.09 = zero_zero_nat ) ) ).
% 3.82/4.09
% 3.82/4.09 % binomial_eq_0
% 3.82/4.09 thf(fact_6713_of__int__floor__le,axiom,
% 3.82/4.09 ! [X: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X ) ) @ X ) ).
% 3.82/4.09
% 3.82/4.09 % of_int_floor_le
% 3.82/4.09 thf(fact_6714_floor__less__cancel,axiom,
% 3.82/4.09 ! [X: real,Y: real] :
% 3.82/4.09 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X ) @ ( archim6058952711729229775r_real @ Y ) )
% 3.82/4.09 => ( ord_less_real @ X @ Y ) ) ).
% 3.82/4.09
% 3.82/4.09 % floor_less_cancel
% 3.82/4.09 thf(fact_6715_Suc__times__binomial,axiom,
% 3.82/4.09 ! [K: nat,N2: nat] :
% 3.82/4.09 ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ ( suc @ N2 ) @ ( suc @ K ) ) )
% 3.82/4.09 = ( times_times_nat @ ( suc @ N2 ) @ ( binomial @ N2 @ K ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % Suc_times_binomial
% 3.82/4.09 thf(fact_6716_Suc__times__binomial__eq,axiom,
% 3.82/4.09 ! [N2: nat,K: nat] :
% 3.82/4.09 ( ( times_times_nat @ ( suc @ N2 ) @ ( binomial @ N2 @ K ) )
% 3.82/4.09 = ( times_times_nat @ ( binomial @ ( suc @ N2 ) @ ( suc @ K ) ) @ ( suc @ K ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % Suc_times_binomial_eq
% 3.82/4.09 thf(fact_6717_binomial__symmetric,axiom,
% 3.82/4.09 ! [K: nat,N2: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ K @ N2 )
% 3.82/4.09 => ( ( binomial @ N2 @ K )
% 3.82/4.09 = ( binomial @ N2 @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % binomial_symmetric
% 3.82/4.09 thf(fact_6718_choose__mult__lemma,axiom,
% 3.82/4.09 ! [M2: nat,R2: nat,K: nat] :
% 3.82/4.09 ( ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M2 @ R2 ) @ K ) @ ( plus_plus_nat @ M2 @ K ) ) @ ( binomial @ ( plus_plus_nat @ M2 @ K ) @ K ) )
% 3.82/4.09 = ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M2 @ R2 ) @ K ) @ K ) @ ( binomial @ ( plus_plus_nat @ M2 @ R2 ) @ M2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % choose_mult_lemma
% 3.82/4.09 thf(fact_6719_binomial__le__pow,axiom,
% 3.82/4.09 ! [R2: nat,N2: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ R2 @ N2 )
% 3.82/4.09 => ( ord_less_eq_nat @ ( binomial @ N2 @ R2 ) @ ( power_power_nat @ N2 @ R2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % binomial_le_pow
% 3.82/4.09 thf(fact_6720_zero__less__binomial,axiom,
% 3.82/4.09 ! [K: nat,N2: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ K @ N2 )
% 3.82/4.09 => ( ord_less_nat @ zero_zero_nat @ ( binomial @ N2 @ K ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % zero_less_binomial
% 3.82/4.09 thf(fact_6721_le__floor__iff,axiom,
% 3.82/4.09 ! [Z3: int,X: real] :
% 3.82/4.09 ( ( ord_less_eq_int @ Z3 @ ( archim6058952711729229775r_real @ X ) )
% 3.82/4.09 = ( ord_less_eq_real @ ( ring_1_of_int_real @ Z3 ) @ X ) ) ).
% 3.82/4.09
% 3.82/4.09 % le_floor_iff
% 3.82/4.09 thf(fact_6722_floor__less__iff,axiom,
% 3.82/4.09 ! [X: real,Z3: int] :
% 3.82/4.09 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X ) @ Z3 )
% 3.82/4.09 = ( ord_less_real @ X @ ( ring_1_of_int_real @ Z3 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % floor_less_iff
% 3.82/4.09 thf(fact_6723_Suc__times__binomial__add,axiom,
% 3.82/4.09 ! [A: nat,B2: nat] :
% 3.82/4.09 ( ( times_times_nat @ ( suc @ A ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B2 ) ) @ ( suc @ A ) ) )
% 3.82/4.09 = ( times_times_nat @ ( suc @ B2 ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B2 ) ) @ A ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % Suc_times_binomial_add
% 3.82/4.09 thf(fact_6724_le__floor__add,axiom,
% 3.82/4.09 ! [X: real,Y: real] : ( ord_less_eq_int @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X ) @ ( archim6058952711729229775r_real @ Y ) ) @ ( archim6058952711729229775r_real @ ( plus_plus_real @ X @ Y ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % le_floor_add
% 3.82/4.09 thf(fact_6725_int__add__floor,axiom,
% 3.82/4.09 ! [Z3: int,X: real] :
% 3.82/4.09 ( ( plus_plus_int @ Z3 @ ( archim6058952711729229775r_real @ X ) )
% 3.82/4.09 = ( archim6058952711729229775r_real @ ( plus_plus_real @ ( ring_1_of_int_real @ Z3 ) @ X ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % int_add_floor
% 3.82/4.09 thf(fact_6726_floor__add__int,axiom,
% 3.82/4.09 ! [X: real,Z3: int] :
% 3.82/4.09 ( ( plus_plus_int @ ( archim6058952711729229775r_real @ X ) @ Z3 )
% 3.82/4.09 = ( archim6058952711729229775r_real @ ( plus_plus_real @ X @ ( ring_1_of_int_real @ Z3 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % floor_add_int
% 3.82/4.09 thf(fact_6727_choose__mult,axiom,
% 3.82/4.09 ! [K: nat,M2: nat,N2: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ K @ M2 )
% 3.82/4.09 => ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.09 => ( ( times_times_nat @ ( binomial @ N2 @ M2 ) @ ( binomial @ M2 @ K ) )
% 3.82/4.09 = ( times_times_nat @ ( binomial @ N2 @ K ) @ ( binomial @ ( minus_minus_nat @ N2 @ K ) @ ( minus_minus_nat @ M2 @ K ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % choose_mult
% 3.82/4.09 thf(fact_6728_binomial__Suc__Suc__eq__times,axiom,
% 3.82/4.09 ! [N2: nat,K: nat] :
% 3.82/4.09 ( ( binomial @ ( suc @ N2 ) @ ( suc @ K ) )
% 3.82/4.09 = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N2 ) @ ( binomial @ N2 @ K ) ) @ ( suc @ K ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % binomial_Suc_Suc_eq_times
% 3.82/4.09 thf(fact_6729_gbinomial__Suc__Suc,axiom,
% 3.82/4.09 ! [A: complex,K: nat] :
% 3.82/4.09 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 3.82/4.09 = ( plus_plus_complex @ ( gbinomial_complex @ A @ K ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % gbinomial_Suc_Suc
% 3.82/4.09 thf(fact_6730_gbinomial__Suc__Suc,axiom,
% 3.82/4.09 ! [A: real,K: nat] :
% 3.82/4.09 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 3.82/4.09 = ( plus_plus_real @ ( gbinomial_real @ A @ K ) @ ( gbinomial_real @ A @ ( suc @ K ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % gbinomial_Suc_Suc
% 3.82/4.09 thf(fact_6731_gbinomial__of__nat__symmetric,axiom,
% 3.82/4.09 ! [K: nat,N2: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ K @ N2 )
% 3.82/4.09 => ( ( gbinomial_real @ ( semiri5074537144036343181t_real @ N2 ) @ K )
% 3.82/4.09 = ( gbinomial_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % gbinomial_of_nat_symmetric
% 3.82/4.09 thf(fact_6732_suminf__finite,axiom,
% 3.82/4.09 ! [N6: set_nat,F: nat > int] :
% 3.82/4.09 ( ( finite_finite_nat @ N6 )
% 3.82/4.09 => ( ! [N3: nat] :
% 3.82/4.09 ( ~ ( member_nat @ N3 @ N6 )
% 3.82/4.09 => ( ( F @ N3 )
% 3.82/4.09 = zero_zero_int ) )
% 3.82/4.09 => ( ( suminf_int @ F )
% 3.82/4.09 = ( groups3539618377306564664at_int @ F @ N6 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % suminf_finite
% 3.82/4.09 thf(fact_6733_suminf__finite,axiom,
% 3.82/4.09 ! [N6: set_nat,F: nat > complex] :
% 3.82/4.09 ( ( finite_finite_nat @ N6 )
% 3.82/4.09 => ( ! [N3: nat] :
% 3.82/4.09 ( ~ ( member_nat @ N3 @ N6 )
% 3.82/4.09 => ( ( F @ N3 )
% 3.82/4.09 = zero_zero_complex ) )
% 3.82/4.09 => ( ( suminf_complex @ F )
% 3.82/4.09 = ( groups2073611262835488442omplex @ F @ N6 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % suminf_finite
% 3.82/4.09 thf(fact_6734_suminf__finite,axiom,
% 3.82/4.09 ! [N6: set_nat,F: nat > nat] :
% 3.82/4.09 ( ( finite_finite_nat @ N6 )
% 3.82/4.09 => ( ! [N3: nat] :
% 3.82/4.09 ( ~ ( member_nat @ N3 @ N6 )
% 3.82/4.09 => ( ( F @ N3 )
% 3.82/4.09 = zero_zero_nat ) )
% 3.82/4.09 => ( ( suminf_nat @ F )
% 3.82/4.09 = ( groups3542108847815614940at_nat @ F @ N6 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % suminf_finite
% 3.82/4.09 thf(fact_6735_suminf__finite,axiom,
% 3.82/4.09 ! [N6: set_nat,F: nat > real] :
% 3.82/4.09 ( ( finite_finite_nat @ N6 )
% 3.82/4.09 => ( ! [N3: nat] :
% 3.82/4.09 ( ~ ( member_nat @ N3 @ N6 )
% 3.82/4.09 => ( ( F @ N3 )
% 3.82/4.09 = zero_zero_real ) )
% 3.82/4.09 => ( ( suminf_real @ F )
% 3.82/4.09 = ( groups6591440286371151544t_real @ F @ N6 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % suminf_finite
% 3.82/4.09 thf(fact_6736_norm__less__p1,axiom,
% 3.82/4.09 ! [X: real] : ( ord_less_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ ( real_V1803761363581548252l_real @ ( real_V7735802525324610683m_real @ X ) ) @ one_one_real ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % norm_less_p1
% 3.82/4.09 thf(fact_6737_norm__less__p1,axiom,
% 3.82/4.09 ! [X: complex] : ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( real_V1022390504157884413omplex @ X ) ) @ one_one_complex ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % norm_less_p1
% 3.82/4.09 thf(fact_6738_one__add__floor,axiom,
% 3.82/4.09 ! [X: real] :
% 3.82/4.09 ( ( plus_plus_int @ ( archim6058952711729229775r_real @ X ) @ one_one_int )
% 3.82/4.09 = ( archim6058952711729229775r_real @ ( plus_plus_real @ X @ one_one_real ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % one_add_floor
% 3.82/4.09 thf(fact_6739_binomial__absorption,axiom,
% 3.82/4.09 ! [K: nat,N2: nat] :
% 3.82/4.09 ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ N2 @ ( suc @ K ) ) )
% 3.82/4.09 = ( times_times_nat @ N2 @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ K ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % binomial_absorption
% 3.82/4.09 thf(fact_6740_gbinomial__addition__formula,axiom,
% 3.82/4.09 ! [A: complex,K: nat] :
% 3.82/4.09 ( ( gbinomial_complex @ A @ ( suc @ K ) )
% 3.82/4.09 = ( plus_plus_complex @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( suc @ K ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % gbinomial_addition_formula
% 3.82/4.09 thf(fact_6741_gbinomial__addition__formula,axiom,
% 3.82/4.09 ! [A: real,K: nat] :
% 3.82/4.09 ( ( gbinomial_real @ A @ ( suc @ K ) )
% 3.82/4.09 = ( plus_plus_real @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ ( suc @ K ) ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % gbinomial_addition_formula
% 3.82/4.09 thf(fact_6742_gbinomial__ge__n__over__k__pow__k,axiom,
% 3.82/4.09 ! [K: nat,A: real] :
% 3.82/4.09 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ K ) @ A )
% 3.82/4.09 => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ K ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % gbinomial_ge_n_over_k_pow_k
% 3.82/4.09 thf(fact_6743_gbinomial__mult__1_H,axiom,
% 3.82/4.09 ! [A: complex,K: nat] :
% 3.82/4.09 ( ( times_times_complex @ ( gbinomial_complex @ A @ K ) @ A )
% 3.82/4.09 = ( plus_plus_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ K ) @ ( gbinomial_complex @ A @ K ) ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % gbinomial_mult_1'
% 3.82/4.09 thf(fact_6744_gbinomial__mult__1_H,axiom,
% 3.82/4.09 ! [A: real,K: nat] :
% 3.82/4.09 ( ( times_times_real @ ( gbinomial_real @ A @ K ) @ A )
% 3.82/4.09 = ( 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 ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % gbinomial_mult_1'
% 3.82/4.09 thf(fact_6745_gbinomial__mult__1,axiom,
% 3.82/4.09 ! [A: complex,K: nat] :
% 3.82/4.09 ( ( times_times_complex @ A @ ( gbinomial_complex @ A @ K ) )
% 3.82/4.09 = ( plus_plus_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ K ) @ ( gbinomial_complex @ A @ K ) ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % gbinomial_mult_1
% 3.82/4.09 thf(fact_6746_gbinomial__mult__1,axiom,
% 3.82/4.09 ! [A: real,K: nat] :
% 3.82/4.09 ( ( times_times_real @ A @ ( gbinomial_real @ A @ K ) )
% 3.82/4.09 = ( 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 ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % gbinomial_mult_1
% 3.82/4.09 thf(fact_6747_floor__split,axiom,
% 3.82/4.09 ! [P: int > $o,T: real] :
% 3.82/4.09 ( ( P @ ( archim6058952711729229775r_real @ T ) )
% 3.82/4.09 = ( ! [I3: int] :
% 3.82/4.09 ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ I3 ) @ T )
% 3.82/4.09 & ( ord_less_real @ T @ ( plus_plus_real @ ( ring_1_of_int_real @ I3 ) @ one_one_real ) ) )
% 3.82/4.09 => ( P @ I3 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % floor_split
% 3.82/4.09 thf(fact_6748_floor__eq__iff,axiom,
% 3.82/4.09 ! [X: real,A: int] :
% 3.82/4.09 ( ( ( archim6058952711729229775r_real @ X )
% 3.82/4.09 = A )
% 3.82/4.09 = ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ X )
% 3.82/4.09 & ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ A ) @ one_one_real ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % floor_eq_iff
% 3.82/4.09 thf(fact_6749_floor__unique,axiom,
% 3.82/4.09 ! [Z3: int,X: real] :
% 3.82/4.09 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z3 ) @ X )
% 3.82/4.09 => ( ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ Z3 ) @ one_one_real ) )
% 3.82/4.09 => ( ( archim6058952711729229775r_real @ X )
% 3.82/4.09 = Z3 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % floor_unique
% 3.82/4.09 thf(fact_6750_binomial__ge__n__over__k__pow__k,axiom,
% 3.82/4.09 ! [K: nat,N2: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ K @ N2 )
% 3.82/4.09 => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ K ) ) @ K ) @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ K ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % binomial_ge_n_over_k_pow_k
% 3.82/4.09 thf(fact_6751_le__mult__floor,axiom,
% 3.82/4.09 ! [A: real,B2: real] :
% 3.82/4.09 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 3.82/4.09 => ( ( ord_less_eq_real @ zero_zero_real @ B2 )
% 3.82/4.09 => ( ord_less_eq_int @ ( times_times_int @ ( archim6058952711729229775r_real @ A ) @ ( archim6058952711729229775r_real @ B2 ) ) @ ( archim6058952711729229775r_real @ ( times_times_real @ A @ B2 ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % le_mult_floor
% 3.82/4.09 thf(fact_6752_less__floor__iff,axiom,
% 3.82/4.09 ! [Z3: int,X: real] :
% 3.82/4.09 ( ( ord_less_int @ Z3 @ ( archim6058952711729229775r_real @ X ) )
% 3.82/4.09 = ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ Z3 ) @ one_one_real ) @ X ) ) ).
% 3.82/4.09
% 3.82/4.09 % less_floor_iff
% 3.82/4.09 thf(fact_6753_floor__le__iff,axiom,
% 3.82/4.09 ! [X: real,Z3: int] :
% 3.82/4.09 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ Z3 )
% 3.82/4.09 = ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ Z3 ) @ one_one_real ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % floor_le_iff
% 3.82/4.09 thf(fact_6754_binomial__mono,axiom,
% 3.82/4.09 ! [K: nat,K6: nat,N2: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ K @ K6 )
% 3.82/4.09 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N2 )
% 3.82/4.09 => ( ord_less_eq_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ K6 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % binomial_mono
% 3.82/4.09 thf(fact_6755_binomial__maximum_H,axiom,
% 3.82/4.09 ! [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 ) ) ).
% 3.82/4.09
% 3.82/4.09 % binomial_maximum'
% 3.82/4.09 thf(fact_6756_binomial__maximum,axiom,
% 3.82/4.09 ! [N2: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % binomial_maximum
% 3.82/4.09 thf(fact_6757_binomial__antimono,axiom,
% 3.82/4.09 ! [K: nat,K6: nat,N2: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ K @ K6 )
% 3.82/4.09 => ( ( ord_less_eq_nat @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ K )
% 3.82/4.09 => ( ( ord_less_eq_nat @ K6 @ N2 )
% 3.82/4.09 => ( ord_less_eq_nat @ ( binomial @ N2 @ K6 ) @ ( binomial @ N2 @ K ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % binomial_antimono
% 3.82/4.09 thf(fact_6758_binomial__le__pow2,axiom,
% 3.82/4.09 ! [N2: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N2 @ K ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 3.82/4.09
% 3.82/4.09 % binomial_le_pow2
% 3.82/4.09 thf(fact_6759_floor__correct,axiom,
% 3.82/4.09 ! [X: real] :
% 3.82/4.09 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X ) ) @ X )
% 3.82/4.09 & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X ) @ one_one_int ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % floor_correct
% 3.82/4.09 thf(fact_6760_choose__reduce__nat,axiom,
% 3.82/4.09 ! [N2: nat,K: nat] :
% 3.82/4.09 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.09 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 3.82/4.09 => ( ( binomial @ N2 @ K )
% 3.82/4.09 = ( 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 ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % choose_reduce_nat
% 3.82/4.09 thf(fact_6761_times__binomial__minus1__eq,axiom,
% 3.82/4.09 ! [K: nat,N2: nat] :
% 3.82/4.09 ( ( ord_less_nat @ zero_zero_nat @ K )
% 3.82/4.09 => ( ( times_times_nat @ K @ ( binomial @ N2 @ K ) )
% 3.82/4.09 = ( times_times_nat @ N2 @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % times_binomial_minus1_eq
% 3.82/4.09 thf(fact_6762_Suc__times__gbinomial,axiom,
% 3.82/4.09 ! [K: nat,A: complex] :
% 3.82/4.09 ( ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) ) )
% 3.82/4.09 = ( times_times_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( gbinomial_complex @ A @ K ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % Suc_times_gbinomial
% 3.82/4.09 thf(fact_6763_Suc__times__gbinomial,axiom,
% 3.82/4.09 ! [K: nat,A: real] :
% 3.82/4.09 ( ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) ) )
% 3.82/4.09 = ( times_times_real @ ( plus_plus_real @ A @ one_one_real ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % Suc_times_gbinomial
% 3.82/4.09 thf(fact_6764_gbinomial__absorption,axiom,
% 3.82/4.09 ! [K: nat,A: complex] :
% 3.82/4.09 ( ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) )
% 3.82/4.09 = ( times_times_complex @ A @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % gbinomial_absorption
% 3.82/4.09 thf(fact_6765_gbinomial__absorption,axiom,
% 3.82/4.09 ! [K: nat,A: real] :
% 3.82/4.09 ( ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ A @ ( suc @ K ) ) )
% 3.82/4.09 = ( times_times_real @ A @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % gbinomial_absorption
% 3.82/4.09 thf(fact_6766_gbinomial__trinomial__revision,axiom,
% 3.82/4.09 ! [K: nat,M2: nat,A: complex] :
% 3.82/4.09 ( ( ord_less_eq_nat @ K @ M2 )
% 3.82/4.09 => ( ( times_times_complex @ ( gbinomial_complex @ A @ M2 ) @ ( gbinomial_complex @ ( semiri8010041392384452111omplex @ M2 ) @ K ) )
% 3.82/4.09 = ( times_times_complex @ ( gbinomial_complex @ A @ K ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( minus_minus_nat @ M2 @ K ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % gbinomial_trinomial_revision
% 3.82/4.09 thf(fact_6767_gbinomial__trinomial__revision,axiom,
% 3.82/4.09 ! [K: nat,M2: nat,A: real] :
% 3.82/4.09 ( ( ord_less_eq_nat @ K @ M2 )
% 3.82/4.09 => ( ( times_times_real @ ( gbinomial_real @ A @ M2 ) @ ( gbinomial_real @ ( semiri5074537144036343181t_real @ M2 ) @ K ) )
% 3.82/4.09 = ( times_times_real @ ( gbinomial_real @ A @ K ) @ ( gbinomial_real @ ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ ( minus_minus_nat @ M2 @ K ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % gbinomial_trinomial_revision
% 3.82/4.09 thf(fact_6768_floor__divide__lower,axiom,
% 3.82/4.09 ! [Q3: real,P5: real] :
% 3.82/4.09 ( ( ord_less_real @ zero_zero_real @ Q3 )
% 3.82/4.09 => ( ord_less_eq_real @ ( times_times_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ ( divide_divide_real @ P5 @ Q3 ) ) ) @ Q3 ) @ P5 ) ) ).
% 3.82/4.09
% 3.82/4.09 % floor_divide_lower
% 3.82/4.09 thf(fact_6769_binomial__less__binomial__Suc,axiom,
% 3.82/4.09 ! [K: nat,N2: nat] :
% 3.82/4.09 ( ( ord_less_nat @ K @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 3.82/4.09 => ( ord_less_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ ( suc @ K ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % binomial_less_binomial_Suc
% 3.82/4.09 thf(fact_6770_binomial__strict__antimono,axiom,
% 3.82/4.09 ! [K: nat,K6: nat,N2: nat] :
% 3.82/4.09 ( ( ord_less_nat @ K @ K6 )
% 3.82/4.09 => ( ( ord_less_eq_nat @ N2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) )
% 3.82/4.09 => ( ( ord_less_eq_nat @ K6 @ N2 )
% 3.82/4.09 => ( ord_less_nat @ ( binomial @ N2 @ K6 ) @ ( binomial @ N2 @ K ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % binomial_strict_antimono
% 3.82/4.09 thf(fact_6771_binomial__strict__mono,axiom,
% 3.82/4.09 ! [K: nat,K6: nat,N2: nat] :
% 3.82/4.09 ( ( ord_less_nat @ K @ K6 )
% 3.82/4.09 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N2 )
% 3.82/4.09 => ( ord_less_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ K6 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % binomial_strict_mono
% 3.82/4.09 thf(fact_6772_central__binomial__odd,axiom,
% 3.82/4.09 ! [N2: nat] :
% 3.82/4.09 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 3.82/4.09 => ( ( binomial @ N2 @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 3.82/4.09 = ( binomial @ N2 @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % central_binomial_odd
% 3.82/4.09 thf(fact_6773_binomial__addition__formula,axiom,
% 3.82/4.09 ! [N2: nat,K: nat] :
% 3.82/4.09 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.09 => ( ( binomial @ N2 @ ( suc @ K ) )
% 3.82/4.09 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( suc @ K ) ) @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ K ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % binomial_addition_formula
% 3.82/4.09 thf(fact_6774_gbinomial__rec,axiom,
% 3.82/4.09 ! [A: complex,K: nat] :
% 3.82/4.09 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 3.82/4.09 = ( times_times_complex @ ( gbinomial_complex @ A @ K ) @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % gbinomial_rec
% 3.82/4.09 thf(fact_6775_gbinomial__rec,axiom,
% 3.82/4.09 ! [A: real,K: nat] :
% 3.82/4.09 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 3.82/4.09 = ( times_times_real @ ( gbinomial_real @ A @ K ) @ ( divide_divide_real @ ( plus_plus_real @ A @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % gbinomial_rec
% 3.82/4.09 thf(fact_6776_gbinomial__factors,axiom,
% 3.82/4.09 ! [A: complex,K: nat] :
% 3.82/4.09 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 3.82/4.09 = ( times_times_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) ) @ ( gbinomial_complex @ A @ K ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % gbinomial_factors
% 3.82/4.09 thf(fact_6777_gbinomial__factors,axiom,
% 3.82/4.09 ! [A: real,K: nat] :
% 3.82/4.09 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 3.82/4.09 = ( times_times_real @ ( divide_divide_real @ ( plus_plus_real @ A @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % gbinomial_factors
% 3.82/4.09 thf(fact_6778_floor__divide__upper,axiom,
% 3.82/4.09 ! [Q3: real,P5: real] :
% 3.82/4.09 ( ( ord_less_real @ zero_zero_real @ Q3 )
% 3.82/4.09 => ( ord_less_real @ P5 @ ( times_times_real @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ ( divide_divide_real @ P5 @ Q3 ) ) ) @ one_one_real ) @ Q3 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % floor_divide_upper
% 3.82/4.09 thf(fact_6779_round__def,axiom,
% 3.82/4.09 ( archim8280529875227126926d_real
% 3.82/4.09 = ( ^ [X4: real] : ( archim6058952711729229775r_real @ ( plus_plus_real @ X4 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % round_def
% 3.82/4.09 thf(fact_6780_gbinomial__minus,axiom,
% 3.82/4.09 ! [A: complex,K: nat] :
% 3.82/4.09 ( ( gbinomial_complex @ ( uminus1482373934393186551omplex @ A ) @ K )
% 3.82/4.09 = ( 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 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % gbinomial_minus
% 3.82/4.09 thf(fact_6781_gbinomial__minus,axiom,
% 3.82/4.09 ! [A: real,K: nat] :
% 3.82/4.09 ( ( gbinomial_real @ ( uminus_uminus_real @ A ) @ K )
% 3.82/4.09 = ( 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 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % gbinomial_minus
% 3.82/4.09 thf(fact_6782_gbinomial__reduce__nat,axiom,
% 3.82/4.09 ! [K: nat,A: complex] :
% 3.82/4.09 ( ( ord_less_nat @ zero_zero_nat @ K )
% 3.82/4.09 => ( ( gbinomial_complex @ A @ K )
% 3.82/4.09 = ( 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 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % gbinomial_reduce_nat
% 3.82/4.09 thf(fact_6783_gbinomial__reduce__nat,axiom,
% 3.82/4.09 ! [K: nat,A: real] :
% 3.82/4.09 ( ( ord_less_nat @ zero_zero_nat @ K )
% 3.82/4.09 => ( ( gbinomial_real @ A @ K )
% 3.82/4.09 = ( 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 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % gbinomial_reduce_nat
% 3.82/4.09 thf(fact_6784_gbinomial__sum__up__index,axiom,
% 3.82/4.09 ! [K: nat,N2: nat] :
% 3.82/4.09 ( ( groups2073611262835488442omplex
% 3.82/4.09 @ ^ [J2: nat] : ( gbinomial_complex @ ( semiri8010041392384452111omplex @ J2 ) @ K )
% 3.82/4.09 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 3.82/4.09 = ( gbinomial_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N2 ) @ one_one_complex ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % gbinomial_sum_up_index
% 3.82/4.09 thf(fact_6785_gbinomial__sum__up__index,axiom,
% 3.82/4.09 ! [K: nat,N2: nat] :
% 3.82/4.09 ( ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [J2: nat] : ( gbinomial_real @ ( semiri5074537144036343181t_real @ J2 ) @ K )
% 3.82/4.09 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 3.82/4.09 = ( gbinomial_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % gbinomial_sum_up_index
% 3.82/4.09 thf(fact_6786_gbinomial__absorption_H,axiom,
% 3.82/4.09 ! [K: nat,A: complex] :
% 3.82/4.09 ( ( ord_less_nat @ zero_zero_nat @ K )
% 3.82/4.09 => ( ( gbinomial_complex @ A @ K )
% 3.82/4.09 = ( times_times_complex @ ( divide1717551699836669952omplex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % gbinomial_absorption'
% 3.82/4.09 thf(fact_6787_gbinomial__absorption_H,axiom,
% 3.82/4.09 ! [K: nat,A: real] :
% 3.82/4.09 ( ( ord_less_nat @ zero_zero_nat @ K )
% 3.82/4.09 => ( ( gbinomial_real @ A @ K )
% 3.82/4.09 = ( 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 ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % gbinomial_absorption'
% 3.82/4.09 thf(fact_6788_floor__log2__div2,axiom,
% 3.82/4.09 ! [N2: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 3.82/4.09 => ( ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 3.82/4.09 = ( 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 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % floor_log2_div2
% 3.82/4.09 thf(fact_6789_floor__log__nat__eq__if,axiom,
% 3.82/4.09 ! [B2: nat,N2: nat,K: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ ( power_power_nat @ B2 @ N2 ) @ K )
% 3.82/4.09 => ( ( ord_less_nat @ K @ ( power_power_nat @ B2 @ ( plus_plus_nat @ N2 @ one_one_nat ) ) )
% 3.82/4.09 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 )
% 3.82/4.09 => ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B2 ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 3.82/4.09 = ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % floor_log_nat_eq_if
% 3.82/4.09 thf(fact_6790_pi__series,axiom,
% 3.82/4.09 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 3.82/4.09 = ( suminf_real
% 3.82/4.09 @ ^ [K2: nat] : ( divide_divide_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % pi_series
% 3.82/4.09 thf(fact_6791_gbinomial__partial__row__sum,axiom,
% 3.82/4.09 ! [A: complex,M2: nat] :
% 3.82/4.09 ( ( groups2073611262835488442omplex
% 3.82/4.09 @ ^ [K2: nat] : ( times_times_complex @ ( gbinomial_complex @ A @ K2 ) @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( semiri8010041392384452111omplex @ K2 ) ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ M2 ) )
% 3.82/4.09 = ( times_times_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M2 ) @ one_one_complex ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( gbinomial_complex @ A @ ( plus_plus_nat @ M2 @ one_one_nat ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % gbinomial_partial_row_sum
% 3.82/4.09 thf(fact_6792_gbinomial__partial__row__sum,axiom,
% 3.82/4.09 ! [A: real,M2: nat] :
% 3.82/4.09 ( ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [K2: nat] : ( times_times_real @ ( gbinomial_real @ A @ K2 ) @ ( minus_minus_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ K2 ) ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ M2 ) )
% 3.82/4.09 = ( times_times_real @ ( divide_divide_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M2 ) @ one_one_real ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( gbinomial_real @ A @ ( plus_plus_nat @ M2 @ one_one_nat ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % gbinomial_partial_row_sum
% 3.82/4.09 thf(fact_6793_choose__even__sum,axiom,
% 3.82/4.09 ! [N2: nat] :
% 3.82/4.09 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.09 => ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 3.82/4.09 @ ( groups2073611262835488442omplex
% 3.82/4.09 @ ^ [I3: nat] : ( if_complex @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ I3 ) ) @ zero_zero_complex )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) )
% 3.82/4.09 = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % choose_even_sum
% 3.82/4.09 thf(fact_6794_choose__even__sum,axiom,
% 3.82/4.09 ! [N2: nat] :
% 3.82/4.09 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.09 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 3.82/4.09 @ ( groups3539618377306564664at_int
% 3.82/4.09 @ ^ [I3: nat] : ( if_int @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ I3 ) ) @ zero_zero_int )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) )
% 3.82/4.09 = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % choose_even_sum
% 3.82/4.09 thf(fact_6795_choose__even__sum,axiom,
% 3.82/4.09 ! [N2: nat] :
% 3.82/4.09 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.09 => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 3.82/4.09 @ ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [I3: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ I3 ) ) @ zero_zero_real )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) )
% 3.82/4.09 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % choose_even_sum
% 3.82/4.09 thf(fact_6796_choose__odd__sum,axiom,
% 3.82/4.09 ! [N2: nat] :
% 3.82/4.09 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.09 => ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 3.82/4.09 @ ( groups2073611262835488442omplex
% 3.82/4.09 @ ^ [I3: nat] :
% 3.82/4.09 ( if_complex
% 3.82/4.09 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 )
% 3.82/4.09 @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ I3 ) )
% 3.82/4.09 @ zero_zero_complex )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) )
% 3.82/4.09 = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % choose_odd_sum
% 3.82/4.09 thf(fact_6797_choose__odd__sum,axiom,
% 3.82/4.09 ! [N2: nat] :
% 3.82/4.09 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.09 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 3.82/4.09 @ ( groups3539618377306564664at_int
% 3.82/4.09 @ ^ [I3: nat] :
% 3.82/4.09 ( if_int
% 3.82/4.09 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 )
% 3.82/4.09 @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ I3 ) )
% 3.82/4.09 @ zero_zero_int )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) )
% 3.82/4.09 = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % choose_odd_sum
% 3.82/4.09 thf(fact_6798_choose__odd__sum,axiom,
% 3.82/4.09 ! [N2: nat] :
% 3.82/4.09 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.09 => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 3.82/4.09 @ ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [I3: nat] :
% 3.82/4.09 ( if_real
% 3.82/4.09 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 )
% 3.82/4.09 @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ I3 ) )
% 3.82/4.09 @ zero_zero_real )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) )
% 3.82/4.09 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % choose_odd_sum
% 3.82/4.09 thf(fact_6799_round__altdef,axiom,
% 3.82/4.09 ( archim8280529875227126926d_real
% 3.82/4.09 = ( ^ [X4: real] : ( if_int @ ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( archim2898591450579166408c_real @ X4 ) ) @ ( archim7802044766580827645g_real @ X4 ) @ ( archim6058952711729229775r_real @ X4 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % round_altdef
% 3.82/4.09 thf(fact_6800_gbinomial__r__part__sum,axiom,
% 3.82/4.09 ! [M2: nat] :
% 3.82/4.09 ( ( groups2073611262835488442omplex @ ( gbinomial_complex @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M2 ) ) @ one_one_complex ) ) @ ( set_ord_atMost_nat @ M2 ) )
% 3.82/4.09 = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % gbinomial_r_part_sum
% 3.82/4.09 thf(fact_6801_gbinomial__r__part__sum,axiom,
% 3.82/4.09 ! [M2: nat] :
% 3.82/4.09 ( ( groups6591440286371151544t_real @ ( gbinomial_real @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M2 ) ) @ one_one_real ) ) @ ( set_ord_atMost_nat @ M2 ) )
% 3.82/4.09 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % gbinomial_r_part_sum
% 3.82/4.09 thf(fact_6802_atMost__eq__iff,axiom,
% 3.82/4.09 ! [X: nat,Y: nat] :
% 3.82/4.09 ( ( ( set_ord_atMost_nat @ X )
% 3.82/4.09 = ( set_ord_atMost_nat @ Y ) )
% 3.82/4.09 = ( X = Y ) ) ).
% 3.82/4.09
% 3.82/4.09 % atMost_eq_iff
% 3.82/4.09 thf(fact_6803_atMost__eq__iff,axiom,
% 3.82/4.09 ! [X: int,Y: int] :
% 3.82/4.09 ( ( ( set_ord_atMost_int @ X )
% 3.82/4.09 = ( set_ord_atMost_int @ Y ) )
% 3.82/4.09 = ( X = Y ) ) ).
% 3.82/4.09
% 3.82/4.09 % atMost_eq_iff
% 3.82/4.09 thf(fact_6804_atMost__iff,axiom,
% 3.82/4.09 ! [I: extended_enat,K: extended_enat] :
% 3.82/4.09 ( ( member_Extended_enat @ I @ ( set_or8332593352340944941d_enat @ K ) )
% 3.82/4.09 = ( ord_le2932123472753598470d_enat @ I @ K ) ) ).
% 3.82/4.09
% 3.82/4.09 % atMost_iff
% 3.82/4.09 thf(fact_6805_atMost__iff,axiom,
% 3.82/4.09 ! [I: real,K: real] :
% 3.82/4.09 ( ( member_real @ I @ ( set_ord_atMost_real @ K ) )
% 3.82/4.09 = ( ord_less_eq_real @ I @ K ) ) ).
% 3.82/4.09
% 3.82/4.09 % atMost_iff
% 3.82/4.09 thf(fact_6806_atMost__iff,axiom,
% 3.82/4.09 ! [I: set_nat,K: set_nat] :
% 3.82/4.09 ( ( member_set_nat @ I @ ( set_or4236626031148496127et_nat @ K ) )
% 3.82/4.09 = ( ord_less_eq_set_nat @ I @ K ) ) ).
% 3.82/4.09
% 3.82/4.09 % atMost_iff
% 3.82/4.09 thf(fact_6807_atMost__iff,axiom,
% 3.82/4.09 ! [I: set_int,K: set_int] :
% 3.82/4.09 ( ( member_set_int @ I @ ( set_or58775011639299419et_int @ K ) )
% 3.82/4.09 = ( ord_less_eq_set_int @ I @ K ) ) ).
% 3.82/4.09
% 3.82/4.09 % atMost_iff
% 3.82/4.09 thf(fact_6808_atMost__iff,axiom,
% 3.82/4.09 ! [I: nat,K: nat] :
% 3.82/4.09 ( ( member_nat @ I @ ( set_ord_atMost_nat @ K ) )
% 3.82/4.09 = ( ord_less_eq_nat @ I @ K ) ) ).
% 3.82/4.09
% 3.82/4.09 % atMost_iff
% 3.82/4.09 thf(fact_6809_atMost__iff,axiom,
% 3.82/4.09 ! [I: int,K: int] :
% 3.82/4.09 ( ( member_int @ I @ ( set_ord_atMost_int @ K ) )
% 3.82/4.09 = ( ord_less_eq_int @ I @ K ) ) ).
% 3.82/4.09
% 3.82/4.09 % atMost_iff
% 3.82/4.09 thf(fact_6810_finite__atMost,axiom,
% 3.82/4.09 ! [K: nat] : ( finite_finite_nat @ ( set_ord_atMost_nat @ K ) ) ).
% 3.82/4.09
% 3.82/4.09 % finite_atMost
% 3.82/4.09 thf(fact_6811_atMost__subset__iff,axiom,
% 3.82/4.09 ! [X: real,Y: real] :
% 3.82/4.09 ( ( ord_less_eq_set_real @ ( set_ord_atMost_real @ X ) @ ( set_ord_atMost_real @ Y ) )
% 3.82/4.09 = ( ord_less_eq_real @ X @ Y ) ) ).
% 3.82/4.09
% 3.82/4.09 % atMost_subset_iff
% 3.82/4.09 thf(fact_6812_atMost__subset__iff,axiom,
% 3.82/4.09 ! [X: set_nat,Y: set_nat] :
% 3.82/4.09 ( ( ord_le6893508408891458716et_nat @ ( set_or4236626031148496127et_nat @ X ) @ ( set_or4236626031148496127et_nat @ Y ) )
% 3.82/4.09 = ( ord_less_eq_set_nat @ X @ Y ) ) ).
% 3.82/4.09
% 3.82/4.09 % atMost_subset_iff
% 3.82/4.09 thf(fact_6813_atMost__subset__iff,axiom,
% 3.82/4.09 ! [X: set_int,Y: set_int] :
% 3.82/4.09 ( ( ord_le4403425263959731960et_int @ ( set_or58775011639299419et_int @ X ) @ ( set_or58775011639299419et_int @ Y ) )
% 3.82/4.09 = ( ord_less_eq_set_int @ X @ Y ) ) ).
% 3.82/4.09
% 3.82/4.09 % atMost_subset_iff
% 3.82/4.09 thf(fact_6814_atMost__subset__iff,axiom,
% 3.82/4.09 ! [X: nat,Y: nat] :
% 3.82/4.09 ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ X ) @ ( set_ord_atMost_nat @ Y ) )
% 3.82/4.09 = ( ord_less_eq_nat @ X @ Y ) ) ).
% 3.82/4.09
% 3.82/4.09 % atMost_subset_iff
% 3.82/4.09 thf(fact_6815_atMost__subset__iff,axiom,
% 3.82/4.09 ! [X: int,Y: int] :
% 3.82/4.09 ( ( ord_less_eq_set_int @ ( set_ord_atMost_int @ X ) @ ( set_ord_atMost_int @ Y ) )
% 3.82/4.09 = ( ord_less_eq_int @ X @ Y ) ) ).
% 3.82/4.09
% 3.82/4.09 % atMost_subset_iff
% 3.82/4.09 thf(fact_6816_frac__of__int,axiom,
% 3.82/4.09 ! [Z3: int] :
% 3.82/4.09 ( ( archim2898591450579166408c_real @ ( ring_1_of_int_real @ Z3 ) )
% 3.82/4.09 = zero_zero_real ) ).
% 3.82/4.09
% 3.82/4.09 % frac_of_int
% 3.82/4.09 thf(fact_6817_Icc__subset__Iic__iff,axiom,
% 3.82/4.09 ! [L: set_nat,H2: set_nat,H3: set_nat] :
% 3.82/4.09 ( ( ord_le6893508408891458716et_nat @ ( set_or4548717258645045905et_nat @ L @ H2 ) @ ( set_or4236626031148496127et_nat @ H3 ) )
% 3.82/4.09 = ( ~ ( ord_less_eq_set_nat @ L @ H2 )
% 3.82/4.09 | ( ord_less_eq_set_nat @ H2 @ H3 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % Icc_subset_Iic_iff
% 3.82/4.09 thf(fact_6818_Icc__subset__Iic__iff,axiom,
% 3.82/4.09 ! [L: set_int,H2: set_int,H3: set_int] :
% 3.82/4.09 ( ( ord_le4403425263959731960et_int @ ( set_or370866239135849197et_int @ L @ H2 ) @ ( set_or58775011639299419et_int @ H3 ) )
% 3.82/4.09 = ( ~ ( ord_less_eq_set_int @ L @ H2 )
% 3.82/4.09 | ( ord_less_eq_set_int @ H2 @ H3 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % Icc_subset_Iic_iff
% 3.82/4.09 thf(fact_6819_Icc__subset__Iic__iff,axiom,
% 3.82/4.09 ! [L: nat,H2: nat,H3: nat] :
% 3.82/4.09 ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ L @ H2 ) @ ( set_ord_atMost_nat @ H3 ) )
% 3.82/4.09 = ( ~ ( ord_less_eq_nat @ L @ H2 )
% 3.82/4.09 | ( ord_less_eq_nat @ H2 @ H3 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % Icc_subset_Iic_iff
% 3.82/4.09 thf(fact_6820_Icc__subset__Iic__iff,axiom,
% 3.82/4.09 ! [L: int,H2: int,H3: int] :
% 3.82/4.09 ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ L @ H2 ) @ ( set_ord_atMost_int @ H3 ) )
% 3.82/4.09 = ( ~ ( ord_less_eq_int @ L @ H2 )
% 3.82/4.09 | ( ord_less_eq_int @ H2 @ H3 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % Icc_subset_Iic_iff
% 3.82/4.09 thf(fact_6821_Icc__subset__Iic__iff,axiom,
% 3.82/4.09 ! [L: real,H2: real,H3: real] :
% 3.82/4.09 ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ L @ H2 ) @ ( set_ord_atMost_real @ H3 ) )
% 3.82/4.09 = ( ~ ( ord_less_eq_real @ L @ H2 )
% 3.82/4.09 | ( ord_less_eq_real @ H2 @ H3 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % Icc_subset_Iic_iff
% 3.82/4.09 thf(fact_6822_sum_OatMost__Suc,axiom,
% 3.82/4.09 ! [G: nat > int,N2: nat] :
% 3.82/4.09 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 3.82/4.09 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum.atMost_Suc
% 3.82/4.09 thf(fact_6823_sum_OatMost__Suc,axiom,
% 3.82/4.09 ! [G: nat > extended_enat,N2: nat] :
% 3.82/4.09 ( ( groups7108830773950497114d_enat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 3.82/4.09 = ( plus_p3455044024723400733d_enat @ ( groups7108830773950497114d_enat @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum.atMost_Suc
% 3.82/4.09 thf(fact_6824_sum_OatMost__Suc,axiom,
% 3.82/4.09 ! [G: nat > nat,N2: nat] :
% 3.82/4.09 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 3.82/4.09 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum.atMost_Suc
% 3.82/4.09 thf(fact_6825_sum_OatMost__Suc,axiom,
% 3.82/4.09 ! [G: nat > real,N2: nat] :
% 3.82/4.09 ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 3.82/4.09 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum.atMost_Suc
% 3.82/4.09 thf(fact_6826_prod_OatMost__Suc,axiom,
% 3.82/4.09 ! [G: nat > real,N2: nat] :
% 3.82/4.09 ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 3.82/4.09 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.atMost_Suc
% 3.82/4.09 thf(fact_6827_prod_OatMost__Suc,axiom,
% 3.82/4.09 ! [G: nat > complex,N2: nat] :
% 3.82/4.09 ( ( groups6464643781859351333omplex @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 3.82/4.09 = ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.atMost_Suc
% 3.82/4.09 thf(fact_6828_prod_OatMost__Suc,axiom,
% 3.82/4.09 ! [G: nat > extended_enat,N2: nat] :
% 3.82/4.09 ( ( groups7961826882256487087d_enat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 3.82/4.09 = ( times_7803423173614009249d_enat @ ( groups7961826882256487087d_enat @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.atMost_Suc
% 3.82/4.09 thf(fact_6829_prod_OatMost__Suc,axiom,
% 3.82/4.09 ! [G: nat > int,N2: nat] :
% 3.82/4.09 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 3.82/4.09 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.atMost_Suc
% 3.82/4.09 thf(fact_6830_prod_OatMost__Suc,axiom,
% 3.82/4.09 ! [G: nat > nat,N2: nat] :
% 3.82/4.09 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 3.82/4.09 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.atMost_Suc
% 3.82/4.09 thf(fact_6831_atMost__0,axiom,
% 3.82/4.09 ( ( set_ord_atMost_nat @ zero_zero_nat )
% 3.82/4.09 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ).
% 3.82/4.09
% 3.82/4.09 % atMost_0
% 3.82/4.09 thf(fact_6832_not__empty__eq__Iic__eq__empty,axiom,
% 3.82/4.09 ! [H2: extended_enat] :
% 3.82/4.09 ( bot_bo7653980558646680370d_enat
% 3.82/4.09 != ( set_or8332593352340944941d_enat @ H2 ) ) ).
% 3.82/4.09
% 3.82/4.09 % not_empty_eq_Iic_eq_empty
% 3.82/4.09 thf(fact_6833_not__empty__eq__Iic__eq__empty,axiom,
% 3.82/4.09 ! [H2: real] :
% 3.82/4.09 ( bot_bot_set_real
% 3.82/4.09 != ( set_ord_atMost_real @ H2 ) ) ).
% 3.82/4.09
% 3.82/4.09 % not_empty_eq_Iic_eq_empty
% 3.82/4.09 thf(fact_6834_not__empty__eq__Iic__eq__empty,axiom,
% 3.82/4.09 ! [H2: nat] :
% 3.82/4.09 ( bot_bot_set_nat
% 3.82/4.09 != ( set_ord_atMost_nat @ H2 ) ) ).
% 3.82/4.09
% 3.82/4.09 % not_empty_eq_Iic_eq_empty
% 3.82/4.09 thf(fact_6835_not__empty__eq__Iic__eq__empty,axiom,
% 3.82/4.09 ! [H2: int] :
% 3.82/4.09 ( bot_bot_set_int
% 3.82/4.09 != ( set_ord_atMost_int @ H2 ) ) ).
% 3.82/4.09
% 3.82/4.09 % not_empty_eq_Iic_eq_empty
% 3.82/4.09 thf(fact_6836_infinite__Iic,axiom,
% 3.82/4.09 ! [A: int] :
% 3.82/4.09 ~ ( finite_finite_int @ ( set_ord_atMost_int @ A ) ) ).
% 3.82/4.09
% 3.82/4.09 % infinite_Iic
% 3.82/4.09 thf(fact_6837_not__Iic__eq__Icc,axiom,
% 3.82/4.09 ! [H3: int,L: int,H2: int] :
% 3.82/4.09 ( ( set_ord_atMost_int @ H3 )
% 3.82/4.09 != ( set_or1266510415728281911st_int @ L @ H2 ) ) ).
% 3.82/4.09
% 3.82/4.09 % not_Iic_eq_Icc
% 3.82/4.09 thf(fact_6838_not__Iic__eq__Icc,axiom,
% 3.82/4.09 ! [H3: real,L: real,H2: real] :
% 3.82/4.09 ( ( set_ord_atMost_real @ H3 )
% 3.82/4.09 != ( set_or1222579329274155063t_real @ L @ H2 ) ) ).
% 3.82/4.09
% 3.82/4.09 % not_Iic_eq_Icc
% 3.82/4.09 thf(fact_6839_atMost__def,axiom,
% 3.82/4.09 ( set_ord_atMost_real
% 3.82/4.09 = ( ^ [U2: real] :
% 3.82/4.09 ( collect_real
% 3.82/4.09 @ ^ [X4: real] : ( ord_less_eq_real @ X4 @ U2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % atMost_def
% 3.82/4.09 thf(fact_6840_atMost__def,axiom,
% 3.82/4.09 ( set_or4236626031148496127et_nat
% 3.82/4.09 = ( ^ [U2: set_nat] :
% 3.82/4.09 ( collect_set_nat
% 3.82/4.09 @ ^ [X4: set_nat] : ( ord_less_eq_set_nat @ X4 @ U2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % atMost_def
% 3.82/4.09 thf(fact_6841_atMost__def,axiom,
% 3.82/4.09 ( set_or58775011639299419et_int
% 3.82/4.09 = ( ^ [U2: set_int] :
% 3.82/4.09 ( collect_set_int
% 3.82/4.09 @ ^ [X4: set_int] : ( ord_less_eq_set_int @ X4 @ U2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % atMost_def
% 3.82/4.09 thf(fact_6842_atMost__def,axiom,
% 3.82/4.09 ( set_ord_atMost_nat
% 3.82/4.09 = ( ^ [U2: nat] :
% 3.82/4.09 ( collect_nat
% 3.82/4.09 @ ^ [X4: nat] : ( ord_less_eq_nat @ X4 @ U2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % atMost_def
% 3.82/4.09 thf(fact_6843_atMost__def,axiom,
% 3.82/4.09 ( set_ord_atMost_int
% 3.82/4.09 = ( ^ [U2: int] :
% 3.82/4.09 ( collect_int
% 3.82/4.09 @ ^ [X4: int] : ( ord_less_eq_int @ X4 @ U2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % atMost_def
% 3.82/4.09 thf(fact_6844_atMost__atLeast0,axiom,
% 3.82/4.09 ( set_ord_atMost_nat
% 3.82/4.09 = ( set_or1269000886237332187st_nat @ zero_zero_nat ) ) ).
% 3.82/4.09
% 3.82/4.09 % atMost_atLeast0
% 3.82/4.09 thf(fact_6845_lessThan__Suc__atMost,axiom,
% 3.82/4.09 ! [K: nat] :
% 3.82/4.09 ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 3.82/4.09 = ( set_ord_atMost_nat @ K ) ) ).
% 3.82/4.09
% 3.82/4.09 % lessThan_Suc_atMost
% 3.82/4.09 thf(fact_6846_atMost__Suc,axiom,
% 3.82/4.09 ! [K: nat] :
% 3.82/4.09 ( ( set_ord_atMost_nat @ ( suc @ K ) )
% 3.82/4.09 = ( insert_nat @ ( suc @ K ) @ ( set_ord_atMost_nat @ K ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % atMost_Suc
% 3.82/4.09 thf(fact_6847_not__Iic__le__Icc,axiom,
% 3.82/4.09 ! [H2: int,L3: int,H3: int] :
% 3.82/4.09 ~ ( ord_less_eq_set_int @ ( set_ord_atMost_int @ H2 ) @ ( set_or1266510415728281911st_int @ L3 @ H3 ) ) ).
% 3.82/4.09
% 3.82/4.09 % not_Iic_le_Icc
% 3.82/4.09 thf(fact_6848_not__Iic__le__Icc,axiom,
% 3.82/4.09 ! [H2: real,L3: real,H3: real] :
% 3.82/4.09 ~ ( ord_less_eq_set_real @ ( set_ord_atMost_real @ H2 ) @ ( set_or1222579329274155063t_real @ L3 @ H3 ) ) ).
% 3.82/4.09
% 3.82/4.09 % not_Iic_le_Icc
% 3.82/4.09 thf(fact_6849_finite__nat__iff__bounded__le,axiom,
% 3.82/4.09 ( finite_finite_nat
% 3.82/4.09 = ( ^ [S6: set_nat] :
% 3.82/4.09 ? [K2: nat] : ( ord_less_eq_set_nat @ S6 @ ( set_ord_atMost_nat @ K2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % finite_nat_iff_bounded_le
% 3.82/4.09 thf(fact_6850_frac__ge__0,axiom,
% 3.82/4.09 ! [X: real] : ( ord_less_eq_real @ zero_zero_real @ ( archim2898591450579166408c_real @ X ) ) ).
% 3.82/4.09
% 3.82/4.09 % frac_ge_0
% 3.82/4.09 thf(fact_6851_frac__lt__1,axiom,
% 3.82/4.09 ! [X: real] : ( ord_less_real @ ( archim2898591450579166408c_real @ X ) @ one_one_real ) ).
% 3.82/4.09
% 3.82/4.09 % frac_lt_1
% 3.82/4.09 thf(fact_6852_frac__1__eq,axiom,
% 3.82/4.09 ! [X: real] :
% 3.82/4.09 ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X @ one_one_real ) )
% 3.82/4.09 = ( archim2898591450579166408c_real @ X ) ) ).
% 3.82/4.09
% 3.82/4.09 % frac_1_eq
% 3.82/4.09 thf(fact_6853_atMost__nat__numeral,axiom,
% 3.82/4.09 ! [K: num] :
% 3.82/4.09 ( ( set_ord_atMost_nat @ ( numeral_numeral_nat @ K ) )
% 3.82/4.09 = ( insert_nat @ ( numeral_numeral_nat @ K ) @ ( set_ord_atMost_nat @ ( pred_numeral @ K ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % atMost_nat_numeral
% 3.82/4.09 thf(fact_6854_Iic__subset__Iio__iff,axiom,
% 3.82/4.09 ! [A: extended_enat,B2: extended_enat] :
% 3.82/4.09 ( ( ord_le7203529160286727270d_enat @ ( set_or8332593352340944941d_enat @ A ) @ ( set_or8419480210114673929d_enat @ B2 ) )
% 3.82/4.09 = ( ord_le72135733267957522d_enat @ A @ B2 ) ) ).
% 3.82/4.09
% 3.82/4.09 % Iic_subset_Iio_iff
% 3.82/4.09 thf(fact_6855_Iic__subset__Iio__iff,axiom,
% 3.82/4.09 ! [A: real,B2: real] :
% 3.82/4.09 ( ( ord_less_eq_set_real @ ( set_ord_atMost_real @ A ) @ ( set_or5984915006950818249n_real @ B2 ) )
% 3.82/4.09 = ( ord_less_real @ A @ B2 ) ) ).
% 3.82/4.09
% 3.82/4.09 % Iic_subset_Iio_iff
% 3.82/4.09 thf(fact_6856_Iic__subset__Iio__iff,axiom,
% 3.82/4.09 ! [A: nat,B2: nat] :
% 3.82/4.09 ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ A ) @ ( set_ord_lessThan_nat @ B2 ) )
% 3.82/4.09 = ( ord_less_nat @ A @ B2 ) ) ).
% 3.82/4.09
% 3.82/4.09 % Iic_subset_Iio_iff
% 3.82/4.09 thf(fact_6857_Iic__subset__Iio__iff,axiom,
% 3.82/4.09 ! [A: int,B2: int] :
% 3.82/4.09 ( ( ord_less_eq_set_int @ ( set_ord_atMost_int @ A ) @ ( set_ord_lessThan_int @ B2 ) )
% 3.82/4.09 = ( ord_less_int @ A @ B2 ) ) ).
% 3.82/4.09
% 3.82/4.09 % Iic_subset_Iio_iff
% 3.82/4.09 thf(fact_6858_sum__choose__upper,axiom,
% 3.82/4.09 ! [M2: nat,N2: nat] :
% 3.82/4.09 ( ( groups3542108847815614940at_nat
% 3.82/4.09 @ ^ [K2: nat] : ( binomial @ K2 @ M2 )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 = ( binomial @ ( suc @ N2 ) @ ( suc @ M2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum_choose_upper
% 3.82/4.09 thf(fact_6859_sum_OatMost__Suc__shift,axiom,
% 3.82/4.09 ! [G: nat > int,N2: nat] :
% 3.82/4.09 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 3.82/4.09 = ( plus_plus_int @ ( G @ zero_zero_nat )
% 3.82/4.09 @ ( groups3539618377306564664at_int
% 3.82/4.09 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum.atMost_Suc_shift
% 3.82/4.09 thf(fact_6860_sum_OatMost__Suc__shift,axiom,
% 3.82/4.09 ! [G: nat > extended_enat,N2: nat] :
% 3.82/4.09 ( ( groups7108830773950497114d_enat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 3.82/4.09 = ( plus_p3455044024723400733d_enat @ ( G @ zero_zero_nat )
% 3.82/4.09 @ ( groups7108830773950497114d_enat
% 3.82/4.09 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum.atMost_Suc_shift
% 3.82/4.09 thf(fact_6861_sum_OatMost__Suc__shift,axiom,
% 3.82/4.09 ! [G: nat > nat,N2: nat] :
% 3.82/4.09 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 3.82/4.09 = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 3.82/4.09 @ ( groups3542108847815614940at_nat
% 3.82/4.09 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum.atMost_Suc_shift
% 3.82/4.09 thf(fact_6862_sum_OatMost__Suc__shift,axiom,
% 3.82/4.09 ! [G: nat > real,N2: nat] :
% 3.82/4.09 ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 3.82/4.09 = ( plus_plus_real @ ( G @ zero_zero_nat )
% 3.82/4.09 @ ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum.atMost_Suc_shift
% 3.82/4.09 thf(fact_6863_sum__telescope,axiom,
% 3.82/4.09 ! [F: nat > int,I: nat] :
% 3.82/4.09 ( ( groups3539618377306564664at_int
% 3.82/4.09 @ ^ [I3: nat] : ( minus_minus_int @ ( F @ I3 ) @ ( F @ ( suc @ I3 ) ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ I ) )
% 3.82/4.09 = ( minus_minus_int @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum_telescope
% 3.82/4.09 thf(fact_6864_sum__telescope,axiom,
% 3.82/4.09 ! [F: nat > real,I: nat] :
% 3.82/4.09 ( ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [I3: nat] : ( minus_minus_real @ ( F @ I3 ) @ ( F @ ( suc @ I3 ) ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ I ) )
% 3.82/4.09 = ( minus_minus_real @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum_telescope
% 3.82/4.09 thf(fact_6865_polyfun__eq__coeffs,axiom,
% 3.82/4.09 ! [C: nat > complex,N2: nat,D: nat > complex] :
% 3.82/4.09 ( ( ! [X4: complex] :
% 3.82/4.09 ( ( groups2073611262835488442omplex
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ X4 @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 = ( groups2073611262835488442omplex
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_complex @ ( D @ I3 ) @ ( power_power_complex @ X4 @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) ) )
% 3.82/4.09 = ( ! [I3: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ I3 @ N2 )
% 3.82/4.09 => ( ( C @ I3 )
% 3.82/4.09 = ( D @ I3 ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % polyfun_eq_coeffs
% 3.82/4.09 thf(fact_6866_polyfun__eq__coeffs,axiom,
% 3.82/4.09 ! [C: nat > real,N2: nat,D: nat > real] :
% 3.82/4.09 ( ( ! [X4: real] :
% 3.82/4.09 ( ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ X4 @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 = ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_real @ ( D @ I3 ) @ ( power_power_real @ X4 @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) ) )
% 3.82/4.09 = ( ! [I3: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ I3 @ N2 )
% 3.82/4.09 => ( ( C @ I3 )
% 3.82/4.09 = ( D @ I3 ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % polyfun_eq_coeffs
% 3.82/4.09 thf(fact_6867_prod_OatMost__Suc__shift,axiom,
% 3.82/4.09 ! [G: nat > real,N2: nat] :
% 3.82/4.09 ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 3.82/4.09 = ( times_times_real @ ( G @ zero_zero_nat )
% 3.82/4.09 @ ( groups129246275422532515t_real
% 3.82/4.09 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.atMost_Suc_shift
% 3.82/4.09 thf(fact_6868_prod_OatMost__Suc__shift,axiom,
% 3.82/4.09 ! [G: nat > complex,N2: nat] :
% 3.82/4.09 ( ( groups6464643781859351333omplex @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 3.82/4.09 = ( times_times_complex @ ( G @ zero_zero_nat )
% 3.82/4.09 @ ( groups6464643781859351333omplex
% 3.82/4.09 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.atMost_Suc_shift
% 3.82/4.09 thf(fact_6869_prod_OatMost__Suc__shift,axiom,
% 3.82/4.09 ! [G: nat > extended_enat,N2: nat] :
% 3.82/4.09 ( ( groups7961826882256487087d_enat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 3.82/4.09 = ( times_7803423173614009249d_enat @ ( G @ zero_zero_nat )
% 3.82/4.09 @ ( groups7961826882256487087d_enat
% 3.82/4.09 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.atMost_Suc_shift
% 3.82/4.09 thf(fact_6870_prod_OatMost__Suc__shift,axiom,
% 3.82/4.09 ! [G: nat > int,N2: nat] :
% 3.82/4.09 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 3.82/4.09 = ( times_times_int @ ( G @ zero_zero_nat )
% 3.82/4.09 @ ( groups705719431365010083at_int
% 3.82/4.09 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.atMost_Suc_shift
% 3.82/4.09 thf(fact_6871_prod_OatMost__Suc__shift,axiom,
% 3.82/4.09 ! [G: nat > nat,N2: nat] :
% 3.82/4.09 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 3.82/4.09 = ( times_times_nat @ ( G @ zero_zero_nat )
% 3.82/4.09 @ ( groups708209901874060359at_nat
% 3.82/4.09 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.atMost_Suc_shift
% 3.82/4.09 thf(fact_6872_sum_Onested__swap_H,axiom,
% 3.82/4.09 ! [A: nat > nat > nat,N2: nat] :
% 3.82/4.09 ( ( groups3542108847815614940at_nat
% 3.82/4.09 @ ^ [I3: nat] : ( groups3542108847815614940at_nat @ ( A @ I3 ) @ ( set_ord_lessThan_nat @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 = ( groups3542108847815614940at_nat
% 3.82/4.09 @ ^ [J2: nat] :
% 3.82/4.09 ( groups3542108847815614940at_nat
% 3.82/4.09 @ ^ [I3: nat] : ( A @ I3 @ J2 )
% 3.82/4.09 @ ( set_or1269000886237332187st_nat @ ( suc @ J2 ) @ N2 ) )
% 3.82/4.09 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum.nested_swap'
% 3.82/4.09 thf(fact_6873_sum_Onested__swap_H,axiom,
% 3.82/4.09 ! [A: nat > nat > real,N2: nat] :
% 3.82/4.09 ( ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [I3: nat] : ( groups6591440286371151544t_real @ ( A @ I3 ) @ ( set_ord_lessThan_nat @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 = ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [J2: nat] :
% 3.82/4.09 ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [I3: nat] : ( A @ I3 @ J2 )
% 3.82/4.09 @ ( set_or1269000886237332187st_nat @ ( suc @ J2 ) @ N2 ) )
% 3.82/4.09 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum.nested_swap'
% 3.82/4.09 thf(fact_6874_prod_Onested__swap_H,axiom,
% 3.82/4.09 ! [A: nat > nat > int,N2: nat] :
% 3.82/4.09 ( ( groups705719431365010083at_int
% 3.82/4.09 @ ^ [I3: nat] : ( groups705719431365010083at_int @ ( A @ I3 ) @ ( set_ord_lessThan_nat @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 = ( groups705719431365010083at_int
% 3.82/4.09 @ ^ [J2: nat] :
% 3.82/4.09 ( groups705719431365010083at_int
% 3.82/4.09 @ ^ [I3: nat] : ( A @ I3 @ J2 )
% 3.82/4.09 @ ( set_or1269000886237332187st_nat @ ( suc @ J2 ) @ N2 ) )
% 3.82/4.09 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.nested_swap'
% 3.82/4.09 thf(fact_6875_prod_Onested__swap_H,axiom,
% 3.82/4.09 ! [A: nat > nat > nat,N2: nat] :
% 3.82/4.09 ( ( groups708209901874060359at_nat
% 3.82/4.09 @ ^ [I3: nat] : ( groups708209901874060359at_nat @ ( A @ I3 ) @ ( set_ord_lessThan_nat @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 = ( groups708209901874060359at_nat
% 3.82/4.09 @ ^ [J2: nat] :
% 3.82/4.09 ( groups708209901874060359at_nat
% 3.82/4.09 @ ^ [I3: nat] : ( A @ I3 @ J2 )
% 3.82/4.09 @ ( set_or1269000886237332187st_nat @ ( suc @ J2 ) @ N2 ) )
% 3.82/4.09 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.nested_swap'
% 3.82/4.09 thf(fact_6876_sum__choose__lower,axiom,
% 3.82/4.09 ! [R2: nat,N2: nat] :
% 3.82/4.09 ( ( groups3542108847815614940at_nat
% 3.82/4.09 @ ^ [K2: nat] : ( binomial @ ( plus_plus_nat @ R2 @ K2 ) @ K2 )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 = ( binomial @ ( suc @ ( plus_plus_nat @ R2 @ N2 ) ) @ N2 ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum_choose_lower
% 3.82/4.09 thf(fact_6877_choose__rising__sum_I2_J,axiom,
% 3.82/4.09 ! [N2: nat,M2: nat] :
% 3.82/4.09 ( ( groups3542108847815614940at_nat
% 3.82/4.09 @ ^ [J2: nat] : ( binomial @ ( plus_plus_nat @ N2 @ J2 ) @ N2 )
% 3.82/4.09 @ ( set_ord_atMost_nat @ M2 ) )
% 3.82/4.09 = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N2 @ M2 ) @ one_one_nat ) @ M2 ) ) ).
% 3.82/4.09
% 3.82/4.09 % choose_rising_sum(2)
% 3.82/4.09 thf(fact_6878_choose__rising__sum_I1_J,axiom,
% 3.82/4.09 ! [N2: nat,M2: nat] :
% 3.82/4.09 ( ( groups3542108847815614940at_nat
% 3.82/4.09 @ ^ [J2: nat] : ( binomial @ ( plus_plus_nat @ N2 @ J2 ) @ N2 )
% 3.82/4.09 @ ( set_ord_atMost_nat @ M2 ) )
% 3.82/4.09 = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N2 @ M2 ) @ one_one_nat ) @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % choose_rising_sum(1)
% 3.82/4.09 thf(fact_6879_frac__eq,axiom,
% 3.82/4.09 ! [X: real] :
% 3.82/4.09 ( ( ( archim2898591450579166408c_real @ X )
% 3.82/4.09 = X )
% 3.82/4.09 = ( ( ord_less_eq_real @ zero_zero_real @ X )
% 3.82/4.09 & ( ord_less_real @ X @ one_one_real ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % frac_eq
% 3.82/4.09 thf(fact_6880_zero__polynom__imp__zero__coeffs,axiom,
% 3.82/4.09 ! [C: nat > complex,N2: nat,K: nat] :
% 3.82/4.09 ( ! [W: complex] :
% 3.82/4.09 ( ( groups2073611262835488442omplex
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ W @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 = zero_zero_complex )
% 3.82/4.09 => ( ( ord_less_eq_nat @ K @ N2 )
% 3.82/4.09 => ( ( C @ K )
% 3.82/4.09 = zero_zero_complex ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % zero_polynom_imp_zero_coeffs
% 3.82/4.09 thf(fact_6881_zero__polynom__imp__zero__coeffs,axiom,
% 3.82/4.09 ! [C: nat > real,N2: nat,K: nat] :
% 3.82/4.09 ( ! [W: real] :
% 3.82/4.09 ( ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ W @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 = zero_zero_real )
% 3.82/4.09 => ( ( ord_less_eq_nat @ K @ N2 )
% 3.82/4.09 => ( ( C @ K )
% 3.82/4.09 = zero_zero_real ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % zero_polynom_imp_zero_coeffs
% 3.82/4.09 thf(fact_6882_polyfun__eq__0,axiom,
% 3.82/4.09 ! [C: nat > complex,N2: nat] :
% 3.82/4.09 ( ( ! [X4: complex] :
% 3.82/4.09 ( ( groups2073611262835488442omplex
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ X4 @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 = zero_zero_complex ) )
% 3.82/4.09 = ( ! [I3: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ I3 @ N2 )
% 3.82/4.09 => ( ( C @ I3 )
% 3.82/4.09 = zero_zero_complex ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % polyfun_eq_0
% 3.82/4.09 thf(fact_6883_polyfun__eq__0,axiom,
% 3.82/4.09 ! [C: nat > real,N2: nat] :
% 3.82/4.09 ( ( ! [X4: real] :
% 3.82/4.09 ( ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ X4 @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 = zero_zero_real ) )
% 3.82/4.09 = ( ! [I3: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ I3 @ N2 )
% 3.82/4.09 => ( ( C @ I3 )
% 3.82/4.09 = zero_zero_real ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % polyfun_eq_0
% 3.82/4.09 thf(fact_6884_frac__add,axiom,
% 3.82/4.09 ! [X: real,Y: real] :
% 3.82/4.09 ( ( ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y ) ) @ one_one_real )
% 3.82/4.09 => ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X @ Y ) )
% 3.82/4.09 = ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y ) ) ) )
% 3.82/4.09 & ( ~ ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y ) ) @ one_one_real )
% 3.82/4.09 => ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X @ Y ) )
% 3.82/4.09 = ( minus_minus_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y ) ) @ one_one_real ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % frac_add
% 3.82/4.09 thf(fact_6885_sum_OatMost__shift,axiom,
% 3.82/4.09 ! [G: nat > int,N2: nat] :
% 3.82/4.09 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 = ( plus_plus_int @ ( G @ zero_zero_nat )
% 3.82/4.09 @ ( groups3539618377306564664at_int
% 3.82/4.09 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 3.82/4.09 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum.atMost_shift
% 3.82/4.09 thf(fact_6886_sum_OatMost__shift,axiom,
% 3.82/4.09 ! [G: nat > extended_enat,N2: nat] :
% 3.82/4.09 ( ( groups7108830773950497114d_enat @ G @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 = ( plus_p3455044024723400733d_enat @ ( G @ zero_zero_nat )
% 3.82/4.09 @ ( groups7108830773950497114d_enat
% 3.82/4.09 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 3.82/4.09 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum.atMost_shift
% 3.82/4.09 thf(fact_6887_sum_OatMost__shift,axiom,
% 3.82/4.09 ! [G: nat > nat,N2: nat] :
% 3.82/4.09 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 3.82/4.09 @ ( groups3542108847815614940at_nat
% 3.82/4.09 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 3.82/4.09 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum.atMost_shift
% 3.82/4.09 thf(fact_6888_sum_OatMost__shift,axiom,
% 3.82/4.09 ! [G: nat > real,N2: nat] :
% 3.82/4.09 ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 = ( plus_plus_real @ ( G @ zero_zero_nat )
% 3.82/4.09 @ ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 3.82/4.09 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum.atMost_shift
% 3.82/4.09 thf(fact_6889_sum__up__index__split,axiom,
% 3.82/4.09 ! [F: nat > int,M2: nat,N2: nat] :
% 3.82/4.09 ( ( groups3539618377306564664at_int @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M2 @ N2 ) ) )
% 3.82/4.09 = ( plus_plus_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_atMost_nat @ M2 ) ) @ ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( plus_plus_nat @ M2 @ N2 ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum_up_index_split
% 3.82/4.09 thf(fact_6890_sum__up__index__split,axiom,
% 3.82/4.09 ! [F: nat > extended_enat,M2: nat,N2: nat] :
% 3.82/4.09 ( ( groups7108830773950497114d_enat @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M2 @ N2 ) ) )
% 3.82/4.09 = ( plus_p3455044024723400733d_enat @ ( groups7108830773950497114d_enat @ F @ ( set_ord_atMost_nat @ M2 ) ) @ ( groups7108830773950497114d_enat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( plus_plus_nat @ M2 @ N2 ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum_up_index_split
% 3.82/4.09 thf(fact_6891_sum__up__index__split,axiom,
% 3.82/4.09 ! [F: nat > nat,M2: nat,N2: nat] :
% 3.82/4.09 ( ( groups3542108847815614940at_nat @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M2 @ N2 ) ) )
% 3.82/4.09 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_atMost_nat @ M2 ) ) @ ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( plus_plus_nat @ M2 @ N2 ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum_up_index_split
% 3.82/4.09 thf(fact_6892_sum__up__index__split,axiom,
% 3.82/4.09 ! [F: nat > real,M2: nat,N2: nat] :
% 3.82/4.09 ( ( groups6591440286371151544t_real @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M2 @ N2 ) ) )
% 3.82/4.09 = ( plus_plus_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_atMost_nat @ M2 ) ) @ ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( plus_plus_nat @ M2 @ N2 ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum_up_index_split
% 3.82/4.09 thf(fact_6893_prod_OatMost__shift,axiom,
% 3.82/4.09 ! [G: nat > real,N2: nat] :
% 3.82/4.09 ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 = ( times_times_real @ ( G @ zero_zero_nat )
% 3.82/4.09 @ ( groups129246275422532515t_real
% 3.82/4.09 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 3.82/4.09 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.atMost_shift
% 3.82/4.09 thf(fact_6894_prod_OatMost__shift,axiom,
% 3.82/4.09 ! [G: nat > complex,N2: nat] :
% 3.82/4.09 ( ( groups6464643781859351333omplex @ G @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 = ( times_times_complex @ ( G @ zero_zero_nat )
% 3.82/4.09 @ ( groups6464643781859351333omplex
% 3.82/4.09 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 3.82/4.09 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.atMost_shift
% 3.82/4.09 thf(fact_6895_prod_OatMost__shift,axiom,
% 3.82/4.09 ! [G: nat > extended_enat,N2: nat] :
% 3.82/4.09 ( ( groups7961826882256487087d_enat @ G @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 = ( times_7803423173614009249d_enat @ ( G @ zero_zero_nat )
% 3.82/4.09 @ ( groups7961826882256487087d_enat
% 3.82/4.09 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 3.82/4.09 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.atMost_shift
% 3.82/4.09 thf(fact_6896_prod_OatMost__shift,axiom,
% 3.82/4.09 ! [G: nat > int,N2: nat] :
% 3.82/4.09 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 = ( times_times_int @ ( G @ zero_zero_nat )
% 3.82/4.09 @ ( groups705719431365010083at_int
% 3.82/4.09 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 3.82/4.09 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.atMost_shift
% 3.82/4.09 thf(fact_6897_prod_OatMost__shift,axiom,
% 3.82/4.09 ! [G: nat > nat,N2: nat] :
% 3.82/4.09 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 = ( times_times_nat @ ( G @ zero_zero_nat )
% 3.82/4.09 @ ( groups708209901874060359at_nat
% 3.82/4.09 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 3.82/4.09 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.atMost_shift
% 3.82/4.09 thf(fact_6898_atLeast1__atMost__eq__remove0,axiom,
% 3.82/4.09 ! [N2: nat] :
% 3.82/4.09 ( ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 3.82/4.09 = ( minus_minus_set_nat @ ( set_ord_atMost_nat @ N2 ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % atLeast1_atMost_eq_remove0
% 3.82/4.09 thf(fact_6899_gbinomial__parallel__sum,axiom,
% 3.82/4.09 ! [A: complex,N2: nat] :
% 3.82/4.09 ( ( groups2073611262835488442omplex
% 3.82/4.09 @ ^ [K2: nat] : ( gbinomial_complex @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ K2 ) ) @ K2 )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 = ( gbinomial_complex @ ( plus_plus_complex @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ N2 ) ) @ one_one_complex ) @ N2 ) ) ).
% 3.82/4.09
% 3.82/4.09 % gbinomial_parallel_sum
% 3.82/4.09 thf(fact_6900_gbinomial__parallel__sum,axiom,
% 3.82/4.09 ! [A: real,N2: nat] :
% 3.82/4.09 ( ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [K2: nat] : ( gbinomial_real @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ K2 ) ) @ K2 )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 = ( gbinomial_real @ ( plus_plus_real @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ N2 ) ) @ one_one_real ) @ N2 ) ) ).
% 3.82/4.09
% 3.82/4.09 % gbinomial_parallel_sum
% 3.82/4.09 thf(fact_6901_sum_Otriangle__reindex__eq,axiom,
% 3.82/4.09 ! [G: nat > nat > nat,N2: nat] :
% 3.82/4.09 ( ( groups977919841031483927at_nat @ ( produc6842872674320459806at_nat @ G )
% 3.82/4.09 @ ( collec3392354462482085612at_nat
% 3.82/4.09 @ ( produc6081775807080527818_nat_o
% 3.82/4.09 @ ^ [I3: nat,J2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I3 @ J2 ) @ N2 ) ) ) )
% 3.82/4.09 = ( groups3542108847815614940at_nat
% 3.82/4.09 @ ^ [K2: nat] :
% 3.82/4.09 ( groups3542108847815614940at_nat
% 3.82/4.09 @ ^ [I3: nat] : ( G @ I3 @ ( minus_minus_nat @ K2 @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ K2 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum.triangle_reindex_eq
% 3.82/4.09 thf(fact_6902_sum_Otriangle__reindex__eq,axiom,
% 3.82/4.09 ! [G: nat > nat > real,N2: nat] :
% 3.82/4.09 ( ( groups4567486121110086003t_real @ ( produc1703576794950452218t_real @ G )
% 3.82/4.09 @ ( collec3392354462482085612at_nat
% 3.82/4.09 @ ( produc6081775807080527818_nat_o
% 3.82/4.09 @ ^ [I3: nat,J2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I3 @ J2 ) @ N2 ) ) ) )
% 3.82/4.09 = ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [K2: nat] :
% 3.82/4.09 ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [I3: nat] : ( G @ I3 @ ( minus_minus_nat @ K2 @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ K2 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum.triangle_reindex_eq
% 3.82/4.09 thf(fact_6903_prod_Otriangle__reindex__eq,axiom,
% 3.82/4.09 ! [G: nat > nat > int,N2: nat] :
% 3.82/4.09 ( ( groups4075276357253098568at_int @ ( produc6840382203811409530at_int @ G )
% 3.82/4.09 @ ( collec3392354462482085612at_nat
% 3.82/4.09 @ ( produc6081775807080527818_nat_o
% 3.82/4.09 @ ^ [I3: nat,J2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I3 @ J2 ) @ N2 ) ) ) )
% 3.82/4.09 = ( groups705719431365010083at_int
% 3.82/4.09 @ ^ [K2: nat] :
% 3.82/4.09 ( groups705719431365010083at_int
% 3.82/4.09 @ ^ [I3: nat] : ( G @ I3 @ ( minus_minus_nat @ K2 @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ K2 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.triangle_reindex_eq
% 3.82/4.09 thf(fact_6904_prod_Otriangle__reindex__eq,axiom,
% 3.82/4.09 ! [G: nat > nat > nat,N2: nat] :
% 3.82/4.09 ( ( groups4077766827762148844at_nat @ ( produc6842872674320459806at_nat @ G )
% 3.82/4.09 @ ( collec3392354462482085612at_nat
% 3.82/4.09 @ ( produc6081775807080527818_nat_o
% 3.82/4.09 @ ^ [I3: nat,J2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I3 @ J2 ) @ N2 ) ) ) )
% 3.82/4.09 = ( groups708209901874060359at_nat
% 3.82/4.09 @ ^ [K2: nat] :
% 3.82/4.09 ( groups708209901874060359at_nat
% 3.82/4.09 @ ^ [I3: nat] : ( G @ I3 @ ( minus_minus_nat @ K2 @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ K2 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.triangle_reindex_eq
% 3.82/4.09 thf(fact_6905_sum__choose__diagonal,axiom,
% 3.82/4.09 ! [M2: nat,N2: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.09 => ( ( groups3542108847815614940at_nat
% 3.82/4.09 @ ^ [K2: nat] : ( binomial @ ( minus_minus_nat @ N2 @ K2 ) @ ( minus_minus_nat @ M2 @ K2 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ M2 ) )
% 3.82/4.09 = ( binomial @ ( suc @ N2 ) @ M2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum_choose_diagonal
% 3.82/4.09 thf(fact_6906_vandermonde,axiom,
% 3.82/4.09 ! [M2: nat,N2: nat,R2: nat] :
% 3.82/4.09 ( ( groups3542108847815614940at_nat
% 3.82/4.09 @ ^ [K2: nat] : ( times_times_nat @ ( binomial @ M2 @ K2 ) @ ( binomial @ N2 @ ( minus_minus_nat @ R2 @ K2 ) ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ R2 ) )
% 3.82/4.09 = ( binomial @ ( plus_plus_nat @ M2 @ N2 ) @ R2 ) ) ).
% 3.82/4.09
% 3.82/4.09 % vandermonde
% 3.82/4.09 thf(fact_6907_sum__gp__basic,axiom,
% 3.82/4.09 ! [X: int,N2: nat] :
% 3.82/4.09 ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_atMost_nat @ N2 ) ) )
% 3.82/4.09 = ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ ( suc @ N2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum_gp_basic
% 3.82/4.09 thf(fact_6908_sum__gp__basic,axiom,
% 3.82/4.09 ! [X: complex,N2: nat] :
% 3.82/4.09 ( ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_atMost_nat @ N2 ) ) )
% 3.82/4.09 = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ ( suc @ N2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum_gp_basic
% 3.82/4.09 thf(fact_6909_sum__gp__basic,axiom,
% 3.82/4.09 ! [X: real,N2: nat] :
% 3.82/4.09 ( ( times_times_real @ ( minus_minus_real @ one_one_real @ X ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_atMost_nat @ N2 ) ) )
% 3.82/4.09 = ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( suc @ N2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum_gp_basic
% 3.82/4.09 thf(fact_6910_polyfun__roots__finite,axiom,
% 3.82/4.09 ! [C: nat > complex,K: nat,N2: nat] :
% 3.82/4.09 ( ( ( C @ K )
% 3.82/4.09 != zero_zero_complex )
% 3.82/4.09 => ( ( ord_less_eq_nat @ K @ N2 )
% 3.82/4.09 => ( finite3207457112153483333omplex
% 3.82/4.09 @ ( collect_complex
% 3.82/4.09 @ ^ [Z6: complex] :
% 3.82/4.09 ( ( groups2073611262835488442omplex
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ Z6 @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 = zero_zero_complex ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % polyfun_roots_finite
% 3.82/4.09 thf(fact_6911_polyfun__roots__finite,axiom,
% 3.82/4.09 ! [C: nat > real,K: nat,N2: nat] :
% 3.82/4.09 ( ( ( C @ K )
% 3.82/4.09 != zero_zero_real )
% 3.82/4.09 => ( ( ord_less_eq_nat @ K @ N2 )
% 3.82/4.09 => ( finite_finite_real
% 3.82/4.09 @ ( collect_real
% 3.82/4.09 @ ^ [Z6: real] :
% 3.82/4.09 ( ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ Z6 @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 = zero_zero_real ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % polyfun_roots_finite
% 3.82/4.09 thf(fact_6912_polyfun__finite__roots,axiom,
% 3.82/4.09 ! [C: nat > complex,N2: nat] :
% 3.82/4.09 ( ( finite3207457112153483333omplex
% 3.82/4.09 @ ( collect_complex
% 3.82/4.09 @ ^ [X4: complex] :
% 3.82/4.09 ( ( groups2073611262835488442omplex
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ X4 @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 = zero_zero_complex ) ) )
% 3.82/4.09 = ( ? [I3: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ I3 @ N2 )
% 3.82/4.09 & ( ( C @ I3 )
% 3.82/4.09 != zero_zero_complex ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % polyfun_finite_roots
% 3.82/4.09 thf(fact_6913_polyfun__finite__roots,axiom,
% 3.82/4.09 ! [C: nat > real,N2: nat] :
% 3.82/4.09 ( ( finite_finite_real
% 3.82/4.09 @ ( collect_real
% 3.82/4.09 @ ^ [X4: real] :
% 3.82/4.09 ( ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ X4 @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 = zero_zero_real ) ) )
% 3.82/4.09 = ( ? [I3: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ I3 @ N2 )
% 3.82/4.09 & ( ( C @ I3 )
% 3.82/4.09 != zero_zero_real ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % polyfun_finite_roots
% 3.82/4.09 thf(fact_6914_polyfun__linear__factor__root,axiom,
% 3.82/4.09 ! [C: nat > int,A: int,N2: nat] :
% 3.82/4.09 ( ( ( groups3539618377306564664at_int
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_int @ ( C @ I3 ) @ ( power_power_int @ A @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 = zero_zero_int )
% 3.82/4.09 => ~ ! [B4: nat > int] :
% 3.82/4.09 ~ ! [Z4: int] :
% 3.82/4.09 ( ( groups3539618377306564664at_int
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_int @ ( C @ I3 ) @ ( power_power_int @ Z4 @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 = ( times_times_int @ ( minus_minus_int @ Z4 @ A )
% 3.82/4.09 @ ( groups3539618377306564664at_int
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_int @ ( B4 @ I3 ) @ ( power_power_int @ Z4 @ I3 ) )
% 3.82/4.09 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % polyfun_linear_factor_root
% 3.82/4.09 thf(fact_6915_polyfun__linear__factor__root,axiom,
% 3.82/4.09 ! [C: nat > complex,A: complex,N2: nat] :
% 3.82/4.09 ( ( ( groups2073611262835488442omplex
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ A @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 = zero_zero_complex )
% 3.82/4.09 => ~ ! [B4: nat > complex] :
% 3.82/4.09 ~ ! [Z4: complex] :
% 3.82/4.09 ( ( groups2073611262835488442omplex
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ Z4 @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 = ( times_times_complex @ ( minus_minus_complex @ Z4 @ A )
% 3.82/4.09 @ ( groups2073611262835488442omplex
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_complex @ ( B4 @ I3 ) @ ( power_power_complex @ Z4 @ I3 ) )
% 3.82/4.09 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % polyfun_linear_factor_root
% 3.82/4.09 thf(fact_6916_polyfun__linear__factor__root,axiom,
% 3.82/4.09 ! [C: nat > real,A: real,N2: nat] :
% 3.82/4.09 ( ( ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ A @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 = zero_zero_real )
% 3.82/4.09 => ~ ! [B4: nat > real] :
% 3.82/4.09 ~ ! [Z4: real] :
% 3.82/4.09 ( ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ Z4 @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 = ( times_times_real @ ( minus_minus_real @ Z4 @ A )
% 3.82/4.09 @ ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_real @ ( B4 @ I3 ) @ ( power_power_real @ Z4 @ I3 ) )
% 3.82/4.09 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % polyfun_linear_factor_root
% 3.82/4.09 thf(fact_6917_polyfun__linear__factor,axiom,
% 3.82/4.09 ! [C: nat > int,N2: nat,A: int] :
% 3.82/4.09 ? [B4: nat > int] :
% 3.82/4.09 ! [Z4: int] :
% 3.82/4.09 ( ( groups3539618377306564664at_int
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_int @ ( C @ I3 ) @ ( power_power_int @ Z4 @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 = ( plus_plus_int
% 3.82/4.09 @ ( times_times_int @ ( minus_minus_int @ Z4 @ A )
% 3.82/4.09 @ ( groups3539618377306564664at_int
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_int @ ( B4 @ I3 ) @ ( power_power_int @ Z4 @ I3 ) )
% 3.82/4.09 @ ( set_ord_lessThan_nat @ N2 ) ) )
% 3.82/4.09 @ ( groups3539618377306564664at_int
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_int @ ( C @ I3 ) @ ( power_power_int @ A @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % polyfun_linear_factor
% 3.82/4.09 thf(fact_6918_polyfun__linear__factor,axiom,
% 3.82/4.09 ! [C: nat > complex,N2: nat,A: complex] :
% 3.82/4.09 ? [B4: nat > complex] :
% 3.82/4.09 ! [Z4: complex] :
% 3.82/4.09 ( ( groups2073611262835488442omplex
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ Z4 @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 = ( plus_plus_complex
% 3.82/4.09 @ ( times_times_complex @ ( minus_minus_complex @ Z4 @ A )
% 3.82/4.09 @ ( groups2073611262835488442omplex
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_complex @ ( B4 @ I3 ) @ ( power_power_complex @ Z4 @ I3 ) )
% 3.82/4.09 @ ( set_ord_lessThan_nat @ N2 ) ) )
% 3.82/4.09 @ ( groups2073611262835488442omplex
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ A @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % polyfun_linear_factor
% 3.82/4.09 thf(fact_6919_polyfun__linear__factor,axiom,
% 3.82/4.09 ! [C: nat > real,N2: nat,A: real] :
% 3.82/4.09 ? [B4: nat > real] :
% 3.82/4.09 ! [Z4: real] :
% 3.82/4.09 ( ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ Z4 @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 = ( plus_plus_real
% 3.82/4.09 @ ( times_times_real @ ( minus_minus_real @ Z4 @ A )
% 3.82/4.09 @ ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_real @ ( B4 @ I3 ) @ ( power_power_real @ Z4 @ I3 ) )
% 3.82/4.09 @ ( set_ord_lessThan_nat @ N2 ) ) )
% 3.82/4.09 @ ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ A @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % polyfun_linear_factor
% 3.82/4.09 thf(fact_6920_sum__power__shift,axiom,
% 3.82/4.09 ! [M2: nat,N2: nat,X: int] :
% 3.82/4.09 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.09 => ( ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 3.82/4.09 = ( times_times_int @ ( power_power_int @ X @ M2 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum_power_shift
% 3.82/4.09 thf(fact_6921_sum__power__shift,axiom,
% 3.82/4.09 ! [M2: nat,N2: nat,X: complex] :
% 3.82/4.09 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.09 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 3.82/4.09 = ( times_times_complex @ ( power_power_complex @ X @ M2 ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum_power_shift
% 3.82/4.09 thf(fact_6922_sum__power__shift,axiom,
% 3.82/4.09 ! [M2: nat,N2: nat,X: real] :
% 3.82/4.09 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.09 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N2 ) )
% 3.82/4.09 = ( times_times_real @ ( power_power_real @ X @ M2 ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum_power_shift
% 3.82/4.09 thf(fact_6923_sum_Otriangle__reindex,axiom,
% 3.82/4.09 ! [G: nat > nat > nat,N2: nat] :
% 3.82/4.09 ( ( groups977919841031483927at_nat @ ( produc6842872674320459806at_nat @ G )
% 3.82/4.09 @ ( collec3392354462482085612at_nat
% 3.82/4.09 @ ( produc6081775807080527818_nat_o
% 3.82/4.09 @ ^ [I3: nat,J2: nat] : ( ord_less_nat @ ( plus_plus_nat @ I3 @ J2 ) @ N2 ) ) ) )
% 3.82/4.09 = ( groups3542108847815614940at_nat
% 3.82/4.09 @ ^ [K2: nat] :
% 3.82/4.09 ( groups3542108847815614940at_nat
% 3.82/4.09 @ ^ [I3: nat] : ( G @ I3 @ ( minus_minus_nat @ K2 @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ K2 ) )
% 3.82/4.09 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum.triangle_reindex
% 3.82/4.09 thf(fact_6924_sum_Otriangle__reindex,axiom,
% 3.82/4.09 ! [G: nat > nat > real,N2: nat] :
% 3.82/4.09 ( ( groups4567486121110086003t_real @ ( produc1703576794950452218t_real @ G )
% 3.82/4.09 @ ( collec3392354462482085612at_nat
% 3.82/4.09 @ ( produc6081775807080527818_nat_o
% 3.82/4.09 @ ^ [I3: nat,J2: nat] : ( ord_less_nat @ ( plus_plus_nat @ I3 @ J2 ) @ N2 ) ) ) )
% 3.82/4.09 = ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [K2: nat] :
% 3.82/4.09 ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [I3: nat] : ( G @ I3 @ ( minus_minus_nat @ K2 @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ K2 ) )
% 3.82/4.09 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum.triangle_reindex
% 3.82/4.09 thf(fact_6925_prod_Otriangle__reindex,axiom,
% 3.82/4.09 ! [G: nat > nat > int,N2: nat] :
% 3.82/4.09 ( ( groups4075276357253098568at_int @ ( produc6840382203811409530at_int @ G )
% 3.82/4.09 @ ( collec3392354462482085612at_nat
% 3.82/4.09 @ ( produc6081775807080527818_nat_o
% 3.82/4.09 @ ^ [I3: nat,J2: nat] : ( ord_less_nat @ ( plus_plus_nat @ I3 @ J2 ) @ N2 ) ) ) )
% 3.82/4.09 = ( groups705719431365010083at_int
% 3.82/4.09 @ ^ [K2: nat] :
% 3.82/4.09 ( groups705719431365010083at_int
% 3.82/4.09 @ ^ [I3: nat] : ( G @ I3 @ ( minus_minus_nat @ K2 @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ K2 ) )
% 3.82/4.09 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.triangle_reindex
% 3.82/4.09 thf(fact_6926_prod_Otriangle__reindex,axiom,
% 3.82/4.09 ! [G: nat > nat > nat,N2: nat] :
% 3.82/4.09 ( ( groups4077766827762148844at_nat @ ( produc6842872674320459806at_nat @ G )
% 3.82/4.09 @ ( collec3392354462482085612at_nat
% 3.82/4.09 @ ( produc6081775807080527818_nat_o
% 3.82/4.09 @ ^ [I3: nat,J2: nat] : ( ord_less_nat @ ( plus_plus_nat @ I3 @ J2 ) @ N2 ) ) ) )
% 3.82/4.09 = ( groups708209901874060359at_nat
% 3.82/4.09 @ ^ [K2: nat] :
% 3.82/4.09 ( groups708209901874060359at_nat
% 3.82/4.09 @ ^ [I3: nat] : ( G @ I3 @ ( minus_minus_nat @ K2 @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ K2 ) )
% 3.82/4.09 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.triangle_reindex
% 3.82/4.09 thf(fact_6927_binomial,axiom,
% 3.82/4.09 ! [A: nat,B2: nat,N2: nat] :
% 3.82/4.09 ( ( power_power_nat @ ( plus_plus_nat @ A @ B2 ) @ N2 )
% 3.82/4.09 = ( groups3542108847815614940at_nat
% 3.82/4.09 @ ^ [K2: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N2 @ K2 ) ) @ ( power_power_nat @ A @ K2 ) ) @ ( power_power_nat @ B2 @ ( minus_minus_nat @ N2 @ K2 ) ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % binomial
% 3.82/4.09 thf(fact_6928_sum_Oin__pairs__0,axiom,
% 3.82/4.09 ! [G: nat > int,N2: nat] :
% 3.82/4.09 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 3.82/4.09 = ( groups3539618377306564664at_int
% 3.82/4.09 @ ^ [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 ) ) ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum.in_pairs_0
% 3.82/4.09 thf(fact_6929_sum_Oin__pairs__0,axiom,
% 3.82/4.09 ! [G: nat > extended_enat,N2: nat] :
% 3.82/4.09 ( ( groups7108830773950497114d_enat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 3.82/4.09 = ( groups7108830773950497114d_enat
% 3.82/4.09 @ ^ [I3: nat] : ( plus_p3455044024723400733d_enat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum.in_pairs_0
% 3.82/4.09 thf(fact_6930_sum_Oin__pairs__0,axiom,
% 3.82/4.09 ! [G: nat > nat,N2: nat] :
% 3.82/4.09 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 3.82/4.09 = ( groups3542108847815614940at_nat
% 3.82/4.09 @ ^ [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 ) ) ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum.in_pairs_0
% 3.82/4.09 thf(fact_6931_sum_Oin__pairs__0,axiom,
% 3.82/4.09 ! [G: nat > real,N2: nat] :
% 3.82/4.09 ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 3.82/4.09 = ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [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 ) ) ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum.in_pairs_0
% 3.82/4.09 thf(fact_6932_polynomial__product,axiom,
% 3.82/4.09 ! [M2: nat,A: nat > int,N2: nat,B2: nat > int,X: int] :
% 3.82/4.09 ( ! [I4: nat] :
% 3.82/4.09 ( ( ord_less_nat @ M2 @ I4 )
% 3.82/4.09 => ( ( A @ I4 )
% 3.82/4.09 = zero_zero_int ) )
% 3.82/4.09 => ( ! [J3: nat] :
% 3.82/4.09 ( ( ord_less_nat @ N2 @ J3 )
% 3.82/4.09 => ( ( B2 @ J3 )
% 3.82/4.09 = zero_zero_int ) )
% 3.82/4.09 => ( ( times_times_int
% 3.82/4.09 @ ( groups3539618377306564664at_int
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_int @ ( A @ I3 ) @ ( power_power_int @ X @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ M2 ) )
% 3.82/4.09 @ ( groups3539618377306564664at_int
% 3.82/4.09 @ ^ [J2: nat] : ( times_times_int @ ( B2 @ J2 ) @ ( power_power_int @ X @ J2 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) )
% 3.82/4.09 = ( groups3539618377306564664at_int
% 3.82/4.09 @ ^ [R4: nat] :
% 3.82/4.09 ( times_times_int
% 3.82/4.09 @ ( groups3539618377306564664at_int
% 3.82/4.09 @ ^ [K2: nat] : ( times_times_int @ ( A @ K2 ) @ ( B2 @ ( minus_minus_nat @ R4 @ K2 ) ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ R4 ) )
% 3.82/4.09 @ ( power_power_int @ X @ R4 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M2 @ N2 ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % polynomial_product
% 3.82/4.09 thf(fact_6933_polynomial__product,axiom,
% 3.82/4.09 ! [M2: nat,A: nat > complex,N2: nat,B2: nat > complex,X: complex] :
% 3.82/4.09 ( ! [I4: nat] :
% 3.82/4.09 ( ( ord_less_nat @ M2 @ I4 )
% 3.82/4.09 => ( ( A @ I4 )
% 3.82/4.09 = zero_zero_complex ) )
% 3.82/4.09 => ( ! [J3: nat] :
% 3.82/4.09 ( ( ord_less_nat @ N2 @ J3 )
% 3.82/4.09 => ( ( B2 @ J3 )
% 3.82/4.09 = zero_zero_complex ) )
% 3.82/4.09 => ( ( times_times_complex
% 3.82/4.09 @ ( groups2073611262835488442omplex
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_complex @ ( A @ I3 ) @ ( power_power_complex @ X @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ M2 ) )
% 3.82/4.09 @ ( groups2073611262835488442omplex
% 3.82/4.09 @ ^ [J2: nat] : ( times_times_complex @ ( B2 @ J2 ) @ ( power_power_complex @ X @ J2 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) )
% 3.82/4.09 = ( groups2073611262835488442omplex
% 3.82/4.09 @ ^ [R4: nat] :
% 3.82/4.09 ( times_times_complex
% 3.82/4.09 @ ( groups2073611262835488442omplex
% 3.82/4.09 @ ^ [K2: nat] : ( times_times_complex @ ( A @ K2 ) @ ( B2 @ ( minus_minus_nat @ R4 @ K2 ) ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ R4 ) )
% 3.82/4.09 @ ( power_power_complex @ X @ R4 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M2 @ N2 ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % polynomial_product
% 3.82/4.09 thf(fact_6934_polynomial__product,axiom,
% 3.82/4.09 ! [M2: nat,A: nat > real,N2: nat,B2: nat > real,X: real] :
% 3.82/4.09 ( ! [I4: nat] :
% 3.82/4.09 ( ( ord_less_nat @ M2 @ I4 )
% 3.82/4.09 => ( ( A @ I4 )
% 3.82/4.09 = zero_zero_real ) )
% 3.82/4.09 => ( ! [J3: nat] :
% 3.82/4.09 ( ( ord_less_nat @ N2 @ J3 )
% 3.82/4.09 => ( ( B2 @ J3 )
% 3.82/4.09 = zero_zero_real ) )
% 3.82/4.09 => ( ( times_times_real
% 3.82/4.09 @ ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_real @ ( A @ I3 ) @ ( power_power_real @ X @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ M2 ) )
% 3.82/4.09 @ ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [J2: nat] : ( times_times_real @ ( B2 @ J2 ) @ ( power_power_real @ X @ J2 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) )
% 3.82/4.09 = ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [R4: nat] :
% 3.82/4.09 ( times_times_real
% 3.82/4.09 @ ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [K2: nat] : ( times_times_real @ ( A @ K2 ) @ ( B2 @ ( minus_minus_nat @ R4 @ K2 ) ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ R4 ) )
% 3.82/4.09 @ ( power_power_real @ X @ R4 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M2 @ N2 ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % polynomial_product
% 3.82/4.09 thf(fact_6935_prod_Oin__pairs__0,axiom,
% 3.82/4.09 ! [G: nat > real,N2: nat] :
% 3.82/4.09 ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 3.82/4.09 = ( groups129246275422532515t_real
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.in_pairs_0
% 3.82/4.09 thf(fact_6936_prod_Oin__pairs__0,axiom,
% 3.82/4.09 ! [G: nat > complex,N2: nat] :
% 3.82/4.09 ( ( groups6464643781859351333omplex @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 3.82/4.09 = ( groups6464643781859351333omplex
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_complex @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.in_pairs_0
% 3.82/4.09 thf(fact_6937_prod_Oin__pairs__0,axiom,
% 3.82/4.09 ! [G: nat > extended_enat,N2: nat] :
% 3.82/4.09 ( ( groups7961826882256487087d_enat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 3.82/4.09 = ( groups7961826882256487087d_enat
% 3.82/4.09 @ ^ [I3: nat] : ( times_7803423173614009249d_enat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.in_pairs_0
% 3.82/4.09 thf(fact_6938_prod_Oin__pairs__0,axiom,
% 3.82/4.09 ! [G: nat > int,N2: nat] :
% 3.82/4.09 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 3.82/4.09 = ( groups705719431365010083at_int
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.in_pairs_0
% 3.82/4.09 thf(fact_6939_prod_Oin__pairs__0,axiom,
% 3.82/4.09 ! [G: nat > nat,N2: nat] :
% 3.82/4.09 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 3.82/4.09 = ( groups708209901874060359at_nat
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.in_pairs_0
% 3.82/4.09 thf(fact_6940_polyfun__eq__const,axiom,
% 3.82/4.09 ! [C: nat > complex,N2: nat,K: complex] :
% 3.82/4.09 ( ( ! [X4: complex] :
% 3.82/4.09 ( ( groups2073611262835488442omplex
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ X4 @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 = K ) )
% 3.82/4.09 = ( ( ( C @ zero_zero_nat )
% 3.82/4.09 = K )
% 3.82/4.09 & ! [X4: nat] :
% 3.82/4.09 ( ( member_nat @ X4 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) )
% 3.82/4.09 => ( ( C @ X4 )
% 3.82/4.09 = zero_zero_complex ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % polyfun_eq_const
% 3.82/4.09 thf(fact_6941_polyfun__eq__const,axiom,
% 3.82/4.09 ! [C: nat > real,N2: nat,K: real] :
% 3.82/4.09 ( ( ! [X4: real] :
% 3.82/4.09 ( ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ X4 @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 = K ) )
% 3.82/4.09 = ( ( ( C @ zero_zero_nat )
% 3.82/4.09 = K )
% 3.82/4.09 & ! [X4: nat] :
% 3.82/4.09 ( ( member_nat @ X4 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) )
% 3.82/4.09 => ( ( C @ X4 )
% 3.82/4.09 = zero_zero_real ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % polyfun_eq_const
% 3.82/4.09 thf(fact_6942_binomial__ring,axiom,
% 3.82/4.09 ! [A: complex,B2: complex,N2: nat] :
% 3.82/4.09 ( ( power_power_complex @ ( plus_plus_complex @ A @ B2 ) @ N2 )
% 3.82/4.09 = ( groups2073611262835488442omplex
% 3.82/4.09 @ ^ [K2: nat] : ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ K2 ) ) @ ( power_power_complex @ A @ K2 ) ) @ ( power_power_complex @ B2 @ ( minus_minus_nat @ N2 @ K2 ) ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % binomial_ring
% 3.82/4.09 thf(fact_6943_binomial__ring,axiom,
% 3.82/4.09 ! [A: extended_enat,B2: extended_enat,N2: nat] :
% 3.82/4.09 ( ( power_8040749407984259932d_enat @ ( plus_p3455044024723400733d_enat @ A @ B2 ) @ N2 )
% 3.82/4.09 = ( groups7108830773950497114d_enat
% 3.82/4.09 @ ^ [K2: nat] : ( times_7803423173614009249d_enat @ ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ ( binomial @ N2 @ K2 ) ) @ ( power_8040749407984259932d_enat @ A @ K2 ) ) @ ( power_8040749407984259932d_enat @ B2 @ ( minus_minus_nat @ N2 @ K2 ) ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % binomial_ring
% 3.82/4.09 thf(fact_6944_binomial__ring,axiom,
% 3.82/4.09 ! [A: int,B2: int,N2: nat] :
% 3.82/4.09 ( ( power_power_int @ ( plus_plus_int @ A @ B2 ) @ N2 )
% 3.82/4.09 = ( groups3539618377306564664at_int
% 3.82/4.09 @ ^ [K2: nat] : ( times_times_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ K2 ) ) @ ( power_power_int @ A @ K2 ) ) @ ( power_power_int @ B2 @ ( minus_minus_nat @ N2 @ K2 ) ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % binomial_ring
% 3.82/4.09 thf(fact_6945_binomial__ring,axiom,
% 3.82/4.09 ! [A: nat,B2: nat,N2: nat] :
% 3.82/4.09 ( ( power_power_nat @ ( plus_plus_nat @ A @ B2 ) @ N2 )
% 3.82/4.09 = ( groups3542108847815614940at_nat
% 3.82/4.09 @ ^ [K2: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N2 @ K2 ) ) @ ( power_power_nat @ A @ K2 ) ) @ ( power_power_nat @ B2 @ ( minus_minus_nat @ N2 @ K2 ) ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % binomial_ring
% 3.82/4.09 thf(fact_6946_binomial__ring,axiom,
% 3.82/4.09 ! [A: real,B2: real,N2: nat] :
% 3.82/4.09 ( ( power_power_real @ ( plus_plus_real @ A @ B2 ) @ N2 )
% 3.82/4.09 = ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [K2: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ K2 ) ) @ ( power_power_real @ A @ K2 ) ) @ ( power_power_real @ B2 @ ( minus_minus_nat @ N2 @ K2 ) ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % binomial_ring
% 3.82/4.09 thf(fact_6947_pochhammer__binomial__sum,axiom,
% 3.82/4.09 ! [A: complex,B2: complex,N2: nat] :
% 3.82/4.09 ( ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ A @ B2 ) @ N2 )
% 3.82/4.09 = ( groups2073611262835488442omplex
% 3.82/4.09 @ ^ [K2: nat] : ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ K2 ) ) @ ( comm_s2602460028002588243omplex @ A @ K2 ) ) @ ( comm_s2602460028002588243omplex @ B2 @ ( minus_minus_nat @ N2 @ K2 ) ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % pochhammer_binomial_sum
% 3.82/4.09 thf(fact_6948_pochhammer__binomial__sum,axiom,
% 3.82/4.09 ! [A: int,B2: int,N2: nat] :
% 3.82/4.09 ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ B2 ) @ N2 )
% 3.82/4.09 = ( groups3539618377306564664at_int
% 3.82/4.09 @ ^ [K2: nat] : ( times_times_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ K2 ) ) @ ( comm_s4660882817536571857er_int @ A @ K2 ) ) @ ( comm_s4660882817536571857er_int @ B2 @ ( minus_minus_nat @ N2 @ K2 ) ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % pochhammer_binomial_sum
% 3.82/4.09 thf(fact_6949_pochhammer__binomial__sum,axiom,
% 3.82/4.09 ! [A: real,B2: real,N2: nat] :
% 3.82/4.09 ( ( comm_s7457072308508201937r_real @ ( plus_plus_real @ A @ B2 ) @ N2 )
% 3.82/4.09 = ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [K2: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ K2 ) ) @ ( comm_s7457072308508201937r_real @ A @ K2 ) ) @ ( comm_s7457072308508201937r_real @ B2 @ ( minus_minus_nat @ N2 @ K2 ) ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % pochhammer_binomial_sum
% 3.82/4.09 thf(fact_6950_polynomial__product__nat,axiom,
% 3.82/4.09 ! [M2: nat,A: nat > nat,N2: nat,B2: nat > nat,X: nat] :
% 3.82/4.09 ( ! [I4: nat] :
% 3.82/4.09 ( ( ord_less_nat @ M2 @ I4 )
% 3.82/4.09 => ( ( A @ I4 )
% 3.82/4.09 = zero_zero_nat ) )
% 3.82/4.09 => ( ! [J3: nat] :
% 3.82/4.09 ( ( ord_less_nat @ N2 @ J3 )
% 3.82/4.09 => ( ( B2 @ J3 )
% 3.82/4.09 = zero_zero_nat ) )
% 3.82/4.09 => ( ( times_times_nat
% 3.82/4.09 @ ( groups3542108847815614940at_nat
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_nat @ ( A @ I3 ) @ ( power_power_nat @ X @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ M2 ) )
% 3.82/4.09 @ ( groups3542108847815614940at_nat
% 3.82/4.09 @ ^ [J2: nat] : ( times_times_nat @ ( B2 @ J2 ) @ ( power_power_nat @ X @ J2 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) )
% 3.82/4.09 = ( groups3542108847815614940at_nat
% 3.82/4.09 @ ^ [R4: nat] :
% 3.82/4.09 ( times_times_nat
% 3.82/4.09 @ ( groups3542108847815614940at_nat
% 3.82/4.09 @ ^ [K2: nat] : ( times_times_nat @ ( A @ K2 ) @ ( B2 @ ( minus_minus_nat @ R4 @ K2 ) ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ R4 ) )
% 3.82/4.09 @ ( power_power_nat @ X @ R4 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M2 @ N2 ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % polynomial_product_nat
% 3.82/4.09 thf(fact_6951_floor__add,axiom,
% 3.82/4.09 ! [X: real,Y: real] :
% 3.82/4.09 ( ( ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y ) ) @ one_one_real )
% 3.82/4.09 => ( ( archim6058952711729229775r_real @ ( plus_plus_real @ X @ Y ) )
% 3.82/4.09 = ( plus_plus_int @ ( archim6058952711729229775r_real @ X ) @ ( archim6058952711729229775r_real @ Y ) ) ) )
% 3.82/4.09 & ( ~ ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y ) ) @ one_one_real )
% 3.82/4.09 => ( ( archim6058952711729229775r_real @ ( plus_plus_real @ X @ Y ) )
% 3.82/4.09 = ( plus_plus_int @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X ) @ ( archim6058952711729229775r_real @ Y ) ) @ one_one_int ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % floor_add
% 3.82/4.09 thf(fact_6952_sum_Ozero__middle,axiom,
% 3.82/4.09 ! [P5: nat,K: nat,G: nat > int,H2: nat > int] :
% 3.82/4.09 ( ( ord_less_eq_nat @ one_one_nat @ P5 )
% 3.82/4.09 => ( ( ord_less_eq_nat @ K @ P5 )
% 3.82/4.09 => ( ( groups3539618377306564664at_int
% 3.82/4.09 @ ^ [J2: nat] : ( if_int @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( if_int @ ( J2 = K ) @ zero_zero_int @ ( H2 @ ( minus_minus_nat @ J2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ P5 ) )
% 3.82/4.09 = ( groups3539618377306564664at_int
% 3.82/4.09 @ ^ [J2: nat] : ( if_int @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( H2 @ J2 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P5 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum.zero_middle
% 3.82/4.09 thf(fact_6953_sum_Ozero__middle,axiom,
% 3.82/4.09 ! [P5: nat,K: nat,G: nat > complex,H2: nat > complex] :
% 3.82/4.09 ( ( ord_less_eq_nat @ one_one_nat @ P5 )
% 3.82/4.09 => ( ( ord_less_eq_nat @ K @ P5 )
% 3.82/4.09 => ( ( groups2073611262835488442omplex
% 3.82/4.09 @ ^ [J2: nat] : ( if_complex @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( if_complex @ ( J2 = K ) @ zero_zero_complex @ ( H2 @ ( minus_minus_nat @ J2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ P5 ) )
% 3.82/4.09 = ( groups2073611262835488442omplex
% 3.82/4.09 @ ^ [J2: nat] : ( if_complex @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( H2 @ J2 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P5 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum.zero_middle
% 3.82/4.09 thf(fact_6954_sum_Ozero__middle,axiom,
% 3.82/4.09 ! [P5: nat,K: nat,G: nat > extended_enat,H2: nat > extended_enat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ one_one_nat @ P5 )
% 3.82/4.09 => ( ( ord_less_eq_nat @ K @ P5 )
% 3.82/4.09 => ( ( groups7108830773950497114d_enat
% 3.82/4.09 @ ^ [J2: nat] : ( if_Extended_enat @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( if_Extended_enat @ ( J2 = K ) @ zero_z5237406670263579293d_enat @ ( H2 @ ( minus_minus_nat @ J2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ P5 ) )
% 3.82/4.09 = ( groups7108830773950497114d_enat
% 3.82/4.09 @ ^ [J2: nat] : ( if_Extended_enat @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( H2 @ J2 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P5 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum.zero_middle
% 3.82/4.09 thf(fact_6955_sum_Ozero__middle,axiom,
% 3.82/4.09 ! [P5: nat,K: nat,G: nat > nat,H2: nat > nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ one_one_nat @ P5 )
% 3.82/4.09 => ( ( ord_less_eq_nat @ K @ P5 )
% 3.82/4.09 => ( ( groups3542108847815614940at_nat
% 3.82/4.09 @ ^ [J2: nat] : ( if_nat @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( if_nat @ ( J2 = K ) @ zero_zero_nat @ ( H2 @ ( minus_minus_nat @ J2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ P5 ) )
% 3.82/4.09 = ( groups3542108847815614940at_nat
% 3.82/4.09 @ ^ [J2: nat] : ( if_nat @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( H2 @ J2 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P5 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum.zero_middle
% 3.82/4.09 thf(fact_6956_sum_Ozero__middle,axiom,
% 3.82/4.09 ! [P5: nat,K: nat,G: nat > real,H2: nat > real] :
% 3.82/4.09 ( ( ord_less_eq_nat @ one_one_nat @ P5 )
% 3.82/4.09 => ( ( ord_less_eq_nat @ K @ P5 )
% 3.82/4.09 => ( ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [J2: nat] : ( if_real @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( if_real @ ( J2 = K ) @ zero_zero_real @ ( H2 @ ( minus_minus_nat @ J2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ P5 ) )
% 3.82/4.09 = ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [J2: nat] : ( if_real @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( H2 @ J2 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P5 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum.zero_middle
% 3.82/4.09 thf(fact_6957_prod_Ozero__middle,axiom,
% 3.82/4.09 ! [P5: nat,K: nat,G: nat > complex,H2: nat > complex] :
% 3.82/4.09 ( ( ord_less_eq_nat @ one_one_nat @ P5 )
% 3.82/4.09 => ( ( ord_less_eq_nat @ K @ P5 )
% 3.82/4.09 => ( ( groups6464643781859351333omplex
% 3.82/4.09 @ ^ [J2: nat] : ( if_complex @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( if_complex @ ( J2 = K ) @ one_one_complex @ ( H2 @ ( minus_minus_nat @ J2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ P5 ) )
% 3.82/4.09 = ( groups6464643781859351333omplex
% 3.82/4.09 @ ^ [J2: nat] : ( if_complex @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( H2 @ J2 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P5 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.zero_middle
% 3.82/4.09 thf(fact_6958_prod_Ozero__middle,axiom,
% 3.82/4.09 ! [P5: nat,K: nat,G: nat > real,H2: nat > real] :
% 3.82/4.09 ( ( ord_less_eq_nat @ one_one_nat @ P5 )
% 3.82/4.09 => ( ( ord_less_eq_nat @ K @ P5 )
% 3.82/4.09 => ( ( groups129246275422532515t_real
% 3.82/4.09 @ ^ [J2: nat] : ( if_real @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( if_real @ ( J2 = K ) @ one_one_real @ ( H2 @ ( minus_minus_nat @ J2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ P5 ) )
% 3.82/4.09 = ( groups129246275422532515t_real
% 3.82/4.09 @ ^ [J2: nat] : ( if_real @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( H2 @ J2 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P5 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.zero_middle
% 3.82/4.09 thf(fact_6959_prod_Ozero__middle,axiom,
% 3.82/4.09 ! [P5: nat,K: nat,G: nat > int,H2: nat > int] :
% 3.82/4.09 ( ( ord_less_eq_nat @ one_one_nat @ P5 )
% 3.82/4.09 => ( ( ord_less_eq_nat @ K @ P5 )
% 3.82/4.09 => ( ( groups705719431365010083at_int
% 3.82/4.09 @ ^ [J2: nat] : ( if_int @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( if_int @ ( J2 = K ) @ one_one_int @ ( H2 @ ( minus_minus_nat @ J2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ P5 ) )
% 3.82/4.09 = ( groups705719431365010083at_int
% 3.82/4.09 @ ^ [J2: nat] : ( if_int @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( H2 @ J2 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P5 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.zero_middle
% 3.82/4.09 thf(fact_6960_prod_Ozero__middle,axiom,
% 3.82/4.09 ! [P5: nat,K: nat,G: nat > nat,H2: nat > nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ one_one_nat @ P5 )
% 3.82/4.09 => ( ( ord_less_eq_nat @ K @ P5 )
% 3.82/4.09 => ( ( groups708209901874060359at_nat
% 3.82/4.09 @ ^ [J2: nat] : ( if_nat @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( if_nat @ ( J2 = K ) @ one_one_nat @ ( H2 @ ( minus_minus_nat @ J2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ P5 ) )
% 3.82/4.09 = ( groups708209901874060359at_nat
% 3.82/4.09 @ ^ [J2: nat] : ( if_nat @ ( ord_less_nat @ J2 @ K ) @ ( G @ J2 ) @ ( H2 @ J2 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P5 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % prod.zero_middle
% 3.82/4.09 thf(fact_6961_gbinomial__partial__sum__poly,axiom,
% 3.82/4.09 ! [M2: nat,A: complex,X: complex,Y: complex] :
% 3.82/4.09 ( ( groups2073611262835488442omplex
% 3.82/4.09 @ ^ [K2: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M2 ) @ A ) @ K2 ) @ ( power_power_complex @ X @ K2 ) ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ M2 @ K2 ) ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ M2 ) )
% 3.82/4.09 = ( groups2073611262835488442omplex
% 3.82/4.09 @ ^ [K2: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( uminus1482373934393186551omplex @ A ) @ K2 ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ X ) @ K2 ) ) @ ( power_power_complex @ ( plus_plus_complex @ X @ Y ) @ ( minus_minus_nat @ M2 @ K2 ) ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ M2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % gbinomial_partial_sum_poly
% 3.82/4.09 thf(fact_6962_gbinomial__partial__sum__poly,axiom,
% 3.82/4.09 ! [M2: nat,A: real,X: real,Y: real] :
% 3.82/4.09 ( ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [K2: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M2 ) @ A ) @ K2 ) @ ( power_power_real @ X @ K2 ) ) @ ( power_power_real @ Y @ ( minus_minus_nat @ M2 @ K2 ) ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ M2 ) )
% 3.82/4.09 = ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [K2: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( uminus_uminus_real @ A ) @ K2 ) @ ( power_power_real @ ( uminus_uminus_real @ X ) @ K2 ) ) @ ( power_power_real @ ( plus_plus_real @ X @ Y ) @ ( minus_minus_nat @ M2 @ K2 ) ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ M2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % gbinomial_partial_sum_poly
% 3.82/4.09 thf(fact_6963_root__polyfun,axiom,
% 3.82/4.09 ! [N2: nat,Z3: complex,A: complex] :
% 3.82/4.09 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 3.82/4.09 => ( ( ( power_power_complex @ Z3 @ N2 )
% 3.82/4.09 = A )
% 3.82/4.09 = ( ( groups2073611262835488442omplex
% 3.82/4.09 @ ^ [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 @ Z3 @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 = zero_zero_complex ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % root_polyfun
% 3.82/4.09 thf(fact_6964_root__polyfun,axiom,
% 3.82/4.09 ! [N2: nat,Z3: int,A: int] :
% 3.82/4.09 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 3.82/4.09 => ( ( ( power_power_int @ Z3 @ N2 )
% 3.82/4.09 = A )
% 3.82/4.09 = ( ( groups3539618377306564664at_int
% 3.82/4.09 @ ^ [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 @ Z3 @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 = zero_zero_int ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % root_polyfun
% 3.82/4.09 thf(fact_6965_root__polyfun,axiom,
% 3.82/4.09 ! [N2: nat,Z3: real,A: real] :
% 3.82/4.09 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 3.82/4.09 => ( ( ( power_power_real @ Z3 @ N2 )
% 3.82/4.09 = A )
% 3.82/4.09 = ( ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [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 @ Z3 @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 = zero_zero_real ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % root_polyfun
% 3.82/4.09 thf(fact_6966_sum__gp0,axiom,
% 3.82/4.09 ! [X: complex,N2: nat] :
% 3.82/4.09 ( ( ( X = one_one_complex )
% 3.82/4.09 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 = ( semiri8010041392384452111omplex @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) )
% 3.82/4.09 & ( ( X != one_one_complex )
% 3.82/4.09 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ ( suc @ N2 ) ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum_gp0
% 3.82/4.09 thf(fact_6967_sum__gp0,axiom,
% 3.82/4.09 ! [X: real,N2: nat] :
% 3.82/4.09 ( ( ( X = one_one_real )
% 3.82/4.09 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 = ( semiri5074537144036343181t_real @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) )
% 3.82/4.09 & ( ( X != one_one_real )
% 3.82/4.09 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 = ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( suc @ N2 ) ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum_gp0
% 3.82/4.09 thf(fact_6968_choose__alternating__linear__sum,axiom,
% 3.82/4.09 ! [N2: nat] :
% 3.82/4.09 ( ( N2 != one_one_nat )
% 3.82/4.09 => ( ( groups2073611262835488442omplex
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_complex @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ I3 ) @ ( semiri8010041392384452111omplex @ I3 ) ) @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ I3 ) ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 = zero_zero_complex ) ) ).
% 3.82/4.09
% 3.82/4.09 % choose_alternating_linear_sum
% 3.82/4.09 thf(fact_6969_choose__alternating__linear__sum,axiom,
% 3.82/4.09 ! [N2: nat] :
% 3.82/4.09 ( ( N2 != one_one_nat )
% 3.82/4.09 => ( ( groups3539618377306564664at_int
% 3.82/4.09 @ ^ [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 ) ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 = zero_zero_int ) ) ).
% 3.82/4.09
% 3.82/4.09 % choose_alternating_linear_sum
% 3.82/4.09 thf(fact_6970_choose__alternating__linear__sum,axiom,
% 3.82/4.09 ! [N2: nat] :
% 3.82/4.09 ( ( N2 != one_one_nat )
% 3.82/4.09 => ( ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [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 ) ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 = zero_zero_real ) ) ).
% 3.82/4.09
% 3.82/4.09 % choose_alternating_linear_sum
% 3.82/4.09 thf(fact_6971_gbinomial__sum__nat__pow2,axiom,
% 3.82/4.09 ! [M2: nat] :
% 3.82/4.09 ( ( groups2073611262835488442omplex
% 3.82/4.09 @ ^ [K2: nat] : ( divide1717551699836669952omplex @ ( gbinomial_complex @ ( semiri8010041392384452111omplex @ ( plus_plus_nat @ M2 @ K2 ) ) @ K2 ) @ ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ K2 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ M2 ) )
% 3.82/4.09 = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ M2 ) ) ).
% 3.82/4.09
% 3.82/4.09 % gbinomial_sum_nat_pow2
% 3.82/4.09 thf(fact_6972_gbinomial__sum__nat__pow2,axiom,
% 3.82/4.09 ! [M2: nat] :
% 3.82/4.09 ( ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [K2: nat] : ( divide_divide_real @ ( gbinomial_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ M2 @ K2 ) ) @ K2 ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ K2 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ M2 ) )
% 3.82/4.09 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ M2 ) ) ).
% 3.82/4.09
% 3.82/4.09 % gbinomial_sum_nat_pow2
% 3.82/4.09 thf(fact_6973_gbinomial__partial__sum__poly__xpos,axiom,
% 3.82/4.09 ! [M2: nat,A: complex,X: complex,Y: complex] :
% 3.82/4.09 ( ( groups2073611262835488442omplex
% 3.82/4.09 @ ^ [K2: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M2 ) @ A ) @ K2 ) @ ( power_power_complex @ X @ K2 ) ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ M2 @ K2 ) ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ M2 ) )
% 3.82/4.09 = ( groups2073611262835488442omplex
% 3.82/4.09 @ ^ [K2: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( minus_minus_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ K2 ) @ A ) @ one_one_complex ) @ K2 ) @ ( power_power_complex @ X @ K2 ) ) @ ( power_power_complex @ ( plus_plus_complex @ X @ Y ) @ ( minus_minus_nat @ M2 @ K2 ) ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ M2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % gbinomial_partial_sum_poly_xpos
% 3.82/4.09 thf(fact_6974_gbinomial__partial__sum__poly__xpos,axiom,
% 3.82/4.09 ! [M2: nat,A: real,X: real,Y: real] :
% 3.82/4.09 ( ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [K2: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M2 ) @ A ) @ K2 ) @ ( power_power_real @ X @ K2 ) ) @ ( power_power_real @ Y @ ( minus_minus_nat @ M2 @ K2 ) ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ M2 ) )
% 3.82/4.09 = ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [K2: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( minus_minus_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ K2 ) @ A ) @ one_one_real ) @ K2 ) @ ( power_power_real @ X @ K2 ) ) @ ( power_power_real @ ( plus_plus_real @ X @ Y ) @ ( minus_minus_nat @ M2 @ K2 ) ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ M2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % gbinomial_partial_sum_poly_xpos
% 3.82/4.09 thf(fact_6975_polyfun__diff__alt,axiom,
% 3.82/4.09 ! [N2: nat,A: nat > int,X: int,Y: int] :
% 3.82/4.09 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 3.82/4.09 => ( ( minus_minus_int
% 3.82/4.09 @ ( groups3539618377306564664at_int
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_int @ ( A @ I3 ) @ ( power_power_int @ X @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 @ ( groups3539618377306564664at_int
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_int @ ( A @ I3 ) @ ( power_power_int @ Y @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) )
% 3.82/4.09 = ( times_times_int @ ( minus_minus_int @ X @ Y )
% 3.82/4.09 @ ( groups3539618377306564664at_int
% 3.82/4.09 @ ^ [J2: nat] :
% 3.82/4.09 ( groups3539618377306564664at_int
% 3.82/4.09 @ ^ [K2: nat] : ( times_times_int @ ( times_times_int @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J2 @ K2 ) @ one_one_nat ) ) @ ( power_power_int @ Y @ K2 ) ) @ ( power_power_int @ X @ J2 ) )
% 3.82/4.09 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ J2 ) ) )
% 3.82/4.09 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % polyfun_diff_alt
% 3.82/4.09 thf(fact_6976_polyfun__diff__alt,axiom,
% 3.82/4.09 ! [N2: nat,A: nat > complex,X: complex,Y: complex] :
% 3.82/4.09 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 3.82/4.09 => ( ( minus_minus_complex
% 3.82/4.09 @ ( groups2073611262835488442omplex
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_complex @ ( A @ I3 ) @ ( power_power_complex @ X @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 @ ( groups2073611262835488442omplex
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_complex @ ( A @ I3 ) @ ( power_power_complex @ Y @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) )
% 3.82/4.09 = ( times_times_complex @ ( minus_minus_complex @ X @ Y )
% 3.82/4.09 @ ( groups2073611262835488442omplex
% 3.82/4.09 @ ^ [J2: nat] :
% 3.82/4.09 ( groups2073611262835488442omplex
% 3.82/4.09 @ ^ [K2: nat] : ( times_times_complex @ ( times_times_complex @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J2 @ K2 ) @ one_one_nat ) ) @ ( power_power_complex @ Y @ K2 ) ) @ ( power_power_complex @ X @ J2 ) )
% 3.82/4.09 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ J2 ) ) )
% 3.82/4.09 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % polyfun_diff_alt
% 3.82/4.09 thf(fact_6977_polyfun__diff__alt,axiom,
% 3.82/4.09 ! [N2: nat,A: nat > real,X: real,Y: real] :
% 3.82/4.09 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 3.82/4.09 => ( ( minus_minus_real
% 3.82/4.09 @ ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_real @ ( A @ I3 ) @ ( power_power_real @ X @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 @ ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_real @ ( A @ I3 ) @ ( power_power_real @ Y @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) )
% 3.82/4.09 = ( times_times_real @ ( minus_minus_real @ X @ Y )
% 3.82/4.09 @ ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [J2: nat] :
% 3.82/4.09 ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [K2: nat] : ( times_times_real @ ( times_times_real @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J2 @ K2 ) @ one_one_nat ) ) @ ( power_power_real @ Y @ K2 ) ) @ ( power_power_real @ X @ J2 ) )
% 3.82/4.09 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ J2 ) ) )
% 3.82/4.09 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % polyfun_diff_alt
% 3.82/4.09 thf(fact_6978_binomial__r__part__sum,axiom,
% 3.82/4.09 ! [M2: nat] :
% 3.82/4.09 ( ( groups3542108847815614940at_nat @ ( binomial @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ one_one_nat ) ) @ ( set_ord_atMost_nat @ M2 ) )
% 3.82/4.09 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % binomial_r_part_sum
% 3.82/4.09 thf(fact_6979_choose__alternating__sum,axiom,
% 3.82/4.09 ! [N2: nat] :
% 3.82/4.09 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.09 => ( ( groups2073611262835488442omplex
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ I3 ) @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ I3 ) ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 = zero_zero_complex ) ) ).
% 3.82/4.09
% 3.82/4.09 % choose_alternating_sum
% 3.82/4.09 thf(fact_6980_choose__alternating__sum,axiom,
% 3.82/4.09 ! [N2: nat] :
% 3.82/4.09 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.09 => ( ( groups3539618377306564664at_int
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ I3 ) @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ I3 ) ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 = zero_zero_int ) ) ).
% 3.82/4.09
% 3.82/4.09 % choose_alternating_sum
% 3.82/4.09 thf(fact_6981_choose__alternating__sum,axiom,
% 3.82/4.09 ! [N2: nat] :
% 3.82/4.09 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.09 => ( ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ I3 ) ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 = zero_zero_real ) ) ).
% 3.82/4.09
% 3.82/4.09 % choose_alternating_sum
% 3.82/4.09 thf(fact_6982_polyfun__extremal__lemma,axiom,
% 3.82/4.09 ! [E2: real,C: nat > complex,N2: nat] :
% 3.82/4.09 ( ( ord_less_real @ zero_zero_real @ E2 )
% 3.82/4.09 => ? [M8: real] :
% 3.82/4.09 ! [Z4: complex] :
% 3.82/4.09 ( ( ord_less_eq_real @ M8 @ ( real_V1022390504157884413omplex @ Z4 ) )
% 3.82/4.09 => ( ord_less_eq_real
% 3.82/4.09 @ ( real_V1022390504157884413omplex
% 3.82/4.09 @ ( groups2073611262835488442omplex
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ Z4 @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) )
% 3.82/4.09 @ ( times_times_real @ E2 @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z4 ) @ ( suc @ N2 ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % polyfun_extremal_lemma
% 3.82/4.09 thf(fact_6983_polyfun__extremal__lemma,axiom,
% 3.82/4.09 ! [E2: real,C: nat > real,N2: nat] :
% 3.82/4.09 ( ( ord_less_real @ zero_zero_real @ E2 )
% 3.82/4.09 => ? [M8: real] :
% 3.82/4.09 ! [Z4: real] :
% 3.82/4.09 ( ( ord_less_eq_real @ M8 @ ( real_V7735802525324610683m_real @ Z4 ) )
% 3.82/4.09 => ( ord_less_eq_real
% 3.82/4.09 @ ( real_V7735802525324610683m_real
% 3.82/4.09 @ ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ Z4 @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) )
% 3.82/4.09 @ ( times_times_real @ E2 @ ( power_power_real @ ( real_V7735802525324610683m_real @ Z4 ) @ ( suc @ N2 ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % polyfun_extremal_lemma
% 3.82/4.09 thf(fact_6984_polyfun__diff,axiom,
% 3.82/4.09 ! [N2: nat,A: nat > int,X: int,Y: int] :
% 3.82/4.09 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 3.82/4.09 => ( ( minus_minus_int
% 3.82/4.09 @ ( groups3539618377306564664at_int
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_int @ ( A @ I3 ) @ ( power_power_int @ X @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 @ ( groups3539618377306564664at_int
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_int @ ( A @ I3 ) @ ( power_power_int @ Y @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) )
% 3.82/4.09 = ( times_times_int @ ( minus_minus_int @ X @ Y )
% 3.82/4.09 @ ( groups3539618377306564664at_int
% 3.82/4.09 @ ^ [J2: nat] :
% 3.82/4.09 ( times_times_int
% 3.82/4.09 @ ( groups3539618377306564664at_int
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_int @ ( A @ I3 ) @ ( power_power_int @ Y @ ( minus_minus_nat @ ( minus_minus_nat @ I3 @ J2 ) @ one_one_nat ) ) )
% 3.82/4.09 @ ( set_or1269000886237332187st_nat @ ( suc @ J2 ) @ N2 ) )
% 3.82/4.09 @ ( power_power_int @ X @ J2 ) )
% 3.82/4.09 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % polyfun_diff
% 3.82/4.09 thf(fact_6985_polyfun__diff,axiom,
% 3.82/4.09 ! [N2: nat,A: nat > complex,X: complex,Y: complex] :
% 3.82/4.09 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 3.82/4.09 => ( ( minus_minus_complex
% 3.82/4.09 @ ( groups2073611262835488442omplex
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_complex @ ( A @ I3 ) @ ( power_power_complex @ X @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 @ ( groups2073611262835488442omplex
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_complex @ ( A @ I3 ) @ ( power_power_complex @ Y @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) )
% 3.82/4.09 = ( times_times_complex @ ( minus_minus_complex @ X @ Y )
% 3.82/4.09 @ ( groups2073611262835488442omplex
% 3.82/4.09 @ ^ [J2: nat] :
% 3.82/4.09 ( times_times_complex
% 3.82/4.09 @ ( groups2073611262835488442omplex
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_complex @ ( A @ I3 ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ ( minus_minus_nat @ I3 @ J2 ) @ one_one_nat ) ) )
% 3.82/4.09 @ ( set_or1269000886237332187st_nat @ ( suc @ J2 ) @ N2 ) )
% 3.82/4.09 @ ( power_power_complex @ X @ J2 ) )
% 3.82/4.09 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % polyfun_diff
% 3.82/4.09 thf(fact_6986_polyfun__diff,axiom,
% 3.82/4.09 ! [N2: nat,A: nat > real,X: real,Y: real] :
% 3.82/4.09 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 3.82/4.09 => ( ( minus_minus_real
% 3.82/4.09 @ ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_real @ ( A @ I3 ) @ ( power_power_real @ X @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.09 @ ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_real @ ( A @ I3 ) @ ( power_power_real @ Y @ I3 ) )
% 3.82/4.09 @ ( set_ord_atMost_nat @ N2 ) ) )
% 3.82/4.09 = ( times_times_real @ ( minus_minus_real @ X @ Y )
% 3.82/4.09 @ ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [J2: nat] :
% 3.82/4.09 ( times_times_real
% 3.82/4.09 @ ( groups6591440286371151544t_real
% 3.82/4.09 @ ^ [I3: nat] : ( times_times_real @ ( A @ I3 ) @ ( power_power_real @ Y @ ( minus_minus_nat @ ( minus_minus_nat @ I3 @ J2 ) @ one_one_nat ) ) )
% 3.82/4.09 @ ( set_or1269000886237332187st_nat @ ( suc @ J2 ) @ N2 ) )
% 3.82/4.09 @ ( power_power_real @ X @ J2 ) )
% 3.82/4.09 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % polyfun_diff
% 3.82/4.09 thf(fact_6987_sin__cos__npi,axiom,
% 3.82/4.09 ! [N2: nat] :
% 3.82/4.09 ( ( 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 ) ) ) )
% 3.82/4.09 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) ) ).
% 3.82/4.09
% 3.82/4.09 % sin_cos_npi
% 3.82/4.09 thf(fact_6988_cos__pi__eq__zero,axiom,
% 3.82/4.09 ! [M2: nat] :
% 3.82/4.09 ( ( cos_real @ ( divide_divide_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 3.82/4.09 = zero_zero_real ) ).
% 3.82/4.09
% 3.82/4.09 % cos_pi_eq_zero
% 3.82/4.09 thf(fact_6989_gbinomial__code,axiom,
% 3.82/4.09 ( gbinomial_complex
% 3.82/4.09 = ( ^ [A3: complex,K2: nat] :
% 3.82/4.09 ( if_complex @ ( K2 = zero_zero_nat ) @ one_one_complex
% 3.82/4.09 @ ( divide1717551699836669952omplex
% 3.82/4.09 @ ( set_fo1517530859248394432omplex
% 3.82/4.09 @ ^ [L2: nat] : ( times_times_complex @ ( minus_minus_complex @ A3 @ ( semiri8010041392384452111omplex @ L2 ) ) )
% 3.82/4.09 @ zero_zero_nat
% 3.82/4.09 @ ( minus_minus_nat @ K2 @ one_one_nat )
% 3.82/4.09 @ one_one_complex )
% 3.82/4.09 @ ( semiri5044797733671781792omplex @ K2 ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % gbinomial_code
% 3.82/4.09 thf(fact_6990_gbinomial__code,axiom,
% 3.82/4.09 ( gbinomial_real
% 3.82/4.09 = ( ^ [A3: real,K2: nat] :
% 3.82/4.09 ( if_real @ ( K2 = zero_zero_nat ) @ one_one_real
% 3.82/4.09 @ ( divide_divide_real
% 3.82/4.09 @ ( set_fo3111899725591712190t_real
% 3.82/4.09 @ ^ [L2: nat] : ( times_times_real @ ( minus_minus_real @ A3 @ ( semiri5074537144036343181t_real @ L2 ) ) )
% 3.82/4.09 @ zero_zero_nat
% 3.82/4.09 @ ( minus_minus_nat @ K2 @ one_one_nat )
% 3.82/4.09 @ one_one_real )
% 3.82/4.09 @ ( semiri2265585572941072030t_real @ K2 ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % gbinomial_code
% 3.82/4.09 thf(fact_6991_sum__pos__lt__pair,axiom,
% 3.82/4.09 ! [F: nat > real,K: nat] :
% 3.82/4.09 ( ( summable_real @ F )
% 3.82/4.09 => ( ! [D5: nat] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( F @ ( plus_plus_nat @ K @ ( times_times_nat @ ( suc @ ( suc @ zero_zero_nat ) ) @ D5 ) ) ) @ ( F @ ( plus_plus_nat @ K @ ( plus_plus_nat @ ( times_times_nat @ ( suc @ ( suc @ zero_zero_nat ) ) @ D5 ) @ one_one_nat ) ) ) ) )
% 3.82/4.09 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) @ ( suminf_real @ F ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum_pos_lt_pair
% 3.82/4.09 thf(fact_6992_binomial__code,axiom,
% 3.82/4.09 ( binomial
% 3.82/4.09 = ( ^ [N: nat,K2: nat] : ( if_nat @ ( ord_less_nat @ N @ K2 ) @ zero_zero_nat @ ( if_nat @ ( ord_less_nat @ N @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K2 ) ) @ ( binomial @ N @ ( minus_minus_nat @ N @ K2 ) ) @ ( divide_divide_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( plus_plus_nat @ ( minus_minus_nat @ N @ K2 ) @ one_one_nat ) @ N @ one_one_nat ) @ ( semiri1408675320244567234ct_nat @ K2 ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % binomial_code
% 3.82/4.09 thf(fact_6993_modulo__int__unfold,axiom,
% 3.82/4.09 ! [L: int,K: int,N2: nat,M2: nat] :
% 3.82/4.09 ( ( ( ( ( sgn_sgn_int @ L )
% 3.82/4.09 = zero_zero_int )
% 3.82/4.09 | ( ( sgn_sgn_int @ K )
% 3.82/4.09 = zero_zero_int )
% 3.82/4.09 | ( N2 = zero_zero_nat ) )
% 3.82/4.09 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 3.82/4.09 = ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M2 ) ) ) )
% 3.82/4.09 & ( ~ ( ( ( sgn_sgn_int @ L )
% 3.82/4.09 = zero_zero_int )
% 3.82/4.09 | ( ( sgn_sgn_int @ K )
% 3.82/4.09 = zero_zero_int )
% 3.82/4.09 | ( N2 = zero_zero_nat ) )
% 3.82/4.09 => ( ( ( ( sgn_sgn_int @ K )
% 3.82/4.09 = ( sgn_sgn_int @ L ) )
% 3.82/4.09 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 3.82/4.09 = ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M2 @ N2 ) ) ) ) )
% 3.82/4.09 & ( ( ( sgn_sgn_int @ K )
% 3.82/4.09 != ( sgn_sgn_int @ L ) )
% 3.82/4.09 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 3.82/4.09 = ( times_times_int @ ( sgn_sgn_int @ L )
% 3.82/4.09 @ ( minus_minus_int
% 3.82/4.09 @ ( semiri1314217659103216013at_int
% 3.82/4.09 @ ( times_times_nat @ N2
% 3.82/4.09 @ ( zero_n2687167440665602831ol_nat
% 3.82/4.09 @ ~ ( dvd_dvd_nat @ N2 @ M2 ) ) ) )
% 3.82/4.09 @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M2 @ N2 ) ) ) ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % modulo_int_unfold
% 3.82/4.09 thf(fact_6994_sgn__sgn,axiom,
% 3.82/4.09 ! [A: int] :
% 3.82/4.09 ( ( sgn_sgn_int @ ( sgn_sgn_int @ A ) )
% 3.82/4.09 = ( sgn_sgn_int @ A ) ) ).
% 3.82/4.09
% 3.82/4.09 % sgn_sgn
% 3.82/4.09 thf(fact_6995_sgn__sgn,axiom,
% 3.82/4.09 ! [A: real] :
% 3.82/4.09 ( ( sgn_sgn_real @ ( sgn_sgn_real @ A ) )
% 3.82/4.09 = ( sgn_sgn_real @ A ) ) ).
% 3.82/4.09
% 3.82/4.09 % sgn_sgn
% 3.82/4.09 thf(fact_6996_of__nat__id,axiom,
% 3.82/4.09 ( semiri1316708129612266289at_nat
% 3.82/4.09 = ( ^ [N: nat] : N ) ) ).
% 3.82/4.09
% 3.82/4.09 % of_nat_id
% 3.82/4.09 thf(fact_6997_sin__zero,axiom,
% 3.82/4.09 ( ( sin_real @ zero_zero_real )
% 3.82/4.09 = zero_zero_real ) ).
% 3.82/4.09
% 3.82/4.09 % sin_zero
% 3.82/4.09 thf(fact_6998_sin__zero,axiom,
% 3.82/4.09 ( ( sin_complex @ zero_zero_complex )
% 3.82/4.09 = zero_zero_complex ) ).
% 3.82/4.09
% 3.82/4.09 % sin_zero
% 3.82/4.09 thf(fact_6999_sgn__0,axiom,
% 3.82/4.09 ( ( sgn_sgn_real @ zero_zero_real )
% 3.82/4.09 = zero_zero_real ) ).
% 3.82/4.09
% 3.82/4.09 % sgn_0
% 3.82/4.09 thf(fact_7000_sgn__0,axiom,
% 3.82/4.09 ( ( sgn_sgn_int @ zero_zero_int )
% 3.82/4.09 = zero_zero_int ) ).
% 3.82/4.09
% 3.82/4.09 % sgn_0
% 3.82/4.09 thf(fact_7001_sgn__0,axiom,
% 3.82/4.09 ( ( sgn_sgn_complex @ zero_zero_complex )
% 3.82/4.09 = zero_zero_complex ) ).
% 3.82/4.09
% 3.82/4.09 % sgn_0
% 3.82/4.09 thf(fact_7002_sgn__zero,axiom,
% 3.82/4.09 ( ( sgn_sgn_real @ zero_zero_real )
% 3.82/4.09 = zero_zero_real ) ).
% 3.82/4.09
% 3.82/4.09 % sgn_zero
% 3.82/4.09 thf(fact_7003_sgn__zero,axiom,
% 3.82/4.09 ( ( sgn_sgn_complex @ zero_zero_complex )
% 3.82/4.09 = zero_zero_complex ) ).
% 3.82/4.09
% 3.82/4.09 % sgn_zero
% 3.82/4.09 thf(fact_7004_sgn__1,axiom,
% 3.82/4.09 ( ( sgn_sgn_complex @ one_one_complex )
% 3.82/4.09 = one_one_complex ) ).
% 3.82/4.09
% 3.82/4.09 % sgn_1
% 3.82/4.09 thf(fact_7005_sgn__1,axiom,
% 3.82/4.09 ( ( sgn_sgn_int @ one_one_int )
% 3.82/4.09 = one_one_int ) ).
% 3.82/4.09
% 3.82/4.09 % sgn_1
% 3.82/4.09 thf(fact_7006_sgn__1,axiom,
% 3.82/4.09 ( ( sgn_sgn_real @ one_one_real )
% 3.82/4.09 = one_one_real ) ).
% 3.82/4.09
% 3.82/4.09 % sgn_1
% 3.82/4.09 thf(fact_7007_sgn__divide,axiom,
% 3.82/4.09 ! [A: real,B2: real] :
% 3.82/4.09 ( ( sgn_sgn_real @ ( divide_divide_real @ A @ B2 ) )
% 3.82/4.09 = ( divide_divide_real @ ( sgn_sgn_real @ A ) @ ( sgn_sgn_real @ B2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sgn_divide
% 3.82/4.09 thf(fact_7008_idom__abs__sgn__class_Osgn__minus,axiom,
% 3.82/4.09 ! [A: int] :
% 3.82/4.09 ( ( sgn_sgn_int @ ( uminus_uminus_int @ A ) )
% 3.82/4.09 = ( uminus_uminus_int @ ( sgn_sgn_int @ A ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % idom_abs_sgn_class.sgn_minus
% 3.82/4.09 thf(fact_7009_idom__abs__sgn__class_Osgn__minus,axiom,
% 3.82/4.09 ! [A: real] :
% 3.82/4.09 ( ( sgn_sgn_real @ ( uminus_uminus_real @ A ) )
% 3.82/4.09 = ( uminus_uminus_real @ ( sgn_sgn_real @ A ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % idom_abs_sgn_class.sgn_minus
% 3.82/4.09 thf(fact_7010_summable__zero,axiom,
% 3.82/4.09 ( summable_nat
% 3.82/4.09 @ ^ [N: nat] : zero_zero_nat ) ).
% 3.82/4.09
% 3.82/4.09 % summable_zero
% 3.82/4.09 thf(fact_7011_summable__zero,axiom,
% 3.82/4.09 ( summable_real
% 3.82/4.09 @ ^ [N: nat] : zero_zero_real ) ).
% 3.82/4.09
% 3.82/4.09 % summable_zero
% 3.82/4.09 thf(fact_7012_summable__zero,axiom,
% 3.82/4.09 ( summable_int
% 3.82/4.09 @ ^ [N: nat] : zero_zero_int ) ).
% 3.82/4.09
% 3.82/4.09 % summable_zero
% 3.82/4.09 thf(fact_7013_summable__zero,axiom,
% 3.82/4.09 ( summable_complex
% 3.82/4.09 @ ^ [N: nat] : zero_zero_complex ) ).
% 3.82/4.09
% 3.82/4.09 % summable_zero
% 3.82/4.09 thf(fact_7014_summable__single,axiom,
% 3.82/4.09 ! [I: nat,F: nat > nat] :
% 3.82/4.09 ( summable_nat
% 3.82/4.09 @ ^ [R4: nat] : ( if_nat @ ( R4 = I ) @ ( F @ R4 ) @ zero_zero_nat ) ) ).
% 3.82/4.09
% 3.82/4.09 % summable_single
% 3.82/4.09 thf(fact_7015_summable__single,axiom,
% 3.82/4.09 ! [I: nat,F: nat > real] :
% 3.82/4.09 ( summable_real
% 3.82/4.09 @ ^ [R4: nat] : ( if_real @ ( R4 = I ) @ ( F @ R4 ) @ zero_zero_real ) ) ).
% 3.82/4.09
% 3.82/4.09 % summable_single
% 3.82/4.09 thf(fact_7016_summable__single,axiom,
% 3.82/4.09 ! [I: nat,F: nat > int] :
% 3.82/4.09 ( summable_int
% 3.82/4.09 @ ^ [R4: nat] : ( if_int @ ( R4 = I ) @ ( F @ R4 ) @ zero_zero_int ) ) ).
% 3.82/4.09
% 3.82/4.09 % summable_single
% 3.82/4.09 thf(fact_7017_summable__single,axiom,
% 3.82/4.09 ! [I: nat,F: nat > complex] :
% 3.82/4.09 ( summable_complex
% 3.82/4.09 @ ^ [R4: nat] : ( if_complex @ ( R4 = I ) @ ( F @ R4 ) @ zero_zero_complex ) ) ).
% 3.82/4.09
% 3.82/4.09 % summable_single
% 3.82/4.09 thf(fact_7018_summable__iff__shift,axiom,
% 3.82/4.09 ! [F: nat > real,K: nat] :
% 3.82/4.09 ( ( summable_real
% 3.82/4.09 @ ^ [N: nat] : ( F @ ( plus_plus_nat @ N @ K ) ) )
% 3.82/4.09 = ( summable_real @ F ) ) ).
% 3.82/4.09
% 3.82/4.09 % summable_iff_shift
% 3.82/4.09 thf(fact_7019_sgn__less,axiom,
% 3.82/4.09 ! [A: real] :
% 3.82/4.09 ( ( ord_less_real @ ( sgn_sgn_real @ A ) @ zero_zero_real )
% 3.82/4.09 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 3.82/4.09
% 3.82/4.09 % sgn_less
% 3.82/4.09 thf(fact_7020_sgn__less,axiom,
% 3.82/4.09 ! [A: int] :
% 3.82/4.09 ( ( ord_less_int @ ( sgn_sgn_int @ A ) @ zero_zero_int )
% 3.82/4.09 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 3.82/4.09
% 3.82/4.09 % sgn_less
% 3.82/4.09 thf(fact_7021_sgn__greater,axiom,
% 3.82/4.09 ! [A: real] :
% 3.82/4.09 ( ( ord_less_real @ zero_zero_real @ ( sgn_sgn_real @ A ) )
% 3.82/4.09 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 3.82/4.09
% 3.82/4.09 % sgn_greater
% 3.82/4.09 thf(fact_7022_sgn__greater,axiom,
% 3.82/4.09 ! [A: int] :
% 3.82/4.09 ( ( ord_less_int @ zero_zero_int @ ( sgn_sgn_int @ A ) )
% 3.82/4.09 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 3.82/4.09
% 3.82/4.09 % sgn_greater
% 3.82/4.09 thf(fact_7023_cos__zero,axiom,
% 3.82/4.09 ( ( cos_real @ zero_zero_real )
% 3.82/4.09 = one_one_real ) ).
% 3.82/4.09
% 3.82/4.09 % cos_zero
% 3.82/4.09 thf(fact_7024_cos__zero,axiom,
% 3.82/4.09 ( ( cos_complex @ zero_zero_complex )
% 3.82/4.09 = one_one_complex ) ).
% 3.82/4.09
% 3.82/4.09 % cos_zero
% 3.82/4.09 thf(fact_7025_divide__sgn,axiom,
% 3.82/4.09 ! [A: real,B2: real] :
% 3.82/4.09 ( ( divide_divide_real @ A @ ( sgn_sgn_real @ B2 ) )
% 3.82/4.09 = ( times_times_real @ A @ ( sgn_sgn_real @ B2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % divide_sgn
% 3.82/4.09 thf(fact_7026_fact__0,axiom,
% 3.82/4.09 ( ( semiri1406184849735516958ct_int @ zero_zero_nat )
% 3.82/4.09 = one_one_int ) ).
% 3.82/4.09
% 3.82/4.09 % fact_0
% 3.82/4.09 thf(fact_7027_fact__0,axiom,
% 3.82/4.09 ( ( semiri5044797733671781792omplex @ zero_zero_nat )
% 3.82/4.09 = one_one_complex ) ).
% 3.82/4.09
% 3.82/4.09 % fact_0
% 3.82/4.09 thf(fact_7028_fact__0,axiom,
% 3.82/4.09 ( ( semiri1408675320244567234ct_nat @ zero_zero_nat )
% 3.82/4.09 = one_one_nat ) ).
% 3.82/4.09
% 3.82/4.09 % fact_0
% 3.82/4.09 thf(fact_7029_fact__0,axiom,
% 3.82/4.09 ( ( semiri2265585572941072030t_real @ zero_zero_nat )
% 3.82/4.09 = one_one_real ) ).
% 3.82/4.09
% 3.82/4.09 % fact_0
% 3.82/4.09 thf(fact_7030_summable__cmult__iff,axiom,
% 3.82/4.09 ! [C: real,F: nat > real] :
% 3.82/4.09 ( ( summable_real
% 3.82/4.09 @ ^ [N: nat] : ( times_times_real @ C @ ( F @ N ) ) )
% 3.82/4.09 = ( ( C = zero_zero_real )
% 3.82/4.09 | ( summable_real @ F ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % summable_cmult_iff
% 3.82/4.09 thf(fact_7031_summable__cmult__iff,axiom,
% 3.82/4.09 ! [C: complex,F: nat > complex] :
% 3.82/4.09 ( ( summable_complex
% 3.82/4.09 @ ^ [N: nat] : ( times_times_complex @ C @ ( F @ N ) ) )
% 3.82/4.09 = ( ( C = zero_zero_complex )
% 3.82/4.09 | ( summable_complex @ F ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % summable_cmult_iff
% 3.82/4.09 thf(fact_7032_summable__divide__iff,axiom,
% 3.82/4.09 ! [F: nat > complex,C: complex] :
% 3.82/4.09 ( ( summable_complex
% 3.82/4.09 @ ^ [N: nat] : ( divide1717551699836669952omplex @ ( F @ N ) @ C ) )
% 3.82/4.09 = ( ( C = zero_zero_complex )
% 3.82/4.09 | ( summable_complex @ F ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % summable_divide_iff
% 3.82/4.09 thf(fact_7033_summable__divide__iff,axiom,
% 3.82/4.09 ! [F: nat > real,C: real] :
% 3.82/4.09 ( ( summable_real
% 3.82/4.09 @ ^ [N: nat] : ( divide_divide_real @ ( F @ N ) @ C ) )
% 3.82/4.09 = ( ( C = zero_zero_real )
% 3.82/4.09 | ( summable_real @ F ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % summable_divide_iff
% 3.82/4.09 thf(fact_7034_summable__If__finite__set,axiom,
% 3.82/4.09 ! [A2: set_nat,F: nat > nat] :
% 3.82/4.09 ( ( finite_finite_nat @ A2 )
% 3.82/4.09 => ( summable_nat
% 3.82/4.09 @ ^ [R4: nat] : ( if_nat @ ( member_nat @ R4 @ A2 ) @ ( F @ R4 ) @ zero_zero_nat ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % summable_If_finite_set
% 3.82/4.09 thf(fact_7035_summable__If__finite__set,axiom,
% 3.82/4.09 ! [A2: set_nat,F: nat > real] :
% 3.82/4.09 ( ( finite_finite_nat @ A2 )
% 3.82/4.09 => ( summable_real
% 3.82/4.09 @ ^ [R4: nat] : ( if_real @ ( member_nat @ R4 @ A2 ) @ ( F @ R4 ) @ zero_zero_real ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % summable_If_finite_set
% 3.82/4.09 thf(fact_7036_summable__If__finite__set,axiom,
% 3.82/4.09 ! [A2: set_nat,F: nat > int] :
% 3.82/4.09 ( ( finite_finite_nat @ A2 )
% 3.82/4.09 => ( summable_int
% 3.82/4.09 @ ^ [R4: nat] : ( if_int @ ( member_nat @ R4 @ A2 ) @ ( F @ R4 ) @ zero_zero_int ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % summable_If_finite_set
% 3.82/4.09 thf(fact_7037_summable__If__finite__set,axiom,
% 3.82/4.09 ! [A2: set_nat,F: nat > complex] :
% 3.82/4.09 ( ( finite_finite_nat @ A2 )
% 3.82/4.09 => ( summable_complex
% 3.82/4.09 @ ^ [R4: nat] : ( if_complex @ ( member_nat @ R4 @ A2 ) @ ( F @ R4 ) @ zero_zero_complex ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % summable_If_finite_set
% 3.82/4.09 thf(fact_7038_summable__If__finite,axiom,
% 3.82/4.09 ! [P: nat > $o,F: nat > nat] :
% 3.82/4.09 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 3.82/4.09 => ( summable_nat
% 3.82/4.09 @ ^ [R4: nat] : ( if_nat @ ( P @ R4 ) @ ( F @ R4 ) @ zero_zero_nat ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % summable_If_finite
% 3.82/4.09 thf(fact_7039_summable__If__finite,axiom,
% 3.82/4.09 ! [P: nat > $o,F: nat > real] :
% 3.82/4.09 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 3.82/4.09 => ( summable_real
% 3.82/4.09 @ ^ [R4: nat] : ( if_real @ ( P @ R4 ) @ ( F @ R4 ) @ zero_zero_real ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % summable_If_finite
% 3.82/4.09 thf(fact_7040_summable__If__finite,axiom,
% 3.82/4.09 ! [P: nat > $o,F: nat > int] :
% 3.82/4.09 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 3.82/4.09 => ( summable_int
% 3.82/4.09 @ ^ [R4: nat] : ( if_int @ ( P @ R4 ) @ ( F @ R4 ) @ zero_zero_int ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % summable_If_finite
% 3.82/4.09 thf(fact_7041_summable__If__finite,axiom,
% 3.82/4.09 ! [P: nat > $o,F: nat > complex] :
% 3.82/4.09 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 3.82/4.09 => ( summable_complex
% 3.82/4.09 @ ^ [R4: nat] : ( if_complex @ ( P @ R4 ) @ ( F @ R4 ) @ zero_zero_complex ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % summable_If_finite
% 3.82/4.09 thf(fact_7042_sgn__pos,axiom,
% 3.82/4.09 ! [A: real] :
% 3.82/4.09 ( ( ord_less_real @ zero_zero_real @ A )
% 3.82/4.09 => ( ( sgn_sgn_real @ A )
% 3.82/4.09 = one_one_real ) ) ).
% 3.82/4.09
% 3.82/4.09 % sgn_pos
% 3.82/4.09 thf(fact_7043_sgn__pos,axiom,
% 3.82/4.09 ! [A: int] :
% 3.82/4.09 ( ( ord_less_int @ zero_zero_int @ A )
% 3.82/4.09 => ( ( sgn_sgn_int @ A )
% 3.82/4.09 = one_one_int ) ) ).
% 3.82/4.09
% 3.82/4.09 % sgn_pos
% 3.82/4.09 thf(fact_7044_fact__Suc__0,axiom,
% 3.82/4.09 ( ( semiri1406184849735516958ct_int @ ( suc @ zero_zero_nat ) )
% 3.82/4.09 = one_one_int ) ).
% 3.82/4.09
% 3.82/4.09 % fact_Suc_0
% 3.82/4.09 thf(fact_7045_fact__Suc__0,axiom,
% 3.82/4.09 ( ( semiri5044797733671781792omplex @ ( suc @ zero_zero_nat ) )
% 3.82/4.09 = one_one_complex ) ).
% 3.82/4.09
% 3.82/4.09 % fact_Suc_0
% 3.82/4.09 thf(fact_7046_fact__Suc__0,axiom,
% 3.82/4.09 ( ( semiri1408675320244567234ct_nat @ ( suc @ zero_zero_nat ) )
% 3.82/4.09 = one_one_nat ) ).
% 3.82/4.09
% 3.82/4.09 % fact_Suc_0
% 3.82/4.09 thf(fact_7047_fact__Suc__0,axiom,
% 3.82/4.09 ( ( semiri2265585572941072030t_real @ ( suc @ zero_zero_nat ) )
% 3.82/4.09 = one_one_real ) ).
% 3.82/4.09
% 3.82/4.09 % fact_Suc_0
% 3.82/4.09 thf(fact_7048_fact__Suc,axiom,
% 3.82/4.09 ! [N2: nat] :
% 3.82/4.09 ( ( semiri5044797733671781792omplex @ ( suc @ N2 ) )
% 3.82/4.09 = ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ N2 ) ) @ ( semiri5044797733671781792omplex @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % fact_Suc
% 3.82/4.09 thf(fact_7049_fact__Suc,axiom,
% 3.82/4.09 ! [N2: nat] :
% 3.82/4.09 ( ( semiri4449623510593786356d_enat @ ( suc @ N2 ) )
% 3.82/4.09 = ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ ( suc @ N2 ) ) @ ( semiri4449623510593786356d_enat @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % fact_Suc
% 3.82/4.09 thf(fact_7050_fact__Suc,axiom,
% 3.82/4.09 ! [N2: nat] :
% 3.82/4.09 ( ( semiri1406184849735516958ct_int @ ( suc @ N2 ) )
% 3.82/4.09 = ( times_times_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) @ ( semiri1406184849735516958ct_int @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % fact_Suc
% 3.82/4.09 thf(fact_7051_fact__Suc,axiom,
% 3.82/4.09 ! [N2: nat] :
% 3.82/4.09 ( ( semiri1408675320244567234ct_nat @ ( suc @ N2 ) )
% 3.82/4.09 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( suc @ N2 ) ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % fact_Suc
% 3.82/4.09 thf(fact_7052_fact__Suc,axiom,
% 3.82/4.09 ! [N2: nat] :
% 3.82/4.09 ( ( semiri2265585572941072030t_real @ ( suc @ N2 ) )
% 3.82/4.09 = ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % fact_Suc
% 3.82/4.09 thf(fact_7053_sgn__mult__self__eq,axiom,
% 3.82/4.09 ! [A: real] :
% 3.82/4.09 ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( sgn_sgn_real @ A ) )
% 3.82/4.09 = ( zero_n3304061248610475627l_real @ ( A != zero_zero_real ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sgn_mult_self_eq
% 3.82/4.09 thf(fact_7054_sgn__mult__self__eq,axiom,
% 3.82/4.09 ! [A: int] :
% 3.82/4.09 ( ( times_times_int @ ( sgn_sgn_int @ A ) @ ( sgn_sgn_int @ A ) )
% 3.82/4.09 = ( zero_n2684676970156552555ol_int @ ( A != zero_zero_int ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sgn_mult_self_eq
% 3.82/4.09 thf(fact_7055_sin__of__real__pi,axiom,
% 3.82/4.09 ( ( sin_real @ ( real_V1803761363581548252l_real @ pi ) )
% 3.82/4.09 = zero_zero_real ) ).
% 3.82/4.09
% 3.82/4.09 % sin_of_real_pi
% 3.82/4.09 thf(fact_7056_sin__of__real__pi,axiom,
% 3.82/4.09 ( ( sin_complex @ ( real_V4546457046886955230omplex @ pi ) )
% 3.82/4.09 = zero_zero_complex ) ).
% 3.82/4.09
% 3.82/4.09 % sin_of_real_pi
% 3.82/4.09 thf(fact_7057_dvd__mult__sgn__iff,axiom,
% 3.82/4.09 ! [L: int,K: int,R2: int] :
% 3.82/4.09 ( ( dvd_dvd_int @ L @ ( times_times_int @ K @ ( sgn_sgn_int @ R2 ) ) )
% 3.82/4.09 = ( ( dvd_dvd_int @ L @ K )
% 3.82/4.09 | ( R2 = zero_zero_int ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % dvd_mult_sgn_iff
% 3.82/4.09 thf(fact_7058_dvd__sgn__mult__iff,axiom,
% 3.82/4.09 ! [L: int,R2: int,K: int] :
% 3.82/4.09 ( ( dvd_dvd_int @ L @ ( times_times_int @ ( sgn_sgn_int @ R2 ) @ K ) )
% 3.82/4.09 = ( ( dvd_dvd_int @ L @ K )
% 3.82/4.09 | ( R2 = zero_zero_int ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % dvd_sgn_mult_iff
% 3.82/4.09 thf(fact_7059_mult__sgn__dvd__iff,axiom,
% 3.82/4.09 ! [L: int,R2: int,K: int] :
% 3.82/4.09 ( ( dvd_dvd_int @ ( times_times_int @ L @ ( sgn_sgn_int @ R2 ) ) @ K )
% 3.82/4.09 = ( ( dvd_dvd_int @ L @ K )
% 3.82/4.09 & ( ( R2 = zero_zero_int )
% 3.82/4.09 => ( K = zero_zero_int ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % mult_sgn_dvd_iff
% 3.82/4.09 thf(fact_7060_sgn__mult__dvd__iff,axiom,
% 3.82/4.09 ! [R2: int,L: int,K: int] :
% 3.82/4.09 ( ( dvd_dvd_int @ ( times_times_int @ ( sgn_sgn_int @ R2 ) @ L ) @ K )
% 3.82/4.09 = ( ( dvd_dvd_int @ L @ K )
% 3.82/4.09 & ( ( R2 = zero_zero_int )
% 3.82/4.09 => ( K = zero_zero_int ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sgn_mult_dvd_iff
% 3.82/4.09 thf(fact_7061_sgn__neg,axiom,
% 3.82/4.09 ! [A: int] :
% 3.82/4.09 ( ( ord_less_int @ A @ zero_zero_int )
% 3.82/4.09 => ( ( sgn_sgn_int @ A )
% 3.82/4.09 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sgn_neg
% 3.82/4.09 thf(fact_7062_sgn__neg,axiom,
% 3.82/4.09 ! [A: real] :
% 3.82/4.09 ( ( ord_less_real @ A @ zero_zero_real )
% 3.82/4.09 => ( ( sgn_sgn_real @ A )
% 3.82/4.09 = ( uminus_uminus_real @ one_one_real ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sgn_neg
% 3.82/4.09 thf(fact_7063_sin__cos__squared__add3,axiom,
% 3.82/4.09 ! [X: real] :
% 3.82/4.09 ( ( plus_plus_real @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ X ) ) @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ X ) ) )
% 3.82/4.09 = one_one_real ) ).
% 3.82/4.09
% 3.82/4.09 % sin_cos_squared_add3
% 3.82/4.09 thf(fact_7064_sin__cos__squared__add3,axiom,
% 3.82/4.09 ! [X: complex] :
% 3.82/4.09 ( ( plus_plus_complex @ ( times_times_complex @ ( cos_complex @ X ) @ ( cos_complex @ X ) ) @ ( times_times_complex @ ( sin_complex @ X ) @ ( sin_complex @ X ) ) )
% 3.82/4.09 = one_one_complex ) ).
% 3.82/4.09
% 3.82/4.09 % sin_cos_squared_add3
% 3.82/4.09 thf(fact_7065_sgn__of__nat,axiom,
% 3.82/4.09 ! [N2: nat] :
% 3.82/4.09 ( ( sgn_sgn_real @ ( semiri5074537144036343181t_real @ N2 ) )
% 3.82/4.09 = ( zero_n3304061248610475627l_real @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sgn_of_nat
% 3.82/4.09 thf(fact_7066_sgn__of__nat,axiom,
% 3.82/4.09 ! [N2: nat] :
% 3.82/4.09 ( ( sgn_sgn_int @ ( semiri1314217659103216013at_int @ N2 ) )
% 3.82/4.09 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sgn_of_nat
% 3.82/4.09 thf(fact_7067_sin__cos__squared__add2,axiom,
% 3.82/4.09 ! [X: real] :
% 3.82/4.09 ( ( plus_plus_real @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sin_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 3.82/4.09 = one_one_real ) ).
% 3.82/4.09
% 3.82/4.09 % sin_cos_squared_add2
% 3.82/4.09 thf(fact_7068_sin__cos__squared__add2,axiom,
% 3.82/4.09 ! [X: complex] :
% 3.82/4.09 ( ( plus_plus_complex @ ( power_power_complex @ ( cos_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sin_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 3.82/4.09 = one_one_complex ) ).
% 3.82/4.09
% 3.82/4.09 % sin_cos_squared_add2
% 3.82/4.09 thf(fact_7069_sin__cos__squared__add,axiom,
% 3.82/4.09 ! [X: real] :
% 3.82/4.09 ( ( plus_plus_real @ ( power_power_real @ ( sin_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 3.82/4.09 = one_one_real ) ).
% 3.82/4.09
% 3.82/4.09 % sin_cos_squared_add
% 3.82/4.09 thf(fact_7070_sin__cos__squared__add,axiom,
% 3.82/4.09 ! [X: complex] :
% 3.82/4.09 ( ( plus_plus_complex @ ( power_power_complex @ ( sin_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( cos_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 3.82/4.09 = one_one_complex ) ).
% 3.82/4.09
% 3.82/4.09 % sin_cos_squared_add
% 3.82/4.09 thf(fact_7071_cos__of__real__pi__half,axiom,
% 3.82/4.09 ( ( cos_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 3.82/4.09 = zero_zero_real ) ).
% 3.82/4.09
% 3.82/4.09 % cos_of_real_pi_half
% 3.82/4.09 thf(fact_7072_cos__of__real__pi__half,axiom,
% 3.82/4.09 ( ( cos_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 3.82/4.09 = zero_zero_complex ) ).
% 3.82/4.09
% 3.82/4.09 % cos_of_real_pi_half
% 3.82/4.09 thf(fact_7073_sin__add,axiom,
% 3.82/4.09 ! [X: real,Y: real] :
% 3.82/4.09 ( ( sin_real @ ( plus_plus_real @ X @ Y ) )
% 3.82/4.09 = ( plus_plus_real @ ( times_times_real @ ( sin_real @ X ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( sin_real @ Y ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sin_add
% 3.82/4.09 thf(fact_7074_sin__add,axiom,
% 3.82/4.09 ! [X: complex,Y: complex] :
% 3.82/4.09 ( ( sin_complex @ ( plus_plus_complex @ X @ Y ) )
% 3.82/4.09 = ( plus_plus_complex @ ( times_times_complex @ ( sin_complex @ X ) @ ( cos_complex @ Y ) ) @ ( times_times_complex @ ( cos_complex @ X ) @ ( sin_complex @ Y ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sin_add
% 3.82/4.09 thf(fact_7075_cos__one__sin__zero,axiom,
% 3.82/4.09 ! [X: real] :
% 3.82/4.09 ( ( ( cos_real @ X )
% 3.82/4.09 = one_one_real )
% 3.82/4.09 => ( ( sin_real @ X )
% 3.82/4.09 = zero_zero_real ) ) ).
% 3.82/4.09
% 3.82/4.09 % cos_one_sin_zero
% 3.82/4.09 thf(fact_7076_cos__one__sin__zero,axiom,
% 3.82/4.09 ! [X: complex] :
% 3.82/4.09 ( ( ( cos_complex @ X )
% 3.82/4.09 = one_one_complex )
% 3.82/4.09 => ( ( sin_complex @ X )
% 3.82/4.09 = zero_zero_complex ) ) ).
% 3.82/4.09
% 3.82/4.09 % cos_one_sin_zero
% 3.82/4.09 thf(fact_7077_fact__ge__self,axiom,
% 3.82/4.09 ! [N2: nat] : ( ord_less_eq_nat @ N2 @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 3.82/4.09
% 3.82/4.09 % fact_ge_self
% 3.82/4.09 thf(fact_7078_fact__mono__nat,axiom,
% 3.82/4.09 ! [M2: nat,N2: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.09 => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M2 ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % fact_mono_nat
% 3.82/4.09 thf(fact_7079_sgn__eq__0__iff,axiom,
% 3.82/4.09 ! [A: real] :
% 3.82/4.09 ( ( ( sgn_sgn_real @ A )
% 3.82/4.09 = zero_zero_real )
% 3.82/4.09 = ( A = zero_zero_real ) ) ).
% 3.82/4.09
% 3.82/4.09 % sgn_eq_0_iff
% 3.82/4.09 thf(fact_7080_sgn__eq__0__iff,axiom,
% 3.82/4.09 ! [A: int] :
% 3.82/4.09 ( ( ( sgn_sgn_int @ A )
% 3.82/4.09 = zero_zero_int )
% 3.82/4.09 = ( A = zero_zero_int ) ) ).
% 3.82/4.09
% 3.82/4.09 % sgn_eq_0_iff
% 3.82/4.09 thf(fact_7081_sgn__eq__0__iff,axiom,
% 3.82/4.09 ! [A: complex] :
% 3.82/4.09 ( ( ( sgn_sgn_complex @ A )
% 3.82/4.09 = zero_zero_complex )
% 3.82/4.09 = ( A = zero_zero_complex ) ) ).
% 3.82/4.09
% 3.82/4.09 % sgn_eq_0_iff
% 3.82/4.09 thf(fact_7082_sgn__0__0,axiom,
% 3.82/4.09 ! [A: real] :
% 3.82/4.09 ( ( ( sgn_sgn_real @ A )
% 3.82/4.09 = zero_zero_real )
% 3.82/4.09 = ( A = zero_zero_real ) ) ).
% 3.82/4.09
% 3.82/4.09 % sgn_0_0
% 3.82/4.09 thf(fact_7083_sgn__0__0,axiom,
% 3.82/4.09 ! [A: int] :
% 3.82/4.09 ( ( ( sgn_sgn_int @ A )
% 3.82/4.09 = zero_zero_int )
% 3.82/4.09 = ( A = zero_zero_int ) ) ).
% 3.82/4.09
% 3.82/4.09 % sgn_0_0
% 3.82/4.09 thf(fact_7084_sgn__zero__iff,axiom,
% 3.82/4.09 ! [X: real] :
% 3.82/4.09 ( ( ( sgn_sgn_real @ X )
% 3.82/4.09 = zero_zero_real )
% 3.82/4.09 = ( X = zero_zero_real ) ) ).
% 3.82/4.09
% 3.82/4.09 % sgn_zero_iff
% 3.82/4.09 thf(fact_7085_sgn__zero__iff,axiom,
% 3.82/4.09 ! [X: complex] :
% 3.82/4.09 ( ( ( sgn_sgn_complex @ X )
% 3.82/4.09 = zero_zero_complex )
% 3.82/4.09 = ( X = zero_zero_complex ) ) ).
% 3.82/4.09
% 3.82/4.09 % sgn_zero_iff
% 3.82/4.09 thf(fact_7086_sgn__mult,axiom,
% 3.82/4.09 ! [A: int,B2: int] :
% 3.82/4.09 ( ( sgn_sgn_int @ ( times_times_int @ A @ B2 ) )
% 3.82/4.09 = ( times_times_int @ ( sgn_sgn_int @ A ) @ ( sgn_sgn_int @ B2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sgn_mult
% 3.82/4.09 thf(fact_7087_sgn__mult,axiom,
% 3.82/4.09 ! [A: real,B2: real] :
% 3.82/4.09 ( ( sgn_sgn_real @ ( times_times_real @ A @ B2 ) )
% 3.82/4.09 = ( times_times_real @ ( sgn_sgn_real @ A ) @ ( sgn_sgn_real @ B2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sgn_mult
% 3.82/4.09 thf(fact_7088_sgn__mult,axiom,
% 3.82/4.09 ! [A: complex,B2: complex] :
% 3.82/4.09 ( ( sgn_sgn_complex @ ( times_times_complex @ A @ B2 ) )
% 3.82/4.09 = ( times_times_complex @ ( sgn_sgn_complex @ A ) @ ( sgn_sgn_complex @ B2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sgn_mult
% 3.82/4.09 thf(fact_7089_same__sgn__sgn__add,axiom,
% 3.82/4.09 ! [B2: int,A: int] :
% 3.82/4.09 ( ( ( sgn_sgn_int @ B2 )
% 3.82/4.09 = ( sgn_sgn_int @ A ) )
% 3.82/4.09 => ( ( sgn_sgn_int @ ( plus_plus_int @ A @ B2 ) )
% 3.82/4.09 = ( sgn_sgn_int @ A ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % same_sgn_sgn_add
% 3.82/4.09 thf(fact_7090_same__sgn__sgn__add,axiom,
% 3.82/4.09 ! [B2: real,A: real] :
% 3.82/4.09 ( ( ( sgn_sgn_real @ B2 )
% 3.82/4.09 = ( sgn_sgn_real @ A ) )
% 3.82/4.09 => ( ( sgn_sgn_real @ ( plus_plus_real @ A @ B2 ) )
% 3.82/4.09 = ( sgn_sgn_real @ A ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % same_sgn_sgn_add
% 3.82/4.09 thf(fact_7091_fact__nonzero,axiom,
% 3.82/4.09 ! [N2: nat] :
% 3.82/4.09 ( ( semiri1406184849735516958ct_int @ N2 )
% 3.82/4.09 != zero_zero_int ) ).
% 3.82/4.09
% 3.82/4.09 % fact_nonzero
% 3.82/4.09 thf(fact_7092_fact__nonzero,axiom,
% 3.82/4.09 ! [N2: nat] :
% 3.82/4.09 ( ( semiri5044797733671781792omplex @ N2 )
% 3.82/4.09 != zero_zero_complex ) ).
% 3.82/4.09
% 3.82/4.09 % fact_nonzero
% 3.82/4.09 thf(fact_7093_fact__nonzero,axiom,
% 3.82/4.09 ! [N2: nat] :
% 3.82/4.09 ( ( semiri4449623510593786356d_enat @ N2 )
% 3.82/4.09 != zero_z5237406670263579293d_enat ) ).
% 3.82/4.09
% 3.82/4.09 % fact_nonzero
% 3.82/4.09 thf(fact_7094_fact__nonzero,axiom,
% 3.82/4.09 ! [N2: nat] :
% 3.82/4.09 ( ( semiri1408675320244567234ct_nat @ N2 )
% 3.82/4.09 != zero_zero_nat ) ).
% 3.82/4.09
% 3.82/4.09 % fact_nonzero
% 3.82/4.09 thf(fact_7095_fact__nonzero,axiom,
% 3.82/4.09 ! [N2: nat] :
% 3.82/4.09 ( ( semiri2265585572941072030t_real @ N2 )
% 3.82/4.09 != zero_zero_real ) ).
% 3.82/4.09
% 3.82/4.09 % fact_nonzero
% 3.82/4.09 thf(fact_7096_summable__const__iff,axiom,
% 3.82/4.09 ! [C: real] :
% 3.82/4.09 ( ( summable_real
% 3.82/4.09 @ ^ [Uu3: nat] : C )
% 3.82/4.09 = ( C = zero_zero_real ) ) ).
% 3.82/4.09
% 3.82/4.09 % summable_const_iff
% 3.82/4.09 thf(fact_7097_summable__const__iff,axiom,
% 3.82/4.09 ! [C: complex] :
% 3.82/4.09 ( ( summable_complex
% 3.82/4.09 @ ^ [Uu3: nat] : C )
% 3.82/4.09 = ( C = zero_zero_complex ) ) ).
% 3.82/4.09
% 3.82/4.09 % summable_const_iff
% 3.82/4.09 thf(fact_7098_summable__comparison__test,axiom,
% 3.82/4.09 ! [F: nat > real,G: nat > real] :
% 3.82/4.09 ( ? [N8: nat] :
% 3.82/4.09 ! [N3: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ N8 @ N3 )
% 3.82/4.09 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 3.82/4.09 => ( ( summable_real @ G )
% 3.82/4.09 => ( summable_real @ F ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % summable_comparison_test
% 3.82/4.09 thf(fact_7099_summable__comparison__test,axiom,
% 3.82/4.09 ! [F: nat > complex,G: nat > real] :
% 3.82/4.09 ( ? [N8: nat] :
% 3.82/4.09 ! [N3: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ N8 @ N3 )
% 3.82/4.09 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 3.82/4.09 => ( ( summable_real @ G )
% 3.82/4.09 => ( summable_complex @ F ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % summable_comparison_test
% 3.82/4.09 thf(fact_7100_summable__comparison__test_H,axiom,
% 3.82/4.09 ! [G: nat > real,N6: nat,F: nat > real] :
% 3.82/4.09 ( ( summable_real @ G )
% 3.82/4.09 => ( ! [N3: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ N6 @ N3 )
% 3.82/4.09 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 3.82/4.09 => ( summable_real @ F ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % summable_comparison_test'
% 3.82/4.09 thf(fact_7101_summable__comparison__test_H,axiom,
% 3.82/4.09 ! [G: nat > real,N6: nat,F: nat > complex] :
% 3.82/4.09 ( ( summable_real @ G )
% 3.82/4.09 => ( ! [N3: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ N6 @ N3 )
% 3.82/4.09 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 3.82/4.09 => ( summable_complex @ F ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % summable_comparison_test'
% 3.82/4.09 thf(fact_7102_summable__add,axiom,
% 3.82/4.09 ! [F: nat > nat,G: nat > nat] :
% 3.82/4.09 ( ( summable_nat @ F )
% 3.82/4.09 => ( ( summable_nat @ G )
% 3.82/4.09 => ( summable_nat
% 3.82/4.09 @ ^ [N: nat] : ( plus_plus_nat @ ( F @ N ) @ ( G @ N ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % summable_add
% 3.82/4.09 thf(fact_7103_summable__add,axiom,
% 3.82/4.09 ! [F: nat > int,G: nat > int] :
% 3.82/4.09 ( ( summable_int @ F )
% 3.82/4.09 => ( ( summable_int @ G )
% 3.82/4.09 => ( summable_int
% 3.82/4.09 @ ^ [N: nat] : ( plus_plus_int @ ( F @ N ) @ ( G @ N ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % summable_add
% 3.82/4.09 thf(fact_7104_summable__add,axiom,
% 3.82/4.09 ! [F: nat > real,G: nat > real] :
% 3.82/4.09 ( ( summable_real @ F )
% 3.82/4.09 => ( ( summable_real @ G )
% 3.82/4.09 => ( summable_real
% 3.82/4.09 @ ^ [N: nat] : ( plus_plus_real @ ( F @ N ) @ ( G @ N ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % summable_add
% 3.82/4.09 thf(fact_7105_cos__diff,axiom,
% 3.82/4.09 ! [X: real,Y: real] :
% 3.82/4.09 ( ( cos_real @ ( minus_minus_real @ X @ Y ) )
% 3.82/4.09 = ( plus_plus_real @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ Y ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % cos_diff
% 3.82/4.09 thf(fact_7106_cos__diff,axiom,
% 3.82/4.09 ! [X: complex,Y: complex] :
% 3.82/4.09 ( ( cos_complex @ ( minus_minus_complex @ X @ Y ) )
% 3.82/4.09 = ( plus_plus_complex @ ( times_times_complex @ ( cos_complex @ X ) @ ( cos_complex @ Y ) ) @ ( times_times_complex @ ( sin_complex @ X ) @ ( sin_complex @ Y ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % cos_diff
% 3.82/4.09 thf(fact_7107_cos__add,axiom,
% 3.82/4.09 ! [X: real,Y: real] :
% 3.82/4.09 ( ( cos_real @ ( plus_plus_real @ X @ Y ) )
% 3.82/4.09 = ( minus_minus_real @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ Y ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % cos_add
% 3.82/4.09 thf(fact_7108_cos__add,axiom,
% 3.82/4.09 ! [X: complex,Y: complex] :
% 3.82/4.09 ( ( cos_complex @ ( plus_plus_complex @ X @ Y ) )
% 3.82/4.09 = ( minus_minus_complex @ ( times_times_complex @ ( cos_complex @ X ) @ ( cos_complex @ Y ) ) @ ( times_times_complex @ ( sin_complex @ X ) @ ( sin_complex @ Y ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % cos_add
% 3.82/4.09 thf(fact_7109_summable__Suc__iff,axiom,
% 3.82/4.09 ! [F: nat > real] :
% 3.82/4.09 ( ( summable_real
% 3.82/4.09 @ ^ [N: nat] : ( F @ ( suc @ N ) ) )
% 3.82/4.09 = ( summable_real @ F ) ) ).
% 3.82/4.09
% 3.82/4.09 % summable_Suc_iff
% 3.82/4.09 thf(fact_7110_summable__ignore__initial__segment,axiom,
% 3.82/4.09 ! [F: nat > real,K: nat] :
% 3.82/4.09 ( ( summable_real @ F )
% 3.82/4.09 => ( summable_real
% 3.82/4.09 @ ^ [N: nat] : ( F @ ( plus_plus_nat @ N @ K ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % summable_ignore_initial_segment
% 3.82/4.09 thf(fact_7111_sin__zero__norm__cos__one,axiom,
% 3.82/4.09 ! [X: real] :
% 3.82/4.09 ( ( ( sin_real @ X )
% 3.82/4.09 = zero_zero_real )
% 3.82/4.09 => ( ( real_V7735802525324610683m_real @ ( cos_real @ X ) )
% 3.82/4.09 = one_one_real ) ) ).
% 3.82/4.09
% 3.82/4.09 % sin_zero_norm_cos_one
% 3.82/4.09 thf(fact_7112_sin__zero__norm__cos__one,axiom,
% 3.82/4.09 ! [X: complex] :
% 3.82/4.09 ( ( ( sin_complex @ X )
% 3.82/4.09 = zero_zero_complex )
% 3.82/4.09 => ( ( real_V1022390504157884413omplex @ ( cos_complex @ X ) )
% 3.82/4.09 = one_one_real ) ) ).
% 3.82/4.09
% 3.82/4.09 % sin_zero_norm_cos_one
% 3.82/4.09 thf(fact_7113_suminf__le,axiom,
% 3.82/4.09 ! [F: nat > real,G: nat > real] :
% 3.82/4.09 ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 3.82/4.09 => ( ( summable_real @ F )
% 3.82/4.09 => ( ( summable_real @ G )
% 3.82/4.09 => ( ord_less_eq_real @ ( suminf_real @ F ) @ ( suminf_real @ G ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % suminf_le
% 3.82/4.09 thf(fact_7114_suminf__le,axiom,
% 3.82/4.09 ! [F: nat > nat,G: nat > nat] :
% 3.82/4.09 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( G @ N3 ) )
% 3.82/4.09 => ( ( summable_nat @ F )
% 3.82/4.09 => ( ( summable_nat @ G )
% 3.82/4.09 => ( ord_less_eq_nat @ ( suminf_nat @ F ) @ ( suminf_nat @ G ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % suminf_le
% 3.82/4.09 thf(fact_7115_suminf__le,axiom,
% 3.82/4.09 ! [F: nat > int,G: nat > int] :
% 3.82/4.09 ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( G @ N3 ) )
% 3.82/4.09 => ( ( summable_int @ F )
% 3.82/4.09 => ( ( summable_int @ G )
% 3.82/4.09 => ( ord_less_eq_int @ ( suminf_int @ F ) @ ( suminf_int @ G ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % suminf_le
% 3.82/4.09 thf(fact_7116_summable__finite,axiom,
% 3.82/4.09 ! [N6: set_nat,F: nat > nat] :
% 3.82/4.09 ( ( finite_finite_nat @ N6 )
% 3.82/4.09 => ( ! [N3: nat] :
% 3.82/4.09 ( ~ ( member_nat @ N3 @ N6 )
% 3.82/4.09 => ( ( F @ N3 )
% 3.82/4.09 = zero_zero_nat ) )
% 3.82/4.09 => ( summable_nat @ F ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % summable_finite
% 3.82/4.09 thf(fact_7117_summable__finite,axiom,
% 3.82/4.09 ! [N6: set_nat,F: nat > real] :
% 3.82/4.09 ( ( finite_finite_nat @ N6 )
% 3.82/4.09 => ( ! [N3: nat] :
% 3.82/4.09 ( ~ ( member_nat @ N3 @ N6 )
% 3.82/4.09 => ( ( F @ N3 )
% 3.82/4.09 = zero_zero_real ) )
% 3.82/4.09 => ( summable_real @ F ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % summable_finite
% 3.82/4.09 thf(fact_7118_summable__finite,axiom,
% 3.82/4.09 ! [N6: set_nat,F: nat > int] :
% 3.82/4.09 ( ( finite_finite_nat @ N6 )
% 3.82/4.09 => ( ! [N3: nat] :
% 3.82/4.09 ( ~ ( member_nat @ N3 @ N6 )
% 3.82/4.09 => ( ( F @ N3 )
% 3.82/4.09 = zero_zero_int ) )
% 3.82/4.09 => ( summable_int @ F ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % summable_finite
% 3.82/4.09 thf(fact_7119_summable__finite,axiom,
% 3.82/4.09 ! [N6: set_nat,F: nat > complex] :
% 3.82/4.09 ( ( finite_finite_nat @ N6 )
% 3.82/4.09 => ( ! [N3: nat] :
% 3.82/4.09 ( ~ ( member_nat @ N3 @ N6 )
% 3.82/4.09 => ( ( F @ N3 )
% 3.82/4.09 = zero_zero_complex ) )
% 3.82/4.09 => ( summable_complex @ F ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % summable_finite
% 3.82/4.09 thf(fact_7120_fact__less__mono__nat,axiom,
% 3.82/4.09 ! [M2: nat,N2: nat] :
% 3.82/4.09 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 3.82/4.09 => ( ( ord_less_nat @ M2 @ N2 )
% 3.82/4.09 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M2 ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % fact_less_mono_nat
% 3.82/4.09 thf(fact_7121_sgn__not__eq__imp,axiom,
% 3.82/4.09 ! [B2: int,A: int] :
% 3.82/4.09 ( ( ( sgn_sgn_int @ B2 )
% 3.82/4.09 != ( sgn_sgn_int @ A ) )
% 3.82/4.09 => ( ( ( sgn_sgn_int @ A )
% 3.82/4.09 != zero_zero_int )
% 3.82/4.09 => ( ( ( sgn_sgn_int @ B2 )
% 3.82/4.09 != zero_zero_int )
% 3.82/4.09 => ( ( sgn_sgn_int @ A )
% 3.82/4.09 = ( uminus_uminus_int @ ( sgn_sgn_int @ B2 ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sgn_not_eq_imp
% 3.82/4.09 thf(fact_7122_sgn__not__eq__imp,axiom,
% 3.82/4.09 ! [B2: real,A: real] :
% 3.82/4.09 ( ( ( sgn_sgn_real @ B2 )
% 3.82/4.09 != ( sgn_sgn_real @ A ) )
% 3.82/4.09 => ( ( ( sgn_sgn_real @ A )
% 3.82/4.09 != zero_zero_real )
% 3.82/4.09 => ( ( ( sgn_sgn_real @ B2 )
% 3.82/4.09 != zero_zero_real )
% 3.82/4.09 => ( ( sgn_sgn_real @ A )
% 3.82/4.09 = ( uminus_uminus_real @ ( sgn_sgn_real @ B2 ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sgn_not_eq_imp
% 3.82/4.09 thf(fact_7123_sgn__minus__1,axiom,
% 3.82/4.09 ( ( sgn_sgn_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 3.82/4.09 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 3.82/4.09
% 3.82/4.09 % sgn_minus_1
% 3.82/4.09 thf(fact_7124_sgn__minus__1,axiom,
% 3.82/4.09 ( ( sgn_sgn_int @ ( uminus_uminus_int @ one_one_int ) )
% 3.82/4.09 = ( uminus_uminus_int @ one_one_int ) ) ).
% 3.82/4.09
% 3.82/4.09 % sgn_minus_1
% 3.82/4.09 thf(fact_7125_sgn__minus__1,axiom,
% 3.82/4.09 ( ( sgn_sgn_real @ ( uminus_uminus_real @ one_one_real ) )
% 3.82/4.09 = ( uminus_uminus_real @ one_one_real ) ) ).
% 3.82/4.09
% 3.82/4.09 % sgn_minus_1
% 3.82/4.09 thf(fact_7126_fact__ge__zero,axiom,
% 3.82/4.09 ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N2 ) ) ).
% 3.82/4.09
% 3.82/4.09 % fact_ge_zero
% 3.82/4.09 thf(fact_7127_fact__ge__zero,axiom,
% 3.82/4.09 ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 3.82/4.09
% 3.82/4.09 % fact_ge_zero
% 3.82/4.09 thf(fact_7128_fact__ge__zero,axiom,
% 3.82/4.09 ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N2 ) ) ).
% 3.82/4.09
% 3.82/4.09 % fact_ge_zero
% 3.82/4.09 thf(fact_7129_fact__gt__zero,axiom,
% 3.82/4.09 ! [N2: nat] : ( ord_less_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N2 ) ) ).
% 3.82/4.09
% 3.82/4.09 % fact_gt_zero
% 3.82/4.09 thf(fact_7130_fact__gt__zero,axiom,
% 3.82/4.09 ! [N2: nat] : ( ord_less_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 3.82/4.09
% 3.82/4.09 % fact_gt_zero
% 3.82/4.09 thf(fact_7131_fact__gt__zero,axiom,
% 3.82/4.09 ! [N2: nat] : ( ord_less_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N2 ) ) ).
% 3.82/4.09
% 3.82/4.09 % fact_gt_zero
% 3.82/4.09 thf(fact_7132_fact__not__neg,axiom,
% 3.82/4.09 ! [N2: nat] :
% 3.82/4.09 ~ ( ord_less_int @ ( semiri1406184849735516958ct_int @ N2 ) @ zero_zero_int ) ).
% 3.82/4.09
% 3.82/4.09 % fact_not_neg
% 3.82/4.09 thf(fact_7133_fact__not__neg,axiom,
% 3.82/4.09 ! [N2: nat] :
% 3.82/4.09 ~ ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ zero_zero_nat ) ).
% 3.82/4.09
% 3.82/4.09 % fact_not_neg
% 3.82/4.09 thf(fact_7134_fact__not__neg,axiom,
% 3.82/4.09 ! [N2: nat] :
% 3.82/4.09 ~ ( ord_less_real @ ( semiri2265585572941072030t_real @ N2 ) @ zero_zero_real ) ).
% 3.82/4.09
% 3.82/4.09 % fact_not_neg
% 3.82/4.09 thf(fact_7135_int__sgnE,axiom,
% 3.82/4.09 ! [K: int] :
% 3.82/4.09 ~ ! [N3: nat,L4: int] :
% 3.82/4.09 ( K
% 3.82/4.09 != ( times_times_int @ ( sgn_sgn_int @ L4 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % int_sgnE
% 3.82/4.09 thf(fact_7136_fact__ge__1,axiom,
% 3.82/4.09 ! [N2: nat] : ( ord_less_eq_int @ one_one_int @ ( semiri1406184849735516958ct_int @ N2 ) ) ).
% 3.82/4.09
% 3.82/4.09 % fact_ge_1
% 3.82/4.09 thf(fact_7137_fact__ge__1,axiom,
% 3.82/4.09 ! [N2: nat] : ( ord_less_eq_nat @ one_one_nat @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 3.82/4.09
% 3.82/4.09 % fact_ge_1
% 3.82/4.09 thf(fact_7138_fact__ge__1,axiom,
% 3.82/4.09 ! [N2: nat] : ( ord_less_eq_real @ one_one_real @ ( semiri2265585572941072030t_real @ N2 ) ) ).
% 3.82/4.09
% 3.82/4.09 % fact_ge_1
% 3.82/4.09 thf(fact_7139_fact__mono,axiom,
% 3.82/4.09 ! [M2: nat,N2: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.09 => ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ M2 ) @ ( semiri1406184849735516958ct_int @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % fact_mono
% 3.82/4.09 thf(fact_7140_fact__mono,axiom,
% 3.82/4.09 ! [M2: nat,N2: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.09 => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M2 ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % fact_mono
% 3.82/4.09 thf(fact_7141_fact__mono,axiom,
% 3.82/4.09 ! [M2: nat,N2: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.09 => ( ord_less_eq_real @ ( semiri2265585572941072030t_real @ M2 ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % fact_mono
% 3.82/4.09 thf(fact_7142_summable__mult__D,axiom,
% 3.82/4.09 ! [C: real,F: nat > real] :
% 3.82/4.09 ( ( summable_real
% 3.82/4.09 @ ^ [N: nat] : ( times_times_real @ C @ ( F @ N ) ) )
% 3.82/4.09 => ( ( C != zero_zero_real )
% 3.82/4.09 => ( summable_real @ F ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % summable_mult_D
% 3.82/4.09 thf(fact_7143_summable__mult__D,axiom,
% 3.82/4.09 ! [C: complex,F: nat > complex] :
% 3.82/4.09 ( ( summable_complex
% 3.82/4.09 @ ^ [N: nat] : ( times_times_complex @ C @ ( F @ N ) ) )
% 3.82/4.09 => ( ( C != zero_zero_complex )
% 3.82/4.09 => ( summable_complex @ F ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % summable_mult_D
% 3.82/4.09 thf(fact_7144_fact__dvd,axiom,
% 3.82/4.09 ! [N2: nat,M2: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ N2 @ M2 )
% 3.82/4.09 => ( dvd_dvd_int @ ( semiri1406184849735516958ct_int @ N2 ) @ ( semiri1406184849735516958ct_int @ M2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % fact_dvd
% 3.82/4.09 thf(fact_7145_fact__dvd,axiom,
% 3.82/4.09 ! [N2: nat,M2: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ N2 @ M2 )
% 3.82/4.09 => ( dvd_dvd_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( semiri1408675320244567234ct_nat @ M2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % fact_dvd
% 3.82/4.09 thf(fact_7146_fact__dvd,axiom,
% 3.82/4.09 ! [N2: nat,M2: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ N2 @ M2 )
% 3.82/4.09 => ( dvd_dvd_real @ ( semiri2265585572941072030t_real @ N2 ) @ ( semiri2265585572941072030t_real @ M2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % fact_dvd
% 3.82/4.09 thf(fact_7147_summable__zero__power,axiom,
% 3.82/4.09 summable_real @ ( power_power_real @ zero_zero_real ) ).
% 3.82/4.09
% 3.82/4.09 % summable_zero_power
% 3.82/4.09 thf(fact_7148_summable__zero__power,axiom,
% 3.82/4.09 summable_complex @ ( power_power_complex @ zero_zero_complex ) ).
% 3.82/4.09
% 3.82/4.09 % summable_zero_power
% 3.82/4.09 thf(fact_7149_summable__zero__power,axiom,
% 3.82/4.09 summable_int @ ( power_power_int @ zero_zero_int ) ).
% 3.82/4.09
% 3.82/4.09 % summable_zero_power
% 3.82/4.09 thf(fact_7150_suminf__add,axiom,
% 3.82/4.09 ! [F: nat > nat,G: nat > nat] :
% 3.82/4.09 ( ( summable_nat @ F )
% 3.82/4.09 => ( ( summable_nat @ G )
% 3.82/4.09 => ( ( plus_plus_nat @ ( suminf_nat @ F ) @ ( suminf_nat @ G ) )
% 3.82/4.09 = ( suminf_nat
% 3.82/4.09 @ ^ [N: nat] : ( plus_plus_nat @ ( F @ N ) @ ( G @ N ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % suminf_add
% 3.82/4.09 thf(fact_7151_suminf__add,axiom,
% 3.82/4.09 ! [F: nat > int,G: nat > int] :
% 3.82/4.09 ( ( summable_int @ F )
% 3.82/4.09 => ( ( summable_int @ G )
% 3.82/4.09 => ( ( plus_plus_int @ ( suminf_int @ F ) @ ( suminf_int @ G ) )
% 3.82/4.09 = ( suminf_int
% 3.82/4.09 @ ^ [N: nat] : ( plus_plus_int @ ( F @ N ) @ ( G @ N ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % suminf_add
% 3.82/4.09 thf(fact_7152_suminf__add,axiom,
% 3.82/4.09 ! [F: nat > real,G: nat > real] :
% 3.82/4.09 ( ( summable_real @ F )
% 3.82/4.09 => ( ( summable_real @ G )
% 3.82/4.09 => ( ( plus_plus_real @ ( suminf_real @ F ) @ ( suminf_real @ G ) )
% 3.82/4.09 = ( suminf_real
% 3.82/4.09 @ ^ [N: nat] : ( plus_plus_real @ ( F @ N ) @ ( G @ N ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % suminf_add
% 3.82/4.09 thf(fact_7153_suminf__nonneg,axiom,
% 3.82/4.09 ! [F: nat > real] :
% 3.82/4.09 ( ( summable_real @ F )
% 3.82/4.09 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 3.82/4.09 => ( ord_less_eq_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % suminf_nonneg
% 3.82/4.09 thf(fact_7154_suminf__nonneg,axiom,
% 3.82/4.09 ! [F: nat > nat] :
% 3.82/4.09 ( ( summable_nat @ F )
% 3.82/4.09 => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 3.82/4.09 => ( ord_less_eq_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % suminf_nonneg
% 3.82/4.09 thf(fact_7155_suminf__nonneg,axiom,
% 3.82/4.09 ! [F: nat > int] :
% 3.82/4.09 ( ( summable_int @ F )
% 3.82/4.09 => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 3.82/4.09 => ( ord_less_eq_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % suminf_nonneg
% 3.82/4.09 thf(fact_7156_suminf__eq__zero__iff,axiom,
% 3.82/4.09 ! [F: nat > real] :
% 3.82/4.09 ( ( summable_real @ F )
% 3.82/4.09 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 3.82/4.09 => ( ( ( suminf_real @ F )
% 3.82/4.09 = zero_zero_real )
% 3.82/4.09 = ( ! [N: nat] :
% 3.82/4.09 ( ( F @ N )
% 3.82/4.09 = zero_zero_real ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % suminf_eq_zero_iff
% 3.82/4.09 thf(fact_7157_suminf__eq__zero__iff,axiom,
% 3.82/4.09 ! [F: nat > nat] :
% 3.82/4.09 ( ( summable_nat @ F )
% 3.82/4.09 => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 3.82/4.09 => ( ( ( suminf_nat @ F )
% 3.82/4.09 = zero_zero_nat )
% 3.82/4.09 = ( ! [N: nat] :
% 3.82/4.09 ( ( F @ N )
% 3.82/4.09 = zero_zero_nat ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % suminf_eq_zero_iff
% 3.82/4.09 thf(fact_7158_suminf__eq__zero__iff,axiom,
% 3.82/4.09 ! [F: nat > int] :
% 3.82/4.09 ( ( summable_int @ F )
% 3.82/4.09 => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 3.82/4.09 => ( ( ( suminf_int @ F )
% 3.82/4.09 = zero_zero_int )
% 3.82/4.09 = ( ! [N: nat] :
% 3.82/4.09 ( ( F @ N )
% 3.82/4.09 = zero_zero_int ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % suminf_eq_zero_iff
% 3.82/4.09 thf(fact_7159_suminf__pos,axiom,
% 3.82/4.09 ! [F: nat > nat] :
% 3.82/4.09 ( ( summable_nat @ F )
% 3.82/4.09 => ( ! [N3: nat] : ( ord_less_nat @ zero_zero_nat @ ( F @ N3 ) )
% 3.82/4.09 => ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % suminf_pos
% 3.82/4.09 thf(fact_7160_suminf__pos,axiom,
% 3.82/4.09 ! [F: nat > real] :
% 3.82/4.09 ( ( summable_real @ F )
% 3.82/4.09 => ( ! [N3: nat] : ( ord_less_real @ zero_zero_real @ ( F @ N3 ) )
% 3.82/4.09 => ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % suminf_pos
% 3.82/4.09 thf(fact_7161_suminf__pos,axiom,
% 3.82/4.09 ! [F: nat > int] :
% 3.82/4.09 ( ( summable_int @ F )
% 3.82/4.09 => ( ! [N3: nat] : ( ord_less_int @ zero_zero_int @ ( F @ N3 ) )
% 3.82/4.09 => ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % suminf_pos
% 3.82/4.09 thf(fact_7162_fact__ge__Suc__0__nat,axiom,
% 3.82/4.09 ! [N2: nat] : ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 3.82/4.09
% 3.82/4.09 % fact_ge_Suc_0_nat
% 3.82/4.09 thf(fact_7163_sgn__1__pos,axiom,
% 3.82/4.09 ! [A: real] :
% 3.82/4.09 ( ( ( sgn_sgn_real @ A )
% 3.82/4.09 = one_one_real )
% 3.82/4.09 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 3.82/4.09
% 3.82/4.09 % sgn_1_pos
% 3.82/4.09 thf(fact_7164_sgn__1__pos,axiom,
% 3.82/4.09 ! [A: int] :
% 3.82/4.09 ( ( ( sgn_sgn_int @ A )
% 3.82/4.09 = one_one_int )
% 3.82/4.09 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 3.82/4.09
% 3.82/4.09 % sgn_1_pos
% 3.82/4.09 thf(fact_7165_dvd__fact,axiom,
% 3.82/4.09 ! [M2: nat,N2: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ one_one_nat @ M2 )
% 3.82/4.09 => ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.09 => ( dvd_dvd_nat @ M2 @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % dvd_fact
% 3.82/4.09 thf(fact_7166_summable__0__powser,axiom,
% 3.82/4.09 ! [F: nat > real] :
% 3.82/4.09 ( summable_real
% 3.82/4.09 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ zero_zero_real @ N ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % summable_0_powser
% 3.82/4.09 thf(fact_7167_summable__0__powser,axiom,
% 3.82/4.09 ! [F: nat > complex] :
% 3.82/4.09 ( summable_complex
% 3.82/4.09 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ zero_zero_complex @ N ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % summable_0_powser
% 3.82/4.09 thf(fact_7168_summable__zero__power_H,axiom,
% 3.82/4.09 ! [F: nat > int] :
% 3.82/4.09 ( summable_int
% 3.82/4.09 @ ^ [N: nat] : ( times_times_int @ ( F @ N ) @ ( power_power_int @ zero_zero_int @ N ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % summable_zero_power'
% 3.82/4.09 thf(fact_7169_summable__zero__power_H,axiom,
% 3.82/4.09 ! [F: nat > real] :
% 3.82/4.09 ( summable_real
% 3.82/4.09 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ zero_zero_real @ N ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % summable_zero_power'
% 3.82/4.09 thf(fact_7170_summable__zero__power_H,axiom,
% 3.82/4.09 ! [F: nat > complex] :
% 3.82/4.09 ( summable_complex
% 3.82/4.09 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ zero_zero_complex @ N ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % summable_zero_power'
% 3.82/4.09 thf(fact_7171_summable__powser__split__head,axiom,
% 3.82/4.09 ! [F: nat > real,Z3: real] :
% 3.82/4.09 ( ( summable_real
% 3.82/4.09 @ ^ [N: nat] : ( times_times_real @ ( F @ ( suc @ N ) ) @ ( power_power_real @ Z3 @ N ) ) )
% 3.82/4.09 = ( summable_real
% 3.82/4.09 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z3 @ N ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % summable_powser_split_head
% 3.82/4.09 thf(fact_7172_summable__powser__split__head,axiom,
% 3.82/4.09 ! [F: nat > complex,Z3: complex] :
% 3.82/4.09 ( ( summable_complex
% 3.82/4.09 @ ^ [N: nat] : ( times_times_complex @ ( F @ ( suc @ N ) ) @ ( power_power_complex @ Z3 @ N ) ) )
% 3.82/4.09 = ( summable_complex
% 3.82/4.09 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z3 @ N ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % summable_powser_split_head
% 3.82/4.09 thf(fact_7173_powser__split__head_I3_J,axiom,
% 3.82/4.09 ! [F: nat > real,Z3: real] :
% 3.82/4.09 ( ( summable_real
% 3.82/4.09 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z3 @ N ) ) )
% 3.82/4.09 => ( summable_real
% 3.82/4.09 @ ^ [N: nat] : ( times_times_real @ ( F @ ( suc @ N ) ) @ ( power_power_real @ Z3 @ N ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % powser_split_head(3)
% 3.82/4.09 thf(fact_7174_powser__split__head_I3_J,axiom,
% 3.82/4.09 ! [F: nat > complex,Z3: complex] :
% 3.82/4.09 ( ( summable_complex
% 3.82/4.09 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z3 @ N ) ) )
% 3.82/4.09 => ( summable_complex
% 3.82/4.09 @ ^ [N: nat] : ( times_times_complex @ ( F @ ( suc @ N ) ) @ ( power_power_complex @ Z3 @ N ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % powser_split_head(3)
% 3.82/4.09 thf(fact_7175_summable__powser__ignore__initial__segment,axiom,
% 3.82/4.09 ! [F: nat > real,M2: nat,Z3: real] :
% 3.82/4.09 ( ( summable_real
% 3.82/4.09 @ ^ [N: nat] : ( times_times_real @ ( F @ ( plus_plus_nat @ N @ M2 ) ) @ ( power_power_real @ Z3 @ N ) ) )
% 3.82/4.09 = ( summable_real
% 3.82/4.09 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z3 @ N ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % summable_powser_ignore_initial_segment
% 3.82/4.09 thf(fact_7176_summable__powser__ignore__initial__segment,axiom,
% 3.82/4.09 ! [F: nat > complex,M2: nat,Z3: complex] :
% 3.82/4.09 ( ( summable_complex
% 3.82/4.09 @ ^ [N: nat] : ( times_times_complex @ ( F @ ( plus_plus_nat @ N @ M2 ) ) @ ( power_power_complex @ Z3 @ N ) ) )
% 3.82/4.09 = ( summable_complex
% 3.82/4.09 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z3 @ N ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % summable_powser_ignore_initial_segment
% 3.82/4.09 thf(fact_7177_fact__less__mono,axiom,
% 3.82/4.09 ! [M2: nat,N2: nat] :
% 3.82/4.09 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 3.82/4.09 => ( ( ord_less_nat @ M2 @ N2 )
% 3.82/4.09 => ( ord_less_int @ ( semiri1406184849735516958ct_int @ M2 ) @ ( semiri1406184849735516958ct_int @ N2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % fact_less_mono
% 3.82/4.09 thf(fact_7178_fact__less__mono,axiom,
% 3.82/4.09 ! [M2: nat,N2: nat] :
% 3.82/4.09 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 3.82/4.09 => ( ( ord_less_nat @ M2 @ N2 )
% 3.82/4.09 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M2 ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % fact_less_mono
% 3.82/4.09 thf(fact_7179_fact__less__mono,axiom,
% 3.82/4.09 ! [M2: nat,N2: nat] :
% 3.82/4.09 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 3.82/4.09 => ( ( ord_less_nat @ M2 @ N2 )
% 3.82/4.09 => ( ord_less_real @ ( semiri2265585572941072030t_real @ M2 ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % fact_less_mono
% 3.82/4.09 thf(fact_7180_sin__times__sin,axiom,
% 3.82/4.09 ! [W2: complex,Z3: complex] :
% 3.82/4.09 ( ( times_times_complex @ ( sin_complex @ W2 ) @ ( sin_complex @ Z3 ) )
% 3.82/4.09 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( cos_complex @ ( minus_minus_complex @ W2 @ Z3 ) ) @ ( cos_complex @ ( plus_plus_complex @ W2 @ Z3 ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sin_times_sin
% 3.82/4.09 thf(fact_7181_sin__times__sin,axiom,
% 3.82/4.09 ! [W2: real,Z3: real] :
% 3.82/4.09 ( ( times_times_real @ ( sin_real @ W2 ) @ ( sin_real @ Z3 ) )
% 3.82/4.09 = ( divide_divide_real @ ( minus_minus_real @ ( cos_real @ ( minus_minus_real @ W2 @ Z3 ) ) @ ( cos_real @ ( plus_plus_real @ W2 @ Z3 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sin_times_sin
% 3.82/4.09 thf(fact_7182_sin__times__cos,axiom,
% 3.82/4.09 ! [W2: complex,Z3: complex] :
% 3.82/4.09 ( ( times_times_complex @ ( sin_complex @ W2 ) @ ( cos_complex @ Z3 ) )
% 3.82/4.09 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( sin_complex @ ( plus_plus_complex @ W2 @ Z3 ) ) @ ( sin_complex @ ( minus_minus_complex @ W2 @ Z3 ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sin_times_cos
% 3.82/4.09 thf(fact_7183_sin__times__cos,axiom,
% 3.82/4.09 ! [W2: real,Z3: real] :
% 3.82/4.09 ( ( times_times_real @ ( sin_real @ W2 ) @ ( cos_real @ Z3 ) )
% 3.82/4.09 = ( divide_divide_real @ ( plus_plus_real @ ( sin_real @ ( plus_plus_real @ W2 @ Z3 ) ) @ ( sin_real @ ( minus_minus_real @ W2 @ Z3 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sin_times_cos
% 3.82/4.09 thf(fact_7184_cos__times__sin,axiom,
% 3.82/4.09 ! [W2: complex,Z3: complex] :
% 3.82/4.09 ( ( times_times_complex @ ( cos_complex @ W2 ) @ ( sin_complex @ Z3 ) )
% 3.82/4.09 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( sin_complex @ ( plus_plus_complex @ W2 @ Z3 ) ) @ ( sin_complex @ ( minus_minus_complex @ W2 @ Z3 ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % cos_times_sin
% 3.82/4.09 thf(fact_7185_cos__times__sin,axiom,
% 3.82/4.09 ! [W2: real,Z3: real] :
% 3.82/4.09 ( ( times_times_real @ ( cos_real @ W2 ) @ ( sin_real @ Z3 ) )
% 3.82/4.09 = ( divide_divide_real @ ( minus_minus_real @ ( sin_real @ ( plus_plus_real @ W2 @ Z3 ) ) @ ( sin_real @ ( minus_minus_real @ W2 @ Z3 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % cos_times_sin
% 3.82/4.09 thf(fact_7186_sin__plus__sin,axiom,
% 3.82/4.09 ! [W2: complex,Z3: complex] :
% 3.82/4.09 ( ( plus_plus_complex @ ( sin_complex @ W2 ) @ ( sin_complex @ Z3 ) )
% 3.82/4.09 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W2 @ Z3 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ W2 @ Z3 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sin_plus_sin
% 3.82/4.09 thf(fact_7187_sin__plus__sin,axiom,
% 3.82/4.09 ! [W2: real,Z3: real] :
% 3.82/4.09 ( ( plus_plus_real @ ( sin_real @ W2 ) @ ( sin_real @ Z3 ) )
% 3.82/4.09 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ ( divide_divide_real @ ( plus_plus_real @ W2 @ Z3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( cos_real @ ( divide_divide_real @ ( minus_minus_real @ W2 @ Z3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sin_plus_sin
% 3.82/4.09 thf(fact_7188_sin__diff__sin,axiom,
% 3.82/4.09 ! [W2: complex,Z3: complex] :
% 3.82/4.09 ( ( minus_minus_complex @ ( sin_complex @ W2 ) @ ( sin_complex @ Z3 ) )
% 3.82/4.09 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ W2 @ Z3 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W2 @ Z3 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sin_diff_sin
% 3.82/4.09 thf(fact_7189_sin__diff__sin,axiom,
% 3.82/4.09 ! [W2: real,Z3: real] :
% 3.82/4.09 ( ( minus_minus_real @ ( sin_real @ W2 ) @ ( sin_real @ Z3 ) )
% 3.82/4.09 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ ( divide_divide_real @ ( minus_minus_real @ W2 @ Z3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( cos_real @ ( divide_divide_real @ ( plus_plus_real @ W2 @ Z3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sin_diff_sin
% 3.82/4.09 thf(fact_7190_cos__diff__cos,axiom,
% 3.82/4.09 ! [W2: complex,Z3: complex] :
% 3.82/4.09 ( ( minus_minus_complex @ ( cos_complex @ W2 ) @ ( cos_complex @ Z3 ) )
% 3.82/4.09 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W2 @ Z3 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ Z3 @ W2 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % cos_diff_cos
% 3.82/4.09 thf(fact_7191_cos__diff__cos,axiom,
% 3.82/4.09 ! [W2: real,Z3: real] :
% 3.82/4.09 ( ( minus_minus_real @ ( cos_real @ W2 ) @ ( cos_real @ Z3 ) )
% 3.82/4.09 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ ( divide_divide_real @ ( plus_plus_real @ W2 @ Z3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( sin_real @ ( divide_divide_real @ ( minus_minus_real @ Z3 @ W2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % cos_diff_cos
% 3.82/4.09 thf(fact_7192_fact__fact__dvd__fact,axiom,
% 3.82/4.09 ! [K: nat,N2: nat] : ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K ) @ ( semiri1406184849735516958ct_int @ N2 ) ) @ ( semiri1406184849735516958ct_int @ ( plus_plus_nat @ K @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % fact_fact_dvd_fact
% 3.82/4.09 thf(fact_7193_fact__fact__dvd__fact,axiom,
% 3.82/4.09 ! [K: nat,N2: nat] : ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) @ ( semiri1408675320244567234ct_nat @ ( plus_plus_nat @ K @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % fact_fact_dvd_fact
% 3.82/4.09 thf(fact_7194_fact__fact__dvd__fact,axiom,
% 3.82/4.09 ! [K: nat,N2: nat] : ( dvd_dvd_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ K @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % fact_fact_dvd_fact
% 3.82/4.09 thf(fact_7195_fact__mod,axiom,
% 3.82/4.09 ! [M2: nat,N2: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.09 => ( ( modulo_modulo_int @ ( semiri1406184849735516958ct_int @ N2 ) @ ( semiri1406184849735516958ct_int @ M2 ) )
% 3.82/4.09 = zero_zero_int ) ) ).
% 3.82/4.09
% 3.82/4.09 % fact_mod
% 3.82/4.09 thf(fact_7196_fact__mod,axiom,
% 3.82/4.09 ! [M2: nat,N2: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.09 => ( ( modulo_modulo_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( semiri1408675320244567234ct_nat @ M2 ) )
% 3.82/4.09 = zero_zero_nat ) ) ).
% 3.82/4.09
% 3.82/4.09 % fact_mod
% 3.82/4.09 thf(fact_7197_fact__le__power,axiom,
% 3.82/4.09 ! [N2: nat] : ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ N2 ) @ ( semiri1314217659103216013at_int @ ( power_power_nat @ N2 @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % fact_le_power
% 3.82/4.09 thf(fact_7198_fact__le__power,axiom,
% 3.82/4.09 ! [N2: nat] : ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( semiri1316708129612266289at_nat @ ( power_power_nat @ N2 @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % fact_le_power
% 3.82/4.09 thf(fact_7199_fact__le__power,axiom,
% 3.82/4.09 ! [N2: nat] : ( ord_less_eq_real @ ( semiri2265585572941072030t_real @ N2 ) @ ( semiri5074537144036343181t_real @ ( power_power_nat @ N2 @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % fact_le_power
% 3.82/4.09 thf(fact_7200_summable__norm__comparison__test,axiom,
% 3.82/4.09 ! [F: nat > complex,G: nat > real] :
% 3.82/4.09 ( ? [N8: nat] :
% 3.82/4.09 ! [N3: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ N8 @ N3 )
% 3.82/4.09 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 3.82/4.09 => ( ( summable_real @ G )
% 3.82/4.09 => ( summable_real
% 3.82/4.09 @ ^ [N: nat] : ( real_V1022390504157884413omplex @ ( F @ N ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % summable_norm_comparison_test
% 3.82/4.09 thf(fact_7201_suminf__pos2,axiom,
% 3.82/4.09 ! [F: nat > real,I: nat] :
% 3.82/4.09 ( ( summable_real @ F )
% 3.82/4.09 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 3.82/4.09 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 3.82/4.09 => ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % suminf_pos2
% 3.82/4.09 thf(fact_7202_suminf__pos2,axiom,
% 3.82/4.09 ! [F: nat > nat,I: nat] :
% 3.82/4.09 ( ( summable_nat @ F )
% 3.82/4.09 => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 3.82/4.09 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I ) )
% 3.82/4.09 => ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % suminf_pos2
% 3.82/4.09 thf(fact_7203_suminf__pos2,axiom,
% 3.82/4.09 ! [F: nat > int,I: nat] :
% 3.82/4.09 ( ( summable_int @ F )
% 3.82/4.09 => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 3.82/4.09 => ( ( ord_less_int @ zero_zero_int @ ( F @ I ) )
% 3.82/4.09 => ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % suminf_pos2
% 3.82/4.09 thf(fact_7204_suminf__pos__iff,axiom,
% 3.82/4.09 ! [F: nat > real] :
% 3.82/4.09 ( ( summable_real @ F )
% 3.82/4.09 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 3.82/4.09 => ( ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) )
% 3.82/4.09 = ( ? [I3: nat] : ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % suminf_pos_iff
% 3.82/4.09 thf(fact_7205_suminf__pos__iff,axiom,
% 3.82/4.09 ! [F: nat > nat] :
% 3.82/4.09 ( ( summable_nat @ F )
% 3.82/4.09 => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 3.82/4.09 => ( ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) )
% 3.82/4.09 = ( ? [I3: nat] : ( ord_less_nat @ zero_zero_nat @ ( F @ I3 ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % suminf_pos_iff
% 3.82/4.09 thf(fact_7206_suminf__pos__iff,axiom,
% 3.82/4.09 ! [F: nat > int] :
% 3.82/4.09 ( ( summable_int @ F )
% 3.82/4.09 => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 3.82/4.09 => ( ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) )
% 3.82/4.09 = ( ? [I3: nat] : ( ord_less_int @ zero_zero_int @ ( F @ I3 ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % suminf_pos_iff
% 3.82/4.09 thf(fact_7207_minus__sin__cos__eq,axiom,
% 3.82/4.09 ! [X: real] :
% 3.82/4.09 ( ( uminus_uminus_real @ ( sin_real @ X ) )
% 3.82/4.09 = ( cos_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % minus_sin_cos_eq
% 3.82/4.09 thf(fact_7208_minus__sin__cos__eq,axiom,
% 3.82/4.09 ! [X: complex] :
% 3.82/4.09 ( ( uminus1482373934393186551omplex @ ( sin_complex @ X ) )
% 3.82/4.09 = ( cos_complex @ ( plus_plus_complex @ X @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % minus_sin_cos_eq
% 3.82/4.09 thf(fact_7209_suminf__le__const,axiom,
% 3.82/4.09 ! [F: nat > int,X: int] :
% 3.82/4.09 ( ( summable_int @ F )
% 3.82/4.09 => ( ! [N3: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X )
% 3.82/4.09 => ( ord_less_eq_int @ ( suminf_int @ F ) @ X ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % suminf_le_const
% 3.82/4.09 thf(fact_7210_suminf__le__const,axiom,
% 3.82/4.09 ! [F: nat > nat,X: nat] :
% 3.82/4.09 ( ( summable_nat @ F )
% 3.82/4.09 => ( ! [N3: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X )
% 3.82/4.09 => ( ord_less_eq_nat @ ( suminf_nat @ F ) @ X ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % suminf_le_const
% 3.82/4.09 thf(fact_7211_suminf__le__const,axiom,
% 3.82/4.09 ! [F: nat > real,X: real] :
% 3.82/4.09 ( ( summable_real @ F )
% 3.82/4.09 => ( ! [N3: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X )
% 3.82/4.09 => ( ord_less_eq_real @ ( suminf_real @ F ) @ X ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % suminf_le_const
% 3.82/4.09 thf(fact_7212_fact__diff__Suc,axiom,
% 3.82/4.09 ! [N2: nat,M2: nat] :
% 3.82/4.09 ( ( ord_less_nat @ N2 @ ( suc @ M2 ) )
% 3.82/4.09 => ( ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ ( suc @ M2 ) @ N2 ) )
% 3.82/4.09 = ( times_times_nat @ ( minus_minus_nat @ ( suc @ M2 ) @ N2 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M2 @ N2 ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % fact_diff_Suc
% 3.82/4.09 thf(fact_7213_sgn__1__neg,axiom,
% 3.82/4.09 ! [A: int] :
% 3.82/4.09 ( ( ( sgn_sgn_int @ A )
% 3.82/4.09 = ( uminus_uminus_int @ one_one_int ) )
% 3.82/4.09 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 3.82/4.09
% 3.82/4.09 % sgn_1_neg
% 3.82/4.09 thf(fact_7214_sgn__1__neg,axiom,
% 3.82/4.09 ! [A: real] :
% 3.82/4.09 ( ( ( sgn_sgn_real @ A )
% 3.82/4.09 = ( uminus_uminus_real @ one_one_real ) )
% 3.82/4.09 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 3.82/4.09
% 3.82/4.09 % sgn_1_neg
% 3.82/4.09 thf(fact_7215_sgn__if,axiom,
% 3.82/4.09 ( sgn_sgn_int
% 3.82/4.09 = ( ^ [X4: int] : ( if_int @ ( X4 = zero_zero_int ) @ zero_zero_int @ ( if_int @ ( ord_less_int @ zero_zero_int @ X4 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sgn_if
% 3.82/4.09 thf(fact_7216_sgn__if,axiom,
% 3.82/4.09 ( sgn_sgn_real
% 3.82/4.09 = ( ^ [X4: real] : ( if_real @ ( X4 = zero_zero_real ) @ zero_zero_real @ ( if_real @ ( ord_less_real @ zero_zero_real @ X4 ) @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sgn_if
% 3.82/4.09 thf(fact_7217_zsgn__def,axiom,
% 3.82/4.09 ( sgn_sgn_int
% 3.82/4.09 = ( ^ [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 ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % zsgn_def
% 3.82/4.09 thf(fact_7218_fact__div__fact__le__pow,axiom,
% 3.82/4.09 ! [R2: nat,N2: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ R2 @ N2 )
% 3.82/4.09 => ( ord_less_eq_nat @ ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ R2 ) ) ) @ ( power_power_nat @ N2 @ R2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % fact_div_fact_le_pow
% 3.82/4.09 thf(fact_7219_binomial__fact__lemma,axiom,
% 3.82/4.09 ! [K: nat,N2: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ K @ N2 )
% 3.82/4.09 => ( ( times_times_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( binomial @ N2 @ K ) )
% 3.82/4.09 = ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % binomial_fact_lemma
% 3.82/4.09 thf(fact_7220_summableI__nonneg__bounded,axiom,
% 3.82/4.09 ! [F: nat > int,X: int] :
% 3.82/4.09 ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 3.82/4.09 => ( ! [N3: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X )
% 3.82/4.09 => ( summable_int @ F ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % summableI_nonneg_bounded
% 3.82/4.09 thf(fact_7221_summableI__nonneg__bounded,axiom,
% 3.82/4.09 ! [F: nat > nat,X: nat] :
% 3.82/4.09 ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 3.82/4.09 => ( ! [N3: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X )
% 3.82/4.09 => ( summable_nat @ F ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % summableI_nonneg_bounded
% 3.82/4.09 thf(fact_7222_summableI__nonneg__bounded,axiom,
% 3.82/4.09 ! [F: nat > real,X: real] :
% 3.82/4.09 ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 3.82/4.09 => ( ! [N3: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X )
% 3.82/4.09 => ( summable_real @ F ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % summableI_nonneg_bounded
% 3.82/4.09 thf(fact_7223_norm__sgn,axiom,
% 3.82/4.09 ! [X: real] :
% 3.82/4.09 ( ( ( X = zero_zero_real )
% 3.82/4.09 => ( ( real_V7735802525324610683m_real @ ( sgn_sgn_real @ X ) )
% 3.82/4.09 = zero_zero_real ) )
% 3.82/4.09 & ( ( X != zero_zero_real )
% 3.82/4.09 => ( ( real_V7735802525324610683m_real @ ( sgn_sgn_real @ X ) )
% 3.82/4.09 = one_one_real ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % norm_sgn
% 3.82/4.09 thf(fact_7224_norm__sgn,axiom,
% 3.82/4.09 ! [X: complex] :
% 3.82/4.09 ( ( ( X = zero_zero_complex )
% 3.82/4.09 => ( ( real_V1022390504157884413omplex @ ( sgn_sgn_complex @ X ) )
% 3.82/4.09 = zero_zero_real ) )
% 3.82/4.09 & ( ( X != zero_zero_complex )
% 3.82/4.09 => ( ( real_V1022390504157884413omplex @ ( sgn_sgn_complex @ X ) )
% 3.82/4.09 = one_one_real ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % norm_sgn
% 3.82/4.09 thf(fact_7225_bounded__imp__summable,axiom,
% 3.82/4.09 ! [A: nat > int,B: int] :
% 3.82/4.09 ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( A @ N3 ) )
% 3.82/4.09 => ( ! [N3: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ A @ ( set_ord_atMost_nat @ N3 ) ) @ B )
% 3.82/4.09 => ( summable_int @ A ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % bounded_imp_summable
% 3.82/4.09 thf(fact_7226_bounded__imp__summable,axiom,
% 3.82/4.09 ! [A: nat > nat,B: nat] :
% 3.82/4.09 ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( A @ N3 ) )
% 3.82/4.09 => ( ! [N3: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ A @ ( set_ord_atMost_nat @ N3 ) ) @ B )
% 3.82/4.09 => ( summable_nat @ A ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % bounded_imp_summable
% 3.82/4.09 thf(fact_7227_bounded__imp__summable,axiom,
% 3.82/4.09 ! [A: nat > real,B: real] :
% 3.82/4.09 ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 3.82/4.09 => ( ! [N3: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ A @ ( set_ord_atMost_nat @ N3 ) ) @ B )
% 3.82/4.09 => ( summable_real @ A ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % bounded_imp_summable
% 3.82/4.09 thf(fact_7228_suminf__split__head,axiom,
% 3.82/4.09 ! [F: nat > real] :
% 3.82/4.09 ( ( summable_real @ F )
% 3.82/4.09 => ( ( suminf_real
% 3.82/4.09 @ ^ [N: nat] : ( F @ ( suc @ N ) ) )
% 3.82/4.09 = ( minus_minus_real @ ( suminf_real @ F ) @ ( F @ zero_zero_nat ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % suminf_split_head
% 3.82/4.09 thf(fact_7229_choose__dvd,axiom,
% 3.82/4.09 ! [K: nat,N2: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ K @ N2 )
% 3.82/4.09 => ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( semiri1406184849735516958ct_int @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % choose_dvd
% 3.82/4.09 thf(fact_7230_choose__dvd,axiom,
% 3.82/4.09 ! [K: nat,N2: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ K @ N2 )
% 3.82/4.09 => ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % choose_dvd
% 3.82/4.09 thf(fact_7231_choose__dvd,axiom,
% 3.82/4.09 ! [K: nat,N2: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ K @ N2 )
% 3.82/4.09 => ( dvd_dvd_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % choose_dvd
% 3.82/4.09 thf(fact_7232_fact__eq__fact__times,axiom,
% 3.82/4.09 ! [N2: nat,M2: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ N2 @ M2 )
% 3.82/4.09 => ( ( semiri1408675320244567234ct_nat @ M2 )
% 3.82/4.09 = ( times_times_nat @ ( semiri1408675320244567234ct_nat @ N2 )
% 3.82/4.09 @ ( groups708209901874060359at_nat
% 3.82/4.09 @ ^ [X4: nat] : X4
% 3.82/4.09 @ ( set_or1269000886237332187st_nat @ ( suc @ N2 ) @ M2 ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % fact_eq_fact_times
% 3.82/4.09 thf(fact_7233_sin__expansion__lemma,axiom,
% 3.82/4.09 ! [X: real,M2: nat] :
% 3.82/4.09 ( ( sin_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M2 ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 3.82/4.09 = ( cos_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M2 ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sin_expansion_lemma
% 3.82/4.09 thf(fact_7234_sum__le__suminf,axiom,
% 3.82/4.09 ! [F: nat > int,I6: set_nat] :
% 3.82/4.09 ( ( summable_int @ F )
% 3.82/4.09 => ( ( finite_finite_nat @ I6 )
% 3.82/4.09 => ( ! [N3: nat] :
% 3.82/4.09 ( ( member_nat @ N3 @ ( uminus5710092332889474511et_nat @ I6 ) )
% 3.82/4.09 => ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) ) )
% 3.82/4.09 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ I6 ) @ ( suminf_int @ F ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum_le_suminf
% 3.82/4.09 thf(fact_7235_sum__le__suminf,axiom,
% 3.82/4.09 ! [F: nat > nat,I6: set_nat] :
% 3.82/4.09 ( ( summable_nat @ F )
% 3.82/4.09 => ( ( finite_finite_nat @ I6 )
% 3.82/4.09 => ( ! [N3: nat] :
% 3.82/4.09 ( ( member_nat @ N3 @ ( uminus5710092332889474511et_nat @ I6 ) )
% 3.82/4.09 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) ) )
% 3.82/4.09 => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ I6 ) @ ( suminf_nat @ F ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum_le_suminf
% 3.82/4.09 thf(fact_7236_sum__le__suminf,axiom,
% 3.82/4.09 ! [F: nat > real,I6: set_nat] :
% 3.82/4.09 ( ( summable_real @ F )
% 3.82/4.09 => ( ( finite_finite_nat @ I6 )
% 3.82/4.09 => ( ! [N3: nat] :
% 3.82/4.09 ( ( member_nat @ N3 @ ( uminus5710092332889474511et_nat @ I6 ) )
% 3.82/4.09 => ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) ) )
% 3.82/4.09 => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ I6 ) @ ( suminf_real @ F ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum_le_suminf
% 3.82/4.09 thf(fact_7237_cos__expansion__lemma,axiom,
% 3.82/4.09 ! [X: real,M2: nat] :
% 3.82/4.09 ( ( cos_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M2 ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 3.82/4.09 = ( uminus_uminus_real @ ( sin_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M2 ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % cos_expansion_lemma
% 3.82/4.09 thf(fact_7238_binomial__altdef__nat,axiom,
% 3.82/4.09 ! [K: nat,N2: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ K @ N2 )
% 3.82/4.09 => ( ( binomial @ N2 @ K )
% 3.82/4.09 = ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ K ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % binomial_altdef_nat
% 3.82/4.09 thf(fact_7239_suminf__split__initial__segment,axiom,
% 3.82/4.09 ! [F: nat > real,K: nat] :
% 3.82/4.09 ( ( summable_real @ F )
% 3.82/4.09 => ( ( suminf_real @ F )
% 3.82/4.09 = ( plus_plus_real
% 3.82/4.09 @ ( suminf_real
% 3.82/4.09 @ ^ [N: nat] : ( F @ ( plus_plus_nat @ N @ K ) ) )
% 3.82/4.09 @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % suminf_split_initial_segment
% 3.82/4.09 thf(fact_7240_suminf__minus__initial__segment,axiom,
% 3.82/4.09 ! [F: nat > real,K: nat] :
% 3.82/4.09 ( ( summable_real @ F )
% 3.82/4.09 => ( ( suminf_real
% 3.82/4.09 @ ^ [N: nat] : ( F @ ( plus_plus_nat @ N @ K ) ) )
% 3.82/4.09 = ( minus_minus_real @ ( suminf_real @ F ) @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % suminf_minus_initial_segment
% 3.82/4.09 thf(fact_7241_fact__div__fact,axiom,
% 3.82/4.09 ! [N2: nat,M2: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ N2 @ M2 )
% 3.82/4.09 => ( ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ M2 ) @ ( semiri1408675320244567234ct_nat @ N2 ) )
% 3.82/4.09 = ( groups708209901874060359at_nat
% 3.82/4.09 @ ^ [X4: nat] : X4
% 3.82/4.09 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ M2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % fact_div_fact
% 3.82/4.09 thf(fact_7242_sum__less__suminf,axiom,
% 3.82/4.09 ! [F: nat > int,N2: nat] :
% 3.82/4.09 ( ( summable_int @ F )
% 3.82/4.09 => ( ! [M3: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ N2 @ M3 )
% 3.82/4.09 => ( ord_less_int @ zero_zero_int @ ( F @ M3 ) ) )
% 3.82/4.09 => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_int @ F ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum_less_suminf
% 3.82/4.09 thf(fact_7243_sum__less__suminf,axiom,
% 3.82/4.09 ! [F: nat > nat,N2: nat] :
% 3.82/4.09 ( ( summable_nat @ F )
% 3.82/4.09 => ( ! [M3: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ N2 @ M3 )
% 3.82/4.09 => ( ord_less_nat @ zero_zero_nat @ ( F @ M3 ) ) )
% 3.82/4.09 => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_nat @ F ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum_less_suminf
% 3.82/4.09 thf(fact_7244_sum__less__suminf,axiom,
% 3.82/4.09 ! [F: nat > real,N2: nat] :
% 3.82/4.09 ( ( summable_real @ F )
% 3.82/4.09 => ( ! [M3: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ N2 @ M3 )
% 3.82/4.09 => ( ord_less_real @ zero_zero_real @ ( F @ M3 ) ) )
% 3.82/4.09 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_real @ F ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sum_less_suminf
% 3.82/4.09 thf(fact_7245_powser__split__head_I1_J,axiom,
% 3.82/4.09 ! [F: nat > real,Z3: real] :
% 3.82/4.09 ( ( summable_real
% 3.82/4.09 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z3 @ N ) ) )
% 3.82/4.09 => ( ( suminf_real
% 3.82/4.09 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z3 @ N ) ) )
% 3.82/4.09 = ( plus_plus_real @ ( F @ zero_zero_nat )
% 3.82/4.09 @ ( times_times_real
% 3.82/4.09 @ ( suminf_real
% 3.82/4.09 @ ^ [N: nat] : ( times_times_real @ ( F @ ( suc @ N ) ) @ ( power_power_real @ Z3 @ N ) ) )
% 3.82/4.09 @ Z3 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % powser_split_head(1)
% 3.82/4.09 thf(fact_7246_powser__split__head_I1_J,axiom,
% 3.82/4.09 ! [F: nat > complex,Z3: complex] :
% 3.82/4.09 ( ( summable_complex
% 3.82/4.09 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z3 @ N ) ) )
% 3.82/4.09 => ( ( suminf_complex
% 3.82/4.09 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z3 @ N ) ) )
% 3.82/4.09 = ( plus_plus_complex @ ( F @ zero_zero_nat )
% 3.82/4.09 @ ( times_times_complex
% 3.82/4.09 @ ( suminf_complex
% 3.82/4.09 @ ^ [N: nat] : ( times_times_complex @ ( F @ ( suc @ N ) ) @ ( power_power_complex @ Z3 @ N ) ) )
% 3.82/4.09 @ Z3 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % powser_split_head(1)
% 3.82/4.09 thf(fact_7247_powser__split__head_I2_J,axiom,
% 3.82/4.09 ! [F: nat > real,Z3: real] :
% 3.82/4.09 ( ( summable_real
% 3.82/4.09 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z3 @ N ) ) )
% 3.82/4.09 => ( ( times_times_real
% 3.82/4.09 @ ( suminf_real
% 3.82/4.09 @ ^ [N: nat] : ( times_times_real @ ( F @ ( suc @ N ) ) @ ( power_power_real @ Z3 @ N ) ) )
% 3.82/4.09 @ Z3 )
% 3.82/4.09 = ( minus_minus_real
% 3.82/4.09 @ ( suminf_real
% 3.82/4.09 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z3 @ N ) ) )
% 3.82/4.09 @ ( F @ zero_zero_nat ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % powser_split_head(2)
% 3.82/4.09 thf(fact_7248_powser__split__head_I2_J,axiom,
% 3.82/4.09 ! [F: nat > complex,Z3: complex] :
% 3.82/4.09 ( ( summable_complex
% 3.82/4.09 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z3 @ N ) ) )
% 3.82/4.09 => ( ( times_times_complex
% 3.82/4.09 @ ( suminf_complex
% 3.82/4.09 @ ^ [N: nat] : ( times_times_complex @ ( F @ ( suc @ N ) ) @ ( power_power_complex @ Z3 @ N ) ) )
% 3.82/4.09 @ Z3 )
% 3.82/4.09 = ( minus_minus_complex
% 3.82/4.09 @ ( suminf_complex
% 3.82/4.09 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z3 @ N ) ) )
% 3.82/4.09 @ ( F @ zero_zero_nat ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % powser_split_head(2)
% 3.82/4.09 thf(fact_7249_summable__partial__sum__bound,axiom,
% 3.82/4.09 ! [F: nat > complex,E2: real] :
% 3.82/4.09 ( ( summable_complex @ F )
% 3.82/4.09 => ( ( ord_less_real @ zero_zero_real @ E2 )
% 3.82/4.09 => ~ ! [N9: nat] :
% 3.82/4.09 ~ ! [M5: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ N9 @ M5 )
% 3.82/4.09 => ! [N7: nat] : ( ord_less_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ M5 @ N7 ) ) ) @ E2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % summable_partial_sum_bound
% 3.82/4.09 thf(fact_7250_summable__partial__sum__bound,axiom,
% 3.82/4.09 ! [F: nat > real,E2: real] :
% 3.82/4.09 ( ( summable_real @ F )
% 3.82/4.09 => ( ( ord_less_real @ zero_zero_real @ E2 )
% 3.82/4.09 => ~ ! [N9: nat] :
% 3.82/4.09 ~ ! [M5: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ N9 @ M5 )
% 3.82/4.09 => ! [N7: nat] : ( ord_less_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ M5 @ N7 ) ) ) @ E2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % summable_partial_sum_bound
% 3.82/4.09 thf(fact_7251_suminf__exist__split,axiom,
% 3.82/4.09 ! [R2: real,F: nat > real] :
% 3.82/4.09 ( ( ord_less_real @ zero_zero_real @ R2 )
% 3.82/4.09 => ( ( summable_real @ F )
% 3.82/4.09 => ? [N9: nat] :
% 3.82/4.09 ! [N7: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ N9 @ N7 )
% 3.82/4.09 => ( ord_less_real
% 3.82/4.09 @ ( real_V7735802525324610683m_real
% 3.82/4.09 @ ( suminf_real
% 3.82/4.09 @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N7 ) ) ) )
% 3.82/4.09 @ R2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % suminf_exist_split
% 3.82/4.09 thf(fact_7252_suminf__exist__split,axiom,
% 3.82/4.09 ! [R2: real,F: nat > complex] :
% 3.82/4.09 ( ( ord_less_real @ zero_zero_real @ R2 )
% 3.82/4.09 => ( ( summable_complex @ F )
% 3.82/4.09 => ? [N9: nat] :
% 3.82/4.09 ! [N7: nat] :
% 3.82/4.09 ( ( ord_less_eq_nat @ N9 @ N7 )
% 3.82/4.09 => ( ord_less_real
% 3.82/4.09 @ ( real_V1022390504157884413omplex
% 3.82/4.09 @ ( suminf_complex
% 3.82/4.09 @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N7 ) ) ) )
% 3.82/4.09 @ R2 ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % suminf_exist_split
% 3.82/4.09 thf(fact_7253_sin__pi__divide__n__ge__0,axiom,
% 3.82/4.09 ! [N2: nat] :
% 3.82/4.09 ( ( N2 != zero_zero_nat )
% 3.82/4.09 => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % sin_pi_divide_n_ge_0
% 3.82/4.09 thf(fact_7254_sin__paired,axiom,
% 3.82/4.09 ! [X: real] :
% 3.82/4.09 ( sums_real
% 3.82/4.09 @ ^ [N: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) )
% 3.82/4.09 @ ( sin_real @ X ) ) ).
% 3.82/4.09
% 3.82/4.09 % sin_paired
% 3.82/4.09 thf(fact_7255_fact__num__eq__if,axiom,
% 3.82/4.09 ( semiri5044797733671781792omplex
% 3.82/4.09 = ( ^ [M: nat] : ( if_complex @ ( M = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % fact_num_eq_if
% 3.82/4.09 thf(fact_7256_fact__num__eq__if,axiom,
% 3.82/4.09 ( semiri4449623510593786356d_enat
% 3.82/4.09 = ( ^ [M: nat] : ( if_Extended_enat @ ( M = zero_zero_nat ) @ one_on7984719198319812577d_enat @ ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ M ) @ ( semiri4449623510593786356d_enat @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % fact_num_eq_if
% 3.82/4.09 thf(fact_7257_fact__num__eq__if,axiom,
% 3.82/4.09 ( semiri1406184849735516958ct_int
% 3.82/4.09 = ( ^ [M: nat] : ( if_int @ ( M = zero_zero_nat ) @ one_one_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ) ).
% 3.82/4.09
% 3.82/4.09 % fact_num_eq_if
% 3.82/4.09 thf(fact_7258_fact__num__eq__if,axiom,
% 3.82/4.09 ( semiri1408675320244567234ct_nat
% 3.82/4.09 = ( ^ [M: nat] : ( if_nat @ ( M = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % fact_num_eq_if
% 3.82/4.10 thf(fact_7259_fact__num__eq__if,axiom,
% 3.82/4.10 ( semiri2265585572941072030t_real
% 3.82/4.10 = ( ^ [M: nat] : ( if_real @ ( M = zero_zero_nat ) @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % fact_num_eq_if
% 3.82/4.10 thf(fact_7260_fact__reduce,axiom,
% 3.82/4.10 ! [N2: nat] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( semiri5044797733671781792omplex @ N2 )
% 3.82/4.10 = ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % fact_reduce
% 3.82/4.10 thf(fact_7261_fact__reduce,axiom,
% 3.82/4.10 ! [N2: nat] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( semiri4449623510593786356d_enat @ N2 )
% 3.82/4.10 = ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ N2 ) @ ( semiri4449623510593786356d_enat @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % fact_reduce
% 3.82/4.10 thf(fact_7262_fact__reduce,axiom,
% 3.82/4.10 ! [N2: nat] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( semiri1406184849735516958ct_int @ N2 )
% 3.82/4.10 = ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % fact_reduce
% 3.82/4.10 thf(fact_7263_fact__reduce,axiom,
% 3.82/4.10 ! [N2: nat] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( semiri1408675320244567234ct_nat @ N2 )
% 3.82/4.10 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % fact_reduce
% 3.82/4.10 thf(fact_7264_fact__reduce,axiom,
% 3.82/4.10 ! [N2: nat] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( semiri2265585572941072030t_real @ N2 )
% 3.82/4.10 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % fact_reduce
% 3.82/4.10 thf(fact_7265_fact__binomial,axiom,
% 3.82/4.10 ! [K: nat,N2: nat] :
% 3.82/4.10 ( ( ord_less_eq_nat @ K @ N2 )
% 3.82/4.10 => ( ( times_times_complex @ ( semiri5044797733671781792omplex @ K ) @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ K ) ) )
% 3.82/4.10 = ( divide1717551699836669952omplex @ ( semiri5044797733671781792omplex @ N2 ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N2 @ K ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % fact_binomial
% 3.82/4.10 thf(fact_7266_fact__binomial,axiom,
% 3.82/4.10 ! [K: nat,N2: nat] :
% 3.82/4.10 ( ( ord_less_eq_nat @ K @ N2 )
% 3.82/4.10 => ( ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ K ) ) )
% 3.82/4.10 = ( divide_divide_real @ ( semiri2265585572941072030t_real @ N2 ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ K ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % fact_binomial
% 3.82/4.10 thf(fact_7267_binomial__fact,axiom,
% 3.82/4.10 ! [K: nat,N2: nat] :
% 3.82/4.10 ( ( ord_less_eq_nat @ K @ N2 )
% 3.82/4.10 => ( ( semiri8010041392384452111omplex @ ( binomial @ N2 @ K ) )
% 3.82/4.10 = ( divide1717551699836669952omplex @ ( semiri5044797733671781792omplex @ N2 ) @ ( times_times_complex @ ( semiri5044797733671781792omplex @ K ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N2 @ K ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % binomial_fact
% 3.82/4.10 thf(fact_7268_binomial__fact,axiom,
% 3.82/4.10 ! [K: nat,N2: nat] :
% 3.82/4.10 ( ( ord_less_eq_nat @ K @ N2 )
% 3.82/4.10 => ( ( semiri5074537144036343181t_real @ ( binomial @ N2 @ K ) )
% 3.82/4.10 = ( divide_divide_real @ ( semiri2265585572941072030t_real @ N2 ) @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ K ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % binomial_fact
% 3.82/4.10 thf(fact_7269_cos__times__cos,axiom,
% 3.82/4.10 ! [W2: complex,Z3: complex] :
% 3.82/4.10 ( ( times_times_complex @ ( cos_complex @ W2 ) @ ( cos_complex @ Z3 ) )
% 3.82/4.10 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( cos_complex @ ( minus_minus_complex @ W2 @ Z3 ) ) @ ( cos_complex @ ( plus_plus_complex @ W2 @ Z3 ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % cos_times_cos
% 3.82/4.10 thf(fact_7270_cos__times__cos,axiom,
% 3.82/4.10 ! [W2: real,Z3: real] :
% 3.82/4.10 ( ( times_times_real @ ( cos_real @ W2 ) @ ( cos_real @ Z3 ) )
% 3.82/4.10 = ( divide_divide_real @ ( plus_plus_real @ ( cos_real @ ( minus_minus_real @ W2 @ Z3 ) ) @ ( cos_real @ ( plus_plus_real @ W2 @ Z3 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % cos_times_cos
% 3.82/4.10 thf(fact_7271_cos__plus__cos,axiom,
% 3.82/4.10 ! [W2: complex,Z3: complex] :
% 3.82/4.10 ( ( plus_plus_complex @ ( cos_complex @ W2 ) @ ( cos_complex @ Z3 ) )
% 3.82/4.10 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W2 @ Z3 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ W2 @ Z3 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % cos_plus_cos
% 3.82/4.10 thf(fact_7272_cos__plus__cos,axiom,
% 3.82/4.10 ! [W2: real,Z3: real] :
% 3.82/4.10 ( ( plus_plus_real @ ( cos_real @ W2 ) @ ( cos_real @ Z3 ) )
% 3.82/4.10 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( cos_real @ ( divide_divide_real @ ( plus_plus_real @ W2 @ Z3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( cos_real @ ( divide_divide_real @ ( minus_minus_real @ W2 @ Z3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % cos_plus_cos
% 3.82/4.10 thf(fact_7273_summable__ratio__test,axiom,
% 3.82/4.10 ! [C: real,N6: nat,F: nat > real] :
% 3.82/4.10 ( ( ord_less_real @ C @ one_one_real )
% 3.82/4.10 => ( ! [N3: nat] :
% 3.82/4.10 ( ( ord_less_eq_nat @ N6 @ N3 )
% 3.82/4.10 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ ( suc @ N3 ) ) ) @ ( times_times_real @ C @ ( real_V7735802525324610683m_real @ ( F @ N3 ) ) ) ) )
% 3.82/4.10 => ( summable_real @ F ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % summable_ratio_test
% 3.82/4.10 thf(fact_7274_summable__ratio__test,axiom,
% 3.82/4.10 ! [C: real,N6: nat,F: nat > complex] :
% 3.82/4.10 ( ( ord_less_real @ C @ one_one_real )
% 3.82/4.10 => ( ! [N3: nat] :
% 3.82/4.10 ( ( ord_less_eq_nat @ N6 @ N3 )
% 3.82/4.10 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ ( suc @ N3 ) ) ) @ ( times_times_real @ C @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) ) ) )
% 3.82/4.10 => ( summable_complex @ F ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % summable_ratio_test
% 3.82/4.10 thf(fact_7275_sum__less__suminf2,axiom,
% 3.82/4.10 ! [F: nat > int,N2: nat,I: nat] :
% 3.82/4.10 ( ( summable_int @ F )
% 3.82/4.10 => ( ! [M3: nat] :
% 3.82/4.10 ( ( ord_less_eq_nat @ N2 @ M3 )
% 3.82/4.10 => ( ord_less_eq_int @ zero_zero_int @ ( F @ M3 ) ) )
% 3.82/4.10 => ( ( ord_less_eq_nat @ N2 @ I )
% 3.82/4.10 => ( ( ord_less_int @ zero_zero_int @ ( F @ I ) )
% 3.82/4.10 => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_int @ F ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % sum_less_suminf2
% 3.82/4.10 thf(fact_7276_sum__less__suminf2,axiom,
% 3.82/4.10 ! [F: nat > nat,N2: nat,I: nat] :
% 3.82/4.10 ( ( summable_nat @ F )
% 3.82/4.10 => ( ! [M3: nat] :
% 3.82/4.10 ( ( ord_less_eq_nat @ N2 @ M3 )
% 3.82/4.10 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ M3 ) ) )
% 3.82/4.10 => ( ( ord_less_eq_nat @ N2 @ I )
% 3.82/4.10 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I ) )
% 3.82/4.10 => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_nat @ F ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % sum_less_suminf2
% 3.82/4.10 thf(fact_7277_sum__less__suminf2,axiom,
% 3.82/4.10 ! [F: nat > real,N2: nat,I: nat] :
% 3.82/4.10 ( ( summable_real @ F )
% 3.82/4.10 => ( ! [M3: nat] :
% 3.82/4.10 ( ( ord_less_eq_nat @ N2 @ M3 )
% 3.82/4.10 => ( ord_less_eq_real @ zero_zero_real @ ( F @ M3 ) ) )
% 3.82/4.10 => ( ( ord_less_eq_nat @ N2 @ I )
% 3.82/4.10 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 3.82/4.10 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_real @ F ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % sum_less_suminf2
% 3.82/4.10 thf(fact_7278_gbinomial__pochhammer_H,axiom,
% 3.82/4.10 ( gbinomial_complex
% 3.82/4.10 = ( ^ [A3: complex,K2: nat] : ( divide1717551699836669952omplex @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ A3 @ ( semiri8010041392384452111omplex @ K2 ) ) @ one_one_complex ) @ K2 ) @ ( semiri5044797733671781792omplex @ K2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % gbinomial_pochhammer'
% 3.82/4.10 thf(fact_7279_gbinomial__pochhammer_H,axiom,
% 3.82/4.10 ( gbinomial_real
% 3.82/4.10 = ( ^ [A3: real,K2: nat] : ( divide_divide_real @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ A3 @ ( semiri5074537144036343181t_real @ K2 ) ) @ one_one_real ) @ K2 ) @ ( semiri2265585572941072030t_real @ K2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % gbinomial_pochhammer'
% 3.82/4.10 thf(fact_7280_Maclaurin__zero,axiom,
% 3.82/4.10 ! [X: real,N2: nat,Diff: nat > nat > real] :
% 3.82/4.10 ( ( X = zero_zero_real )
% 3.82/4.10 => ( ( N2 != zero_zero_nat )
% 3.82/4.10 => ( ( groups6591440286371151544t_real
% 3.82/4.10 @ ^ [M: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M @ zero_zero_nat ) @ ( semiri2265585572941072030t_real @ M ) ) @ ( power_power_real @ X @ M ) )
% 3.82/4.10 @ ( set_ord_lessThan_nat @ N2 ) )
% 3.82/4.10 = ( Diff @ zero_zero_nat @ zero_zero_nat ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % Maclaurin_zero
% 3.82/4.10 thf(fact_7281_Maclaurin__zero,axiom,
% 3.82/4.10 ! [X: real,N2: nat,Diff: nat > real > real] :
% 3.82/4.10 ( ( X = zero_zero_real )
% 3.82/4.10 => ( ( N2 != zero_zero_nat )
% 3.82/4.10 => ( ( groups6591440286371151544t_real
% 3.82/4.10 @ ^ [M: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M ) ) @ ( power_power_real @ X @ M ) )
% 3.82/4.10 @ ( set_ord_lessThan_nat @ N2 ) )
% 3.82/4.10 = ( Diff @ zero_zero_nat @ zero_zero_real ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % Maclaurin_zero
% 3.82/4.10 thf(fact_7282_Maclaurin__zero,axiom,
% 3.82/4.10 ! [X: real,N2: nat,Diff: nat > int > real] :
% 3.82/4.10 ( ( X = zero_zero_real )
% 3.82/4.10 => ( ( N2 != zero_zero_nat )
% 3.82/4.10 => ( ( groups6591440286371151544t_real
% 3.82/4.10 @ ^ [M: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M @ zero_zero_int ) @ ( semiri2265585572941072030t_real @ M ) ) @ ( power_power_real @ X @ M ) )
% 3.82/4.10 @ ( set_ord_lessThan_nat @ N2 ) )
% 3.82/4.10 = ( Diff @ zero_zero_nat @ zero_zero_int ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % Maclaurin_zero
% 3.82/4.10 thf(fact_7283_Maclaurin__zero,axiom,
% 3.82/4.10 ! [X: real,N2: nat,Diff: nat > complex > real] :
% 3.82/4.10 ( ( X = zero_zero_real )
% 3.82/4.10 => ( ( N2 != zero_zero_nat )
% 3.82/4.10 => ( ( groups6591440286371151544t_real
% 3.82/4.10 @ ^ [M: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M @ zero_zero_complex ) @ ( semiri2265585572941072030t_real @ M ) ) @ ( power_power_real @ X @ M ) )
% 3.82/4.10 @ ( set_ord_lessThan_nat @ N2 ) )
% 3.82/4.10 = ( Diff @ zero_zero_nat @ zero_zero_complex ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % Maclaurin_zero
% 3.82/4.10 thf(fact_7284_Maclaurin__zero,axiom,
% 3.82/4.10 ! [X: real,N2: nat,Diff: nat > extended_enat > real] :
% 3.82/4.10 ( ( X = zero_zero_real )
% 3.82/4.10 => ( ( N2 != zero_zero_nat )
% 3.82/4.10 => ( ( groups6591440286371151544t_real
% 3.82/4.10 @ ^ [M: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M @ zero_z5237406670263579293d_enat ) @ ( semiri2265585572941072030t_real @ M ) ) @ ( power_power_real @ X @ M ) )
% 3.82/4.10 @ ( set_ord_lessThan_nat @ N2 ) )
% 3.82/4.10 = ( Diff @ zero_zero_nat @ zero_z5237406670263579293d_enat ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % Maclaurin_zero
% 3.82/4.10 thf(fact_7285_Maclaurin__cos__expansion2,axiom,
% 3.82/4.10 ! [X: real,N2: nat] :
% 3.82/4.10 ( ( ord_less_real @ zero_zero_real @ X )
% 3.82/4.10 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ? [T6: real] :
% 3.82/4.10 ( ( ord_less_real @ zero_zero_real @ T6 )
% 3.82/4.10 & ( ord_less_real @ T6 @ X )
% 3.82/4.10 & ( ( cos_real @ X )
% 3.82/4.10 = ( plus_plus_real
% 3.82/4.10 @ ( groups6591440286371151544t_real
% 3.82/4.10 @ ^ [M: nat] : ( times_times_real @ ( cos_coeff @ M ) @ ( power_power_real @ X @ M ) )
% 3.82/4.10 @ ( set_ord_lessThan_nat @ N2 ) )
% 3.82/4.10 @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X @ N2 ) ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % Maclaurin_cos_expansion2
% 3.82/4.10 thf(fact_7286_Maclaurin__minus__cos__expansion,axiom,
% 3.82/4.10 ! [N2: nat,X: real] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( ord_less_real @ X @ zero_zero_real )
% 3.82/4.10 => ? [T6: real] :
% 3.82/4.10 ( ( ord_less_real @ X @ T6 )
% 3.82/4.10 & ( ord_less_real @ T6 @ zero_zero_real )
% 3.82/4.10 & ( ( cos_real @ X )
% 3.82/4.10 = ( plus_plus_real
% 3.82/4.10 @ ( groups6591440286371151544t_real
% 3.82/4.10 @ ^ [M: nat] : ( times_times_real @ ( cos_coeff @ M ) @ ( power_power_real @ X @ M ) )
% 3.82/4.10 @ ( set_ord_lessThan_nat @ N2 ) )
% 3.82/4.10 @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X @ N2 ) ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % Maclaurin_minus_cos_expansion
% 3.82/4.10 thf(fact_7287_sin__pi__divide__n__gt__0,axiom,
% 3.82/4.10 ! [N2: nat] :
% 3.82/4.10 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 3.82/4.10 => ( ord_less_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % sin_pi_divide_n_gt_0
% 3.82/4.10 thf(fact_7288_gbinomial__Suc,axiom,
% 3.82/4.10 ! [A: real,K: nat] :
% 3.82/4.10 ( ( gbinomial_real @ A @ ( suc @ K ) )
% 3.82/4.10 = ( divide_divide_real
% 3.82/4.10 @ ( groups129246275422532515t_real
% 3.82/4.10 @ ^ [I3: nat] : ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ I3 ) )
% 3.82/4.10 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 3.82/4.10 @ ( semiri2265585572941072030t_real @ ( suc @ K ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % gbinomial_Suc
% 3.82/4.10 thf(fact_7289_gbinomial__Suc,axiom,
% 3.82/4.10 ! [A: int,K: nat] :
% 3.82/4.10 ( ( gbinomial_int @ A @ ( suc @ K ) )
% 3.82/4.10 = ( divide_divide_int
% 3.82/4.10 @ ( groups705719431365010083at_int
% 3.82/4.10 @ ^ [I3: nat] : ( minus_minus_int @ A @ ( semiri1314217659103216013at_int @ I3 ) )
% 3.82/4.10 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 3.82/4.10 @ ( semiri1406184849735516958ct_int @ ( suc @ K ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % gbinomial_Suc
% 3.82/4.10 thf(fact_7290_gbinomial__Suc,axiom,
% 3.82/4.10 ! [A: nat,K: nat] :
% 3.82/4.10 ( ( gbinomial_nat @ A @ ( suc @ K ) )
% 3.82/4.10 = ( divide_divide_nat
% 3.82/4.10 @ ( groups708209901874060359at_nat
% 3.82/4.10 @ ^ [I3: nat] : ( minus_minus_nat @ A @ ( semiri1316708129612266289at_nat @ I3 ) )
% 3.82/4.10 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 3.82/4.10 @ ( semiri1408675320244567234ct_nat @ ( suc @ K ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % gbinomial_Suc
% 3.82/4.10 thf(fact_7291_divide__int__unfold,axiom,
% 3.82/4.10 ! [L: int,K: int,N2: nat,M2: nat] :
% 3.82/4.10 ( ( ( ( ( sgn_sgn_int @ L )
% 3.82/4.10 = zero_zero_int )
% 3.82/4.10 | ( ( sgn_sgn_int @ K )
% 3.82/4.10 = zero_zero_int )
% 3.82/4.10 | ( N2 = zero_zero_nat ) )
% 3.82/4.10 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 3.82/4.10 = zero_zero_int ) )
% 3.82/4.10 & ( ~ ( ( ( sgn_sgn_int @ L )
% 3.82/4.10 = zero_zero_int )
% 3.82/4.10 | ( ( sgn_sgn_int @ K )
% 3.82/4.10 = zero_zero_int )
% 3.82/4.10 | ( N2 = zero_zero_nat ) )
% 3.82/4.10 => ( ( ( ( sgn_sgn_int @ K )
% 3.82/4.10 = ( sgn_sgn_int @ L ) )
% 3.82/4.10 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 3.82/4.10 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M2 @ N2 ) ) ) )
% 3.82/4.10 & ( ( ( sgn_sgn_int @ K )
% 3.82/4.10 != ( sgn_sgn_int @ L ) )
% 3.82/4.10 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 3.82/4.10 = ( uminus_uminus_int
% 3.82/4.10 @ ( semiri1314217659103216013at_int
% 3.82/4.10 @ ( plus_plus_nat @ ( divide_divide_nat @ M2 @ N2 )
% 3.82/4.10 @ ( zero_n2687167440665602831ol_nat
% 3.82/4.10 @ ~ ( dvd_dvd_nat @ N2 @ M2 ) ) ) ) ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % divide_int_unfold
% 3.82/4.10 thf(fact_7292_Maclaurin__sin__expansion3,axiom,
% 3.82/4.10 ! [N2: nat,X: real] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( ord_less_real @ zero_zero_real @ X )
% 3.82/4.10 => ? [T6: real] :
% 3.82/4.10 ( ( ord_less_real @ zero_zero_real @ T6 )
% 3.82/4.10 & ( ord_less_real @ T6 @ X )
% 3.82/4.10 & ( ( sin_real @ X )
% 3.82/4.10 = ( plus_plus_real
% 3.82/4.10 @ ( groups6591440286371151544t_real
% 3.82/4.10 @ ^ [M: nat] : ( times_times_real @ ( sin_coeff @ M ) @ ( power_power_real @ X @ M ) )
% 3.82/4.10 @ ( set_ord_lessThan_nat @ N2 ) )
% 3.82/4.10 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X @ N2 ) ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % Maclaurin_sin_expansion3
% 3.82/4.10 thf(fact_7293_listrel1p__def,axiom,
% 3.82/4.10 ( listrel1p_nat
% 3.82/4.10 = ( ^ [R4: nat > nat > $o,Xs3: list_nat,Ys3: list_nat] : ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Xs3 @ Ys3 ) @ ( listrel1_nat @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ R4 ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % listrel1p_def
% 3.82/4.10 thf(fact_7294_listrel1p__def,axiom,
% 3.82/4.10 ( listrel1p_int
% 3.82/4.10 = ( ^ [R4: int > int > $o,Xs3: list_int,Ys3: list_int] : ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Xs3 @ Ys3 ) @ ( listrel1_int @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ R4 ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % listrel1p_def
% 3.82/4.10 thf(fact_7295_sin__x__sin__y,axiom,
% 3.82/4.10 ! [X: complex,Y: complex] :
% 3.82/4.10 ( sums_complex
% 3.82/4.10 @ ^ [P6: nat] :
% 3.82/4.10 ( groups2073611262835488442omplex
% 3.82/4.10 @ ^ [N: nat] :
% 3.82/4.10 ( if_complex
% 3.82/4.10 @ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P6 )
% 3.82/4.10 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 3.82/4.10 @ ( 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 @ P6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P6 @ N ) ) ) ) @ ( semiri2265585572941072030t_real @ P6 ) ) ) @ ( power_power_complex @ X @ N ) ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ P6 @ N ) ) )
% 3.82/4.10 @ zero_zero_complex )
% 3.82/4.10 @ ( set_ord_atMost_nat @ P6 ) )
% 3.82/4.10 @ ( times_times_complex @ ( sin_complex @ X ) @ ( sin_complex @ Y ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % sin_x_sin_y
% 3.82/4.10 thf(fact_7296_sin__x__sin__y,axiom,
% 3.82/4.10 ! [X: real,Y: real] :
% 3.82/4.10 ( sums_real
% 3.82/4.10 @ ^ [P6: nat] :
% 3.82/4.10 ( groups6591440286371151544t_real
% 3.82/4.10 @ ^ [N: nat] :
% 3.82/4.10 ( if_real
% 3.82/4.10 @ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P6 )
% 3.82/4.10 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 3.82/4.10 @ ( 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 @ P6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P6 @ N ) ) ) ) @ ( semiri2265585572941072030t_real @ P6 ) ) ) @ ( power_power_real @ X @ N ) ) @ ( power_power_real @ Y @ ( minus_minus_nat @ P6 @ N ) ) )
% 3.82/4.10 @ zero_zero_real )
% 3.82/4.10 @ ( set_ord_atMost_nat @ P6 ) )
% 3.82/4.10 @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ Y ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % sin_x_sin_y
% 3.82/4.10 thf(fact_7297_sums__cos__x__plus__y,axiom,
% 3.82/4.10 ! [X: complex,Y: complex] :
% 3.82/4.10 ( sums_complex
% 3.82/4.10 @ ^ [P6: nat] :
% 3.82/4.10 ( groups2073611262835488442omplex
% 3.82/4.10 @ ^ [N: nat] : ( if_complex @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P6 ) @ ( 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 @ P6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P6 @ N ) ) ) ) @ ( semiri2265585572941072030t_real @ P6 ) ) @ ( power_power_complex @ X @ N ) ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ P6 @ N ) ) ) @ zero_zero_complex )
% 3.82/4.10 @ ( set_ord_atMost_nat @ P6 ) )
% 3.82/4.10 @ ( cos_complex @ ( plus_plus_complex @ X @ Y ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % sums_cos_x_plus_y
% 3.82/4.10 thf(fact_7298_sums__cos__x__plus__y,axiom,
% 3.82/4.10 ! [X: real,Y: real] :
% 3.82/4.10 ( sums_real
% 3.82/4.10 @ ^ [P6: nat] :
% 3.82/4.10 ( groups6591440286371151544t_real
% 3.82/4.10 @ ^ [N: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P6 ) @ ( 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 @ P6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P6 @ N ) ) ) ) @ ( semiri2265585572941072030t_real @ P6 ) ) @ ( power_power_real @ X @ N ) ) @ ( power_power_real @ Y @ ( minus_minus_nat @ P6 @ N ) ) ) @ zero_zero_real )
% 3.82/4.10 @ ( set_ord_atMost_nat @ P6 ) )
% 3.82/4.10 @ ( cos_real @ ( plus_plus_real @ X @ Y ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % sums_cos_x_plus_y
% 3.82/4.10 thf(fact_7299_cos__x__cos__y,axiom,
% 3.82/4.10 ! [X: complex,Y: complex] :
% 3.82/4.10 ( sums_complex
% 3.82/4.10 @ ^ [P6: nat] :
% 3.82/4.10 ( groups2073611262835488442omplex
% 3.82/4.10 @ ^ [N: nat] :
% 3.82/4.10 ( if_complex
% 3.82/4.10 @ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P6 )
% 3.82/4.10 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 3.82/4.10 @ ( 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 @ P6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P6 @ N ) ) ) ) @ ( semiri2265585572941072030t_real @ P6 ) ) @ ( power_power_complex @ X @ N ) ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ P6 @ N ) ) )
% 3.82/4.10 @ zero_zero_complex )
% 3.82/4.10 @ ( set_ord_atMost_nat @ P6 ) )
% 3.82/4.10 @ ( times_times_complex @ ( cos_complex @ X ) @ ( cos_complex @ Y ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % cos_x_cos_y
% 3.82/4.10 thf(fact_7300_cos__x__cos__y,axiom,
% 3.82/4.10 ! [X: real,Y: real] :
% 3.82/4.10 ( sums_real
% 3.82/4.10 @ ^ [P6: nat] :
% 3.82/4.10 ( groups6591440286371151544t_real
% 3.82/4.10 @ ^ [N: nat] :
% 3.82/4.10 ( if_real
% 3.82/4.10 @ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P6 )
% 3.82/4.10 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 3.82/4.10 @ ( 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 @ P6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P6 @ N ) ) ) ) @ ( semiri2265585572941072030t_real @ P6 ) ) @ ( power_power_real @ X @ N ) ) @ ( power_power_real @ Y @ ( minus_minus_nat @ P6 @ N ) ) )
% 3.82/4.10 @ zero_zero_real )
% 3.82/4.10 @ ( set_ord_atMost_nat @ P6 ) )
% 3.82/4.10 @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % cos_x_cos_y
% 3.82/4.10 thf(fact_7301_sin__coeff__def,axiom,
% 3.82/4.10 ( sin_coeff
% 3.82/4.10 = ( ^ [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 ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % sin_coeff_def
% 3.82/4.10 thf(fact_7302_scaleR__cancel__right,axiom,
% 3.82/4.10 ! [A: real,X: real,B2: real] :
% 3.82/4.10 ( ( ( real_V1485227260804924795R_real @ A @ X )
% 3.82/4.10 = ( real_V1485227260804924795R_real @ B2 @ X ) )
% 3.82/4.10 = ( ( A = B2 )
% 3.82/4.10 | ( X = zero_zero_real ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % scaleR_cancel_right
% 3.82/4.10 thf(fact_7303_scaleR__cancel__right,axiom,
% 3.82/4.10 ! [A: real,X: complex,B2: real] :
% 3.82/4.10 ( ( ( real_V2046097035970521341omplex @ A @ X )
% 3.82/4.10 = ( real_V2046097035970521341omplex @ B2 @ X ) )
% 3.82/4.10 = ( ( A = B2 )
% 3.82/4.10 | ( X = zero_zero_complex ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % scaleR_cancel_right
% 3.82/4.10 thf(fact_7304_scaleR__zero__right,axiom,
% 3.82/4.10 ! [A: real] :
% 3.82/4.10 ( ( real_V1485227260804924795R_real @ A @ zero_zero_real )
% 3.82/4.10 = zero_zero_real ) ).
% 3.82/4.10
% 3.82/4.10 % scaleR_zero_right
% 3.82/4.10 thf(fact_7305_scaleR__zero__right,axiom,
% 3.82/4.10 ! [A: real] :
% 3.82/4.10 ( ( real_V2046097035970521341omplex @ A @ zero_zero_complex )
% 3.82/4.10 = zero_zero_complex ) ).
% 3.82/4.10
% 3.82/4.10 % scaleR_zero_right
% 3.82/4.10 thf(fact_7306_scaleR__eq__0__iff,axiom,
% 3.82/4.10 ! [A: real,X: real] :
% 3.82/4.10 ( ( ( real_V1485227260804924795R_real @ A @ X )
% 3.82/4.10 = zero_zero_real )
% 3.82/4.10 = ( ( A = zero_zero_real )
% 3.82/4.10 | ( X = zero_zero_real ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % scaleR_eq_0_iff
% 3.82/4.10 thf(fact_7307_scaleR__eq__0__iff,axiom,
% 3.82/4.10 ! [A: real,X: complex] :
% 3.82/4.10 ( ( ( real_V2046097035970521341omplex @ A @ X )
% 3.82/4.10 = zero_zero_complex )
% 3.82/4.10 = ( ( A = zero_zero_real )
% 3.82/4.10 | ( X = zero_zero_complex ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % scaleR_eq_0_iff
% 3.82/4.10 thf(fact_7308_scaleR__zero__left,axiom,
% 3.82/4.10 ! [X: real] :
% 3.82/4.10 ( ( real_V1485227260804924795R_real @ zero_zero_real @ X )
% 3.82/4.10 = zero_zero_real ) ).
% 3.82/4.10
% 3.82/4.10 % scaleR_zero_left
% 3.82/4.10 thf(fact_7309_scaleR__zero__left,axiom,
% 3.82/4.10 ! [X: complex] :
% 3.82/4.10 ( ( real_V2046097035970521341omplex @ zero_zero_real @ X )
% 3.82/4.10 = zero_zero_complex ) ).
% 3.82/4.10
% 3.82/4.10 % scaleR_zero_left
% 3.82/4.10 thf(fact_7310_scaleR__eq__iff,axiom,
% 3.82/4.10 ! [B2: real,U: real,A: real] :
% 3.82/4.10 ( ( ( plus_plus_real @ B2 @ ( real_V1485227260804924795R_real @ U @ A ) )
% 3.82/4.10 = ( plus_plus_real @ A @ ( real_V1485227260804924795R_real @ U @ B2 ) ) )
% 3.82/4.10 = ( ( A = B2 )
% 3.82/4.10 | ( U = one_one_real ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % scaleR_eq_iff
% 3.82/4.10 thf(fact_7311_sin__coeff__0,axiom,
% 3.82/4.10 ( ( sin_coeff @ zero_zero_nat )
% 3.82/4.10 = zero_zero_real ) ).
% 3.82/4.10
% 3.82/4.10 % sin_coeff_0
% 3.82/4.10 thf(fact_7312_scaleR__collapse,axiom,
% 3.82/4.10 ! [U: real,A: real] :
% 3.82/4.10 ( ( plus_plus_real @ ( real_V1485227260804924795R_real @ ( minus_minus_real @ one_one_real @ U ) @ A ) @ ( real_V1485227260804924795R_real @ U @ A ) )
% 3.82/4.10 = A ) ).
% 3.82/4.10
% 3.82/4.10 % scaleR_collapse
% 3.82/4.10 thf(fact_7313_scaleR__half__double,axiom,
% 3.82/4.10 ! [A: real] :
% 3.82/4.10 ( ( real_V1485227260804924795R_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( plus_plus_real @ A @ A ) )
% 3.82/4.10 = A ) ).
% 3.82/4.10
% 3.82/4.10 % scaleR_half_double
% 3.82/4.10 thf(fact_7314_scaleR__right__imp__eq,axiom,
% 3.82/4.10 ! [X: real,A: real,B2: real] :
% 3.82/4.10 ( ( X != zero_zero_real )
% 3.82/4.10 => ( ( ( real_V1485227260804924795R_real @ A @ X )
% 3.82/4.10 = ( real_V1485227260804924795R_real @ B2 @ X ) )
% 3.82/4.10 => ( A = B2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % scaleR_right_imp_eq
% 3.82/4.10 thf(fact_7315_scaleR__right__imp__eq,axiom,
% 3.82/4.10 ! [X: complex,A: real,B2: real] :
% 3.82/4.10 ( ( X != zero_zero_complex )
% 3.82/4.10 => ( ( ( real_V2046097035970521341omplex @ A @ X )
% 3.82/4.10 = ( real_V2046097035970521341omplex @ B2 @ X ) )
% 3.82/4.10 => ( A = B2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % scaleR_right_imp_eq
% 3.82/4.10 thf(fact_7316_scaleR__right__distrib,axiom,
% 3.82/4.10 ! [A: real,X: real,Y: real] :
% 3.82/4.10 ( ( real_V1485227260804924795R_real @ A @ ( plus_plus_real @ X @ Y ) )
% 3.82/4.10 = ( plus_plus_real @ ( real_V1485227260804924795R_real @ A @ X ) @ ( real_V1485227260804924795R_real @ A @ Y ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % scaleR_right_distrib
% 3.82/4.10 thf(fact_7317_scaleR__left_Oadd,axiom,
% 3.82/4.10 ! [X: real,Y: real,Xa2: real] :
% 3.82/4.10 ( ( real_V1485227260804924795R_real @ ( plus_plus_real @ X @ Y ) @ Xa2 )
% 3.82/4.10 = ( plus_plus_real @ ( real_V1485227260804924795R_real @ X @ Xa2 ) @ ( real_V1485227260804924795R_real @ Y @ Xa2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % scaleR_left.add
% 3.82/4.10 thf(fact_7318_scaleR__left__distrib,axiom,
% 3.82/4.10 ! [A: real,B2: real,X: real] :
% 3.82/4.10 ( ( real_V1485227260804924795R_real @ ( plus_plus_real @ A @ B2 ) @ X )
% 3.82/4.10 = ( plus_plus_real @ ( real_V1485227260804924795R_real @ A @ X ) @ ( real_V1485227260804924795R_real @ B2 @ X ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % scaleR_left_distrib
% 3.82/4.10 thf(fact_7319_scaleR__right__mono__neg,axiom,
% 3.82/4.10 ! [B2: real,A: real,C: real] :
% 3.82/4.10 ( ( ord_less_eq_real @ B2 @ A )
% 3.82/4.10 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 3.82/4.10 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ C ) @ ( real_V1485227260804924795R_real @ B2 @ C ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % scaleR_right_mono_neg
% 3.82/4.10 thf(fact_7320_scaleR__right__mono,axiom,
% 3.82/4.10 ! [A: real,B2: real,X: real] :
% 3.82/4.10 ( ( ord_less_eq_real @ A @ B2 )
% 3.82/4.10 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 3.82/4.10 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X ) @ ( real_V1485227260804924795R_real @ B2 @ X ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % scaleR_right_mono
% 3.82/4.10 thf(fact_7321_scaleR__le__cancel__left,axiom,
% 3.82/4.10 ! [C: real,A: real,B2: real] :
% 3.82/4.10 ( ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ C @ A ) @ ( real_V1485227260804924795R_real @ C @ B2 ) )
% 3.82/4.10 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.10 => ( ord_less_eq_real @ A @ B2 ) )
% 3.82/4.10 & ( ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.10 => ( ord_less_eq_real @ B2 @ A ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % scaleR_le_cancel_left
% 3.82/4.10 thf(fact_7322_scaleR__le__cancel__left__neg,axiom,
% 3.82/4.10 ! [C: real,A: real,B2: real] :
% 3.82/4.10 ( ( ord_less_real @ C @ zero_zero_real )
% 3.82/4.10 => ( ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ C @ A ) @ ( real_V1485227260804924795R_real @ C @ B2 ) )
% 3.82/4.10 = ( ord_less_eq_real @ B2 @ A ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % scaleR_le_cancel_left_neg
% 3.82/4.10 thf(fact_7323_scaleR__le__cancel__left__pos,axiom,
% 3.82/4.10 ! [C: real,A: real,B2: real] :
% 3.82/4.10 ( ( ord_less_real @ zero_zero_real @ C )
% 3.82/4.10 => ( ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ C @ A ) @ ( real_V1485227260804924795R_real @ C @ B2 ) )
% 3.82/4.10 = ( ord_less_eq_real @ A @ B2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % scaleR_le_cancel_left_pos
% 3.82/4.10 thf(fact_7324_scaleR__left__mono,axiom,
% 3.82/4.10 ! [X: real,Y: real,A: real] :
% 3.82/4.10 ( ( ord_less_eq_real @ X @ Y )
% 3.82/4.10 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 3.82/4.10 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X ) @ ( real_V1485227260804924795R_real @ A @ Y ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % scaleR_left_mono
% 3.82/4.10 thf(fact_7325_scaleR__left__mono__neg,axiom,
% 3.82/4.10 ! [B2: real,A: real,C: real] :
% 3.82/4.10 ( ( ord_less_eq_real @ B2 @ A )
% 3.82/4.10 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 3.82/4.10 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ C @ A ) @ ( real_V1485227260804924795R_real @ C @ B2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % scaleR_left_mono_neg
% 3.82/4.10 thf(fact_7326_eq__vector__fraction__iff,axiom,
% 3.82/4.10 ! [X: real,U: real,V: real,A: real] :
% 3.82/4.10 ( ( X
% 3.82/4.10 = ( real_V1485227260804924795R_real @ ( divide_divide_real @ U @ V ) @ A ) )
% 3.82/4.10 = ( ( ( V = zero_zero_real )
% 3.82/4.10 => ( X = zero_zero_real ) )
% 3.82/4.10 & ( ( V != zero_zero_real )
% 3.82/4.10 => ( ( real_V1485227260804924795R_real @ V @ X )
% 3.82/4.10 = ( real_V1485227260804924795R_real @ U @ A ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % eq_vector_fraction_iff
% 3.82/4.10 thf(fact_7327_eq__vector__fraction__iff,axiom,
% 3.82/4.10 ! [X: complex,U: real,V: real,A: complex] :
% 3.82/4.10 ( ( X
% 3.82/4.10 = ( real_V2046097035970521341omplex @ ( divide_divide_real @ U @ V ) @ A ) )
% 3.82/4.10 = ( ( ( V = zero_zero_real )
% 3.82/4.10 => ( X = zero_zero_complex ) )
% 3.82/4.10 & ( ( V != zero_zero_real )
% 3.82/4.10 => ( ( real_V2046097035970521341omplex @ V @ X )
% 3.82/4.10 = ( real_V2046097035970521341omplex @ U @ A ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % eq_vector_fraction_iff
% 3.82/4.10 thf(fact_7328_vector__fraction__eq__iff,axiom,
% 3.82/4.10 ! [U: real,V: real,A: real,X: real] :
% 3.82/4.10 ( ( ( real_V1485227260804924795R_real @ ( divide_divide_real @ U @ V ) @ A )
% 3.82/4.10 = X )
% 3.82/4.10 = ( ( ( V = zero_zero_real )
% 3.82/4.10 => ( X = zero_zero_real ) )
% 3.82/4.10 & ( ( V != zero_zero_real )
% 3.82/4.10 => ( ( real_V1485227260804924795R_real @ U @ A )
% 3.82/4.10 = ( real_V1485227260804924795R_real @ V @ X ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % vector_fraction_eq_iff
% 3.82/4.10 thf(fact_7329_vector__fraction__eq__iff,axiom,
% 3.82/4.10 ! [U: real,V: real,A: complex,X: complex] :
% 3.82/4.10 ( ( ( real_V2046097035970521341omplex @ ( divide_divide_real @ U @ V ) @ A )
% 3.82/4.10 = X )
% 3.82/4.10 = ( ( ( V = zero_zero_real )
% 3.82/4.10 => ( X = zero_zero_complex ) )
% 3.82/4.10 & ( ( V != zero_zero_real )
% 3.82/4.10 => ( ( real_V2046097035970521341omplex @ U @ A )
% 3.82/4.10 = ( real_V2046097035970521341omplex @ V @ X ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % vector_fraction_eq_iff
% 3.82/4.10 thf(fact_7330_Real__Vector__Spaces_Ole__add__iff2,axiom,
% 3.82/4.10 ! [A: real,E2: real,C: real,B2: real,D: real] :
% 3.82/4.10 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ B2 @ E2 ) @ D ) )
% 3.82/4.10 = ( ord_less_eq_real @ C @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ ( minus_minus_real @ B2 @ A ) @ E2 ) @ D ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % Real_Vector_Spaces.le_add_iff2
% 3.82/4.10 thf(fact_7331_Real__Vector__Spaces_Ole__add__iff1,axiom,
% 3.82/4.10 ! [A: real,E2: real,C: real,B2: real,D: real] :
% 3.82/4.10 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ B2 @ E2 ) @ D ) )
% 3.82/4.10 = ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ ( minus_minus_real @ A @ B2 ) @ E2 ) @ C ) @ D ) ) ).
% 3.82/4.10
% 3.82/4.10 % Real_Vector_Spaces.le_add_iff1
% 3.82/4.10 thf(fact_7332_zero__le__scaleR__iff,axiom,
% 3.82/4.10 ! [A: real,B2: real] :
% 3.82/4.10 ( ( ord_less_eq_real @ zero_zero_real @ ( real_V1485227260804924795R_real @ A @ B2 ) )
% 3.82/4.10 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 3.82/4.10 & ( ord_less_eq_real @ zero_zero_real @ B2 ) )
% 3.82/4.10 | ( ( ord_less_real @ A @ zero_zero_real )
% 3.82/4.10 & ( ord_less_eq_real @ B2 @ zero_zero_real ) )
% 3.82/4.10 | ( A = zero_zero_real ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % zero_le_scaleR_iff
% 3.82/4.10 thf(fact_7333_scaleR__le__0__iff,axiom,
% 3.82/4.10 ! [A: real,B2: real] :
% 3.82/4.10 ( ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ B2 ) @ zero_zero_real )
% 3.82/4.10 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 3.82/4.10 & ( ord_less_eq_real @ B2 @ zero_zero_real ) )
% 3.82/4.10 | ( ( ord_less_real @ A @ zero_zero_real )
% 3.82/4.10 & ( ord_less_eq_real @ zero_zero_real @ B2 ) )
% 3.82/4.10 | ( A = zero_zero_real ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % scaleR_le_0_iff
% 3.82/4.10 thf(fact_7334_scaleR__nonpos__nonpos,axiom,
% 3.82/4.10 ! [A: real,B2: real] :
% 3.82/4.10 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 3.82/4.10 => ( ( ord_less_eq_real @ B2 @ zero_zero_real )
% 3.82/4.10 => ( ord_less_eq_real @ zero_zero_real @ ( real_V1485227260804924795R_real @ A @ B2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % scaleR_nonpos_nonpos
% 3.82/4.10 thf(fact_7335_scaleR__nonpos__nonneg,axiom,
% 3.82/4.10 ! [A: real,X: real] :
% 3.82/4.10 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 3.82/4.10 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 3.82/4.10 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X ) @ zero_zero_real ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % scaleR_nonpos_nonneg
% 3.82/4.10 thf(fact_7336_scaleR__nonneg__nonpos,axiom,
% 3.82/4.10 ! [A: real,X: real] :
% 3.82/4.10 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 3.82/4.10 => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 3.82/4.10 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X ) @ zero_zero_real ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % scaleR_nonneg_nonpos
% 3.82/4.10 thf(fact_7337_scaleR__nonneg__nonneg,axiom,
% 3.82/4.10 ! [A: real,X: real] :
% 3.82/4.10 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 3.82/4.10 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 3.82/4.10 => ( ord_less_eq_real @ zero_zero_real @ ( real_V1485227260804924795R_real @ A @ X ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % scaleR_nonneg_nonneg
% 3.82/4.10 thf(fact_7338_split__scaleR__pos__le,axiom,
% 3.82/4.10 ! [A: real,B2: real] :
% 3.82/4.10 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 3.82/4.10 & ( ord_less_eq_real @ zero_zero_real @ B2 ) )
% 3.82/4.10 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 3.82/4.10 & ( ord_less_eq_real @ B2 @ zero_zero_real ) ) )
% 3.82/4.10 => ( ord_less_eq_real @ zero_zero_real @ ( real_V1485227260804924795R_real @ A @ B2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % split_scaleR_pos_le
% 3.82/4.10 thf(fact_7339_split__scaleR__neg__le,axiom,
% 3.82/4.10 ! [A: real,X: real] :
% 3.82/4.10 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 3.82/4.10 & ( ord_less_eq_real @ X @ zero_zero_real ) )
% 3.82/4.10 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 3.82/4.10 & ( ord_less_eq_real @ zero_zero_real @ X ) ) )
% 3.82/4.10 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X ) @ zero_zero_real ) ) ).
% 3.82/4.10
% 3.82/4.10 % split_scaleR_neg_le
% 3.82/4.10 thf(fact_7340_scaleR__mono_H,axiom,
% 3.82/4.10 ! [A: real,B2: real,C: real,D: real] :
% 3.82/4.10 ( ( ord_less_eq_real @ A @ B2 )
% 3.82/4.10 => ( ( ord_less_eq_real @ C @ D )
% 3.82/4.10 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 3.82/4.10 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 3.82/4.10 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ C ) @ ( real_V1485227260804924795R_real @ B2 @ D ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % scaleR_mono'
% 3.82/4.10 thf(fact_7341_scaleR__mono,axiom,
% 3.82/4.10 ! [A: real,B2: real,X: real,Y: real] :
% 3.82/4.10 ( ( ord_less_eq_real @ A @ B2 )
% 3.82/4.10 => ( ( ord_less_eq_real @ X @ Y )
% 3.82/4.10 => ( ( ord_less_eq_real @ zero_zero_real @ B2 )
% 3.82/4.10 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 3.82/4.10 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X ) @ ( real_V1485227260804924795R_real @ B2 @ Y ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % scaleR_mono
% 3.82/4.10 thf(fact_7342_scaleR__left__le__one__le,axiom,
% 3.82/4.10 ! [X: real,A: real] :
% 3.82/4.10 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 3.82/4.10 => ( ( ord_less_eq_real @ A @ one_one_real )
% 3.82/4.10 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X ) @ X ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % scaleR_left_le_one_le
% 3.82/4.10 thf(fact_7343_scaleR__2,axiom,
% 3.82/4.10 ! [X: real] :
% 3.82/4.10 ( ( real_V1485227260804924795R_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X )
% 3.82/4.10 = ( plus_plus_real @ X @ X ) ) ).
% 3.82/4.10
% 3.82/4.10 % scaleR_2
% 3.82/4.10 thf(fact_7344_sin__coeff__Suc,axiom,
% 3.82/4.10 ! [N2: nat] :
% 3.82/4.10 ( ( sin_coeff @ ( suc @ N2 ) )
% 3.82/4.10 = ( divide_divide_real @ ( cos_coeff @ N2 ) @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % sin_coeff_Suc
% 3.82/4.10 thf(fact_7345_cos__coeff__Suc,axiom,
% 3.82/4.10 ! [N2: nat] :
% 3.82/4.10 ( ( cos_coeff @ ( suc @ N2 ) )
% 3.82/4.10 = ( divide_divide_real @ ( uminus_uminus_real @ ( sin_coeff @ N2 ) ) @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % cos_coeff_Suc
% 3.82/4.10 thf(fact_7346_summable__arctan__series,axiom,
% 3.82/4.10 ! [X: real] :
% 3.82/4.10 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 3.82/4.10 => ( summable_real
% 3.82/4.10 @ ^ [K2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % summable_arctan_series
% 3.82/4.10 thf(fact_7347_diffs__equiv,axiom,
% 3.82/4.10 ! [C: nat > complex,X: complex] :
% 3.82/4.10 ( ( summable_complex
% 3.82/4.10 @ ^ [N: nat] : ( times_times_complex @ ( diffs_complex @ C @ N ) @ ( power_power_complex @ X @ N ) ) )
% 3.82/4.10 => ( sums_complex
% 3.82/4.10 @ ^ [N: nat] : ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( C @ N ) ) @ ( power_power_complex @ X @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) )
% 3.82/4.10 @ ( suminf_complex
% 3.82/4.10 @ ^ [N: nat] : ( times_times_complex @ ( diffs_complex @ C @ N ) @ ( power_power_complex @ X @ N ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % diffs_equiv
% 3.82/4.10 thf(fact_7348_diffs__equiv,axiom,
% 3.82/4.10 ! [C: nat > real,X: real] :
% 3.82/4.10 ( ( summable_real
% 3.82/4.10 @ ^ [N: nat] : ( times_times_real @ ( diffs_real @ C @ N ) @ ( power_power_real @ X @ N ) ) )
% 3.82/4.10 => ( sums_real
% 3.82/4.10 @ ^ [N: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( C @ N ) ) @ ( power_power_real @ X @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) )
% 3.82/4.10 @ ( suminf_real
% 3.82/4.10 @ ^ [N: nat] : ( times_times_real @ ( diffs_real @ C @ N ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % diffs_equiv
% 3.82/4.10 thf(fact_7349_tan__double,axiom,
% 3.82/4.10 ! [X: complex] :
% 3.82/4.10 ( ( ( cos_complex @ X )
% 3.82/4.10 != zero_zero_complex )
% 3.82/4.10 => ( ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) )
% 3.82/4.10 != zero_zero_complex )
% 3.82/4.10 => ( ( tan_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) )
% 3.82/4.10 = ( divide1717551699836669952omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( tan_complex @ X ) ) @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( tan_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % tan_double
% 3.82/4.10 thf(fact_7350_tan__double,axiom,
% 3.82/4.10 ! [X: real] :
% 3.82/4.10 ( ( ( cos_real @ X )
% 3.82/4.10 != zero_zero_real )
% 3.82/4.10 => ( ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 3.82/4.10 != zero_zero_real )
% 3.82/4.10 => ( ( tan_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 3.82/4.10 = ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( tan_real @ X ) ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % tan_double
% 3.82/4.10 thf(fact_7351_tan__half,axiom,
% 3.82/4.10 ( tan_complex
% 3.82/4.10 = ( ^ [X4: complex] : ( divide1717551699836669952omplex @ ( sin_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X4 ) ) @ ( plus_plus_complex @ ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X4 ) ) @ one_one_complex ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % tan_half
% 3.82/4.10 thf(fact_7352_tan__half,axiom,
% 3.82/4.10 ( tan_real
% 3.82/4.10 = ( ^ [X4: real] : ( divide_divide_real @ ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) ) @ ( plus_plus_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) ) @ one_one_real ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % tan_half
% 3.82/4.10 thf(fact_7353_int__ge__less__than2__def,axiom,
% 3.82/4.10 ( int_ge_less_than2
% 3.82/4.10 = ( ^ [D4: int] :
% 3.82/4.10 ( collec213857154873943460nt_int
% 3.82/4.10 @ ( produc4947309494688390418_int_o
% 3.82/4.10 @ ^ [Z7: int,Z6: int] :
% 3.82/4.10 ( ( ord_less_eq_int @ D4 @ Z6 )
% 3.82/4.10 & ( ord_less_int @ Z7 @ Z6 ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % int_ge_less_than2_def
% 3.82/4.10 thf(fact_7354_abs__idempotent,axiom,
% 3.82/4.10 ! [A: real] :
% 3.82/4.10 ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 3.82/4.10 = ( abs_abs_real @ A ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_idempotent
% 3.82/4.10 thf(fact_7355_abs__idempotent,axiom,
% 3.82/4.10 ! [A: int] :
% 3.82/4.10 ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 3.82/4.10 = ( abs_abs_int @ A ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_idempotent
% 3.82/4.10 thf(fact_7356_abs__abs,axiom,
% 3.82/4.10 ! [A: real] :
% 3.82/4.10 ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 3.82/4.10 = ( abs_abs_real @ A ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_abs
% 3.82/4.10 thf(fact_7357_abs__abs,axiom,
% 3.82/4.10 ! [A: int] :
% 3.82/4.10 ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 3.82/4.10 = ( abs_abs_int @ A ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_abs
% 3.82/4.10 thf(fact_7358_abs__0,axiom,
% 3.82/4.10 ( ( abs_abs_real @ zero_zero_real )
% 3.82/4.10 = zero_zero_real ) ).
% 3.82/4.10
% 3.82/4.10 % abs_0
% 3.82/4.10 thf(fact_7359_abs__0,axiom,
% 3.82/4.10 ( ( abs_abs_int @ zero_zero_int )
% 3.82/4.10 = zero_zero_int ) ).
% 3.82/4.10
% 3.82/4.10 % abs_0
% 3.82/4.10 thf(fact_7360_abs__0,axiom,
% 3.82/4.10 ( ( abs_abs_complex @ zero_zero_complex )
% 3.82/4.10 = zero_zero_complex ) ).
% 3.82/4.10
% 3.82/4.10 % abs_0
% 3.82/4.10 thf(fact_7361_abs__zero,axiom,
% 3.82/4.10 ( ( abs_abs_real @ zero_zero_real )
% 3.82/4.10 = zero_zero_real ) ).
% 3.82/4.10
% 3.82/4.10 % abs_zero
% 3.82/4.10 thf(fact_7362_abs__zero,axiom,
% 3.82/4.10 ( ( abs_abs_int @ zero_zero_int )
% 3.82/4.10 = zero_zero_int ) ).
% 3.82/4.10
% 3.82/4.10 % abs_zero
% 3.82/4.10 thf(fact_7363_abs__eq__0,axiom,
% 3.82/4.10 ! [A: real] :
% 3.82/4.10 ( ( ( abs_abs_real @ A )
% 3.82/4.10 = zero_zero_real )
% 3.82/4.10 = ( A = zero_zero_real ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_eq_0
% 3.82/4.10 thf(fact_7364_abs__eq__0,axiom,
% 3.82/4.10 ! [A: int] :
% 3.82/4.10 ( ( ( abs_abs_int @ A )
% 3.82/4.10 = zero_zero_int )
% 3.82/4.10 = ( A = zero_zero_int ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_eq_0
% 3.82/4.10 thf(fact_7365_abs__0__eq,axiom,
% 3.82/4.10 ! [A: real] :
% 3.82/4.10 ( ( zero_zero_real
% 3.82/4.10 = ( abs_abs_real @ A ) )
% 3.82/4.10 = ( A = zero_zero_real ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_0_eq
% 3.82/4.10 thf(fact_7366_abs__0__eq,axiom,
% 3.82/4.10 ! [A: int] :
% 3.82/4.10 ( ( zero_zero_int
% 3.82/4.10 = ( abs_abs_int @ A ) )
% 3.82/4.10 = ( A = zero_zero_int ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_0_eq
% 3.82/4.10 thf(fact_7367_abs__mult__self__eq,axiom,
% 3.82/4.10 ! [A: int] :
% 3.82/4.10 ( ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ A ) )
% 3.82/4.10 = ( times_times_int @ A @ A ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_mult_self_eq
% 3.82/4.10 thf(fact_7368_abs__mult__self__eq,axiom,
% 3.82/4.10 ! [A: real] :
% 3.82/4.10 ( ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ A ) )
% 3.82/4.10 = ( times_times_real @ A @ A ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_mult_self_eq
% 3.82/4.10 thf(fact_7369_abs__1,axiom,
% 3.82/4.10 ( ( abs_abs_int @ one_one_int )
% 3.82/4.10 = one_one_int ) ).
% 3.82/4.10
% 3.82/4.10 % abs_1
% 3.82/4.10 thf(fact_7370_abs__1,axiom,
% 3.82/4.10 ( ( abs_abs_complex @ one_one_complex )
% 3.82/4.10 = one_one_complex ) ).
% 3.82/4.10
% 3.82/4.10 % abs_1
% 3.82/4.10 thf(fact_7371_abs__1,axiom,
% 3.82/4.10 ( ( abs_abs_real @ one_one_real )
% 3.82/4.10 = one_one_real ) ).
% 3.82/4.10
% 3.82/4.10 % abs_1
% 3.82/4.10 thf(fact_7372_abs__add__abs,axiom,
% 3.82/4.10 ! [A: int,B2: int] :
% 3.82/4.10 ( ( abs_abs_int @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B2 ) ) )
% 3.82/4.10 = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_add_abs
% 3.82/4.10 thf(fact_7373_abs__add__abs,axiom,
% 3.82/4.10 ! [A: real,B2: real] :
% 3.82/4.10 ( ( abs_abs_real @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B2 ) ) )
% 3.82/4.10 = ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_add_abs
% 3.82/4.10 thf(fact_7374_abs__divide,axiom,
% 3.82/4.10 ! [A: real,B2: real] :
% 3.82/4.10 ( ( abs_abs_real @ ( divide_divide_real @ A @ B2 ) )
% 3.82/4.10 = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_divide
% 3.82/4.10 thf(fact_7375_abs__minus__cancel,axiom,
% 3.82/4.10 ! [A: int] :
% 3.82/4.10 ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 3.82/4.10 = ( abs_abs_int @ A ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_minus_cancel
% 3.82/4.10 thf(fact_7376_abs__minus__cancel,axiom,
% 3.82/4.10 ! [A: real] :
% 3.82/4.10 ( ( abs_abs_real @ ( uminus_uminus_real @ A ) )
% 3.82/4.10 = ( abs_abs_real @ A ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_minus_cancel
% 3.82/4.10 thf(fact_7377_abs__minus,axiom,
% 3.82/4.10 ! [A: int] :
% 3.82/4.10 ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 3.82/4.10 = ( abs_abs_int @ A ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_minus
% 3.82/4.10 thf(fact_7378_abs__minus,axiom,
% 3.82/4.10 ! [A: real] :
% 3.82/4.10 ( ( abs_abs_real @ ( uminus_uminus_real @ A ) )
% 3.82/4.10 = ( abs_abs_real @ A ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_minus
% 3.82/4.10 thf(fact_7379_abs__dvd__iff,axiom,
% 3.82/4.10 ! [M2: real,K: real] :
% 3.82/4.10 ( ( dvd_dvd_real @ ( abs_abs_real @ M2 ) @ K )
% 3.82/4.10 = ( dvd_dvd_real @ M2 @ K ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_dvd_iff
% 3.82/4.10 thf(fact_7380_abs__dvd__iff,axiom,
% 3.82/4.10 ! [M2: int,K: int] :
% 3.82/4.10 ( ( dvd_dvd_int @ ( abs_abs_int @ M2 ) @ K )
% 3.82/4.10 = ( dvd_dvd_int @ M2 @ K ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_dvd_iff
% 3.82/4.10 thf(fact_7381_dvd__abs__iff,axiom,
% 3.82/4.10 ! [M2: real,K: real] :
% 3.82/4.10 ( ( dvd_dvd_real @ M2 @ ( abs_abs_real @ K ) )
% 3.82/4.10 = ( dvd_dvd_real @ M2 @ K ) ) ).
% 3.82/4.10
% 3.82/4.10 % dvd_abs_iff
% 3.82/4.10 thf(fact_7382_dvd__abs__iff,axiom,
% 3.82/4.10 ! [M2: int,K: int] :
% 3.82/4.10 ( ( dvd_dvd_int @ M2 @ ( abs_abs_int @ K ) )
% 3.82/4.10 = ( dvd_dvd_int @ M2 @ K ) ) ).
% 3.82/4.10
% 3.82/4.10 % dvd_abs_iff
% 3.82/4.10 thf(fact_7383_abs__of__nat,axiom,
% 3.82/4.10 ! [N2: nat] :
% 3.82/4.10 ( ( abs_abs_real @ ( semiri5074537144036343181t_real @ N2 ) )
% 3.82/4.10 = ( semiri5074537144036343181t_real @ N2 ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_of_nat
% 3.82/4.10 thf(fact_7384_abs__of__nat,axiom,
% 3.82/4.10 ! [N2: nat] :
% 3.82/4.10 ( ( abs_abs_int @ ( semiri1314217659103216013at_int @ N2 ) )
% 3.82/4.10 = ( semiri1314217659103216013at_int @ N2 ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_of_nat
% 3.82/4.10 thf(fact_7385_of__int__abs,axiom,
% 3.82/4.10 ! [X: int] :
% 3.82/4.10 ( ( ring_1_of_int_int @ ( abs_abs_int @ X ) )
% 3.82/4.10 = ( abs_abs_int @ ( ring_1_of_int_int @ X ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % of_int_abs
% 3.82/4.10 thf(fact_7386_of__int__abs,axiom,
% 3.82/4.10 ! [X: int] :
% 3.82/4.10 ( ( ring_1_of_int_real @ ( abs_abs_int @ X ) )
% 3.82/4.10 = ( abs_abs_real @ ( ring_1_of_int_real @ X ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % of_int_abs
% 3.82/4.10 thf(fact_7387_tan__zero,axiom,
% 3.82/4.10 ( ( tan_real @ zero_zero_real )
% 3.82/4.10 = zero_zero_real ) ).
% 3.82/4.10
% 3.82/4.10 % tan_zero
% 3.82/4.10 thf(fact_7388_tan__zero,axiom,
% 3.82/4.10 ( ( tan_complex @ zero_zero_complex )
% 3.82/4.10 = zero_zero_complex ) ).
% 3.82/4.10
% 3.82/4.10 % tan_zero
% 3.82/4.10 thf(fact_7389_abs__bool__eq,axiom,
% 3.82/4.10 ! [P: $o] :
% 3.82/4.10 ( ( abs_abs_real @ ( zero_n3304061248610475627l_real @ P ) )
% 3.82/4.10 = ( zero_n3304061248610475627l_real @ P ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_bool_eq
% 3.82/4.10 thf(fact_7390_abs__bool__eq,axiom,
% 3.82/4.10 ! [P: $o] :
% 3.82/4.10 ( ( abs_abs_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 3.82/4.10 = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_bool_eq
% 3.82/4.10 thf(fact_7391_abs__of__nonneg,axiom,
% 3.82/4.10 ! [A: real] :
% 3.82/4.10 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 3.82/4.10 => ( ( abs_abs_real @ A )
% 3.82/4.10 = A ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_of_nonneg
% 3.82/4.10 thf(fact_7392_abs__of__nonneg,axiom,
% 3.82/4.10 ! [A: int] :
% 3.82/4.10 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 3.82/4.10 => ( ( abs_abs_int @ A )
% 3.82/4.10 = A ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_of_nonneg
% 3.82/4.10 thf(fact_7393_abs__le__self__iff,axiom,
% 3.82/4.10 ! [A: real] :
% 3.82/4.10 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ A )
% 3.82/4.10 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_le_self_iff
% 3.82/4.10 thf(fact_7394_abs__le__self__iff,axiom,
% 3.82/4.10 ! [A: int] :
% 3.82/4.10 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ A )
% 3.82/4.10 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_le_self_iff
% 3.82/4.10 thf(fact_7395_abs__le__zero__iff,axiom,
% 3.82/4.10 ! [A: real] :
% 3.82/4.10 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ zero_zero_real )
% 3.82/4.10 = ( A = zero_zero_real ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_le_zero_iff
% 3.82/4.10 thf(fact_7396_abs__le__zero__iff,axiom,
% 3.82/4.10 ! [A: int] :
% 3.82/4.10 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ zero_zero_int )
% 3.82/4.10 = ( A = zero_zero_int ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_le_zero_iff
% 3.82/4.10 thf(fact_7397_zero__less__abs__iff,axiom,
% 3.82/4.10 ! [A: real] :
% 3.82/4.10 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ A ) )
% 3.82/4.10 = ( A != zero_zero_real ) ) ).
% 3.82/4.10
% 3.82/4.10 % zero_less_abs_iff
% 3.82/4.10 thf(fact_7398_zero__less__abs__iff,axiom,
% 3.82/4.10 ! [A: int] :
% 3.82/4.10 ( ( ord_less_int @ zero_zero_int @ ( abs_abs_int @ A ) )
% 3.82/4.10 = ( A != zero_zero_int ) ) ).
% 3.82/4.10
% 3.82/4.10 % zero_less_abs_iff
% 3.82/4.10 thf(fact_7399_sum__abs,axiom,
% 3.82/4.10 ! [F: int > int,A2: set_int] :
% 3.82/4.10 ( ord_less_eq_int @ ( abs_abs_int @ ( groups4538972089207619220nt_int @ F @ A2 ) )
% 3.82/4.10 @ ( groups4538972089207619220nt_int
% 3.82/4.10 @ ^ [I3: int] : ( abs_abs_int @ ( F @ I3 ) )
% 3.82/4.10 @ A2 ) ) ).
% 3.82/4.10
% 3.82/4.10 % sum_abs
% 3.82/4.10 thf(fact_7400_sum__abs,axiom,
% 3.82/4.10 ! [F: nat > real,A2: set_nat] :
% 3.82/4.10 ( ord_less_eq_real @ ( abs_abs_real @ ( groups6591440286371151544t_real @ F @ A2 ) )
% 3.82/4.10 @ ( groups6591440286371151544t_real
% 3.82/4.10 @ ^ [I3: nat] : ( abs_abs_real @ ( F @ I3 ) )
% 3.82/4.10 @ A2 ) ) ).
% 3.82/4.10
% 3.82/4.10 % sum_abs
% 3.82/4.10 thf(fact_7401_divide__le__0__abs__iff,axiom,
% 3.82/4.10 ! [A: real,B2: real] :
% 3.82/4.10 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B2 ) ) @ zero_zero_real )
% 3.82/4.10 = ( ( ord_less_eq_real @ A @ zero_zero_real )
% 3.82/4.10 | ( B2 = zero_zero_real ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % divide_le_0_abs_iff
% 3.82/4.10 thf(fact_7402_zero__le__divide__abs__iff,axiom,
% 3.82/4.10 ! [A: real,B2: real] :
% 3.82/4.10 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B2 ) ) )
% 3.82/4.10 = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 3.82/4.10 | ( B2 = zero_zero_real ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % zero_le_divide_abs_iff
% 3.82/4.10 thf(fact_7403_abs__of__nonpos,axiom,
% 3.82/4.10 ! [A: real] :
% 3.82/4.10 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 3.82/4.10 => ( ( abs_abs_real @ A )
% 3.82/4.10 = ( uminus_uminus_real @ A ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_of_nonpos
% 3.82/4.10 thf(fact_7404_abs__of__nonpos,axiom,
% 3.82/4.10 ! [A: int] :
% 3.82/4.10 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 3.82/4.10 => ( ( abs_abs_int @ A )
% 3.82/4.10 = ( uminus_uminus_int @ A ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_of_nonpos
% 3.82/4.10 thf(fact_7405_abs__sgn__eq__1,axiom,
% 3.82/4.10 ! [A: real] :
% 3.82/4.10 ( ( A != zero_zero_real )
% 3.82/4.10 => ( ( abs_abs_real @ ( sgn_sgn_real @ A ) )
% 3.82/4.10 = one_one_real ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_sgn_eq_1
% 3.82/4.10 thf(fact_7406_abs__sgn__eq__1,axiom,
% 3.82/4.10 ! [A: int] :
% 3.82/4.10 ( ( A != zero_zero_int )
% 3.82/4.10 => ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 3.82/4.10 = one_one_int ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_sgn_eq_1
% 3.82/4.10 thf(fact_7407_sgn__abs,axiom,
% 3.82/4.10 ! [A: real] :
% 3.82/4.10 ( ( abs_abs_real @ ( sgn_sgn_real @ A ) )
% 3.82/4.10 = ( zero_n3304061248610475627l_real @ ( A != zero_zero_real ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % sgn_abs
% 3.82/4.10 thf(fact_7408_sgn__abs,axiom,
% 3.82/4.10 ! [A: complex] :
% 3.82/4.10 ( ( abs_abs_complex @ ( sgn_sgn_complex @ A ) )
% 3.82/4.10 = ( zero_n1201886186963655149omplex @ ( A != zero_zero_complex ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % sgn_abs
% 3.82/4.10 thf(fact_7409_sgn__abs,axiom,
% 3.82/4.10 ! [A: int] :
% 3.82/4.10 ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 3.82/4.10 = ( zero_n2684676970156552555ol_int @ ( A != zero_zero_int ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % sgn_abs
% 3.82/4.10 thf(fact_7410_idom__abs__sgn__class_Oabs__sgn,axiom,
% 3.82/4.10 ! [A: real] :
% 3.82/4.10 ( ( sgn_sgn_real @ ( abs_abs_real @ A ) )
% 3.82/4.10 = ( zero_n3304061248610475627l_real @ ( A != zero_zero_real ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % idom_abs_sgn_class.abs_sgn
% 3.82/4.10 thf(fact_7411_idom__abs__sgn__class_Oabs__sgn,axiom,
% 3.82/4.10 ! [A: complex] :
% 3.82/4.10 ( ( sgn_sgn_complex @ ( abs_abs_complex @ A ) )
% 3.82/4.10 = ( zero_n1201886186963655149omplex @ ( A != zero_zero_complex ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % idom_abs_sgn_class.abs_sgn
% 3.82/4.10 thf(fact_7412_idom__abs__sgn__class_Oabs__sgn,axiom,
% 3.82/4.10 ! [A: int] :
% 3.82/4.10 ( ( sgn_sgn_int @ ( abs_abs_int @ A ) )
% 3.82/4.10 = ( zero_n2684676970156552555ol_int @ ( A != zero_zero_int ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % idom_abs_sgn_class.abs_sgn
% 3.82/4.10 thf(fact_7413_sum__abs__ge__zero,axiom,
% 3.82/4.10 ! [F: int > int,A2: set_int] :
% 3.82/4.10 ( ord_less_eq_int @ zero_zero_int
% 3.82/4.10 @ ( groups4538972089207619220nt_int
% 3.82/4.10 @ ^ [I3: int] : ( abs_abs_int @ ( F @ I3 ) )
% 3.82/4.10 @ A2 ) ) ).
% 3.82/4.10
% 3.82/4.10 % sum_abs_ge_zero
% 3.82/4.10 thf(fact_7414_sum__abs__ge__zero,axiom,
% 3.82/4.10 ! [F: nat > real,A2: set_nat] :
% 3.82/4.10 ( ord_less_eq_real @ zero_zero_real
% 3.82/4.10 @ ( groups6591440286371151544t_real
% 3.82/4.10 @ ^ [I3: nat] : ( abs_abs_real @ ( F @ I3 ) )
% 3.82/4.10 @ A2 ) ) ).
% 3.82/4.10
% 3.82/4.10 % sum_abs_ge_zero
% 3.82/4.10 thf(fact_7415_zero__less__power__abs__iff,axiom,
% 3.82/4.10 ! [A: real,N2: nat] :
% 3.82/4.10 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N2 ) )
% 3.82/4.10 = ( ( A != zero_zero_real )
% 3.82/4.10 | ( N2 = zero_zero_nat ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % zero_less_power_abs_iff
% 3.82/4.10 thf(fact_7416_zero__less__power__abs__iff,axiom,
% 3.82/4.10 ! [A: int,N2: nat] :
% 3.82/4.10 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N2 ) )
% 3.82/4.10 = ( ( A != zero_zero_int )
% 3.82/4.10 | ( N2 = zero_zero_nat ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % zero_less_power_abs_iff
% 3.82/4.10 thf(fact_7417_norm__of__real__add1,axiom,
% 3.82/4.10 ! [X: real] :
% 3.82/4.10 ( ( real_V7735802525324610683m_real @ ( plus_plus_real @ ( real_V1803761363581548252l_real @ X ) @ one_one_real ) )
% 3.82/4.10 = ( abs_abs_real @ ( plus_plus_real @ X @ one_one_real ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % norm_of_real_add1
% 3.82/4.10 thf(fact_7418_norm__of__real__add1,axiom,
% 3.82/4.10 ! [X: real] :
% 3.82/4.10 ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ X ) @ one_one_complex ) )
% 3.82/4.10 = ( abs_abs_real @ ( plus_plus_real @ X @ one_one_real ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % norm_of_real_add1
% 3.82/4.10 thf(fact_7419_norm__of__real__addn,axiom,
% 3.82/4.10 ! [X: real,B2: num] :
% 3.82/4.10 ( ( real_V7735802525324610683m_real @ ( plus_plus_real @ ( real_V1803761363581548252l_real @ X ) @ ( numeral_numeral_real @ B2 ) ) )
% 3.82/4.10 = ( abs_abs_real @ ( plus_plus_real @ X @ ( numeral_numeral_real @ B2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % norm_of_real_addn
% 3.82/4.10 thf(fact_7420_norm__of__real__addn,axiom,
% 3.82/4.10 ! [X: real,B2: num] :
% 3.82/4.10 ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ X ) @ ( numera6690914467698888265omplex @ B2 ) ) )
% 3.82/4.10 = ( abs_abs_real @ ( plus_plus_real @ X @ ( numeral_numeral_real @ B2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % norm_of_real_addn
% 3.82/4.10 thf(fact_7421_abs__minus__commute,axiom,
% 3.82/4.10 ! [A: int,B2: int] :
% 3.82/4.10 ( ( abs_abs_int @ ( minus_minus_int @ A @ B2 ) )
% 3.82/4.10 = ( abs_abs_int @ ( minus_minus_int @ B2 @ A ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_minus_commute
% 3.82/4.10 thf(fact_7422_abs__minus__commute,axiom,
% 3.82/4.10 ! [A: real,B2: real] :
% 3.82/4.10 ( ( abs_abs_real @ ( minus_minus_real @ A @ B2 ) )
% 3.82/4.10 = ( abs_abs_real @ ( minus_minus_real @ B2 @ A ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_minus_commute
% 3.82/4.10 thf(fact_7423_abs__eq__iff,axiom,
% 3.82/4.10 ! [X: int,Y: int] :
% 3.82/4.10 ( ( ( abs_abs_int @ X )
% 3.82/4.10 = ( abs_abs_int @ Y ) )
% 3.82/4.10 = ( ( X = Y )
% 3.82/4.10 | ( X
% 3.82/4.10 = ( uminus_uminus_int @ Y ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_eq_iff
% 3.82/4.10 thf(fact_7424_abs__eq__iff,axiom,
% 3.82/4.10 ! [X: real,Y: real] :
% 3.82/4.10 ( ( ( abs_abs_real @ X )
% 3.82/4.10 = ( abs_abs_real @ Y ) )
% 3.82/4.10 = ( ( X = Y )
% 3.82/4.10 | ( X
% 3.82/4.10 = ( uminus_uminus_real @ Y ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_eq_iff
% 3.82/4.10 thf(fact_7425_dvd__if__abs__eq,axiom,
% 3.82/4.10 ! [L: real,K: real] :
% 3.82/4.10 ( ( ( abs_abs_real @ L )
% 3.82/4.10 = ( abs_abs_real @ K ) )
% 3.82/4.10 => ( dvd_dvd_real @ L @ K ) ) ).
% 3.82/4.10
% 3.82/4.10 % dvd_if_abs_eq
% 3.82/4.10 thf(fact_7426_dvd__if__abs__eq,axiom,
% 3.82/4.10 ! [L: int,K: int] :
% 3.82/4.10 ( ( ( abs_abs_int @ L )
% 3.82/4.10 = ( abs_abs_int @ K ) )
% 3.82/4.10 => ( dvd_dvd_int @ L @ K ) ) ).
% 3.82/4.10
% 3.82/4.10 % dvd_if_abs_eq
% 3.82/4.10 thf(fact_7427_abs__one,axiom,
% 3.82/4.10 ( ( abs_abs_int @ one_one_int )
% 3.82/4.10 = one_one_int ) ).
% 3.82/4.10
% 3.82/4.10 % abs_one
% 3.82/4.10 thf(fact_7428_abs__one,axiom,
% 3.82/4.10 ( ( abs_abs_real @ one_one_real )
% 3.82/4.10 = one_one_real ) ).
% 3.82/4.10
% 3.82/4.10 % abs_one
% 3.82/4.10 thf(fact_7429_abs__mult,axiom,
% 3.82/4.10 ! [A: int,B2: int] :
% 3.82/4.10 ( ( abs_abs_int @ ( times_times_int @ A @ B2 ) )
% 3.82/4.10 = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_mult
% 3.82/4.10 thf(fact_7430_abs__mult,axiom,
% 3.82/4.10 ! [A: real,B2: real] :
% 3.82/4.10 ( ( abs_abs_real @ ( times_times_real @ A @ B2 ) )
% 3.82/4.10 = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_mult
% 3.82/4.10 thf(fact_7431_abs__mult,axiom,
% 3.82/4.10 ! [A: complex,B2: complex] :
% 3.82/4.10 ( ( abs_abs_complex @ ( times_times_complex @ A @ B2 ) )
% 3.82/4.10 = ( times_times_complex @ ( abs_abs_complex @ A ) @ ( abs_abs_complex @ B2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_mult
% 3.82/4.10 thf(fact_7432_abs__eq__0__iff,axiom,
% 3.82/4.10 ! [A: real] :
% 3.82/4.10 ( ( ( abs_abs_real @ A )
% 3.82/4.10 = zero_zero_real )
% 3.82/4.10 = ( A = zero_zero_real ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_eq_0_iff
% 3.82/4.10 thf(fact_7433_abs__eq__0__iff,axiom,
% 3.82/4.10 ! [A: int] :
% 3.82/4.10 ( ( ( abs_abs_int @ A )
% 3.82/4.10 = zero_zero_int )
% 3.82/4.10 = ( A = zero_zero_int ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_eq_0_iff
% 3.82/4.10 thf(fact_7434_abs__eq__0__iff,axiom,
% 3.82/4.10 ! [A: complex] :
% 3.82/4.10 ( ( ( abs_abs_complex @ A )
% 3.82/4.10 = zero_zero_complex )
% 3.82/4.10 = ( A = zero_zero_complex ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_eq_0_iff
% 3.82/4.10 thf(fact_7435_abs__le__D1,axiom,
% 3.82/4.10 ! [A: real,B2: real] :
% 3.82/4.10 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B2 )
% 3.82/4.10 => ( ord_less_eq_real @ A @ B2 ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_le_D1
% 3.82/4.10 thf(fact_7436_abs__le__D1,axiom,
% 3.82/4.10 ! [A: int,B2: int] :
% 3.82/4.10 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B2 )
% 3.82/4.10 => ( ord_less_eq_int @ A @ B2 ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_le_D1
% 3.82/4.10 thf(fact_7437_abs__ge__self,axiom,
% 3.82/4.10 ! [A: real] : ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_ge_self
% 3.82/4.10 thf(fact_7438_abs__ge__self,axiom,
% 3.82/4.10 ! [A: int] : ( ord_less_eq_int @ A @ ( abs_abs_int @ A ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_ge_self
% 3.82/4.10 thf(fact_7439_abs__ge__zero,axiom,
% 3.82/4.10 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( abs_abs_real @ A ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_ge_zero
% 3.82/4.10 thf(fact_7440_abs__ge__zero,axiom,
% 3.82/4.10 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( abs_abs_int @ A ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_ge_zero
% 3.82/4.10 thf(fact_7441_abs__of__pos,axiom,
% 3.82/4.10 ! [A: real] :
% 3.82/4.10 ( ( ord_less_real @ zero_zero_real @ A )
% 3.82/4.10 => ( ( abs_abs_real @ A )
% 3.82/4.10 = A ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_of_pos
% 3.82/4.10 thf(fact_7442_abs__of__pos,axiom,
% 3.82/4.10 ! [A: int] :
% 3.82/4.10 ( ( ord_less_int @ zero_zero_int @ A )
% 3.82/4.10 => ( ( abs_abs_int @ A )
% 3.82/4.10 = A ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_of_pos
% 3.82/4.10 thf(fact_7443_abs__not__less__zero,axiom,
% 3.82/4.10 ! [A: real] :
% 3.82/4.10 ~ ( ord_less_real @ ( abs_abs_real @ A ) @ zero_zero_real ) ).
% 3.82/4.10
% 3.82/4.10 % abs_not_less_zero
% 3.82/4.10 thf(fact_7444_abs__not__less__zero,axiom,
% 3.82/4.10 ! [A: int] :
% 3.82/4.10 ~ ( ord_less_int @ ( abs_abs_int @ A ) @ zero_zero_int ) ).
% 3.82/4.10
% 3.82/4.10 % abs_not_less_zero
% 3.82/4.10 thf(fact_7445_abs__triangle__ineq,axiom,
% 3.82/4.10 ! [A: real,B2: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( plus_plus_real @ A @ B2 ) ) @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_triangle_ineq
% 3.82/4.10 thf(fact_7446_abs__triangle__ineq,axiom,
% 3.82/4.10 ! [A: int,B2: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( plus_plus_int @ A @ B2 ) ) @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_triangle_ineq
% 3.82/4.10 thf(fact_7447_abs__mult__less,axiom,
% 3.82/4.10 ! [A: real,C: real,B2: real,D: real] :
% 3.82/4.10 ( ( ord_less_real @ ( abs_abs_real @ A ) @ C )
% 3.82/4.10 => ( ( ord_less_real @ ( abs_abs_real @ B2 ) @ D )
% 3.82/4.10 => ( ord_less_real @ ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B2 ) ) @ ( times_times_real @ C @ D ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_mult_less
% 3.82/4.10 thf(fact_7448_abs__mult__less,axiom,
% 3.82/4.10 ! [A: int,C: int,B2: int,D: int] :
% 3.82/4.10 ( ( ord_less_int @ ( abs_abs_int @ A ) @ C )
% 3.82/4.10 => ( ( ord_less_int @ ( abs_abs_int @ B2 ) @ D )
% 3.82/4.10 => ( ord_less_int @ ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B2 ) ) @ ( times_times_int @ C @ D ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_mult_less
% 3.82/4.10 thf(fact_7449_abs__triangle__ineq2__sym,axiom,
% 3.82/4.10 ! [A: real,B2: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B2 ) ) @ ( abs_abs_real @ ( minus_minus_real @ B2 @ A ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_triangle_ineq2_sym
% 3.82/4.10 thf(fact_7450_abs__triangle__ineq2__sym,axiom,
% 3.82/4.10 ! [A: int,B2: int] : ( ord_less_eq_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B2 ) ) @ ( abs_abs_int @ ( minus_minus_int @ B2 @ A ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_triangle_ineq2_sym
% 3.82/4.10 thf(fact_7451_abs__triangle__ineq3,axiom,
% 3.82/4.10 ! [A: real,B2: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B2 ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ A @ B2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_triangle_ineq3
% 3.82/4.10 thf(fact_7452_abs__triangle__ineq3,axiom,
% 3.82/4.10 ! [A: int,B2: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B2 ) ) ) @ ( abs_abs_int @ ( minus_minus_int @ A @ B2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_triangle_ineq3
% 3.82/4.10 thf(fact_7453_abs__triangle__ineq2,axiom,
% 3.82/4.10 ! [A: real,B2: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B2 ) ) @ ( abs_abs_real @ ( minus_minus_real @ A @ B2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_triangle_ineq2
% 3.82/4.10 thf(fact_7454_abs__triangle__ineq2,axiom,
% 3.82/4.10 ! [A: int,B2: int] : ( ord_less_eq_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B2 ) ) @ ( abs_abs_int @ ( minus_minus_int @ A @ B2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_triangle_ineq2
% 3.82/4.10 thf(fact_7455_nonzero__abs__divide,axiom,
% 3.82/4.10 ! [B2: real,A: real] :
% 3.82/4.10 ( ( B2 != zero_zero_real )
% 3.82/4.10 => ( ( abs_abs_real @ ( divide_divide_real @ A @ B2 ) )
% 3.82/4.10 = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % nonzero_abs_divide
% 3.82/4.10 thf(fact_7456_abs__ge__minus__self,axiom,
% 3.82/4.10 ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ ( abs_abs_real @ A ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_ge_minus_self
% 3.82/4.10 thf(fact_7457_abs__ge__minus__self,axiom,
% 3.82/4.10 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ ( abs_abs_int @ A ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_ge_minus_self
% 3.82/4.10 thf(fact_7458_abs__le__iff,axiom,
% 3.82/4.10 ! [A: real,B2: real] :
% 3.82/4.10 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B2 )
% 3.82/4.10 = ( ( ord_less_eq_real @ A @ B2 )
% 3.82/4.10 & ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_le_iff
% 3.82/4.10 thf(fact_7459_abs__le__iff,axiom,
% 3.82/4.10 ! [A: int,B2: int] :
% 3.82/4.10 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B2 )
% 3.82/4.10 = ( ( ord_less_eq_int @ A @ B2 )
% 3.82/4.10 & ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_le_iff
% 3.82/4.10 thf(fact_7460_abs__le__D2,axiom,
% 3.82/4.10 ! [A: real,B2: real] :
% 3.82/4.10 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B2 )
% 3.82/4.10 => ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B2 ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_le_D2
% 3.82/4.10 thf(fact_7461_abs__le__D2,axiom,
% 3.82/4.10 ! [A: int,B2: int] :
% 3.82/4.10 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B2 )
% 3.82/4.10 => ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B2 ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_le_D2
% 3.82/4.10 thf(fact_7462_abs__leI,axiom,
% 3.82/4.10 ! [A: real,B2: real] :
% 3.82/4.10 ( ( ord_less_eq_real @ A @ B2 )
% 3.82/4.10 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B2 )
% 3.82/4.10 => ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_leI
% 3.82/4.10 thf(fact_7463_abs__leI,axiom,
% 3.82/4.10 ! [A: int,B2: int] :
% 3.82/4.10 ( ( ord_less_eq_int @ A @ B2 )
% 3.82/4.10 => ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B2 )
% 3.82/4.10 => ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_leI
% 3.82/4.10 thf(fact_7464_abs__less__iff,axiom,
% 3.82/4.10 ! [A: int,B2: int] :
% 3.82/4.10 ( ( ord_less_int @ ( abs_abs_int @ A ) @ B2 )
% 3.82/4.10 = ( ( ord_less_int @ A @ B2 )
% 3.82/4.10 & ( ord_less_int @ ( uminus_uminus_int @ A ) @ B2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_less_iff
% 3.82/4.10 thf(fact_7465_abs__less__iff,axiom,
% 3.82/4.10 ! [A: real,B2: real] :
% 3.82/4.10 ( ( ord_less_real @ ( abs_abs_real @ A ) @ B2 )
% 3.82/4.10 = ( ( ord_less_real @ A @ B2 )
% 3.82/4.10 & ( ord_less_real @ ( uminus_uminus_real @ A ) @ B2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_less_iff
% 3.82/4.10 thf(fact_7466_linordered__idom__class_Oabs__sgn,axiom,
% 3.82/4.10 ( abs_abs_int
% 3.82/4.10 = ( ^ [K2: int] : ( times_times_int @ K2 @ ( sgn_sgn_int @ K2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % linordered_idom_class.abs_sgn
% 3.82/4.10 thf(fact_7467_linordered__idom__class_Oabs__sgn,axiom,
% 3.82/4.10 ( abs_abs_real
% 3.82/4.10 = ( ^ [K2: real] : ( times_times_real @ K2 @ ( sgn_sgn_real @ K2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % linordered_idom_class.abs_sgn
% 3.82/4.10 thf(fact_7468_abs__mult__sgn,axiom,
% 3.82/4.10 ! [A: int] :
% 3.82/4.10 ( ( times_times_int @ ( abs_abs_int @ A ) @ ( sgn_sgn_int @ A ) )
% 3.82/4.10 = A ) ).
% 3.82/4.10
% 3.82/4.10 % abs_mult_sgn
% 3.82/4.10 thf(fact_7469_abs__mult__sgn,axiom,
% 3.82/4.10 ! [A: real] :
% 3.82/4.10 ( ( times_times_real @ ( abs_abs_real @ A ) @ ( sgn_sgn_real @ A ) )
% 3.82/4.10 = A ) ).
% 3.82/4.10
% 3.82/4.10 % abs_mult_sgn
% 3.82/4.10 thf(fact_7470_abs__mult__sgn,axiom,
% 3.82/4.10 ! [A: complex] :
% 3.82/4.10 ( ( times_times_complex @ ( abs_abs_complex @ A ) @ ( sgn_sgn_complex @ A ) )
% 3.82/4.10 = A ) ).
% 3.82/4.10
% 3.82/4.10 % abs_mult_sgn
% 3.82/4.10 thf(fact_7471_sgn__mult__abs,axiom,
% 3.82/4.10 ! [A: int] :
% 3.82/4.10 ( ( times_times_int @ ( sgn_sgn_int @ A ) @ ( abs_abs_int @ A ) )
% 3.82/4.10 = A ) ).
% 3.82/4.10
% 3.82/4.10 % sgn_mult_abs
% 3.82/4.10 thf(fact_7472_sgn__mult__abs,axiom,
% 3.82/4.10 ! [A: real] :
% 3.82/4.10 ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( abs_abs_real @ A ) )
% 3.82/4.10 = A ) ).
% 3.82/4.10
% 3.82/4.10 % sgn_mult_abs
% 3.82/4.10 thf(fact_7473_sgn__mult__abs,axiom,
% 3.82/4.10 ! [A: complex] :
% 3.82/4.10 ( ( times_times_complex @ ( sgn_sgn_complex @ A ) @ ( abs_abs_complex @ A ) )
% 3.82/4.10 = A ) ).
% 3.82/4.10
% 3.82/4.10 % sgn_mult_abs
% 3.82/4.10 thf(fact_7474_mult__sgn__abs,axiom,
% 3.82/4.10 ! [X: int] :
% 3.82/4.10 ( ( times_times_int @ ( sgn_sgn_int @ X ) @ ( abs_abs_int @ X ) )
% 3.82/4.10 = X ) ).
% 3.82/4.10
% 3.82/4.10 % mult_sgn_abs
% 3.82/4.10 thf(fact_7475_mult__sgn__abs,axiom,
% 3.82/4.10 ! [X: real] :
% 3.82/4.10 ( ( times_times_real @ ( sgn_sgn_real @ X ) @ ( abs_abs_real @ X ) )
% 3.82/4.10 = X ) ).
% 3.82/4.10
% 3.82/4.10 % mult_sgn_abs
% 3.82/4.10 thf(fact_7476_same__sgn__abs__add,axiom,
% 3.82/4.10 ! [B2: int,A: int] :
% 3.82/4.10 ( ( ( sgn_sgn_int @ B2 )
% 3.82/4.10 = ( sgn_sgn_int @ A ) )
% 3.82/4.10 => ( ( abs_abs_int @ ( plus_plus_int @ A @ B2 ) )
% 3.82/4.10 = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % same_sgn_abs_add
% 3.82/4.10 thf(fact_7477_same__sgn__abs__add,axiom,
% 3.82/4.10 ! [B2: real,A: real] :
% 3.82/4.10 ( ( ( sgn_sgn_real @ B2 )
% 3.82/4.10 = ( sgn_sgn_real @ A ) )
% 3.82/4.10 => ( ( abs_abs_real @ ( plus_plus_real @ A @ B2 ) )
% 3.82/4.10 = ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % same_sgn_abs_add
% 3.82/4.10 thf(fact_7478_dense__eq0__I,axiom,
% 3.82/4.10 ! [X: real] :
% 3.82/4.10 ( ! [E: real] :
% 3.82/4.10 ( ( ord_less_real @ zero_zero_real @ E )
% 3.82/4.10 => ( ord_less_eq_real @ ( abs_abs_real @ X ) @ E ) )
% 3.82/4.10 => ( X = zero_zero_real ) ) ).
% 3.82/4.10
% 3.82/4.10 % dense_eq0_I
% 3.82/4.10 thf(fact_7479_abs__mult__pos,axiom,
% 3.82/4.10 ! [X: real,Y: real] :
% 3.82/4.10 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 3.82/4.10 => ( ( times_times_real @ ( abs_abs_real @ Y ) @ X )
% 3.82/4.10 = ( abs_abs_real @ ( times_times_real @ Y @ X ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_mult_pos
% 3.82/4.10 thf(fact_7480_abs__mult__pos,axiom,
% 3.82/4.10 ! [X: int,Y: int] :
% 3.82/4.10 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 3.82/4.10 => ( ( times_times_int @ ( abs_abs_int @ Y ) @ X )
% 3.82/4.10 = ( abs_abs_int @ ( times_times_int @ Y @ X ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_mult_pos
% 3.82/4.10 thf(fact_7481_abs__eq__mult,axiom,
% 3.82/4.10 ! [A: real,B2: real] :
% 3.82/4.10 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 3.82/4.10 | ( ord_less_eq_real @ A @ zero_zero_real ) )
% 3.82/4.10 & ( ( ord_less_eq_real @ zero_zero_real @ B2 )
% 3.82/4.10 | ( ord_less_eq_real @ B2 @ zero_zero_real ) ) )
% 3.82/4.10 => ( ( abs_abs_real @ ( times_times_real @ A @ B2 ) )
% 3.82/4.10 = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_eq_mult
% 3.82/4.10 thf(fact_7482_abs__eq__mult,axiom,
% 3.82/4.10 ! [A: int,B2: int] :
% 3.82/4.10 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 3.82/4.10 | ( ord_less_eq_int @ A @ zero_zero_int ) )
% 3.82/4.10 & ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 3.82/4.10 | ( ord_less_eq_int @ B2 @ zero_zero_int ) ) )
% 3.82/4.10 => ( ( abs_abs_int @ ( times_times_int @ A @ B2 ) )
% 3.82/4.10 = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_eq_mult
% 3.82/4.10 thf(fact_7483_abs__eq__iff_H,axiom,
% 3.82/4.10 ! [A: real,B2: real] :
% 3.82/4.10 ( ( ( abs_abs_real @ A )
% 3.82/4.10 = B2 )
% 3.82/4.10 = ( ( ord_less_eq_real @ zero_zero_real @ B2 )
% 3.82/4.10 & ( ( A = B2 )
% 3.82/4.10 | ( A
% 3.82/4.10 = ( uminus_uminus_real @ B2 ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_eq_iff'
% 3.82/4.10 thf(fact_7484_abs__eq__iff_H,axiom,
% 3.82/4.10 ! [A: int,B2: int] :
% 3.82/4.10 ( ( ( abs_abs_int @ A )
% 3.82/4.10 = B2 )
% 3.82/4.10 = ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 3.82/4.10 & ( ( A = B2 )
% 3.82/4.10 | ( A
% 3.82/4.10 = ( uminus_uminus_int @ B2 ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_eq_iff'
% 3.82/4.10 thf(fact_7485_eq__abs__iff_H,axiom,
% 3.82/4.10 ! [A: real,B2: real] :
% 3.82/4.10 ( ( A
% 3.82/4.10 = ( abs_abs_real @ B2 ) )
% 3.82/4.10 = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 3.82/4.10 & ( ( B2 = A )
% 3.82/4.10 | ( B2
% 3.82/4.10 = ( uminus_uminus_real @ A ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % eq_abs_iff'
% 3.82/4.10 thf(fact_7486_eq__abs__iff_H,axiom,
% 3.82/4.10 ! [A: int,B2: int] :
% 3.82/4.10 ( ( A
% 3.82/4.10 = ( abs_abs_int @ B2 ) )
% 3.82/4.10 = ( ( ord_less_eq_int @ zero_zero_int @ A )
% 3.82/4.10 & ( ( B2 = A )
% 3.82/4.10 | ( B2
% 3.82/4.10 = ( uminus_uminus_int @ A ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % eq_abs_iff'
% 3.82/4.10 thf(fact_7487_abs__minus__le__zero,axiom,
% 3.82/4.10 ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( abs_abs_real @ A ) ) @ zero_zero_real ) ).
% 3.82/4.10
% 3.82/4.10 % abs_minus_le_zero
% 3.82/4.10 thf(fact_7488_abs__minus__le__zero,axiom,
% 3.82/4.10 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( abs_abs_int @ A ) ) @ zero_zero_int ) ).
% 3.82/4.10
% 3.82/4.10 % abs_minus_le_zero
% 3.82/4.10 thf(fact_7489_abs__div__pos,axiom,
% 3.82/4.10 ! [Y: real,X: real] :
% 3.82/4.10 ( ( ord_less_real @ zero_zero_real @ Y )
% 3.82/4.10 => ( ( divide_divide_real @ ( abs_abs_real @ X ) @ Y )
% 3.82/4.10 = ( abs_abs_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_div_pos
% 3.82/4.10 thf(fact_7490_zero__le__power__abs,axiom,
% 3.82/4.10 ! [A: real,N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N2 ) ) ).
% 3.82/4.10
% 3.82/4.10 % zero_le_power_abs
% 3.82/4.10 thf(fact_7491_zero__le__power__abs,axiom,
% 3.82/4.10 ! [A: int,N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N2 ) ) ).
% 3.82/4.10
% 3.82/4.10 % zero_le_power_abs
% 3.82/4.10 thf(fact_7492_abs__if__raw,axiom,
% 3.82/4.10 ( abs_abs_int
% 3.82/4.10 = ( ^ [A3: int] : ( if_int @ ( ord_less_int @ A3 @ zero_zero_int ) @ ( uminus_uminus_int @ A3 ) @ A3 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_if_raw
% 3.82/4.10 thf(fact_7493_abs__if__raw,axiom,
% 3.82/4.10 ( abs_abs_real
% 3.82/4.10 = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_if_raw
% 3.82/4.10 thf(fact_7494_abs__if,axiom,
% 3.82/4.10 ( abs_abs_int
% 3.82/4.10 = ( ^ [A3: int] : ( if_int @ ( ord_less_int @ A3 @ zero_zero_int ) @ ( uminus_uminus_int @ A3 ) @ A3 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_if
% 3.82/4.10 thf(fact_7495_abs__if,axiom,
% 3.82/4.10 ( abs_abs_real
% 3.82/4.10 = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_if
% 3.82/4.10 thf(fact_7496_abs__of__neg,axiom,
% 3.82/4.10 ! [A: int] :
% 3.82/4.10 ( ( ord_less_int @ A @ zero_zero_int )
% 3.82/4.10 => ( ( abs_abs_int @ A )
% 3.82/4.10 = ( uminus_uminus_int @ A ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_of_neg
% 3.82/4.10 thf(fact_7497_abs__of__neg,axiom,
% 3.82/4.10 ! [A: real] :
% 3.82/4.10 ( ( ord_less_real @ A @ zero_zero_real )
% 3.82/4.10 => ( ( abs_abs_real @ A )
% 3.82/4.10 = ( uminus_uminus_real @ A ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_of_neg
% 3.82/4.10 thf(fact_7498_abs__diff__le__iff,axiom,
% 3.82/4.10 ! [X: real,A: real,R2: real] :
% 3.82/4.10 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ X @ A ) ) @ R2 )
% 3.82/4.10 = ( ( ord_less_eq_real @ ( minus_minus_real @ A @ R2 ) @ X )
% 3.82/4.10 & ( ord_less_eq_real @ X @ ( plus_plus_real @ A @ R2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_diff_le_iff
% 3.82/4.10 thf(fact_7499_abs__diff__le__iff,axiom,
% 3.82/4.10 ! [X: int,A: int,R2: int] :
% 3.82/4.10 ( ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ X @ A ) ) @ R2 )
% 3.82/4.10 = ( ( ord_less_eq_int @ ( minus_minus_int @ A @ R2 ) @ X )
% 3.82/4.10 & ( ord_less_eq_int @ X @ ( plus_plus_int @ A @ R2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_diff_le_iff
% 3.82/4.10 thf(fact_7500_abs__triangle__ineq4,axiom,
% 3.82/4.10 ! [A: real,B2: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ A @ B2 ) ) @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_triangle_ineq4
% 3.82/4.10 thf(fact_7501_abs__triangle__ineq4,axiom,
% 3.82/4.10 ! [A: int,B2: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ A @ B2 ) ) @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_triangle_ineq4
% 3.82/4.10 thf(fact_7502_abs__diff__triangle__ineq,axiom,
% 3.82/4.10 ! [A: real,B2: real,C: real,D: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B2 ) @ ( plus_plus_real @ C @ D ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ ( minus_minus_real @ A @ C ) ) @ ( abs_abs_real @ ( minus_minus_real @ B2 @ D ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_diff_triangle_ineq
% 3.82/4.10 thf(fact_7503_abs__diff__triangle__ineq,axiom,
% 3.82/4.10 ! [A: int,B2: int,C: int,D: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( plus_plus_int @ A @ B2 ) @ ( plus_plus_int @ C @ D ) ) ) @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ A @ C ) ) @ ( abs_abs_int @ ( minus_minus_int @ B2 @ D ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_diff_triangle_ineq
% 3.82/4.10 thf(fact_7504_abs__diff__less__iff,axiom,
% 3.82/4.10 ! [X: real,A: real,R2: real] :
% 3.82/4.10 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ A ) ) @ R2 )
% 3.82/4.10 = ( ( ord_less_real @ ( minus_minus_real @ A @ R2 ) @ X )
% 3.82/4.10 & ( ord_less_real @ X @ ( plus_plus_real @ A @ R2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_diff_less_iff
% 3.82/4.10 thf(fact_7505_abs__diff__less__iff,axiom,
% 3.82/4.10 ! [X: int,A: int,R2: int] :
% 3.82/4.10 ( ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X @ A ) ) @ R2 )
% 3.82/4.10 = ( ( ord_less_int @ ( minus_minus_int @ A @ R2 ) @ X )
% 3.82/4.10 & ( ord_less_int @ X @ ( plus_plus_int @ A @ R2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_diff_less_iff
% 3.82/4.10 thf(fact_7506_abs__sgn__eq,axiom,
% 3.82/4.10 ! [A: real] :
% 3.82/4.10 ( ( ( A = zero_zero_real )
% 3.82/4.10 => ( ( abs_abs_real @ ( sgn_sgn_real @ A ) )
% 3.82/4.10 = zero_zero_real ) )
% 3.82/4.10 & ( ( A != zero_zero_real )
% 3.82/4.10 => ( ( abs_abs_real @ ( sgn_sgn_real @ A ) )
% 3.82/4.10 = one_one_real ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_sgn_eq
% 3.82/4.10 thf(fact_7507_abs__sgn__eq,axiom,
% 3.82/4.10 ! [A: int] :
% 3.82/4.10 ( ( ( A = zero_zero_int )
% 3.82/4.10 => ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 3.82/4.10 = zero_zero_int ) )
% 3.82/4.10 & ( ( A != zero_zero_int )
% 3.82/4.10 => ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 3.82/4.10 = one_one_int ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_sgn_eq
% 3.82/4.10 thf(fact_7508_summable__rabs__comparison__test,axiom,
% 3.82/4.10 ! [F: nat > real,G: nat > real] :
% 3.82/4.10 ( ? [N8: nat] :
% 3.82/4.10 ! [N3: nat] :
% 3.82/4.10 ( ( ord_less_eq_nat @ N8 @ N3 )
% 3.82/4.10 => ( ord_less_eq_real @ ( abs_abs_real @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 3.82/4.10 => ( ( summable_real @ G )
% 3.82/4.10 => ( summable_real
% 3.82/4.10 @ ^ [N: nat] : ( abs_abs_real @ ( F @ N ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % summable_rabs_comparison_test
% 3.82/4.10 thf(fact_7509_abs__add__one__gt__zero,axiom,
% 3.82/4.10 ! [X: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ ( abs_abs_real @ X ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_add_one_gt_zero
% 3.82/4.10 thf(fact_7510_abs__add__one__gt__zero,axiom,
% 3.82/4.10 ! [X: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( abs_abs_int @ X ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_add_one_gt_zero
% 3.82/4.10 thf(fact_7511_of__int__leD,axiom,
% 3.82/4.10 ! [N2: int,X: real] :
% 3.82/4.10 ( ( ord_less_eq_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N2 ) ) @ X )
% 3.82/4.10 => ( ( N2 = zero_zero_int )
% 3.82/4.10 | ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % of_int_leD
% 3.82/4.10 thf(fact_7512_of__int__leD,axiom,
% 3.82/4.10 ! [N2: int,X: int] :
% 3.82/4.10 ( ( ord_less_eq_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N2 ) ) @ X )
% 3.82/4.10 => ( ( N2 = zero_zero_int )
% 3.82/4.10 | ( ord_less_eq_int @ one_one_int @ X ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % of_int_leD
% 3.82/4.10 thf(fact_7513_of__int__lessD,axiom,
% 3.82/4.10 ! [N2: int,X: real] :
% 3.82/4.10 ( ( ord_less_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N2 ) ) @ X )
% 3.82/4.10 => ( ( N2 = zero_zero_int )
% 3.82/4.10 | ( ord_less_real @ one_one_real @ X ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % of_int_lessD
% 3.82/4.10 thf(fact_7514_of__int__lessD,axiom,
% 3.82/4.10 ! [N2: int,X: int] :
% 3.82/4.10 ( ( ord_less_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N2 ) ) @ X )
% 3.82/4.10 => ( ( N2 = zero_zero_int )
% 3.82/4.10 | ( ord_less_int @ one_one_int @ X ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % of_int_lessD
% 3.82/4.10 thf(fact_7515_sgn__power__injE,axiom,
% 3.82/4.10 ! [A: real,N2: nat,X: real,B2: real] :
% 3.82/4.10 ( ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( power_power_real @ ( abs_abs_real @ A ) @ N2 ) )
% 3.82/4.10 = X )
% 3.82/4.10 => ( ( X
% 3.82/4.10 = ( times_times_real @ ( sgn_sgn_real @ B2 ) @ ( power_power_real @ ( abs_abs_real @ B2 ) @ N2 ) ) )
% 3.82/4.10 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( A = B2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % sgn_power_injE
% 3.82/4.10 thf(fact_7516_round__diff__minimal,axiom,
% 3.82/4.10 ! [Z3: real,M2: int] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z3 @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ Z3 ) ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ Z3 @ ( ring_1_of_int_real @ M2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % round_diff_minimal
% 3.82/4.10 thf(fact_7517_diffs__def,axiom,
% 3.82/4.10 ( diffs_complex
% 3.82/4.10 = ( ^ [C3: nat > complex,N: nat] : ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ N ) ) @ ( C3 @ ( suc @ N ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % diffs_def
% 3.82/4.10 thf(fact_7518_diffs__def,axiom,
% 3.82/4.10 ( diffs_real
% 3.82/4.10 = ( ^ [C3: nat > real,N: nat] : ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) @ ( C3 @ ( suc @ N ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % diffs_def
% 3.82/4.10 thf(fact_7519_diffs__def,axiom,
% 3.82/4.10 ( diffs_int
% 3.82/4.10 = ( ^ [C3: nat > int,N: nat] : ( times_times_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) @ ( C3 @ ( suc @ N ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % diffs_def
% 3.82/4.10 thf(fact_7520_abs__le__square__iff,axiom,
% 3.82/4.10 ! [X: real,Y: real] :
% 3.82/4.10 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( abs_abs_real @ Y ) )
% 3.82/4.10 = ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_le_square_iff
% 3.82/4.10 thf(fact_7521_abs__le__square__iff,axiom,
% 3.82/4.10 ! [X: int,Y: int] :
% 3.82/4.10 ( ( ord_less_eq_int @ ( abs_abs_int @ X ) @ ( abs_abs_int @ Y ) )
% 3.82/4.10 = ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_le_square_iff
% 3.82/4.10 thf(fact_7522_power2__le__iff__abs__le,axiom,
% 3.82/4.10 ! [Y: real,X: real] :
% 3.82/4.10 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 3.82/4.10 => ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 3.82/4.10 = ( ord_less_eq_real @ ( abs_abs_real @ X ) @ Y ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % power2_le_iff_abs_le
% 3.82/4.10 thf(fact_7523_power2__le__iff__abs__le,axiom,
% 3.82/4.10 ! [Y: int,X: int] :
% 3.82/4.10 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 3.82/4.10 => ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 3.82/4.10 = ( ord_less_eq_int @ ( abs_abs_int @ X ) @ Y ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % power2_le_iff_abs_le
% 3.82/4.10 thf(fact_7524_abs__sqrt__wlog,axiom,
% 3.82/4.10 ! [P: real > real > $o,X: real] :
% 3.82/4.10 ( ! [X5: real] :
% 3.82/4.10 ( ( ord_less_eq_real @ zero_zero_real @ X5 )
% 3.82/4.10 => ( P @ X5 @ ( power_power_real @ X5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 3.82/4.10 => ( P @ ( abs_abs_real @ X ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_sqrt_wlog
% 3.82/4.10 thf(fact_7525_abs__sqrt__wlog,axiom,
% 3.82/4.10 ! [P: int > int > $o,X: int] :
% 3.82/4.10 ( ! [X5: int] :
% 3.82/4.10 ( ( ord_less_eq_int @ zero_zero_int @ X5 )
% 3.82/4.10 => ( P @ X5 @ ( power_power_int @ X5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 3.82/4.10 => ( P @ ( abs_abs_int @ X ) @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_sqrt_wlog
% 3.82/4.10 thf(fact_7526_abs__square__le__1,axiom,
% 3.82/4.10 ! [X: real] :
% 3.82/4.10 ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 3.82/4.10 = ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_square_le_1
% 3.82/4.10 thf(fact_7527_abs__square__le__1,axiom,
% 3.82/4.10 ! [X: int] :
% 3.82/4.10 ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 3.82/4.10 = ( ord_less_eq_int @ ( abs_abs_int @ X ) @ one_one_int ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_square_le_1
% 3.82/4.10 thf(fact_7528_abs__square__less__1,axiom,
% 3.82/4.10 ! [X: real] :
% 3.82/4.10 ( ( ord_less_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 3.82/4.10 = ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_square_less_1
% 3.82/4.10 thf(fact_7529_abs__square__less__1,axiom,
% 3.82/4.10 ! [X: int] :
% 3.82/4.10 ( ( ord_less_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 3.82/4.10 = ( ord_less_int @ ( abs_abs_int @ X ) @ one_one_int ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_square_less_1
% 3.82/4.10 thf(fact_7530_power__mono__even,axiom,
% 3.82/4.10 ! [N2: nat,A: real,B2: real] :
% 3.82/4.10 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 3.82/4.10 => ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B2 ) )
% 3.82/4.10 => ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B2 @ N2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % power_mono_even
% 3.82/4.10 thf(fact_7531_power__mono__even,axiom,
% 3.82/4.10 ! [N2: nat,A: int,B2: int] :
% 3.82/4.10 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 3.82/4.10 => ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B2 ) )
% 3.82/4.10 => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B2 @ N2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % power_mono_even
% 3.82/4.10 thf(fact_7532_convex__sum__bound__le,axiom,
% 3.82/4.10 ! [I6: set_Extended_enat,X: extended_enat > real,A: extended_enat > real,B2: real,Delta: real] :
% 3.82/4.10 ( ! [I4: extended_enat] :
% 3.82/4.10 ( ( member_Extended_enat @ I4 @ I6 )
% 3.82/4.10 => ( ord_less_eq_real @ zero_zero_real @ ( X @ I4 ) ) )
% 3.82/4.10 => ( ( ( groups4148127829035722712t_real @ X @ I6 )
% 3.82/4.10 = one_one_real )
% 3.82/4.10 => ( ! [I4: extended_enat] :
% 3.82/4.10 ( ( member_Extended_enat @ I4 @ I6 )
% 3.82/4.10 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I4 ) @ B2 ) ) @ Delta ) )
% 3.82/4.10 => ( ord_less_eq_real
% 3.82/4.10 @ ( abs_abs_real
% 3.82/4.10 @ ( minus_minus_real
% 3.82/4.10 @ ( groups4148127829035722712t_real
% 3.82/4.10 @ ^ [I3: extended_enat] : ( times_times_real @ ( A @ I3 ) @ ( X @ I3 ) )
% 3.82/4.10 @ I6 )
% 3.82/4.10 @ B2 ) )
% 3.82/4.10 @ Delta ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % convex_sum_bound_le
% 3.82/4.10 thf(fact_7533_convex__sum__bound__le,axiom,
% 3.82/4.10 ! [I6: set_real,X: real > real,A: real > real,B2: real,Delta: real] :
% 3.82/4.10 ( ! [I4: real] :
% 3.82/4.10 ( ( member_real @ I4 @ I6 )
% 3.82/4.10 => ( ord_less_eq_real @ zero_zero_real @ ( X @ I4 ) ) )
% 3.82/4.10 => ( ( ( groups8097168146408367636l_real @ X @ I6 )
% 3.82/4.10 = one_one_real )
% 3.82/4.10 => ( ! [I4: real] :
% 3.82/4.10 ( ( member_real @ I4 @ I6 )
% 3.82/4.10 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I4 ) @ B2 ) ) @ Delta ) )
% 3.82/4.10 => ( ord_less_eq_real
% 3.82/4.10 @ ( abs_abs_real
% 3.82/4.10 @ ( minus_minus_real
% 3.82/4.10 @ ( groups8097168146408367636l_real
% 3.82/4.10 @ ^ [I3: real] : ( times_times_real @ ( A @ I3 ) @ ( X @ I3 ) )
% 3.82/4.10 @ I6 )
% 3.82/4.10 @ B2 ) )
% 3.82/4.10 @ Delta ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % convex_sum_bound_le
% 3.82/4.10 thf(fact_7534_convex__sum__bound__le,axiom,
% 3.82/4.10 ! [I6: set_set_nat,X: set_nat > real,A: set_nat > real,B2: real,Delta: real] :
% 3.82/4.10 ( ! [I4: set_nat] :
% 3.82/4.10 ( ( member_set_nat @ I4 @ I6 )
% 3.82/4.10 => ( ord_less_eq_real @ zero_zero_real @ ( X @ I4 ) ) )
% 3.82/4.10 => ( ( ( groups5107569545109728110t_real @ X @ I6 )
% 3.82/4.10 = one_one_real )
% 3.82/4.10 => ( ! [I4: set_nat] :
% 3.82/4.10 ( ( member_set_nat @ I4 @ I6 )
% 3.82/4.10 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I4 ) @ B2 ) ) @ Delta ) )
% 3.82/4.10 => ( ord_less_eq_real
% 3.82/4.10 @ ( abs_abs_real
% 3.82/4.10 @ ( minus_minus_real
% 3.82/4.10 @ ( groups5107569545109728110t_real
% 3.82/4.10 @ ^ [I3: set_nat] : ( times_times_real @ ( A @ I3 ) @ ( X @ I3 ) )
% 3.82/4.10 @ I6 )
% 3.82/4.10 @ B2 ) )
% 3.82/4.10 @ Delta ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % convex_sum_bound_le
% 3.82/4.10 thf(fact_7535_convex__sum__bound__le,axiom,
% 3.82/4.10 ! [I6: set_int,X: int > real,A: int > real,B2: real,Delta: real] :
% 3.82/4.10 ( ! [I4: int] :
% 3.82/4.10 ( ( member_int @ I4 @ I6 )
% 3.82/4.10 => ( ord_less_eq_real @ zero_zero_real @ ( X @ I4 ) ) )
% 3.82/4.10 => ( ( ( groups8778361861064173332t_real @ X @ I6 )
% 3.82/4.10 = one_one_real )
% 3.82/4.10 => ( ! [I4: int] :
% 3.82/4.10 ( ( member_int @ I4 @ I6 )
% 3.82/4.10 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I4 ) @ B2 ) ) @ Delta ) )
% 3.82/4.10 => ( ord_less_eq_real
% 3.82/4.10 @ ( abs_abs_real
% 3.82/4.10 @ ( minus_minus_real
% 3.82/4.10 @ ( groups8778361861064173332t_real
% 3.82/4.10 @ ^ [I3: int] : ( times_times_real @ ( A @ I3 ) @ ( X @ I3 ) )
% 3.82/4.10 @ I6 )
% 3.82/4.10 @ B2 ) )
% 3.82/4.10 @ Delta ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % convex_sum_bound_le
% 3.82/4.10 thf(fact_7536_convex__sum__bound__le,axiom,
% 3.82/4.10 ! [I6: set_Extended_enat,X: extended_enat > int,A: extended_enat > int,B2: int,Delta: int] :
% 3.82/4.10 ( ! [I4: extended_enat] :
% 3.82/4.10 ( ( member_Extended_enat @ I4 @ I6 )
% 3.82/4.10 => ( ord_less_eq_int @ zero_zero_int @ ( X @ I4 ) ) )
% 3.82/4.10 => ( ( ( groups2025484359314973016at_int @ X @ I6 )
% 3.82/4.10 = one_one_int )
% 3.82/4.10 => ( ! [I4: extended_enat] :
% 3.82/4.10 ( ( member_Extended_enat @ I4 @ I6 )
% 3.82/4.10 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( A @ I4 ) @ B2 ) ) @ Delta ) )
% 3.82/4.10 => ( ord_less_eq_int
% 3.82/4.10 @ ( abs_abs_int
% 3.82/4.10 @ ( minus_minus_int
% 3.82/4.10 @ ( groups2025484359314973016at_int
% 3.82/4.10 @ ^ [I3: extended_enat] : ( times_times_int @ ( A @ I3 ) @ ( X @ I3 ) )
% 3.82/4.10 @ I6 )
% 3.82/4.10 @ B2 ) )
% 3.82/4.10 @ Delta ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % convex_sum_bound_le
% 3.82/4.10 thf(fact_7537_convex__sum__bound__le,axiom,
% 3.82/4.10 ! [I6: set_real,X: real > int,A: real > int,B2: int,Delta: int] :
% 3.82/4.10 ( ! [I4: real] :
% 3.82/4.10 ( ( member_real @ I4 @ I6 )
% 3.82/4.10 => ( ord_less_eq_int @ zero_zero_int @ ( X @ I4 ) ) )
% 3.82/4.10 => ( ( ( groups1932886352136224148al_int @ X @ I6 )
% 3.82/4.10 = one_one_int )
% 3.82/4.10 => ( ! [I4: real] :
% 3.82/4.10 ( ( member_real @ I4 @ I6 )
% 3.82/4.10 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( A @ I4 ) @ B2 ) ) @ Delta ) )
% 3.82/4.10 => ( ord_less_eq_int
% 3.82/4.10 @ ( abs_abs_int
% 3.82/4.10 @ ( minus_minus_int
% 3.82/4.10 @ ( groups1932886352136224148al_int
% 3.82/4.10 @ ^ [I3: real] : ( times_times_int @ ( A @ I3 ) @ ( X @ I3 ) )
% 3.82/4.10 @ I6 )
% 3.82/4.10 @ B2 ) )
% 3.82/4.10 @ Delta ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % convex_sum_bound_le
% 3.82/4.10 thf(fact_7538_convex__sum__bound__le,axiom,
% 3.82/4.10 ! [I6: set_set_nat,X: set_nat > int,A: set_nat > int,B2: int,Delta: int] :
% 3.82/4.10 ( ! [I4: set_nat] :
% 3.82/4.10 ( ( member_set_nat @ I4 @ I6 )
% 3.82/4.10 => ( ord_less_eq_int @ zero_zero_int @ ( X @ I4 ) ) )
% 3.82/4.10 => ( ( ( groups8292507037921071086at_int @ X @ I6 )
% 3.82/4.10 = one_one_int )
% 3.82/4.10 => ( ! [I4: set_nat] :
% 3.82/4.10 ( ( member_set_nat @ I4 @ I6 )
% 3.82/4.10 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( A @ I4 ) @ B2 ) ) @ Delta ) )
% 3.82/4.10 => ( ord_less_eq_int
% 3.82/4.10 @ ( abs_abs_int
% 3.82/4.10 @ ( minus_minus_int
% 3.82/4.10 @ ( groups8292507037921071086at_int
% 3.82/4.10 @ ^ [I3: set_nat] : ( times_times_int @ ( A @ I3 ) @ ( X @ I3 ) )
% 3.82/4.10 @ I6 )
% 3.82/4.10 @ B2 ) )
% 3.82/4.10 @ Delta ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % convex_sum_bound_le
% 3.82/4.10 thf(fact_7539_convex__sum__bound__le,axiom,
% 3.82/4.10 ! [I6: set_nat,X: nat > int,A: nat > int,B2: int,Delta: int] :
% 3.82/4.10 ( ! [I4: nat] :
% 3.82/4.10 ( ( member_nat @ I4 @ I6 )
% 3.82/4.10 => ( ord_less_eq_int @ zero_zero_int @ ( X @ I4 ) ) )
% 3.82/4.10 => ( ( ( groups3539618377306564664at_int @ X @ I6 )
% 3.82/4.10 = one_one_int )
% 3.82/4.10 => ( ! [I4: nat] :
% 3.82/4.10 ( ( member_nat @ I4 @ I6 )
% 3.82/4.10 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( A @ I4 ) @ B2 ) ) @ Delta ) )
% 3.82/4.10 => ( ord_less_eq_int
% 3.82/4.10 @ ( abs_abs_int
% 3.82/4.10 @ ( minus_minus_int
% 3.82/4.10 @ ( groups3539618377306564664at_int
% 3.82/4.10 @ ^ [I3: nat] : ( times_times_int @ ( A @ I3 ) @ ( X @ I3 ) )
% 3.82/4.10 @ I6 )
% 3.82/4.10 @ B2 ) )
% 3.82/4.10 @ Delta ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % convex_sum_bound_le
% 3.82/4.10 thf(fact_7540_convex__sum__bound__le,axiom,
% 3.82/4.10 ! [I6: set_int,X: int > int,A: int > int,B2: int,Delta: int] :
% 3.82/4.10 ( ! [I4: int] :
% 3.82/4.10 ( ( member_int @ I4 @ I6 )
% 3.82/4.10 => ( ord_less_eq_int @ zero_zero_int @ ( X @ I4 ) ) )
% 3.82/4.10 => ( ( ( groups4538972089207619220nt_int @ X @ I6 )
% 3.82/4.10 = one_one_int )
% 3.82/4.10 => ( ! [I4: int] :
% 3.82/4.10 ( ( member_int @ I4 @ I6 )
% 3.82/4.10 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( A @ I4 ) @ B2 ) ) @ Delta ) )
% 3.82/4.10 => ( ord_less_eq_int
% 3.82/4.10 @ ( abs_abs_int
% 3.82/4.10 @ ( minus_minus_int
% 3.82/4.10 @ ( groups4538972089207619220nt_int
% 3.82/4.10 @ ^ [I3: int] : ( times_times_int @ ( A @ I3 ) @ ( X @ I3 ) )
% 3.82/4.10 @ I6 )
% 3.82/4.10 @ B2 ) )
% 3.82/4.10 @ Delta ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % convex_sum_bound_le
% 3.82/4.10 thf(fact_7541_convex__sum__bound__le,axiom,
% 3.82/4.10 ! [I6: set_nat,X: nat > real,A: nat > real,B2: real,Delta: real] :
% 3.82/4.10 ( ! [I4: nat] :
% 3.82/4.10 ( ( member_nat @ I4 @ I6 )
% 3.82/4.10 => ( ord_less_eq_real @ zero_zero_real @ ( X @ I4 ) ) )
% 3.82/4.10 => ( ( ( groups6591440286371151544t_real @ X @ I6 )
% 3.82/4.10 = one_one_real )
% 3.82/4.10 => ( ! [I4: nat] :
% 3.82/4.10 ( ( member_nat @ I4 @ I6 )
% 3.82/4.10 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I4 ) @ B2 ) ) @ Delta ) )
% 3.82/4.10 => ( ord_less_eq_real
% 3.82/4.10 @ ( abs_abs_real
% 3.82/4.10 @ ( minus_minus_real
% 3.82/4.10 @ ( groups6591440286371151544t_real
% 3.82/4.10 @ ^ [I3: nat] : ( times_times_real @ ( A @ I3 ) @ ( X @ I3 ) )
% 3.82/4.10 @ I6 )
% 3.82/4.10 @ B2 ) )
% 3.82/4.10 @ Delta ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % convex_sum_bound_le
% 3.82/4.10 thf(fact_7542_monoseq__arctan__series,axiom,
% 3.82/4.10 ! [X: real] :
% 3.82/4.10 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 3.82/4.10 => ( topolo6980174941875973593q_real
% 3.82/4.10 @ ^ [N: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % monoseq_arctan_series
% 3.82/4.10 thf(fact_7543_arctan__series,axiom,
% 3.82/4.10 ! [X: real] :
% 3.82/4.10 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 3.82/4.10 => ( ( arctan @ X )
% 3.82/4.10 = ( suminf_real
% 3.82/4.10 @ ^ [K2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % arctan_series
% 3.82/4.10 thf(fact_7544_int__ge__less__than__def,axiom,
% 3.82/4.10 ( int_ge_less_than
% 3.82/4.10 = ( ^ [D4: int] :
% 3.82/4.10 ( collec213857154873943460nt_int
% 3.82/4.10 @ ( produc4947309494688390418_int_o
% 3.82/4.10 @ ^ [Z7: int,Z6: int] :
% 3.82/4.10 ( ( ord_less_eq_int @ D4 @ Z7 )
% 3.82/4.10 & ( ord_less_int @ Z7 @ Z6 ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % int_ge_less_than_def
% 3.82/4.10 thf(fact_7545_Maclaurin__exp__lt,axiom,
% 3.82/4.10 ! [X: real,N2: nat] :
% 3.82/4.10 ( ( X != zero_zero_real )
% 3.82/4.10 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ? [T6: real] :
% 3.82/4.10 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T6 ) )
% 3.82/4.10 & ( ord_less_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 3.82/4.10 & ( ( exp_real @ X )
% 3.82/4.10 = ( plus_plus_real
% 3.82/4.10 @ ( groups6591440286371151544t_real
% 3.82/4.10 @ ^ [M: nat] : ( divide_divide_real @ ( power_power_real @ X @ M ) @ ( semiri2265585572941072030t_real @ M ) )
% 3.82/4.10 @ ( set_ord_lessThan_nat @ N2 ) )
% 3.82/4.10 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T6 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X @ N2 ) ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % Maclaurin_exp_lt
% 3.82/4.10 thf(fact_7546_xor__Suc__0__eq,axiom,
% 3.82/4.10 ! [N2: nat] :
% 3.82/4.10 ( ( bit_se6528837805403552850or_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 3.82/4.10 = ( minus_minus_nat @ ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 3.82/4.10 @ ( zero_n2687167440665602831ol_nat
% 3.82/4.10 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % xor_Suc_0_eq
% 3.82/4.10 thf(fact_7547_zdvd1__eq,axiom,
% 3.82/4.10 ! [X: int] :
% 3.82/4.10 ( ( dvd_dvd_int @ X @ one_one_int )
% 3.82/4.10 = ( ( abs_abs_int @ X )
% 3.82/4.10 = one_one_int ) ) ).
% 3.82/4.10
% 3.82/4.10 % zdvd1_eq
% 3.82/4.10 thf(fact_7548_zabs__less__one__iff,axiom,
% 3.82/4.10 ! [Z3: int] :
% 3.82/4.10 ( ( ord_less_int @ ( abs_abs_int @ Z3 ) @ one_one_int )
% 3.82/4.10 = ( Z3 = zero_zero_int ) ) ).
% 3.82/4.10
% 3.82/4.10 % zabs_less_one_iff
% 3.82/4.10 thf(fact_7549_xor__nat__numerals_I4_J,axiom,
% 3.82/4.10 ! [X: num] :
% 3.82/4.10 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 3.82/4.10 = ( numeral_numeral_nat @ ( bit0 @ X ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % xor_nat_numerals(4)
% 3.82/4.10 thf(fact_7550_xor__nat__numerals_I3_J,axiom,
% 3.82/4.10 ! [X: num] :
% 3.82/4.10 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 3.82/4.10 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % xor_nat_numerals(3)
% 3.82/4.10 thf(fact_7551_xor__nat__numerals_I2_J,axiom,
% 3.82/4.10 ! [Y: num] :
% 3.82/4.10 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 3.82/4.10 = ( numeral_numeral_nat @ ( bit0 @ Y ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % xor_nat_numerals(2)
% 3.82/4.10 thf(fact_7552_xor__nat__numerals_I1_J,axiom,
% 3.82/4.10 ! [Y: num] :
% 3.82/4.10 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 3.82/4.10 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % xor_nat_numerals(1)
% 3.82/4.10 thf(fact_7553_zdvd__antisym__abs,axiom,
% 3.82/4.10 ! [A: int,B2: int] :
% 3.82/4.10 ( ( dvd_dvd_int @ A @ B2 )
% 3.82/4.10 => ( ( dvd_dvd_int @ B2 @ A )
% 3.82/4.10 => ( ( abs_abs_int @ A )
% 3.82/4.10 = ( abs_abs_int @ B2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % zdvd_antisym_abs
% 3.82/4.10 thf(fact_7554_abs__zmult__eq__1,axiom,
% 3.82/4.10 ! [M2: int,N2: int] :
% 3.82/4.10 ( ( ( abs_abs_int @ ( times_times_int @ M2 @ N2 ) )
% 3.82/4.10 = one_one_int )
% 3.82/4.10 => ( ( abs_abs_int @ M2 )
% 3.82/4.10 = one_one_int ) ) ).
% 3.82/4.10
% 3.82/4.10 % abs_zmult_eq_1
% 3.82/4.10 thf(fact_7555_infinite__int__iff__unbounded__le,axiom,
% 3.82/4.10 ! [S2: set_int] :
% 3.82/4.10 ( ( ~ ( finite_finite_int @ S2 ) )
% 3.82/4.10 = ( ! [M: int] :
% 3.82/4.10 ? [N: int] :
% 3.82/4.10 ( ( ord_less_eq_int @ M @ ( abs_abs_int @ N ) )
% 3.82/4.10 & ( member_int @ N @ S2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % infinite_int_iff_unbounded_le
% 3.82/4.10 thf(fact_7556_infinite__int__iff__unbounded,axiom,
% 3.82/4.10 ! [S2: set_int] :
% 3.82/4.10 ( ( ~ ( finite_finite_int @ S2 ) )
% 3.82/4.10 = ( ! [M: int] :
% 3.82/4.10 ? [N: int] :
% 3.82/4.10 ( ( ord_less_int @ M @ ( abs_abs_int @ N ) )
% 3.82/4.10 & ( member_int @ N @ S2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % infinite_int_iff_unbounded
% 3.82/4.10 thf(fact_7557_zabs__def,axiom,
% 3.82/4.10 ( abs_abs_int
% 3.82/4.10 = ( ^ [I3: int] : ( if_int @ ( ord_less_int @ I3 @ zero_zero_int ) @ ( uminus_uminus_int @ I3 ) @ I3 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % zabs_def
% 3.82/4.10 thf(fact_7558_dvd__imp__le__int,axiom,
% 3.82/4.10 ! [I: int,D: int] :
% 3.82/4.10 ( ( I != zero_zero_int )
% 3.82/4.10 => ( ( dvd_dvd_int @ D @ I )
% 3.82/4.10 => ( ord_less_eq_int @ ( abs_abs_int @ D ) @ ( abs_abs_int @ I ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % dvd_imp_le_int
% 3.82/4.10 thf(fact_7559_zdvd__mult__cancel1,axiom,
% 3.82/4.10 ! [M2: int,N2: int] :
% 3.82/4.10 ( ( M2 != zero_zero_int )
% 3.82/4.10 => ( ( dvd_dvd_int @ ( times_times_int @ M2 @ N2 ) @ M2 )
% 3.82/4.10 = ( ( abs_abs_int @ N2 )
% 3.82/4.10 = one_one_int ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % zdvd_mult_cancel1
% 3.82/4.10 thf(fact_7560_nat__intermed__int__val,axiom,
% 3.82/4.10 ! [M2: nat,N2: nat,F: nat > int,K: int] :
% 3.82/4.10 ( ! [I4: nat] :
% 3.82/4.10 ( ( ( ord_less_eq_nat @ M2 @ I4 )
% 3.82/4.10 & ( ord_less_nat @ I4 @ N2 ) )
% 3.82/4.10 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) ) ) @ one_one_int ) )
% 3.82/4.10 => ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.10 => ( ( ord_less_eq_int @ ( F @ M2 ) @ K )
% 3.82/4.10 => ( ( ord_less_eq_int @ K @ ( F @ N2 ) )
% 3.82/4.10 => ? [I4: nat] :
% 3.82/4.10 ( ( ord_less_eq_nat @ M2 @ I4 )
% 3.82/4.10 & ( ord_less_eq_nat @ I4 @ N2 )
% 3.82/4.10 & ( ( F @ I4 )
% 3.82/4.10 = K ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % nat_intermed_int_val
% 3.82/4.10 thf(fact_7561_nat__ivt__aux,axiom,
% 3.82/4.10 ! [N2: nat,F: nat > int,K: int] :
% 3.82/4.10 ( ! [I4: nat] :
% 3.82/4.10 ( ( ord_less_nat @ I4 @ N2 )
% 3.82/4.10 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) ) ) @ one_one_int ) )
% 3.82/4.10 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 3.82/4.10 => ( ( ord_less_eq_int @ K @ ( F @ N2 ) )
% 3.82/4.10 => ? [I4: nat] :
% 3.82/4.10 ( ( ord_less_eq_nat @ I4 @ N2 )
% 3.82/4.10 & ( ( F @ I4 )
% 3.82/4.10 = K ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % nat_ivt_aux
% 3.82/4.10 thf(fact_7562_xor__nat__unfold,axiom,
% 3.82/4.10 ( bit_se6528837805403552850or_nat
% 3.82/4.10 = ( ^ [M: nat,N: nat] : ( if_nat @ ( M = zero_zero_nat ) @ N @ ( if_nat @ ( N = zero_zero_nat ) @ M @ ( plus_plus_nat @ ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ M @ ( 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 @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % xor_nat_unfold
% 3.82/4.10 thf(fact_7563_nat0__intermed__int__val,axiom,
% 3.82/4.10 ! [N2: nat,F: nat > int,K: int] :
% 3.82/4.10 ( ! [I4: nat] :
% 3.82/4.10 ( ( ord_less_nat @ I4 @ N2 )
% 3.82/4.10 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( plus_plus_nat @ I4 @ one_one_nat ) ) @ ( F @ I4 ) ) ) @ one_one_int ) )
% 3.82/4.10 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 3.82/4.10 => ( ( ord_less_eq_int @ K @ ( F @ N2 ) )
% 3.82/4.10 => ? [I4: nat] :
% 3.82/4.10 ( ( ord_less_eq_nat @ I4 @ N2 )
% 3.82/4.10 & ( ( F @ I4 )
% 3.82/4.10 = K ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % nat0_intermed_int_val
% 3.82/4.10 thf(fact_7564_xor__nat__rec,axiom,
% 3.82/4.10 ( bit_se6528837805403552850or_nat
% 3.82/4.10 = ( ^ [M: nat,N: nat] :
% 3.82/4.10 ( plus_plus_nat
% 3.82/4.10 @ ( zero_n2687167440665602831ol_nat
% 3.82/4.10 @ ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 3.82/4.10 != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 3.82/4.10 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % xor_nat_rec
% 3.82/4.10 thf(fact_7565_exp__ge__one__plus__x__over__n__power__n,axiom,
% 3.82/4.10 ! [N2: nat,X: real] :
% 3.82/4.10 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ X )
% 3.82/4.10 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ord_less_eq_real @ ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N2 ) ) ) @ N2 ) @ ( exp_real @ X ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % exp_ge_one_plus_x_over_n_power_n
% 3.82/4.10 thf(fact_7566_exp__ge__one__minus__x__over__n__power__n,axiom,
% 3.82/4.10 ! [X: real,N2: nat] :
% 3.82/4.10 ( ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ N2 ) )
% 3.82/4.10 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ord_less_eq_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N2 ) ) ) @ N2 ) @ ( exp_real @ ( uminus_uminus_real @ X ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % exp_ge_one_minus_x_over_n_power_n
% 3.82/4.10 thf(fact_7567_Suc__0__xor__eq,axiom,
% 3.82/4.10 ! [N2: nat] :
% 3.82/4.10 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 3.82/4.10 = ( minus_minus_nat @ ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 3.82/4.10 @ ( zero_n2687167440665602831ol_nat
% 3.82/4.10 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % Suc_0_xor_eq
% 3.82/4.10 thf(fact_7568_divide__int__def,axiom,
% 3.82/4.10 ( divide_divide_int
% 3.82/4.10 = ( ^ [K2: int,L2: int] :
% 3.82/4.10 ( if_int @ ( L2 = zero_zero_int ) @ zero_zero_int
% 3.82/4.10 @ ( if_int
% 3.82/4.10 @ ( ( sgn_sgn_int @ K2 )
% 3.82/4.10 = ( sgn_sgn_int @ L2 ) )
% 3.82/4.10 @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) )
% 3.82/4.10 @ ( uminus_uminus_int
% 3.82/4.10 @ ( semiri1314217659103216013at_int
% 3.82/4.10 @ ( plus_plus_nat @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) )
% 3.82/4.10 @ ( zero_n2687167440665602831ol_nat
% 3.82/4.10 @ ~ ( dvd_dvd_int @ L2 @ K2 ) ) ) ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % divide_int_def
% 3.82/4.10 thf(fact_7569_nat__int,axiom,
% 3.82/4.10 ! [N2: nat] :
% 3.82/4.10 ( ( nat2 @ ( semiri1314217659103216013at_int @ N2 ) )
% 3.82/4.10 = N2 ) ).
% 3.82/4.10
% 3.82/4.10 % nat_int
% 3.82/4.10 thf(fact_7570_nat__numeral,axiom,
% 3.82/4.10 ! [K: num] :
% 3.82/4.10 ( ( nat2 @ ( numeral_numeral_int @ K ) )
% 3.82/4.10 = ( numeral_numeral_nat @ K ) ) ).
% 3.82/4.10
% 3.82/4.10 % nat_numeral
% 3.82/4.10 thf(fact_7571_nat__of__bool,axiom,
% 3.82/4.10 ! [P: $o] :
% 3.82/4.10 ( ( nat2 @ ( zero_n2684676970156552555ol_int @ P ) )
% 3.82/4.10 = ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 3.82/4.10
% 3.82/4.10 % nat_of_bool
% 3.82/4.10 thf(fact_7572_nat__1,axiom,
% 3.82/4.10 ( ( nat2 @ one_one_int )
% 3.82/4.10 = ( suc @ zero_zero_nat ) ) ).
% 3.82/4.10
% 3.82/4.10 % nat_1
% 3.82/4.10 thf(fact_7573_nat__le__0,axiom,
% 3.82/4.10 ! [Z3: int] :
% 3.82/4.10 ( ( ord_less_eq_int @ Z3 @ zero_zero_int )
% 3.82/4.10 => ( ( nat2 @ Z3 )
% 3.82/4.10 = zero_zero_nat ) ) ).
% 3.82/4.10
% 3.82/4.10 % nat_le_0
% 3.82/4.10 thf(fact_7574_nat__0__iff,axiom,
% 3.82/4.10 ! [I: int] :
% 3.82/4.10 ( ( ( nat2 @ I )
% 3.82/4.10 = zero_zero_nat )
% 3.82/4.10 = ( ord_less_eq_int @ I @ zero_zero_int ) ) ).
% 3.82/4.10
% 3.82/4.10 % nat_0_iff
% 3.82/4.10 thf(fact_7575_zless__nat__conj,axiom,
% 3.82/4.10 ! [W2: int,Z3: int] :
% 3.82/4.10 ( ( ord_less_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z3 ) )
% 3.82/4.10 = ( ( ord_less_int @ zero_zero_int @ Z3 )
% 3.82/4.10 & ( ord_less_int @ W2 @ Z3 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % zless_nat_conj
% 3.82/4.10 thf(fact_7576_nat__neg__numeral,axiom,
% 3.82/4.10 ! [K: num] :
% 3.82/4.10 ( ( nat2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 3.82/4.10 = zero_zero_nat ) ).
% 3.82/4.10
% 3.82/4.10 % nat_neg_numeral
% 3.82/4.10 thf(fact_7577_nat__zminus__int,axiom,
% 3.82/4.10 ! [N2: nat] :
% 3.82/4.10 ( ( nat2 @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 3.82/4.10 = zero_zero_nat ) ).
% 3.82/4.10
% 3.82/4.10 % nat_zminus_int
% 3.82/4.10 thf(fact_7578_int__nat__eq,axiom,
% 3.82/4.10 ! [Z3: int] :
% 3.82/4.10 ( ( ( ord_less_eq_int @ zero_zero_int @ Z3 )
% 3.82/4.10 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z3 ) )
% 3.82/4.10 = Z3 ) )
% 3.82/4.10 & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z3 )
% 3.82/4.10 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z3 ) )
% 3.82/4.10 = zero_zero_int ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % int_nat_eq
% 3.82/4.10 thf(fact_7579_zero__less__nat__eq,axiom,
% 3.82/4.10 ! [Z3: int] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ ( nat2 @ Z3 ) )
% 3.82/4.10 = ( ord_less_int @ zero_zero_int @ Z3 ) ) ).
% 3.82/4.10
% 3.82/4.10 % zero_less_nat_eq
% 3.82/4.10 thf(fact_7580_diff__nat__numeral,axiom,
% 3.82/4.10 ! [V: num,V3: num] :
% 3.82/4.10 ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ ( numeral_numeral_nat @ V3 ) )
% 3.82/4.10 = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ V3 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % diff_nat_numeral
% 3.82/4.10 thf(fact_7581_numeral__power__eq__nat__cancel__iff,axiom,
% 3.82/4.10 ! [X: num,N2: nat,Y: int] :
% 3.82/4.10 ( ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 )
% 3.82/4.10 = ( nat2 @ Y ) )
% 3.82/4.10 = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 )
% 3.82/4.10 = Y ) ) ).
% 3.82/4.10
% 3.82/4.10 % numeral_power_eq_nat_cancel_iff
% 3.82/4.10 thf(fact_7582_nat__eq__numeral__power__cancel__iff,axiom,
% 3.82/4.10 ! [Y: int,X: num,N2: nat] :
% 3.82/4.10 ( ( ( nat2 @ Y )
% 3.82/4.10 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) )
% 3.82/4.10 = ( Y
% 3.82/4.10 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % nat_eq_numeral_power_cancel_iff
% 3.82/4.10 thf(fact_7583_dvd__nat__abs__iff,axiom,
% 3.82/4.10 ! [N2: nat,K: int] :
% 3.82/4.10 ( ( dvd_dvd_nat @ N2 @ ( nat2 @ ( abs_abs_int @ K ) ) )
% 3.82/4.10 = ( dvd_dvd_int @ ( semiri1314217659103216013at_int @ N2 ) @ K ) ) ).
% 3.82/4.10
% 3.82/4.10 % dvd_nat_abs_iff
% 3.82/4.10 thf(fact_7584_nat__abs__dvd__iff,axiom,
% 3.82/4.10 ! [K: int,N2: nat] :
% 3.82/4.10 ( ( dvd_dvd_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ N2 )
% 3.82/4.10 = ( dvd_dvd_int @ K @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % nat_abs_dvd_iff
% 3.82/4.10 thf(fact_7585_nat__ceiling__le__eq,axiom,
% 3.82/4.10 ! [X: real,A: nat] :
% 3.82/4.10 ( ( ord_less_eq_nat @ ( nat2 @ ( archim7802044766580827645g_real @ X ) ) @ A )
% 3.82/4.10 = ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ A ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % nat_ceiling_le_eq
% 3.82/4.10 thf(fact_7586_one__less__nat__eq,axiom,
% 3.82/4.10 ! [Z3: int] :
% 3.82/4.10 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z3 ) )
% 3.82/4.10 = ( ord_less_int @ one_one_int @ Z3 ) ) ).
% 3.82/4.10
% 3.82/4.10 % one_less_nat_eq
% 3.82/4.10 thf(fact_7587_nat__numeral__diff__1,axiom,
% 3.82/4.10 ! [V: num] :
% 3.82/4.10 ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ one_one_nat )
% 3.82/4.10 = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ one_one_int ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % nat_numeral_diff_1
% 3.82/4.10 thf(fact_7588_numeral__power__less__nat__cancel__iff,axiom,
% 3.82/4.10 ! [X: num,N2: nat,A: int] :
% 3.82/4.10 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) @ ( nat2 @ A ) )
% 3.82/4.10 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) @ A ) ) ).
% 3.82/4.10
% 3.82/4.10 % numeral_power_less_nat_cancel_iff
% 3.82/4.10 thf(fact_7589_nat__less__numeral__power__cancel__iff,axiom,
% 3.82/4.10 ! [A: int,X: num,N2: nat] :
% 3.82/4.10 ( ( ord_less_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) )
% 3.82/4.10 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % nat_less_numeral_power_cancel_iff
% 3.82/4.10 thf(fact_7590_nat__le__numeral__power__cancel__iff,axiom,
% 3.82/4.10 ! [A: int,X: num,N2: nat] :
% 3.82/4.10 ( ( ord_less_eq_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) )
% 3.82/4.10 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % nat_le_numeral_power_cancel_iff
% 3.82/4.10 thf(fact_7591_numeral__power__le__nat__cancel__iff,axiom,
% 3.82/4.10 ! [X: num,N2: nat,A: int] :
% 3.82/4.10 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) @ ( nat2 @ A ) )
% 3.82/4.10 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) @ A ) ) ).
% 3.82/4.10
% 3.82/4.10 % numeral_power_le_nat_cancel_iff
% 3.82/4.10 thf(fact_7592_nat__zero__as__int,axiom,
% 3.82/4.10 ( zero_zero_nat
% 3.82/4.10 = ( nat2 @ zero_zero_int ) ) ).
% 3.82/4.10
% 3.82/4.10 % nat_zero_as_int
% 3.82/4.10 thf(fact_7593_nat__mono,axiom,
% 3.82/4.10 ! [X: int,Y: int] :
% 3.82/4.10 ( ( ord_less_eq_int @ X @ Y )
% 3.82/4.10 => ( ord_less_eq_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % nat_mono
% 3.82/4.10 thf(fact_7594_ex__nat,axiom,
% 3.82/4.10 ( ( ^ [P2: nat > $o] :
% 3.82/4.10 ? [X7: nat] : ( P2 @ X7 ) )
% 3.82/4.10 = ( ^ [P3: nat > $o] :
% 3.82/4.10 ? [X4: int] :
% 3.82/4.10 ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 3.82/4.10 & ( P3 @ ( nat2 @ X4 ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % ex_nat
% 3.82/4.10 thf(fact_7595_all__nat,axiom,
% 3.82/4.10 ( ( ^ [P2: nat > $o] :
% 3.82/4.10 ! [X7: nat] : ( P2 @ X7 ) )
% 3.82/4.10 = ( ^ [P3: nat > $o] :
% 3.82/4.10 ! [X4: int] :
% 3.82/4.10 ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 3.82/4.10 => ( P3 @ ( nat2 @ X4 ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % all_nat
% 3.82/4.10 thf(fact_7596_eq__nat__nat__iff,axiom,
% 3.82/4.10 ! [Z3: int,Z8: int] :
% 3.82/4.10 ( ( ord_less_eq_int @ zero_zero_int @ Z3 )
% 3.82/4.10 => ( ( ord_less_eq_int @ zero_zero_int @ Z8 )
% 3.82/4.10 => ( ( ( nat2 @ Z3 )
% 3.82/4.10 = ( nat2 @ Z8 ) )
% 3.82/4.10 = ( Z3 = Z8 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % eq_nat_nat_iff
% 3.82/4.10 thf(fact_7597_nat__mono__iff,axiom,
% 3.82/4.10 ! [Z3: int,W2: int] :
% 3.82/4.10 ( ( ord_less_int @ zero_zero_int @ Z3 )
% 3.82/4.10 => ( ( ord_less_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z3 ) )
% 3.82/4.10 = ( ord_less_int @ W2 @ Z3 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % nat_mono_iff
% 3.82/4.10 thf(fact_7598_zless__nat__eq__int__zless,axiom,
% 3.82/4.10 ! [M2: nat,Z3: int] :
% 3.82/4.10 ( ( ord_less_nat @ M2 @ ( nat2 @ Z3 ) )
% 3.82/4.10 = ( ord_less_int @ ( semiri1314217659103216013at_int @ M2 ) @ Z3 ) ) ).
% 3.82/4.10
% 3.82/4.10 % zless_nat_eq_int_zless
% 3.82/4.10 thf(fact_7599_nat__le__iff,axiom,
% 3.82/4.10 ! [X: int,N2: nat] :
% 3.82/4.10 ( ( ord_less_eq_nat @ ( nat2 @ X ) @ N2 )
% 3.82/4.10 = ( ord_less_eq_int @ X @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % nat_le_iff
% 3.82/4.10 thf(fact_7600_int__eq__iff,axiom,
% 3.82/4.10 ! [M2: nat,Z3: int] :
% 3.82/4.10 ( ( ( semiri1314217659103216013at_int @ M2 )
% 3.82/4.10 = Z3 )
% 3.82/4.10 = ( ( M2
% 3.82/4.10 = ( nat2 @ Z3 ) )
% 3.82/4.10 & ( ord_less_eq_int @ zero_zero_int @ Z3 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % int_eq_iff
% 3.82/4.10 thf(fact_7601_nat__0__le,axiom,
% 3.82/4.10 ! [Z3: int] :
% 3.82/4.10 ( ( ord_less_eq_int @ zero_zero_int @ Z3 )
% 3.82/4.10 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z3 ) )
% 3.82/4.10 = Z3 ) ) ).
% 3.82/4.10
% 3.82/4.10 % nat_0_le
% 3.82/4.10 thf(fact_7602_nat__int__add,axiom,
% 3.82/4.10 ! [A: nat,B2: nat] :
% 3.82/4.10 ( ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B2 ) ) )
% 3.82/4.10 = ( plus_plus_nat @ A @ B2 ) ) ).
% 3.82/4.10
% 3.82/4.10 % nat_int_add
% 3.82/4.10 thf(fact_7603_nat__abs__mult__distrib,axiom,
% 3.82/4.10 ! [W2: int,Z3: int] :
% 3.82/4.10 ( ( nat2 @ ( abs_abs_int @ ( times_times_int @ W2 @ Z3 ) ) )
% 3.82/4.10 = ( times_times_nat @ ( nat2 @ ( abs_abs_int @ W2 ) ) @ ( nat2 @ ( abs_abs_int @ Z3 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % nat_abs_mult_distrib
% 3.82/4.10 thf(fact_7604_nat__plus__as__int,axiom,
% 3.82/4.10 ( plus_plus_nat
% 3.82/4.10 = ( ^ [A3: nat,B3: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % nat_plus_as_int
% 3.82/4.10 thf(fact_7605_nat__less__eq__zless,axiom,
% 3.82/4.10 ! [W2: int,Z3: int] :
% 3.82/4.10 ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 3.82/4.10 => ( ( ord_less_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z3 ) )
% 3.82/4.10 = ( ord_less_int @ W2 @ Z3 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % nat_less_eq_zless
% 3.82/4.10 thf(fact_7606_nat__le__eq__zle,axiom,
% 3.82/4.10 ! [W2: int,Z3: int] :
% 3.82/4.10 ( ( ( ord_less_int @ zero_zero_int @ W2 )
% 3.82/4.10 | ( ord_less_eq_int @ zero_zero_int @ Z3 ) )
% 3.82/4.10 => ( ( ord_less_eq_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z3 ) )
% 3.82/4.10 = ( ord_less_eq_int @ W2 @ Z3 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % nat_le_eq_zle
% 3.82/4.10 thf(fact_7607_nat__eq__iff,axiom,
% 3.82/4.10 ! [W2: int,M2: nat] :
% 3.82/4.10 ( ( ( nat2 @ W2 )
% 3.82/4.10 = M2 )
% 3.82/4.10 = ( ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 3.82/4.10 => ( W2
% 3.82/4.10 = ( semiri1314217659103216013at_int @ M2 ) ) )
% 3.82/4.10 & ( ~ ( ord_less_eq_int @ zero_zero_int @ W2 )
% 3.82/4.10 => ( M2 = zero_zero_nat ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % nat_eq_iff
% 3.82/4.10 thf(fact_7608_nat__eq__iff2,axiom,
% 3.82/4.10 ! [M2: nat,W2: int] :
% 3.82/4.10 ( ( M2
% 3.82/4.10 = ( nat2 @ W2 ) )
% 3.82/4.10 = ( ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 3.82/4.10 => ( W2
% 3.82/4.10 = ( semiri1314217659103216013at_int @ M2 ) ) )
% 3.82/4.10 & ( ~ ( ord_less_eq_int @ zero_zero_int @ W2 )
% 3.82/4.10 => ( M2 = zero_zero_nat ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % nat_eq_iff2
% 3.82/4.10 thf(fact_7609_split__nat,axiom,
% 3.82/4.10 ! [P: nat > $o,I: int] :
% 3.82/4.10 ( ( P @ ( nat2 @ I ) )
% 3.82/4.10 = ( ! [N: nat] :
% 3.82/4.10 ( ( I
% 3.82/4.10 = ( semiri1314217659103216013at_int @ N ) )
% 3.82/4.10 => ( P @ N ) )
% 3.82/4.10 & ( ( ord_less_int @ I @ zero_zero_int )
% 3.82/4.10 => ( P @ zero_zero_nat ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % split_nat
% 3.82/4.10 thf(fact_7610_le__nat__iff,axiom,
% 3.82/4.10 ! [K: int,N2: nat] :
% 3.82/4.10 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 3.82/4.10 => ( ( ord_less_eq_nat @ N2 @ ( nat2 @ K ) )
% 3.82/4.10 = ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N2 ) @ K ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % le_nat_iff
% 3.82/4.10 thf(fact_7611_nat__add__distrib,axiom,
% 3.82/4.10 ! [Z3: int,Z8: int] :
% 3.82/4.10 ( ( ord_less_eq_int @ zero_zero_int @ Z3 )
% 3.82/4.10 => ( ( ord_less_eq_int @ zero_zero_int @ Z8 )
% 3.82/4.10 => ( ( nat2 @ ( plus_plus_int @ Z3 @ Z8 ) )
% 3.82/4.10 = ( plus_plus_nat @ ( nat2 @ Z3 ) @ ( nat2 @ Z8 ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % nat_add_distrib
% 3.82/4.10 thf(fact_7612_nat__mult__distrib,axiom,
% 3.82/4.10 ! [Z3: int,Z8: int] :
% 3.82/4.10 ( ( ord_less_eq_int @ zero_zero_int @ Z3 )
% 3.82/4.10 => ( ( nat2 @ ( times_times_int @ Z3 @ Z8 ) )
% 3.82/4.10 = ( times_times_nat @ ( nat2 @ Z3 ) @ ( nat2 @ Z8 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % nat_mult_distrib
% 3.82/4.10 thf(fact_7613_Suc__as__int,axiom,
% 3.82/4.10 ( suc
% 3.82/4.10 = ( ^ [A3: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A3 ) @ one_one_int ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % Suc_as_int
% 3.82/4.10 thf(fact_7614_forall__pos__mono__1,axiom,
% 3.82/4.10 ! [P: real > $o,E2: real] :
% 3.82/4.10 ( ! [D5: real,E: real] :
% 3.82/4.10 ( ( ord_less_real @ D5 @ E )
% 3.82/4.10 => ( ( P @ D5 )
% 3.82/4.10 => ( P @ E ) ) )
% 3.82/4.10 => ( ! [N3: nat] : ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) )
% 3.82/4.10 => ( ( ord_less_real @ zero_zero_real @ E2 )
% 3.82/4.10 => ( P @ E2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % forall_pos_mono_1
% 3.82/4.10 thf(fact_7615_real__arch__inverse,axiom,
% 3.82/4.10 ! [E2: real] :
% 3.82/4.10 ( ( ord_less_real @ zero_zero_real @ E2 )
% 3.82/4.10 = ( ? [N: nat] :
% 3.82/4.10 ( ( N != zero_zero_nat )
% 3.82/4.10 & ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N ) ) )
% 3.82/4.10 & ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N ) ) @ E2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % real_arch_inverse
% 3.82/4.10 thf(fact_7616_forall__pos__mono,axiom,
% 3.82/4.10 ! [P: real > $o,E2: real] :
% 3.82/4.10 ( ! [D5: real,E: real] :
% 3.82/4.10 ( ( ord_less_real @ D5 @ E )
% 3.82/4.10 => ( ( P @ D5 )
% 3.82/4.10 => ( P @ E ) ) )
% 3.82/4.10 => ( ! [N3: nat] :
% 3.82/4.10 ( ( N3 != zero_zero_nat )
% 3.82/4.10 => ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N3 ) ) ) )
% 3.82/4.10 => ( ( ord_less_real @ zero_zero_real @ E2 )
% 3.82/4.10 => ( P @ E2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % forall_pos_mono
% 3.82/4.10 thf(fact_7617_nat__diff__distrib_H,axiom,
% 3.82/4.10 ! [X: int,Y: int] :
% 3.82/4.10 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 3.82/4.10 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 3.82/4.10 => ( ( nat2 @ ( minus_minus_int @ X @ Y ) )
% 3.82/4.10 = ( minus_minus_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % nat_diff_distrib'
% 3.82/4.10 thf(fact_7618_nat__diff__distrib,axiom,
% 3.82/4.10 ! [Z8: int,Z3: int] :
% 3.82/4.10 ( ( ord_less_eq_int @ zero_zero_int @ Z8 )
% 3.82/4.10 => ( ( ord_less_eq_int @ Z8 @ Z3 )
% 3.82/4.10 => ( ( nat2 @ ( minus_minus_int @ Z3 @ Z8 ) )
% 3.82/4.10 = ( minus_minus_nat @ ( nat2 @ Z3 ) @ ( nat2 @ Z8 ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % nat_diff_distrib
% 3.82/4.10 thf(fact_7619_nat__abs__triangle__ineq,axiom,
% 3.82/4.10 ! [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 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % nat_abs_triangle_ineq
% 3.82/4.10 thf(fact_7620_nat__floor__neg,axiom,
% 3.82/4.10 ! [X: real] :
% 3.82/4.10 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 3.82/4.10 => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 3.82/4.10 = zero_zero_nat ) ) ).
% 3.82/4.10
% 3.82/4.10 % nat_floor_neg
% 3.82/4.10 thf(fact_7621_nat__power__eq,axiom,
% 3.82/4.10 ! [Z3: int,N2: nat] :
% 3.82/4.10 ( ( ord_less_eq_int @ zero_zero_int @ Z3 )
% 3.82/4.10 => ( ( nat2 @ ( power_power_int @ Z3 @ N2 ) )
% 3.82/4.10 = ( power_power_nat @ ( nat2 @ Z3 ) @ N2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % nat_power_eq
% 3.82/4.10 thf(fact_7622_floor__eq3,axiom,
% 3.82/4.10 ! [N2: nat,X: real] :
% 3.82/4.10 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ X )
% 3.82/4.10 => ( ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) )
% 3.82/4.10 => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 3.82/4.10 = N2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % floor_eq3
% 3.82/4.10 thf(fact_7623_le__nat__floor,axiom,
% 3.82/4.10 ! [X: nat,A: real] :
% 3.82/4.10 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ A )
% 3.82/4.10 => ( ord_less_eq_nat @ X @ ( nat2 @ ( archim6058952711729229775r_real @ A ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % le_nat_floor
% 3.82/4.10 thf(fact_7624_nat__2,axiom,
% 3.82/4.10 ( ( nat2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 3.82/4.10 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % nat_2
% 3.82/4.10 thf(fact_7625_Suc__nat__eq__nat__zadd1,axiom,
% 3.82/4.10 ! [Z3: int] :
% 3.82/4.10 ( ( ord_less_eq_int @ zero_zero_int @ Z3 )
% 3.82/4.10 => ( ( suc @ ( nat2 @ Z3 ) )
% 3.82/4.10 = ( nat2 @ ( plus_plus_int @ one_one_int @ Z3 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % Suc_nat_eq_nat_zadd1
% 3.82/4.10 thf(fact_7626_nat__less__iff,axiom,
% 3.82/4.10 ! [W2: int,M2: nat] :
% 3.82/4.10 ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 3.82/4.10 => ( ( ord_less_nat @ ( nat2 @ W2 ) @ M2 )
% 3.82/4.10 = ( ord_less_int @ W2 @ ( semiri1314217659103216013at_int @ M2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % nat_less_iff
% 3.82/4.10 thf(fact_7627_nat__mult__distrib__neg,axiom,
% 3.82/4.10 ! [Z3: int,Z8: int] :
% 3.82/4.10 ( ( ord_less_eq_int @ Z3 @ zero_zero_int )
% 3.82/4.10 => ( ( nat2 @ ( times_times_int @ Z3 @ Z8 ) )
% 3.82/4.10 = ( times_times_nat @ ( nat2 @ ( uminus_uminus_int @ Z3 ) ) @ ( nat2 @ ( uminus_uminus_int @ Z8 ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % nat_mult_distrib_neg
% 3.82/4.10 thf(fact_7628_nat__abs__int__diff,axiom,
% 3.82/4.10 ! [A: nat,B2: nat] :
% 3.82/4.10 ( ( ( ord_less_eq_nat @ A @ B2 )
% 3.82/4.10 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) )
% 3.82/4.10 = ( minus_minus_nat @ B2 @ A ) ) )
% 3.82/4.10 & ( ~ ( ord_less_eq_nat @ A @ B2 )
% 3.82/4.10 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) )
% 3.82/4.10 = ( minus_minus_nat @ A @ B2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % nat_abs_int_diff
% 3.82/4.10 thf(fact_7629_floor__eq4,axiom,
% 3.82/4.10 ! [N2: nat,X: real] :
% 3.82/4.10 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N2 ) @ X )
% 3.82/4.10 => ( ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) )
% 3.82/4.10 => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 3.82/4.10 = N2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % floor_eq4
% 3.82/4.10 thf(fact_7630_diff__nat__eq__if,axiom,
% 3.82/4.10 ! [Z8: int,Z3: int] :
% 3.82/4.10 ( ( ( ord_less_int @ Z8 @ zero_zero_int )
% 3.82/4.10 => ( ( minus_minus_nat @ ( nat2 @ Z3 ) @ ( nat2 @ Z8 ) )
% 3.82/4.10 = ( nat2 @ Z3 ) ) )
% 3.82/4.10 & ( ~ ( ord_less_int @ Z8 @ zero_zero_int )
% 3.82/4.10 => ( ( minus_minus_nat @ ( nat2 @ Z3 ) @ ( nat2 @ Z8 ) )
% 3.82/4.10 = ( if_nat @ ( ord_less_int @ ( minus_minus_int @ Z3 @ Z8 ) @ zero_zero_int ) @ zero_zero_nat @ ( nat2 @ ( minus_minus_int @ Z3 @ Z8 ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % diff_nat_eq_if
% 3.82/4.10 thf(fact_7631_nat__dvd__iff,axiom,
% 3.82/4.10 ! [Z3: int,M2: nat] :
% 3.82/4.10 ( ( dvd_dvd_nat @ ( nat2 @ Z3 ) @ M2 )
% 3.82/4.10 = ( ( ( ord_less_eq_int @ zero_zero_int @ Z3 )
% 3.82/4.10 => ( dvd_dvd_int @ Z3 @ ( semiri1314217659103216013at_int @ M2 ) ) )
% 3.82/4.10 & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z3 )
% 3.82/4.10 => ( M2 = zero_zero_nat ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % nat_dvd_iff
% 3.82/4.10 thf(fact_7632_or__nat__unfold,axiom,
% 3.82/4.10 ( bit_se1412395901928357646or_nat
% 3.82/4.10 = ( ^ [M: nat,N: nat] : ( if_nat @ ( M = zero_zero_nat ) @ N @ ( if_nat @ ( N = zero_zero_nat ) @ M @ ( plus_plus_nat @ ( ord_max_nat @ ( modulo_modulo_nat @ M @ ( 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 @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % or_nat_unfold
% 3.82/4.10 thf(fact_7633_Sum__Ico__nat,axiom,
% 3.82/4.10 ! [M2: nat,N2: nat] :
% 3.82/4.10 ( ( groups3542108847815614940at_nat
% 3.82/4.10 @ ^ [X4: nat] : X4
% 3.82/4.10 @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) )
% 3.82/4.10 = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N2 @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ ( times_times_nat @ M2 @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % Sum_Ico_nat
% 3.82/4.10 thf(fact_7634_VEBT_Osize_I3_J,axiom,
% 3.82/4.10 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 3.82/4.10 ( ( size_size_VEBT_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 3.82/4.10 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ size_size_VEBT_VEBT @ X13 ) @ ( size_size_VEBT_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % VEBT.size(3)
% 3.82/4.10 thf(fact_7635_Cauchy__iff2,axiom,
% 3.82/4.10 ( topolo4055970368930404560y_real
% 3.82/4.10 = ( ^ [X6: nat > real] :
% 3.82/4.10 ! [J2: nat] :
% 3.82/4.10 ? [M9: nat] :
% 3.82/4.10 ! [M: nat] :
% 3.82/4.10 ( ( ord_less_eq_nat @ M9 @ M )
% 3.82/4.10 => ! [N: nat] :
% 3.82/4.10 ( ( ord_less_eq_nat @ M9 @ N )
% 3.82/4.10 => ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ ( X6 @ M ) @ ( X6 @ N ) ) ) @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ J2 ) ) ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % Cauchy_iff2
% 3.82/4.10 thf(fact_7636_finite__atLeastLessThan,axiom,
% 3.82/4.10 ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or4665077453230672383an_nat @ L @ U ) ) ).
% 3.82/4.10
% 3.82/4.10 % finite_atLeastLessThan
% 3.82/4.10 thf(fact_7637_atLeastLessThan__singleton,axiom,
% 3.82/4.10 ! [M2: nat] :
% 3.82/4.10 ( ( set_or4665077453230672383an_nat @ M2 @ ( suc @ M2 ) )
% 3.82/4.10 = ( insert_nat @ M2 @ bot_bot_set_nat ) ) ).
% 3.82/4.10
% 3.82/4.10 % atLeastLessThan_singleton
% 3.82/4.10 thf(fact_7638_or__nat__numerals_I2_J,axiom,
% 3.82/4.10 ! [Y: num] :
% 3.82/4.10 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 3.82/4.10 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % or_nat_numerals(2)
% 3.82/4.10 thf(fact_7639_or__nat__numerals_I4_J,axiom,
% 3.82/4.10 ! [X: num] :
% 3.82/4.10 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 3.82/4.10 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % or_nat_numerals(4)
% 3.82/4.10 thf(fact_7640_or__nat__numerals_I3_J,axiom,
% 3.82/4.10 ! [X: num] :
% 3.82/4.10 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 3.82/4.10 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % or_nat_numerals(3)
% 3.82/4.10 thf(fact_7641_or__nat__numerals_I1_J,axiom,
% 3.82/4.10 ! [Y: num] :
% 3.82/4.10 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 3.82/4.10 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % or_nat_numerals(1)
% 3.82/4.10 thf(fact_7642_ex__nat__less__eq,axiom,
% 3.82/4.10 ! [N2: nat,P: nat > $o] :
% 3.82/4.10 ( ( ? [M: nat] :
% 3.82/4.10 ( ( ord_less_nat @ M @ N2 )
% 3.82/4.10 & ( P @ M ) ) )
% 3.82/4.10 = ( ? [X4: nat] :
% 3.82/4.10 ( ( member_nat @ X4 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 3.82/4.10 & ( P @ X4 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % ex_nat_less_eq
% 3.82/4.10 thf(fact_7643_all__nat__less__eq,axiom,
% 3.82/4.10 ! [N2: nat,P: nat > $o] :
% 3.82/4.10 ( ( ! [M: nat] :
% 3.82/4.10 ( ( ord_less_nat @ M @ N2 )
% 3.82/4.10 => ( P @ M ) ) )
% 3.82/4.10 = ( ! [X4: nat] :
% 3.82/4.10 ( ( member_nat @ X4 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 3.82/4.10 => ( P @ X4 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % all_nat_less_eq
% 3.82/4.10 thf(fact_7644_atLeastLessThanSuc__atLeastAtMost,axiom,
% 3.82/4.10 ! [L: nat,U: nat] :
% 3.82/4.10 ( ( set_or4665077453230672383an_nat @ L @ ( suc @ U ) )
% 3.82/4.10 = ( set_or1269000886237332187st_nat @ L @ U ) ) ).
% 3.82/4.10
% 3.82/4.10 % atLeastLessThanSuc_atLeastAtMost
% 3.82/4.10 thf(fact_7645_lessThan__atLeast0,axiom,
% 3.82/4.10 ( set_ord_lessThan_nat
% 3.82/4.10 = ( set_or4665077453230672383an_nat @ zero_zero_nat ) ) ).
% 3.82/4.10
% 3.82/4.10 % lessThan_atLeast0
% 3.82/4.10 thf(fact_7646_atLeastLessThan0,axiom,
% 3.82/4.10 ! [M2: nat] :
% 3.82/4.10 ( ( set_or4665077453230672383an_nat @ M2 @ zero_zero_nat )
% 3.82/4.10 = bot_bot_set_nat ) ).
% 3.82/4.10
% 3.82/4.10 % atLeastLessThan0
% 3.82/4.10 thf(fact_7647_atLeast0__lessThan__Suc,axiom,
% 3.82/4.10 ! [N2: nat] :
% 3.82/4.10 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 3.82/4.10 = ( insert_nat @ N2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % atLeast0_lessThan_Suc
% 3.82/4.10 thf(fact_7648_subset__eq__atLeast0__lessThan__finite,axiom,
% 3.82/4.10 ! [N6: set_nat,N2: nat] :
% 3.82/4.10 ( ( ord_less_eq_set_nat @ N6 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 3.82/4.10 => ( finite_finite_nat @ N6 ) ) ).
% 3.82/4.10
% 3.82/4.10 % subset_eq_atLeast0_lessThan_finite
% 3.82/4.10 thf(fact_7649_atLeastLessThanSuc,axiom,
% 3.82/4.10 ! [M2: nat,N2: nat] :
% 3.82/4.10 ( ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.10 => ( ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N2 ) )
% 3.82/4.10 = ( insert_nat @ N2 @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) )
% 3.82/4.10 & ( ~ ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.10 => ( ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N2 ) )
% 3.82/4.10 = bot_bot_set_nat ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % atLeastLessThanSuc
% 3.82/4.10 thf(fact_7650_prod__Suc__Suc__fact,axiom,
% 3.82/4.10 ! [N2: nat] :
% 3.82/4.10 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 3.82/4.10 = ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 3.82/4.10
% 3.82/4.10 % prod_Suc_Suc_fact
% 3.82/4.10 thf(fact_7651_prod__Suc__fact,axiom,
% 3.82/4.10 ! [N2: nat] :
% 3.82/4.10 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 3.82/4.10 = ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 3.82/4.10
% 3.82/4.10 % prod_Suc_fact
% 3.82/4.10 thf(fact_7652_atLeastLessThan__nat__numeral,axiom,
% 3.82/4.10 ! [M2: nat,K: num] :
% 3.82/4.10 ( ( ( ord_less_eq_nat @ M2 @ ( pred_numeral @ K ) )
% 3.82/4.10 => ( ( set_or4665077453230672383an_nat @ M2 @ ( numeral_numeral_nat @ K ) )
% 3.82/4.10 = ( insert_nat @ ( pred_numeral @ K ) @ ( set_or4665077453230672383an_nat @ M2 @ ( pred_numeral @ K ) ) ) ) )
% 3.82/4.10 & ( ~ ( ord_less_eq_nat @ M2 @ ( pred_numeral @ K ) )
% 3.82/4.10 => ( ( set_or4665077453230672383an_nat @ M2 @ ( numeral_numeral_nat @ K ) )
% 3.82/4.10 = bot_bot_set_nat ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % atLeastLessThan_nat_numeral
% 3.82/4.10 thf(fact_7653_atLeast1__lessThan__eq__remove0,axiom,
% 3.82/4.10 ! [N2: nat] :
% 3.82/4.10 ( ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 3.82/4.10 = ( minus_minus_set_nat @ ( set_ord_lessThan_nat @ N2 ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % atLeast1_lessThan_eq_remove0
% 3.82/4.10 thf(fact_7654_Suc__0__or__eq,axiom,
% 3.82/4.10 ! [N2: nat] :
% 3.82/4.10 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 3.82/4.10 = ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % Suc_0_or_eq
% 3.82/4.10 thf(fact_7655_or__Suc__0__eq,axiom,
% 3.82/4.10 ! [N2: nat] :
% 3.82/4.10 ( ( bit_se1412395901928357646or_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 3.82/4.10 = ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % or_Suc_0_eq
% 3.82/4.10 thf(fact_7656_or__nat__rec,axiom,
% 3.82/4.10 ( bit_se1412395901928357646or_nat
% 3.82/4.10 = ( ^ [M: nat,N: nat] :
% 3.82/4.10 ( plus_plus_nat
% 3.82/4.10 @ ( zero_n2687167440665602831ol_nat
% 3.82/4.10 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 3.82/4.10 | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 3.82/4.10 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % or_nat_rec
% 3.82/4.10 thf(fact_7657_sum__power2,axiom,
% 3.82/4.10 ! [K: nat] :
% 3.82/4.10 ( ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) )
% 3.82/4.10 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) @ one_one_nat ) ) ).
% 3.82/4.10
% 3.82/4.10 % sum_power2
% 3.82/4.10 thf(fact_7658_Chebyshev__sum__upper__nat,axiom,
% 3.82/4.10 ! [N2: nat,A: nat > nat,B2: nat > nat] :
% 3.82/4.10 ( ! [I4: nat,J3: nat] :
% 3.82/4.10 ( ( ord_less_eq_nat @ I4 @ J3 )
% 3.82/4.10 => ( ( ord_less_nat @ J3 @ N2 )
% 3.82/4.10 => ( ord_less_eq_nat @ ( A @ I4 ) @ ( A @ J3 ) ) ) )
% 3.82/4.10 => ( ! [I4: nat,J3: nat] :
% 3.82/4.10 ( ( ord_less_eq_nat @ I4 @ J3 )
% 3.82/4.10 => ( ( ord_less_nat @ J3 @ N2 )
% 3.82/4.10 => ( ord_less_eq_nat @ ( B2 @ J3 ) @ ( B2 @ I4 ) ) ) )
% 3.82/4.10 => ( ord_less_eq_nat
% 3.82/4.10 @ ( times_times_nat @ N2
% 3.82/4.10 @ ( groups3542108847815614940at_nat
% 3.82/4.10 @ ^ [I3: nat] : ( times_times_nat @ ( A @ I3 ) @ ( B2 @ I3 ) )
% 3.82/4.10 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) )
% 3.82/4.10 @ ( times_times_nat @ ( groups3542108847815614940at_nat @ A @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) @ ( groups3542108847815614940at_nat @ B2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % Chebyshev_sum_upper_nat
% 3.82/4.10 thf(fact_7659_VEBT_Osize__gen_I1_J,axiom,
% 3.82/4.10 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 3.82/4.10 ( ( vEBT_size_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 3.82/4.10 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ vEBT_size_VEBT @ X13 ) @ ( vEBT_size_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % VEBT.size_gen(1)
% 3.82/4.10 thf(fact_7660_finite__atLeastLessThan__int,axiom,
% 3.82/4.10 ! [L: int,U: int] : ( finite_finite_int @ ( set_or4662586982721622107an_int @ L @ U ) ) ).
% 3.82/4.10
% 3.82/4.10 % finite_atLeastLessThan_int
% 3.82/4.10 thf(fact_7661_finite__atLeastZeroLessThan__int,axiom,
% 3.82/4.10 ! [U: int] : ( finite_finite_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) ) ).
% 3.82/4.10
% 3.82/4.10 % finite_atLeastZeroLessThan_int
% 3.82/4.10 thf(fact_7662_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 3.82/4.10 ! [L: int,U: int] :
% 3.82/4.10 ( ( set_or4662586982721622107an_int @ L @ ( plus_plus_int @ U @ one_one_int ) )
% 3.82/4.10 = ( set_or1266510415728281911st_int @ L @ U ) ) ).
% 3.82/4.10
% 3.82/4.10 % atLeastLessThanPlusOne_atLeastAtMost_int
% 3.82/4.10 thf(fact_7663_VEBT_Osize__gen_I2_J,axiom,
% 3.82/4.10 ! [X21: $o,X222: $o] :
% 3.82/4.10 ( ( vEBT_size_VEBT @ ( vEBT_Leaf @ X21 @ X222 ) )
% 3.82/4.10 = zero_zero_nat ) ).
% 3.82/4.10
% 3.82/4.10 % VEBT.size_gen(2)
% 3.82/4.10 thf(fact_7664_card__lessThan,axiom,
% 3.82/4.10 ! [U: nat] :
% 3.82/4.10 ( ( finite_card_nat @ ( set_ord_lessThan_nat @ U ) )
% 3.82/4.10 = U ) ).
% 3.82/4.10
% 3.82/4.10 % card_lessThan
% 3.82/4.10 thf(fact_7665_card__Collect__less__nat,axiom,
% 3.82/4.10 ! [N2: nat] :
% 3.82/4.10 ( ( finite_card_nat
% 3.82/4.10 @ ( collect_nat
% 3.82/4.10 @ ^ [I3: nat] : ( ord_less_nat @ I3 @ N2 ) ) )
% 3.82/4.10 = N2 ) ).
% 3.82/4.10
% 3.82/4.10 % card_Collect_less_nat
% 3.82/4.10 thf(fact_7666_card__atMost,axiom,
% 3.82/4.10 ! [U: nat] :
% 3.82/4.10 ( ( finite_card_nat @ ( set_ord_atMost_nat @ U ) )
% 3.82/4.10 = ( suc @ U ) ) ).
% 3.82/4.10
% 3.82/4.10 % card_atMost
% 3.82/4.10 thf(fact_7667_card__atLeastLessThan,axiom,
% 3.82/4.10 ! [L: nat,U: nat] :
% 3.82/4.10 ( ( finite_card_nat @ ( set_or4665077453230672383an_nat @ L @ U ) )
% 3.82/4.10 = ( minus_minus_nat @ U @ L ) ) ).
% 3.82/4.10
% 3.82/4.10 % card_atLeastLessThan
% 3.82/4.10 thf(fact_7668_card__Collect__le__nat,axiom,
% 3.82/4.10 ! [N2: nat] :
% 3.82/4.10 ( ( finite_card_nat
% 3.82/4.10 @ ( collect_nat
% 3.82/4.10 @ ^ [I3: nat] : ( ord_less_eq_nat @ I3 @ N2 ) ) )
% 3.82/4.10 = ( suc @ N2 ) ) ).
% 3.82/4.10
% 3.82/4.10 % card_Collect_le_nat
% 3.82/4.10 thf(fact_7669_card__atLeastAtMost,axiom,
% 3.82/4.10 ! [L: nat,U: nat] :
% 3.82/4.10 ( ( finite_card_nat @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 3.82/4.10 = ( minus_minus_nat @ ( suc @ U ) @ L ) ) ).
% 3.82/4.10
% 3.82/4.10 % card_atLeastAtMost
% 3.82/4.10 thf(fact_7670_card__atLeastLessThan__int,axiom,
% 3.82/4.10 ! [L: int,U: int] :
% 3.82/4.10 ( ( finite_card_int @ ( set_or4662586982721622107an_int @ L @ U ) )
% 3.82/4.10 = ( nat2 @ ( minus_minus_int @ U @ L ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % card_atLeastLessThan_int
% 3.82/4.10 thf(fact_7671_card__atLeastAtMost__int,axiom,
% 3.82/4.10 ! [L: int,U: int] :
% 3.82/4.10 ( ( finite_card_int @ ( set_or1266510415728281911st_int @ L @ U ) )
% 3.82/4.10 = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ U @ L ) @ one_one_int ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % card_atLeastAtMost_int
% 3.82/4.10 thf(fact_7672_push__bit__of__Suc__0,axiom,
% 3.82/4.10 ! [N2: nat] :
% 3.82/4.10 ( ( bit_se547839408752420682it_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 3.82/4.10 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 3.82/4.10
% 3.82/4.10 % push_bit_of_Suc_0
% 3.82/4.10 thf(fact_7673_card__atLeastZeroLessThan__int,axiom,
% 3.82/4.10 ! [U: int] :
% 3.82/4.10 ( ( finite_card_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) )
% 3.82/4.10 = ( nat2 @ U ) ) ).
% 3.82/4.10
% 3.82/4.10 % card_atLeastZeroLessThan_int
% 3.82/4.10 thf(fact_7674_nat_Odisc__eq__case_I1_J,axiom,
% 3.82/4.10 ! [Nat: nat] :
% 3.82/4.10 ( ( Nat = zero_zero_nat )
% 3.82/4.10 = ( case_nat_o @ $true
% 3.82/4.10 @ ^ [Uu3: nat] : $false
% 3.82/4.10 @ Nat ) ) ).
% 3.82/4.10
% 3.82/4.10 % nat.disc_eq_case(1)
% 3.82/4.10 thf(fact_7675_nat_Odisc__eq__case_I2_J,axiom,
% 3.82/4.10 ! [Nat: nat] :
% 3.82/4.10 ( ( Nat != zero_zero_nat )
% 3.82/4.10 = ( case_nat_o @ $false
% 3.82/4.10 @ ^ [Uu3: nat] : $true
% 3.82/4.10 @ Nat ) ) ).
% 3.82/4.10
% 3.82/4.10 % nat.disc_eq_case(2)
% 3.82/4.10 thf(fact_7676_bit__push__bit__iff__int,axiom,
% 3.82/4.10 ! [M2: nat,K: int,N2: nat] :
% 3.82/4.10 ( ( bit_se1146084159140164899it_int @ ( bit_se545348938243370406it_int @ M2 @ K ) @ N2 )
% 3.82/4.10 = ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.10 & ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % bit_push_bit_iff_int
% 3.82/4.10 thf(fact_7677_card__less__Suc2,axiom,
% 3.82/4.10 ! [M7: set_nat,I: nat] :
% 3.82/4.10 ( ~ ( member_nat @ zero_zero_nat @ M7 )
% 3.82/4.10 => ( ( finite_card_nat
% 3.82/4.10 @ ( collect_nat
% 3.82/4.10 @ ^ [K2: nat] :
% 3.82/4.10 ( ( member_nat @ ( suc @ K2 ) @ M7 )
% 3.82/4.10 & ( ord_less_nat @ K2 @ I ) ) ) )
% 3.82/4.10 = ( finite_card_nat
% 3.82/4.10 @ ( collect_nat
% 3.82/4.10 @ ^ [K2: nat] :
% 3.82/4.10 ( ( member_nat @ K2 @ M7 )
% 3.82/4.10 & ( ord_less_nat @ K2 @ ( suc @ I ) ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % card_less_Suc2
% 3.82/4.10 thf(fact_7678_card__less__Suc,axiom,
% 3.82/4.10 ! [M7: set_nat,I: nat] :
% 3.82/4.10 ( ( member_nat @ zero_zero_nat @ M7 )
% 3.82/4.10 => ( ( suc
% 3.82/4.10 @ ( finite_card_nat
% 3.82/4.10 @ ( collect_nat
% 3.82/4.10 @ ^ [K2: nat] :
% 3.82/4.10 ( ( member_nat @ ( suc @ K2 ) @ M7 )
% 3.82/4.10 & ( ord_less_nat @ K2 @ I ) ) ) ) )
% 3.82/4.10 = ( finite_card_nat
% 3.82/4.10 @ ( collect_nat
% 3.82/4.10 @ ^ [K2: nat] :
% 3.82/4.10 ( ( member_nat @ K2 @ M7 )
% 3.82/4.10 & ( ord_less_nat @ K2 @ ( suc @ I ) ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % card_less_Suc
% 3.82/4.10 thf(fact_7679_card__less,axiom,
% 3.82/4.10 ! [M7: set_nat,I: nat] :
% 3.82/4.10 ( ( member_nat @ zero_zero_nat @ M7 )
% 3.82/4.10 => ( ( finite_card_nat
% 3.82/4.10 @ ( collect_nat
% 3.82/4.10 @ ^ [K2: nat] :
% 3.82/4.10 ( ( member_nat @ K2 @ M7 )
% 3.82/4.10 & ( ord_less_nat @ K2 @ ( suc @ I ) ) ) ) )
% 3.82/4.10 != zero_zero_nat ) ) ).
% 3.82/4.10
% 3.82/4.10 % card_less
% 3.82/4.10 thf(fact_7680_bit__push__bit__iff__nat,axiom,
% 3.82/4.10 ! [M2: nat,Q3: nat,N2: nat] :
% 3.82/4.10 ( ( bit_se1148574629649215175it_nat @ ( bit_se547839408752420682it_nat @ M2 @ Q3 ) @ N2 )
% 3.82/4.10 = ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.10 & ( bit_se1148574629649215175it_nat @ Q3 @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % bit_push_bit_iff_nat
% 3.82/4.10 thf(fact_7681_subset__card__intvl__is__intvl,axiom,
% 3.82/4.10 ! [A2: set_nat,K: nat] :
% 3.82/4.10 ( ( ord_less_eq_set_nat @ A2 @ ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) )
% 3.82/4.10 => ( A2
% 3.82/4.10 = ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % subset_card_intvl_is_intvl
% 3.82/4.10 thf(fact_7682_less__eq__nat_Osimps_I2_J,axiom,
% 3.82/4.10 ! [M2: nat,N2: nat] :
% 3.82/4.10 ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N2 )
% 3.82/4.10 = ( case_nat_o @ $false @ ( ord_less_eq_nat @ M2 ) @ N2 ) ) ).
% 3.82/4.10
% 3.82/4.10 % less_eq_nat.simps(2)
% 3.82/4.10 thf(fact_7683_max__Suc2,axiom,
% 3.82/4.10 ! [M2: nat,N2: nat] :
% 3.82/4.10 ( ( ord_max_nat @ M2 @ ( suc @ N2 ) )
% 3.82/4.10 = ( case_nat_nat @ ( suc @ N2 )
% 3.82/4.10 @ ^ [M4: nat] : ( suc @ ( ord_max_nat @ M4 @ N2 ) )
% 3.82/4.10 @ M2 ) ) ).
% 3.82/4.10
% 3.82/4.10 % max_Suc2
% 3.82/4.10 thf(fact_7684_max__Suc1,axiom,
% 3.82/4.10 ! [N2: nat,M2: nat] :
% 3.82/4.10 ( ( ord_max_nat @ ( suc @ N2 ) @ M2 )
% 3.82/4.10 = ( case_nat_nat @ ( suc @ N2 )
% 3.82/4.10 @ ^ [M4: nat] : ( suc @ ( ord_max_nat @ N2 @ M4 ) )
% 3.82/4.10 @ M2 ) ) ).
% 3.82/4.10
% 3.82/4.10 % max_Suc1
% 3.82/4.10 thf(fact_7685_subset__eq__atLeast0__lessThan__card,axiom,
% 3.82/4.10 ! [N6: set_nat,N2: nat] :
% 3.82/4.10 ( ( ord_less_eq_set_nat @ N6 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 3.82/4.10 => ( ord_less_eq_nat @ ( finite_card_nat @ N6 ) @ N2 ) ) ).
% 3.82/4.10
% 3.82/4.10 % subset_eq_atLeast0_lessThan_card
% 3.82/4.10 thf(fact_7686_card__sum__le__nat__sum,axiom,
% 3.82/4.10 ! [S2: set_nat] :
% 3.82/4.10 ( ord_less_eq_nat
% 3.82/4.10 @ ( groups3542108847815614940at_nat
% 3.82/4.10 @ ^ [X4: nat] : X4
% 3.82/4.10 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( finite_card_nat @ S2 ) ) )
% 3.82/4.10 @ ( groups3542108847815614940at_nat
% 3.82/4.10 @ ^ [X4: nat] : X4
% 3.82/4.10 @ S2 ) ) ).
% 3.82/4.10
% 3.82/4.10 % card_sum_le_nat_sum
% 3.82/4.10 thf(fact_7687_card__nth__roots,axiom,
% 3.82/4.10 ! [C: complex,N2: nat] :
% 3.82/4.10 ( ( C != zero_zero_complex )
% 3.82/4.10 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( finite_card_complex
% 3.82/4.10 @ ( collect_complex
% 3.82/4.10 @ ^ [Z6: complex] :
% 3.82/4.10 ( ( power_power_complex @ Z6 @ N2 )
% 3.82/4.10 = C ) ) )
% 3.82/4.10 = N2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % card_nth_roots
% 3.82/4.10 thf(fact_7688_card__roots__unity__eq,axiom,
% 3.82/4.10 ! [N2: nat] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( finite_card_complex
% 3.82/4.10 @ ( collect_complex
% 3.82/4.10 @ ^ [Z6: complex] :
% 3.82/4.10 ( ( power_power_complex @ Z6 @ N2 )
% 3.82/4.10 = one_one_complex ) ) )
% 3.82/4.10 = N2 ) ) ).
% 3.82/4.10
% 3.82/4.10 % card_roots_unity_eq
% 3.82/4.10 thf(fact_7689_diff__Suc,axiom,
% 3.82/4.10 ! [M2: nat,N2: nat] :
% 3.82/4.10 ( ( minus_minus_nat @ M2 @ ( suc @ N2 ) )
% 3.82/4.10 = ( case_nat_nat @ zero_zero_nat
% 3.82/4.10 @ ^ [K2: nat] : K2
% 3.82/4.10 @ ( minus_minus_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % diff_Suc
% 3.82/4.10 thf(fact_7690_binomial__def,axiom,
% 3.82/4.10 ( binomial
% 3.82/4.10 = ( ^ [N: nat,K2: nat] :
% 3.82/4.10 ( finite_card_set_nat
% 3.82/4.10 @ ( collect_set_nat
% 3.82/4.10 @ ^ [K7: set_nat] :
% 3.82/4.10 ( ( member_set_nat @ K7 @ ( pow_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) )
% 3.82/4.10 & ( ( finite_card_nat @ K7 )
% 3.82/4.10 = K2 ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % binomial_def
% 3.82/4.10 thf(fact_7691_pred__def,axiom,
% 3.82/4.10 ( pred
% 3.82/4.10 = ( case_nat_nat @ zero_zero_nat
% 3.82/4.10 @ ^ [X24: nat] : X24 ) ) ).
% 3.82/4.10
% 3.82/4.10 % pred_def
% 3.82/4.10 thf(fact_7692_bezw__0,axiom,
% 3.82/4.10 ! [X: nat] :
% 3.82/4.10 ( ( bezw @ X @ zero_zero_nat )
% 3.82/4.10 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) ).
% 3.82/4.10
% 3.82/4.10 % bezw_0
% 3.82/4.10 thf(fact_7693_prod__decode__aux_Osimps,axiom,
% 3.82/4.10 ( nat_prod_decode_aux
% 3.82/4.10 = ( ^ [K2: nat,M: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ M @ K2 ) @ ( product_Pair_nat_nat @ M @ ( minus_minus_nat @ K2 @ M ) ) @ ( nat_prod_decode_aux @ ( suc @ K2 ) @ ( minus_minus_nat @ M @ ( suc @ K2 ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % prod_decode_aux.simps
% 3.82/4.10 thf(fact_7694_prod__decode__aux_Oelims,axiom,
% 3.82/4.10 ! [X: nat,Xa2: nat,Y: product_prod_nat_nat] :
% 3.82/4.10 ( ( ( nat_prod_decode_aux @ X @ Xa2 )
% 3.82/4.10 = Y )
% 3.82/4.10 => ( ( ( ord_less_eq_nat @ Xa2 @ X )
% 3.82/4.10 => ( Y
% 3.82/4.10 = ( product_Pair_nat_nat @ Xa2 @ ( minus_minus_nat @ X @ Xa2 ) ) ) )
% 3.82/4.10 & ( ~ ( ord_less_eq_nat @ Xa2 @ X )
% 3.82/4.10 => ( Y
% 3.82/4.10 = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa2 @ ( suc @ X ) ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % prod_decode_aux.elims
% 3.82/4.10 thf(fact_7695_finite__enumerate,axiom,
% 3.82/4.10 ! [S2: set_nat] :
% 3.82/4.10 ( ( finite_finite_nat @ S2 )
% 3.82/4.10 => ? [R3: nat > nat] :
% 3.82/4.10 ( ( strict1292158309912662752at_nat @ R3 @ ( set_ord_lessThan_nat @ ( finite_card_nat @ S2 ) ) )
% 3.82/4.10 & ! [N7: nat] :
% 3.82/4.10 ( ( ord_less_nat @ N7 @ ( finite_card_nat @ S2 ) )
% 3.82/4.10 => ( member_nat @ ( R3 @ N7 ) @ S2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % finite_enumerate
% 3.82/4.10 thf(fact_7696_root__powr__inverse,axiom,
% 3.82/4.10 ! [N2: nat,X: real] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( ord_less_real @ zero_zero_real @ X )
% 3.82/4.10 => ( ( root @ N2 @ X )
% 3.82/4.10 = ( powr_real @ X @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % root_powr_inverse
% 3.82/4.10 thf(fact_7697_real__root__Suc__0,axiom,
% 3.82/4.10 ! [X: real] :
% 3.82/4.10 ( ( root @ ( suc @ zero_zero_nat ) @ X )
% 3.82/4.10 = X ) ).
% 3.82/4.10
% 3.82/4.10 % real_root_Suc_0
% 3.82/4.10 thf(fact_7698_root__0,axiom,
% 3.82/4.10 ! [X: real] :
% 3.82/4.10 ( ( root @ zero_zero_nat @ X )
% 3.82/4.10 = zero_zero_real ) ).
% 3.82/4.10
% 3.82/4.10 % root_0
% 3.82/4.10 thf(fact_7699_real__root__eq__iff,axiom,
% 3.82/4.10 ! [N2: nat,X: real,Y: real] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( ( root @ N2 @ X )
% 3.82/4.10 = ( root @ N2 @ Y ) )
% 3.82/4.10 = ( X = Y ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % real_root_eq_iff
% 3.82/4.10 thf(fact_7700_drop__bit__of__Suc__0,axiom,
% 3.82/4.10 ! [N2: nat] :
% 3.82/4.10 ( ( bit_se8570568707652914677it_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 3.82/4.10 = ( zero_n2687167440665602831ol_nat @ ( N2 = zero_zero_nat ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % drop_bit_of_Suc_0
% 3.82/4.10 thf(fact_7701_drop__bit__Suc__minus__bit0,axiom,
% 3.82/4.10 ! [N2: nat,K: num] :
% 3.82/4.10 ( ( bit_se8568078237143864401it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 3.82/4.10 = ( bit_se8568078237143864401it_int @ N2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % drop_bit_Suc_minus_bit0
% 3.82/4.10 thf(fact_7702_real__root__eq__0__iff,axiom,
% 3.82/4.10 ! [N2: nat,X: real] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( ( root @ N2 @ X )
% 3.82/4.10 = zero_zero_real )
% 3.82/4.10 = ( X = zero_zero_real ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % real_root_eq_0_iff
% 3.82/4.10 thf(fact_7703_real__root__less__iff,axiom,
% 3.82/4.10 ! [N2: nat,X: real,Y: real] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( ord_less_real @ ( root @ N2 @ X ) @ ( root @ N2 @ Y ) )
% 3.82/4.10 = ( ord_less_real @ X @ Y ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % real_root_less_iff
% 3.82/4.10 thf(fact_7704_real__root__le__iff,axiom,
% 3.82/4.10 ! [N2: nat,X: real,Y: real] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( ord_less_eq_real @ ( root @ N2 @ X ) @ ( root @ N2 @ Y ) )
% 3.82/4.10 = ( ord_less_eq_real @ X @ Y ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % real_root_le_iff
% 3.82/4.10 thf(fact_7705_real__root__one,axiom,
% 3.82/4.10 ! [N2: nat] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( root @ N2 @ one_one_real )
% 3.82/4.10 = one_one_real ) ) ).
% 3.82/4.10
% 3.82/4.10 % real_root_one
% 3.82/4.10 thf(fact_7706_real__root__eq__1__iff,axiom,
% 3.82/4.10 ! [N2: nat,X: real] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( ( root @ N2 @ X )
% 3.82/4.10 = one_one_real )
% 3.82/4.10 = ( X = one_one_real ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % real_root_eq_1_iff
% 3.82/4.10 thf(fact_7707_real__root__gt__0__iff,axiom,
% 3.82/4.10 ! [N2: nat,Y: real] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( ord_less_real @ zero_zero_real @ ( root @ N2 @ Y ) )
% 3.82/4.10 = ( ord_less_real @ zero_zero_real @ Y ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % real_root_gt_0_iff
% 3.82/4.10 thf(fact_7708_real__root__lt__0__iff,axiom,
% 3.82/4.10 ! [N2: nat,X: real] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( ord_less_real @ ( root @ N2 @ X ) @ zero_zero_real )
% 3.82/4.10 = ( ord_less_real @ X @ zero_zero_real ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % real_root_lt_0_iff
% 3.82/4.10 thf(fact_7709_real__root__ge__0__iff,axiom,
% 3.82/4.10 ! [N2: nat,Y: real] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( ord_less_eq_real @ zero_zero_real @ ( root @ N2 @ Y ) )
% 3.82/4.10 = ( ord_less_eq_real @ zero_zero_real @ Y ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % real_root_ge_0_iff
% 3.82/4.10 thf(fact_7710_real__root__le__0__iff,axiom,
% 3.82/4.10 ! [N2: nat,X: real] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( ord_less_eq_real @ ( root @ N2 @ X ) @ zero_zero_real )
% 3.82/4.10 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % real_root_le_0_iff
% 3.82/4.10 thf(fact_7711_real__root__gt__1__iff,axiom,
% 3.82/4.10 ! [N2: nat,Y: real] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( ord_less_real @ one_one_real @ ( root @ N2 @ Y ) )
% 3.82/4.10 = ( ord_less_real @ one_one_real @ Y ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % real_root_gt_1_iff
% 3.82/4.10 thf(fact_7712_real__root__lt__1__iff,axiom,
% 3.82/4.10 ! [N2: nat,X: real] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( ord_less_real @ ( root @ N2 @ X ) @ one_one_real )
% 3.82/4.10 = ( ord_less_real @ X @ one_one_real ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % real_root_lt_1_iff
% 3.82/4.10 thf(fact_7713_real__root__ge__1__iff,axiom,
% 3.82/4.10 ! [N2: nat,Y: real] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( ord_less_eq_real @ one_one_real @ ( root @ N2 @ Y ) )
% 3.82/4.10 = ( ord_less_eq_real @ one_one_real @ Y ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % real_root_ge_1_iff
% 3.82/4.10 thf(fact_7714_real__root__le__1__iff,axiom,
% 3.82/4.10 ! [N2: nat,X: real] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( ord_less_eq_real @ ( root @ N2 @ X ) @ one_one_real )
% 3.82/4.10 = ( ord_less_eq_real @ X @ one_one_real ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % real_root_le_1_iff
% 3.82/4.10 thf(fact_7715_drop__bit__Suc__minus__bit1,axiom,
% 3.82/4.10 ! [N2: nat,K: num] :
% 3.82/4.10 ( ( bit_se8568078237143864401it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 3.82/4.10 = ( bit_se8568078237143864401it_int @ N2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % drop_bit_Suc_minus_bit1
% 3.82/4.10 thf(fact_7716_real__root__pow__pos2,axiom,
% 3.82/4.10 ! [N2: nat,X: real] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 3.82/4.10 => ( ( power_power_real @ ( root @ N2 @ X ) @ N2 )
% 3.82/4.10 = X ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % real_root_pow_pos2
% 3.82/4.10 thf(fact_7717_real__root__less__mono,axiom,
% 3.82/4.10 ! [N2: nat,X: real,Y: real] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( ord_less_real @ X @ Y )
% 3.82/4.10 => ( ord_less_real @ ( root @ N2 @ X ) @ ( root @ N2 @ Y ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % real_root_less_mono
% 3.82/4.10 thf(fact_7718_real__root__le__mono,axiom,
% 3.82/4.10 ! [N2: nat,X: real,Y: real] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( ord_less_eq_real @ X @ Y )
% 3.82/4.10 => ( ord_less_eq_real @ ( root @ N2 @ X ) @ ( root @ N2 @ Y ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % real_root_le_mono
% 3.82/4.10 thf(fact_7719_real__root__power,axiom,
% 3.82/4.10 ! [N2: nat,X: real,K: nat] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( root @ N2 @ ( power_power_real @ X @ K ) )
% 3.82/4.10 = ( power_power_real @ ( root @ N2 @ X ) @ K ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % real_root_power
% 3.82/4.10 thf(fact_7720_real__root__abs,axiom,
% 3.82/4.10 ! [N2: nat,X: real] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( root @ N2 @ ( abs_abs_real @ X ) )
% 3.82/4.10 = ( abs_abs_real @ ( root @ N2 @ X ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % real_root_abs
% 3.82/4.10 thf(fact_7721_sgn__root,axiom,
% 3.82/4.10 ! [N2: nat,X: real] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( sgn_sgn_real @ ( root @ N2 @ X ) )
% 3.82/4.10 = ( sgn_sgn_real @ X ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % sgn_root
% 3.82/4.10 thf(fact_7722_real__root__gt__zero,axiom,
% 3.82/4.10 ! [N2: nat,X: real] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( ord_less_real @ zero_zero_real @ X )
% 3.82/4.10 => ( ord_less_real @ zero_zero_real @ ( root @ N2 @ X ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % real_root_gt_zero
% 3.82/4.10 thf(fact_7723_real__root__strict__decreasing,axiom,
% 3.82/4.10 ! [N2: nat,N6: nat,X: real] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( ord_less_nat @ N2 @ N6 )
% 3.82/4.10 => ( ( ord_less_real @ one_one_real @ X )
% 3.82/4.10 => ( ord_less_real @ ( root @ N6 @ X ) @ ( root @ N2 @ X ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % real_root_strict_decreasing
% 3.82/4.10 thf(fact_7724_root__abs__power,axiom,
% 3.82/4.10 ! [N2: nat,Y: real] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( abs_abs_real @ ( root @ N2 @ ( power_power_real @ Y @ N2 ) ) )
% 3.82/4.10 = ( abs_abs_real @ Y ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % root_abs_power
% 3.82/4.10 thf(fact_7725_real__root__pos__pos,axiom,
% 3.82/4.10 ! [N2: nat,X: real] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( ord_less_real @ zero_zero_real @ X )
% 3.82/4.10 => ( ord_less_eq_real @ zero_zero_real @ ( root @ N2 @ X ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % real_root_pos_pos
% 3.82/4.10 thf(fact_7726_real__root__strict__increasing,axiom,
% 3.82/4.10 ! [N2: nat,N6: nat,X: real] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( ord_less_nat @ N2 @ N6 )
% 3.82/4.10 => ( ( ord_less_real @ zero_zero_real @ X )
% 3.82/4.10 => ( ( ord_less_real @ X @ one_one_real )
% 3.82/4.10 => ( ord_less_real @ ( root @ N2 @ X ) @ ( root @ N6 @ X ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % real_root_strict_increasing
% 3.82/4.10 thf(fact_7727_real__root__decreasing,axiom,
% 3.82/4.10 ! [N2: nat,N6: nat,X: real] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( ord_less_eq_nat @ N2 @ N6 )
% 3.82/4.10 => ( ( ord_less_eq_real @ one_one_real @ X )
% 3.82/4.10 => ( ord_less_eq_real @ ( root @ N6 @ X ) @ ( root @ N2 @ X ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % real_root_decreasing
% 3.82/4.10 thf(fact_7728_real__root__pow__pos,axiom,
% 3.82/4.10 ! [N2: nat,X: real] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( ord_less_real @ zero_zero_real @ X )
% 3.82/4.10 => ( ( power_power_real @ ( root @ N2 @ X ) @ N2 )
% 3.82/4.10 = X ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % real_root_pow_pos
% 3.82/4.10 thf(fact_7729_real__root__pos__unique,axiom,
% 3.82/4.10 ! [N2: nat,Y: real,X: real] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 3.82/4.10 => ( ( ( power_power_real @ Y @ N2 )
% 3.82/4.10 = X )
% 3.82/4.10 => ( ( root @ N2 @ X )
% 3.82/4.10 = Y ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % real_root_pos_unique
% 3.82/4.10 thf(fact_7730_real__root__power__cancel,axiom,
% 3.82/4.10 ! [N2: nat,X: real] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 3.82/4.10 => ( ( root @ N2 @ ( power_power_real @ X @ N2 ) )
% 3.82/4.10 = X ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % real_root_power_cancel
% 3.82/4.10 thf(fact_7731_real__root__increasing,axiom,
% 3.82/4.10 ! [N2: nat,N6: nat,X: real] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( ord_less_eq_nat @ N2 @ N6 )
% 3.82/4.10 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 3.82/4.10 => ( ( ord_less_eq_real @ X @ one_one_real )
% 3.82/4.10 => ( ord_less_eq_real @ ( root @ N2 @ X ) @ ( root @ N6 @ X ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % real_root_increasing
% 3.82/4.10 thf(fact_7732_root__sgn__power,axiom,
% 3.82/4.10 ! [N2: nat,Y: real] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( root @ N2 @ ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N2 ) ) )
% 3.82/4.10 = Y ) ) ).
% 3.82/4.10
% 3.82/4.10 % root_sgn_power
% 3.82/4.10 thf(fact_7733_sgn__power__root,axiom,
% 3.82/4.10 ! [N2: nat,X: real] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( times_times_real @ ( sgn_sgn_real @ ( root @ N2 @ X ) ) @ ( power_power_real @ ( abs_abs_real @ ( root @ N2 @ X ) ) @ N2 ) )
% 3.82/4.10 = X ) ) ).
% 3.82/4.10
% 3.82/4.10 % sgn_power_root
% 3.82/4.10 thf(fact_7734_ln__root,axiom,
% 3.82/4.10 ! [N2: nat,B2: real] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( ord_less_real @ zero_zero_real @ B2 )
% 3.82/4.10 => ( ( ln_ln_real @ ( root @ N2 @ B2 ) )
% 3.82/4.10 = ( divide_divide_real @ ( ln_ln_real @ B2 ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % ln_root
% 3.82/4.10 thf(fact_7735_log__root,axiom,
% 3.82/4.10 ! [N2: nat,A: real,B2: real] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( ord_less_real @ zero_zero_real @ A )
% 3.82/4.10 => ( ( log @ B2 @ ( root @ N2 @ A ) )
% 3.82/4.10 = ( divide_divide_real @ ( log @ B2 @ A ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % log_root
% 3.82/4.10 thf(fact_7736_log__base__root,axiom,
% 3.82/4.10 ! [N2: nat,B2: real,X: real] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( ord_less_real @ zero_zero_real @ B2 )
% 3.82/4.10 => ( ( log @ ( root @ N2 @ B2 ) @ X )
% 3.82/4.10 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ B2 @ X ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % log_base_root
% 3.82/4.10 thf(fact_7737_split__root,axiom,
% 3.82/4.10 ! [P: real > $o,N2: nat,X: real] :
% 3.82/4.10 ( ( P @ ( root @ N2 @ X ) )
% 3.82/4.10 = ( ( ( N2 = zero_zero_nat )
% 3.82/4.10 => ( P @ zero_zero_real ) )
% 3.82/4.10 & ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ! [Y5: real] :
% 3.82/4.10 ( ( ( times_times_real @ ( sgn_sgn_real @ Y5 ) @ ( power_power_real @ ( abs_abs_real @ Y5 ) @ N2 ) )
% 3.82/4.10 = X )
% 3.82/4.10 => ( P @ Y5 ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % split_root
% 3.82/4.10 thf(fact_7738_Sup__nat__empty,axiom,
% 3.82/4.10 ( ( complete_Sup_Sup_nat @ bot_bot_set_nat )
% 3.82/4.10 = zero_zero_nat ) ).
% 3.82/4.10
% 3.82/4.10 % Sup_nat_empty
% 3.82/4.10 thf(fact_7739_Inf__nat__def1,axiom,
% 3.82/4.10 ! [K5: set_nat] :
% 3.82/4.10 ( ( K5 != bot_bot_set_nat )
% 3.82/4.10 => ( member_nat @ ( complete_Inf_Inf_nat @ K5 ) @ K5 ) ) ).
% 3.82/4.10
% 3.82/4.10 % Inf_nat_def1
% 3.82/4.10 thf(fact_7740_card__greaterThanLessThan__int,axiom,
% 3.82/4.10 ! [L: int,U: int] :
% 3.82/4.10 ( ( finite_card_int @ ( set_or5832277885323065728an_int @ L @ U ) )
% 3.82/4.10 = ( nat2 @ ( minus_minus_int @ U @ ( plus_plus_int @ L @ one_one_int ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % card_greaterThanLessThan_int
% 3.82/4.10 thf(fact_7741_Suc__funpow,axiom,
% 3.82/4.10 ! [N2: nat] :
% 3.82/4.10 ( ( compow_nat_nat @ N2 @ suc )
% 3.82/4.10 = ( plus_plus_nat @ N2 ) ) ).
% 3.82/4.10
% 3.82/4.10 % Suc_funpow
% 3.82/4.10 thf(fact_7742_finite__greaterThanLessThan__int,axiom,
% 3.82/4.10 ! [L: int,U: int] : ( finite_finite_int @ ( set_or5832277885323065728an_int @ L @ U ) ) ).
% 3.82/4.10
% 3.82/4.10 % finite_greaterThanLessThan_int
% 3.82/4.10 thf(fact_7743_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 3.82/4.10 ! [L: int,U: int] :
% 3.82/4.10 ( ( set_or4662586982721622107an_int @ ( plus_plus_int @ L @ one_one_int ) @ U )
% 3.82/4.10 = ( set_or5832277885323065728an_int @ L @ U ) ) ).
% 3.82/4.10
% 3.82/4.10 % atLeastPlusOneLessThan_greaterThanLessThan_int
% 3.82/4.10 thf(fact_7744_finite__greaterThanLessThan,axiom,
% 3.82/4.10 ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or5834768355832116004an_nat @ L @ U ) ) ).
% 3.82/4.10
% 3.82/4.10 % finite_greaterThanLessThan
% 3.82/4.10 thf(fact_7745_card__greaterThanLessThan,axiom,
% 3.82/4.10 ! [L: nat,U: nat] :
% 3.82/4.10 ( ( finite_card_nat @ ( set_or5834768355832116004an_nat @ L @ U ) )
% 3.82/4.10 = ( minus_minus_nat @ U @ ( suc @ L ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % card_greaterThanLessThan
% 3.82/4.10 thf(fact_7746_atLeastSucLessThan__greaterThanLessThan,axiom,
% 3.82/4.10 ! [L: nat,U: nat] :
% 3.82/4.10 ( ( set_or4665077453230672383an_nat @ ( suc @ L ) @ U )
% 3.82/4.10 = ( set_or5834768355832116004an_nat @ L @ U ) ) ).
% 3.82/4.10
% 3.82/4.10 % atLeastSucLessThan_greaterThanLessThan
% 3.82/4.10 thf(fact_7747_max__nat_Osemilattice__neutr__order__axioms,axiom,
% 3.82/4.10 ( semila1623282765462674594er_nat @ ord_max_nat @ zero_zero_nat
% 3.82/4.10 @ ^ [X4: nat,Y5: nat] : ( ord_less_eq_nat @ Y5 @ X4 )
% 3.82/4.10 @ ^ [X4: nat,Y5: nat] : ( ord_less_nat @ Y5 @ X4 ) ) ).
% 3.82/4.10
% 3.82/4.10 % max_nat.semilattice_neutr_order_axioms
% 3.82/4.10 thf(fact_7748_times__int_Oabs__eq,axiom,
% 3.82/4.10 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 3.82/4.10 ( ( times_times_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 3.82/4.10 = ( abs_Integ
% 3.82/4.10 @ ( produc27273713700761075at_nat
% 3.82/4.10 @ ^ [X4: nat,Y5: nat] :
% 3.82/4.10 ( produc2626176000494625587at_nat
% 3.82/4.10 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X4 @ U2 ) @ ( times_times_nat @ Y5 @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X4 @ V4 ) @ ( times_times_nat @ Y5 @ U2 ) ) ) )
% 3.82/4.10 @ Xa2
% 3.82/4.10 @ X ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % times_int.abs_eq
% 3.82/4.10 thf(fact_7749_Gcd__remove0__nat,axiom,
% 3.82/4.10 ! [M7: set_nat] :
% 3.82/4.10 ( ( finite_finite_nat @ M7 )
% 3.82/4.10 => ( ( gcd_Gcd_nat @ M7 )
% 3.82/4.10 = ( gcd_Gcd_nat @ ( minus_minus_set_nat @ M7 @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % Gcd_remove0_nat
% 3.82/4.10 thf(fact_7750_int_Oabs__induct,axiom,
% 3.82/4.10 ! [P: int > $o,X: int] :
% 3.82/4.10 ( ! [Y3: product_prod_nat_nat] : ( P @ ( abs_Integ @ Y3 ) )
% 3.82/4.10 => ( P @ X ) ) ).
% 3.82/4.10
% 3.82/4.10 % int.abs_induct
% 3.82/4.10 thf(fact_7751_eq__Abs__Integ,axiom,
% 3.82/4.10 ! [Z3: int] :
% 3.82/4.10 ~ ! [X5: nat,Y3: nat] :
% 3.82/4.10 ( Z3
% 3.82/4.10 != ( abs_Integ @ ( product_Pair_nat_nat @ X5 @ Y3 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % eq_Abs_Integ
% 3.82/4.10 thf(fact_7752_nat_Oabs__eq,axiom,
% 3.82/4.10 ! [X: product_prod_nat_nat] :
% 3.82/4.10 ( ( nat2 @ ( abs_Integ @ X ) )
% 3.82/4.10 = ( produc6842872674320459806at_nat @ minus_minus_nat @ X ) ) ).
% 3.82/4.10
% 3.82/4.10 % nat.abs_eq
% 3.82/4.10 thf(fact_7753_zero__int__def,axiom,
% 3.82/4.10 ( zero_zero_int
% 3.82/4.10 = ( abs_Integ @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % zero_int_def
% 3.82/4.10 thf(fact_7754_int__def,axiom,
% 3.82/4.10 ( semiri1314217659103216013at_int
% 3.82/4.10 = ( ^ [N: nat] : ( abs_Integ @ ( product_Pair_nat_nat @ N @ zero_zero_nat ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % int_def
% 3.82/4.10 thf(fact_7755_uminus__int_Oabs__eq,axiom,
% 3.82/4.10 ! [X: product_prod_nat_nat] :
% 3.82/4.10 ( ( uminus_uminus_int @ ( abs_Integ @ X ) )
% 3.82/4.10 = ( abs_Integ
% 3.82/4.10 @ ( produc2626176000494625587at_nat
% 3.82/4.10 @ ^ [X4: nat,Y5: nat] : ( product_Pair_nat_nat @ Y5 @ X4 )
% 3.82/4.10 @ X ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % uminus_int.abs_eq
% 3.82/4.10 thf(fact_7756_one__int__def,axiom,
% 3.82/4.10 ( one_one_int
% 3.82/4.10 = ( abs_Integ @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % one_int_def
% 3.82/4.10 thf(fact_7757_less__int_Oabs__eq,axiom,
% 3.82/4.10 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 3.82/4.10 ( ( ord_less_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 3.82/4.10 = ( produc8739625826339149834_nat_o
% 3.82/4.10 @ ^ [X4: nat,Y5: nat] :
% 3.82/4.10 ( produc6081775807080527818_nat_o
% 3.82/4.10 @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X4 @ V4 ) @ ( plus_plus_nat @ U2 @ Y5 ) ) )
% 3.82/4.10 @ Xa2
% 3.82/4.10 @ X ) ) ).
% 3.82/4.10
% 3.82/4.10 % less_int.abs_eq
% 3.82/4.10 thf(fact_7758_less__eq__int_Oabs__eq,axiom,
% 3.82/4.10 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 3.82/4.10 ( ( ord_less_eq_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 3.82/4.10 = ( produc8739625826339149834_nat_o
% 3.82/4.10 @ ^ [X4: nat,Y5: nat] :
% 3.82/4.10 ( produc6081775807080527818_nat_o
% 3.82/4.10 @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X4 @ V4 ) @ ( plus_plus_nat @ U2 @ Y5 ) ) )
% 3.82/4.10 @ Xa2
% 3.82/4.10 @ X ) ) ).
% 3.82/4.10
% 3.82/4.10 % less_eq_int.abs_eq
% 3.82/4.10 thf(fact_7759_plus__int_Oabs__eq,axiom,
% 3.82/4.10 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 3.82/4.10 ( ( plus_plus_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 3.82/4.10 = ( abs_Integ
% 3.82/4.10 @ ( produc27273713700761075at_nat
% 3.82/4.10 @ ^ [X4: nat,Y5: nat] :
% 3.82/4.10 ( produc2626176000494625587at_nat
% 3.82/4.10 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ U2 ) @ ( plus_plus_nat @ Y5 @ V4 ) ) )
% 3.82/4.10 @ Xa2
% 3.82/4.10 @ X ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % plus_int.abs_eq
% 3.82/4.10 thf(fact_7760_minus__int_Oabs__eq,axiom,
% 3.82/4.10 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 3.82/4.10 ( ( minus_minus_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 3.82/4.10 = ( abs_Integ
% 3.82/4.10 @ ( produc27273713700761075at_nat
% 3.82/4.10 @ ^ [X4: nat,Y5: nat] :
% 3.82/4.10 ( produc2626176000494625587at_nat
% 3.82/4.10 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ V4 ) @ ( plus_plus_nat @ Y5 @ U2 ) ) )
% 3.82/4.10 @ Xa2
% 3.82/4.10 @ X ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % minus_int.abs_eq
% 3.82/4.10 thf(fact_7761_num__of__nat_Osimps_I2_J,axiom,
% 3.82/4.10 ! [N2: nat] :
% 3.82/4.10 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( num_of_nat @ ( suc @ N2 ) )
% 3.82/4.10 = ( inc @ ( num_of_nat @ N2 ) ) ) )
% 3.82/4.10 & ( ~ ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( num_of_nat @ ( suc @ N2 ) )
% 3.82/4.10 = one ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % num_of_nat.simps(2)
% 3.82/4.10 thf(fact_7762_num__of__nat_Osimps_I1_J,axiom,
% 3.82/4.10 ( ( num_of_nat @ zero_zero_nat )
% 3.82/4.10 = one ) ).
% 3.82/4.10
% 3.82/4.10 % num_of_nat.simps(1)
% 3.82/4.10 thf(fact_7763_numeral__num__of__nat,axiom,
% 3.82/4.10 ! [N2: nat] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( numeral_numeral_nat @ ( num_of_nat @ N2 ) )
% 3.82/4.10 = N2 ) ) ).
% 3.82/4.10
% 3.82/4.10 % numeral_num_of_nat
% 3.82/4.10 thf(fact_7764_num__of__nat__One,axiom,
% 3.82/4.10 ! [N2: nat] :
% 3.82/4.10 ( ( ord_less_eq_nat @ N2 @ one_one_nat )
% 3.82/4.10 => ( ( num_of_nat @ N2 )
% 3.82/4.10 = one ) ) ).
% 3.82/4.10
% 3.82/4.10 % num_of_nat_One
% 3.82/4.10 thf(fact_7765_num__of__nat__double,axiom,
% 3.82/4.10 ! [N2: nat] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( num_of_nat @ ( plus_plus_nat @ N2 @ N2 ) )
% 3.82/4.10 = ( bit0 @ ( num_of_nat @ N2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % num_of_nat_double
% 3.82/4.10 thf(fact_7766_num__of__nat__plus__distrib,axiom,
% 3.82/4.10 ! [M2: nat,N2: nat] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 3.82/4.10 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( num_of_nat @ ( plus_plus_nat @ M2 @ N2 ) )
% 3.82/4.10 = ( plus_plus_num @ ( num_of_nat @ M2 ) @ ( num_of_nat @ N2 ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % num_of_nat_plus_distrib
% 3.82/4.10 thf(fact_7767_nth__sorted__list__of__set__greaterThanLessThan,axiom,
% 3.82/4.10 ! [N2: nat,J: nat,I: nat] :
% 3.82/4.10 ( ( ord_less_nat @ N2 @ ( minus_minus_nat @ J @ ( suc @ I ) ) )
% 3.82/4.10 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I @ J ) ) @ N2 )
% 3.82/4.10 = ( suc @ ( plus_plus_nat @ I @ N2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % nth_sorted_list_of_set_greaterThanLessThan
% 3.82/4.10 thf(fact_7768_less__eq__int_Orep__eq,axiom,
% 3.82/4.10 ( ord_less_eq_int
% 3.82/4.10 = ( ^ [X4: int,Xa3: int] :
% 3.82/4.10 ( produc8739625826339149834_nat_o
% 3.82/4.10 @ ^ [Y5: nat,Z6: nat] :
% 3.82/4.10 ( produc6081775807080527818_nat_o
% 3.82/4.10 @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ Y5 @ V4 ) @ ( plus_plus_nat @ U2 @ Z6 ) ) )
% 3.82/4.10 @ ( rep_Integ @ X4 )
% 3.82/4.10 @ ( rep_Integ @ Xa3 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % less_eq_int.rep_eq
% 3.82/4.10 thf(fact_7769_less__int_Orep__eq,axiom,
% 3.82/4.10 ( ord_less_int
% 3.82/4.10 = ( ^ [X4: int,Xa3: int] :
% 3.82/4.10 ( produc8739625826339149834_nat_o
% 3.82/4.10 @ ^ [Y5: nat,Z6: nat] :
% 3.82/4.10 ( produc6081775807080527818_nat_o
% 3.82/4.10 @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ Y5 @ V4 ) @ ( plus_plus_nat @ U2 @ Z6 ) ) )
% 3.82/4.10 @ ( rep_Integ @ X4 )
% 3.82/4.10 @ ( rep_Integ @ Xa3 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % less_int.rep_eq
% 3.82/4.10 thf(fact_7770_nat_Orep__eq,axiom,
% 3.82/4.10 ( nat2
% 3.82/4.10 = ( ^ [X4: int] : ( produc6842872674320459806at_nat @ minus_minus_nat @ ( rep_Integ @ X4 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % nat.rep_eq
% 3.82/4.10 thf(fact_7771_nth__sorted__list__of__set__greaterThanAtMost,axiom,
% 3.82/4.10 ! [N2: nat,J: nat,I: nat] :
% 3.82/4.10 ( ( ord_less_nat @ N2 @ ( minus_minus_nat @ J @ I ) )
% 3.82/4.10 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I @ J ) ) @ N2 )
% 3.82/4.10 = ( suc @ ( plus_plus_nat @ I @ N2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % nth_sorted_list_of_set_greaterThanAtMost
% 3.82/4.10 thf(fact_7772_uminus__int__def,axiom,
% 3.82/4.10 ( uminus_uminus_int
% 3.82/4.10 = ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ
% 3.82/4.10 @ ( produc2626176000494625587at_nat
% 3.82/4.10 @ ^ [X4: nat,Y5: nat] : ( product_Pair_nat_nat @ Y5 @ X4 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % uminus_int_def
% 3.82/4.10 thf(fact_7773_prod__encode__def,axiom,
% 3.82/4.10 ( nat_prod_encode
% 3.82/4.10 = ( produc6842872674320459806at_nat
% 3.82/4.10 @ ^ [M: nat,N: nat] : ( plus_plus_nat @ ( nat_triangle @ ( plus_plus_nat @ M @ N ) ) @ M ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % prod_encode_def
% 3.82/4.10 thf(fact_7774_finite__greaterThanAtMost,axiom,
% 3.82/4.10 ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or6659071591806873216st_nat @ L @ U ) ) ).
% 3.82/4.10
% 3.82/4.10 % finite_greaterThanAtMost
% 3.82/4.10 thf(fact_7775_card__greaterThanAtMost,axiom,
% 3.82/4.10 ! [L: nat,U: nat] :
% 3.82/4.10 ( ( finite_card_nat @ ( set_or6659071591806873216st_nat @ L @ U ) )
% 3.82/4.10 = ( minus_minus_nat @ U @ L ) ) ).
% 3.82/4.10
% 3.82/4.10 % card_greaterThanAtMost
% 3.82/4.10 thf(fact_7776_atLeastSucAtMost__greaterThanAtMost,axiom,
% 3.82/4.10 ! [L: nat,U: nat] :
% 3.82/4.10 ( ( set_or1269000886237332187st_nat @ ( suc @ L ) @ U )
% 3.82/4.10 = ( set_or6659071591806873216st_nat @ L @ U ) ) ).
% 3.82/4.10
% 3.82/4.10 % atLeastSucAtMost_greaterThanAtMost
% 3.82/4.10 thf(fact_7777_le__prod__encode__1,axiom,
% 3.82/4.10 ! [A: nat,B2: nat] : ( ord_less_eq_nat @ A @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % le_prod_encode_1
% 3.82/4.10 thf(fact_7778_le__prod__encode__2,axiom,
% 3.82/4.10 ! [B2: nat,A: nat] : ( ord_less_eq_nat @ B2 @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % le_prod_encode_2
% 3.82/4.10 thf(fact_7779_prod__encode__prod__decode__aux,axiom,
% 3.82/4.10 ! [K: nat,M2: nat] :
% 3.82/4.10 ( ( nat_prod_encode @ ( nat_prod_decode_aux @ K @ M2 ) )
% 3.82/4.10 = ( plus_plus_nat @ ( nat_triangle @ K ) @ M2 ) ) ).
% 3.82/4.10
% 3.82/4.10 % prod_encode_prod_decode_aux
% 3.82/4.10 thf(fact_7780_times__int__def,axiom,
% 3.82/4.10 ( times_times_int
% 3.82/4.10 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 3.82/4.10 @ ( produc27273713700761075at_nat
% 3.82/4.10 @ ^ [X4: nat,Y5: nat] :
% 3.82/4.10 ( produc2626176000494625587at_nat
% 3.82/4.10 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X4 @ U2 ) @ ( times_times_nat @ Y5 @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X4 @ V4 ) @ ( times_times_nat @ Y5 @ U2 ) ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % times_int_def
% 3.82/4.10 thf(fact_7781_minus__int__def,axiom,
% 3.82/4.10 ( minus_minus_int
% 3.82/4.10 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 3.82/4.10 @ ( produc27273713700761075at_nat
% 3.82/4.10 @ ^ [X4: nat,Y5: nat] :
% 3.82/4.10 ( produc2626176000494625587at_nat
% 3.82/4.10 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ V4 ) @ ( plus_plus_nat @ Y5 @ U2 ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % minus_int_def
% 3.82/4.10 thf(fact_7782_plus__int__def,axiom,
% 3.82/4.10 ( plus_plus_int
% 3.82/4.10 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 3.82/4.10 @ ( produc27273713700761075at_nat
% 3.82/4.10 @ ^ [X4: nat,Y5: nat] :
% 3.82/4.10 ( produc2626176000494625587at_nat
% 3.82/4.10 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ U2 ) @ ( plus_plus_nat @ Y5 @ V4 ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % plus_int_def
% 3.82/4.10 thf(fact_7783_image__minus__const__atLeastLessThan__nat,axiom,
% 3.82/4.10 ! [C: nat,Y: nat,X: nat] :
% 3.82/4.10 ( ( ( ord_less_nat @ C @ Y )
% 3.82/4.10 => ( ( image_nat_nat
% 3.82/4.10 @ ^ [I3: nat] : ( minus_minus_nat @ I3 @ C )
% 3.82/4.10 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 3.82/4.10 = ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ X @ C ) @ ( minus_minus_nat @ Y @ C ) ) ) )
% 3.82/4.10 & ( ~ ( ord_less_nat @ C @ Y )
% 3.82/4.10 => ( ( ( ord_less_nat @ X @ Y )
% 3.82/4.10 => ( ( image_nat_nat
% 3.82/4.10 @ ^ [I3: nat] : ( minus_minus_nat @ I3 @ C )
% 3.82/4.10 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 3.82/4.10 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 3.82/4.10 & ( ~ ( ord_less_nat @ X @ Y )
% 3.82/4.10 => ( ( image_nat_nat
% 3.82/4.10 @ ^ [I3: nat] : ( minus_minus_nat @ I3 @ C )
% 3.82/4.10 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 3.82/4.10 = bot_bot_set_nat ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % image_minus_const_atLeastLessThan_nat
% 3.82/4.10 thf(fact_7784_finite__greaterThanAtMost__int,axiom,
% 3.82/4.10 ! [L: int,U: int] : ( finite_finite_int @ ( set_or6656581121297822940st_int @ L @ U ) ) ).
% 3.82/4.10
% 3.82/4.10 % finite_greaterThanAtMost_int
% 3.82/4.10 thf(fact_7785_image__Suc__atLeastAtMost,axiom,
% 3.82/4.10 ! [I: nat,J: nat] :
% 3.82/4.10 ( ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ I @ J ) )
% 3.82/4.10 = ( set_or1269000886237332187st_nat @ ( suc @ I ) @ ( suc @ J ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % image_Suc_atLeastAtMost
% 3.82/4.10 thf(fact_7786_image__Suc__atLeastLessThan,axiom,
% 3.82/4.10 ! [I: nat,J: nat] :
% 3.82/4.10 ( ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ I @ J ) )
% 3.82/4.10 = ( set_or4665077453230672383an_nat @ ( suc @ I ) @ ( suc @ J ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % image_Suc_atLeastLessThan
% 3.82/4.10 thf(fact_7787_card__greaterThanAtMost__int,axiom,
% 3.82/4.10 ! [L: int,U: int] :
% 3.82/4.10 ( ( finite_card_int @ ( set_or6656581121297822940st_int @ L @ U ) )
% 3.82/4.10 = ( nat2 @ ( minus_minus_int @ U @ L ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % card_greaterThanAtMost_int
% 3.82/4.10 thf(fact_7788_zero__notin__Suc__image,axiom,
% 3.82/4.10 ! [A2: set_nat] :
% 3.82/4.10 ~ ( member_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ A2 ) ) ).
% 3.82/4.10
% 3.82/4.10 % zero_notin_Suc_image
% 3.82/4.10 thf(fact_7789_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 3.82/4.10 ! [L: int,U: int] :
% 3.82/4.10 ( ( set_or1266510415728281911st_int @ ( plus_plus_int @ L @ one_one_int ) @ U )
% 3.82/4.10 = ( set_or6656581121297822940st_int @ L @ U ) ) ).
% 3.82/4.10
% 3.82/4.10 % atLeastPlusOneAtMost_greaterThanAtMost_int
% 3.82/4.10 thf(fact_7790_image__Suc__lessThan,axiom,
% 3.82/4.10 ! [N2: nat] :
% 3.82/4.10 ( ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N2 ) )
% 3.82/4.10 = ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ).
% 3.82/4.10
% 3.82/4.10 % image_Suc_lessThan
% 3.82/4.10 thf(fact_7791_image__Suc__atMost,axiom,
% 3.82/4.10 ! [N2: nat] :
% 3.82/4.10 ( ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N2 ) )
% 3.82/4.10 = ( set_or1269000886237332187st_nat @ one_one_nat @ ( suc @ N2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % image_Suc_atMost
% 3.82/4.10 thf(fact_7792_atLeast0__atMost__Suc__eq__insert__0,axiom,
% 3.82/4.10 ! [N2: nat] :
% 3.82/4.10 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 3.82/4.10 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % atLeast0_atMost_Suc_eq_insert_0
% 3.82/4.10 thf(fact_7793_atLeast0__lessThan__Suc__eq__insert__0,axiom,
% 3.82/4.10 ! [N2: nat] :
% 3.82/4.10 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 3.82/4.10 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % atLeast0_lessThan_Suc_eq_insert_0
% 3.82/4.10 thf(fact_7794_lessThan__Suc__eq__insert__0,axiom,
% 3.82/4.10 ! [N2: nat] :
% 3.82/4.10 ( ( set_ord_lessThan_nat @ ( suc @ N2 ) )
% 3.82/4.10 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % lessThan_Suc_eq_insert_0
% 3.82/4.10 thf(fact_7795_atMost__Suc__eq__insert__0,axiom,
% 3.82/4.10 ! [N2: nat] :
% 3.82/4.10 ( ( set_ord_atMost_nat @ ( suc @ N2 ) )
% 3.82/4.10 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % atMost_Suc_eq_insert_0
% 3.82/4.10 thf(fact_7796_of__nat__eq__id,axiom,
% 3.82/4.10 semiri1316708129612266289at_nat = id_nat ).
% 3.82/4.10
% 3.82/4.10 % of_nat_eq_id
% 3.82/4.10 thf(fact_7797_less__int__def,axiom,
% 3.82/4.10 ( ord_less_int
% 3.82/4.10 = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 3.82/4.10 @ ( produc8739625826339149834_nat_o
% 3.82/4.10 @ ^ [X4: nat,Y5: nat] :
% 3.82/4.10 ( produc6081775807080527818_nat_o
% 3.82/4.10 @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X4 @ V4 ) @ ( plus_plus_nat @ U2 @ Y5 ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % less_int_def
% 3.82/4.10 thf(fact_7798_less__eq__int__def,axiom,
% 3.82/4.10 ( ord_less_eq_int
% 3.82/4.10 = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 3.82/4.10 @ ( produc8739625826339149834_nat_o
% 3.82/4.10 @ ^ [X4: nat,Y5: nat] :
% 3.82/4.10 ( produc6081775807080527818_nat_o
% 3.82/4.10 @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X4 @ V4 ) @ ( plus_plus_nat @ U2 @ Y5 ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % less_eq_int_def
% 3.82/4.10 thf(fact_7799_finite__int__iff__bounded__le,axiom,
% 3.82/4.10 ( finite_finite_int
% 3.82/4.10 = ( ^ [S6: set_int] :
% 3.82/4.10 ? [K2: int] : ( ord_less_eq_set_int @ ( image_int_int @ abs_abs_int @ S6 ) @ ( set_ord_atMost_int @ K2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % finite_int_iff_bounded_le
% 3.82/4.10 thf(fact_7800_finite__int__iff__bounded,axiom,
% 3.82/4.10 ( finite_finite_int
% 3.82/4.10 = ( ^ [S6: set_int] :
% 3.82/4.10 ? [K2: int] : ( ord_less_eq_set_int @ ( image_int_int @ abs_abs_int @ S6 ) @ ( set_ord_lessThan_int @ K2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % finite_int_iff_bounded
% 3.82/4.10 thf(fact_7801_nat__def,axiom,
% 3.82/4.10 ( nat2
% 3.82/4.10 = ( map_fu2345160673673942751at_nat @ rep_Integ @ id_nat @ ( produc6842872674320459806at_nat @ minus_minus_nat ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % nat_def
% 3.82/4.10 thf(fact_7802_image__int__atLeastAtMost,axiom,
% 3.82/4.10 ! [A: nat,B2: nat] :
% 3.82/4.10 ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ A @ B2 ) )
% 3.82/4.10 = ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % image_int_atLeastAtMost
% 3.82/4.10 thf(fact_7803_image__int__atLeastLessThan,axiom,
% 3.82/4.10 ! [A: nat,B2: nat] :
% 3.82/4.10 ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or4665077453230672383an_nat @ A @ B2 ) )
% 3.82/4.10 = ( set_or4662586982721622107an_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % image_int_atLeastLessThan
% 3.82/4.10 thf(fact_7804_image__add__int__atLeastLessThan,axiom,
% 3.82/4.10 ! [L: int,U: int] :
% 3.82/4.10 ( ( image_int_int
% 3.82/4.10 @ ^ [X4: int] : ( plus_plus_int @ X4 @ L )
% 3.82/4.10 @ ( set_or4662586982721622107an_int @ zero_zero_int @ ( minus_minus_int @ U @ L ) ) )
% 3.82/4.10 = ( set_or4662586982721622107an_int @ L @ U ) ) ).
% 3.82/4.10
% 3.82/4.10 % image_add_int_atLeastLessThan
% 3.82/4.10 thf(fact_7805_image__atLeastZeroLessThan__int,axiom,
% 3.82/4.10 ! [U: int] :
% 3.82/4.10 ( ( ord_less_eq_int @ zero_zero_int @ U )
% 3.82/4.10 => ( ( set_or4662586982721622107an_int @ zero_zero_int @ U )
% 3.82/4.10 = ( image_nat_int @ semiri1314217659103216013at_int @ ( set_ord_lessThan_nat @ ( nat2 @ U ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % image_atLeastZeroLessThan_int
% 3.82/4.10 thf(fact_7806_card__UNIV__unit,axiom,
% 3.82/4.10 ( ( finite410649719033368117t_unit @ top_to1996260823553986621t_unit )
% 3.82/4.10 = one_one_nat ) ).
% 3.82/4.10
% 3.82/4.10 % card_UNIV_unit
% 3.82/4.10 thf(fact_7807_range__mult,axiom,
% 3.82/4.10 ! [A: real] :
% 3.82/4.10 ( ( ( A = zero_zero_real )
% 3.82/4.10 => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 3.82/4.10 = ( insert_real @ zero_zero_real @ bot_bot_set_real ) ) )
% 3.82/4.10 & ( ( A != zero_zero_real )
% 3.82/4.10 => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 3.82/4.10 = top_top_set_real ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % range_mult
% 3.82/4.10 thf(fact_7808_nat__not__finite,axiom,
% 3.82/4.10 ~ ( finite_finite_nat @ top_top_set_nat ) ).
% 3.82/4.10
% 3.82/4.10 % nat_not_finite
% 3.82/4.10 thf(fact_7809_infinite__UNIV__nat,axiom,
% 3.82/4.10 ~ ( finite_finite_nat @ top_top_set_nat ) ).
% 3.82/4.10
% 3.82/4.10 % infinite_UNIV_nat
% 3.82/4.10 thf(fact_7810_infinite__UNIV__int,axiom,
% 3.82/4.10 ~ ( finite_finite_int @ top_top_set_int ) ).
% 3.82/4.10
% 3.82/4.10 % infinite_UNIV_int
% 3.82/4.10 thf(fact_7811_UN__lessThan__UNIV,axiom,
% 3.82/4.10 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_lessThan_nat @ top_top_set_nat ) )
% 3.82/4.10 = top_top_set_nat ) ).
% 3.82/4.10
% 3.82/4.10 % UN_lessThan_UNIV
% 3.82/4.10 thf(fact_7812_UN__atMost__UNIV,axiom,
% 3.82/4.10 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atMost_nat @ top_top_set_nat ) )
% 3.82/4.10 = top_top_set_nat ) ).
% 3.82/4.10
% 3.82/4.10 % UN_atMost_UNIV
% 3.82/4.10 thf(fact_7813_int__in__range__abs,axiom,
% 3.82/4.10 ! [N2: nat] : ( member_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( image_int_int @ abs_abs_int @ top_top_set_int ) ) ).
% 3.82/4.10
% 3.82/4.10 % int_in_range_abs
% 3.82/4.10 thf(fact_7814_UNIV__nat__eq,axiom,
% 3.82/4.10 ( top_top_set_nat
% 3.82/4.10 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ top_top_set_nat ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % UNIV_nat_eq
% 3.82/4.10 thf(fact_7815_range__mod,axiom,
% 3.82/4.10 ! [N2: nat] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( image_nat_nat
% 3.82/4.10 @ ^ [M: nat] : ( modulo_modulo_nat @ M @ N2 )
% 3.82/4.10 @ top_top_set_nat )
% 3.82/4.10 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % range_mod
% 3.82/4.10 thf(fact_7816_root__def,axiom,
% 3.82/4.10 ( root
% 3.82/4.10 = ( ^ [N: nat,X4: real] :
% 3.82/4.10 ( if_real @ ( N = zero_zero_nat ) @ zero_zero_real
% 3.82/4.10 @ ( the_in5290026491893676941l_real @ top_top_set_real
% 3.82/4.10 @ ^ [Y5: real] : ( times_times_real @ ( sgn_sgn_real @ Y5 ) @ ( power_power_real @ ( abs_abs_real @ Y5 ) @ N ) )
% 3.82/4.10 @ X4 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % root_def
% 3.82/4.10 thf(fact_7817_DERIV__real__root__generic,axiom,
% 3.82/4.10 ! [N2: nat,X: real,D6: real] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( X != zero_zero_real )
% 3.82/4.10 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 3.82/4.10 => ( ( ord_less_real @ zero_zero_real @ X )
% 3.82/4.10 => ( D6
% 3.82/4.10 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( root @ N2 @ X ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) )
% 3.82/4.10 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 3.82/4.10 => ( ( ord_less_real @ X @ zero_zero_real )
% 3.82/4.10 => ( D6
% 3.82/4.10 = ( uminus_uminus_real @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( root @ N2 @ X ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ) )
% 3.82/4.10 => ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 3.82/4.10 => ( D6
% 3.82/4.10 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( root @ N2 @ X ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) )
% 3.82/4.10 => ( has_fi5821293074295781190e_real @ ( root @ N2 ) @ D6 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % DERIV_real_root_generic
% 3.82/4.10 thf(fact_7818_DERIV__even__real__root,axiom,
% 3.82/4.10 ! [N2: nat,X: real] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 3.82/4.10 => ( ( ord_less_real @ X @ zero_zero_real )
% 3.82/4.10 => ( has_fi5821293074295781190e_real @ ( root @ N2 ) @ ( inverse_inverse_real @ ( times_times_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ ( power_power_real @ ( root @ N2 @ X ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % DERIV_even_real_root
% 3.82/4.10 thf(fact_7819_DERIV__power__series_H,axiom,
% 3.82/4.10 ! [R: real,F: nat > real,X0: real] :
% 3.82/4.10 ( ! [X5: real] :
% 3.82/4.10 ( ( member_real @ X5 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R ) @ R ) )
% 3.82/4.10 => ( summable_real
% 3.82/4.10 @ ^ [N: nat] : ( times_times_real @ ( times_times_real @ ( F @ N ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) @ ( power_power_real @ X5 @ N ) ) ) )
% 3.82/4.10 => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R ) @ R ) )
% 3.82/4.10 => ( ( ord_less_real @ zero_zero_real @ R )
% 3.82/4.10 => ( has_fi5821293074295781190e_real
% 3.82/4.10 @ ^ [X4: real] :
% 3.82/4.10 ( suminf_real
% 3.82/4.10 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ X4 @ ( suc @ N ) ) ) )
% 3.82/4.10 @ ( suminf_real
% 3.82/4.10 @ ^ [N: nat] : ( times_times_real @ ( times_times_real @ ( F @ N ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) @ ( power_power_real @ X0 @ N ) ) )
% 3.82/4.10 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % DERIV_power_series'
% 3.82/4.10 thf(fact_7820_DERIV__real__root,axiom,
% 3.82/4.10 ! [N2: nat,X: real] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( ord_less_real @ zero_zero_real @ X )
% 3.82/4.10 => ( has_fi5821293074295781190e_real @ ( root @ N2 ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( root @ N2 @ X ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % DERIV_real_root
% 3.82/4.10 thf(fact_7821_Maclaurin__all__le,axiom,
% 3.82/4.10 ! [Diff: nat > real > real,F: real > real,X: real,N2: nat] :
% 3.82/4.10 ( ( ( Diff @ zero_zero_nat )
% 3.82/4.10 = F )
% 3.82/4.10 => ( ! [M3: nat,X5: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 3.82/4.10 => ? [T6: real] :
% 3.82/4.10 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 3.82/4.10 & ( ( F @ X )
% 3.82/4.10 = ( plus_plus_real
% 3.82/4.10 @ ( groups6591440286371151544t_real
% 3.82/4.10 @ ^ [M: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M ) ) @ ( power_power_real @ X @ M ) )
% 3.82/4.10 @ ( set_ord_lessThan_nat @ N2 ) )
% 3.82/4.10 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T6 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X @ N2 ) ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % Maclaurin_all_le
% 3.82/4.10 thf(fact_7822_Maclaurin__all__le__objl,axiom,
% 3.82/4.10 ! [Diff: nat > real > real,F: real > real,X: real,N2: nat] :
% 3.82/4.10 ( ( ( ( Diff @ zero_zero_nat )
% 3.82/4.10 = F )
% 3.82/4.10 & ! [M3: nat,X5: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) )
% 3.82/4.10 => ? [T6: real] :
% 3.82/4.10 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 3.82/4.10 & ( ( F @ X )
% 3.82/4.10 = ( plus_plus_real
% 3.82/4.10 @ ( groups6591440286371151544t_real
% 3.82/4.10 @ ^ [M: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M ) ) @ ( power_power_real @ X @ M ) )
% 3.82/4.10 @ ( set_ord_lessThan_nat @ N2 ) )
% 3.82/4.10 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T6 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X @ N2 ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % Maclaurin_all_le_objl
% 3.82/4.10 thf(fact_7823_DERIV__odd__real__root,axiom,
% 3.82/4.10 ! [N2: nat,X: real] :
% 3.82/4.10 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 3.82/4.10 => ( ( X != zero_zero_real )
% 3.82/4.10 => ( has_fi5821293074295781190e_real @ ( root @ N2 ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( root @ N2 @ X ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % DERIV_odd_real_root
% 3.82/4.10 thf(fact_7824_Maclaurin__minus,axiom,
% 3.82/4.10 ! [H2: real,N2: nat,Diff: nat > real > real,F: real > real] :
% 3.82/4.10 ( ( ord_less_real @ H2 @ zero_zero_real )
% 3.82/4.10 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( ( Diff @ zero_zero_nat )
% 3.82/4.10 = F )
% 3.82/4.10 => ( ! [M3: nat,T6: real] :
% 3.82/4.10 ( ( ( ord_less_nat @ M3 @ N2 )
% 3.82/4.10 & ( ord_less_eq_real @ H2 @ T6 )
% 3.82/4.10 & ( ord_less_eq_real @ T6 @ zero_zero_real ) )
% 3.82/4.10 => ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 3.82/4.10 => ? [T6: real] :
% 3.82/4.10 ( ( ord_less_real @ H2 @ T6 )
% 3.82/4.10 & ( ord_less_real @ T6 @ zero_zero_real )
% 3.82/4.10 & ( ( F @ H2 )
% 3.82/4.10 = ( plus_plus_real
% 3.82/4.10 @ ( groups6591440286371151544t_real
% 3.82/4.10 @ ^ [M: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M ) ) @ ( power_power_real @ H2 @ M ) )
% 3.82/4.10 @ ( set_ord_lessThan_nat @ N2 ) )
% 3.82/4.10 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T6 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ H2 @ N2 ) ) ) ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % Maclaurin_minus
% 3.82/4.10 thf(fact_7825_Maclaurin2,axiom,
% 3.82/4.10 ! [H2: real,Diff: nat > real > real,F: real > real,N2: nat] :
% 3.82/4.10 ( ( ord_less_real @ zero_zero_real @ H2 )
% 3.82/4.10 => ( ( ( Diff @ zero_zero_nat )
% 3.82/4.10 = F )
% 3.82/4.10 => ( ! [M3: nat,T6: real] :
% 3.82/4.10 ( ( ( ord_less_nat @ M3 @ N2 )
% 3.82/4.10 & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 3.82/4.10 & ( ord_less_eq_real @ T6 @ H2 ) )
% 3.82/4.10 => ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 3.82/4.10 => ? [T6: real] :
% 3.82/4.10 ( ( ord_less_real @ zero_zero_real @ T6 )
% 3.82/4.10 & ( ord_less_eq_real @ T6 @ H2 )
% 3.82/4.10 & ( ( F @ H2 )
% 3.82/4.10 = ( plus_plus_real
% 3.82/4.10 @ ( groups6591440286371151544t_real
% 3.82/4.10 @ ^ [M: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M ) ) @ ( power_power_real @ H2 @ M ) )
% 3.82/4.10 @ ( set_ord_lessThan_nat @ N2 ) )
% 3.82/4.10 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T6 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ H2 @ N2 ) ) ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % Maclaurin2
% 3.82/4.10 thf(fact_7826_Maclaurin,axiom,
% 3.82/4.10 ! [H2: real,N2: nat,Diff: nat > real > real,F: real > real] :
% 3.82/4.10 ( ( ord_less_real @ zero_zero_real @ H2 )
% 3.82/4.10 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( ( Diff @ zero_zero_nat )
% 3.82/4.10 = F )
% 3.82/4.10 => ( ! [M3: nat,T6: real] :
% 3.82/4.10 ( ( ( ord_less_nat @ M3 @ N2 )
% 3.82/4.10 & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 3.82/4.10 & ( ord_less_eq_real @ T6 @ H2 ) )
% 3.82/4.10 => ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 3.82/4.10 => ? [T6: real] :
% 3.82/4.10 ( ( ord_less_real @ zero_zero_real @ T6 )
% 3.82/4.10 & ( ord_less_real @ T6 @ H2 )
% 3.82/4.10 & ( ( F @ H2 )
% 3.82/4.10 = ( plus_plus_real
% 3.82/4.10 @ ( groups6591440286371151544t_real
% 3.82/4.10 @ ^ [M: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M ) ) @ ( power_power_real @ H2 @ M ) )
% 3.82/4.10 @ ( set_ord_lessThan_nat @ N2 ) )
% 3.82/4.10 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T6 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ H2 @ N2 ) ) ) ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % Maclaurin
% 3.82/4.10 thf(fact_7827_Maclaurin__all__lt,axiom,
% 3.82/4.10 ! [Diff: nat > real > real,F: real > real,N2: nat,X: real] :
% 3.82/4.10 ( ( ( Diff @ zero_zero_nat )
% 3.82/4.10 = F )
% 3.82/4.10 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( X != zero_zero_real )
% 3.82/4.10 => ( ! [M3: nat,X5: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 3.82/4.10 => ? [T6: real] :
% 3.82/4.10 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T6 ) )
% 3.82/4.10 & ( ord_less_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 3.82/4.10 & ( ( F @ X )
% 3.82/4.10 = ( plus_plus_real
% 3.82/4.10 @ ( groups6591440286371151544t_real
% 3.82/4.10 @ ^ [M: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M ) ) @ ( power_power_real @ X @ M ) )
% 3.82/4.10 @ ( set_ord_lessThan_nat @ N2 ) )
% 3.82/4.10 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T6 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X @ N2 ) ) ) ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % Maclaurin_all_lt
% 3.82/4.10 thf(fact_7828_Maclaurin__bi__le,axiom,
% 3.82/4.10 ! [Diff: nat > real > real,F: real > real,N2: nat,X: real] :
% 3.82/4.10 ( ( ( Diff @ zero_zero_nat )
% 3.82/4.10 = F )
% 3.82/4.10 => ( ! [M3: nat,T6: real] :
% 3.82/4.10 ( ( ( ord_less_nat @ M3 @ N2 )
% 3.82/4.10 & ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) ) )
% 3.82/4.10 => ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 3.82/4.10 => ? [T6: real] :
% 3.82/4.10 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 3.82/4.10 & ( ( F @ X )
% 3.82/4.10 = ( plus_plus_real
% 3.82/4.10 @ ( groups6591440286371151544t_real
% 3.82/4.10 @ ^ [M: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M ) ) @ ( power_power_real @ X @ M ) )
% 3.82/4.10 @ ( set_ord_lessThan_nat @ N2 ) )
% 3.82/4.10 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T6 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X @ N2 ) ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % Maclaurin_bi_le
% 3.82/4.10 thf(fact_7829_Taylor,axiom,
% 3.82/4.10 ! [N2: nat,Diff: nat > real > real,F: real > real,A: real,B2: real,C: real,X: real] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( ( Diff @ zero_zero_nat )
% 3.82/4.10 = F )
% 3.82/4.10 => ( ! [M3: nat,T6: real] :
% 3.82/4.10 ( ( ( ord_less_nat @ M3 @ N2 )
% 3.82/4.10 & ( ord_less_eq_real @ A @ T6 )
% 3.82/4.10 & ( ord_less_eq_real @ T6 @ B2 ) )
% 3.82/4.10 => ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 3.82/4.10 => ( ( ord_less_eq_real @ A @ C )
% 3.82/4.10 => ( ( ord_less_eq_real @ C @ B2 )
% 3.82/4.10 => ( ( ord_less_eq_real @ A @ X )
% 3.82/4.10 => ( ( ord_less_eq_real @ X @ B2 )
% 3.82/4.10 => ( ( X != C )
% 3.82/4.10 => ? [T6: real] :
% 3.82/4.10 ( ( ( ord_less_real @ X @ C )
% 3.82/4.10 => ( ( ord_less_real @ X @ T6 )
% 3.82/4.10 & ( ord_less_real @ T6 @ C ) ) )
% 3.82/4.10 & ( ~ ( ord_less_real @ X @ C )
% 3.82/4.10 => ( ( ord_less_real @ C @ T6 )
% 3.82/4.10 & ( ord_less_real @ T6 @ X ) ) )
% 3.82/4.10 & ( ( F @ X )
% 3.82/4.10 = ( plus_plus_real
% 3.82/4.10 @ ( groups6591440286371151544t_real
% 3.82/4.10 @ ^ [M: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M @ C ) @ ( semiri2265585572941072030t_real @ M ) ) @ ( power_power_real @ ( minus_minus_real @ X @ C ) @ M ) )
% 3.82/4.10 @ ( set_ord_lessThan_nat @ N2 ) )
% 3.82/4.10 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T6 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ ( minus_minus_real @ X @ C ) @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % Taylor
% 3.82/4.10 thf(fact_7830_Taylor__up,axiom,
% 3.82/4.10 ! [N2: nat,Diff: nat > real > real,F: real > real,A: real,B2: real,C: real] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( ( Diff @ zero_zero_nat )
% 3.82/4.10 = F )
% 3.82/4.10 => ( ! [M3: nat,T6: real] :
% 3.82/4.10 ( ( ( ord_less_nat @ M3 @ N2 )
% 3.82/4.10 & ( ord_less_eq_real @ A @ T6 )
% 3.82/4.10 & ( ord_less_eq_real @ T6 @ B2 ) )
% 3.82/4.10 => ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 3.82/4.10 => ( ( ord_less_eq_real @ A @ C )
% 3.82/4.10 => ( ( ord_less_real @ C @ B2 )
% 3.82/4.10 => ? [T6: real] :
% 3.82/4.10 ( ( ord_less_real @ C @ T6 )
% 3.82/4.10 & ( ord_less_real @ T6 @ B2 )
% 3.82/4.10 & ( ( F @ B2 )
% 3.82/4.10 = ( plus_plus_real
% 3.82/4.10 @ ( groups6591440286371151544t_real
% 3.82/4.10 @ ^ [M: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M @ C ) @ ( semiri2265585572941072030t_real @ M ) ) @ ( power_power_real @ ( minus_minus_real @ B2 @ C ) @ M ) )
% 3.82/4.10 @ ( set_ord_lessThan_nat @ N2 ) )
% 3.82/4.10 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T6 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ ( minus_minus_real @ B2 @ C ) @ N2 ) ) ) ) ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % Taylor_up
% 3.82/4.10 thf(fact_7831_Taylor__down,axiom,
% 3.82/4.10 ! [N2: nat,Diff: nat > real > real,F: real > real,A: real,B2: real,C: real] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( ( Diff @ zero_zero_nat )
% 3.82/4.10 = F )
% 3.82/4.10 => ( ! [M3: nat,T6: real] :
% 3.82/4.10 ( ( ( ord_less_nat @ M3 @ N2 )
% 3.82/4.10 & ( ord_less_eq_real @ A @ T6 )
% 3.82/4.10 & ( ord_less_eq_real @ T6 @ B2 ) )
% 3.82/4.10 => ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 3.82/4.10 => ( ( ord_less_real @ A @ C )
% 3.82/4.10 => ( ( ord_less_eq_real @ C @ B2 )
% 3.82/4.10 => ? [T6: real] :
% 3.82/4.10 ( ( ord_less_real @ A @ T6 )
% 3.82/4.10 & ( ord_less_real @ T6 @ C )
% 3.82/4.10 & ( ( F @ A )
% 3.82/4.10 = ( plus_plus_real
% 3.82/4.10 @ ( groups6591440286371151544t_real
% 3.82/4.10 @ ^ [M: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M @ C ) @ ( semiri2265585572941072030t_real @ M ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ M ) )
% 3.82/4.10 @ ( set_ord_lessThan_nat @ N2 ) )
% 3.82/4.10 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T6 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ N2 ) ) ) ) ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % Taylor_down
% 3.82/4.10 thf(fact_7832_Maclaurin__lemma2,axiom,
% 3.82/4.10 ! [N2: nat,H2: real,Diff: nat > real > real,K: nat,B: real] :
% 3.82/4.10 ( ! [M3: nat,T6: real] :
% 3.82/4.10 ( ( ( ord_less_nat @ M3 @ N2 )
% 3.82/4.10 & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 3.82/4.10 & ( ord_less_eq_real @ T6 @ H2 ) )
% 3.82/4.10 => ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 3.82/4.10 => ( ( N2
% 3.82/4.10 = ( suc @ K ) )
% 3.82/4.10 => ! [M5: nat,T7: real] :
% 3.82/4.10 ( ( ( ord_less_nat @ M5 @ N2 )
% 3.82/4.10 & ( ord_less_eq_real @ zero_zero_real @ T7 )
% 3.82/4.10 & ( ord_less_eq_real @ T7 @ H2 ) )
% 3.82/4.10 => ( has_fi5821293074295781190e_real
% 3.82/4.10 @ ^ [U2: real] :
% 3.82/4.10 ( minus_minus_real @ ( Diff @ M5 @ U2 )
% 3.82/4.10 @ ( plus_plus_real
% 3.82/4.10 @ ( groups6591440286371151544t_real
% 3.82/4.10 @ ^ [P6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ M5 @ P6 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P6 ) ) @ ( power_power_real @ U2 @ P6 ) )
% 3.82/4.10 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ M5 ) ) )
% 3.82/4.10 @ ( times_times_real @ B @ ( divide_divide_real @ ( power_power_real @ U2 @ ( minus_minus_nat @ N2 @ M5 ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ M5 ) ) ) ) ) )
% 3.82/4.10 @ ( minus_minus_real @ ( Diff @ ( suc @ M5 ) @ T7 )
% 3.82/4.10 @ ( plus_plus_real
% 3.82/4.10 @ ( groups6591440286371151544t_real
% 3.82/4.10 @ ^ [P6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ ( suc @ M5 ) @ P6 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P6 ) ) @ ( power_power_real @ T7 @ P6 ) )
% 3.82/4.10 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ ( suc @ M5 ) ) ) )
% 3.82/4.10 @ ( times_times_real @ B @ ( divide_divide_real @ ( power_power_real @ T7 @ ( minus_minus_nat @ N2 @ ( suc @ M5 ) ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ ( suc @ M5 ) ) ) ) ) ) )
% 3.82/4.10 @ ( topolo2177554685111907308n_real @ T7 @ top_top_set_real ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % Maclaurin_lemma2
% 3.82/4.10 thf(fact_7833_DERIV__arctan__series,axiom,
% 3.82/4.10 ! [X: real] :
% 3.82/4.10 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 3.82/4.10 => ( has_fi5821293074295781190e_real
% 3.82/4.10 @ ^ [X9: real] :
% 3.82/4.10 ( suminf_real
% 3.82/4.10 @ ^ [K2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X9 @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) )
% 3.82/4.10 @ ( suminf_real
% 3.82/4.10 @ ^ [K2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( power_power_real @ X @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 3.82/4.10 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % DERIV_arctan_series
% 3.82/4.10 thf(fact_7834_DERIV__pow,axiom,
% 3.82/4.10 ! [N2: nat,X: real,S: set_real] :
% 3.82/4.10 ( has_fi5821293074295781190e_real
% 3.82/4.10 @ ^ [X4: real] : ( power_power_real @ X4 @ N2 )
% 3.82/4.10 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ X @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) )
% 3.82/4.10 @ ( topolo2177554685111907308n_real @ X @ S ) ) ).
% 3.82/4.10
% 3.82/4.10 % DERIV_pow
% 3.82/4.10 thf(fact_7835_Gcd__eq__Max,axiom,
% 3.82/4.10 ! [M7: set_nat] :
% 3.82/4.10 ( ( finite_finite_nat @ M7 )
% 3.82/4.10 => ( ( M7 != bot_bot_set_nat )
% 3.82/4.10 => ( ~ ( member_nat @ zero_zero_nat @ M7 )
% 3.82/4.10 => ( ( gcd_Gcd_nat @ M7 )
% 3.82/4.10 = ( lattic8265883725875713057ax_nat
% 3.82/4.10 @ ( comple7806235888213564991et_nat
% 3.82/4.10 @ ( image_nat_set_nat
% 3.82/4.10 @ ^ [M: nat] :
% 3.82/4.10 ( collect_nat
% 3.82/4.10 @ ^ [D4: nat] : ( dvd_dvd_nat @ D4 @ M ) )
% 3.82/4.10 @ M7 ) ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % Gcd_eq_Max
% 3.82/4.10 thf(fact_7836_Max__divisors__self__nat,axiom,
% 3.82/4.10 ! [N2: nat] :
% 3.82/4.10 ( ( N2 != zero_zero_nat )
% 3.82/4.10 => ( ( lattic8265883725875713057ax_nat
% 3.82/4.10 @ ( collect_nat
% 3.82/4.10 @ ^ [D4: nat] : ( dvd_dvd_nat @ D4 @ N2 ) ) )
% 3.82/4.10 = N2 ) ) ).
% 3.82/4.10
% 3.82/4.10 % Max_divisors_self_nat
% 3.82/4.10 thf(fact_7837_card__le__Suc__Max,axiom,
% 3.82/4.10 ! [S2: set_nat] :
% 3.82/4.10 ( ( finite_finite_nat @ S2 )
% 3.82/4.10 => ( ord_less_eq_nat @ ( finite_card_nat @ S2 ) @ ( suc @ ( lattic8265883725875713057ax_nat @ S2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % card_le_Suc_Max
% 3.82/4.10 thf(fact_7838_Sup__nat__def,axiom,
% 3.82/4.10 ( complete_Sup_Sup_nat
% 3.82/4.10 = ( ^ [X6: set_nat] : ( if_nat @ ( X6 = bot_bot_set_nat ) @ zero_zero_nat @ ( lattic8265883725875713057ax_nat @ X6 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % Sup_nat_def
% 3.82/4.10 thf(fact_7839_divide__nat__def,axiom,
% 3.82/4.10 ( divide_divide_nat
% 3.82/4.10 = ( ^ [M: nat,N: nat] :
% 3.82/4.10 ( if_nat @ ( N = zero_zero_nat ) @ zero_zero_nat
% 3.82/4.10 @ ( lattic8265883725875713057ax_nat
% 3.82/4.10 @ ( collect_nat
% 3.82/4.10 @ ^ [K2: nat] : ( ord_less_eq_nat @ ( times_times_nat @ K2 @ N ) @ M ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % divide_nat_def
% 3.82/4.10 thf(fact_7840_summable__Leibniz_I3_J,axiom,
% 3.82/4.10 ! [A: nat > real] :
% 3.82/4.10 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 3.82/4.10 => ( ( topolo6980174941875973593q_real @ A )
% 3.82/4.10 => ( ( ord_less_real @ ( A @ zero_zero_nat ) @ zero_zero_real )
% 3.82/4.10 => ! [N7: nat] :
% 3.82/4.10 ( member_real
% 3.82/4.10 @ ( suminf_real
% 3.82/4.10 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) )
% 3.82/4.10 @ ( set_or1222579329274155063t_real
% 3.82/4.10 @ ( groups6591440286371151544t_real
% 3.82/4.10 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 3.82/4.10 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) @ one_one_nat ) ) )
% 3.82/4.10 @ ( groups6591440286371151544t_real
% 3.82/4.10 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 3.82/4.10 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) ) ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % summable_Leibniz(3)
% 3.82/4.10 thf(fact_7841_summable__Leibniz_I2_J,axiom,
% 3.82/4.10 ! [A: nat > real] :
% 3.82/4.10 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 3.82/4.10 => ( ( topolo6980174941875973593q_real @ A )
% 3.82/4.10 => ( ( ord_less_real @ zero_zero_real @ ( A @ zero_zero_nat ) )
% 3.82/4.10 => ! [N7: nat] :
% 3.82/4.10 ( member_real
% 3.82/4.10 @ ( suminf_real
% 3.82/4.10 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) )
% 3.82/4.10 @ ( set_or1222579329274155063t_real
% 3.82/4.10 @ ( groups6591440286371151544t_real
% 3.82/4.10 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 3.82/4.10 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) ) )
% 3.82/4.10 @ ( groups6591440286371151544t_real
% 3.82/4.10 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 3.82/4.10 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) @ one_one_nat ) ) ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % summable_Leibniz(2)
% 3.82/4.10 thf(fact_7842_summable__Leibniz_H_I4_J,axiom,
% 3.82/4.10 ! [A: nat > real,N2: nat] :
% 3.82/4.10 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 3.82/4.10 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 3.82/4.10 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 3.82/4.10 => ( ord_less_eq_real
% 3.82/4.10 @ ( suminf_real
% 3.82/4.10 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) )
% 3.82/4.10 @ ( groups6591440286371151544t_real
% 3.82/4.10 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 3.82/4.10 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % summable_Leibniz'(4)
% 3.82/4.10 thf(fact_7843_summable__Leibniz_H_I5_J,axiom,
% 3.82/4.10 ! [A: nat > real] :
% 3.82/4.10 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 3.82/4.10 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 3.82/4.10 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 3.82/4.10 => ( filterlim_nat_real
% 3.82/4.10 @ ^ [N: nat] :
% 3.82/4.10 ( groups6591440286371151544t_real
% 3.82/4.10 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 3.82/4.10 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) )
% 3.82/4.10 @ ( topolo2815343760600316023s_real
% 3.82/4.10 @ ( suminf_real
% 3.82/4.10 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) ) )
% 3.82/4.10 @ at_top_nat ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % summable_Leibniz'(5)
% 3.82/4.10 thf(fact_7844_trivial__limit__sequentially,axiom,
% 3.82/4.10 at_top_nat != bot_bot_filter_nat ).
% 3.82/4.10
% 3.82/4.10 % trivial_limit_sequentially
% 3.82/4.10 thf(fact_7845_filterlim__Suc,axiom,
% 3.82/4.10 filterlim_nat_nat @ suc @ at_top_nat @ at_top_nat ).
% 3.82/4.10
% 3.82/4.10 % filterlim_Suc
% 3.82/4.10 thf(fact_7846_mult__nat__right__at__top,axiom,
% 3.82/4.10 ! [C: nat] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ C )
% 3.82/4.10 => ( filterlim_nat_nat
% 3.82/4.10 @ ^ [X4: nat] : ( times_times_nat @ X4 @ C )
% 3.82/4.10 @ at_top_nat
% 3.82/4.10 @ at_top_nat ) ) ).
% 3.82/4.10
% 3.82/4.10 % mult_nat_right_at_top
% 3.82/4.10 thf(fact_7847_mult__nat__left__at__top,axiom,
% 3.82/4.10 ! [C: nat] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ C )
% 3.82/4.10 => ( filterlim_nat_nat @ ( times_times_nat @ C ) @ at_top_nat @ at_top_nat ) ) ).
% 3.82/4.10
% 3.82/4.10 % mult_nat_left_at_top
% 3.82/4.10 thf(fact_7848_nested__sequence__unique,axiom,
% 3.82/4.10 ! [F: nat > real,G: nat > real] :
% 3.82/4.10 ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 3.82/4.10 => ( ! [N3: nat] : ( ord_less_eq_real @ ( G @ ( suc @ N3 ) ) @ ( G @ N3 ) )
% 3.82/4.10 => ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 3.82/4.10 => ( ( filterlim_nat_real
% 3.82/4.10 @ ^ [N: nat] : ( minus_minus_real @ ( F @ N ) @ ( G @ N ) )
% 3.82/4.10 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 3.82/4.10 @ at_top_nat )
% 3.82/4.10 => ? [L4: real] :
% 3.82/4.10 ( ! [N7: nat] : ( ord_less_eq_real @ ( F @ N7 ) @ L4 )
% 3.82/4.10 & ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat )
% 3.82/4.10 & ! [N7: nat] : ( ord_less_eq_real @ L4 @ ( G @ N7 ) )
% 3.82/4.10 & ( filterlim_nat_real @ G @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % nested_sequence_unique
% 3.82/4.10 thf(fact_7849_LIMSEQ__inverse__zero,axiom,
% 3.82/4.10 ! [X8: nat > real] :
% 3.82/4.10 ( ! [R3: real] :
% 3.82/4.10 ? [N8: nat] :
% 3.82/4.10 ! [N3: nat] :
% 3.82/4.10 ( ( ord_less_eq_nat @ N8 @ N3 )
% 3.82/4.10 => ( ord_less_real @ R3 @ ( X8 @ N3 ) ) )
% 3.82/4.10 => ( filterlim_nat_real
% 3.82/4.10 @ ^ [N: nat] : ( inverse_inverse_real @ ( X8 @ N ) )
% 3.82/4.10 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 3.82/4.10 @ at_top_nat ) ) ).
% 3.82/4.10
% 3.82/4.10 % LIMSEQ_inverse_zero
% 3.82/4.10 thf(fact_7850_LIMSEQ__inverse__real__of__nat,axiom,
% 3.82/4.10 ( filterlim_nat_real
% 3.82/4.10 @ ^ [N: nat] : ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 3.82/4.10 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 3.82/4.10 @ at_top_nat ) ).
% 3.82/4.10
% 3.82/4.10 % LIMSEQ_inverse_real_of_nat
% 3.82/4.10 thf(fact_7851_LIMSEQ__inverse__real__of__nat__add,axiom,
% 3.82/4.10 ! [R2: real] :
% 3.82/4.10 ( filterlim_nat_real
% 3.82/4.10 @ ^ [N: nat] : ( plus_plus_real @ R2 @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) )
% 3.82/4.10 @ ( topolo2815343760600316023s_real @ R2 )
% 3.82/4.10 @ at_top_nat ) ).
% 3.82/4.10
% 3.82/4.10 % LIMSEQ_inverse_real_of_nat_add
% 3.82/4.10 thf(fact_7852_increasing__LIMSEQ,axiom,
% 3.82/4.10 ! [F: nat > real,L: real] :
% 3.82/4.10 ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 3.82/4.10 => ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ L )
% 3.82/4.10 => ( ! [E: real] :
% 3.82/4.10 ( ( ord_less_real @ zero_zero_real @ E )
% 3.82/4.10 => ? [N7: nat] : ( ord_less_eq_real @ L @ ( plus_plus_real @ ( F @ N7 ) @ E ) ) )
% 3.82/4.10 => ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L ) @ at_top_nat ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % increasing_LIMSEQ
% 3.82/4.10 thf(fact_7853_LIMSEQ__inverse__real__of__nat__add__minus,axiom,
% 3.82/4.10 ! [R2: real] :
% 3.82/4.10 ( filterlim_nat_real
% 3.82/4.10 @ ^ [N: nat] : ( plus_plus_real @ R2 @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) )
% 3.82/4.10 @ ( topolo2815343760600316023s_real @ R2 )
% 3.82/4.10 @ at_top_nat ) ).
% 3.82/4.10
% 3.82/4.10 % LIMSEQ_inverse_real_of_nat_add_minus
% 3.82/4.10 thf(fact_7854_LIMSEQ__inverse__real__of__nat__add__minus__mult,axiom,
% 3.82/4.10 ! [R2: real] :
% 3.82/4.10 ( filterlim_nat_real
% 3.82/4.10 @ ^ [N: nat] : ( times_times_real @ R2 @ ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) ) )
% 3.82/4.10 @ ( topolo2815343760600316023s_real @ R2 )
% 3.82/4.10 @ at_top_nat ) ).
% 3.82/4.10
% 3.82/4.10 % LIMSEQ_inverse_real_of_nat_add_minus_mult
% 3.82/4.10 thf(fact_7855_summable,axiom,
% 3.82/4.10 ! [A: nat > real] :
% 3.82/4.10 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 3.82/4.10 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 3.82/4.10 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 3.82/4.10 => ( summable_real
% 3.82/4.10 @ ^ [N: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( A @ N ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % summable
% 3.82/4.10 thf(fact_7856_zeroseq__arctan__series,axiom,
% 3.82/4.10 ! [X: real] :
% 3.82/4.10 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 3.82/4.10 => ( filterlim_nat_real
% 3.82/4.10 @ ^ [N: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) )
% 3.82/4.10 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 3.82/4.10 @ at_top_nat ) ) ).
% 3.82/4.10
% 3.82/4.10 % zeroseq_arctan_series
% 3.82/4.10 thf(fact_7857_summable__Leibniz_H_I2_J,axiom,
% 3.82/4.10 ! [A: nat > real,N2: nat] :
% 3.82/4.10 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 3.82/4.10 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 3.82/4.10 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 3.82/4.10 => ( ord_less_eq_real
% 3.82/4.10 @ ( groups6591440286371151544t_real
% 3.82/4.10 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 3.82/4.10 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 3.82/4.10 @ ( suminf_real
% 3.82/4.10 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % summable_Leibniz'(2)
% 3.82/4.10 thf(fact_7858_summable__Leibniz_H_I3_J,axiom,
% 3.82/4.10 ! [A: nat > real] :
% 3.82/4.10 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 3.82/4.10 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 3.82/4.10 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 3.82/4.10 => ( filterlim_nat_real
% 3.82/4.10 @ ^ [N: nat] :
% 3.82/4.10 ( groups6591440286371151544t_real
% 3.82/4.10 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 3.82/4.10 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 3.82/4.10 @ ( topolo2815343760600316023s_real
% 3.82/4.10 @ ( suminf_real
% 3.82/4.10 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) ) )
% 3.82/4.10 @ at_top_nat ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % summable_Leibniz'(3)
% 3.82/4.10 thf(fact_7859_sums__alternating__upper__lower,axiom,
% 3.82/4.10 ! [A: nat > real] :
% 3.82/4.10 ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 3.82/4.10 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 3.82/4.10 => ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 3.82/4.10 => ? [L4: real] :
% 3.82/4.10 ( ! [N7: nat] :
% 3.82/4.10 ( ord_less_eq_real
% 3.82/4.10 @ ( groups6591440286371151544t_real
% 3.82/4.10 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 3.82/4.10 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) ) )
% 3.82/4.10 @ L4 )
% 3.82/4.10 & ( filterlim_nat_real
% 3.82/4.10 @ ^ [N: nat] :
% 3.82/4.10 ( groups6591440286371151544t_real
% 3.82/4.10 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 3.82/4.10 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 3.82/4.10 @ ( topolo2815343760600316023s_real @ L4 )
% 3.82/4.10 @ at_top_nat )
% 3.82/4.10 & ! [N7: nat] :
% 3.82/4.10 ( ord_less_eq_real @ L4
% 3.82/4.10 @ ( groups6591440286371151544t_real
% 3.82/4.10 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 3.82/4.10 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) @ one_one_nat ) ) ) )
% 3.82/4.10 & ( filterlim_nat_real
% 3.82/4.10 @ ^ [N: nat] :
% 3.82/4.10 ( groups6591440286371151544t_real
% 3.82/4.10 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 3.82/4.10 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) )
% 3.82/4.10 @ ( topolo2815343760600316023s_real @ L4 )
% 3.82/4.10 @ at_top_nat ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % sums_alternating_upper_lower
% 3.82/4.10 thf(fact_7860_summable__Leibniz_I5_J,axiom,
% 3.82/4.10 ! [A: nat > real] :
% 3.82/4.10 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 3.82/4.10 => ( ( topolo6980174941875973593q_real @ A )
% 3.82/4.10 => ( filterlim_nat_real
% 3.82/4.10 @ ^ [N: nat] :
% 3.82/4.10 ( groups6591440286371151544t_real
% 3.82/4.10 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 3.82/4.10 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) )
% 3.82/4.10 @ ( topolo2815343760600316023s_real
% 3.82/4.10 @ ( suminf_real
% 3.82/4.10 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) ) )
% 3.82/4.10 @ at_top_nat ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % summable_Leibniz(5)
% 3.82/4.10 thf(fact_7861_eventually__sequentially__Suc,axiom,
% 3.82/4.10 ! [P: nat > $o] :
% 3.82/4.10 ( ( eventually_nat
% 3.82/4.10 @ ^ [I3: nat] : ( P @ ( suc @ I3 ) )
% 3.82/4.10 @ at_top_nat )
% 3.82/4.10 = ( eventually_nat @ P @ at_top_nat ) ) ).
% 3.82/4.10
% 3.82/4.10 % eventually_sequentially_Suc
% 3.82/4.10 thf(fact_7862_eventually__sequentially__seg,axiom,
% 3.82/4.10 ! [P: nat > $o,K: nat] :
% 3.82/4.10 ( ( eventually_nat
% 3.82/4.10 @ ^ [N: nat] : ( P @ ( plus_plus_nat @ N @ K ) )
% 3.82/4.10 @ at_top_nat )
% 3.82/4.10 = ( eventually_nat @ P @ at_top_nat ) ) ).
% 3.82/4.10
% 3.82/4.10 % eventually_sequentially_seg
% 3.82/4.10 thf(fact_7863_eventually__sequentiallyI,axiom,
% 3.82/4.10 ! [C: nat,P: nat > $o] :
% 3.82/4.10 ( ! [X5: nat] :
% 3.82/4.10 ( ( ord_less_eq_nat @ C @ X5 )
% 3.82/4.10 => ( P @ X5 ) )
% 3.82/4.10 => ( eventually_nat @ P @ at_top_nat ) ) ).
% 3.82/4.10
% 3.82/4.10 % eventually_sequentiallyI
% 3.82/4.10 thf(fact_7864_eventually__sequentially,axiom,
% 3.82/4.10 ! [P: nat > $o] :
% 3.82/4.10 ( ( eventually_nat @ P @ at_top_nat )
% 3.82/4.10 = ( ? [N5: nat] :
% 3.82/4.10 ! [N: nat] :
% 3.82/4.10 ( ( ord_less_eq_nat @ N5 @ N )
% 3.82/4.10 => ( P @ N ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % eventually_sequentially
% 3.82/4.10 thf(fact_7865_le__sequentially,axiom,
% 3.82/4.10 ! [F3: filter_nat] :
% 3.82/4.10 ( ( ord_le2510731241096832064er_nat @ F3 @ at_top_nat )
% 3.82/4.10 = ( ! [N5: nat] : ( eventually_nat @ ( ord_less_eq_nat @ N5 ) @ F3 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % le_sequentially
% 3.82/4.10 thf(fact_7866_sequentially__offset,axiom,
% 3.82/4.10 ! [P: nat > $o,K: nat] :
% 3.82/4.10 ( ( eventually_nat @ P @ at_top_nat )
% 3.82/4.10 => ( eventually_nat
% 3.82/4.10 @ ^ [I3: nat] : ( P @ ( plus_plus_nat @ I3 @ K ) )
% 3.82/4.10 @ at_top_nat ) ) ).
% 3.82/4.10
% 3.82/4.10 % sequentially_offset
% 3.82/4.10 thf(fact_7867_filterlim__pow__at__bot__even,axiom,
% 3.82/4.10 ! [N2: nat,F: real > real,F3: filter_real] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( filterlim_real_real @ F @ at_bot_real @ F3 )
% 3.82/4.10 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 3.82/4.10 => ( filterlim_real_real
% 3.82/4.10 @ ^ [X4: real] : ( power_power_real @ ( F @ X4 ) @ N2 )
% 3.82/4.10 @ at_top_real
% 3.82/4.10 @ F3 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % filterlim_pow_at_bot_even
% 3.82/4.10 thf(fact_7868_filterlim__pow__at__bot__odd,axiom,
% 3.82/4.10 ! [N2: nat,F: real > real,F3: filter_real] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( ( filterlim_real_real @ F @ at_bot_real @ F3 )
% 3.82/4.10 => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 3.82/4.10 => ( filterlim_real_real
% 3.82/4.10 @ ^ [X4: real] : ( power_power_real @ ( F @ X4 ) @ N2 )
% 3.82/4.10 @ at_bot_real
% 3.82/4.10 @ F3 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % filterlim_pow_at_bot_odd
% 3.82/4.10 thf(fact_7869_card_Ocomp__fun__commute__on,axiom,
% 3.82/4.10 ( ( comp_nat_nat_nat @ suc @ suc )
% 3.82/4.10 = ( comp_nat_nat_nat @ suc @ suc ) ) ).
% 3.82/4.10
% 3.82/4.10 % card.comp_fun_commute_on
% 3.82/4.10 thf(fact_7870_infinite__int__iff__infinite__nat__abs,axiom,
% 3.82/4.10 ! [S2: set_int] :
% 3.82/4.10 ( ( ~ ( finite_finite_int @ S2 ) )
% 3.82/4.10 = ( ~ ( finite_finite_nat @ ( image_int_nat @ ( comp_int_nat_int @ nat2 @ abs_abs_int ) @ S2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % infinite_int_iff_infinite_nat_abs
% 3.82/4.10 thf(fact_7871_mono__Suc,axiom,
% 3.82/4.10 order_mono_nat_nat @ suc ).
% 3.82/4.10
% 3.82/4.10 % mono_Suc
% 3.82/4.10 thf(fact_7872_mono__times__nat,axiom,
% 3.82/4.10 ! [N2: nat] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( order_mono_nat_nat @ ( times_times_nat @ N2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % mono_times_nat
% 3.82/4.10 thf(fact_7873_greaterThan__0,axiom,
% 3.82/4.10 ( ( set_or1210151606488870762an_nat @ zero_zero_nat )
% 3.82/4.10 = ( image_nat_nat @ suc @ top_top_set_nat ) ) ).
% 3.82/4.10
% 3.82/4.10 % greaterThan_0
% 3.82/4.10 thf(fact_7874_greaterThan__Suc,axiom,
% 3.82/4.10 ! [K: nat] :
% 3.82/4.10 ( ( set_or1210151606488870762an_nat @ ( suc @ K ) )
% 3.82/4.10 = ( minus_minus_set_nat @ ( set_or1210151606488870762an_nat @ K ) @ ( insert_nat @ ( suc @ K ) @ bot_bot_set_nat ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % greaterThan_Suc
% 3.82/4.10 thf(fact_7875_mono__ge2__power__minus__self,axiom,
% 3.82/4.10 ! [K: nat] :
% 3.82/4.10 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 3.82/4.10 => ( order_mono_nat_nat
% 3.82/4.10 @ ^ [M: nat] : ( minus_minus_nat @ ( power_power_nat @ K @ M ) @ M ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % mono_ge2_power_minus_self
% 3.82/4.10 thf(fact_7876_INT__greaterThan__UNIV,axiom,
% 3.82/4.10 ( ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ set_or1210151606488870762an_nat @ top_top_set_nat ) )
% 3.82/4.10 = bot_bot_set_nat ) ).
% 3.82/4.10
% 3.82/4.10 % INT_greaterThan_UNIV
% 3.82/4.10 thf(fact_7877_atLeast__0,axiom,
% 3.82/4.10 ( ( set_ord_atLeast_nat @ zero_zero_nat )
% 3.82/4.10 = top_top_set_nat ) ).
% 3.82/4.10
% 3.82/4.10 % atLeast_0
% 3.82/4.10 thf(fact_7878_atLeast__Suc__greaterThan,axiom,
% 3.82/4.10 ! [K: nat] :
% 3.82/4.10 ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 3.82/4.10 = ( set_or1210151606488870762an_nat @ K ) ) ).
% 3.82/4.10
% 3.82/4.10 % atLeast_Suc_greaterThan
% 3.82/4.10 thf(fact_7879_UN__atLeast__UNIV,axiom,
% 3.82/4.10 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atLeast_nat @ top_top_set_nat ) )
% 3.82/4.10 = top_top_set_nat ) ).
% 3.82/4.10
% 3.82/4.10 % UN_atLeast_UNIV
% 3.82/4.10 thf(fact_7880_atLeast__Suc,axiom,
% 3.82/4.10 ! [K: nat] :
% 3.82/4.10 ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 3.82/4.10 = ( minus_minus_set_nat @ ( set_ord_atLeast_nat @ K ) @ ( insert_nat @ K @ bot_bot_set_nat ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % atLeast_Suc
% 3.82/4.10 thf(fact_7881_range__abs__Nats,axiom,
% 3.82/4.10 ( ( image_int_int @ abs_abs_int @ top_top_set_int )
% 3.82/4.10 = semiring_1_Nats_int ) ).
% 3.82/4.10
% 3.82/4.10 % range_abs_Nats
% 3.82/4.10 thf(fact_7882_inj__sgn__power,axiom,
% 3.82/4.10 ! [N2: nat] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( inj_on_real_real
% 3.82/4.10 @ ^ [Y5: real] : ( times_times_real @ ( sgn_sgn_real @ Y5 ) @ ( power_power_real @ ( abs_abs_real @ Y5 ) @ N2 ) )
% 3.82/4.10 @ top_top_set_real ) ) ).
% 3.82/4.10
% 3.82/4.10 % inj_sgn_power
% 3.82/4.10 thf(fact_7883_measure__function__int,axiom,
% 3.82/4.10 fun_is_measure_int @ ( comp_int_nat_int @ nat2 @ abs_abs_int ) ).
% 3.82/4.10
% 3.82/4.10 % measure_function_int
% 3.82/4.10 thf(fact_7884_inj__Suc,axiom,
% 3.82/4.10 ! [N6: set_nat] : ( inj_on_nat_nat @ suc @ N6 ) ).
% 3.82/4.10
% 3.82/4.10 % inj_Suc
% 3.82/4.10 thf(fact_7885_inj__on__diff__nat,axiom,
% 3.82/4.10 ! [N6: set_nat,K: nat] :
% 3.82/4.10 ( ! [N3: nat] :
% 3.82/4.10 ( ( member_nat @ N3 @ N6 )
% 3.82/4.10 => ( ord_less_eq_nat @ K @ N3 ) )
% 3.82/4.10 => ( inj_on_nat_nat
% 3.82/4.10 @ ^ [N: nat] : ( minus_minus_nat @ N @ K )
% 3.82/4.10 @ N6 ) ) ).
% 3.82/4.10
% 3.82/4.10 % inj_on_diff_nat
% 3.82/4.10 thf(fact_7886_inj__on__set__encode,axiom,
% 3.82/4.10 inj_on_set_nat_nat @ nat_set_encode @ ( collect_set_nat @ finite_finite_nat ) ).
% 3.82/4.10
% 3.82/4.10 % inj_on_set_encode
% 3.82/4.10 thf(fact_7887_pred__nat__def,axiom,
% 3.82/4.10 ( pred_nat
% 3.82/4.10 = ( collec3392354462482085612at_nat
% 3.82/4.10 @ ( produc6081775807080527818_nat_o
% 3.82/4.10 @ ^ [M: nat,N: nat] :
% 3.82/4.10 ( N
% 3.82/4.10 = ( suc @ M ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % pred_nat_def
% 3.82/4.10 thf(fact_7888_VEBT__internal_Ovalid_H_Oelims_I3_J,axiom,
% 3.82/4.10 ! [X: vEBT_VEBT,Xa2: nat] :
% 3.82/4.10 ( ~ ( vEBT_VEBT_valid @ X @ Xa2 )
% 3.82/4.10 => ( ( ? [Uu2: $o,Uv2: $o] :
% 3.82/4.10 ( X
% 3.82/4.10 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 3.82/4.10 => ( Xa2 = one_one_nat ) )
% 3.82/4.10 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 3.82/4.10 ( ( X
% 3.82/4.10 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 3.82/4.10 => ( ( Deg2 = Xa2 )
% 3.82/4.10 & ! [X5: vEBT_VEBT] :
% 3.82/4.10 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 3.82/4.10 => ( vEBT_VEBT_valid @ X5 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 3.82/4.10 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 3.82/4.10 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 3.82/4.10 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 3.82/4.10 & ( case_o184042715313410164at_nat
% 3.82/4.10 @ ( ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X6 )
% 3.82/4.10 & ! [X4: vEBT_VEBT] :
% 3.82/4.10 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 3.82/4.10 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X6 ) ) )
% 3.82/4.10 @ ( produc6081775807080527818_nat_o
% 3.82/4.10 @ ^ [Mi3: nat,Ma3: nat] :
% 3.82/4.10 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 3.82/4.10 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 3.82/4.10 & ! [I3: nat] :
% 3.82/4.10 ( ( 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 ) ) ) ) ) )
% 3.82/4.10 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ X6 ) )
% 3.82/4.10 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 3.82/4.10 & ( ( Mi3 = Ma3 )
% 3.82/4.10 => ! [X4: vEBT_VEBT] :
% 3.82/4.10 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 3.82/4.10 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X6 ) ) )
% 3.82/4.10 & ( ( Mi3 != Ma3 )
% 3.82/4.10 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 3.82/4.10 & ! [X4: nat] :
% 3.82/4.10 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 3.82/4.10 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X4 )
% 3.82/4.10 => ( ( ord_less_nat @ Mi3 @ X4 )
% 3.82/4.10 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) )
% 3.82/4.10 @ Mima ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % VEBT_internal.valid'.elims(3)
% 3.82/4.10 thf(fact_7889_VEBT__internal_Ovalid_H_Oelims_I2_J,axiom,
% 3.82/4.10 ! [X: vEBT_VEBT,Xa2: nat] :
% 3.82/4.10 ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 3.82/4.10 => ( ( ? [Uu2: $o,Uv2: $o] :
% 3.82/4.10 ( X
% 3.82/4.10 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 3.82/4.10 => ( Xa2 != one_one_nat ) )
% 3.82/4.10 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 3.82/4.10 ( ( X
% 3.82/4.10 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 3.82/4.10 => ~ ( ( Deg2 = Xa2 )
% 3.82/4.10 & ! [X2: vEBT_VEBT] :
% 3.82/4.10 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 3.82/4.10 => ( vEBT_VEBT_valid @ X2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 3.82/4.10 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 3.82/4.10 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 3.82/4.10 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 3.82/4.10 & ( case_o184042715313410164at_nat
% 3.82/4.10 @ ( ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X6 )
% 3.82/4.10 & ! [X4: vEBT_VEBT] :
% 3.82/4.10 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 3.82/4.10 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X6 ) ) )
% 3.82/4.10 @ ( produc6081775807080527818_nat_o
% 3.82/4.10 @ ^ [Mi3: nat,Ma3: nat] :
% 3.82/4.10 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 3.82/4.10 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 3.82/4.10 & ! [I3: nat] :
% 3.82/4.10 ( ( 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 ) ) ) ) ) )
% 3.82/4.10 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ X6 ) )
% 3.82/4.10 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 3.82/4.10 & ( ( Mi3 = Ma3 )
% 3.82/4.10 => ! [X4: vEBT_VEBT] :
% 3.82/4.10 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 3.82/4.10 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X6 ) ) )
% 3.82/4.10 & ( ( Mi3 != Ma3 )
% 3.82/4.10 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 3.82/4.10 & ! [X4: nat] :
% 3.82/4.10 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 3.82/4.10 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X4 )
% 3.82/4.10 => ( ( ord_less_nat @ Mi3 @ X4 )
% 3.82/4.10 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) )
% 3.82/4.10 @ Mima ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % VEBT_internal.valid'.elims(2)
% 3.82/4.10 thf(fact_7890_VEBT__internal_Ovalid_H_Oelims_I1_J,axiom,
% 3.82/4.10 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 3.82/4.10 ( ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 3.82/4.10 = Y )
% 3.82/4.10 => ( ( ? [Uu2: $o,Uv2: $o] :
% 3.82/4.10 ( X
% 3.82/4.10 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 3.82/4.10 => ( Y
% 3.82/4.10 = ( Xa2 != one_one_nat ) ) )
% 3.82/4.10 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 3.82/4.10 ( ( X
% 3.82/4.10 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 3.82/4.10 => ( Y
% 3.82/4.10 = ( ~ ( ( Deg2 = Xa2 )
% 3.82/4.10 & ! [X4: vEBT_VEBT] :
% 3.82/4.10 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 3.82/4.10 => ( vEBT_VEBT_valid @ X4 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 3.82/4.10 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 3.82/4.10 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 3.82/4.10 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 3.82/4.10 & ( case_o184042715313410164at_nat
% 3.82/4.10 @ ( ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X6 )
% 3.82/4.10 & ! [X4: vEBT_VEBT] :
% 3.82/4.10 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 3.82/4.10 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X6 ) ) )
% 3.82/4.10 @ ( produc6081775807080527818_nat_o
% 3.82/4.10 @ ^ [Mi3: nat,Ma3: nat] :
% 3.82/4.10 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 3.82/4.10 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 3.82/4.10 & ! [I3: nat] :
% 3.82/4.10 ( ( 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 ) ) ) ) ) )
% 3.82/4.10 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ X6 ) )
% 3.82/4.10 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 3.82/4.10 & ( ( Mi3 = Ma3 )
% 3.82/4.10 => ! [X4: vEBT_VEBT] :
% 3.82/4.10 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 3.82/4.10 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X6 ) ) )
% 3.82/4.10 & ( ( Mi3 != Ma3 )
% 3.82/4.10 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 3.82/4.10 & ! [X4: nat] :
% 3.82/4.10 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 3.82/4.10 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X4 )
% 3.82/4.10 => ( ( ord_less_nat @ Mi3 @ X4 )
% 3.82/4.10 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) )
% 3.82/4.10 @ Mima ) ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % VEBT_internal.valid'.elims(1)
% 3.82/4.10 thf(fact_7891_VEBT__internal_Ovalid_H_Osimps_I2_J,axiom,
% 3.82/4.10 ! [Mima2: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,Deg3: nat] :
% 3.82/4.10 ( ( vEBT_VEBT_valid @ ( vEBT_Node @ Mima2 @ Deg @ TreeList2 @ Summary ) @ Deg3 )
% 3.82/4.10 = ( ( Deg = Deg3 )
% 3.82/4.10 & ! [X4: vEBT_VEBT] :
% 3.82/4.10 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 3.82/4.10 => ( vEBT_VEBT_valid @ X4 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 3.82/4.10 & ( vEBT_VEBT_valid @ Summary @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 3.82/4.10 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 3.82/4.10 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 3.82/4.10 & ( case_o184042715313410164at_nat
% 3.82/4.10 @ ( ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X6 )
% 3.82/4.10 & ! [X4: vEBT_VEBT] :
% 3.82/4.10 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 3.82/4.10 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X6 ) ) )
% 3.82/4.10 @ ( produc6081775807080527818_nat_o
% 3.82/4.10 @ ^ [Mi3: nat,Ma3: nat] :
% 3.82/4.10 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 3.82/4.10 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 3.82/4.10 & ! [I3: nat] :
% 3.82/4.10 ( ( 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 ) ) ) ) ) )
% 3.82/4.10 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X6 ) )
% 3.82/4.10 = ( vEBT_V8194947554948674370ptions @ Summary @ I3 ) ) )
% 3.82/4.10 & ( ( Mi3 = Ma3 )
% 3.82/4.10 => ! [X4: vEBT_VEBT] :
% 3.82/4.10 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 3.82/4.10 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X6 ) ) )
% 3.82/4.10 & ( ( Mi3 != Ma3 )
% 3.82/4.10 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 3.82/4.10 & ! [X4: nat] :
% 3.82/4.10 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 3.82/4.10 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X4 )
% 3.82/4.10 => ( ( ord_less_nat @ Mi3 @ X4 )
% 3.82/4.10 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) )
% 3.82/4.10 @ Mima2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % VEBT_internal.valid'.simps(2)
% 3.82/4.10 thf(fact_7892_VEBT__internal_Ovalid_H_Opelims_I1_J,axiom,
% 3.82/4.10 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 3.82/4.10 ( ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 3.82/4.10 = Y )
% 3.82/4.10 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 3.82/4.10 => ( ! [Uu2: $o,Uv2: $o] :
% 3.82/4.10 ( ( X
% 3.82/4.10 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 3.82/4.10 => ( ( Y
% 3.82/4.10 = ( Xa2 = one_one_nat ) )
% 3.82/4.10 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) ) )
% 3.82/4.10 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 3.82/4.10 ( ( X
% 3.82/4.10 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 3.82/4.10 => ( ( Y
% 3.82/4.10 = ( ( Deg2 = Xa2 )
% 3.82/4.10 & ! [X4: vEBT_VEBT] :
% 3.82/4.10 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 3.82/4.10 => ( vEBT_VEBT_valid @ X4 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 3.82/4.10 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 3.82/4.10 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 3.82/4.10 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 3.82/4.10 & ( case_o184042715313410164at_nat
% 3.82/4.10 @ ( ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X6 )
% 3.82/4.10 & ! [X4: vEBT_VEBT] :
% 3.82/4.10 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 3.82/4.10 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X6 ) ) )
% 3.82/4.10 @ ( produc6081775807080527818_nat_o
% 3.82/4.10 @ ^ [Mi3: nat,Ma3: nat] :
% 3.82/4.10 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 3.82/4.10 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 3.82/4.10 & ! [I3: nat] :
% 3.82/4.10 ( ( 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 ) ) ) ) ) )
% 3.82/4.10 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ X6 ) )
% 3.82/4.10 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 3.82/4.10 & ( ( Mi3 = Ma3 )
% 3.82/4.10 => ! [X4: vEBT_VEBT] :
% 3.82/4.10 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 3.82/4.10 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X6 ) ) )
% 3.82/4.10 & ( ( Mi3 != Ma3 )
% 3.82/4.10 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 3.82/4.10 & ! [X4: nat] :
% 3.82/4.10 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 3.82/4.10 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X4 )
% 3.82/4.10 => ( ( ord_less_nat @ Mi3 @ X4 )
% 3.82/4.10 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) )
% 3.82/4.10 @ Mima ) ) )
% 3.82/4.10 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % VEBT_internal.valid'.pelims(1)
% 3.82/4.10 thf(fact_7893_VEBT__internal_Ovalid_H_Opelims_I2_J,axiom,
% 3.82/4.10 ! [X: vEBT_VEBT,Xa2: nat] :
% 3.82/4.10 ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 3.82/4.10 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 3.82/4.10 => ( ! [Uu2: $o,Uv2: $o] :
% 3.82/4.10 ( ( X
% 3.82/4.10 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 3.82/4.10 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) )
% 3.82/4.10 => ( Xa2 != one_one_nat ) ) )
% 3.82/4.10 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 3.82/4.10 ( ( X
% 3.82/4.10 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 3.82/4.10 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Xa2 ) )
% 3.82/4.10 => ~ ( ( Deg2 = Xa2 )
% 3.82/4.10 & ! [X2: vEBT_VEBT] :
% 3.82/4.10 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 3.82/4.10 => ( vEBT_VEBT_valid @ X2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 3.82/4.10 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 3.82/4.10 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 3.82/4.10 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 3.82/4.10 & ( case_o184042715313410164at_nat
% 3.82/4.10 @ ( ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X6 )
% 3.82/4.10 & ! [X4: vEBT_VEBT] :
% 3.82/4.10 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 3.82/4.10 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X6 ) ) )
% 3.82/4.10 @ ( produc6081775807080527818_nat_o
% 3.82/4.10 @ ^ [Mi3: nat,Ma3: nat] :
% 3.82/4.10 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 3.82/4.10 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 3.82/4.10 & ! [I3: nat] :
% 3.82/4.10 ( ( 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 ) ) ) ) ) )
% 3.82/4.10 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ X6 ) )
% 3.82/4.10 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 3.82/4.10 & ( ( Mi3 = Ma3 )
% 3.82/4.10 => ! [X4: vEBT_VEBT] :
% 3.82/4.10 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 3.82/4.10 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X6 ) ) )
% 3.82/4.10 & ( ( Mi3 != Ma3 )
% 3.82/4.10 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 3.82/4.10 & ! [X4: nat] :
% 3.82/4.10 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 3.82/4.10 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X4 )
% 3.82/4.10 => ( ( ord_less_nat @ Mi3 @ X4 )
% 3.82/4.10 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) )
% 3.82/4.10 @ Mima ) ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % VEBT_internal.valid'.pelims(2)
% 3.82/4.10 thf(fact_7894_VEBT__internal_Ovalid_H_Opelims_I3_J,axiom,
% 3.82/4.10 ! [X: vEBT_VEBT,Xa2: nat] :
% 3.82/4.10 ( ~ ( vEBT_VEBT_valid @ X @ Xa2 )
% 3.82/4.10 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 3.82/4.10 => ( ! [Uu2: $o,Uv2: $o] :
% 3.82/4.10 ( ( X
% 3.82/4.10 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 3.82/4.10 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) )
% 3.82/4.10 => ( Xa2 = one_one_nat ) ) )
% 3.82/4.10 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 3.82/4.10 ( ( X
% 3.82/4.10 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 3.82/4.10 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Xa2 ) )
% 3.82/4.10 => ( ( Deg2 = Xa2 )
% 3.82/4.10 & ! [X5: vEBT_VEBT] :
% 3.82/4.10 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 3.82/4.10 => ( vEBT_VEBT_valid @ X5 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 3.82/4.10 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 3.82/4.10 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 3.82/4.10 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 3.82/4.10 & ( case_o184042715313410164at_nat
% 3.82/4.10 @ ( ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X6 )
% 3.82/4.10 & ! [X4: vEBT_VEBT] :
% 3.82/4.10 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 3.82/4.10 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X6 ) ) )
% 3.82/4.10 @ ( produc6081775807080527818_nat_o
% 3.82/4.10 @ ^ [Mi3: nat,Ma3: nat] :
% 3.82/4.10 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 3.82/4.10 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 3.82/4.10 & ! [I3: nat] :
% 3.82/4.10 ( ( 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 ) ) ) ) ) )
% 3.82/4.10 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ X6 ) )
% 3.82/4.10 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 3.82/4.10 & ( ( Mi3 = Ma3 )
% 3.82/4.10 => ! [X4: vEBT_VEBT] :
% 3.82/4.10 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 3.82/4.10 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X6 ) ) )
% 3.82/4.10 & ( ( Mi3 != Ma3 )
% 3.82/4.10 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 3.82/4.10 & ! [X4: nat] :
% 3.82/4.10 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 3.82/4.10 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X4 )
% 3.82/4.10 => ( ( ord_less_nat @ Mi3 @ X4 )
% 3.82/4.10 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) )
% 3.82/4.10 @ Mima ) ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % VEBT_internal.valid'.pelims(3)
% 3.82/4.10 thf(fact_7895_atLeastLessThan__add__Un,axiom,
% 3.82/4.10 ! [I: nat,J: nat,K: nat] :
% 3.82/4.10 ( ( ord_less_eq_nat @ I @ J )
% 3.82/4.10 => ( ( set_or4665077453230672383an_nat @ I @ ( plus_plus_nat @ J @ K ) )
% 3.82/4.10 = ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ I @ J ) @ ( set_or4665077453230672383an_nat @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % atLeastLessThan_add_Un
% 3.82/4.10 thf(fact_7896_sup__int__def,axiom,
% 3.82/4.10 sup_sup_int = ord_max_int ).
% 3.82/4.10
% 3.82/4.10 % sup_int_def
% 3.82/4.10 thf(fact_7897_sup__nat__def,axiom,
% 3.82/4.10 sup_sup_nat = ord_max_nat ).
% 3.82/4.10
% 3.82/4.10 % sup_nat_def
% 3.82/4.10 thf(fact_7898_Rats__eq__int__div__nat,axiom,
% 3.82/4.10 ( field_5140801741446780682s_real
% 3.82/4.10 = ( collect_real
% 3.82/4.10 @ ^ [Uu3: real] :
% 3.82/4.10 ? [I3: int,N: nat] :
% 3.82/4.10 ( ( Uu3
% 3.82/4.10 = ( divide_divide_real @ ( ring_1_of_int_real @ I3 ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 3.82/4.10 & ( N != zero_zero_nat ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % Rats_eq_int_div_nat
% 3.82/4.10 thf(fact_7899_less__eq,axiom,
% 3.82/4.10 ! [M2: nat,N2: nat] :
% 3.82/4.10 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M2 @ N2 ) @ ( transi6264000038957366511cl_nat @ pred_nat ) )
% 3.82/4.10 = ( ord_less_nat @ M2 @ N2 ) ) ).
% 3.82/4.10
% 3.82/4.10 % less_eq
% 3.82/4.10 thf(fact_7900_pred__nat__trancl__eq__le,axiom,
% 3.82/4.10 ! [M2: nat,N2: nat] :
% 3.82/4.10 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M2 @ N2 ) @ ( transi2905341329935302413cl_nat @ pred_nat ) )
% 3.82/4.10 = ( ord_less_eq_nat @ M2 @ N2 ) ) ).
% 3.82/4.10
% 3.82/4.10 % pred_nat_trancl_eq_le
% 3.82/4.10 thf(fact_7901_bdd__above__nat,axiom,
% 3.82/4.10 condit2214826472909112428ve_nat = finite_finite_nat ).
% 3.82/4.10
% 3.82/4.10 % bdd_above_nat
% 3.82/4.10 thf(fact_7902_take__bit__num__simps_I1_J,axiom,
% 3.82/4.10 ! [M2: num] :
% 3.82/4.10 ( ( bit_take_bit_num @ zero_zero_nat @ M2 )
% 3.82/4.10 = none_num ) ).
% 3.82/4.10
% 3.82/4.10 % take_bit_num_simps(1)
% 3.82/4.10 thf(fact_7903_take__bit__num__simps_I2_J,axiom,
% 3.82/4.10 ! [N2: nat] :
% 3.82/4.10 ( ( bit_take_bit_num @ ( suc @ N2 ) @ one )
% 3.82/4.10 = ( some_num @ one ) ) ).
% 3.82/4.10
% 3.82/4.10 % take_bit_num_simps(2)
% 3.82/4.10 thf(fact_7904_take__bit__num__simps_I3_J,axiom,
% 3.82/4.10 ! [N2: nat,M2: num] :
% 3.82/4.10 ( ( bit_take_bit_num @ ( suc @ N2 ) @ ( bit0 @ M2 ) )
% 3.82/4.10 = ( case_o6005452278849405969um_num @ none_num
% 3.82/4.10 @ ^ [Q5: num] : ( some_num @ ( bit0 @ Q5 ) )
% 3.82/4.10 @ ( bit_take_bit_num @ N2 @ M2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % take_bit_num_simps(3)
% 3.82/4.10 thf(fact_7905_take__bit__num__simps_I4_J,axiom,
% 3.82/4.10 ! [N2: nat,M2: num] :
% 3.82/4.10 ( ( bit_take_bit_num @ ( suc @ N2 ) @ ( bit1 @ M2 ) )
% 3.82/4.10 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N2 @ M2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % take_bit_num_simps(4)
% 3.82/4.10 thf(fact_7906_take__bit__num__def,axiom,
% 3.82/4.10 ( bit_take_bit_num
% 3.82/4.10 = ( ^ [N: nat,M: num] :
% 3.82/4.10 ( if_option_num
% 3.82/4.10 @ ( ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ M ) )
% 3.82/4.10 = zero_zero_nat )
% 3.82/4.10 @ none_num
% 3.82/4.10 @ ( some_num @ ( num_of_nat @ ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ M ) ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % take_bit_num_def
% 3.82/4.10 thf(fact_7907_min__Suc__Suc,axiom,
% 3.82/4.10 ! [M2: nat,N2: nat] :
% 3.82/4.10 ( ( ord_min_nat @ ( suc @ M2 ) @ ( suc @ N2 ) )
% 3.82/4.10 = ( suc @ ( ord_min_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % min_Suc_Suc
% 3.82/4.10 thf(fact_7908_min__0L,axiom,
% 3.82/4.10 ! [N2: nat] :
% 3.82/4.10 ( ( ord_min_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 = zero_zero_nat ) ).
% 3.82/4.10
% 3.82/4.10 % min_0L
% 3.82/4.10 thf(fact_7909_min__0R,axiom,
% 3.82/4.10 ! [N2: nat] :
% 3.82/4.10 ( ( ord_min_nat @ N2 @ zero_zero_nat )
% 3.82/4.10 = zero_zero_nat ) ).
% 3.82/4.10
% 3.82/4.10 % min_0R
% 3.82/4.10 thf(fact_7910_min__numeral__Suc,axiom,
% 3.82/4.10 ! [K: num,N2: nat] :
% 3.82/4.10 ( ( ord_min_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N2 ) )
% 3.82/4.10 = ( suc @ ( ord_min_nat @ ( pred_numeral @ K ) @ N2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % min_numeral_Suc
% 3.82/4.10 thf(fact_7911_min__Suc__numeral,axiom,
% 3.82/4.10 ! [N2: nat,K: num] :
% 3.82/4.10 ( ( ord_min_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 3.82/4.10 = ( suc @ ( ord_min_nat @ N2 @ ( pred_numeral @ K ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % min_Suc_numeral
% 3.82/4.10 thf(fact_7912_min__diff,axiom,
% 3.82/4.10 ! [M2: nat,I: nat,N2: nat] :
% 3.82/4.10 ( ( ord_min_nat @ ( minus_minus_nat @ M2 @ I ) @ ( minus_minus_nat @ N2 @ I ) )
% 3.82/4.10 = ( minus_minus_nat @ ( ord_min_nat @ M2 @ N2 ) @ I ) ) ).
% 3.82/4.10
% 3.82/4.10 % min_diff
% 3.82/4.10 thf(fact_7913_nat__mult__min__left,axiom,
% 3.82/4.10 ! [M2: nat,N2: nat,Q3: nat] :
% 3.82/4.10 ( ( times_times_nat @ ( ord_min_nat @ M2 @ N2 ) @ Q3 )
% 3.82/4.10 = ( ord_min_nat @ ( times_times_nat @ M2 @ Q3 ) @ ( times_times_nat @ N2 @ Q3 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % nat_mult_min_left
% 3.82/4.10 thf(fact_7914_nat__mult__min__right,axiom,
% 3.82/4.10 ! [M2: nat,N2: nat,Q3: nat] :
% 3.82/4.10 ( ( times_times_nat @ M2 @ ( ord_min_nat @ N2 @ Q3 ) )
% 3.82/4.10 = ( ord_min_nat @ ( times_times_nat @ M2 @ N2 ) @ ( times_times_nat @ M2 @ Q3 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % nat_mult_min_right
% 3.82/4.10 thf(fact_7915_min__Suc2,axiom,
% 3.82/4.10 ! [M2: nat,N2: nat] :
% 3.82/4.10 ( ( ord_min_nat @ M2 @ ( suc @ N2 ) )
% 3.82/4.10 = ( case_nat_nat @ zero_zero_nat
% 3.82/4.10 @ ^ [M4: nat] : ( suc @ ( ord_min_nat @ M4 @ N2 ) )
% 3.82/4.10 @ M2 ) ) ).
% 3.82/4.10
% 3.82/4.10 % min_Suc2
% 3.82/4.10 thf(fact_7916_min__Suc1,axiom,
% 3.82/4.10 ! [N2: nat,M2: nat] :
% 3.82/4.10 ( ( ord_min_nat @ ( suc @ N2 ) @ M2 )
% 3.82/4.10 = ( case_nat_nat @ zero_zero_nat
% 3.82/4.10 @ ^ [M4: nat] : ( suc @ ( ord_min_nat @ N2 @ M4 ) )
% 3.82/4.10 @ M2 ) ) ).
% 3.82/4.10
% 3.82/4.10 % min_Suc1
% 3.82/4.10 thf(fact_7917_inf__nat__def,axiom,
% 3.82/4.10 inf_inf_nat = ord_min_nat ).
% 3.82/4.10
% 3.82/4.10 % inf_nat_def
% 3.82/4.10 thf(fact_7918_inf__int__def,axiom,
% 3.82/4.10 inf_inf_int = ord_min_int ).
% 3.82/4.10
% 3.82/4.10 % inf_int_def
% 3.82/4.10 thf(fact_7919_bij__betw__roots__unity,axiom,
% 3.82/4.10 ! [N2: nat] :
% 3.82/4.10 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( bij_betw_nat_complex
% 3.82/4.10 @ ^ [K2: nat] : ( cis @ ( divide_divide_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( semiri5074537144036343181t_real @ K2 ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 3.82/4.10 @ ( set_ord_lessThan_nat @ N2 )
% 3.82/4.10 @ ( collect_complex
% 3.82/4.10 @ ^ [Z6: complex] :
% 3.82/4.10 ( ( power_power_complex @ Z6 @ N2 )
% 3.82/4.10 = one_one_complex ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % bij_betw_roots_unity
% 3.82/4.10 thf(fact_7920_sorted__list__of__set__greaterThanAtMost,axiom,
% 3.82/4.10 ! [I: nat,J: nat] :
% 3.82/4.10 ( ( ord_less_eq_nat @ ( suc @ I ) @ J )
% 3.82/4.10 => ( ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I @ J ) )
% 3.82/4.10 = ( cons_nat @ ( suc @ I ) @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ ( suc @ I ) @ J ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % sorted_list_of_set_greaterThanAtMost
% 3.82/4.10 thf(fact_7921_sorted__list__of__set__greaterThanLessThan,axiom,
% 3.82/4.10 ! [I: nat,J: nat] :
% 3.82/4.10 ( ( ord_less_nat @ ( suc @ I ) @ J )
% 3.82/4.10 => ( ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I @ J ) )
% 3.82/4.10 = ( cons_nat @ ( suc @ I ) @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ ( suc @ I ) @ J ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % sorted_list_of_set_greaterThanLessThan
% 3.82/4.10 thf(fact_7922_bij__betw__Suc,axiom,
% 3.82/4.10 ! [M7: set_nat,N6: set_nat] :
% 3.82/4.10 ( ( bij_betw_nat_nat @ suc @ M7 @ N6 )
% 3.82/4.10 = ( ( image_nat_nat @ suc @ M7 )
% 3.82/4.10 = N6 ) ) ).
% 3.82/4.10
% 3.82/4.10 % bij_betw_Suc
% 3.82/4.10 thf(fact_7923_bij__betw__nth__root__unity,axiom,
% 3.82/4.10 ! [C: complex,N2: nat] :
% 3.82/4.10 ( ( C != zero_zero_complex )
% 3.82/4.10 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.10 => ( bij_be1856998921033663316omplex @ ( times_times_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ ( root @ N2 @ ( real_V1022390504157884413omplex @ C ) ) ) @ ( cis @ ( divide_divide_real @ ( arg @ C ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) )
% 3.82/4.10 @ ( collect_complex
% 3.82/4.10 @ ^ [Z6: complex] :
% 3.82/4.10 ( ( power_power_complex @ Z6 @ N2 )
% 3.82/4.10 = one_one_complex ) )
% 3.82/4.10 @ ( collect_complex
% 3.82/4.10 @ ^ [Z6: complex] :
% 3.82/4.10 ( ( power_power_complex @ Z6 @ N2 )
% 3.82/4.10 = C ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % bij_betw_nth_root_unity
% 3.82/4.10 thf(fact_7924_sorted__list__of__set__lessThan__Suc,axiom,
% 3.82/4.10 ! [K: nat] :
% 3.82/4.10 ( ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ ( suc @ K ) ) )
% 3.82/4.10 = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ K ) ) @ ( cons_nat @ K @ nil_nat ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % sorted_list_of_set_lessThan_Suc
% 3.82/4.10 thf(fact_7925_sorted__list__of__set__atMost__Suc,axiom,
% 3.82/4.10 ! [K: nat] :
% 3.82/4.10 ( ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ ( suc @ K ) ) )
% 3.82/4.10 = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ K ) ) @ ( cons_nat @ ( suc @ K ) @ nil_nat ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % sorted_list_of_set_atMost_Suc
% 3.82/4.10 thf(fact_7926_list__encode_Oelims,axiom,
% 3.82/4.10 ! [X: list_nat,Y: nat] :
% 3.82/4.10 ( ( ( nat_list_encode @ X )
% 3.82/4.10 = Y )
% 3.82/4.10 => ( ( ( X = nil_nat )
% 3.82/4.10 => ( Y != zero_zero_nat ) )
% 3.82/4.10 => ~ ! [X5: nat,Xs2: list_nat] :
% 3.82/4.10 ( ( X
% 3.82/4.10 = ( cons_nat @ X5 @ Xs2 ) )
% 3.82/4.10 => ( Y
% 3.82/4.10 != ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X5 @ ( nat_list_encode @ Xs2 ) ) ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % list_encode.elims
% 3.82/4.10 thf(fact_7927_list__encode_Osimps_I1_J,axiom,
% 3.82/4.10 ( ( nat_list_encode @ nil_nat )
% 3.82/4.10 = zero_zero_nat ) ).
% 3.82/4.10
% 3.82/4.10 % list_encode.simps(1)
% 3.82/4.10 thf(fact_7928_list__encode_Osimps_I2_J,axiom,
% 3.82/4.10 ! [X: nat,Xs: list_nat] :
% 3.82/4.10 ( ( nat_list_encode @ ( cons_nat @ X @ Xs ) )
% 3.82/4.10 = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X @ ( nat_list_encode @ Xs ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % list_encode.simps(2)
% 3.82/4.10 thf(fact_7929_upto__aux__rec,axiom,
% 3.82/4.10 ( upto_aux
% 3.82/4.10 = ( ^ [I3: int,J2: int,Js: list_int] : ( if_list_int @ ( ord_less_int @ J2 @ I3 ) @ Js @ ( upto_aux @ I3 @ ( minus_minus_int @ J2 @ one_one_int ) @ ( cons_int @ J2 @ Js ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % upto_aux_rec
% 3.82/4.10 thf(fact_7930_upto_Opsimps,axiom,
% 3.82/4.10 ! [I: int,J: int] :
% 3.82/4.10 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I @ J ) )
% 3.82/4.10 => ( ( ( ord_less_eq_int @ I @ J )
% 3.82/4.10 => ( ( upto @ I @ J )
% 3.82/4.10 = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) )
% 3.82/4.10 & ( ~ ( ord_less_eq_int @ I @ J )
% 3.82/4.10 => ( ( upto @ I @ J )
% 3.82/4.10 = nil_int ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % upto.psimps
% 3.82/4.10 thf(fact_7931_upto_Opelims,axiom,
% 3.82/4.10 ! [X: int,Xa2: int,Y: list_int] :
% 3.82/4.10 ( ( ( upto @ X @ Xa2 )
% 3.82/4.10 = Y )
% 3.82/4.10 => ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X @ Xa2 ) )
% 3.82/4.10 => ~ ( ( ( ( ord_less_eq_int @ X @ Xa2 )
% 3.82/4.10 => ( Y
% 3.82/4.10 = ( cons_int @ X @ ( upto @ ( plus_plus_int @ X @ one_one_int ) @ Xa2 ) ) ) )
% 3.82/4.10 & ( ~ ( ord_less_eq_int @ X @ Xa2 )
% 3.82/4.10 => ( Y = nil_int ) ) )
% 3.82/4.10 => ~ ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X @ Xa2 ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % upto.pelims
% 3.82/4.10 thf(fact_7932_upto__Nil,axiom,
% 3.82/4.10 ! [I: int,J: int] :
% 3.82/4.10 ( ( ( upto @ I @ J )
% 3.82/4.10 = nil_int )
% 3.82/4.10 = ( ord_less_int @ J @ I ) ) ).
% 3.82/4.10
% 3.82/4.10 % upto_Nil
% 3.82/4.10 thf(fact_7933_upto__Nil2,axiom,
% 3.82/4.10 ! [I: int,J: int] :
% 3.82/4.10 ( ( nil_int
% 3.82/4.10 = ( upto @ I @ J ) )
% 3.82/4.10 = ( ord_less_int @ J @ I ) ) ).
% 3.82/4.10
% 3.82/4.10 % upto_Nil2
% 3.82/4.10 thf(fact_7934_upto__empty,axiom,
% 3.82/4.10 ! [J: int,I: int] :
% 3.82/4.10 ( ( ord_less_int @ J @ I )
% 3.82/4.10 => ( ( upto @ I @ J )
% 3.82/4.10 = nil_int ) ) ).
% 3.82/4.10
% 3.82/4.10 % upto_empty
% 3.82/4.10 thf(fact_7935_upto__single,axiom,
% 3.82/4.10 ! [I: int] :
% 3.82/4.10 ( ( upto @ I @ I )
% 3.82/4.10 = ( cons_int @ I @ nil_int ) ) ).
% 3.82/4.10
% 3.82/4.10 % upto_single
% 3.82/4.10 thf(fact_7936_nth__upto,axiom,
% 3.82/4.10 ! [I: int,K: nat,J: int] :
% 3.82/4.10 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K ) ) @ J )
% 3.82/4.10 => ( ( nth_int @ ( upto @ I @ J ) @ K )
% 3.82/4.10 = ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % nth_upto
% 3.82/4.10 thf(fact_7937_length__upto,axiom,
% 3.82/4.10 ! [I: int,J: int] :
% 3.82/4.10 ( ( size_size_list_int @ ( upto @ I @ J ) )
% 3.82/4.10 = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ J @ I ) @ one_one_int ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % length_upto
% 3.82/4.10 thf(fact_7938_upto__rec__numeral_I1_J,axiom,
% 3.82/4.10 ! [M2: num,N2: num] :
% 3.82/4.10 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N2 ) )
% 3.82/4.10 => ( ( upto @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N2 ) )
% 3.82/4.10 = ( cons_int @ ( numeral_numeral_int @ M2 ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M2 ) @ one_one_int ) @ ( numeral_numeral_int @ N2 ) ) ) ) )
% 3.82/4.10 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N2 ) )
% 3.82/4.10 => ( ( upto @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N2 ) )
% 3.82/4.10 = nil_int ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % upto_rec_numeral(1)
% 3.82/4.10 thf(fact_7939_upto__rec__numeral_I2_J,axiom,
% 3.82/4.10 ! [M2: num,N2: num] :
% 3.82/4.10 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 3.82/4.10 => ( ( upto @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 3.82/4.10 = ( cons_int @ ( numeral_numeral_int @ M2 ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M2 ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) )
% 3.82/4.10 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 3.82/4.10 => ( ( upto @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 3.82/4.10 = nil_int ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % upto_rec_numeral(2)
% 3.82/4.10 thf(fact_7940_upto__rec__numeral_I3_J,axiom,
% 3.82/4.10 ! [M2: num,N2: num] :
% 3.82/4.10 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N2 ) )
% 3.82/4.10 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N2 ) )
% 3.82/4.10 = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ one_one_int ) @ ( numeral_numeral_int @ N2 ) ) ) ) )
% 3.82/4.10 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N2 ) )
% 3.82/4.10 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N2 ) )
% 3.82/4.10 = nil_int ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % upto_rec_numeral(3)
% 3.82/4.10 thf(fact_7941_upto__rec__numeral_I4_J,axiom,
% 3.82/4.10 ! [M2: num,N2: num] :
% 3.82/4.10 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 3.82/4.10 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 3.82/4.10 = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) )
% 3.82/4.10 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 3.82/4.10 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 3.82/4.10 = nil_int ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % upto_rec_numeral(4)
% 3.82/4.10 thf(fact_7942_upto__code,axiom,
% 3.82/4.10 ( upto
% 3.82/4.10 = ( ^ [I3: int,J2: int] : ( upto_aux @ I3 @ J2 @ nil_int ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % upto_code
% 3.82/4.10 thf(fact_7943_upto__aux__def,axiom,
% 3.82/4.10 ( upto_aux
% 3.82/4.10 = ( ^ [I3: int,J2: int] : ( append_int @ ( upto @ I3 @ J2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % upto_aux_def
% 3.82/4.10 thf(fact_7944_distinct__upto,axiom,
% 3.82/4.10 ! [I: int,J: int] : ( distinct_int @ ( upto @ I @ J ) ) ).
% 3.82/4.10
% 3.82/4.10 % distinct_upto
% 3.82/4.10 thf(fact_7945_atLeastAtMost__upto,axiom,
% 3.82/4.10 ( set_or1266510415728281911st_int
% 3.82/4.10 = ( ^ [I3: int,J2: int] : ( set_int2 @ ( upto @ I3 @ J2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % atLeastAtMost_upto
% 3.82/4.10 thf(fact_7946_upto__split2,axiom,
% 3.82/4.10 ! [I: int,J: int,K: int] :
% 3.82/4.10 ( ( ord_less_eq_int @ I @ J )
% 3.82/4.10 => ( ( ord_less_eq_int @ J @ K )
% 3.82/4.10 => ( ( upto @ I @ K )
% 3.82/4.10 = ( append_int @ ( upto @ I @ J ) @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % upto_split2
% 3.82/4.10 thf(fact_7947_upto__split1,axiom,
% 3.82/4.10 ! [I: int,J: int,K: int] :
% 3.82/4.10 ( ( ord_less_eq_int @ I @ J )
% 3.82/4.10 => ( ( ord_less_eq_int @ J @ K )
% 3.82/4.10 => ( ( upto @ I @ K )
% 3.82/4.10 = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( upto @ J @ K ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % upto_split1
% 3.82/4.10 thf(fact_7948_atLeastLessThan__upto,axiom,
% 3.82/4.10 ( set_or4662586982721622107an_int
% 3.82/4.10 = ( ^ [I3: int,J2: int] : ( set_int2 @ ( upto @ I3 @ ( minus_minus_int @ J2 @ one_one_int ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % atLeastLessThan_upto
% 3.82/4.10 thf(fact_7949_greaterThanAtMost__upto,axiom,
% 3.82/4.10 ( set_or6656581121297822940st_int
% 3.82/4.10 = ( ^ [I3: int,J2: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I3 @ one_one_int ) @ J2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % greaterThanAtMost_upto
% 3.82/4.10 thf(fact_7950_upto_Osimps,axiom,
% 3.82/4.10 ( upto
% 3.82/4.10 = ( ^ [I3: int,J2: int] : ( if_list_int @ ( ord_less_eq_int @ I3 @ J2 ) @ ( cons_int @ I3 @ ( upto @ ( plus_plus_int @ I3 @ one_one_int ) @ J2 ) ) @ nil_int ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % upto.simps
% 3.82/4.10 thf(fact_7951_upto_Oelims,axiom,
% 3.82/4.10 ! [X: int,Xa2: int,Y: list_int] :
% 3.82/4.10 ( ( ( upto @ X @ Xa2 )
% 3.82/4.10 = Y )
% 3.82/4.10 => ( ( ( ord_less_eq_int @ X @ Xa2 )
% 3.82/4.10 => ( Y
% 3.82/4.10 = ( cons_int @ X @ ( upto @ ( plus_plus_int @ X @ one_one_int ) @ Xa2 ) ) ) )
% 3.82/4.10 & ( ~ ( ord_less_eq_int @ X @ Xa2 )
% 3.82/4.10 => ( Y = nil_int ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % upto.elims
% 3.82/4.10 thf(fact_7952_upto__rec1,axiom,
% 3.82/4.10 ! [I: int,J: int] :
% 3.82/4.10 ( ( ord_less_eq_int @ I @ J )
% 3.82/4.10 => ( ( upto @ I @ J )
% 3.82/4.10 = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % upto_rec1
% 3.82/4.10 thf(fact_7953_upto__rec2,axiom,
% 3.82/4.10 ! [I: int,J: int] :
% 3.82/4.10 ( ( ord_less_eq_int @ I @ J )
% 3.82/4.10 => ( ( upto @ I @ J )
% 3.82/4.10 = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ nil_int ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % upto_rec2
% 3.82/4.10 thf(fact_7954_greaterThanLessThan__upto,axiom,
% 3.82/4.10 ( set_or5832277885323065728an_int
% 3.82/4.10 = ( ^ [I3: int,J2: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I3 @ one_one_int ) @ ( minus_minus_int @ J2 @ one_one_int ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % greaterThanLessThan_upto
% 3.82/4.10 thf(fact_7955_upto__split3,axiom,
% 3.82/4.10 ! [I: int,J: int,K: int] :
% 3.82/4.10 ( ( ord_less_eq_int @ I @ J )
% 3.82/4.10 => ( ( ord_less_eq_int @ J @ K )
% 3.82/4.10 => ( ( upto @ I @ K )
% 3.82/4.10 = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % upto_split3
% 3.82/4.10 thf(fact_7956_list__encode_Opelims,axiom,
% 3.82/4.10 ! [X: list_nat,Y: nat] :
% 3.82/4.10 ( ( ( nat_list_encode @ X )
% 3.82/4.10 = Y )
% 3.82/4.10 => ( ( accp_list_nat @ nat_list_encode_rel @ X )
% 3.82/4.10 => ( ( ( X = nil_nat )
% 3.82/4.10 => ( ( Y = zero_zero_nat )
% 3.82/4.10 => ~ ( accp_list_nat @ nat_list_encode_rel @ nil_nat ) ) )
% 3.82/4.10 => ~ ! [X5: nat,Xs2: list_nat] :
% 3.82/4.10 ( ( X
% 3.82/4.10 = ( cons_nat @ X5 @ Xs2 ) )
% 3.82/4.10 => ( ( Y
% 3.82/4.10 = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X5 @ ( nat_list_encode @ Xs2 ) ) ) ) )
% 3.82/4.10 => ~ ( accp_list_nat @ nat_list_encode_rel @ ( cons_nat @ X5 @ Xs2 ) ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % list_encode.pelims
% 3.82/4.10 thf(fact_7957_upt__rec__numeral,axiom,
% 3.82/4.10 ! [M2: num,N2: num] :
% 3.82/4.10 ( ( ( ord_less_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N2 ) )
% 3.82/4.10 => ( ( upt @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N2 ) )
% 3.82/4.10 = ( cons_nat @ ( numeral_numeral_nat @ M2 ) @ ( upt @ ( suc @ ( numeral_numeral_nat @ M2 ) ) @ ( numeral_numeral_nat @ N2 ) ) ) ) )
% 3.82/4.10 & ( ~ ( ord_less_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N2 ) )
% 3.82/4.10 => ( ( upt @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N2 ) )
% 3.82/4.10 = nil_nat ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % upt_rec_numeral
% 3.82/4.10 thf(fact_7958_remdups__upt,axiom,
% 3.82/4.10 ! [M2: nat,N2: nat] :
% 3.82/4.10 ( ( remdups_nat @ ( upt @ M2 @ N2 ) )
% 3.82/4.10 = ( upt @ M2 @ N2 ) ) ).
% 3.82/4.10
% 3.82/4.10 % remdups_upt
% 3.82/4.10 thf(fact_7959_tl__upt,axiom,
% 3.82/4.10 ! [M2: nat,N2: nat] :
% 3.82/4.10 ( ( tl_nat @ ( upt @ M2 @ N2 ) )
% 3.82/4.10 = ( upt @ ( suc @ M2 ) @ N2 ) ) ).
% 3.82/4.10
% 3.82/4.10 % tl_upt
% 3.82/4.10 thf(fact_7960_hd__upt,axiom,
% 3.82/4.10 ! [I: nat,J: nat] :
% 3.82/4.10 ( ( ord_less_nat @ I @ J )
% 3.82/4.10 => ( ( hd_nat @ ( upt @ I @ J ) )
% 3.82/4.10 = I ) ) ).
% 3.82/4.10
% 3.82/4.10 % hd_upt
% 3.82/4.10 thf(fact_7961_drop__upt,axiom,
% 3.82/4.10 ! [M2: nat,I: nat,J: nat] :
% 3.82/4.10 ( ( drop_nat @ M2 @ ( upt @ I @ J ) )
% 3.82/4.10 = ( upt @ ( plus_plus_nat @ I @ M2 ) @ J ) ) ).
% 3.82/4.10
% 3.82/4.10 % drop_upt
% 3.82/4.10 thf(fact_7962_length__upt,axiom,
% 3.82/4.10 ! [I: nat,J: nat] :
% 3.82/4.10 ( ( size_size_list_nat @ ( upt @ I @ J ) )
% 3.82/4.10 = ( minus_minus_nat @ J @ I ) ) ).
% 3.82/4.10
% 3.82/4.10 % length_upt
% 3.82/4.10 thf(fact_7963_take__upt,axiom,
% 3.82/4.10 ! [I: nat,M2: nat,N2: nat] :
% 3.82/4.10 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ M2 ) @ N2 )
% 3.82/4.10 => ( ( take_nat @ M2 @ ( upt @ I @ N2 ) )
% 3.82/4.10 = ( upt @ I @ ( plus_plus_nat @ I @ M2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % take_upt
% 3.82/4.10 thf(fact_7964_upt__conv__Nil,axiom,
% 3.82/4.10 ! [J: nat,I: nat] :
% 3.82/4.10 ( ( ord_less_eq_nat @ J @ I )
% 3.82/4.10 => ( ( upt @ I @ J )
% 3.82/4.10 = nil_nat ) ) ).
% 3.82/4.10
% 3.82/4.10 % upt_conv_Nil
% 3.82/4.10 thf(fact_7965_sorted__list__of__set__range,axiom,
% 3.82/4.10 ! [M2: nat,N2: nat] :
% 3.82/4.10 ( ( linord2614967742042102400et_nat @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) )
% 3.82/4.10 = ( upt @ M2 @ N2 ) ) ).
% 3.82/4.10
% 3.82/4.10 % sorted_list_of_set_range
% 3.82/4.10 thf(fact_7966_upt__eq__Nil__conv,axiom,
% 3.82/4.10 ! [I: nat,J: nat] :
% 3.82/4.10 ( ( ( upt @ I @ J )
% 3.82/4.10 = nil_nat )
% 3.82/4.10 = ( ( J = zero_zero_nat )
% 3.82/4.10 | ( ord_less_eq_nat @ J @ I ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % upt_eq_Nil_conv
% 3.82/4.10 thf(fact_7967_nth__upt,axiom,
% 3.82/4.10 ! [I: nat,K: nat,J: nat] :
% 3.82/4.10 ( ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J )
% 3.82/4.10 => ( ( nth_nat @ ( upt @ I @ J ) @ K )
% 3.82/4.10 = ( plus_plus_nat @ I @ K ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % nth_upt
% 3.82/4.10 thf(fact_7968_upt__0,axiom,
% 3.82/4.10 ! [I: nat] :
% 3.82/4.10 ( ( upt @ I @ zero_zero_nat )
% 3.82/4.10 = nil_nat ) ).
% 3.82/4.10
% 3.82/4.10 % upt_0
% 3.82/4.10 thf(fact_7969_upt__conv__Cons__Cons,axiom,
% 3.82/4.10 ! [M2: nat,N2: nat,Ns: list_nat,Q3: nat] :
% 3.82/4.10 ( ( ( cons_nat @ M2 @ ( cons_nat @ N2 @ Ns ) )
% 3.82/4.10 = ( upt @ M2 @ Q3 ) )
% 3.82/4.10 = ( ( cons_nat @ N2 @ Ns )
% 3.82/4.10 = ( upt @ ( suc @ M2 ) @ Q3 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % upt_conv_Cons_Cons
% 3.82/4.10 thf(fact_7970_greaterThanAtMost__upt,axiom,
% 3.82/4.10 ( set_or6659071591806873216st_nat
% 3.82/4.10 = ( ^ [N: nat,M: nat] : ( set_nat2 @ ( upt @ ( suc @ N ) @ ( suc @ M ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % greaterThanAtMost_upt
% 3.82/4.10 thf(fact_7971_distinct__upt,axiom,
% 3.82/4.10 ! [I: nat,J: nat] : ( distinct_nat @ ( upt @ I @ J ) ) ).
% 3.82/4.10
% 3.82/4.10 % distinct_upt
% 3.82/4.10 thf(fact_7972_atLeastAtMost__upt,axiom,
% 3.82/4.10 ( set_or1269000886237332187st_nat
% 3.82/4.10 = ( ^ [N: nat,M: nat] : ( set_nat2 @ ( upt @ N @ ( suc @ M ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % atLeastAtMost_upt
% 3.82/4.10 thf(fact_7973_atLeastLessThan__upt,axiom,
% 3.82/4.10 ( set_or4665077453230672383an_nat
% 3.82/4.10 = ( ^ [I3: nat,J2: nat] : ( set_nat2 @ ( upt @ I3 @ J2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % atLeastLessThan_upt
% 3.82/4.10 thf(fact_7974_atLeast__upt,axiom,
% 3.82/4.10 ( set_ord_lessThan_nat
% 3.82/4.10 = ( ^ [N: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ N ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % atLeast_upt
% 3.82/4.10 thf(fact_7975_greaterThanLessThan__upt,axiom,
% 3.82/4.10 ( set_or5834768355832116004an_nat
% 3.82/4.10 = ( ^ [N: nat,M: nat] : ( set_nat2 @ ( upt @ ( suc @ N ) @ M ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % greaterThanLessThan_upt
% 3.82/4.10 thf(fact_7976_atMost__upto,axiom,
% 3.82/4.10 ( set_ord_atMost_nat
% 3.82/4.10 = ( ^ [N: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ ( suc @ N ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % atMost_upto
% 3.82/4.10 thf(fact_7977_upt__conv__Cons,axiom,
% 3.82/4.10 ! [I: nat,J: nat] :
% 3.82/4.10 ( ( ord_less_nat @ I @ J )
% 3.82/4.10 => ( ( upt @ I @ J )
% 3.82/4.10 = ( cons_nat @ I @ ( upt @ ( suc @ I ) @ J ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % upt_conv_Cons
% 3.82/4.10 thf(fact_7978_upt__add__eq__append,axiom,
% 3.82/4.10 ! [I: nat,J: nat,K: nat] :
% 3.82/4.10 ( ( ord_less_eq_nat @ I @ J )
% 3.82/4.10 => ( ( upt @ I @ ( plus_plus_nat @ J @ K ) )
% 3.82/4.10 = ( append_nat @ ( upt @ I @ J ) @ ( upt @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % upt_add_eq_append
% 3.82/4.10 thf(fact_7979_upt__eq__Cons__conv,axiom,
% 3.82/4.10 ! [I: nat,J: nat,X: nat,Xs: list_nat] :
% 3.82/4.10 ( ( ( upt @ I @ J )
% 3.82/4.10 = ( cons_nat @ X @ Xs ) )
% 3.82/4.10 = ( ( ord_less_nat @ I @ J )
% 3.82/4.10 & ( I = X )
% 3.82/4.10 & ( ( upt @ ( plus_plus_nat @ I @ one_one_nat ) @ J )
% 3.82/4.10 = Xs ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % upt_eq_Cons_conv
% 3.82/4.10 thf(fact_7980_upt__rec,axiom,
% 3.82/4.10 ( upt
% 3.82/4.10 = ( ^ [I3: nat,J2: nat] : ( if_list_nat @ ( ord_less_nat @ I3 @ J2 ) @ ( cons_nat @ I3 @ ( upt @ ( suc @ I3 ) @ J2 ) ) @ nil_nat ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % upt_rec
% 3.82/4.10 thf(fact_7981_upt__Suc,axiom,
% 3.82/4.10 ! [I: nat,J: nat] :
% 3.82/4.10 ( ( ( ord_less_eq_nat @ I @ J )
% 3.82/4.10 => ( ( upt @ I @ ( suc @ J ) )
% 3.82/4.10 = ( append_nat @ ( upt @ I @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) )
% 3.82/4.10 & ( ~ ( ord_less_eq_nat @ I @ J )
% 3.82/4.10 => ( ( upt @ I @ ( suc @ J ) )
% 3.82/4.10 = nil_nat ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % upt_Suc
% 3.82/4.10 thf(fact_7982_upt__Suc__append,axiom,
% 3.82/4.10 ! [I: nat,J: nat] :
% 3.82/4.10 ( ( ord_less_eq_nat @ I @ J )
% 3.82/4.10 => ( ( upt @ I @ ( suc @ J ) )
% 3.82/4.10 = ( append_nat @ ( upt @ I @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % upt_Suc_append
% 3.82/4.10 thf(fact_7983_map__Suc__upt,axiom,
% 3.82/4.10 ! [M2: nat,N2: nat] :
% 3.82/4.10 ( ( map_nat_nat @ suc @ ( upt @ M2 @ N2 ) )
% 3.82/4.10 = ( upt @ ( suc @ M2 ) @ ( suc @ N2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % map_Suc_upt
% 3.82/4.10 thf(fact_7984_map__add__upt,axiom,
% 3.82/4.10 ! [N2: nat,M2: nat] :
% 3.82/4.10 ( ( map_nat_nat
% 3.82/4.10 @ ^ [I3: nat] : ( plus_plus_nat @ I3 @ N2 )
% 3.82/4.10 @ ( upt @ zero_zero_nat @ M2 ) )
% 3.82/4.10 = ( upt @ N2 @ ( plus_plus_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % map_add_upt
% 3.82/4.10 thf(fact_7985_map__decr__upt,axiom,
% 3.82/4.10 ! [M2: nat,N2: nat] :
% 3.82/4.10 ( ( map_nat_nat
% 3.82/4.10 @ ^ [N: nat] : ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) )
% 3.82/4.10 @ ( upt @ ( suc @ M2 ) @ ( suc @ N2 ) ) )
% 3.82/4.10 = ( upt @ M2 @ N2 ) ) ).
% 3.82/4.10
% 3.82/4.10 % map_decr_upt
% 3.82/4.10 thf(fact_7986_sum__list__upt,axiom,
% 3.82/4.10 ! [M2: nat,N2: nat] :
% 3.82/4.10 ( ( ord_less_eq_nat @ M2 @ N2 )
% 3.82/4.10 => ( ( groups4561878855575611511st_nat @ ( upt @ M2 @ N2 ) )
% 3.82/4.10 = ( groups3542108847815614940at_nat
% 3.82/4.10 @ ^ [X4: nat] : X4
% 3.82/4.10 @ ( set_or4665077453230672383an_nat @ M2 @ N2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % sum_list_upt
% 3.82/4.10 thf(fact_7987_card__length__sum__list__rec,axiom,
% 3.82/4.10 ! [M2: nat,N6: nat] :
% 3.82/4.10 ( ( ord_less_eq_nat @ one_one_nat @ M2 )
% 3.82/4.10 => ( ( finite_card_list_nat
% 3.82/4.10 @ ( collect_list_nat
% 3.82/4.10 @ ^ [L2: list_nat] :
% 3.82/4.10 ( ( ( size_size_list_nat @ L2 )
% 3.82/4.10 = M2 )
% 3.82/4.10 & ( ( groups4561878855575611511st_nat @ L2 )
% 3.82/4.10 = N6 ) ) ) )
% 3.82/4.10 = ( plus_plus_nat
% 3.82/4.10 @ ( finite_card_list_nat
% 3.82/4.10 @ ( collect_list_nat
% 3.82/4.10 @ ^ [L2: list_nat] :
% 3.82/4.10 ( ( ( size_size_list_nat @ L2 )
% 3.82/4.10 = ( minus_minus_nat @ M2 @ one_one_nat ) )
% 3.82/4.10 & ( ( groups4561878855575611511st_nat @ L2 )
% 3.82/4.10 = N6 ) ) ) )
% 3.82/4.10 @ ( finite_card_list_nat
% 3.82/4.10 @ ( collect_list_nat
% 3.82/4.10 @ ^ [L2: list_nat] :
% 3.82/4.10 ( ( ( size_size_list_nat @ L2 )
% 3.82/4.10 = M2 )
% 3.82/4.10 & ( ( plus_plus_nat @ ( groups4561878855575611511st_nat @ L2 ) @ one_one_nat )
% 3.82/4.10 = N6 ) ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % card_length_sum_list_rec
% 3.82/4.10 thf(fact_7988_card__length__sum__list,axiom,
% 3.82/4.10 ! [M2: nat,N6: nat] :
% 3.82/4.10 ( ( finite_card_list_nat
% 3.82/4.10 @ ( collect_list_nat
% 3.82/4.10 @ ^ [L2: list_nat] :
% 3.82/4.10 ( ( ( size_size_list_nat @ L2 )
% 3.82/4.10 = M2 )
% 3.82/4.10 & ( ( groups4561878855575611511st_nat @ L2 )
% 3.82/4.10 = N6 ) ) ) )
% 3.82/4.10 = ( binomial @ ( minus_minus_nat @ ( plus_plus_nat @ N6 @ M2 ) @ one_one_nat ) @ N6 ) ) ).
% 3.82/4.10
% 3.82/4.10 % card_length_sum_list
% 3.82/4.10 thf(fact_7989_sorted__wrt__upt,axiom,
% 3.82/4.10 ! [M2: nat,N2: nat] : ( sorted_wrt_nat @ ord_less_nat @ ( upt @ M2 @ N2 ) ) ).
% 3.82/4.10
% 3.82/4.10 % sorted_wrt_upt
% 3.82/4.10 thf(fact_7990_sorted__upt,axiom,
% 3.82/4.10 ! [M2: nat,N2: nat] : ( sorted_wrt_nat @ ord_less_eq_nat @ ( upt @ M2 @ N2 ) ) ).
% 3.82/4.10
% 3.82/4.10 % sorted_upt
% 3.82/4.10 thf(fact_7991_sorted__wrt__less__idx,axiom,
% 3.82/4.10 ! [Ns: list_nat,I: nat] :
% 3.82/4.10 ( ( sorted_wrt_nat @ ord_less_nat @ Ns )
% 3.82/4.10 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Ns ) )
% 3.82/4.10 => ( ord_less_eq_nat @ I @ ( nth_nat @ Ns @ I ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % sorted_wrt_less_idx
% 3.82/4.10 thf(fact_7992_sorted__wrt__upto,axiom,
% 3.82/4.10 ! [I: int,J: int] : ( sorted_wrt_int @ ord_less_int @ ( upto @ I @ J ) ) ).
% 3.82/4.10
% 3.82/4.10 % sorted_wrt_upto
% 3.82/4.10 thf(fact_7993_sorted__upto,axiom,
% 3.82/4.10 ! [M2: int,N2: int] : ( sorted_wrt_int @ ord_less_eq_int @ ( upto @ M2 @ N2 ) ) ).
% 3.82/4.10
% 3.82/4.10 % sorted_upto
% 3.82/4.10 thf(fact_7994_pairs__le__eq__Sigma,axiom,
% 3.82/4.10 ! [M2: nat] :
% 3.82/4.10 ( ( collec3392354462482085612at_nat
% 3.82/4.10 @ ( produc6081775807080527818_nat_o
% 3.82/4.10 @ ^ [I3: nat,J2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I3 @ J2 ) @ M2 ) ) )
% 3.82/4.10 = ( produc457027306803732586at_nat @ ( set_ord_atMost_nat @ M2 )
% 3.82/4.10 @ ^ [R4: nat] : ( set_ord_atMost_nat @ ( minus_minus_nat @ M2 @ R4 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % pairs_le_eq_Sigma
% 3.82/4.10 thf(fact_7995_natLess__def,axiom,
% 3.82/4.10 ( bNF_Ca8459412986667044542atLess
% 3.82/4.10 = ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % natLess_def
% 3.82/4.10 thf(fact_7996_Restr__natLeq,axiom,
% 3.82/4.10 ! [N2: nat] :
% 3.82/4.10 ( ( inf_in2572325071724192079at_nat @ bNF_Ca8665028551170535155natLeq
% 3.82/4.10 @ ( produc457027306803732586at_nat
% 3.82/4.10 @ ( collect_nat
% 3.82/4.10 @ ^ [X4: nat] : ( ord_less_nat @ X4 @ N2 ) )
% 3.82/4.10 @ ^ [Uu3: nat] :
% 3.82/4.10 ( collect_nat
% 3.82/4.10 @ ^ [X4: nat] : ( ord_less_nat @ X4 @ N2 ) ) ) )
% 3.82/4.10 = ( collec3392354462482085612at_nat
% 3.82/4.10 @ ( produc6081775807080527818_nat_o
% 3.82/4.10 @ ^ [X4: nat,Y5: nat] :
% 3.82/4.10 ( ( ord_less_nat @ X4 @ N2 )
% 3.82/4.10 & ( ord_less_nat @ Y5 @ N2 )
% 3.82/4.10 & ( ord_less_eq_nat @ X4 @ Y5 ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % Restr_natLeq
% 3.82/4.10 thf(fact_7997_natLeq__def,axiom,
% 3.82/4.10 ( bNF_Ca8665028551170535155natLeq
% 3.82/4.10 = ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_eq_nat ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % natLeq_def
% 3.82/4.10 thf(fact_7998_Restr__natLeq2,axiom,
% 3.82/4.10 ! [N2: nat] :
% 3.82/4.10 ( ( inf_in2572325071724192079at_nat @ bNF_Ca8665028551170535155natLeq
% 3.82/4.10 @ ( produc457027306803732586at_nat @ ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N2 )
% 3.82/4.10 @ ^ [Uu3: nat] : ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N2 ) ) )
% 3.82/4.10 = ( collec3392354462482085612at_nat
% 3.82/4.10 @ ( produc6081775807080527818_nat_o
% 3.82/4.10 @ ^ [X4: nat,Y5: nat] :
% 3.82/4.10 ( ( ord_less_nat @ X4 @ N2 )
% 3.82/4.10 & ( ord_less_nat @ Y5 @ N2 )
% 3.82/4.10 & ( ord_less_eq_nat @ X4 @ Y5 ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % Restr_natLeq2
% 3.82/4.10 thf(fact_7999_natLeq__underS__less,axiom,
% 3.82/4.10 ! [N2: nat] :
% 3.82/4.10 ( ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N2 )
% 3.82/4.10 = ( collect_nat
% 3.82/4.10 @ ^ [X4: nat] : ( ord_less_nat @ X4 @ N2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % natLeq_underS_less
% 3.82/4.10 thf(fact_8000_sort__upt,axiom,
% 3.82/4.10 ! [M2: nat,N2: nat] :
% 3.82/4.10 ( ( linord738340561235409698at_nat
% 3.82/4.10 @ ^ [X4: nat] : X4
% 3.82/4.10 @ ( upt @ M2 @ N2 ) )
% 3.82/4.10 = ( upt @ M2 @ N2 ) ) ).
% 3.82/4.10
% 3.82/4.10 % sort_upt
% 3.82/4.10 thf(fact_8001_sort__upto,axiom,
% 3.82/4.10 ! [I: int,J: int] :
% 3.82/4.10 ( ( linord1735203802627413978nt_int
% 3.82/4.10 @ ^ [X4: int] : X4
% 3.82/4.10 @ ( upto @ I @ J ) )
% 3.82/4.10 = ( upto @ I @ J ) ) ).
% 3.82/4.10
% 3.82/4.10 % sort_upto
% 3.82/4.10 thf(fact_8002_Field__natLeq__on,axiom,
% 3.82/4.10 ! [N2: nat] :
% 3.82/4.10 ( ( field_nat
% 3.82/4.10 @ ( collec3392354462482085612at_nat
% 3.82/4.10 @ ( produc6081775807080527818_nat_o
% 3.82/4.10 @ ^ [X4: nat,Y5: nat] :
% 3.82/4.10 ( ( ord_less_nat @ X4 @ N2 )
% 3.82/4.10 & ( ord_less_nat @ Y5 @ N2 )
% 3.82/4.10 & ( ord_less_eq_nat @ X4 @ Y5 ) ) ) ) )
% 3.82/4.10 = ( collect_nat
% 3.82/4.10 @ ^ [X4: nat] : ( ord_less_nat @ X4 @ N2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % Field_natLeq_on
% 3.82/4.10 thf(fact_8003_wf__less,axiom,
% 3.82/4.10 wf_nat @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ).
% 3.82/4.10
% 3.82/4.10 % wf_less
% 3.82/4.10 thf(fact_8004_wf__int__ge__less__than2,axiom,
% 3.82/4.10 ! [D: int] : ( wf_int @ ( int_ge_less_than2 @ D ) ) ).
% 3.82/4.10
% 3.82/4.10 % wf_int_ge_less_than2
% 3.82/4.10 thf(fact_8005_wf__int__ge__less__than,axiom,
% 3.82/4.10 ! [D: int] : ( wf_int @ ( int_ge_less_than @ D ) ) ).
% 3.82/4.10
% 3.82/4.10 % wf_int_ge_less_than
% 3.82/4.10 thf(fact_8006_infinite__enumerate,axiom,
% 3.82/4.10 ! [S2: set_nat] :
% 3.82/4.10 ( ~ ( finite_finite_nat @ S2 )
% 3.82/4.10 => ? [R3: nat > nat] :
% 3.82/4.10 ( ( order_5726023648592871131at_nat @ R3 )
% 3.82/4.10 & ! [N7: nat] : ( member_nat @ ( R3 @ N7 ) @ S2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % infinite_enumerate
% 3.82/4.10 thf(fact_8007_strict__mono__imp__increasing,axiom,
% 3.82/4.10 ! [F: nat > nat,N2: nat] :
% 3.82/4.10 ( ( order_5726023648592871131at_nat @ F )
% 3.82/4.10 => ( ord_less_eq_nat @ N2 @ ( F @ N2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % strict_mono_imp_increasing
% 3.82/4.10 thf(fact_8008_enumerate__Ex,axiom,
% 3.82/4.10 ! [S2: set_nat,S: nat] :
% 3.82/4.10 ( ~ ( finite_finite_nat @ S2 )
% 3.82/4.10 => ( ( member_nat @ S @ S2 )
% 3.82/4.10 => ? [N3: nat] :
% 3.82/4.10 ( ( infini8530281810654367211te_nat @ S2 @ N3 )
% 3.82/4.10 = S ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % enumerate_Ex
% 3.82/4.10 thf(fact_8009_le__enumerate,axiom,
% 3.82/4.10 ! [S2: set_nat,N2: nat] :
% 3.82/4.10 ( ~ ( finite_finite_nat @ S2 )
% 3.82/4.10 => ( ord_less_eq_nat @ N2 @ ( infini8530281810654367211te_nat @ S2 @ N2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % le_enumerate
% 3.82/4.10 thf(fact_8010_strict__mono__enumerate,axiom,
% 3.82/4.10 ! [S2: set_nat] :
% 3.82/4.10 ( ~ ( finite_finite_nat @ S2 )
% 3.82/4.10 => ( order_5726023648592871131at_nat @ ( infini8530281810654367211te_nat @ S2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % strict_mono_enumerate
% 3.82/4.10 thf(fact_8011_range__enumerate,axiom,
% 3.82/4.10 ! [S2: set_nat] :
% 3.82/4.10 ( ~ ( finite_finite_nat @ S2 )
% 3.82/4.10 => ( ( image_nat_nat @ ( infini8530281810654367211te_nat @ S2 ) @ top_top_set_nat )
% 3.82/4.10 = S2 ) ) ).
% 3.82/4.10
% 3.82/4.10 % range_enumerate
% 3.82/4.10 thf(fact_8012_finite__le__enumerate,axiom,
% 3.82/4.10 ! [S2: set_nat,N2: nat] :
% 3.82/4.10 ( ( finite_finite_nat @ S2 )
% 3.82/4.10 => ( ( ord_less_nat @ N2 @ ( finite_card_nat @ S2 ) )
% 3.82/4.10 => ( ord_less_eq_nat @ N2 @ ( infini8530281810654367211te_nat @ S2 @ N2 ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % finite_le_enumerate
% 3.82/4.10 thf(fact_8013_bij__enumerate,axiom,
% 3.82/4.10 ! [S2: set_nat] :
% 3.82/4.10 ( ~ ( finite_finite_nat @ S2 )
% 3.82/4.10 => ( bij_betw_nat_nat @ ( infini8530281810654367211te_nat @ S2 ) @ top_top_set_nat @ S2 ) ) ).
% 3.82/4.10
% 3.82/4.10 % bij_enumerate
% 3.82/4.10 thf(fact_8014_Least__eq__0,axiom,
% 3.82/4.10 ! [P: nat > $o] :
% 3.82/4.10 ( ( P @ zero_zero_nat )
% 3.82/4.10 => ( ( ord_Least_nat @ P )
% 3.82/4.10 = zero_zero_nat ) ) ).
% 3.82/4.10
% 3.82/4.10 % Least_eq_0
% 3.82/4.10 thf(fact_8015_Least__Suc2,axiom,
% 3.82/4.10 ! [P: nat > $o,N2: nat,Q: nat > $o,M2: nat] :
% 3.82/4.10 ( ( P @ N2 )
% 3.82/4.10 => ( ( Q @ M2 )
% 3.82/4.10 => ( ~ ( P @ zero_zero_nat )
% 3.82/4.10 => ( ! [K3: nat] :
% 3.82/4.10 ( ( P @ ( suc @ K3 ) )
% 3.82/4.10 = ( Q @ K3 ) )
% 3.82/4.10 => ( ( ord_Least_nat @ P )
% 3.82/4.10 = ( suc @ ( ord_Least_nat @ Q ) ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % Least_Suc2
% 3.82/4.10 thf(fact_8016_Least__Suc,axiom,
% 3.82/4.10 ! [P: nat > $o,N2: nat] :
% 3.82/4.10 ( ( P @ N2 )
% 3.82/4.10 => ( ~ ( P @ zero_zero_nat )
% 3.82/4.10 => ( ( ord_Least_nat @ P )
% 3.82/4.10 = ( suc
% 3.82/4.10 @ ( ord_Least_nat
% 3.82/4.10 @ ^ [M: nat] : ( P @ ( suc @ M ) ) ) ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % Least_Suc
% 3.82/4.10 thf(fact_8017_last__upt,axiom,
% 3.82/4.10 ! [I: nat,J: nat] :
% 3.82/4.10 ( ( ord_less_nat @ I @ J )
% 3.82/4.10 => ( ( last_nat @ ( upt @ I @ J ) )
% 3.82/4.10 = ( minus_minus_nat @ J @ one_one_nat ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % last_upt
% 3.82/4.10 thf(fact_8018_vimage__Suc__insert__0,axiom,
% 3.82/4.10 ! [A2: set_nat] :
% 3.82/4.10 ( ( vimage_nat_nat @ suc @ ( insert_nat @ zero_zero_nat @ A2 ) )
% 3.82/4.10 = ( vimage_nat_nat @ suc @ A2 ) ) ).
% 3.82/4.10
% 3.82/4.10 % vimage_Suc_insert_0
% 3.82/4.10 thf(fact_8019_finite__vimage__Suc__iff,axiom,
% 3.82/4.10 ! [F3: set_nat] :
% 3.82/4.10 ( ( finite_finite_nat @ ( vimage_nat_nat @ suc @ F3 ) )
% 3.82/4.10 = ( finite_finite_nat @ F3 ) ) ).
% 3.82/4.10
% 3.82/4.10 % finite_vimage_Suc_iff
% 3.82/4.10 thf(fact_8020_vimage__Suc__insert__Suc,axiom,
% 3.82/4.10 ! [N2: nat,A2: set_nat] :
% 3.82/4.10 ( ( vimage_nat_nat @ suc @ ( insert_nat @ ( suc @ N2 ) @ A2 ) )
% 3.82/4.10 = ( insert_nat @ N2 @ ( vimage_nat_nat @ suc @ A2 ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % vimage_Suc_insert_Suc
% 3.82/4.10 thf(fact_8021_set__decode__div__2,axiom,
% 3.82/4.10 ! [X: nat] :
% 3.82/4.10 ( ( nat_set_decode @ ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 3.82/4.10 = ( vimage_nat_nat @ suc @ ( nat_set_decode @ X ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % set_decode_div_2
% 3.82/4.10 thf(fact_8022_set__encode__vimage__Suc,axiom,
% 3.82/4.10 ! [A2: set_nat] :
% 3.82/4.10 ( ( nat_set_encode @ ( vimage_nat_nat @ suc @ A2 ) )
% 3.82/4.10 = ( divide_divide_nat @ ( nat_set_encode @ A2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 3.82/4.10
% 3.82/4.10 % set_encode_vimage_Suc
% 3.82/4.10 thf(fact_8023_GreatestI__nat,axiom,
% 3.82/4.10 ! [P: nat > $o,K: nat,B2: nat] :
% 3.82/4.10 ( ( P @ K )
% 3.82/4.11 => ( ! [Y3: nat] :
% 3.82/4.11 ( ( P @ Y3 )
% 3.82/4.11 => ( ord_less_eq_nat @ Y3 @ B2 ) )
% 3.82/4.11 => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % GreatestI_nat
% 3.82/4.11 thf(fact_8024_Greatest__le__nat,axiom,
% 3.82/4.11 ! [P: nat > $o,K: nat,B2: nat] :
% 3.82/4.11 ( ( P @ K )
% 3.82/4.11 => ( ! [Y3: nat] :
% 3.82/4.11 ( ( P @ Y3 )
% 3.82/4.11 => ( ord_less_eq_nat @ Y3 @ B2 ) )
% 3.82/4.11 => ( ord_less_eq_nat @ K @ ( order_Greatest_nat @ P ) ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % Greatest_le_nat
% 3.82/4.11 thf(fact_8025_GreatestI__ex__nat,axiom,
% 3.82/4.11 ! [P: nat > $o,B2: nat] :
% 3.82/4.11 ( ? [X_1: nat] : ( P @ X_1 )
% 3.82/4.11 => ( ! [Y3: nat] :
% 3.82/4.11 ( ( P @ Y3 )
% 3.82/4.11 => ( ord_less_eq_nat @ Y3 @ B2 ) )
% 3.82/4.11 => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % GreatestI_ex_nat
% 3.82/4.11 thf(fact_8026_natLeq__on__wo__rel,axiom,
% 3.82/4.11 ! [N2: nat] :
% 3.82/4.11 ( bNF_We3818239936649020644el_nat
% 3.82/4.11 @ ( collec3392354462482085612at_nat
% 3.82/4.11 @ ( produc6081775807080527818_nat_o
% 3.82/4.11 @ ^ [X4: nat,Y5: nat] :
% 3.82/4.11 ( ( ord_less_nat @ X4 @ N2 )
% 3.82/4.11 & ( ord_less_nat @ Y5 @ N2 )
% 3.82/4.11 & ( ord_less_eq_nat @ X4 @ Y5 ) ) ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % natLeq_on_wo_rel
% 3.82/4.11 thf(fact_8027_Suc__0__mod__numeral,axiom,
% 3.82/4.11 ! [K: num] :
% 3.82/4.11 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 3.82/4.11 = ( product_snd_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % Suc_0_mod_numeral
% 3.82/4.11 thf(fact_8028_Suc__0__div__numeral,axiom,
% 3.82/4.11 ! [K: num] :
% 3.82/4.11 ( ( divide_divide_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 3.82/4.11 = ( product_fst_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % Suc_0_div_numeral
% 3.82/4.11 thf(fact_8029_bezw__non__0,axiom,
% 3.82/4.11 ! [Y: nat,X: nat] :
% 3.82/4.11 ( ( ord_less_nat @ zero_zero_nat @ Y )
% 3.82/4.11 => ( ( bezw @ X @ Y )
% 3.82/4.11 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Y ) ) ) ) ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % bezw_non_0
% 3.82/4.11 thf(fact_8030_bezw_Oelims,axiom,
% 3.82/4.11 ! [X: nat,Xa2: nat,Y: product_prod_int_int] :
% 3.82/4.11 ( ( ( bezw @ X @ Xa2 )
% 3.82/4.11 = Y )
% 3.82/4.11 => ( ( ( Xa2 = zero_zero_nat )
% 3.82/4.11 => ( Y
% 3.82/4.11 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 3.82/4.11 & ( ( Xa2 != zero_zero_nat )
% 3.82/4.11 => ( Y
% 3.82/4.11 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Xa2 ) ) ) ) ) ) ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % bezw.elims
% 3.82/4.11 thf(fact_8031_bezw_Osimps,axiom,
% 3.82/4.11 ( bezw
% 3.82/4.11 = ( ^ [X4: 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 @ X4 @ Y5 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y5 @ ( modulo_modulo_nat @ X4 @ Y5 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y5 @ ( modulo_modulo_nat @ X4 @ Y5 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X4 @ Y5 ) ) ) ) ) ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % bezw.simps
% 3.82/4.11 thf(fact_8032_bezw_Opelims,axiom,
% 3.82/4.11 ! [X: nat,Xa2: nat,Y: product_prod_int_int] :
% 3.82/4.11 ( ( ( bezw @ X @ Xa2 )
% 3.82/4.11 = Y )
% 3.82/4.11 => ( ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) )
% 3.82/4.11 => ~ ( ( ( ( Xa2 = zero_zero_nat )
% 3.82/4.11 => ( Y
% 3.82/4.11 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 3.82/4.11 & ( ( Xa2 != zero_zero_nat )
% 3.82/4.11 => ( Y
% 3.82/4.11 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Xa2 ) ) ) ) ) ) ) )
% 3.82/4.11 => ~ ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) ) ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % bezw.pelims
% 3.82/4.11 thf(fact_8033_pair__lessI2,axiom,
% 3.82/4.11 ! [A: nat,B2: nat,S: nat,T: nat] :
% 3.82/4.11 ( ( ord_less_eq_nat @ A @ B2 )
% 3.82/4.11 => ( ( ord_less_nat @ S @ T )
% 3.82/4.11 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S ) @ ( product_Pair_nat_nat @ B2 @ T ) ) @ fun_pair_less ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % pair_lessI2
% 3.82/4.11 thf(fact_8034_pair__less__iff1,axiom,
% 3.82/4.11 ! [X: nat,Y: nat,Z3: nat] :
% 3.82/4.11 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( product_Pair_nat_nat @ X @ Z3 ) ) @ fun_pair_less )
% 3.82/4.11 = ( ord_less_nat @ Y @ Z3 ) ) ).
% 3.82/4.11
% 3.82/4.11 % pair_less_iff1
% 3.82/4.11 thf(fact_8035_pair__lessI1,axiom,
% 3.82/4.11 ! [A: nat,B2: nat,S: nat,T: nat] :
% 3.82/4.11 ( ( ord_less_nat @ A @ B2 )
% 3.82/4.11 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S ) @ ( product_Pair_nat_nat @ B2 @ T ) ) @ fun_pair_less ) ) ).
% 3.82/4.11
% 3.82/4.11 % pair_lessI1
% 3.82/4.11 thf(fact_8036_prod__decode__aux_Opelims,axiom,
% 3.82/4.11 ! [X: nat,Xa2: nat,Y: product_prod_nat_nat] :
% 3.82/4.11 ( ( ( nat_prod_decode_aux @ X @ Xa2 )
% 3.82/4.11 = Y )
% 3.82/4.11 => ( ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) )
% 3.82/4.11 => ~ ( ( ( ( ord_less_eq_nat @ Xa2 @ X )
% 3.82/4.11 => ( Y
% 3.82/4.11 = ( product_Pair_nat_nat @ Xa2 @ ( minus_minus_nat @ X @ Xa2 ) ) ) )
% 3.82/4.11 & ( ~ ( ord_less_eq_nat @ Xa2 @ X )
% 3.82/4.11 => ( Y
% 3.82/4.11 = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa2 @ ( suc @ X ) ) ) ) ) )
% 3.82/4.11 => ~ ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) ) ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % prod_decode_aux.pelims
% 3.82/4.11 thf(fact_8037_pair__leqI2,axiom,
% 3.82/4.11 ! [A: nat,B2: nat,S: nat,T: nat] :
% 3.82/4.11 ( ( ord_less_eq_nat @ A @ B2 )
% 3.82/4.11 => ( ( ord_less_eq_nat @ S @ T )
% 3.82/4.11 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S ) @ ( product_Pair_nat_nat @ B2 @ T ) ) @ fun_pair_leq ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % pair_leqI2
% 3.82/4.11 thf(fact_8038_pair__leqI1,axiom,
% 3.82/4.11 ! [A: nat,B2: nat,S: nat,T: nat] :
% 3.82/4.11 ( ( ord_less_nat @ A @ B2 )
% 3.82/4.11 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S ) @ ( product_Pair_nat_nat @ B2 @ T ) ) @ fun_pair_leq ) ) ).
% 3.82/4.11
% 3.82/4.11 % pair_leqI1
% 3.82/4.11 thf(fact_8039_gcd__nat_Oordering__top__axioms,axiom,
% 3.82/4.11 ( ordering_top_nat @ dvd_dvd_nat
% 3.82/4.11 @ ^ [M: nat,N: nat] :
% 3.82/4.11 ( ( dvd_dvd_nat @ M @ N )
% 3.82/4.11 & ( M != N ) )
% 3.82/4.11 @ zero_zero_nat ) ).
% 3.82/4.11
% 3.82/4.11 % gcd_nat.ordering_top_axioms
% 3.82/4.11 thf(fact_8040_bot__nat__0_Oordering__top__axioms,axiom,
% 3.82/4.11 ( ordering_top_nat
% 3.82/4.11 @ ^ [X4: nat,Y5: nat] : ( ord_less_eq_nat @ Y5 @ X4 )
% 3.82/4.11 @ ^ [X4: nat,Y5: nat] : ( ord_less_nat @ Y5 @ X4 )
% 3.82/4.11 @ zero_zero_nat ) ).
% 3.82/4.11
% 3.82/4.11 % bot_nat_0.ordering_top_axioms
% 3.82/4.11 thf(fact_8041_less__eq__enat__def,axiom,
% 3.82/4.11 ( ord_le2932123472753598470d_enat
% 3.82/4.11 = ( ^ [M: extended_enat] :
% 3.82/4.11 ( extended_case_enat_o
% 3.82/4.11 @ ^ [N1: nat] :
% 3.82/4.11 ( extended_case_enat_o
% 3.82/4.11 @ ^ [M1: nat] : ( ord_less_eq_nat @ M1 @ N1 )
% 3.82/4.11 @ $false
% 3.82/4.11 @ M )
% 3.82/4.11 @ $true ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % less_eq_enat_def
% 3.82/4.11 thf(fact_8042_less__enat__def,axiom,
% 3.82/4.11 ( ord_le72135733267957522d_enat
% 3.82/4.11 = ( ^ [M: extended_enat,N: extended_enat] :
% 3.82/4.11 ( extended_case_enat_o
% 3.82/4.11 @ ^ [M1: nat] : ( extended_case_enat_o @ ( ord_less_nat @ M1 ) @ $true @ N )
% 3.82/4.11 @ $false
% 3.82/4.11 @ M ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % less_enat_def
% 3.82/4.11 thf(fact_8043_prod__decode__triangle__add,axiom,
% 3.82/4.11 ! [K: nat,M2: nat] :
% 3.82/4.11 ( ( nat_prod_decode @ ( plus_plus_nat @ ( nat_triangle @ K ) @ M2 ) )
% 3.82/4.11 = ( nat_prod_decode_aux @ K @ M2 ) ) ).
% 3.82/4.11
% 3.82/4.11 % prod_decode_triangle_add
% 3.82/4.11 thf(fact_8044_prod__decode__def,axiom,
% 3.82/4.11 ( nat_prod_decode
% 3.82/4.11 = ( nat_prod_decode_aux @ zero_zero_nat ) ) ).
% 3.82/4.11
% 3.82/4.11 % prod_decode_def
% 3.82/4.11 thf(fact_8045_list__decode_Opinduct,axiom,
% 3.82/4.11 ! [A0: nat,P: nat > $o] :
% 3.82/4.11 ( ( accp_nat @ nat_list_decode_rel @ A0 )
% 3.82/4.11 => ( ( ( accp_nat @ nat_list_decode_rel @ zero_zero_nat )
% 3.82/4.11 => ( P @ zero_zero_nat ) )
% 3.82/4.11 => ( ! [N3: nat] :
% 3.82/4.11 ( ( accp_nat @ nat_list_decode_rel @ ( suc @ N3 ) )
% 3.82/4.11 => ( ! [X2: nat,Y6: nat] :
% 3.82/4.11 ( ( ( product_Pair_nat_nat @ X2 @ Y6 )
% 3.82/4.11 = ( nat_prod_decode @ N3 ) )
% 3.82/4.11 => ( P @ Y6 ) )
% 3.82/4.11 => ( P @ ( suc @ N3 ) ) ) )
% 3.82/4.11 => ( P @ A0 ) ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % list_decode.pinduct
% 3.82/4.11 thf(fact_8046_list__decode_Oelims,axiom,
% 3.82/4.11 ! [X: nat,Y: list_nat] :
% 3.82/4.11 ( ( ( nat_list_decode @ X )
% 3.82/4.11 = Y )
% 3.82/4.11 => ( ( ( X = zero_zero_nat )
% 3.82/4.11 => ( Y != nil_nat ) )
% 3.82/4.11 => ~ ! [N3: nat] :
% 3.82/4.11 ( ( X
% 3.82/4.11 = ( suc @ N3 ) )
% 3.82/4.11 => ( Y
% 3.82/4.11 != ( produc2761476792215241774st_nat
% 3.82/4.11 @ ^ [X4: nat,Y5: nat] : ( cons_nat @ X4 @ ( nat_list_decode @ Y5 ) )
% 3.82/4.11 @ ( nat_prod_decode @ N3 ) ) ) ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % list_decode.elims
% 3.82/4.11 thf(fact_8047_list__decode_Opsimps_I1_J,axiom,
% 3.82/4.11 ( ( accp_nat @ nat_list_decode_rel @ zero_zero_nat )
% 3.82/4.11 => ( ( nat_list_decode @ zero_zero_nat )
% 3.82/4.11 = nil_nat ) ) ).
% 3.82/4.11
% 3.82/4.11 % list_decode.psimps(1)
% 3.82/4.11 thf(fact_8048_list__decode_Osimps_I1_J,axiom,
% 3.82/4.11 ( ( nat_list_decode @ zero_zero_nat )
% 3.82/4.11 = nil_nat ) ).
% 3.82/4.11
% 3.82/4.11 % list_decode.simps(1)
% 3.82/4.11 thf(fact_8049_list__decode_Opsimps_I2_J,axiom,
% 3.82/4.11 ! [N2: nat] :
% 3.82/4.11 ( ( accp_nat @ nat_list_decode_rel @ ( suc @ N2 ) )
% 3.82/4.11 => ( ( nat_list_decode @ ( suc @ N2 ) )
% 3.82/4.11 = ( produc2761476792215241774st_nat
% 3.82/4.11 @ ^ [X4: nat,Y5: nat] : ( cons_nat @ X4 @ ( nat_list_decode @ Y5 ) )
% 3.82/4.11 @ ( nat_prod_decode @ N2 ) ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % list_decode.psimps(2)
% 3.82/4.11 thf(fact_8050_list__decode_Osimps_I2_J,axiom,
% 3.82/4.11 ! [N2: nat] :
% 3.82/4.11 ( ( nat_list_decode @ ( suc @ N2 ) )
% 3.82/4.11 = ( produc2761476792215241774st_nat
% 3.82/4.11 @ ^ [X4: nat,Y5: nat] : ( cons_nat @ X4 @ ( nat_list_decode @ Y5 ) )
% 3.82/4.11 @ ( nat_prod_decode @ N2 ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % list_decode.simps(2)
% 3.82/4.11 thf(fact_8051_list__decode_Opelims,axiom,
% 3.82/4.11 ! [X: nat,Y: list_nat] :
% 3.82/4.11 ( ( ( nat_list_decode @ X )
% 3.82/4.11 = Y )
% 3.82/4.11 => ( ( accp_nat @ nat_list_decode_rel @ X )
% 3.82/4.11 => ( ( ( X = zero_zero_nat )
% 3.82/4.11 => ( ( Y = nil_nat )
% 3.82/4.11 => ~ ( accp_nat @ nat_list_decode_rel @ zero_zero_nat ) ) )
% 3.82/4.11 => ~ ! [N3: nat] :
% 3.82/4.11 ( ( X
% 3.82/4.11 = ( suc @ N3 ) )
% 3.82/4.11 => ( ( Y
% 3.82/4.11 = ( produc2761476792215241774st_nat
% 3.82/4.11 @ ^ [X4: nat,Y5: nat] : ( cons_nat @ X4 @ ( nat_list_decode @ Y5 ) )
% 3.82/4.11 @ ( nat_prod_decode @ N3 ) ) )
% 3.82/4.11 => ~ ( accp_nat @ nat_list_decode_rel @ ( suc @ N3 ) ) ) ) ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % list_decode.pelims
% 3.82/4.11 thf(fact_8052_UNIV__char__of__nat,axiom,
% 3.82/4.11 ( top_top_set_char
% 3.82/4.11 = ( image_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % UNIV_char_of_nat
% 3.82/4.11 thf(fact_8053_inj__on__char__of__nat,axiom,
% 3.82/4.11 inj_on_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % inj_on_char_of_nat
% 3.82/4.11 thf(fact_8054_range__nat__of__char,axiom,
% 3.82/4.11 ( ( image_char_nat @ comm_s629917340098488124ar_nat @ top_top_set_char )
% 3.82/4.11 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % range_nat_of_char
% 3.82/4.11 thf(fact_8055_one__int_Otransfer,axiom,
% 3.82/4.11 pcr_int @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) @ one_one_int ).
% 3.82/4.11
% 3.82/4.11 % one_int.transfer
% 3.82/4.11 thf(fact_8056_zero__int_Otransfer,axiom,
% 3.82/4.11 pcr_int @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) @ zero_zero_int ).
% 3.82/4.11
% 3.82/4.11 % zero_int.transfer
% 3.82/4.11 thf(fact_8057_nat__of__char__less__256,axiom,
% 3.82/4.11 ! [C: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C ) @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % nat_of_char_less_256
% 3.82/4.11 thf(fact_8058_Rats__abs__nat__div__natE,axiom,
% 3.82/4.11 ! [X: real] :
% 3.82/4.11 ( ( member_real @ X @ field_5140801741446780682s_real )
% 3.82/4.11 => ~ ! [M3: nat,N3: nat] :
% 3.82/4.11 ( ( N3 != zero_zero_nat )
% 3.82/4.11 => ( ( ( abs_abs_real @ X )
% 3.82/4.11 = ( divide_divide_real @ ( semiri5074537144036343181t_real @ M3 ) @ ( semiri5074537144036343181t_real @ N3 ) ) )
% 3.82/4.11 => ~ ( algebr934650988132801477me_nat @ M3 @ N3 ) ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % Rats_abs_nat_div_natE
% 3.82/4.11 thf(fact_8059_coprime__Suc__left__nat,axiom,
% 3.82/4.11 ! [N2: nat] : ( algebr934650988132801477me_nat @ ( suc @ N2 ) @ N2 ) ).
% 3.82/4.11
% 3.82/4.11 % coprime_Suc_left_nat
% 3.82/4.11 thf(fact_8060_coprime__Suc__right__nat,axiom,
% 3.82/4.11 ! [N2: nat] : ( algebr934650988132801477me_nat @ N2 @ ( suc @ N2 ) ) ).
% 3.82/4.11
% 3.82/4.11 % coprime_Suc_right_nat
% 3.82/4.11 thf(fact_8061_coprime__Suc__0__left,axiom,
% 3.82/4.11 ! [N2: nat] : ( algebr934650988132801477me_nat @ ( suc @ zero_zero_nat ) @ N2 ) ).
% 3.82/4.11
% 3.82/4.11 % coprime_Suc_0_left
% 3.82/4.11 thf(fact_8062_coprime__Suc__0__right,axiom,
% 3.82/4.11 ! [N2: nat] : ( algebr934650988132801477me_nat @ N2 @ ( suc @ zero_zero_nat ) ) ).
% 3.82/4.11
% 3.82/4.11 % coprime_Suc_0_right
% 3.82/4.11 thf(fact_8063_eventually__prod__sequentially,axiom,
% 3.82/4.11 ! [P: product_prod_nat_nat > $o] :
% 3.82/4.11 ( ( eventu1038000079068216329at_nat @ P @ ( prod_filter_nat_nat @ at_top_nat @ at_top_nat ) )
% 3.82/4.11 = ( ? [N5: nat] :
% 3.82/4.11 ! [M: nat] :
% 3.82/4.11 ( ( ord_less_eq_nat @ N5 @ M )
% 3.82/4.11 => ! [N: nat] :
% 3.82/4.11 ( ( ord_less_eq_nat @ N5 @ N )
% 3.82/4.11 => ( P @ ( product_Pair_nat_nat @ N @ M ) ) ) ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % eventually_prod_sequentially
% 3.82/4.11 thf(fact_8064_coprime__diff__one__left__nat,axiom,
% 3.82/4.11 ! [N2: nat] :
% 3.82/4.11 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.11 => ( algebr934650988132801477me_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) @ N2 ) ) ).
% 3.82/4.11
% 3.82/4.11 % coprime_diff_one_left_nat
% 3.82/4.11 thf(fact_8065_coprime__diff__one__right__nat,axiom,
% 3.82/4.11 ! [N2: nat] :
% 3.82/4.11 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.82/4.11 => ( algebr934650988132801477me_nat @ N2 @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % coprime_diff_one_right_nat
% 3.82/4.11 thf(fact_8066_minus__int_Otransfer,axiom,
% 3.82/4.11 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 3.82/4.11 @ ( produc27273713700761075at_nat
% 3.82/4.11 @ ^ [X4: nat,Y5: nat] :
% 3.82/4.11 ( produc2626176000494625587at_nat
% 3.82/4.11 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ V4 ) @ ( plus_plus_nat @ Y5 @ U2 ) ) ) )
% 3.82/4.11 @ minus_minus_int ) ).
% 3.82/4.11
% 3.82/4.11 % minus_int.transfer
% 3.82/4.11 thf(fact_8067_plus__int_Otransfer,axiom,
% 3.82/4.11 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 3.82/4.11 @ ( produc27273713700761075at_nat
% 3.82/4.11 @ ^ [X4: nat,Y5: nat] :
% 3.82/4.11 ( produc2626176000494625587at_nat
% 3.82/4.11 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ U2 ) @ ( plus_plus_nat @ Y5 @ V4 ) ) ) )
% 3.82/4.11 @ plus_plus_int ) ).
% 3.82/4.11
% 3.82/4.11 % plus_int.transfer
% 3.82/4.11 thf(fact_8068_less__int_Otransfer,axiom,
% 3.82/4.11 ( bNF_re717283939379294677_int_o @ pcr_int
% 3.82/4.11 @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 3.82/4.11 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 ) )
% 3.82/4.11 @ ( produc8739625826339149834_nat_o
% 3.82/4.11 @ ^ [X4: nat,Y5: nat] :
% 3.82/4.11 ( produc6081775807080527818_nat_o
% 3.82/4.11 @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X4 @ V4 ) @ ( plus_plus_nat @ U2 @ Y5 ) ) ) )
% 3.82/4.11 @ ord_less_int ) ).
% 3.82/4.11
% 3.82/4.11 % less_int.transfer
% 3.82/4.11 thf(fact_8069_less__eq__int_Otransfer,axiom,
% 3.82/4.11 ( bNF_re717283939379294677_int_o @ pcr_int
% 3.82/4.11 @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 3.82/4.11 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 ) )
% 3.82/4.11 @ ( produc8739625826339149834_nat_o
% 3.82/4.11 @ ^ [X4: nat,Y5: nat] :
% 3.82/4.11 ( produc6081775807080527818_nat_o
% 3.82/4.11 @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X4 @ V4 ) @ ( plus_plus_nat @ U2 @ Y5 ) ) ) )
% 3.82/4.11 @ ord_less_eq_int ) ).
% 3.82/4.11
% 3.82/4.11 % less_eq_int.transfer
% 3.82/4.11 thf(fact_8070_times__int_Otransfer,axiom,
% 3.82/4.11 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 3.82/4.11 @ ( produc27273713700761075at_nat
% 3.82/4.11 @ ^ [X4: nat,Y5: nat] :
% 3.82/4.11 ( produc2626176000494625587at_nat
% 3.82/4.11 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X4 @ U2 ) @ ( times_times_nat @ Y5 @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X4 @ V4 ) @ ( times_times_nat @ Y5 @ U2 ) ) ) ) )
% 3.82/4.11 @ times_times_int ) ).
% 3.82/4.11
% 3.82/4.11 % times_int.transfer
% 3.82/4.11 thf(fact_8071_uminus__int_Otransfer,axiom,
% 3.82/4.11 ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int
% 3.82/4.11 @ ( produc2626176000494625587at_nat
% 3.82/4.11 @ ^ [X4: nat,Y5: nat] : ( product_Pair_nat_nat @ Y5 @ X4 ) )
% 3.82/4.11 @ uminus_uminus_int ) ).
% 3.82/4.11
% 3.82/4.11 % uminus_int.transfer
% 3.82/4.11 thf(fact_8072_nat_Otransfer,axiom,
% 3.82/4.11 ( bNF_re4555766996558763186at_nat @ pcr_int
% 3.82/4.11 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 3.82/4.11 @ ( produc6842872674320459806at_nat @ minus_minus_nat )
% 3.82/4.11 @ nat2 ) ).
% 3.82/4.11
% 3.82/4.11 % nat.transfer
% 3.82/4.11 thf(fact_8073_int__transfer,axiom,
% 3.82/4.11 ( bNF_re6830278522597306478at_int
% 3.82/4.11 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 3.82/4.11 @ pcr_int
% 3.82/4.11 @ ^ [N: nat] : ( product_Pair_nat_nat @ N @ zero_zero_nat )
% 3.82/4.11 @ semiri1314217659103216013at_int ) ).
% 3.82/4.11
% 3.82/4.11 % int_transfer
% 3.82/4.11 thf(fact_8074_times__int_Orsp,axiom,
% 3.82/4.11 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 3.82/4.11 @ ( produc27273713700761075at_nat
% 3.82/4.11 @ ^ [X4: nat,Y5: nat] :
% 3.82/4.11 ( produc2626176000494625587at_nat
% 3.82/4.11 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X4 @ U2 ) @ ( times_times_nat @ Y5 @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X4 @ V4 ) @ ( times_times_nat @ Y5 @ U2 ) ) ) ) )
% 3.82/4.11 @ ( produc27273713700761075at_nat
% 3.82/4.11 @ ^ [X4: nat,Y5: nat] :
% 3.82/4.11 ( produc2626176000494625587at_nat
% 3.82/4.11 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X4 @ U2 ) @ ( times_times_nat @ Y5 @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X4 @ V4 ) @ ( times_times_nat @ Y5 @ U2 ) ) ) ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % times_int.rsp
% 3.82/4.11 thf(fact_8075_intrel__iff,axiom,
% 3.82/4.11 ! [X: nat,Y: nat,U: nat,V: nat] :
% 3.82/4.11 ( ( intrel @ ( product_Pair_nat_nat @ X @ Y ) @ ( product_Pair_nat_nat @ U @ V ) )
% 3.82/4.11 = ( ( plus_plus_nat @ X @ V )
% 3.82/4.11 = ( plus_plus_nat @ U @ Y ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % intrel_iff
% 3.82/4.11 thf(fact_8076_nat_Orsp,axiom,
% 3.82/4.11 ( bNF_re8246922863344978751at_nat @ intrel
% 3.82/4.11 @ ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 )
% 3.82/4.11 @ ( produc6842872674320459806at_nat @ minus_minus_nat )
% 3.82/4.11 @ ( produc6842872674320459806at_nat @ minus_minus_nat ) ) ).
% 3.82/4.11
% 3.82/4.11 % nat.rsp
% 3.82/4.11 thf(fact_8077_uminus__int_Orsp,axiom,
% 3.82/4.11 ( bNF_re2241393799969408733at_nat @ intrel @ intrel
% 3.82/4.11 @ ( produc2626176000494625587at_nat
% 3.82/4.11 @ ^ [X4: nat,Y5: nat] : ( product_Pair_nat_nat @ Y5 @ X4 ) )
% 3.82/4.11 @ ( produc2626176000494625587at_nat
% 3.82/4.11 @ ^ [X4: nat,Y5: nat] : ( product_Pair_nat_nat @ Y5 @ X4 ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % uminus_int.rsp
% 3.82/4.11 thf(fact_8078_int_Oabs__eq__iff,axiom,
% 3.82/4.11 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 3.82/4.11 ( ( ( abs_Integ @ X )
% 3.82/4.11 = ( abs_Integ @ Y ) )
% 3.82/4.11 = ( intrel @ X @ Y ) ) ).
% 3.82/4.11
% 3.82/4.11 % int.abs_eq_iff
% 3.82/4.11 thf(fact_8079_zero__int_Orsp,axiom,
% 3.82/4.11 intrel @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 3.82/4.11
% 3.82/4.11 % zero_int.rsp
% 3.82/4.11 thf(fact_8080_one__int_Orsp,axiom,
% 3.82/4.11 intrel @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ).
% 3.82/4.11
% 3.82/4.11 % one_int.rsp
% 3.82/4.11 thf(fact_8081_intrel__def,axiom,
% 3.82/4.11 ( intrel
% 3.82/4.11 = ( produc8739625826339149834_nat_o
% 3.82/4.11 @ ^ [X4: nat,Y5: nat] :
% 3.82/4.11 ( produc6081775807080527818_nat_o
% 3.82/4.11 @ ^ [U2: nat,V4: nat] :
% 3.82/4.11 ( ( plus_plus_nat @ X4 @ V4 )
% 3.82/4.11 = ( plus_plus_nat @ U2 @ Y5 ) ) ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % intrel_def
% 3.82/4.11 thf(fact_8082_less__int_Orsp,axiom,
% 3.82/4.11 ( bNF_re4202695980764964119_nat_o @ intrel
% 3.82/4.11 @ ( bNF_re3666534408544137501at_o_o @ intrel
% 3.82/4.11 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 ) )
% 3.82/4.11 @ ( produc8739625826339149834_nat_o
% 3.82/4.11 @ ^ [X4: nat,Y5: nat] :
% 3.82/4.11 ( produc6081775807080527818_nat_o
% 3.82/4.11 @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X4 @ V4 ) @ ( plus_plus_nat @ U2 @ Y5 ) ) ) )
% 3.82/4.11 @ ( produc8739625826339149834_nat_o
% 3.82/4.11 @ ^ [X4: nat,Y5: nat] :
% 3.82/4.11 ( produc6081775807080527818_nat_o
% 3.82/4.11 @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X4 @ V4 ) @ ( plus_plus_nat @ U2 @ Y5 ) ) ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % less_int.rsp
% 3.82/4.11 thf(fact_8083_less__eq__int_Orsp,axiom,
% 3.82/4.11 ( bNF_re4202695980764964119_nat_o @ intrel
% 3.82/4.11 @ ( bNF_re3666534408544137501at_o_o @ intrel
% 3.82/4.11 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 ) )
% 3.82/4.11 @ ( produc8739625826339149834_nat_o
% 3.82/4.11 @ ^ [X4: nat,Y5: nat] :
% 3.82/4.11 ( produc6081775807080527818_nat_o
% 3.82/4.11 @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X4 @ V4 ) @ ( plus_plus_nat @ U2 @ Y5 ) ) ) )
% 3.82/4.11 @ ( produc8739625826339149834_nat_o
% 3.82/4.11 @ ^ [X4: nat,Y5: nat] :
% 3.82/4.11 ( produc6081775807080527818_nat_o
% 3.82/4.11 @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X4 @ V4 ) @ ( plus_plus_nat @ U2 @ Y5 ) ) ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % less_eq_int.rsp
% 3.82/4.11 thf(fact_8084_int_Orel__eq__transfer,axiom,
% 3.82/4.11 ( bNF_re717283939379294677_int_o @ pcr_int
% 3.82/4.11 @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 3.82/4.11 @ ^ [Y4: $o,Z2: $o] : ( Y4 = Z2 ) )
% 3.82/4.11 @ intrel
% 3.82/4.11 @ ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) ) ).
% 3.82/4.11
% 3.82/4.11 % int.rel_eq_transfer
% 3.82/4.11 thf(fact_8085_minus__int_Orsp,axiom,
% 3.82/4.11 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 3.82/4.11 @ ( produc27273713700761075at_nat
% 3.82/4.11 @ ^ [X4: nat,Y5: nat] :
% 3.82/4.11 ( produc2626176000494625587at_nat
% 3.82/4.11 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ V4 ) @ ( plus_plus_nat @ Y5 @ U2 ) ) ) )
% 3.82/4.11 @ ( produc27273713700761075at_nat
% 3.82/4.11 @ ^ [X4: nat,Y5: nat] :
% 3.82/4.11 ( produc2626176000494625587at_nat
% 3.82/4.11 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ V4 ) @ ( plus_plus_nat @ Y5 @ U2 ) ) ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % minus_int.rsp
% 3.82/4.11 thf(fact_8086_plus__int_Orsp,axiom,
% 3.82/4.11 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 3.82/4.11 @ ( produc27273713700761075at_nat
% 3.82/4.11 @ ^ [X4: nat,Y5: nat] :
% 3.82/4.11 ( produc2626176000494625587at_nat
% 3.82/4.11 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ U2 ) @ ( plus_plus_nat @ Y5 @ V4 ) ) ) )
% 3.82/4.11 @ ( produc27273713700761075at_nat
% 3.82/4.11 @ ^ [X4: nat,Y5: nat] :
% 3.82/4.11 ( produc2626176000494625587at_nat
% 3.82/4.11 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ U2 ) @ ( plus_plus_nat @ Y5 @ V4 ) ) ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % plus_int.rsp
% 3.82/4.11 thf(fact_8087_int_Obi__total,axiom,
% 3.82/4.11 bi_tot896582865486249351at_int @ pcr_int ).
% 3.82/4.11
% 3.82/4.11 % int.bi_total
% 3.82/4.11 thf(fact_8088_less__than__iff,axiom,
% 3.82/4.11 ! [X: nat,Y: nat] :
% 3.82/4.11 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ less_than )
% 3.82/4.11 = ( ord_less_nat @ X @ Y ) ) ).
% 3.82/4.11
% 3.82/4.11 % less_than_iff
% 3.82/4.11 thf(fact_8089_elimnum,axiom,
% 3.82/4.11 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N2: nat] :
% 3.82/4.11 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ N2 )
% 3.82/4.11 => ( ( vEBT_VEBT_elim_dead @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 3.82/4.11 = ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % elimnum
% 3.82/4.11 thf(fact_8090_idiff__enat__0__right,axiom,
% 3.82/4.11 ! [N2: extended_enat] :
% 3.82/4.11 ( ( minus_3235023915231533773d_enat @ N2 @ ( extended_enat2 @ zero_zero_nat ) )
% 3.82/4.11 = N2 ) ).
% 3.82/4.11
% 3.82/4.11 % idiff_enat_0_right
% 3.82/4.11 thf(fact_8091_idiff__enat__0,axiom,
% 3.82/4.11 ! [N2: extended_enat] :
% 3.82/4.11 ( ( minus_3235023915231533773d_enat @ ( extended_enat2 @ zero_zero_nat ) @ N2 )
% 3.82/4.11 = ( extended_enat2 @ zero_zero_nat ) ) ).
% 3.82/4.11
% 3.82/4.11 % idiff_enat_0
% 3.82/4.11 thf(fact_8092_plus__enat__simps_I1_J,axiom,
% 3.82/4.11 ! [M2: nat,N2: nat] :
% 3.82/4.11 ( ( plus_p3455044024723400733d_enat @ ( extended_enat2 @ M2 ) @ ( extended_enat2 @ N2 ) )
% 3.82/4.11 = ( extended_enat2 @ ( plus_plus_nat @ M2 @ N2 ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % plus_enat_simps(1)
% 3.82/4.11 thf(fact_8093_enat__ord__simps_I2_J,axiom,
% 3.82/4.11 ! [M2: nat,N2: nat] :
% 3.82/4.11 ( ( ord_le72135733267957522d_enat @ ( extended_enat2 @ M2 ) @ ( extended_enat2 @ N2 ) )
% 3.82/4.11 = ( ord_less_nat @ M2 @ N2 ) ) ).
% 3.82/4.11
% 3.82/4.11 % enat_ord_simps(2)
% 3.82/4.11 thf(fact_8094_enat__ord__simps_I1_J,axiom,
% 3.82/4.11 ! [M2: nat,N2: nat] :
% 3.82/4.11 ( ( ord_le2932123472753598470d_enat @ ( extended_enat2 @ M2 ) @ ( extended_enat2 @ N2 ) )
% 3.82/4.11 = ( ord_less_eq_nat @ M2 @ N2 ) ) ).
% 3.82/4.11
% 3.82/4.11 % enat_ord_simps(1)
% 3.82/4.11 thf(fact_8095_numeral__less__enat__iff,axiom,
% 3.82/4.11 ! [M2: num,N2: nat] :
% 3.82/4.11 ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M2 ) @ ( extended_enat2 @ N2 ) )
% 3.82/4.11 = ( ord_less_nat @ ( numeral_numeral_nat @ M2 ) @ N2 ) ) ).
% 3.82/4.11
% 3.82/4.11 % numeral_less_enat_iff
% 3.82/4.11 thf(fact_8096_numeral__le__enat__iff,axiom,
% 3.82/4.11 ! [M2: num,N2: nat] :
% 3.82/4.11 ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M2 ) @ ( extended_enat2 @ N2 ) )
% 3.82/4.11 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ M2 ) @ N2 ) ) ).
% 3.82/4.11
% 3.82/4.11 % numeral_le_enat_iff
% 3.82/4.11 thf(fact_8097_Suc__ile__eq,axiom,
% 3.82/4.11 ! [M2: nat,N2: extended_enat] :
% 3.82/4.11 ( ( ord_le2932123472753598470d_enat @ ( extended_enat2 @ ( suc @ M2 ) ) @ N2 )
% 3.82/4.11 = ( ord_le72135733267957522d_enat @ ( extended_enat2 @ M2 ) @ N2 ) ) ).
% 3.82/4.11
% 3.82/4.11 % Suc_ile_eq
% 3.82/4.11 thf(fact_8098_finite__enat__bounded,axiom,
% 3.82/4.11 ! [A2: set_Extended_enat,N2: nat] :
% 3.82/4.11 ( ! [Y3: extended_enat] :
% 3.82/4.11 ( ( member_Extended_enat @ Y3 @ A2 )
% 3.82/4.11 => ( ord_le2932123472753598470d_enat @ Y3 @ ( extended_enat2 @ N2 ) ) )
% 3.82/4.11 => ( finite4001608067531595151d_enat @ A2 ) ) ).
% 3.82/4.11
% 3.82/4.11 % finite_enat_bounded
% 3.82/4.11 thf(fact_8099_iadd__le__enat__iff,axiom,
% 3.82/4.11 ! [X: extended_enat,Y: extended_enat,N2: nat] :
% 3.82/4.11 ( ( ord_le2932123472753598470d_enat @ ( plus_p3455044024723400733d_enat @ X @ Y ) @ ( extended_enat2 @ N2 ) )
% 3.82/4.11 = ( ? [Y7: nat,X9: nat] :
% 3.82/4.11 ( ( X
% 3.82/4.11 = ( extended_enat2 @ X9 ) )
% 3.82/4.11 & ( Y
% 3.82/4.11 = ( extended_enat2 @ Y7 ) )
% 3.82/4.11 & ( ord_less_eq_nat @ ( plus_plus_nat @ X9 @ Y7 ) @ N2 ) ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % iadd_le_enat_iff
% 3.82/4.11 thf(fact_8100_enat__0__iff_I2_J,axiom,
% 3.82/4.11 ! [X: nat] :
% 3.82/4.11 ( ( zero_z5237406670263579293d_enat
% 3.82/4.11 = ( extended_enat2 @ X ) )
% 3.82/4.11 = ( X = zero_zero_nat ) ) ).
% 3.82/4.11
% 3.82/4.11 % enat_0_iff(2)
% 3.82/4.11 thf(fact_8101_enat__0__iff_I1_J,axiom,
% 3.82/4.11 ! [X: nat] :
% 3.82/4.11 ( ( ( extended_enat2 @ X )
% 3.82/4.11 = zero_z5237406670263579293d_enat )
% 3.82/4.11 = ( X = zero_zero_nat ) ) ).
% 3.82/4.11
% 3.82/4.11 % enat_0_iff(1)
% 3.82/4.11 thf(fact_8102_zero__enat__def,axiom,
% 3.82/4.11 ( zero_z5237406670263579293d_enat
% 3.82/4.11 = ( extended_enat2 @ zero_zero_nat ) ) ).
% 3.82/4.11
% 3.82/4.11 % zero_enat_def
% 3.82/4.11 thf(fact_8103_less__enatE,axiom,
% 3.82/4.11 ! [N2: extended_enat,M2: nat] :
% 3.82/4.11 ( ( ord_le72135733267957522d_enat @ N2 @ ( extended_enat2 @ M2 ) )
% 3.82/4.11 => ~ ! [K3: nat] :
% 3.82/4.11 ( ( N2
% 3.82/4.11 = ( extended_enat2 @ K3 ) )
% 3.82/4.11 => ~ ( ord_less_nat @ K3 @ M2 ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % less_enatE
% 3.82/4.11 thf(fact_8104_elimcomplete,axiom,
% 3.82/4.11 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N2: nat] :
% 3.82/4.11 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ N2 )
% 3.82/4.11 => ( ( vEBT_VEBT_elim_dead @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ extend5688581933313929465d_enat )
% 3.82/4.11 = ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % elimcomplete
% 3.82/4.11 thf(fact_8105_times__enat__simps_I4_J,axiom,
% 3.82/4.11 ! [M2: nat] :
% 3.82/4.11 ( ( ( M2 = zero_zero_nat )
% 3.82/4.11 => ( ( times_7803423173614009249d_enat @ ( extended_enat2 @ M2 ) @ extend5688581933313929465d_enat )
% 3.82/4.11 = zero_z5237406670263579293d_enat ) )
% 3.82/4.11 & ( ( M2 != zero_zero_nat )
% 3.82/4.11 => ( ( times_7803423173614009249d_enat @ ( extended_enat2 @ M2 ) @ extend5688581933313929465d_enat )
% 3.82/4.11 = extend5688581933313929465d_enat ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % times_enat_simps(4)
% 3.82/4.11 thf(fact_8106_times__enat__simps_I3_J,axiom,
% 3.82/4.11 ! [N2: nat] :
% 3.82/4.11 ( ( ( N2 = zero_zero_nat )
% 3.82/4.11 => ( ( times_7803423173614009249d_enat @ extend5688581933313929465d_enat @ ( extended_enat2 @ N2 ) )
% 3.82/4.11 = zero_z5237406670263579293d_enat ) )
% 3.82/4.11 & ( ( N2 != zero_zero_nat )
% 3.82/4.11 => ( ( times_7803423173614009249d_enat @ extend5688581933313929465d_enat @ ( extended_enat2 @ N2 ) )
% 3.82/4.11 = extend5688581933313929465d_enat ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % times_enat_simps(3)
% 3.82/4.11 thf(fact_8107_Inf__enat__def,axiom,
% 3.82/4.11 ( comple2295165028678016749d_enat
% 3.82/4.11 = ( ^ [A5: set_Extended_enat] :
% 3.82/4.11 ( if_Extended_enat @ ( A5 = bot_bo7653980558646680370d_enat ) @ extend5688581933313929465d_enat
% 3.82/4.11 @ ( ord_Le1955565732374568822d_enat
% 3.82/4.11 @ ^ [X4: extended_enat] : ( member_Extended_enat @ X4 @ A5 ) ) ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % Inf_enat_def
% 3.82/4.11 thf(fact_8108_bot__enat__def,axiom,
% 3.82/4.11 bot_bo4199563552545308370d_enat = zero_z5237406670263579293d_enat ).
% 3.82/4.11
% 3.82/4.11 % bot_enat_def
% 3.82/4.11 thf(fact_8109_Sup__enat__def,axiom,
% 3.82/4.11 ( comple4398354569131411667d_enat
% 3.82/4.11 = ( ^ [A5: set_Extended_enat] : ( if_Extended_enat @ ( A5 = bot_bo7653980558646680370d_enat ) @ zero_z5237406670263579293d_enat @ ( if_Extended_enat @ ( finite4001608067531595151d_enat @ A5 ) @ ( lattic921264341876707157d_enat @ A5 ) @ extend5688581933313929465d_enat ) ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % Sup_enat_def
% 3.82/4.11 thf(fact_8110_times__enat__def,axiom,
% 3.82/4.11 ( times_7803423173614009249d_enat
% 3.82/4.11 = ( ^ [M: extended_enat,N: extended_enat] :
% 3.82/4.11 ( extend3600170679010898289d_enat
% 3.82/4.11 @ ^ [O: nat] :
% 3.82/4.11 ( extend3600170679010898289d_enat
% 3.82/4.11 @ ^ [P6: nat] : ( extended_enat2 @ ( times_times_nat @ O @ P6 ) )
% 3.82/4.11 @ ( if_Extended_enat @ ( O = zero_zero_nat ) @ zero_z5237406670263579293d_enat @ extend5688581933313929465d_enat )
% 3.82/4.11 @ N )
% 3.82/4.11 @ ( if_Extended_enat @ ( N = zero_z5237406670263579293d_enat ) @ zero_z5237406670263579293d_enat @ extend5688581933313929465d_enat )
% 3.82/4.11 @ M ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % times_enat_def
% 3.82/4.11 thf(fact_8111_plus__enat__def,axiom,
% 3.82/4.11 ( plus_p3455044024723400733d_enat
% 3.82/4.11 = ( ^ [M: extended_enat,N: extended_enat] :
% 3.82/4.11 ( extend3600170679010898289d_enat
% 3.82/4.11 @ ^ [O: nat] :
% 3.82/4.11 ( extend3600170679010898289d_enat
% 3.82/4.11 @ ^ [P6: nat] : ( extended_enat2 @ ( plus_plus_nat @ O @ P6 ) )
% 3.82/4.11 @ extend5688581933313929465d_enat
% 3.82/4.11 @ N )
% 3.82/4.11 @ extend5688581933313929465d_enat
% 3.82/4.11 @ M ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % plus_enat_def
% 3.82/4.11 thf(fact_8112_eSuc__Max,axiom,
% 3.82/4.11 ! [A2: set_Extended_enat] :
% 3.82/4.11 ( ( finite4001608067531595151d_enat @ A2 )
% 3.82/4.11 => ( ( A2 != bot_bo7653980558646680370d_enat )
% 3.82/4.11 => ( ( extended_eSuc @ ( lattic921264341876707157d_enat @ A2 ) )
% 3.82/4.11 = ( lattic921264341876707157d_enat @ ( image_80655429650038917d_enat @ extended_eSuc @ A2 ) ) ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % eSuc_Max
% 3.82/4.11 thf(fact_8113_eSuc__def,axiom,
% 3.82/4.11 ( extended_eSuc
% 3.82/4.11 = ( extend3600170679010898289d_enat
% 3.82/4.11 @ ^ [N: nat] : ( extended_enat2 @ ( suc @ N ) )
% 3.82/4.11 @ extend5688581933313929465d_enat ) ) ).
% 3.82/4.11
% 3.82/4.11 % eSuc_def
% 3.82/4.11 thf(fact_8114_enat__eSuc__iff,axiom,
% 3.82/4.11 ! [Y: nat,X: extended_enat] :
% 3.82/4.11 ( ( ( extended_enat2 @ Y )
% 3.82/4.11 = ( extended_eSuc @ X ) )
% 3.82/4.11 = ( ? [N: nat] :
% 3.82/4.11 ( ( Y
% 3.82/4.11 = ( suc @ N ) )
% 3.82/4.11 & ( ( extended_enat2 @ N )
% 3.82/4.11 = X ) ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % enat_eSuc_iff
% 3.82/4.11 thf(fact_8115_eSuc__enat__iff,axiom,
% 3.82/4.11 ! [X: extended_enat,Y: nat] :
% 3.82/4.11 ( ( ( extended_eSuc @ X )
% 3.82/4.11 = ( extended_enat2 @ Y ) )
% 3.82/4.11 = ( ? [N: nat] :
% 3.82/4.11 ( ( Y
% 3.82/4.11 = ( suc @ N ) )
% 3.82/4.11 & ( X
% 3.82/4.11 = ( extended_enat2 @ N ) ) ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % eSuc_enat_iff
% 3.82/4.11 thf(fact_8116_eSuc__enat,axiom,
% 3.82/4.11 ! [N2: nat] :
% 3.82/4.11 ( ( extended_eSuc @ ( extended_enat2 @ N2 ) )
% 3.82/4.11 = ( extended_enat2 @ ( suc @ N2 ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % eSuc_enat
% 3.82/4.11 thf(fact_8117_eSuc__Sup,axiom,
% 3.82/4.11 ! [A2: set_Extended_enat] :
% 3.82/4.11 ( ( A2 != bot_bo7653980558646680370d_enat )
% 3.82/4.11 => ( ( extended_eSuc @ ( comple4398354569131411667d_enat @ A2 ) )
% 3.82/4.11 = ( comple4398354569131411667d_enat @ ( image_80655429650038917d_enat @ extended_eSuc @ A2 ) ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % eSuc_Sup
% 3.82/4.11 thf(fact_8118_natLeq__on__well__order__on,axiom,
% 3.82/4.11 ! [N2: nat] :
% 3.82/4.11 ( order_2888998067076097458on_nat
% 3.82/4.11 @ ( collect_nat
% 3.82/4.11 @ ^ [X4: nat] : ( ord_less_nat @ X4 @ N2 ) )
% 3.82/4.11 @ ( collec3392354462482085612at_nat
% 3.82/4.11 @ ( produc6081775807080527818_nat_o
% 3.82/4.11 @ ^ [X4: nat,Y5: nat] :
% 3.82/4.11 ( ( ord_less_nat @ X4 @ N2 )
% 3.82/4.11 & ( ord_less_nat @ Y5 @ N2 )
% 3.82/4.11 & ( ord_less_eq_nat @ X4 @ Y5 ) ) ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % natLeq_on_well_order_on
% 3.82/4.11 thf(fact_8119_natLeq__on__Well__order,axiom,
% 3.82/4.11 ! [N2: nat] :
% 3.82/4.11 ( order_2888998067076097458on_nat
% 3.82/4.11 @ ( field_nat
% 3.82/4.11 @ ( collec3392354462482085612at_nat
% 3.82/4.11 @ ( produc6081775807080527818_nat_o
% 3.82/4.11 @ ^ [X4: nat,Y5: nat] :
% 3.82/4.11 ( ( ord_less_nat @ X4 @ N2 )
% 3.82/4.11 & ( ord_less_nat @ Y5 @ N2 )
% 3.82/4.11 & ( ord_less_eq_nat @ X4 @ Y5 ) ) ) ) )
% 3.82/4.11 @ ( collec3392354462482085612at_nat
% 3.82/4.11 @ ( produc6081775807080527818_nat_o
% 3.82/4.11 @ ^ [X4: nat,Y5: nat] :
% 3.82/4.11 ( ( ord_less_nat @ X4 @ N2 )
% 3.82/4.11 & ( ord_less_nat @ Y5 @ N2 )
% 3.82/4.11 & ( ord_less_eq_nat @ X4 @ Y5 ) ) ) ) ) ).
% 3.82/4.11
% 3.82/4.11 % natLeq_on_Well_order
% 3.82/4.11
% 3.82/4.11 % Helper facts (29)
% 3.82/4.11 thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
% 3.82/4.11 ! [X: int,Y: int] :
% 3.82/4.11 ( ( if_int @ $false @ X @ Y )
% 3.82/4.11 = Y ) ).
% 3.82/4.11
% 3.82/4.11 thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
% 3.82/4.11 ! [X: int,Y: int] :
% 3.82/4.11 ( ( if_int @ $true @ X @ Y )
% 3.82/4.11 = X ) ).
% 3.82/4.11
% 3.82/4.11 thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 3.82/4.11 ! [X: nat,Y: nat] :
% 3.82/4.11 ( ( if_nat @ $false @ X @ Y )
% 3.82/4.11 = Y ) ).
% 3.82/4.11
% 3.82/4.11 thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 3.82/4.11 ! [X: nat,Y: nat] :
% 3.82/4.11 ( ( if_nat @ $true @ X @ Y )
% 3.82/4.11 = X ) ).
% 3.82/4.11
% 3.82/4.11 thf(help_If_2_1_If_001t__Real__Oreal_T,axiom,
% 3.82/4.11 ! [X: real,Y: real] :
% 3.82/4.11 ( ( if_real @ $false @ X @ Y )
% 3.82/4.11 = Y ) ).
% 3.82/4.11
% 3.82/4.11 thf(help_If_1_1_If_001t__Real__Oreal_T,axiom,
% 3.82/4.11 ! [X: real,Y: real] :
% 3.82/4.11 ( ( if_real @ $true @ X @ Y )
% 3.82/4.11 = X ) ).
% 3.82/4.11
% 3.82/4.11 thf(help_If_2_1_If_001t__Complex__Ocomplex_T,axiom,
% 3.82/4.11 ! [X: complex,Y: complex] :
% 3.82/4.11 ( ( if_complex @ $false @ X @ Y )
% 3.82/4.11 = Y ) ).
% 3.82/4.11
% 3.82/4.11 thf(help_If_1_1_If_001t__Complex__Ocomplex_T,axiom,
% 3.82/4.11 ! [X: complex,Y: complex] :
% 3.82/4.11 ( ( if_complex @ $true @ X @ Y )
% 3.82/4.11 = X ) ).
% 3.82/4.11
% 3.82/4.11 thf(help_If_2_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 3.82/4.11 ! [X: extended_enat,Y: extended_enat] :
% 3.82/4.11 ( ( if_Extended_enat @ $false @ X @ Y )
% 3.82/4.11 = Y ) ).
% 3.82/4.11
% 3.82/4.11 thf(help_If_1_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 3.82/4.11 ! [X: extended_enat,Y: extended_enat] :
% 3.82/4.11 ( ( if_Extended_enat @ $true @ X @ Y )
% 3.82/4.11 = X ) ).
% 3.82/4.11
% 3.82/4.11 thf(help_If_2_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 3.82/4.11 ! [X: set_int,Y: set_int] :
% 3.82/4.11 ( ( if_set_int @ $false @ X @ Y )
% 3.82/4.11 = Y ) ).
% 3.82/4.11
% 3.82/4.11 thf(help_If_1_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 3.82/4.11 ! [X: set_int,Y: set_int] :
% 3.82/4.11 ( ( if_set_int @ $true @ X @ Y )
% 3.82/4.11 = X ) ).
% 3.82/4.11
% 3.82/4.11 thf(help_If_2_1_If_001t__Set__Oset_It__Nat__Onat_J_T,axiom,
% 3.82/4.11 ! [X: set_nat,Y: set_nat] :
% 3.82/4.11 ( ( if_set_nat @ $false @ X @ Y )
% 3.82/4.11 = Y ) ).
% 3.82/4.11
% 3.82/4.11 thf(help_If_1_1_If_001t__Set__Oset_It__Nat__Onat_J_T,axiom,
% 3.82/4.11 ! [X: set_nat,Y: set_nat] :
% 3.82/4.11 ( ( if_set_nat @ $true @ X @ Y )
% 3.82/4.11 = X ) ).
% 3.82/4.11
% 3.82/4.11 thf(help_If_2_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 3.82/4.11 ! [X: vEBT_VEBT,Y: vEBT_VEBT] :
% 3.82/4.11 ( ( if_VEBT_VEBT @ $false @ X @ Y )
% 3.82/4.11 = Y ) ).
% 3.82/4.11
% 3.82/4.11 thf(help_If_1_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 3.82/4.11 ! [X: vEBT_VEBT,Y: vEBT_VEBT] :
% 3.82/4.11 ( ( if_VEBT_VEBT @ $true @ X @ Y )
% 3.82/4.11 = X ) ).
% 3.82/4.11
% 3.82/4.11 thf(help_If_2_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 3.82/4.11 ! [X: list_int,Y: list_int] :
% 3.82/4.11 ( ( if_list_int @ $false @ X @ Y )
% 3.82/4.11 = Y ) ).
% 3.82/4.11
% 3.82/4.11 thf(help_If_1_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 3.82/4.11 ! [X: list_int,Y: list_int] :
% 3.82/4.11 ( ( if_list_int @ $true @ X @ Y )
% 3.82/4.11 = X ) ).
% 3.82/4.11
% 3.82/4.11 thf(help_If_2_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 3.82/4.11 ! [X: list_nat,Y: list_nat] :
% 3.82/4.11 ( ( if_list_nat @ $false @ X @ Y )
% 3.82/4.11 = Y ) ).
% 3.82/4.11
% 3.82/4.11 thf(help_If_1_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 3.82/4.11 ! [X: list_nat,Y: list_nat] :
% 3.82/4.11 ( ( if_list_nat @ $true @ X @ Y )
% 3.82/4.11 = X ) ).
% 3.82/4.11
% 3.82/4.11 thf(help_If_2_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 3.82/4.11 ! [X: int > int,Y: int > int] :
% 3.82/4.11 ( ( if_int_int @ $false @ X @ Y )
% 3.82/4.11 = Y ) ).
% 3.82/4.11
% 3.82/4.11 thf(help_If_1_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 3.82/4.11 ! [X: int > int,Y: int > int] :
% 3.82/4.11 ( ( if_int_int @ $true @ X @ Y )
% 3.82/4.11 = X ) ).
% 3.82/4.11
% 3.82/4.11 thf(help_If_2_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 3.82/4.11 ! [X: option_num,Y: option_num] :
% 3.82/4.11 ( ( if_option_num @ $false @ X @ Y )
% 3.82/4.11 = Y ) ).
% 3.82/4.11
% 3.82/4.11 thf(help_If_1_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 3.82/4.11 ! [X: option_num,Y: option_num] :
% 3.82/4.11 ( ( if_option_num @ $true @ X @ Y )
% 3.82/4.11 = X ) ).
% 3.82/4.11
% 3.82/4.11 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 3.82/4.11 ! [X: product_prod_int_int,Y: product_prod_int_int] :
% 3.82/4.11 ( ( if_Pro3027730157355071871nt_int @ $false @ X @ Y )
% 3.82/4.11 = Y ) ).
% 3.82/4.11
% 3.82/4.11 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 3.82/4.11 ! [X: product_prod_int_int,Y: product_prod_int_int] :
% 3.82/4.11 ( ( if_Pro3027730157355071871nt_int @ $true @ X @ Y )
% 3.82/4.11 = X ) ).
% 3.82/4.11
% 3.82/4.11 thf(help_If_3_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 3.82/4.11 ! [P: $o] :
% 3.82/4.11 ( ( P = $true )
% 3.82/4.11 | ( P = $false ) ) ).
% 3.82/4.11
% 3.82/4.11 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 3.82/4.11 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 3.82/4.11 ( ( if_Pro6206227464963214023at_nat @ $false @ X @ Y )
% 3.82/4.11 = Y ) ).
% 3.82/4.11
% 3.82/4.11 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 3.82/4.11 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 3.82/4.11 ( ( if_Pro6206227464963214023at_nat @ $true @ X @ Y )
% 3.82/4.11 = X ) ).
% 3.82/4.11
% 3.82/4.11 % Conjectures (1)
% 4.71/5.16 thf(conj_0,conjecture,
% 4.71/5.16 ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) @ ( vEBT_VEBT_low @ mi @ na ) ) ) @ i )
% 4.71/5.16 = ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) @ ( vEBT_VEBT_low @ mi @ na ) ) ) ).
% 4.71/5.16
% 4.71/5.16 %------------------------------------------------------------------------------
% 4.71/5.16 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.VTsQyQAQCY/cvc5---1.0.5_31553.p...
% 4.71/5.16 (declare-sort $$unsorted 0)
% 4.71/5.16 (declare-sort tptp.set_Pr1542805901266377927at_nat 0)
% 4.71/5.16 (declare-sort tptp.produc4471711990508489141at_nat 0)
% 4.71/5.16 (declare-sort tptp.produc6392793444374437607at_nat 0)
% 4.71/5.16 (declare-sort tptp.list_P8469869581646625389at_nat 0)
% 4.71/5.16 (declare-sort tptp.set_Pr8693737435421807431at_nat 0)
% 4.71/5.16 (declare-sort tptp.set_Pr1916528119006554503T_VEBT 0)
% 4.71/5.16 (declare-sort tptp.produc859450856879609959at_nat 0)
% 4.71/5.16 (declare-sort tptp.produc9211091688327510695T_VEBT 0)
% 4.71/5.16 (declare-sort tptp.set_Pr3451248702717554689st_nat 0)
% 4.71/5.16 (declare-sort tptp.set_Pr765067013931698361st_int 0)
% 4.71/5.16 (declare-sort tptp.list_P7413028617227757229T_VEBT 0)
% 4.71/5.16 (declare-sort tptp.set_Pr6192946355708809607T_VEBT 0)
% 4.71/5.16 (declare-sort tptp.produc7248412053542808358at_nat 0)
% 4.71/5.16 (declare-sort tptp.produc1828647624359046049st_nat 0)
% 4.71/5.16 (declare-sort tptp.produc1186641810826059865st_int 0)
% 4.71/5.16 (declare-sort tptp.list_P7037539587688870467BT_nat 0)
% 4.71/5.16 (declare-sort tptp.list_P4547456442757143711BT_int 0)
% 4.71/5.16 (declare-sort tptp.list_P5647936690300460905T_VEBT 0)
% 4.71/5.16 (declare-sort tptp.list_P7524865323317820941T_VEBT 0)
% 4.71/5.16 (declare-sort tptp.produc8243902056947475879T_VEBT 0)
% 4.71/5.16 (declare-sort tptp.set_Pr7556676689462069481BT_nat 0)
% 4.71/5.16 (declare-sort tptp.option4927543243414619207at_nat 0)
% 4.71/5.16 (declare-sort tptp.filter1242075044329608583at_nat 0)
% 4.71/5.16 (declare-sort tptp.list_P6011104703257516679at_nat 0)
% 4.71/5.16 (declare-sort tptp.list_P3521021558325789923at_int 0)
% 4.71/5.16 (declare-sort tptp.list_P8198026277950538467nt_nat 0)
% 4.71/5.16 (declare-sort tptp.list_P5707943133018811711nt_int 0)
% 4.71/5.16 (declare-sort tptp.produc9072475918466114483BT_nat 0)
% 4.71/5.16 (declare-sort tptp.produc4894624898956917775BT_int 0)
% 4.71/5.16 (declare-sort tptp.produc8025551001238799321T_VEBT 0)
% 4.71/5.16 (declare-sort tptp.produc1531783533982839933T_VEBT 0)
% 4.71/5.16 (declare-sort tptp.set_Pr1261947904930325089at_nat 0)
% 4.71/5.16 (declare-sort tptp.set_Pr958786334691620121nt_int 0)
% 4.71/5.16 (declare-sort tptp.set_list_VEBT_VEBT 0)
% 4.71/5.16 (declare-sort tptp.set_li5464603477888414924d_enat 0)
% 4.71/5.16 (declare-sort tptp.set_se7270636423289371942d_enat 0)
% 4.71/5.16 (declare-sort tptp.product_prod_nat_nat 0)
% 4.71/5.16 (declare-sort tptp.product_prod_nat_int 0)
% 4.71/5.16 (declare-sort tptp.product_prod_int_nat 0)
% 4.71/5.16 (declare-sort tptp.product_prod_int_int 0)
% 4.71/5.16 (declare-sort tptp.set_list_complex 0)
% 4.71/5.16 (declare-sort tptp.set_set_complex 0)
% 4.71/5.16 (declare-sort tptp.option_VEBT_VEBT 0)
% 4.71/5.16 (declare-sort tptp.option_set_nat 0)
% 4.71/5.16 (declare-sort tptp.option_Extended_enat 0)
% 4.71/5.16 (declare-sort tptp.list_VEBT_VEBT 0)
% 4.71/5.16 (declare-sort tptp.set_list_nat 0)
% 4.71/5.16 (declare-sort tptp.set_list_int 0)
% 4.71/5.16 (declare-sort tptp.list_set_nat 0)
% 4.71/5.16 (declare-sort tptp.set_VEBT_VEBT 0)
% 4.71/5.16 (declare-sort tptp.set_set_nat 0)
% 4.71/5.16 (declare-sort tptp.set_set_int 0)
% 4.71/5.16 (declare-sort tptp.list_Extended_enat 0)
% 4.71/5.16 (declare-sort tptp.set_Product_unit 0)
% 4.71/5.16 (declare-sort tptp.set_Extended_enat 0)
% 4.71/5.16 (declare-sort tptp.list_complex 0)
% 4.71/5.16 (declare-sort tptp.set_complex 0)
% 4.71/5.16 (declare-sort tptp.option_real 0)
% 4.71/5.16 (declare-sort tptp.filter_real 0)
% 4.71/5.16 (declare-sort tptp.option_num 0)
% 4.71/5.16 (declare-sort tptp.option_nat 0)
% 4.71/5.16 (declare-sort tptp.option_int 0)
% 4.71/5.16 (declare-sort tptp.filter_nat 0)
% 4.71/5.16 (declare-sort tptp.set_char 0)
% 4.71/5.16 (declare-sort tptp.list_real 0)
% 4.71/5.16 (declare-sort tptp.set_real 0)
% 4.71/5.16 (declare-sort tptp.list_num 0)
% 4.71/5.16 (declare-sort tptp.list_nat 0)
% 4.71/5.16 (declare-sort tptp.list_int 0)
% 4.71/5.16 (declare-sort tptp.vEBT_VEBT 0)
% 4.71/5.16 (declare-sort tptp.set_num 0)
% 4.71/5.16 (declare-sort tptp.set_nat 0)
% 4.71/5.16 (declare-sort tptp.set_int 0)
% 4.71/5.16 (declare-sort tptp.extended_enat 0)
% 4.71/5.16 (declare-sort tptp.complex 0)
% 4.71/5.16 (declare-sort tptp.char 0)
% 4.71/5.16 (declare-sort tptp.real 0)
% 4.71/5.16 (declare-sort tptp.num 0)
% 4.71/5.16 (declare-sort tptp.nat 0)
% 4.71/5.16 (declare-sort tptp.int 0)
% 4.71/5.16 (declare-fun tptp.archim7802044766580827645g_real (tptp.real) tptp.int)
% 4.71/5.16 (declare-fun tptp.archim6058952711729229775r_real (tptp.real) tptp.int)
% 4.71/5.16 (declare-fun tptp.archim2898591450579166408c_real (tptp.real) tptp.real)
% 4.71/5.16 (declare-fun tptp.archim8280529875227126926d_real (tptp.real) tptp.int)
% 4.71/5.16 (declare-fun tptp.bNF_Ca8665028551170535155natLeq () tptp.set_Pr1261947904930325089at_nat)
% 4.71/5.16 (declare-fun tptp.bNF_Ca8459412986667044542atLess () tptp.set_Pr1261947904930325089at_nat)
% 4.71/5.16 (declare-fun tptp.bNF_re6830278522597306478at_int ((-> tptp.nat tptp.nat Bool) (-> tptp.product_prod_nat_nat tptp.int Bool) (-> tptp.nat tptp.product_prod_nat_nat) (-> tptp.nat tptp.int)) Bool)
% 4.71/5.16 (declare-fun tptp.bNF_re717283939379294677_int_o ((-> tptp.product_prod_nat_nat tptp.int Bool) (-> (-> tptp.product_prod_nat_nat Bool) (-> tptp.int Bool) Bool) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) (-> tptp.int tptp.int Bool)) Bool)
% 4.71/5.16 (declare-fun tptp.bNF_re7408651293131936558nt_int ((-> tptp.product_prod_nat_nat tptp.int Bool) (-> (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat) (-> tptp.int tptp.int) Bool) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat) (-> tptp.int tptp.int tptp.int)) Bool)
% 4.71/5.16 (declare-fun tptp.bNF_re6644619430987730960nt_o_o ((-> tptp.product_prod_nat_nat tptp.int Bool) (-> Bool Bool Bool) (-> tptp.product_prod_nat_nat Bool) (-> tptp.int Bool)) Bool)
% 4.71/5.16 (declare-fun tptp.bNF_re4555766996558763186at_nat ((-> tptp.product_prod_nat_nat tptp.int Bool) (-> tptp.nat tptp.nat Bool) (-> tptp.product_prod_nat_nat tptp.nat) (-> tptp.int tptp.nat)) Bool)
% 4.71/5.16 (declare-fun tptp.bNF_re7400052026677387805at_int ((-> tptp.product_prod_nat_nat tptp.int Bool) (-> tptp.product_prod_nat_nat tptp.int Bool) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat) (-> tptp.int tptp.int)) Bool)
% 4.71/5.16 (declare-fun tptp.bNF_re4202695980764964119_nat_o ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) (-> (-> tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat Bool) Bool) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) Bool)
% 4.71/5.16 (declare-fun tptp.bNF_re3099431351363272937at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) (-> (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) Bool)
% 4.71/5.16 (declare-fun tptp.bNF_re3666534408544137501at_o_o ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) (-> Bool Bool Bool) (-> tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat Bool)) Bool)
% 4.71/5.16 (declare-fun tptp.bNF_re8246922863344978751at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) (-> tptp.nat tptp.nat Bool) (-> tptp.product_prod_nat_nat tptp.nat) (-> tptp.product_prod_nat_nat tptp.nat)) Bool)
% 4.71/5.16 (declare-fun tptp.bNF_re2241393799969408733at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) Bool)
% 4.71/5.16 (declare-fun tptp.bNF_We3818239936649020644el_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 4.71/5.16 (declare-fun tptp.binomial (tptp.nat tptp.nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.gbinomial_complex (tptp.complex tptp.nat) tptp.complex)
% 4.71/5.16 (declare-fun tptp.gbinomial_int (tptp.int tptp.nat) tptp.int)
% 4.71/5.16 (declare-fun tptp.gbinomial_nat (tptp.nat tptp.nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.gbinomial_real (tptp.real tptp.nat) tptp.real)
% 4.71/5.16 (declare-fun tptp.bit_and_int_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 4.71/5.16 (declare-fun tptp.bit_concat_bit (tptp.nat tptp.int tptp.int) tptp.int)
% 4.71/5.16 (declare-fun tptp.bit_ri631733984087533419it_int (tptp.nat tptp.int) tptp.int)
% 4.71/5.16 (declare-fun tptp.bit_se725231765392027082nd_int (tptp.int tptp.int) tptp.int)
% 4.71/5.16 (declare-fun tptp.bit_se727722235901077358nd_nat (tptp.nat tptp.nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.bit_se8568078237143864401it_int (tptp.nat tptp.int) tptp.int)
% 4.71/5.16 (declare-fun tptp.bit_se8570568707652914677it_nat (tptp.nat tptp.nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.bit_se2159334234014336723it_int (tptp.nat tptp.int) tptp.int)
% 4.71/5.16 (declare-fun tptp.bit_se2161824704523386999it_nat (tptp.nat tptp.nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.bit_se2000444600071755411sk_int (tptp.nat) tptp.int)
% 4.71/5.16 (declare-fun tptp.bit_se2002935070580805687sk_nat (tptp.nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.bit_se1412395901928357646or_nat (tptp.nat tptp.nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.bit_se545348938243370406it_int (tptp.nat tptp.int) tptp.int)
% 4.71/5.16 (declare-fun tptp.bit_se547839408752420682it_nat (tptp.nat tptp.nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.bit_se7879613467334960850it_int (tptp.nat tptp.int) tptp.int)
% 4.71/5.16 (declare-fun tptp.bit_se7882103937844011126it_nat (tptp.nat tptp.nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.bit_se2923211474154528505it_int (tptp.nat tptp.int) tptp.int)
% 4.71/5.16 (declare-fun tptp.bit_se2925701944663578781it_nat (tptp.nat tptp.nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.bit_se4203085406695923979it_int (tptp.nat tptp.int) tptp.int)
% 4.71/5.16 (declare-fun tptp.bit_se4205575877204974255it_nat (tptp.nat tptp.nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.bit_se6528837805403552850or_nat (tptp.nat tptp.nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.bit_se1146084159140164899it_int (tptp.int tptp.nat) Bool)
% 4.71/5.16 (declare-fun tptp.bit_se1148574629649215175it_nat (tptp.nat tptp.nat) Bool)
% 4.71/5.16 (declare-fun tptp.bit_take_bit_num (tptp.nat tptp.num) tptp.option_num)
% 4.71/5.16 (declare-fun tptp.comple2295165028678016749d_enat (tptp.set_Extended_enat) tptp.extended_enat)
% 4.71/5.16 (declare-fun tptp.complete_Inf_Inf_nat (tptp.set_nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.comple7806235888213564991et_nat (tptp.set_set_nat) tptp.set_nat)
% 4.71/5.16 (declare-fun tptp.comple4398354569131411667d_enat (tptp.set_Extended_enat) tptp.extended_enat)
% 4.71/5.16 (declare-fun tptp.complete_Sup_Sup_nat (tptp.set_nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.comple7399068483239264473et_nat (tptp.set_set_nat) tptp.set_nat)
% 4.71/5.16 (declare-fun tptp.arg (tptp.complex) tptp.real)
% 4.71/5.16 (declare-fun tptp.cis (tptp.real) tptp.complex)
% 4.71/5.16 (declare-fun tptp.condit2214826472909112428ve_nat (tptp.set_nat) Bool)
% 4.71/5.16 (declare-fun tptp.has_fi5821293074295781190e_real ((-> tptp.real tptp.real) tptp.real tptp.filter_real) Bool)
% 4.71/5.16 (declare-fun tptp.divmod_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 4.71/5.16 (declare-fun tptp.unique6319869463603278526ux_int (tptp.product_prod_int_int) Bool)
% 4.71/5.16 (declare-fun tptp.unique6322359934112328802ux_nat (tptp.product_prod_nat_nat) Bool)
% 4.71/5.16 (declare-fun tptp.unique5052692396658037445od_int (tptp.num tptp.num) tptp.product_prod_int_int)
% 4.71/5.16 (declare-fun tptp.unique5055182867167087721od_nat (tptp.num tptp.num) tptp.product_prod_nat_nat)
% 4.71/5.16 (declare-fun tptp.unique5024387138958732305ep_int (tptp.num tptp.product_prod_int_int) tptp.product_prod_int_int)
% 4.71/5.16 (declare-fun tptp.unique5026877609467782581ep_nat (tptp.num tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 4.71/5.16 (declare-fun tptp.extended_eSuc (tptp.extended_enat) tptp.extended_enat)
% 4.71/5.16 (declare-fun tptp.extended_enat2 (tptp.nat) tptp.extended_enat)
% 4.71/5.16 (declare-fun tptp.extended_case_enat_o ((-> tptp.nat Bool) Bool tptp.extended_enat) Bool)
% 4.71/5.16 (declare-fun tptp.extend3600170679010898289d_enat ((-> tptp.nat tptp.extended_enat) tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 4.71/5.16 (declare-fun tptp.extend5688581933313929465d_enat () tptp.extended_enat)
% 4.71/5.16 (declare-fun tptp.comm_s2602460028002588243omplex (tptp.complex tptp.nat) tptp.complex)
% 4.71/5.16 (declare-fun tptp.comm_s3181272606743183617d_enat (tptp.extended_enat tptp.nat) tptp.extended_enat)
% 4.71/5.16 (declare-fun tptp.comm_s4660882817536571857er_int (tptp.int tptp.nat) tptp.int)
% 4.71/5.16 (declare-fun tptp.comm_s4663373288045622133er_nat (tptp.nat tptp.nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.comm_s7457072308508201937r_real (tptp.real tptp.nat) tptp.real)
% 4.71/5.16 (declare-fun tptp.semiri5044797733671781792omplex (tptp.nat) tptp.complex)
% 4.71/5.16 (declare-fun tptp.semiri4449623510593786356d_enat (tptp.nat) tptp.extended_enat)
% 4.71/5.16 (declare-fun tptp.semiri1406184849735516958ct_int (tptp.nat) tptp.int)
% 4.71/5.16 (declare-fun tptp.semiri1408675320244567234ct_nat (tptp.nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.semiri2265585572941072030t_real (tptp.nat) tptp.real)
% 4.71/5.16 (declare-fun tptp.inverse_inverse_real (tptp.real) tptp.real)
% 4.71/5.16 (declare-fun tptp.at_bot_real () tptp.filter_real)
% 4.71/5.16 (declare-fun tptp.at_top_nat () tptp.filter_nat)
% 4.71/5.16 (declare-fun tptp.at_top_real () tptp.filter_real)
% 4.71/5.16 (declare-fun tptp.eventually_nat ((-> tptp.nat Bool) tptp.filter_nat) Bool)
% 4.71/5.16 (declare-fun tptp.eventu1038000079068216329at_nat ((-> tptp.product_prod_nat_nat Bool) tptp.filter1242075044329608583at_nat) Bool)
% 4.71/5.16 (declare-fun tptp.filterlim_nat_nat ((-> tptp.nat tptp.nat) tptp.filter_nat tptp.filter_nat) Bool)
% 4.71/5.16 (declare-fun tptp.filterlim_nat_real ((-> tptp.nat tptp.real) tptp.filter_real tptp.filter_nat) Bool)
% 4.71/5.16 (declare-fun tptp.filterlim_real_real ((-> tptp.real tptp.real) tptp.filter_real tptp.filter_real) Bool)
% 4.71/5.16 (declare-fun tptp.prod_filter_nat_nat (tptp.filter_nat tptp.filter_nat) tptp.filter1242075044329608583at_nat)
% 4.71/5.16 (declare-fun tptp.finite_card_complex (tptp.set_complex) tptp.nat)
% 4.71/5.16 (declare-fun tptp.finite_card_int (tptp.set_int) tptp.nat)
% 4.71/5.16 (declare-fun tptp.finite_card_list_nat (tptp.set_list_nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.finite_card_nat (tptp.set_nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.finite410649719033368117t_unit (tptp.set_Product_unit) tptp.nat)
% 4.71/5.16 (declare-fun tptp.finite_card_set_nat (tptp.set_set_nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.finite3207457112153483333omplex (tptp.set_complex) Bool)
% 4.71/5.16 (declare-fun tptp.finite4001608067531595151d_enat (tptp.set_Extended_enat) Bool)
% 4.71/5.16 (declare-fun tptp.finite_finite_int (tptp.set_int) Bool)
% 4.71/5.16 (declare-fun tptp.finite8712137658972009173omplex (tptp.set_list_complex) Bool)
% 4.71/5.16 (declare-fun tptp.finite1862508098717546133d_enat (tptp.set_li5464603477888414924d_enat) Bool)
% 4.71/5.16 (declare-fun tptp.finite3922522038869484883st_int (tptp.set_list_int) Bool)
% 4.71/5.16 (declare-fun tptp.finite8100373058378681591st_nat (tptp.set_list_nat) Bool)
% 4.71/5.16 (declare-fun tptp.finite3004134309566078307T_VEBT (tptp.set_list_VEBT_VEBT) Bool)
% 4.71/5.16 (declare-fun tptp.finite_finite_nat (tptp.set_nat) Bool)
% 4.71/5.16 (declare-fun tptp.finite_finite_real (tptp.set_real) Bool)
% 4.71/5.16 (declare-fun tptp.finite6551019134538273531omplex (tptp.set_set_complex) Bool)
% 4.71/5.16 (declare-fun tptp.finite5468666774076196335d_enat (tptp.set_se7270636423289371942d_enat) Bool)
% 4.71/5.16 (declare-fun tptp.finite6197958912794628473et_int (tptp.set_set_int) Bool)
% 4.71/5.16 (declare-fun tptp.finite1152437895449049373et_nat (tptp.set_set_nat) Bool)
% 4.71/5.16 (declare-fun tptp.finite5795047828879050333T_VEBT (tptp.set_VEBT_VEBT) Bool)
% 4.71/5.16 (declare-fun tptp.bij_be1856998921033663316omplex ((-> tptp.complex tptp.complex) tptp.set_complex tptp.set_complex) Bool)
% 4.71/5.16 (declare-fun tptp.bij_betw_nat_complex ((-> tptp.nat tptp.complex) tptp.set_nat tptp.set_complex) Bool)
% 4.71/5.16 (declare-fun tptp.bij_betw_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat tptp.set_nat) Bool)
% 4.71/5.16 (declare-fun tptp.comp_int_nat_int ((-> tptp.int tptp.nat) (-> tptp.int tptp.int) tptp.int) tptp.nat)
% 4.71/5.16 (declare-fun tptp.comp_nat_nat_nat ((-> tptp.nat tptp.nat) (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.id_o (Bool) Bool)
% 4.71/5.16 (declare-fun tptp.id_nat (tptp.nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.inj_on_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) Bool)
% 4.71/5.16 (declare-fun tptp.inj_on_nat_char ((-> tptp.nat tptp.char) tptp.set_nat) Bool)
% 4.71/5.16 (declare-fun tptp.inj_on_real_real ((-> tptp.real tptp.real) tptp.set_real) Bool)
% 4.71/5.16 (declare-fun tptp.inj_on_set_nat_nat ((-> tptp.set_nat tptp.nat) tptp.set_set_nat) Bool)
% 4.71/5.16 (declare-fun tptp.map_fu434086159418415080_int_o ((-> tptp.int tptp.product_prod_nat_nat) (-> (-> tptp.product_prod_nat_nat Bool) tptp.int Bool) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) tptp.int tptp.int) Bool)
% 4.71/5.16 (declare-fun tptp.map_fu4960017516451851995nt_int ((-> tptp.int tptp.product_prod_nat_nat) (-> (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.int tptp.int) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.int tptp.int) tptp.int)
% 4.71/5.16 (declare-fun tptp.map_fu4826362097070443709at_o_o ((-> tptp.int tptp.product_prod_nat_nat) (-> Bool Bool) (-> tptp.product_prod_nat_nat Bool) tptp.int) Bool)
% 4.71/5.16 (declare-fun tptp.map_fu2345160673673942751at_nat ((-> tptp.int tptp.product_prod_nat_nat) (-> tptp.nat tptp.nat) (-> tptp.product_prod_nat_nat tptp.nat) tptp.int) tptp.nat)
% 4.71/5.16 (declare-fun tptp.map_fu3667384564859982768at_int ((-> tptp.int tptp.product_prod_nat_nat) (-> tptp.product_prod_nat_nat tptp.int) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.int) tptp.int)
% 4.71/5.16 (declare-fun tptp.strict1292158309912662752at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) Bool)
% 4.71/5.16 (declare-fun tptp.the_in5290026491893676941l_real (tptp.set_real (-> tptp.real tptp.real) tptp.real) tptp.real)
% 4.71/5.16 (declare-fun tptp.fun_is_measure_int ((-> tptp.int tptp.nat)) Bool)
% 4.71/5.16 (declare-fun tptp.fun_pair_leq () tptp.set_Pr8693737435421807431at_nat)
% 4.71/5.16 (declare-fun tptp.fun_pair_less () tptp.set_Pr8693737435421807431at_nat)
% 4.71/5.16 (declare-fun tptp.gcd_Gcd_nat (tptp.set_nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.bezw (tptp.nat tptp.nat) tptp.product_prod_int_int)
% 4.71/5.16 (declare-fun tptp.bezw_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 4.71/5.16 (declare-fun tptp.abs_abs_complex (tptp.complex) tptp.complex)
% 4.71/5.16 (declare-fun tptp.abs_abs_int (tptp.int) tptp.int)
% 4.71/5.16 (declare-fun tptp.abs_abs_real (tptp.real) tptp.real)
% 4.71/5.16 (declare-fun tptp.minus_2020553357622893040enat_o ((-> tptp.extended_enat Bool) (-> tptp.extended_enat Bool) tptp.extended_enat) Bool)
% 4.71/5.16 (declare-fun tptp.minus_minus_int_o ((-> tptp.int Bool) (-> tptp.int Bool) tptp.int) Bool)
% 4.71/5.16 (declare-fun tptp.minus_1139252259498527702_nat_o ((-> tptp.list_nat Bool) (-> tptp.list_nat Bool) tptp.list_nat) Bool)
% 4.71/5.16 (declare-fun tptp.minus_minus_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool) tptp.nat) Bool)
% 4.71/5.16 (declare-fun tptp.minus_minus_real_o ((-> tptp.real Bool) (-> tptp.real Bool) tptp.real) Bool)
% 4.71/5.16 (declare-fun tptp.minus_6910147592129066416_nat_o ((-> tptp.set_nat Bool) (-> tptp.set_nat Bool) tptp.set_nat) Bool)
% 4.71/5.16 (declare-fun tptp.minus_minus_complex (tptp.complex tptp.complex) tptp.complex)
% 4.71/5.16 (declare-fun tptp.minus_3235023915231533773d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 4.71/5.16 (declare-fun tptp.minus_minus_int (tptp.int tptp.int) tptp.int)
% 4.71/5.16 (declare-fun tptp.minus_minus_nat (tptp.nat tptp.nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.minus_minus_real (tptp.real tptp.real) tptp.real)
% 4.71/5.16 (declare-fun tptp.minus_811609699411566653omplex (tptp.set_complex tptp.set_complex) tptp.set_complex)
% 4.71/5.16 (declare-fun tptp.minus_925952699566721837d_enat (tptp.set_Extended_enat tptp.set_Extended_enat) tptp.set_Extended_enat)
% 4.71/5.16 (declare-fun tptp.minus_minus_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 4.71/5.16 (declare-fun tptp.minus_7954133019191499631st_nat (tptp.set_list_nat tptp.set_list_nat) tptp.set_list_nat)
% 4.71/5.16 (declare-fun tptp.minus_minus_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 4.71/5.16 (declare-fun tptp.minus_minus_set_real (tptp.set_real tptp.set_real) tptp.set_real)
% 4.71/5.16 (declare-fun tptp.minus_2163939370556025621et_nat (tptp.set_set_nat tptp.set_set_nat) tptp.set_set_nat)
% 4.71/5.16 (declare-fun tptp.one_one_complex () tptp.complex)
% 4.71/5.16 (declare-fun tptp.one_on7984719198319812577d_enat () tptp.extended_enat)
% 4.71/5.16 (declare-fun tptp.one_one_int () tptp.int)
% 4.71/5.16 (declare-fun tptp.one_one_nat () tptp.nat)
% 4.71/5.16 (declare-fun tptp.one_one_real () tptp.real)
% 4.71/5.16 (declare-fun tptp.plus_plus_complex (tptp.complex tptp.complex) tptp.complex)
% 4.71/5.16 (declare-fun tptp.plus_p3455044024723400733d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 4.71/5.16 (declare-fun tptp.plus_plus_int (tptp.int tptp.int) tptp.int)
% 4.71/5.16 (declare-fun tptp.plus_plus_nat (tptp.nat tptp.nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.plus_plus_num (tptp.num tptp.num) tptp.num)
% 4.71/5.16 (declare-fun tptp.plus_plus_real (tptp.real tptp.real) tptp.real)
% 4.71/5.16 (declare-fun tptp.sgn_sgn_complex (tptp.complex) tptp.complex)
% 4.71/5.16 (declare-fun tptp.sgn_sgn_int (tptp.int) tptp.int)
% 4.71/5.16 (declare-fun tptp.sgn_sgn_real (tptp.real) tptp.real)
% 4.71/5.16 (declare-fun tptp.times_times_complex (tptp.complex tptp.complex) tptp.complex)
% 4.71/5.16 (declare-fun tptp.times_7803423173614009249d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 4.71/5.16 (declare-fun tptp.times_times_int (tptp.int tptp.int) tptp.int)
% 4.71/5.16 (declare-fun tptp.times_times_nat (tptp.nat tptp.nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.times_times_real (tptp.real tptp.real) tptp.real)
% 4.71/5.16 (declare-fun tptp.uminus6636779312473996640enat_o ((-> tptp.extended_enat Bool) tptp.extended_enat) Bool)
% 4.71/5.16 (declare-fun tptp.uminus_uminus_int_o ((-> tptp.int Bool) tptp.int) Bool)
% 4.71/5.16 (declare-fun tptp.uminus5770388063884162150_nat_o ((-> tptp.list_nat Bool) tptp.list_nat) Bool)
% 4.71/5.16 (declare-fun tptp.uminus_uminus_nat_o ((-> tptp.nat Bool) tptp.nat) Bool)
% 4.71/5.16 (declare-fun tptp.uminus_uminus_real_o ((-> tptp.real Bool) tptp.real) Bool)
% 4.71/5.16 (declare-fun tptp.uminus6401447641752708672_nat_o ((-> tptp.set_nat Bool) tptp.set_nat) Bool)
% 4.71/5.16 (declare-fun tptp.uminus1482373934393186551omplex (tptp.complex) tptp.complex)
% 4.71/5.16 (declare-fun tptp.uminus_uminus_int (tptp.int) tptp.int)
% 4.71/5.16 (declare-fun tptp.uminus_uminus_real (tptp.real) tptp.real)
% 4.71/5.16 (declare-fun tptp.uminus417252749190364093d_enat (tptp.set_Extended_enat) tptp.set_Extended_enat)
% 4.71/5.16 (declare-fun tptp.uminus1532241313380277803et_int (tptp.set_int) tptp.set_int)
% 4.71/5.16 (declare-fun tptp.uminus3195874150345416415st_nat (tptp.set_list_nat) tptp.set_list_nat)
% 4.71/5.16 (declare-fun tptp.uminus5710092332889474511et_nat (tptp.set_nat) tptp.set_nat)
% 4.71/5.16 (declare-fun tptp.uminus612125837232591019t_real (tptp.set_real) tptp.set_real)
% 4.71/5.16 (declare-fun tptp.uminus613421341184616069et_nat (tptp.set_set_nat) tptp.set_set_nat)
% 4.71/5.16 (declare-fun tptp.zero_zero_complex () tptp.complex)
% 4.71/5.16 (declare-fun tptp.zero_z5237406670263579293d_enat () tptp.extended_enat)
% 4.71/5.16 (declare-fun tptp.zero_zero_int () tptp.int)
% 4.71/5.16 (declare-fun tptp.zero_zero_nat () tptp.nat)
% 4.71/5.16 (declare-fun tptp.zero_zero_real () tptp.real)
% 4.71/5.16 (declare-fun tptp.groups7754918857620584856omplex ((-> tptp.complex tptp.complex) tptp.set_complex) tptp.complex)
% 4.71/5.16 (declare-fun tptp.groups1752964319039525884d_enat ((-> tptp.complex tptp.extended_enat) tptp.set_complex) tptp.extended_enat)
% 4.71/5.16 (declare-fun tptp.groups5690904116761175830ex_int ((-> tptp.complex tptp.int) tptp.set_complex) tptp.int)
% 4.71/5.16 (declare-fun tptp.groups5693394587270226106ex_nat ((-> tptp.complex tptp.nat) tptp.set_complex) tptp.nat)
% 4.71/5.16 (declare-fun tptp.groups5808333547571424918x_real ((-> tptp.complex tptp.real) tptp.set_complex) tptp.real)
% 4.71/5.16 (declare-fun tptp.groups6818542070133387226omplex ((-> tptp.extended_enat tptp.complex) tptp.set_Extended_enat) tptp.complex)
% 4.71/5.16 (declare-fun tptp.groups2433450451889696826d_enat ((-> tptp.extended_enat tptp.extended_enat) tptp.set_Extended_enat) tptp.extended_enat)
% 4.71/5.16 (declare-fun tptp.groups2025484359314973016at_int ((-> tptp.extended_enat tptp.int) tptp.set_Extended_enat) tptp.int)
% 4.71/5.16 (declare-fun tptp.groups2027974829824023292at_nat ((-> tptp.extended_enat tptp.nat) tptp.set_Extended_enat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.groups4148127829035722712t_real ((-> tptp.extended_enat tptp.real) tptp.set_Extended_enat) tptp.real)
% 4.71/5.16 (declare-fun tptp.groups4225252721152677374d_enat ((-> tptp.int tptp.extended_enat) tptp.set_int) tptp.extended_enat)
% 4.71/5.16 (declare-fun tptp.groups4538972089207619220nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 4.71/5.16 (declare-fun tptp.groups4541462559716669496nt_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.nat)
% 4.71/5.16 (declare-fun tptp.groups8778361861064173332t_real ((-> tptp.int tptp.real) tptp.set_int) tptp.real)
% 4.71/5.16 (declare-fun tptp.groups2073611262835488442omplex ((-> tptp.nat tptp.complex) tptp.set_nat) tptp.complex)
% 4.71/5.16 (declare-fun tptp.groups7108830773950497114d_enat ((-> tptp.nat tptp.extended_enat) tptp.set_nat) tptp.extended_enat)
% 4.71/5.16 (declare-fun tptp.groups3539618377306564664at_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.int)
% 4.71/5.16 (declare-fun tptp.groups3542108847815614940at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.groups6591440286371151544t_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.real)
% 4.71/5.16 (declare-fun tptp.groups977919841031483927at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.set_Pr1261947904930325089at_nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.groups4567486121110086003t_real ((-> tptp.product_prod_nat_nat tptp.real) tptp.set_Pr1261947904930325089at_nat) tptp.real)
% 4.71/5.16 (declare-fun tptp.groups5754745047067104278omplex ((-> tptp.real tptp.complex) tptp.set_real) tptp.complex)
% 4.71/5.16 (declare-fun tptp.groups2800946370649118462d_enat ((-> tptp.real tptp.extended_enat) tptp.set_real) tptp.extended_enat)
% 4.71/5.16 (declare-fun tptp.groups1932886352136224148al_int ((-> tptp.real tptp.int) tptp.set_real) tptp.int)
% 4.71/5.16 (declare-fun tptp.groups1935376822645274424al_nat ((-> tptp.real tptp.nat) tptp.set_real) tptp.nat)
% 4.71/5.16 (declare-fun tptp.groups8097168146408367636l_real ((-> tptp.real tptp.real) tptp.set_real) tptp.real)
% 4.71/5.16 (declare-fun tptp.groups8292507037921071086at_int ((-> tptp.set_nat tptp.int) tptp.set_set_nat) tptp.int)
% 4.71/5.16 (declare-fun tptp.groups8294997508430121362at_nat ((-> tptp.set_nat tptp.nat) tptp.set_set_nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.groups5107569545109728110t_real ((-> tptp.set_nat tptp.real) tptp.set_set_nat) tptp.real)
% 4.71/5.16 (declare-fun tptp.groups771621172384141258BT_nat ((-> tptp.vEBT_VEBT tptp.nat) tptp.set_VEBT_VEBT) tptp.nat)
% 4.71/5.16 (declare-fun tptp.groups3708469109370488835omplex ((-> tptp.complex tptp.complex) tptp.set_complex) tptp.complex)
% 4.71/5.16 (declare-fun tptp.groups8780218893797010257d_enat ((-> tptp.complex tptp.extended_enat) tptp.set_complex) tptp.extended_enat)
% 4.71/5.16 (declare-fun tptp.groups858564598930262913ex_int ((-> tptp.complex tptp.int) tptp.set_complex) tptp.int)
% 4.71/5.16 (declare-fun tptp.groups861055069439313189ex_nat ((-> tptp.complex tptp.nat) tptp.set_complex) tptp.nat)
% 4.71/5.16 (declare-fun tptp.groups766887009212190081x_real ((-> tptp.complex tptp.real) tptp.set_complex) tptp.real)
% 4.71/5.16 (declare-fun tptp.groups4622424608036095791omplex ((-> tptp.extended_enat tptp.complex) tptp.set_Extended_enat) tptp.complex)
% 4.71/5.16 (declare-fun tptp.groups8932437906259616549d_enat ((-> tptp.extended_enat tptp.extended_enat) tptp.set_Extended_enat) tptp.extended_enat)
% 4.71/5.16 (declare-fun tptp.groups2878480467620962989at_int ((-> tptp.extended_enat tptp.int) tptp.set_Extended_enat) tptp.int)
% 4.71/5.16 (declare-fun tptp.groups2880970938130013265at_nat ((-> tptp.extended_enat tptp.nat) tptp.set_Extended_enat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.groups97031904164794029t_real ((-> tptp.extended_enat tptp.real) tptp.set_Extended_enat) tptp.real)
% 4.71/5.16 (declare-fun tptp.groups7440179247065528705omplex ((-> tptp.int tptp.complex) tptp.set_int) tptp.complex)
% 4.71/5.16 (declare-fun tptp.groups5078248829458667347d_enat ((-> tptp.int tptp.extended_enat) tptp.set_int) tptp.extended_enat)
% 4.71/5.16 (declare-fun tptp.groups1705073143266064639nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 4.71/5.16 (declare-fun tptp.groups1707563613775114915nt_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.nat)
% 4.71/5.16 (declare-fun tptp.groups2316167850115554303t_real ((-> tptp.int tptp.real) tptp.set_int) tptp.real)
% 4.71/5.16 (declare-fun tptp.groups6464643781859351333omplex ((-> tptp.nat tptp.complex) tptp.set_nat) tptp.complex)
% 4.71/5.16 (declare-fun tptp.groups7961826882256487087d_enat ((-> tptp.nat tptp.extended_enat) tptp.set_nat) tptp.extended_enat)
% 4.71/5.16 (declare-fun tptp.groups705719431365010083at_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.int)
% 4.71/5.16 (declare-fun tptp.groups708209901874060359at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.groups129246275422532515t_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.real)
% 4.71/5.16 (declare-fun tptp.groups4075276357253098568at_int ((-> tptp.product_prod_nat_nat tptp.int) tptp.set_Pr1261947904930325089at_nat) tptp.int)
% 4.71/5.16 (declare-fun tptp.groups4077766827762148844at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.set_Pr1261947904930325089at_nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.groups713298508707869441omplex ((-> tptp.real tptp.complex) tptp.set_real) tptp.complex)
% 4.71/5.16 (declare-fun tptp.groups7973222482632965587d_enat ((-> tptp.real tptp.extended_enat) tptp.set_real) tptp.extended_enat)
% 4.71/5.16 (declare-fun tptp.groups4694064378042380927al_int ((-> tptp.real tptp.int) tptp.set_real) tptp.int)
% 4.71/5.16 (declare-fun tptp.groups4696554848551431203al_nat ((-> tptp.real tptp.nat) tptp.set_real) tptp.nat)
% 4.71/5.16 (declare-fun tptp.groups1681761925125756287l_real ((-> tptp.real tptp.real) tptp.set_real) tptp.real)
% 4.71/5.16 (declare-fun tptp.groups3619160379726066777t_real ((-> tptp.set_nat tptp.real) tptp.set_set_nat) tptp.real)
% 4.71/5.16 (declare-fun tptp.groups4561878855575611511st_nat (tptp.list_nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.if_int_int (Bool (-> tptp.int tptp.int) (-> tptp.int tptp.int) tptp.int) tptp.int)
% 4.71/5.16 (declare-fun tptp.if_complex (Bool tptp.complex tptp.complex) tptp.complex)
% 4.71/5.16 (declare-fun tptp.if_Extended_enat (Bool tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 4.71/5.16 (declare-fun tptp.if_int (Bool tptp.int tptp.int) tptp.int)
% 4.71/5.16 (declare-fun tptp.if_list_int (Bool tptp.list_int tptp.list_int) tptp.list_int)
% 4.71/5.16 (declare-fun tptp.if_list_nat (Bool tptp.list_nat tptp.list_nat) tptp.list_nat)
% 4.71/5.16 (declare-fun tptp.if_nat (Bool tptp.nat tptp.nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.if_option_num (Bool tptp.option_num tptp.option_num) tptp.option_num)
% 4.71/5.16 (declare-fun tptp.if_Pro3027730157355071871nt_int (Bool tptp.product_prod_int_int tptp.product_prod_int_int) tptp.product_prod_int_int)
% 4.71/5.16 (declare-fun tptp.if_Pro6206227464963214023at_nat (Bool tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 4.71/5.16 (declare-fun tptp.if_real (Bool tptp.real tptp.real) tptp.real)
% 4.71/5.16 (declare-fun tptp.if_set_int (Bool tptp.set_int tptp.set_int) tptp.set_int)
% 4.71/5.16 (declare-fun tptp.if_set_nat (Bool tptp.set_nat tptp.set_nat) tptp.set_nat)
% 4.71/5.16 (declare-fun tptp.if_VEBT_VEBT (Bool tptp.vEBT_VEBT tptp.vEBT_VEBT) tptp.vEBT_VEBT)
% 4.71/5.16 (declare-fun tptp.infini8530281810654367211te_nat (tptp.set_nat tptp.nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.abs_Integ (tptp.product_prod_nat_nat) tptp.int)
% 4.71/5.16 (declare-fun tptp.rep_Integ (tptp.int) tptp.product_prod_nat_nat)
% 4.71/5.16 (declare-fun tptp.int_ge_less_than (tptp.int) tptp.set_Pr958786334691620121nt_int)
% 4.71/5.16 (declare-fun tptp.int_ge_less_than2 (tptp.int) tptp.set_Pr958786334691620121nt_int)
% 4.71/5.16 (declare-fun tptp.intrel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 4.71/5.16 (declare-fun tptp.nat2 (tptp.int) tptp.nat)
% 4.71/5.16 (declare-fun tptp.pcr_int (tptp.product_prod_nat_nat tptp.int) Bool)
% 4.71/5.16 (declare-fun tptp.ring_17405671764205052669omplex (tptp.int) tptp.complex)
% 4.71/5.16 (declare-fun tptp.ring_1_of_int_int (tptp.int) tptp.int)
% 4.71/5.16 (declare-fun tptp.ring_1_of_int_real (tptp.int) tptp.real)
% 4.71/5.16 (declare-fun tptp.inf_inf_int (tptp.int tptp.int) tptp.int)
% 4.71/5.16 (declare-fun tptp.inf_inf_nat (tptp.nat tptp.nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.inf_in2572325071724192079at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 4.71/5.16 (declare-fun tptp.semila1623282765462674594er_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat (-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool)) Bool)
% 4.71/5.16 (declare-fun tptp.sup_sup_int (tptp.int tptp.int) tptp.int)
% 4.71/5.16 (declare-fun tptp.sup_sup_nat (tptp.nat tptp.nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.sup_sup_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 4.71/5.16 (declare-fun tptp.lattic921264341876707157d_enat (tptp.set_Extended_enat) tptp.extended_enat)
% 4.71/5.16 (declare-fun tptp.lattic8265883725875713057ax_nat (tptp.set_nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.lattic7796887085614042845d_enat ((-> tptp.complex tptp.extended_enat) tptp.set_complex) tptp.complex)
% 4.71/5.16 (declare-fun tptp.lattic5364784637807008409ex_nat ((-> tptp.complex tptp.nat) tptp.set_complex) tptp.complex)
% 4.71/5.16 (declare-fun tptp.lattic8794016678065449205x_real ((-> tptp.complex tptp.real) tptp.set_complex) tptp.complex)
% 4.71/5.16 (declare-fun tptp.lattic1996716550891908761d_enat ((-> tptp.extended_enat tptp.extended_enat) tptp.set_Extended_enat) tptp.extended_enat)
% 4.71/5.16 (declare-fun tptp.lattic3845382081240766429at_nat ((-> tptp.extended_enat tptp.nat) tptp.set_Extended_enat) tptp.extended_enat)
% 4.71/5.16 (declare-fun tptp.lattic1189837152898106425t_real ((-> tptp.extended_enat tptp.real) tptp.set_Extended_enat) tptp.extended_enat)
% 4.71/5.16 (declare-fun tptp.lattic6042659972569420511d_enat ((-> tptp.int tptp.extended_enat) tptp.set_int) tptp.int)
% 4.71/5.16 (declare-fun tptp.lattic8446286672483414039nt_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.int)
% 4.71/5.16 (declare-fun tptp.lattic2675449441010098035t_real ((-> tptp.int tptp.real) tptp.set_int) tptp.int)
% 4.71/5.16 (declare-fun tptp.lattic8926238025367240251d_enat ((-> tptp.nat tptp.extended_enat) tptp.set_nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.lattic7446932960582359483at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.lattic488527866317076247t_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.lattic9066027731366277983d_enat ((-> tptp.real tptp.extended_enat) tptp.set_real) tptp.real)
% 4.71/5.16 (declare-fun tptp.lattic5055836439445974935al_nat ((-> tptp.real tptp.nat) tptp.set_real) tptp.real)
% 4.71/5.16 (declare-fun tptp.lattic8440615504127631091l_real ((-> tptp.real tptp.real) tptp.set_real) tptp.real)
% 4.71/5.16 (declare-fun tptp.append_int (tptp.list_int tptp.list_int) tptp.list_int)
% 4.71/5.16 (declare-fun tptp.append_nat (tptp.list_nat tptp.list_nat) tptp.list_nat)
% 4.71/5.16 (declare-fun tptp.count_list_complex (tptp.list_complex tptp.complex) tptp.nat)
% 4.71/5.16 (declare-fun tptp.count_101369445342291426d_enat (tptp.list_Extended_enat tptp.extended_enat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.count_list_int (tptp.list_int tptp.int) tptp.nat)
% 4.71/5.16 (declare-fun tptp.count_list_nat (tptp.list_nat tptp.nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.count_list_real (tptp.list_real tptp.real) tptp.nat)
% 4.71/5.16 (declare-fun tptp.count_list_set_nat (tptp.list_set_nat tptp.set_nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.count_list_VEBT_VEBT (tptp.list_VEBT_VEBT tptp.vEBT_VEBT) tptp.nat)
% 4.71/5.16 (declare-fun tptp.distinct_int (tptp.list_int) Bool)
% 4.71/5.16 (declare-fun tptp.distinct_nat (tptp.list_nat) Bool)
% 4.71/5.16 (declare-fun tptp.drop_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 4.71/5.16 (declare-fun tptp.enumerate_int (tptp.nat tptp.list_int) tptp.list_P3521021558325789923at_int)
% 4.71/5.16 (declare-fun tptp.enumerate_nat (tptp.nat tptp.list_nat) tptp.list_P6011104703257516679at_nat)
% 4.71/5.16 (declare-fun tptp.enumerate_VEBT_VEBT (tptp.nat tptp.list_VEBT_VEBT) tptp.list_P5647936690300460905T_VEBT)
% 4.71/5.16 (declare-fun tptp.find_Extended_enat ((-> tptp.extended_enat Bool) tptp.list_Extended_enat) tptp.option_Extended_enat)
% 4.71/5.16 (declare-fun tptp.find_int ((-> tptp.int Bool) tptp.list_int) tptp.option_int)
% 4.71/5.16 (declare-fun tptp.find_nat ((-> tptp.nat Bool) tptp.list_nat) tptp.option_nat)
% 4.71/5.16 (declare-fun tptp.find_num ((-> tptp.num Bool) tptp.list_num) tptp.option_num)
% 4.71/5.16 (declare-fun tptp.find_P8199882355184865565at_nat ((-> tptp.product_prod_nat_nat Bool) tptp.list_P6011104703257516679at_nat) tptp.option4927543243414619207at_nat)
% 4.71/5.16 (declare-fun tptp.find_real ((-> tptp.real Bool) tptp.list_real) tptp.option_real)
% 4.71/5.16 (declare-fun tptp.find_set_nat ((-> tptp.set_nat Bool) tptp.list_set_nat) tptp.option_set_nat)
% 4.71/5.16 (declare-fun tptp.find_VEBT_VEBT ((-> tptp.vEBT_VEBT Bool) tptp.list_VEBT_VEBT) tptp.option_VEBT_VEBT)
% 4.71/5.16 (declare-fun tptp.gen_length_int (tptp.nat tptp.list_int) tptp.nat)
% 4.71/5.16 (declare-fun tptp.gen_length_nat (tptp.nat tptp.list_nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.gen_length_VEBT_VEBT (tptp.nat tptp.list_VEBT_VEBT) tptp.nat)
% 4.71/5.16 (declare-fun tptp.last_nat (tptp.list_nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.linord1735203802627413978nt_int ((-> tptp.int tptp.int) tptp.list_int) tptp.list_int)
% 4.71/5.16 (declare-fun tptp.linord738340561235409698at_nat ((-> tptp.nat tptp.nat) tptp.list_nat) tptp.list_nat)
% 4.71/5.16 (declare-fun tptp.linord2614967742042102400et_nat (tptp.set_nat) tptp.list_nat)
% 4.71/5.16 (declare-fun tptp.cons_int (tptp.int tptp.list_int) tptp.list_int)
% 4.71/5.16 (declare-fun tptp.cons_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 4.71/5.16 (declare-fun tptp.nil_int () tptp.list_int)
% 4.71/5.16 (declare-fun tptp.nil_nat () tptp.list_nat)
% 4.71/5.16 (declare-fun tptp.hd_nat (tptp.list_nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.map_nat_nat ((-> tptp.nat tptp.nat) tptp.list_nat) tptp.list_nat)
% 4.71/5.16 (declare-fun tptp.set_complex2 (tptp.list_complex) tptp.set_complex)
% 4.71/5.16 (declare-fun tptp.set_Extended_enat2 (tptp.list_Extended_enat) tptp.set_Extended_enat)
% 4.71/5.16 (declare-fun tptp.set_int2 (tptp.list_int) tptp.set_int)
% 4.71/5.16 (declare-fun tptp.set_nat2 (tptp.list_nat) tptp.set_nat)
% 4.71/5.16 (declare-fun tptp.set_num2 (tptp.list_num) tptp.set_num)
% 4.71/5.16 (declare-fun tptp.set_Pr5648618587558075414at_nat (tptp.list_P6011104703257516679at_nat) tptp.set_Pr1261947904930325089at_nat)
% 4.71/5.16 (declare-fun tptp.set_real2 (tptp.list_real) tptp.set_real)
% 4.71/5.16 (declare-fun tptp.set_set_nat2 (tptp.list_set_nat) tptp.set_set_nat)
% 4.71/5.16 (declare-fun tptp.set_VEBT_VEBT2 (tptp.list_VEBT_VEBT) tptp.set_VEBT_VEBT)
% 4.71/5.16 (declare-fun tptp.size_list_VEBT_VEBT ((-> tptp.vEBT_VEBT tptp.nat) tptp.list_VEBT_VEBT) tptp.nat)
% 4.71/5.16 (declare-fun tptp.tl_nat (tptp.list_nat) tptp.list_nat)
% 4.71/5.16 (declare-fun tptp.list_u3071683517702156500d_enat (tptp.list_Extended_enat tptp.nat tptp.extended_enat) tptp.list_Extended_enat)
% 4.71/5.16 (declare-fun tptp.list_update_int (tptp.list_int tptp.nat tptp.int) tptp.list_int)
% 4.71/5.16 (declare-fun tptp.list_update_nat (tptp.list_nat tptp.nat tptp.nat) tptp.list_nat)
% 4.71/5.16 (declare-fun tptp.list_u6180841689913720943at_nat (tptp.list_P6011104703257516679at_nat tptp.nat tptp.product_prod_nat_nat) tptp.list_P6011104703257516679at_nat)
% 4.71/5.16 (declare-fun tptp.list_update_real (tptp.list_real tptp.nat tptp.real) tptp.list_real)
% 4.71/5.16 (declare-fun tptp.list_update_set_nat (tptp.list_set_nat tptp.nat tptp.set_nat) tptp.list_set_nat)
% 4.71/5.16 (declare-fun tptp.list_u1324408373059187874T_VEBT (tptp.list_VEBT_VEBT tptp.nat tptp.vEBT_VEBT) tptp.list_VEBT_VEBT)
% 4.71/5.16 (declare-fun tptp.listrel1_int (tptp.set_Pr958786334691620121nt_int) tptp.set_Pr765067013931698361st_int)
% 4.71/5.16 (declare-fun tptp.listrel1_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr3451248702717554689st_nat)
% 4.71/5.16 (declare-fun tptp.listre4828114922151135584at_nat (tptp.set_Pr8693737435421807431at_nat) tptp.set_Pr1542805901266377927at_nat)
% 4.71/5.16 (declare-fun tptp.listrel1_VEBT_VEBT (tptp.set_Pr6192946355708809607T_VEBT) tptp.set_Pr1916528119006554503T_VEBT)
% 4.71/5.16 (declare-fun tptp.listrel1p_int ((-> tptp.int tptp.int Bool) tptp.list_int tptp.list_int) Bool)
% 4.71/5.16 (declare-fun tptp.listrel1p_nat ((-> tptp.nat tptp.nat Bool) tptp.list_nat tptp.list_nat) Bool)
% 4.71/5.16 (declare-fun tptp.nth_Extended_enat (tptp.list_Extended_enat tptp.nat) tptp.extended_enat)
% 4.71/5.16 (declare-fun tptp.nth_int (tptp.list_int tptp.nat) tptp.int)
% 4.71/5.16 (declare-fun tptp.nth_nat (tptp.list_nat tptp.nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.nth_num (tptp.list_num tptp.nat) tptp.num)
% 4.71/5.16 (declare-fun tptp.nth_Pr4439495888332055232nt_int (tptp.list_P5707943133018811711nt_int tptp.nat) tptp.product_prod_int_int)
% 4.71/5.16 (declare-fun tptp.nth_Pr8617346907841251940nt_nat (tptp.list_P8198026277950538467nt_nat tptp.nat) tptp.product_prod_int_nat)
% 4.71/5.16 (declare-fun tptp.nth_Pr3474266648193625910T_VEBT (tptp.list_P7524865323317820941T_VEBT tptp.nat) tptp.produc1531783533982839933T_VEBT)
% 4.71/5.16 (declare-fun tptp.nth_Pr3440142176431000676at_int (tptp.list_P3521021558325789923at_int tptp.nat) tptp.product_prod_nat_int)
% 4.71/5.16 (declare-fun tptp.nth_Pr7617993195940197384at_nat (tptp.list_P6011104703257516679at_nat tptp.nat) tptp.product_prod_nat_nat)
% 4.71/5.16 (declare-fun tptp.nth_Pr744662078594809490T_VEBT (tptp.list_P5647936690300460905T_VEBT tptp.nat) tptp.produc8025551001238799321T_VEBT)
% 4.71/5.16 (declare-fun tptp.nth_Pr6744343527793145070at_nat (tptp.list_P8469869581646625389at_nat tptp.nat) tptp.produc859450856879609959at_nat)
% 4.71/5.16 (declare-fun tptp.nth_Pr6837108013167703752BT_int (tptp.list_P4547456442757143711BT_int tptp.nat) tptp.produc4894624898956917775BT_int)
% 4.71/5.16 (declare-fun tptp.nth_Pr1791586995822124652BT_nat (tptp.list_P7037539587688870467BT_nat tptp.nat) tptp.produc9072475918466114483BT_nat)
% 4.71/5.16 (declare-fun tptp.nth_Pr4953567300277697838T_VEBT (tptp.list_P7413028617227757229T_VEBT tptp.nat) tptp.produc8243902056947475879T_VEBT)
% 4.71/5.16 (declare-fun tptp.nth_real (tptp.list_real tptp.nat) tptp.real)
% 4.71/5.16 (declare-fun tptp.nth_set_nat (tptp.list_set_nat tptp.nat) tptp.set_nat)
% 4.71/5.16 (declare-fun tptp.nth_VEBT_VEBT (tptp.list_VEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 4.71/5.16 (declare-fun tptp.product_int_int (tptp.list_int tptp.list_int) tptp.list_P5707943133018811711nt_int)
% 4.71/5.16 (declare-fun tptp.product_int_nat (tptp.list_int tptp.list_nat) tptp.list_P8198026277950538467nt_nat)
% 4.71/5.16 (declare-fun tptp.produc662631939642741121T_VEBT (tptp.list_int tptp.list_VEBT_VEBT) tptp.list_P7524865323317820941T_VEBT)
% 4.71/5.16 (declare-fun tptp.product_nat_int (tptp.list_nat tptp.list_int) tptp.list_P3521021558325789923at_int)
% 4.71/5.16 (declare-fun tptp.product_nat_nat (tptp.list_nat tptp.list_nat) tptp.list_P6011104703257516679at_nat)
% 4.71/5.16 (declare-fun tptp.produc7156399406898700509T_VEBT (tptp.list_nat tptp.list_VEBT_VEBT) tptp.list_P5647936690300460905T_VEBT)
% 4.71/5.16 (declare-fun tptp.produc3544356994491977349at_nat (tptp.list_P6011104703257516679at_nat tptp.list_P6011104703257516679at_nat) tptp.list_P8469869581646625389at_nat)
% 4.71/5.16 (declare-fun tptp.produc7292646706713671643BT_int (tptp.list_VEBT_VEBT tptp.list_int) tptp.list_P4547456442757143711BT_int)
% 4.71/5.16 (declare-fun tptp.produc7295137177222721919BT_nat (tptp.list_VEBT_VEBT tptp.list_nat) tptp.list_P7037539587688870467BT_nat)
% 4.71/5.16 (declare-fun tptp.produc4743750530478302277T_VEBT (tptp.list_VEBT_VEBT tptp.list_VEBT_VEBT) tptp.list_P7413028617227757229T_VEBT)
% 4.71/5.16 (declare-fun tptp.remdups_nat (tptp.list_nat) tptp.list_nat)
% 4.71/5.16 (declare-fun tptp.replic7216382294607269926d_enat (tptp.nat tptp.extended_enat) tptp.list_Extended_enat)
% 4.71/5.16 (declare-fun tptp.replicate_int (tptp.nat tptp.int) tptp.list_int)
% 4.71/5.16 (declare-fun tptp.replicate_nat (tptp.nat tptp.nat) tptp.list_nat)
% 4.71/5.16 (declare-fun tptp.replicate_real (tptp.nat tptp.real) tptp.list_real)
% 4.71/5.16 (declare-fun tptp.replicate_set_nat (tptp.nat tptp.set_nat) tptp.list_set_nat)
% 4.71/5.16 (declare-fun tptp.replicate_VEBT_VEBT (tptp.nat tptp.vEBT_VEBT) tptp.list_VEBT_VEBT)
% 4.71/5.16 (declare-fun tptp.sorted_wrt_int ((-> tptp.int tptp.int Bool) tptp.list_int) Bool)
% 4.71/5.16 (declare-fun tptp.sorted_wrt_nat ((-> tptp.nat tptp.nat Bool) tptp.list_nat) Bool)
% 4.71/5.16 (declare-fun tptp.take_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 4.71/5.16 (declare-fun tptp.upt (tptp.nat tptp.nat) tptp.list_nat)
% 4.71/5.16 (declare-fun tptp.upto (tptp.int tptp.int) tptp.list_int)
% 4.71/5.16 (declare-fun tptp.upto_aux (tptp.int tptp.int tptp.list_int) tptp.list_int)
% 4.71/5.16 (declare-fun tptp.upto_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 4.71/5.16 (declare-fun tptp.suc (tptp.nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.compow_nat_nat (tptp.nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.case_nat_o (Bool (-> tptp.nat Bool) tptp.nat) Bool)
% 4.71/5.16 (declare-fun tptp.case_nat_nat (tptp.nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.pred (tptp.nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.semiring_1_Nats_int () tptp.set_int)
% 4.71/5.16 (declare-fun tptp.semiri8010041392384452111omplex (tptp.nat) tptp.complex)
% 4.71/5.16 (declare-fun tptp.semiri4216267220026989637d_enat (tptp.nat) tptp.extended_enat)
% 4.71/5.16 (declare-fun tptp.semiri1314217659103216013at_int (tptp.nat) tptp.int)
% 4.71/5.16 (declare-fun tptp.semiri1316708129612266289at_nat (tptp.nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.semiri5074537144036343181t_real (tptp.nat) tptp.real)
% 4.71/5.16 (declare-fun tptp.semiri2816024913162550771omplex ((-> tptp.complex tptp.complex) tptp.nat tptp.complex) tptp.complex)
% 4.71/5.16 (declare-fun tptp.semiri8563196900006977889d_enat ((-> tptp.extended_enat tptp.extended_enat) tptp.nat tptp.extended_enat) tptp.extended_enat)
% 4.71/5.16 (declare-fun tptp.semiri8420488043553186161ux_int ((-> tptp.int tptp.int) tptp.nat tptp.int) tptp.int)
% 4.71/5.16 (declare-fun tptp.semiri8422978514062236437ux_nat ((-> tptp.nat tptp.nat) tptp.nat tptp.nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.semiri7260567687927622513x_real ((-> tptp.real tptp.real) tptp.nat tptp.real) tptp.real)
% 4.71/5.16 (declare-fun tptp.size_s3451745648224563538omplex (tptp.list_complex) tptp.nat)
% 4.71/5.16 (declare-fun tptp.size_s3941691890525107288d_enat (tptp.list_Extended_enat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.size_size_list_int (tptp.list_int) tptp.nat)
% 4.71/5.16 (declare-fun tptp.size_size_list_nat (tptp.list_nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.size_size_list_num (tptp.list_num) tptp.nat)
% 4.71/5.16 (declare-fun tptp.size_s5157815400016825771nt_int (tptp.list_P5707943133018811711nt_int) tptp.nat)
% 4.71/5.16 (declare-fun tptp.size_s7647898544948552527nt_nat (tptp.list_P8198026277950538467nt_nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.size_s6639371672096860321T_VEBT (tptp.list_P7524865323317820941T_VEBT) tptp.nat)
% 4.71/5.16 (declare-fun tptp.size_s2970893825323803983at_int (tptp.list_P3521021558325789923at_int) tptp.nat)
% 4.71/5.16 (declare-fun tptp.size_s5460976970255530739at_nat (tptp.list_P6011104703257516679at_nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.size_s4762443039079500285T_VEBT (tptp.list_P5647936690300460905T_VEBT) tptp.nat)
% 4.71/5.16 (declare-fun tptp.size_s3661962791536183091BT_int (tptp.list_P4547456442757143711BT_int) tptp.nat)
% 4.71/5.16 (declare-fun tptp.size_s6152045936467909847BT_nat (tptp.list_P7037539587688870467BT_nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.size_s7466405169056248089T_VEBT (tptp.list_P7413028617227757229T_VEBT) tptp.nat)
% 4.71/5.16 (declare-fun tptp.size_size_list_real (tptp.list_real) tptp.nat)
% 4.71/5.16 (declare-fun tptp.size_s3254054031482475050et_nat (tptp.list_set_nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.size_s6755466524823107622T_VEBT (tptp.list_VEBT_VEBT) tptp.nat)
% 4.71/5.16 (declare-fun tptp.size_size_num (tptp.num) tptp.nat)
% 4.71/5.16 (declare-fun tptp.size_size_option_num (tptp.option_num) tptp.nat)
% 4.71/5.16 (declare-fun tptp.size_s170228958280169651at_nat (tptp.option4927543243414619207at_nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.size_size_VEBT_VEBT (tptp.vEBT_VEBT) tptp.nat)
% 4.71/5.16 (declare-fun tptp.nat_list_decode (tptp.nat) tptp.list_nat)
% 4.71/5.16 (declare-fun tptp.nat_list_decode_rel (tptp.nat tptp.nat) Bool)
% 4.71/5.16 (declare-fun tptp.nat_list_encode (tptp.list_nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.nat_list_encode_rel (tptp.list_nat tptp.list_nat) Bool)
% 4.71/5.16 (declare-fun tptp.nat_prod_decode (tptp.nat) tptp.product_prod_nat_nat)
% 4.71/5.16 (declare-fun tptp.nat_prod_decode_aux (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 4.71/5.16 (declare-fun tptp.nat_pr5047031295181774490ux_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 4.71/5.16 (declare-fun tptp.nat_prod_encode (tptp.product_prod_nat_nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.nat_set_decode (tptp.nat) tptp.set_nat)
% 4.71/5.16 (declare-fun tptp.nat_set_encode (tptp.set_nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.nat_triangle (tptp.nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.root (tptp.nat tptp.real) tptp.real)
% 4.71/5.16 (declare-fun tptp.inc (tptp.num) tptp.num)
% 4.71/5.16 (declare-fun tptp.bit0 (tptp.num) tptp.num)
% 4.71/5.16 (declare-fun tptp.bit1 (tptp.num) tptp.num)
% 4.71/5.16 (declare-fun tptp.one () tptp.num)
% 4.71/5.16 (declare-fun tptp.size_num (tptp.num) tptp.nat)
% 4.71/5.16 (declare-fun tptp.num_of_nat (tptp.nat) tptp.num)
% 4.71/5.16 (declare-fun tptp.numera6690914467698888265omplex (tptp.num) tptp.complex)
% 4.71/5.16 (declare-fun tptp.numera1916890842035813515d_enat (tptp.num) tptp.extended_enat)
% 4.71/5.16 (declare-fun tptp.numeral_numeral_int (tptp.num) tptp.int)
% 4.71/5.16 (declare-fun tptp.numeral_numeral_nat (tptp.num) tptp.nat)
% 4.71/5.16 (declare-fun tptp.numeral_numeral_real (tptp.num) tptp.real)
% 4.71/5.16 (declare-fun tptp.pred_numeral (tptp.num) tptp.nat)
% 4.71/5.16 (declare-fun tptp.none_Extended_enat () tptp.option_Extended_enat)
% 4.71/5.16 (declare-fun tptp.none_int () tptp.option_int)
% 4.71/5.16 (declare-fun tptp.none_nat () tptp.option_nat)
% 4.71/5.16 (declare-fun tptp.none_num () tptp.option_num)
% 4.71/5.16 (declare-fun tptp.none_P5556105721700978146at_nat () tptp.option4927543243414619207at_nat)
% 4.71/5.16 (declare-fun tptp.none_real () tptp.option_real)
% 4.71/5.16 (declare-fun tptp.none_set_nat () tptp.option_set_nat)
% 4.71/5.16 (declare-fun tptp.none_VEBT_VEBT () tptp.option_VEBT_VEBT)
% 4.71/5.16 (declare-fun tptp.some_int (tptp.int) tptp.option_int)
% 4.71/5.16 (declare-fun tptp.some_nat (tptp.nat) tptp.option_nat)
% 4.71/5.16 (declare-fun tptp.some_num (tptp.num) tptp.option_num)
% 4.71/5.16 (declare-fun tptp.some_P7363390416028606310at_nat (tptp.product_prod_nat_nat) tptp.option4927543243414619207at_nat)
% 4.71/5.16 (declare-fun tptp.some_VEBT_VEBT (tptp.vEBT_VEBT) tptp.option_VEBT_VEBT)
% 4.71/5.16 (declare-fun tptp.case_o184042715313410164at_nat (Bool (-> tptp.product_prod_nat_nat Bool) tptp.option4927543243414619207at_nat) Bool)
% 4.71/5.16 (declare-fun tptp.case_option_num_num (tptp.num (-> tptp.num tptp.num) tptp.option_num) tptp.num)
% 4.71/5.16 (declare-fun tptp.case_o6005452278849405969um_num (tptp.option_num (-> tptp.num tptp.option_num) tptp.option_num) tptp.option_num)
% 4.71/5.16 (declare-fun tptp.size_option_num ((-> tptp.num tptp.nat) tptp.option_num) tptp.nat)
% 4.71/5.16 (declare-fun tptp.size_o8335143837870341156at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.option4927543243414619207at_nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.order_underS_nat (tptp.set_Pr1261947904930325089at_nat tptp.nat) tptp.set_nat)
% 4.71/5.16 (declare-fun tptp.order_2888998067076097458on_nat (tptp.set_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 4.71/5.16 (declare-fun tptp.bot_bo1954855461789132331enat_o (tptp.extended_enat) Bool)
% 4.71/5.16 (declare-fun tptp.bot_bot_int_int_o (tptp.int tptp.int) Bool)
% 4.71/5.16 (declare-fun tptp.bot_bot_int_o (tptp.int) Bool)
% 4.71/5.16 (declare-fun tptp.bot_bot_list_nat_o (tptp.list_nat) Bool)
% 4.71/5.16 (declare-fun tptp.bot_bot_nat_nat_o (tptp.nat tptp.nat) Bool)
% 4.71/5.16 (declare-fun tptp.bot_bot_nat_o (tptp.nat) Bool)
% 4.71/5.16 (declare-fun tptp.bot_bo4898103413517107610_nat_o (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 4.71/5.16 (declare-fun tptp.bot_bot_real_o (tptp.real) Bool)
% 4.71/5.16 (declare-fun tptp.bot_bot_set_nat_o (tptp.set_nat) Bool)
% 4.71/5.16 (declare-fun tptp.bot_bo1565574316222977092_nat_o (tptp.vEBT_VEBT tptp.nat) Bool)
% 4.71/5.16 (declare-fun tptp.bot_bo4199563552545308370d_enat () tptp.extended_enat)
% 4.71/5.16 (declare-fun tptp.bot_bot_filter_nat () tptp.filter_nat)
% 4.71/5.16 (declare-fun tptp.bot_bot_nat () tptp.nat)
% 4.71/5.16 (declare-fun tptp.bot_bot_set_complex () tptp.set_complex)
% 4.71/5.16 (declare-fun tptp.bot_bo7653980558646680370d_enat () tptp.set_Extended_enat)
% 4.71/5.16 (declare-fun tptp.bot_bot_set_int () tptp.set_int)
% 4.71/5.16 (declare-fun tptp.bot_bot_set_list_nat () tptp.set_list_nat)
% 4.71/5.16 (declare-fun tptp.bot_bot_set_nat () tptp.set_nat)
% 4.71/5.16 (declare-fun tptp.bot_bo1796632182523588997nt_int () tptp.set_Pr958786334691620121nt_int)
% 4.71/5.16 (declare-fun tptp.bot_bo2099793752762293965at_nat () tptp.set_Pr1261947904930325089at_nat)
% 4.71/5.16 (declare-fun tptp.bot_bo5327735625951526323at_nat () tptp.set_Pr8693737435421807431at_nat)
% 4.71/5.16 (declare-fun tptp.bot_bo1642239108664514429BT_nat () tptp.set_Pr7556676689462069481BT_nat)
% 4.71/5.16 (declare-fun tptp.bot_bot_set_real () tptp.set_real)
% 4.71/5.16 (declare-fun tptp.bot_bot_set_set_int () tptp.set_set_int)
% 4.71/5.16 (declare-fun tptp.bot_bot_set_set_nat () tptp.set_set_nat)
% 4.71/5.16 (declare-fun tptp.bot_bo8194388402131092736T_VEBT () tptp.set_VEBT_VEBT)
% 4.71/5.16 (declare-fun tptp.ord_Le1955565732374568822d_enat ((-> tptp.extended_enat Bool)) tptp.extended_enat)
% 4.71/5.16 (declare-fun tptp.ord_Least_nat ((-> tptp.nat Bool)) tptp.nat)
% 4.71/5.16 (declare-fun tptp.ord_le8499522857272258027enat_o ((-> tptp.extended_enat Bool) (-> tptp.extended_enat Bool)) Bool)
% 4.71/5.16 (declare-fun tptp.ord_less_int_o ((-> tptp.int Bool) (-> tptp.int Bool)) Bool)
% 4.71/5.16 (declare-fun tptp.ord_less_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool)) Bool)
% 4.71/5.16 (declare-fun tptp.ord_less_real_o ((-> tptp.real Bool) (-> tptp.real Bool)) Bool)
% 4.71/5.16 (declare-fun tptp.ord_less_set_nat_o ((-> tptp.set_nat Bool) (-> tptp.set_nat Bool)) Bool)
% 4.71/5.16 (declare-fun tptp.ord_le72135733267957522d_enat (tptp.extended_enat tptp.extended_enat) Bool)
% 4.71/5.16 (declare-fun tptp.ord_less_int (tptp.int tptp.int) Bool)
% 4.71/5.16 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 4.71/5.16 (declare-fun tptp.ord_less_num (tptp.num tptp.num) Bool)
% 4.71/5.16 (declare-fun tptp.ord_less_real (tptp.real tptp.real) Bool)
% 4.71/5.16 (declare-fun tptp.ord_less_set_complex (tptp.set_complex tptp.set_complex) Bool)
% 4.71/5.16 (declare-fun tptp.ord_le2529575680413868914d_enat (tptp.set_Extended_enat tptp.set_Extended_enat) Bool)
% 4.71/5.16 (declare-fun tptp.ord_less_set_int (tptp.set_int tptp.set_int) Bool)
% 4.71/5.16 (declare-fun tptp.ord_less_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 4.71/5.16 (declare-fun tptp.ord_less_set_real (tptp.set_real tptp.set_real) Bool)
% 4.71/5.16 (declare-fun tptp.ord_less_set_set_int (tptp.set_set_int tptp.set_set_int) Bool)
% 4.71/5.16 (declare-fun tptp.ord_less_set_set_nat (tptp.set_set_nat tptp.set_set_nat) Bool)
% 4.71/5.16 (declare-fun tptp.ord_le100613205991271927enat_o ((-> tptp.extended_enat Bool) (-> tptp.extended_enat Bool)) Bool)
% 4.71/5.16 (declare-fun tptp.ord_less_eq_int_o ((-> tptp.int Bool) (-> tptp.int Bool)) Bool)
% 4.71/5.16 (declare-fun tptp.ord_less_eq_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool)) Bool)
% 4.71/5.16 (declare-fun tptp.ord_less_eq_real_o ((-> tptp.real Bool) (-> tptp.real Bool)) Bool)
% 4.71/5.16 (declare-fun tptp.ord_le3964352015994296041_nat_o ((-> tptp.set_nat Bool) (-> tptp.set_nat Bool)) Bool)
% 4.71/5.16 (declare-fun tptp.ord_le2932123472753598470d_enat (tptp.extended_enat tptp.extended_enat) Bool)
% 4.71/5.16 (declare-fun tptp.ord_le2510731241096832064er_nat (tptp.filter_nat tptp.filter_nat) Bool)
% 4.71/5.16 (declare-fun tptp.ord_less_eq_int (tptp.int tptp.int) Bool)
% 4.71/5.16 (declare-fun tptp.ord_less_eq_nat (tptp.nat tptp.nat) Bool)
% 4.71/5.16 (declare-fun tptp.ord_less_eq_num (tptp.num tptp.num) Bool)
% 4.71/5.16 (declare-fun tptp.ord_less_eq_real (tptp.real tptp.real) Bool)
% 4.71/5.16 (declare-fun tptp.ord_le211207098394363844omplex (tptp.set_complex tptp.set_complex) Bool)
% 4.71/5.16 (declare-fun tptp.ord_le7203529160286727270d_enat (tptp.set_Extended_enat tptp.set_Extended_enat) Bool)
% 4.71/5.16 (declare-fun tptp.ord_less_eq_set_int (tptp.set_int tptp.set_int) Bool)
% 4.71/5.16 (declare-fun tptp.ord_le6045566169113846134st_nat (tptp.set_list_nat tptp.set_list_nat) Bool)
% 4.71/5.16 (declare-fun tptp.ord_less_eq_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 4.71/5.16 (declare-fun tptp.ord_less_eq_set_real (tptp.set_real tptp.set_real) Bool)
% 4.71/5.16 (declare-fun tptp.ord_le4403425263959731960et_int (tptp.set_set_int tptp.set_set_int) Bool)
% 4.71/5.16 (declare-fun tptp.ord_le6893508408891458716et_nat (tptp.set_set_nat tptp.set_set_nat) Bool)
% 4.71/5.16 (declare-fun tptp.ord_le4337996190870823476T_VEBT (tptp.set_VEBT_VEBT tptp.set_VEBT_VEBT) Bool)
% 4.71/5.16 (declare-fun tptp.ord_ma741700101516333627d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 4.71/5.16 (declare-fun tptp.ord_max_int (tptp.int tptp.int) tptp.int)
% 4.71/5.16 (declare-fun tptp.ord_max_nat (tptp.nat tptp.nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.ord_max_real (tptp.real tptp.real) tptp.real)
% 4.71/5.16 (declare-fun tptp.ord_ma4205026669011143323d_enat (tptp.set_Extended_enat tptp.set_Extended_enat) tptp.set_Extended_enat)
% 4.71/5.16 (declare-fun tptp.ord_max_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 4.71/5.16 (declare-fun tptp.ord_max_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 4.71/5.16 (declare-fun tptp.ord_max_set_real (tptp.set_real tptp.set_real) tptp.set_real)
% 4.71/5.16 (declare-fun tptp.ord_min_int (tptp.int tptp.int) tptp.int)
% 4.71/5.16 (declare-fun tptp.ord_min_nat (tptp.nat tptp.nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.order_Greatest_nat ((-> tptp.nat Bool)) tptp.nat)
% 4.71/5.16 (declare-fun tptp.order_mono_nat_nat ((-> tptp.nat tptp.nat)) Bool)
% 4.71/5.16 (declare-fun tptp.order_5726023648592871131at_nat ((-> tptp.nat tptp.nat)) Bool)
% 4.71/5.16 (declare-fun tptp.ordering_top_nat ((-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool) tptp.nat) Bool)
% 4.71/5.16 (declare-fun tptp.top_top_set_int () tptp.set_int)
% 4.71/5.16 (declare-fun tptp.top_top_set_nat () tptp.set_nat)
% 4.71/5.16 (declare-fun tptp.top_to1996260823553986621t_unit () tptp.set_Product_unit)
% 4.71/5.16 (declare-fun tptp.top_top_set_real () tptp.set_real)
% 4.71/5.16 (declare-fun tptp.top_top_set_char () tptp.set_char)
% 4.71/5.16 (declare-fun tptp.power_power_complex (tptp.complex tptp.nat) tptp.complex)
% 4.71/5.16 (declare-fun tptp.power_8040749407984259932d_enat (tptp.extended_enat tptp.nat) tptp.extended_enat)
% 4.71/5.16 (declare-fun tptp.power_power_int (tptp.int tptp.nat) tptp.int)
% 4.71/5.16 (declare-fun tptp.power_power_nat (tptp.nat tptp.nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.power_power_real (tptp.real tptp.nat) tptp.real)
% 4.71/5.16 (declare-fun tptp.produc3209952032786966637at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.produc7248412053542808358at_nat) tptp.produc4471711990508489141at_nat)
% 4.71/5.16 (declare-fun tptp.product_Pair_int_int (tptp.int tptp.int) tptp.product_prod_int_int)
% 4.71/5.16 (declare-fun tptp.product_Pair_int_nat (tptp.int tptp.nat) tptp.product_prod_int_nat)
% 4.71/5.16 (declare-fun tptp.produc3329399203697025711T_VEBT (tptp.int tptp.vEBT_VEBT) tptp.produc1531783533982839933T_VEBT)
% 4.71/5.16 (declare-fun tptp.produc364263696895485585st_int (tptp.list_int tptp.list_int) tptp.produc1186641810826059865st_int)
% 4.71/5.16 (declare-fun tptp.produc2694037385005941721st_nat (tptp.list_nat tptp.list_nat) tptp.produc1828647624359046049st_nat)
% 4.71/5.16 (declare-fun tptp.produc5943733680697469783at_nat (tptp.list_P6011104703257516679at_nat tptp.list_P6011104703257516679at_nat) tptp.produc6392793444374437607at_nat)
% 4.71/5.16 (declare-fun tptp.produc3897820843166775703T_VEBT (tptp.list_VEBT_VEBT tptp.list_VEBT_VEBT) tptp.produc9211091688327510695T_VEBT)
% 4.71/5.16 (declare-fun tptp.product_Pair_nat_int (tptp.nat tptp.int) tptp.product_prod_nat_int)
% 4.71/5.16 (declare-fun tptp.product_Pair_nat_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 4.71/5.16 (declare-fun tptp.produc487386426758144856at_nat (tptp.nat tptp.product_prod_nat_nat) tptp.produc7248412053542808358at_nat)
% 4.71/5.16 (declare-fun tptp.produc599794634098209291T_VEBT (tptp.nat tptp.vEBT_VEBT) tptp.produc8025551001238799321T_VEBT)
% 4.71/5.16 (declare-fun tptp.produc6161850002892822231at_nat (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.produc859450856879609959at_nat)
% 4.71/5.16 (declare-fun tptp.produc736041933913180425BT_int (tptp.vEBT_VEBT tptp.int) tptp.produc4894624898956917775BT_int)
% 4.71/5.16 (declare-fun tptp.produc738532404422230701BT_nat (tptp.vEBT_VEBT tptp.nat) tptp.produc9072475918466114483BT_nat)
% 4.71/5.16 (declare-fun tptp.produc537772716801021591T_VEBT (tptp.vEBT_VEBT tptp.vEBT_VEBT) tptp.produc8243902056947475879T_VEBT)
% 4.71/5.16 (declare-fun tptp.produc457027306803732586at_nat (tptp.set_nat (-> tptp.nat tptp.set_nat)) tptp.set_Pr1261947904930325089at_nat)
% 4.71/5.16 (declare-fun tptp.produc4947309494688390418_int_o ((-> tptp.int tptp.int Bool) tptp.product_prod_int_int) Bool)
% 4.71/5.16 (declare-fun tptp.produc4245557441103728435nt_int ((-> tptp.int tptp.int tptp.product_prod_int_int) tptp.product_prod_int_int) tptp.product_prod_int_int)
% 4.71/5.16 (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)
% 4.71/5.16 (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)
% 4.71/5.16 (declare-fun tptp.produc6081775807080527818_nat_o ((-> tptp.nat tptp.nat Bool) tptp.product_prod_nat_nat) Bool)
% 4.71/5.16 (declare-fun tptp.produc1917071388513777916omplex ((-> tptp.nat tptp.nat tptp.complex) tptp.product_prod_nat_nat) tptp.complex)
% 4.71/5.16 (declare-fun tptp.produc2676513652042109336d_enat ((-> tptp.nat tptp.nat tptp.extended_enat) tptp.product_prod_nat_nat) tptp.extended_enat)
% 4.71/5.16 (declare-fun tptp.produc6840382203811409530at_int ((-> tptp.nat tptp.nat tptp.int) tptp.product_prod_nat_nat) tptp.int)
% 4.71/5.16 (declare-fun tptp.produc2761476792215241774st_nat ((-> tptp.nat tptp.nat tptp.list_nat) tptp.product_prod_nat_nat) tptp.list_nat)
% 4.71/5.16 (declare-fun tptp.produc6842872674320459806at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.product_prod_nat_nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.produc2626176000494625587at_nat ((-> tptp.nat tptp.nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 4.71/5.16 (declare-fun tptp.produc1703576794950452218t_real ((-> tptp.nat tptp.nat tptp.real) tptp.product_prod_nat_nat) tptp.real)
% 4.71/5.16 (declare-fun tptp.product_fst_int_int (tptp.product_prod_int_int) tptp.int)
% 4.71/5.16 (declare-fun tptp.product_fst_nat_nat (tptp.product_prod_nat_nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.product_snd_int_int (tptp.product_prod_int_int) tptp.int)
% 4.71/5.16 (declare-fun tptp.product_snd_nat_nat (tptp.product_prod_nat_nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.field_5140801741446780682s_real () tptp.set_real)
% 4.71/5.16 (declare-fun tptp.real_V1022390504157884413omplex (tptp.complex) tptp.real)
% 4.71/5.16 (declare-fun tptp.real_V7735802525324610683m_real (tptp.real) tptp.real)
% 4.71/5.16 (declare-fun tptp.real_V4546457046886955230omplex (tptp.real) tptp.complex)
% 4.71/5.16 (declare-fun tptp.real_V1803761363581548252l_real (tptp.real) tptp.real)
% 4.71/5.16 (declare-fun tptp.real_V2046097035970521341omplex (tptp.real tptp.complex) tptp.complex)
% 4.71/5.16 (declare-fun tptp.real_V1485227260804924795R_real (tptp.real tptp.real) tptp.real)
% 4.71/5.16 (declare-fun tptp.field_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_nat)
% 4.71/5.16 (declare-fun tptp.algebr934650988132801477me_nat (tptp.nat tptp.nat) Bool)
% 4.71/5.16 (declare-fun tptp.divide1717551699836669952omplex (tptp.complex tptp.complex) tptp.complex)
% 4.71/5.16 (declare-fun tptp.divide_divide_int (tptp.int tptp.int) tptp.int)
% 4.71/5.16 (declare-fun tptp.divide_divide_nat (tptp.nat tptp.nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.divide_divide_real (tptp.real tptp.real) tptp.real)
% 4.71/5.16 (declare-fun tptp.dvd_dvd_complex (tptp.complex tptp.complex) Bool)
% 4.71/5.16 (declare-fun tptp.dvd_dv3785147216227455552d_enat (tptp.extended_enat tptp.extended_enat) Bool)
% 4.71/5.16 (declare-fun tptp.dvd_dvd_int (tptp.int tptp.int) Bool)
% 4.71/5.16 (declare-fun tptp.dvd_dvd_nat (tptp.nat tptp.nat) Bool)
% 4.71/5.16 (declare-fun tptp.dvd_dvd_real (tptp.real tptp.real) Bool)
% 4.71/5.16 (declare-fun tptp.modulo_modulo_int (tptp.int tptp.int) tptp.int)
% 4.71/5.16 (declare-fun tptp.modulo_modulo_nat (tptp.nat tptp.nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.zero_n1201886186963655149omplex (Bool) tptp.complex)
% 4.71/5.16 (declare-fun tptp.zero_n1046097342994218471d_enat (Bool) tptp.extended_enat)
% 4.71/5.16 (declare-fun tptp.zero_n2684676970156552555ol_int (Bool) tptp.int)
% 4.71/5.16 (declare-fun tptp.zero_n2687167440665602831ol_nat (Bool) tptp.nat)
% 4.71/5.16 (declare-fun tptp.zero_n3304061248610475627l_real (Bool) tptp.real)
% 4.71/5.16 (declare-fun tptp.suminf_complex ((-> tptp.nat tptp.complex)) tptp.complex)
% 4.71/5.16 (declare-fun tptp.suminf_int ((-> tptp.nat tptp.int)) tptp.int)
% 4.71/5.16 (declare-fun tptp.suminf_nat ((-> tptp.nat tptp.nat)) tptp.nat)
% 4.71/5.16 (declare-fun tptp.suminf_real ((-> tptp.nat tptp.real)) tptp.real)
% 4.71/5.16 (declare-fun tptp.summable_complex ((-> tptp.nat tptp.complex)) Bool)
% 4.71/5.16 (declare-fun tptp.summable_int ((-> tptp.nat tptp.int)) Bool)
% 4.71/5.16 (declare-fun tptp.summable_nat ((-> tptp.nat tptp.nat)) Bool)
% 4.71/5.16 (declare-fun tptp.summable_real ((-> tptp.nat tptp.real)) Bool)
% 4.71/5.16 (declare-fun tptp.sums_complex ((-> tptp.nat tptp.complex) tptp.complex) Bool)
% 4.71/5.16 (declare-fun tptp.sums_int ((-> tptp.nat tptp.int) tptp.int) Bool)
% 4.71/5.16 (declare-fun tptp.sums_nat ((-> tptp.nat tptp.nat) tptp.nat) Bool)
% 4.71/5.16 (declare-fun tptp.sums_real ((-> tptp.nat tptp.real) tptp.real) Bool)
% 4.71/5.16 (declare-fun tptp.collect_complex ((-> tptp.complex Bool)) tptp.set_complex)
% 4.71/5.16 (declare-fun tptp.collec4429806609662206161d_enat ((-> tptp.extended_enat Bool)) tptp.set_Extended_enat)
% 4.71/5.16 (declare-fun tptp.collect_int ((-> tptp.int Bool)) tptp.set_int)
% 4.71/5.16 (declare-fun tptp.collect_list_complex ((-> tptp.list_complex Bool)) tptp.set_list_complex)
% 4.71/5.16 (declare-fun tptp.collec8433460942617342167d_enat ((-> tptp.list_Extended_enat Bool)) tptp.set_li5464603477888414924d_enat)
% 4.71/5.16 (declare-fun tptp.collect_list_int ((-> tptp.list_int Bool)) tptp.set_list_int)
% 4.71/5.16 (declare-fun tptp.collect_list_nat ((-> tptp.list_nat Bool)) tptp.set_list_nat)
% 4.71/5.16 (declare-fun tptp.collec5608196760682091941T_VEBT ((-> tptp.list_VEBT_VEBT Bool)) tptp.set_list_VEBT_VEBT)
% 4.71/5.16 (declare-fun tptp.collect_nat ((-> tptp.nat Bool)) tptp.set_nat)
% 4.71/5.16 (declare-fun tptp.collec213857154873943460nt_int ((-> tptp.product_prod_int_int Bool)) tptp.set_Pr958786334691620121nt_int)
% 4.71/5.16 (declare-fun tptp.collec3392354462482085612at_nat ((-> tptp.product_prod_nat_nat Bool)) tptp.set_Pr1261947904930325089at_nat)
% 4.71/5.16 (declare-fun tptp.collect_real ((-> tptp.real Bool)) tptp.set_real)
% 4.71/5.16 (declare-fun tptp.collect_set_complex ((-> tptp.set_complex Bool)) tptp.set_set_complex)
% 4.71/5.16 (declare-fun tptp.collec2260605976452661553d_enat ((-> tptp.set_Extended_enat Bool)) tptp.set_se7270636423289371942d_enat)
% 4.71/5.16 (declare-fun tptp.collect_set_int ((-> tptp.set_int Bool)) tptp.set_set_int)
% 4.71/5.16 (declare-fun tptp.collect_set_nat ((-> tptp.set_nat Bool)) tptp.set_set_nat)
% 4.71/5.16 (declare-fun tptp.pow_nat (tptp.set_nat) tptp.set_set_nat)
% 4.71/5.16 (declare-fun tptp.image_80655429650038917d_enat ((-> tptp.extended_enat tptp.extended_enat) tptp.set_Extended_enat) tptp.set_Extended_enat)
% 4.71/5.16 (declare-fun tptp.image_int_int ((-> tptp.int tptp.int) tptp.set_int) tptp.set_int)
% 4.71/5.16 (declare-fun tptp.image_int_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.set_nat)
% 4.71/5.16 (declare-fun tptp.image_nat_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.set_int)
% 4.71/5.16 (declare-fun tptp.image_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.set_nat)
% 4.71/5.16 (declare-fun tptp.image_nat_set_nat ((-> tptp.nat tptp.set_nat) tptp.set_nat) tptp.set_set_nat)
% 4.71/5.16 (declare-fun tptp.image_nat_char ((-> tptp.nat tptp.char) tptp.set_nat) tptp.set_char)
% 4.71/5.16 (declare-fun tptp.image_real_real ((-> tptp.real tptp.real) tptp.set_real) tptp.set_real)
% 4.71/5.16 (declare-fun tptp.image_char_nat ((-> tptp.char tptp.nat) tptp.set_char) tptp.set_nat)
% 4.71/5.16 (declare-fun tptp.insert_complex (tptp.complex tptp.set_complex) tptp.set_complex)
% 4.71/5.16 (declare-fun tptp.insert_Extended_enat (tptp.extended_enat tptp.set_Extended_enat) tptp.set_Extended_enat)
% 4.71/5.16 (declare-fun tptp.insert_int (tptp.int tptp.set_int) tptp.set_int)
% 4.71/5.16 (declare-fun tptp.insert_list_nat (tptp.list_nat tptp.set_list_nat) tptp.set_list_nat)
% 4.71/5.16 (declare-fun tptp.insert_nat (tptp.nat tptp.set_nat) tptp.set_nat)
% 4.71/5.16 (declare-fun tptp.insert_real (tptp.real tptp.set_real) tptp.set_real)
% 4.71/5.16 (declare-fun tptp.insert_set_nat (tptp.set_nat tptp.set_set_nat) tptp.set_set_nat)
% 4.71/5.16 (declare-fun tptp.insert_VEBT_VEBT (tptp.vEBT_VEBT tptp.set_VEBT_VEBT) tptp.set_VEBT_VEBT)
% 4.71/5.16 (declare-fun tptp.vimage_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.set_nat)
% 4.71/5.16 (declare-fun tptp.set_fo1517530859248394432omplex ((-> tptp.nat tptp.complex tptp.complex) tptp.nat tptp.nat tptp.complex) tptp.complex)
% 4.71/5.16 (declare-fun tptp.set_fo2538466533108834004d_enat ((-> tptp.nat tptp.extended_enat tptp.extended_enat) tptp.nat tptp.nat tptp.extended_enat) tptp.extended_enat)
% 4.71/5.16 (declare-fun tptp.set_fo2581907887559384638at_int ((-> tptp.nat tptp.int tptp.int) tptp.nat tptp.nat tptp.int) tptp.int)
% 4.71/5.16 (declare-fun tptp.set_fo2584398358068434914at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat tptp.nat tptp.nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.set_fo3111899725591712190t_real ((-> tptp.nat tptp.real tptp.real) tptp.nat tptp.nat tptp.real) tptp.real)
% 4.71/5.16 (declare-fun tptp.set_or5403411693681687835d_enat (tptp.extended_enat tptp.extended_enat) tptp.set_Extended_enat)
% 4.71/5.16 (declare-fun tptp.set_or1266510415728281911st_int (tptp.int tptp.int) tptp.set_int)
% 4.71/5.16 (declare-fun tptp.set_or1269000886237332187st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 4.71/5.16 (declare-fun tptp.set_or1222579329274155063t_real (tptp.real tptp.real) tptp.set_real)
% 4.71/5.16 (declare-fun tptp.set_or370866239135849197et_int (tptp.set_int tptp.set_int) tptp.set_set_int)
% 4.71/5.16 (declare-fun tptp.set_or4548717258645045905et_nat (tptp.set_nat tptp.set_nat) tptp.set_set_nat)
% 4.71/5.16 (declare-fun tptp.set_or4662586982721622107an_int (tptp.int tptp.int) tptp.set_int)
% 4.71/5.16 (declare-fun tptp.set_or4665077453230672383an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 4.71/5.16 (declare-fun tptp.set_ord_atLeast_nat (tptp.nat) tptp.set_nat)
% 4.71/5.16 (declare-fun tptp.set_or8332593352340944941d_enat (tptp.extended_enat) tptp.set_Extended_enat)
% 4.71/5.16 (declare-fun tptp.set_ord_atMost_int (tptp.int) tptp.set_int)
% 4.71/5.16 (declare-fun tptp.set_ord_atMost_nat (tptp.nat) tptp.set_nat)
% 4.71/5.16 (declare-fun tptp.set_ord_atMost_real (tptp.real) tptp.set_real)
% 4.71/5.16 (declare-fun tptp.set_or58775011639299419et_int (tptp.set_int) tptp.set_set_int)
% 4.71/5.16 (declare-fun tptp.set_or4236626031148496127et_nat (tptp.set_nat) tptp.set_set_nat)
% 4.71/5.16 (declare-fun tptp.set_or6656581121297822940st_int (tptp.int tptp.int) tptp.set_int)
% 4.71/5.16 (declare-fun tptp.set_or6659071591806873216st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 4.71/5.16 (declare-fun tptp.set_or5832277885323065728an_int (tptp.int tptp.int) tptp.set_int)
% 4.71/5.16 (declare-fun tptp.set_or5834768355832116004an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 4.71/5.16 (declare-fun tptp.set_or1633881224788618240n_real (tptp.real tptp.real) tptp.set_real)
% 4.71/5.16 (declare-fun tptp.set_or1210151606488870762an_nat (tptp.nat) tptp.set_nat)
% 4.71/5.16 (declare-fun tptp.set_or8419480210114673929d_enat (tptp.extended_enat) tptp.set_Extended_enat)
% 4.71/5.16 (declare-fun tptp.set_ord_lessThan_int (tptp.int) tptp.set_int)
% 4.71/5.16 (declare-fun tptp.set_ord_lessThan_nat (tptp.nat) tptp.set_nat)
% 4.71/5.16 (declare-fun tptp.set_or5984915006950818249n_real (tptp.real) tptp.set_real)
% 4.71/5.16 (declare-fun tptp.set_or890127255671739683et_nat (tptp.set_nat) tptp.set_set_nat)
% 4.71/5.16 (declare-fun tptp.comm_s629917340098488124ar_nat (tptp.char) tptp.nat)
% 4.71/5.16 (declare-fun tptp.unique3096191561947761185of_nat (tptp.nat) tptp.char)
% 4.71/5.16 (declare-fun tptp.topolo6980174941875973593q_real ((-> tptp.nat tptp.real)) Bool)
% 4.71/5.16 (declare-fun tptp.topolo2177554685111907308n_real (tptp.real tptp.set_real) tptp.filter_real)
% 4.71/5.16 (declare-fun tptp.topolo2815343760600316023s_real (tptp.real) tptp.filter_real)
% 4.71/5.16 (declare-fun tptp.topolo4055970368930404560y_real ((-> tptp.nat tptp.real)) Bool)
% 4.71/5.16 (declare-fun tptp.arcosh_real (tptp.real) tptp.real)
% 4.71/5.16 (declare-fun tptp.arctan (tptp.real) tptp.real)
% 4.71/5.16 (declare-fun tptp.arsinh_real (tptp.real) tptp.real)
% 4.71/5.16 (declare-fun tptp.artanh_real (tptp.real) tptp.real)
% 4.71/5.16 (declare-fun tptp.cos_complex (tptp.complex) tptp.complex)
% 4.71/5.16 (declare-fun tptp.cos_real (tptp.real) tptp.real)
% 4.71/5.16 (declare-fun tptp.cos_coeff (tptp.nat) tptp.real)
% 4.71/5.16 (declare-fun tptp.diffs_complex ((-> tptp.nat tptp.complex) tptp.nat) tptp.complex)
% 4.71/5.16 (declare-fun tptp.diffs_int ((-> tptp.nat tptp.int) tptp.nat) tptp.int)
% 4.71/5.16 (declare-fun tptp.diffs_real ((-> tptp.nat tptp.real) tptp.nat) tptp.real)
% 4.71/5.16 (declare-fun tptp.exp_real (tptp.real) tptp.real)
% 4.71/5.16 (declare-fun tptp.ln_ln_real (tptp.real) tptp.real)
% 4.71/5.16 (declare-fun tptp.log (tptp.real tptp.real) tptp.real)
% 4.71/5.16 (declare-fun tptp.pi () tptp.real)
% 4.71/5.16 (declare-fun tptp.powr_real (tptp.real tptp.real) tptp.real)
% 4.71/5.16 (declare-fun tptp.sin_complex (tptp.complex) tptp.complex)
% 4.71/5.16 (declare-fun tptp.sin_real (tptp.real) tptp.real)
% 4.71/5.16 (declare-fun tptp.sin_coeff (tptp.nat) tptp.real)
% 4.71/5.16 (declare-fun tptp.tan_complex (tptp.complex) tptp.complex)
% 4.71/5.16 (declare-fun tptp.tan_real (tptp.real) tptp.real)
% 4.71/5.16 (declare-fun tptp.bi_tot896582865486249351at_int ((-> tptp.product_prod_nat_nat tptp.int Bool)) Bool)
% 4.71/5.16 (declare-fun tptp.transi2905341329935302413cl_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 4.71/5.16 (declare-fun tptp.transi6264000038957366511cl_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 4.71/5.16 (declare-fun tptp.vEBT_Leaf (Bool Bool) tptp.vEBT_VEBT)
% 4.71/5.16 (declare-fun tptp.vEBT_Node (tptp.option4927543243414619207at_nat tptp.nat tptp.list_VEBT_VEBT tptp.vEBT_VEBT) tptp.vEBT_VEBT)
% 4.71/5.16 (declare-fun tptp.vEBT_size_VEBT (tptp.vEBT_VEBT) tptp.nat)
% 4.71/5.16 (declare-fun tptp.vEBT_V8194947554948674370ptions (tptp.vEBT_VEBT tptp.nat) Bool)
% 4.71/5.16 (declare-fun tptp.vEBT_VEBT_elim_dead (tptp.vEBT_VEBT tptp.extended_enat) tptp.vEBT_VEBT)
% 4.71/5.16 (declare-fun tptp.vEBT_VEBT_high (tptp.nat tptp.nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.vEBT_V5917875025757280293ildren (tptp.nat tptp.list_VEBT_VEBT tptp.nat) Bool)
% 4.71/5.16 (declare-fun tptp.vEBT_VEBT_low (tptp.nat tptp.nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.vEBT_VEBT_membermima (tptp.vEBT_VEBT tptp.nat) Bool)
% 4.71/5.16 (declare-fun tptp.vEBT_V4351362008482014158ma_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 4.71/5.16 (declare-fun tptp.vEBT_V5719532721284313246member (tptp.vEBT_VEBT tptp.nat) Bool)
% 4.71/5.16 (declare-fun tptp.vEBT_V5765760719290551771er_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 4.71/5.16 (declare-fun tptp.vEBT_VEBT_valid (tptp.vEBT_VEBT tptp.nat) Bool)
% 4.71/5.16 (declare-fun tptp.vEBT_VEBT_valid_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 4.71/5.16 (declare-fun tptp.vEBT_invar_vebt (tptp.vEBT_VEBT tptp.nat) Bool)
% 4.71/5.16 (declare-fun tptp.vEBT_set_vebt (tptp.vEBT_VEBT) tptp.set_nat)
% 4.71/5.16 (declare-fun tptp.vEBT_vebt_buildup (tptp.nat) tptp.vEBT_VEBT)
% 4.71/5.16 (declare-fun tptp.vEBT_v4011308405150292612up_rel (tptp.nat tptp.nat) Bool)
% 4.71/5.16 (declare-fun tptp.vEBT_vebt_insert (tptp.vEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 4.71/5.16 (declare-fun tptp.vEBT_vebt_insert_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 4.71/5.16 (declare-fun tptp.vEBT_VEBT_bit_concat (tptp.nat tptp.nat tptp.nat) tptp.nat)
% 4.71/5.16 (declare-fun tptp.vEBT_VEBT_minNull (tptp.vEBT_VEBT) Bool)
% 4.71/5.16 (declare-fun tptp.vEBT_VEBT_set_vebt (tptp.vEBT_VEBT) tptp.set_nat)
% 4.71/5.16 (declare-fun tptp.vEBT_vebt_member (tptp.vEBT_VEBT tptp.nat) Bool)
% 4.71/5.16 (declare-fun tptp.vEBT_vebt_member_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 4.71/5.16 (declare-fun tptp.accp_list_nat ((-> tptp.list_nat tptp.list_nat Bool) tptp.list_nat) Bool)
% 4.71/5.16 (declare-fun tptp.accp_nat ((-> tptp.nat tptp.nat Bool) tptp.nat) Bool)
% 4.71/5.16 (declare-fun tptp.accp_P1096762738010456898nt_int ((-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) tptp.product_prod_int_int) Bool)
% 4.71/5.16 (declare-fun tptp.accp_P4275260045618599050at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) tptp.product_prod_nat_nat) Bool)
% 4.71/5.16 (declare-fun tptp.accp_P2887432264394892906BT_nat ((-> tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat Bool) tptp.produc9072475918466114483BT_nat) Bool)
% 4.71/5.16 (declare-fun tptp.less_than () tptp.set_Pr1261947904930325089at_nat)
% 4.71/5.16 (declare-fun tptp.pred_nat () tptp.set_Pr1261947904930325089at_nat)
% 4.71/5.16 (declare-fun tptp.wf_int (tptp.set_Pr958786334691620121nt_int) Bool)
% 4.71/5.16 (declare-fun tptp.wf_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 4.71/5.16 (declare-fun tptp.member_complex (tptp.complex tptp.set_complex) Bool)
% 4.71/5.16 (declare-fun tptp.member_Extended_enat (tptp.extended_enat tptp.set_Extended_enat) Bool)
% 4.71/5.16 (declare-fun tptp.member_int (tptp.int tptp.set_int) Bool)
% 4.71/5.16 (declare-fun tptp.member_list_int (tptp.list_int tptp.set_list_int) Bool)
% 4.71/5.16 (declare-fun tptp.member_list_nat (tptp.list_nat tptp.set_list_nat) Bool)
% 4.71/5.16 (declare-fun tptp.member2936631157270082147T_VEBT (tptp.list_VEBT_VEBT tptp.set_list_VEBT_VEBT) Bool)
% 4.71/5.16 (declare-fun tptp.member_nat (tptp.nat tptp.set_nat) Bool)
% 4.71/5.16 (declare-fun tptp.member_num (tptp.num tptp.set_num) Bool)
% 4.71/5.16 (declare-fun tptp.member5262025264175285858nt_int (tptp.product_prod_int_int tptp.set_Pr958786334691620121nt_int) Bool)
% 4.71/5.16 (declare-fun tptp.member6698963635872716290st_int (tptp.produc1186641810826059865st_int tptp.set_Pr765067013931698361st_int) Bool)
% 4.71/5.16 (declare-fun tptp.member7340969449405702474st_nat (tptp.produc1828647624359046049st_nat tptp.set_Pr3451248702717554689st_nat) Bool)
% 4.71/5.16 (declare-fun tptp.member6693912407220327184at_nat (tptp.produc6392793444374437607at_nat tptp.set_Pr1542805901266377927at_nat) Bool)
% 4.71/5.16 (declare-fun tptp.member4439316823752958928T_VEBT (tptp.produc9211091688327510695T_VEBT tptp.set_Pr1916528119006554503T_VEBT) Bool)
% 4.71/5.16 (declare-fun tptp.member8440522571783428010at_nat (tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 4.71/5.16 (declare-fun tptp.member8206827879206165904at_nat (tptp.produc859450856879609959at_nat tptp.set_Pr8693737435421807431at_nat) Bool)
% 4.71/5.16 (declare-fun tptp.member373505688050248522BT_nat (tptp.produc9072475918466114483BT_nat tptp.set_Pr7556676689462069481BT_nat) Bool)
% 4.71/5.16 (declare-fun tptp.member568628332442017744T_VEBT (tptp.produc8243902056947475879T_VEBT tptp.set_Pr6192946355708809607T_VEBT) Bool)
% 4.71/5.16 (declare-fun tptp.member_real (tptp.real tptp.set_real) Bool)
% 4.71/5.16 (declare-fun tptp.member_set_int (tptp.set_int tptp.set_set_int) Bool)
% 4.71/5.16 (declare-fun tptp.member_set_nat (tptp.set_nat tptp.set_set_nat) Bool)
% 4.71/5.16 (declare-fun tptp.member_VEBT_VEBT (tptp.vEBT_VEBT tptp.set_VEBT_VEBT) Bool)
% 4.71/5.16 (declare-fun tptp.deg () tptp.nat)
% 4.71/5.16 (declare-fun tptp.i () tptp.nat)
% 4.71/5.16 (declare-fun tptp.m () tptp.nat)
% 4.71/5.16 (declare-fun tptp.ma () tptp.nat)
% 4.71/5.16 (declare-fun tptp.mi () tptp.nat)
% 4.71/5.16 (declare-fun tptp.na () tptp.nat)
% 4.71/5.16 (declare-fun tptp.summary () tptp.vEBT_VEBT)
% 4.71/5.16 (declare-fun tptp.treeList () tptp.list_VEBT_VEBT)
% 4.71/5.16 (declare-fun tptp.xa () tptp.nat)
% 4.71/5.16 (assert (= tptp.i (@ (@ tptp.vEBT_VEBT_high tptp.mi) tptp.na)))
% 4.71/5.16 (assert (let ((_let_1 (@ (@ tptp.vEBT_VEBT_high tptp.mi) tptp.na))) (let ((_let_2 (@ (@ tptp.vEBT_vebt_insert (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_1)) (@ (@ tptp.vEBT_VEBT_low tptp.mi) tptp.na)))) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT tptp.treeList) _let_1) _let_2)) _let_1) _let_2))))
% 4.71/5.16 (assert (forall ((X tptp.nat) (D tptp.nat)) (= (@ (@ (@ tptp.vEBT_VEBT_bit_concat (@ (@ tptp.vEBT_VEBT_high X) D)) (@ (@ tptp.vEBT_VEBT_low X) D)) D) X)))
% 4.71/5.16 (assert (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ (@ tptp.vEBT_VEBT_high tptp.mi) tptp.na))))
% 4.71/5.16 (assert (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ (@ tptp.vEBT_VEBT_high tptp.mi) tptp.na))) X_1))))
% 4.71/5.16 (assert (forall ((Xs tptp.list_nat) (I tptp.nat)) (= (@ (@ (@ tptp.list_update_nat Xs) I) (@ (@ tptp.nth_nat Xs) I)) Xs)))
% 4.71/5.16 (assert (forall ((Xs tptp.list_int) (I tptp.nat)) (= (@ (@ (@ tptp.list_update_int Xs) I) (@ (@ tptp.nth_int Xs) I)) Xs)))
% 4.71/5.16 (assert (forall ((Xs tptp.list_VEBT_VEBT) (I tptp.nat)) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) (@ (@ tptp.nth_VEBT_VEBT Xs) I)) Xs)))
% 4.71/5.16 (assert (forall ((I tptp.nat) (J tptp.nat) (Xs tptp.list_nat) (X tptp.nat)) (=> (not (= I J)) (= (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs) I) X)) J) (@ (@ tptp.nth_nat Xs) J)))))
% 4.71/5.16 (assert (forall ((I tptp.nat) (J tptp.nat) (Xs tptp.list_int) (X tptp.int)) (=> (not (= I J)) (= (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int Xs) I) X)) J) (@ (@ tptp.nth_int Xs) J)))))
% 4.71/5.16 (assert (forall ((I tptp.nat) (J tptp.nat) (Xs tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (not (= I J)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) X)) J) (@ (@ tptp.nth_VEBT_VEBT Xs) J)))))
% 4.71/5.16 (assert (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ (@ tptp.vEBT_VEBT_high tptp.mi) tptp.na))) X_1))))
% 4.71/5.16 (assert (forall ((Xs tptp.list_int) (I tptp.nat) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.list_update_int Xs) I))) (= (@ (@ (@ tptp.list_update_int (@ _let_1 X)) I) Y) (@ _let_1 Y)))))
% 4.71/5.16 (assert (forall ((Xs tptp.list_nat) (I tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.list_update_nat Xs) I))) (= (@ (@ (@ tptp.list_update_nat (@ _let_1 X)) I) Y) (@ _let_1 Y)))))
% 4.71/5.16 (assert (forall ((Xs tptp.list_VEBT_VEBT) (I tptp.nat) (X tptp.vEBT_VEBT) (Y tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I))) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ _let_1 X)) I) Y) (@ _let_1 Y)))))
% 4.71/5.16 (assert (let ((_let_1 (@ (@ tptp.vEBT_VEBT_high tptp.mi) tptp.na))) (=> (not (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_1))) (= tptp.summary (@ (@ tptp.vEBT_vebt_insert tptp.summary) _let_1)))))
% 4.71/5.16 (assert (forall ((X2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.vEBT_VEBT_high tptp.mi) tptp.na))) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT tptp.treeList) _let_1) (@ (@ tptp.vEBT_vebt_insert (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_1)) (@ (@ tptp.vEBT_VEBT_low tptp.mi) tptp.na))))) (@ (@ tptp.vEBT_invar_vebt X2) tptp.na)))))
% 4.71/5.16 (assert (not (@ (@ tptp.ord_less_nat tptp.mi) tptp.xa)))
% 4.71/5.16 (assert (forall ((I tptp.nat) (I2 tptp.nat) (Xs tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT) (X3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.list_u1324408373059187874T_VEBT Xs))) (=> (not (= I I2)) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ (@ _let_1 I) X)) I2) X3) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ (@ _let_1 I2) X3)) I) X))))))
% 4.71/5.16 (assert (forall ((I tptp.nat) (I2 tptp.nat) (Xs tptp.list_int) (X tptp.int) (X3 tptp.int)) (let ((_let_1 (@ tptp.list_update_int Xs))) (=> (not (= I I2)) (= (@ (@ (@ tptp.list_update_int (@ (@ _let_1 I) X)) I2) X3) (@ (@ (@ tptp.list_update_int (@ (@ _let_1 I2) X3)) I) X))))))
% 4.71/5.16 (assert (forall ((I tptp.nat) (I2 tptp.nat) (Xs tptp.list_nat) (X tptp.nat) (X3 tptp.nat)) (let ((_let_1 (@ tptp.list_update_nat Xs))) (=> (not (= I I2)) (= (@ (@ (@ tptp.list_update_nat (@ (@ _let_1 I) X)) I2) X3) (@ (@ (@ tptp.list_update_nat (@ (@ _let_1 I2) X3)) I) X))))))
% 4.71/5.16 (assert (= tptp.vEBT_V5917875025757280293ildren (lambda ((N tptp.nat) (TreeList tptp.list_VEBT_VEBT) (X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) (@ (@ tptp.vEBT_VEBT_high X4) N))) (@ (@ tptp.vEBT_VEBT_low X4) N)))))
% 4.71/5.16 (assert (@ (@ tptp.ord_less_eq_nat tptp.mi) tptp.ma))
% 4.71/5.16 (assert (let ((_let_1 (@ (@ tptp.vEBT_VEBT_high tptp.mi) tptp.na))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_1))) (@ (@ tptp.vEBT_vebt_insert tptp.summary) _let_1)) tptp.summary)) tptp.m)))
% 4.71/5.16 (assert (forall ((T tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull T)) (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) X_12)))))
% 4.71/5.16 (assert (forall ((T tptp.vEBT_VEBT) (X tptp.nat)) (=> (@ tptp.vEBT_VEBT_minNull T) (not (@ (@ tptp.vEBT_vebt_member T) X)))))
% 4.71/5.16 (assert (@ (@ tptp.vEBT_invar_vebt tptp.summary) tptp.m))
% 4.71/5.16 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (= (@ (@ tptp.vEBT_V8194947554948674370ptions T) X) (@ (@ tptp.vEBT_vebt_member T) X)))))
% 4.71/5.16 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions T) X) (@ (@ tptp.vEBT_vebt_member T) X)))))
% 4.71/5.16 (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)))))))
% 4.71/5.16 (assert (@ (@ tptp.ord_less_nat tptp.xa) tptp.mi))
% 4.71/5.16 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (= (@ (@ tptp.vEBT_vebt_member T) X) (@ (@ tptp.member_nat X) (@ tptp.vEBT_set_vebt T))))))
% 4.71/5.16 (assert (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 tptp.treeList)) (@ (@ tptp.vEBT_invar_vebt X2) tptp.na))))
% 4.71/5.16 (assert (not (@ (@ tptp.vEBT_V8194947554948674370ptions tptp.summary) tptp.i)))
% 4.71/5.16 (assert (and (not (= tptp.xa tptp.mi)) (not (= tptp.xa tptp.ma))))
% 4.71/5.16 (assert (= (@ tptp.suc tptp.na) tptp.m))
% 4.71/5.16 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (= (@ tptp.vEBT_set_vebt T) (@ tptp.vEBT_VEBT_set_vebt T)))))
% 4.71/5.16 (assert (= tptp.vEBT_VEBT_valid tptp.vEBT_invar_vebt))
% 4.71/5.16 (assert (forall ((T tptp.vEBT_VEBT) (D tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) D) (@ (@ tptp.vEBT_VEBT_valid T) D))))
% 4.71/5.16 (assert (forall ((T tptp.vEBT_VEBT) (D tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid T) D) (@ (@ tptp.vEBT_invar_vebt T) D))))
% 4.71/5.16 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real X) X)))
% 4.71/5.16 (assert (forall ((X tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat X) X)))
% 4.71/5.16 (assert (forall ((X tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int X) X)))
% 4.71/5.16 (assert (forall ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat X) X)))
% 4.71/5.16 (assert (forall ((X tptp.int)) (@ (@ tptp.ord_less_eq_int X) X)))
% 4.71/5.16 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real A) A)))
% 4.71/5.16 (assert (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A) A)))
% 4.71/5.16 (assert (forall ((A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A) A)))
% 4.71/5.16 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)))
% 4.71/5.16 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) A)))
% 4.71/5.16 (assert (forall ((Xs tptp.list_Extended_enat) (P (-> tptp.extended_enat Bool)) (N2 tptp.nat)) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ tptp.set_Extended_enat2 Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s3941691890525107288d_enat Xs)) (@ P (@ (@ tptp.nth_Extended_enat Xs) N2))))))
% 4.71/5.16 (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))))))
% 4.71/5.16 (assert (forall ((Xs tptp.list_set_nat) (P (-> tptp.set_nat Bool)) (N2 tptp.nat)) (=> (forall ((X5 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X5) (@ tptp.set_set_nat2 Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s3254054031482475050et_nat Xs)) (@ P (@ (@ tptp.nth_set_nat Xs) N2))))))
% 4.71/5.16 (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))))))
% 4.71/5.16 (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))))))
% 4.71/5.16 (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))))))
% 4.71/5.16 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 4.71/5.16 (assert (= tptp.deg (@ (@ tptp.plus_plus_nat tptp.na) tptp.m)))
% 4.71/5.16 (assert (= tptp.ord_less_nat (lambda ((M tptp.nat) (N tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M) N) (not (= M N))))))
% 4.71/5.16 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N2) (@ (@ tptp.ord_less_eq_nat M2) N2))))
% 4.71/5.16 (assert (forall ((X tptp.nat)) (=> (forall ((N3 tptp.nat)) (not (= X (@ (@ tptp.plus_plus_nat N3) N3)))) (not (forall ((N3 tptp.nat)) (not (= X (@ (@ tptp.plus_plus_nat N3) (@ tptp.suc N3)))))))))
% 4.71/5.16 (assert (forall ((T tptp.vEBT_VEBT)) (not (@ (@ tptp.vEBT_invar_vebt T) tptp.zero_zero_nat))))
% 4.71/5.16 (assert (forall ((T tptp.vEBT_VEBT)) (not (@ (@ tptp.vEBT_invar_vebt T) tptp.zero_zero_nat))))
% 4.71/5.16 (assert (forall ((Nat tptp.nat) (Nat2 tptp.nat)) (= (= (@ tptp.suc Nat) (@ tptp.suc Nat2)) (= Nat Nat2))))
% 4.71/5.16 (assert (forall ((X22 tptp.nat) (Y2 tptp.nat)) (= (= (@ tptp.suc X22) (@ tptp.suc Y2)) (= X22 Y2))))
% 4.71/5.16 (assert (forall ((A tptp.extended_enat) (P (-> tptp.extended_enat Bool))) (= (@ (@ tptp.member_Extended_enat A) (@ tptp.collec4429806609662206161d_enat P)) (@ P A))))
% 4.71/5.16 (assert (forall ((A tptp.real) (P (-> tptp.real Bool))) (= (@ (@ tptp.member_real A) (@ tptp.collect_real P)) (@ P A))))
% 4.71/5.16 (assert (forall ((A tptp.list_nat) (P (-> tptp.list_nat Bool))) (= (@ (@ tptp.member_list_nat A) (@ tptp.collect_list_nat P)) (@ P A))))
% 4.71/5.16 (assert (forall ((A tptp.set_nat) (P (-> tptp.set_nat Bool))) (= (@ (@ tptp.member_set_nat A) (@ tptp.collect_set_nat P)) (@ P A))))
% 4.71/5.16 (assert (forall ((A tptp.nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat A) (@ tptp.collect_nat P)) (@ P A))))
% 4.71/5.16 (assert (forall ((A tptp.int) (P (-> tptp.int Bool))) (= (@ (@ tptp.member_int A) (@ tptp.collect_int P)) (@ P A))))
% 4.71/5.16 (assert (forall ((A2 tptp.set_Extended_enat)) (= (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (@ (@ tptp.member_Extended_enat X4) A2))) A2)))
% 4.71/5.16 (assert (forall ((A2 tptp.set_real)) (= (@ tptp.collect_real (lambda ((X4 tptp.real)) (@ (@ tptp.member_real X4) A2))) A2)))
% 4.71/5.16 (assert (forall ((A2 tptp.set_list_nat)) (= (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (@ (@ tptp.member_list_nat X4) A2))) A2)))
% 4.71/5.16 (assert (forall ((A2 tptp.set_set_nat)) (= (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (@ (@ tptp.member_set_nat X4) A2))) A2)))
% 4.71/5.16 (assert (forall ((A2 tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) A2))) A2)))
% 4.71/5.16 (assert (forall ((A2 tptp.set_int)) (= (@ tptp.collect_int (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) A2))) A2)))
% 4.71/5.16 (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)))))
% 4.71/5.16 (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)))))
% 4.71/5.16 (assert (forall ((P (-> tptp.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (=> (forall ((X5 tptp.set_nat)) (= (@ P X5) (@ Q X5))) (= (@ tptp.collect_set_nat P) (@ tptp.collect_set_nat Q)))))
% 4.71/5.16 (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)))))
% 4.71/5.16 (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)))))
% 4.71/5.16 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc M2)) (@ tptp.suc N2)) (@ (@ tptp.ord_less_nat M2) N2))))
% 4.71/5.16 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N2) (@ (@ tptp.ord_less_nat (@ tptp.suc M2)) (@ tptp.suc N2)))))
% 4.71/5.16 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat N2) (@ tptp.suc N2))))
% 4.71/5.16 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) tptp.zero_zero_nat))))
% 4.71/5.16 (assert (forall ((N2 tptp.nat)) (= (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 4.71/5.16 (assert (forall ((A tptp.nat)) (= (not (= A tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A))))
% 4.71/5.16 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) (@ tptp.suc M2)) (@ (@ tptp.ord_less_eq_nat N2) M2))))
% 4.71/5.16 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N2)))
% 4.71/5.16 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A)))
% 4.71/5.16 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M2))) (= (@ _let_1 (@ tptp.suc N2)) (@ tptp.suc (@ _let_1 N2))))))
% 4.71/5.16 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat M2) tptp.zero_zero_nat) M2)))
% 4.71/5.16 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat M2) N2) tptp.zero_zero_nat) (and (= M2 tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat)))))
% 4.71/5.16 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M2)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M2) N2)))))
% 4.71/5.16 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M2)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M2) N2)))))
% 4.71/5.16 (assert (forall ((Xs tptp.list_VEBT_VEBT) (I tptp.nat) (X tptp.vEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) X)) (@ tptp.size_s6755466524823107622T_VEBT Xs))))
% 4.71/5.16 (assert (forall ((Xs tptp.list_int) (I tptp.nat) (X tptp.int)) (= (@ tptp.size_size_list_int (@ (@ (@ tptp.list_update_int Xs) I) X)) (@ tptp.size_size_list_int Xs))))
% 4.71/5.16 (assert (forall ((Xs tptp.list_nat) (I tptp.nat) (X tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ (@ tptp.list_update_nat Xs) I) X)) (@ tptp.size_size_list_nat Xs))))
% 4.71/5.16 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat N2) (@ tptp.suc tptp.zero_zero_nat)) (= N2 tptp.zero_zero_nat))))
% 4.71/5.16 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suc N2))))
% 4.71/5.16 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N2)) (or (@ _let_1 M2) (@ _let_1 N2))))))
% 4.71/5.16 (assert (forall ((Xs tptp.list_VEBT_VEBT) (I tptp.nat) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) I) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) X) Xs))))
% 4.71/5.16 (assert (forall ((Xs tptp.list_int) (I tptp.nat) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs)) I) (= (@ (@ (@ tptp.list_update_int Xs) I) X) Xs))))
% 4.71/5.16 (assert (forall ((Xs tptp.list_nat) (I tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs)) I) (= (@ (@ (@ tptp.list_update_nat Xs) I) X) Xs))))
% 4.71/5.16 (assert (forall ((I tptp.nat) (Xs tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) X)) I) X))))
% 4.71/5.16 (assert (forall ((I tptp.nat) (Xs tptp.list_int) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int Xs) I) X)) I) X))))
% 4.71/5.16 (assert (forall ((I tptp.nat) (Xs tptp.list_nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs) I) X)) I) X))))
% 4.71/5.16 (assert (forall ((I tptp.nat) (Xs tptp.list_VEBT_VEBT) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_VEBT_VEBT Xs))) (let ((_let_2 (@ tptp.size_s6755466524823107622T_VEBT Xs))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ tptp.set_VEBT_VEBT2 Xs))))))))
% 4.71/5.16 (assert (forall ((I tptp.nat) (Xs tptp.list_int) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs))) (let ((_let_2 (@ tptp.size_size_list_int Xs))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int (@ (@ (@ tptp.list_update_int Xs) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ tptp.set_int2 Xs))))))))
% 4.71/5.16 (assert (forall ((I tptp.nat) (Xs tptp.list_nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (let ((_let_2 (@ tptp.size_size_list_nat Xs))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat (@ (@ (@ tptp.list_update_nat Xs) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ tptp.set_nat2 Xs))))))))
% 4.71/5.16 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N2) (not (forall ((Q2 tptp.nat)) (not (= N2 (@ tptp.suc (@ (@ tptp.plus_plus_nat M2) Q2)))))))))
% 4.71/5.16 (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))))))))
% 4.71/5.16 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (exists ((M tptp.nat)) (= N2 (@ tptp.suc M))))))
% 4.71/5.16 (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))))))))
% 4.71/5.16 (assert (forall ((I tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_nat I) (@ tptp.suc (@ (@ tptp.plus_plus_nat I) M2)))))
% 4.71/5.16 (assert (forall ((I tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_nat I) (@ tptp.suc (@ (@ tptp.plus_plus_nat M2) I)))))
% 4.71/5.16 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (exists ((M3 tptp.nat)) (= N2 (@ tptp.suc M3))))))
% 4.71/5.16 (assert (= tptp.ord_less_nat (lambda ((M tptp.nat) (N tptp.nat)) (exists ((K2 tptp.nat)) (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M) K2)))))))
% 4.71/5.16 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N2) (exists ((K3 tptp.nat)) (= N2 (@ tptp.suc (@ (@ tptp.plus_plus_nat M2) K3)))))))
% 4.71/5.16 (assert (forall ((N2 tptp.nat)) (exists ((Xs2 tptp.list_VEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) N2))))
% 4.71/5.16 (assert (forall ((N2 tptp.nat)) (exists ((Xs2 tptp.list_int)) (= (@ tptp.size_size_list_int Xs2) N2))))
% 4.71/5.16 (assert (forall ((N2 tptp.nat)) (exists ((Xs2 tptp.list_nat)) (= (@ tptp.size_size_list_nat Xs2) N2))))
% 4.71/5.16 (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)))))
% 4.71/5.16 (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)))))
% 4.71/5.16 (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)))))
% 4.71/5.16 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat M2) (@ tptp.suc N2)) (or (= M2 tptp.zero_zero_nat) (exists ((J2 tptp.nat)) (and (= M2 (@ tptp.suc J2)) (@ (@ tptp.ord_less_nat J2) N2)))))))
% 4.71/5.16 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (= (@ (@ tptp.plus_plus_nat I) K3) J))))))
% 4.71/5.16 (assert (forall ((X tptp.list_VEBT_VEBT) (Y tptp.list_VEBT_VEBT)) (=> (not (= (@ tptp.size_s6755466524823107622T_VEBT X) (@ tptp.size_s6755466524823107622T_VEBT Y))) (not (= X Y)))))
% 4.71/5.16 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (= (@ tptp.size_size_num X) (@ tptp.size_size_num Y))) (not (= X Y)))))
% 4.71/5.16 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.vEBT_VEBT)) (=> (not (= (@ tptp.size_size_VEBT_VEBT X) (@ tptp.size_size_VEBT_VEBT Y))) (not (= X Y)))))
% 4.71/5.16 (assert (forall ((X tptp.list_int) (Y tptp.list_int)) (=> (not (= (@ tptp.size_size_list_int X) (@ tptp.size_size_list_int Y))) (not (= X Y)))))
% 4.71/5.16 (assert (forall ((X tptp.list_nat) (Y tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat X) (@ tptp.size_size_list_nat Y))) (not (= X Y)))))
% 4.71/5.16 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (exists ((M3 tptp.nat)) (= N2 (@ tptp.suc M3))))))
% 4.71/5.16 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat M2) N2) M2) (= N2 tptp.zero_zero_nat))))
% 4.71/5.16 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M2)) N2) (@ (@ tptp.plus_plus_nat M2) (@ tptp.suc N2)))))
% 4.71/5.16 (assert (forall ((M2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M2)))))
% 4.71/5.16 (assert (forall ((M2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M2)))))
% 4.71/5.16 (assert (forall ((M2 tptp.nat)) (not (= (@ tptp.suc M2) tptp.zero_zero_nat))))
% 4.71/5.16 (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)))))
% 4.71/5.16 (assert (forall ((N2 tptp.nat)) (not (= N2 (@ tptp.suc N2)))))
% 4.71/5.16 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (M2 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 M2) N2))))))
% 4.71/5.16 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.plus_plus_nat M2) N2)) (or (and (= M2 _let_1) (= N2 tptp.zero_zero_nat)) (and (= M2 tptp.zero_zero_nat) (= N2 _let_1)))))))
% 4.71/5.16 (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)))))
% 4.71/5.16 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (= (@ tptp.suc X) (@ tptp.suc Y)) (= X Y))))
% 4.71/5.16 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.plus_plus_nat M2) N2) _let_1) (or (and (= M2 _let_1) (= N2 tptp.zero_zero_nat)) (and (= M2 tptp.zero_zero_nat) (= N2 _let_1)))))))
% 4.71/5.16 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M2)) N2) (@ tptp.suc (@ (@ tptp.plus_plus_nat M2) N2)))))
% 4.71/5.16 (assert (forall ((Y tptp.nat)) (=> (not (= Y tptp.zero_zero_nat)) (not (forall ((Nat3 tptp.nat)) (not (= Y (@ tptp.suc Nat3))))))))
% 4.71/5.16 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) N2) N2)))
% 4.71/5.16 (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)))))))
% 4.71/5.16 (assert (forall ((Nat tptp.nat) (X22 tptp.nat)) (=> (= Nat (@ tptp.suc X22)) (not (= Nat tptp.zero_zero_nat)))))
% 4.71/5.16 (assert (forall ((Nat2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc Nat2)))))
% 4.71/5.16 (assert (forall ((Nat2 tptp.nat)) (not (= (@ tptp.suc Nat2) tptp.zero_zero_nat))))
% 4.71/5.16 (assert (forall ((X22 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc X22)))))
% 4.71/5.16 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N2))) (=> (not (@ _let_1 M2)) (= (@ _let_1 (@ tptp.suc M2)) (= N2 M2))))))
% 4.71/5.16 (assert (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I) 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 I))))))
% 4.71/5.16 (assert (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I) J) (=> (forall ((I4 tptp.nat)) (@ (@ P I4) (@ tptp.suc I4))) (=> (forall ((I4 tptp.nat) (J3 tptp.nat) (K3 tptp.nat)) (let ((_let_1 (@ P I4))) (=> (@ (@ tptp.ord_less_nat I4) J3) (=> (@ (@ tptp.ord_less_nat J3) K3) (=> (@ _let_1 J3) (=> (@ (@ P J3) K3) (@ _let_1 K3))))))) (@ (@ P I) J))))))
% 4.71/5.16 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat J) K) (@ (@ tptp.ord_less_nat (@ tptp.suc I)) K)))))
% 4.71/5.16 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M2)) (@ tptp.suc N2)) (@ (@ tptp.ord_less_nat M2) N2))))
% 4.71/5.16 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N2))) (=> (not (@ _let_1 M2)) (=> (@ _let_1 (@ tptp.suc M2)) (= M2 N2))))))
% 4.71/5.16 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N2)) M2) (exists ((M4 tptp.nat)) (and (= M2 (@ tptp.suc M4)) (@ (@ tptp.ord_less_nat N2) M4))))))
% 4.71/5.16 (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)))))))
% 4.71/5.16 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat M2) N2)) (@ (@ tptp.ord_less_nat N2) (@ tptp.suc M2)))))
% 4.71/5.16 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M2))) (= (@ _let_1 (@ tptp.suc N2)) (or (@ _let_1 N2) (= M2 N2))))))
% 4.71/5.16 (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)))))))
% 4.71/5.16 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M2))) (=> (@ _let_1 N2) (@ _let_1 (@ tptp.suc N2))))))
% 4.71/5.16 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M2))) (=> (@ _let_1 (@ tptp.suc N2)) (=> (not (@ _let_1 N2)) (= M2 N2))))))
% 4.71/5.16 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc M2))) (=> (@ (@ tptp.ord_less_nat M2) N2) (=> (not (= _let_1 N2)) (@ (@ tptp.ord_less_nat _let_1) N2))))))
% 4.71/5.16 (assert (forall ((I tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc I)) K) (not (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J3) (not (= K (@ tptp.suc J3)))))))))
% 4.71/5.16 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M2)) N2) (@ (@ tptp.ord_less_nat M2) N2))))
% 4.71/5.16 (assert (forall ((I tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K) (=> (not (= K (@ tptp.suc I))) (not (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J3) (not (= K (@ tptp.suc J3))))))))))
% 4.71/5.16 (assert (forall ((K tptp.nat) (L tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) L) (=> (= (@ (@ tptp.plus_plus_nat M2) L) (@ (@ tptp.plus_plus_nat K) N2)) (@ (@ tptp.ord_less_nat M2) N2)))))
% 4.71/5.16 (assert (forall ((I tptp.nat) (J tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M2) J))))))
% 4.71/5.16 (assert (forall ((I tptp.nat) (J tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M2))))))
% 4.71/5.16 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) K)))))
% 4.71/5.16 (assert (forall ((J tptp.nat) (I tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat J) I)) I))))
% 4.71/5.16 (assert (forall ((I tptp.nat) (J tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) J)) I))))
% 4.71/5.16 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat K) L) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L))))))
% 4.71/5.16 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) J)) K) (@ (@ tptp.ord_less_nat I) K))))
% 4.71/5.16 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (R (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (=> (forall ((X5 tptp.nat)) (@ (@ R X5) X5)) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ R X5))) (=> (@ _let_1 Y3) (=> (@ (@ R Y3) Z) (@ _let_1 Z))))) (=> (forall ((N3 tptp.nat)) (@ (@ R N3) (@ tptp.suc N3))) (@ (@ R M2) N2)))))))
% 4.71/5.16 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (=> (@ P M2) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N3) (=> (@ P N3) (@ P (@ tptp.suc N3))))) (@ P N2))))))
% 4.71/5.16 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M5)) N3) (@ P M5))) (@ P N3))) (@ P N2))))
% 4.71/5.16 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat M2) N2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) M2))))
% 4.71/5.16 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) N2))))
% 4.71/5.16 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.ord_less_eq_nat M2))) (= (@ _let_2 _let_1) (or (@ _let_2 N2) (= M2 _let_1)))))))
% 4.71/5.16 (assert (forall ((N2 tptp.nat) (M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) M6) (exists ((M3 tptp.nat)) (= M6 (@ tptp.suc M3))))))
% 4.71/5.16 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat M2))) (=> (@ _let_1 N2) (@ _let_1 (@ tptp.suc N2))))))
% 4.71/5.16 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.ord_less_eq_nat M2))) (=> (@ _let_2 _let_1) (=> (not (@ _let_2 N2)) (= M2 _let_1)))))))
% 4.71/5.16 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N2) (@ (@ tptp.ord_less_eq_nat M2) N2))))
% 4.71/5.16 (assert (= tptp.ord_less_eq_nat (lambda ((M tptp.nat) (N tptp.nat)) (exists ((K2 tptp.nat)) (= N (@ (@ tptp.plus_plus_nat M) K2))))))
% 4.71/5.16 (assert (forall ((I tptp.nat) (J tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M2) J))))))
% 4.71/5.16 (assert (forall ((I tptp.nat) (J tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M2))))))
% 4.71/5.16 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) K)))))
% 4.71/5.16 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ (@ tptp.ord_less_eq_nat K) L) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L))))))
% 4.71/5.16 (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))))))
% 4.71/5.16 (assert (forall ((M2 tptp.nat) (K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M2) K)) N2) (@ (@ tptp.ord_less_eq_nat K) N2))))
% 4.71/5.16 (assert (forall ((M2 tptp.nat) (K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M2) K)) N2) (@ (@ tptp.ord_less_eq_nat M2) N2))))
% 4.71/5.16 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) (@ (@ tptp.plus_plus_nat M2) N2))))
% 4.71/5.16 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) (@ (@ tptp.plus_plus_nat N2) M2))))
% 4.71/5.16 (assert (forall ((M2 tptp.nat) (K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M2) K)) N2) (not (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (not (@ (@ tptp.ord_less_eq_nat K) N2)))))))
% 4.71/5.16 (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 ((M5 tptp.nat)) (and (@ (@ tptp.ord_less_nat M5) N3) (not (@ P M5))))))) (@ P N2)))))
% 4.71/5.16 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N2) (not (= N2 tptp.zero_zero_nat)))))
% 4.71/5.16 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) tptp.zero_zero_nat))))
% 4.71/5.16 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) tptp.zero_zero_nat))))
% 4.71/5.16 (assert (forall ((N2 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= N2 tptp.zero_zero_nat))))
% 4.71/5.16 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 4.71/5.16 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))))
% 4.71/5.16 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N2) tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat))))
% 4.71/5.16 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 4.71/5.16 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 4.71/5.16 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N2)))
% 4.71/5.16 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P N2) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat K3) N2) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I5) K3) (not (@ P I5)))) (@ P (@ tptp.suc K3))))))))
% 4.71/5.16 (assert (forall ((X tptp.extended_enat) (Xs tptp.list_Extended_enat)) (=> (@ (@ tptp.member_Extended_enat X) (@ tptp.set_Extended_enat2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s3941691890525107288d_enat Xs)))))
% 4.71/5.16 (assert (forall ((X tptp.real) (Xs tptp.list_real)) (=> (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_real Xs)))))
% 4.71/5.16 (assert (forall ((X tptp.set_nat) (Xs tptp.list_set_nat)) (=> (@ (@ tptp.member_set_nat X) (@ tptp.set_set_nat2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s3254054031482475050et_nat Xs)))))
% 4.71/5.16 (assert (forall ((X tptp.vEBT_VEBT) (Xs tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s6755466524823107622T_VEBT Xs)))))
% 4.71/5.16 (assert (forall ((X tptp.int) (Xs tptp.list_int)) (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_int Xs)))))
% 4.71/5.16 (assert (forall ((X tptp.nat) (Xs tptp.list_nat)) (=> (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_nat Xs)))))
% 4.71/5.16 (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))))
% 4.71/5.16 (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))))
% 4.71/5.16 (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))))
% 4.71/5.16 (assert (forall ((Xs tptp.list_Extended_enat) (B tptp.set_Extended_enat)) (= (@ (@ tptp.ord_le7203529160286727270d_enat (@ tptp.set_Extended_enat2 Xs)) B) (forall ((X4 tptp.extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat X4))) (=> (@ _let_1 (@ tptp.set_Extended_enat2 Xs)) (@ _let_1 B)))))))
% 4.71/5.16 (assert (forall ((Xs tptp.list_real) (B tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 Xs)) B) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.member_real X4))) (=> (@ _let_1 (@ tptp.set_real2 Xs)) (@ _let_1 B)))))))
% 4.71/5.16 (assert (forall ((Xs tptp.list_set_nat) (B tptp.set_set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.set_set_nat2 Xs)) B) (forall ((X4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X4))) (=> (@ _let_1 (@ tptp.set_set_nat2 Xs)) (@ _let_1 B)))))))
% 4.71/5.16 (assert (forall ((Xs tptp.list_VEBT_VEBT) (B tptp.set_VEBT_VEBT)) (= (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) B) (forall ((X4 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.member_VEBT_VEBT X4))) (=> (@ _let_1 (@ tptp.set_VEBT_VEBT2 Xs)) (@ _let_1 B)))))))
% 4.71/5.16 (assert (forall ((Xs tptp.list_nat) (B tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) B) (forall ((X4 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X4))) (=> (@ _let_1 (@ tptp.set_nat2 Xs)) (@ _let_1 B)))))))
% 4.71/5.16 (assert (forall ((Xs tptp.list_int) (B tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) B) (forall ((X4 tptp.int)) (let ((_let_1 (@ tptp.member_int X4))) (=> (@ _let_1 (@ tptp.set_int2 Xs)) (@ _let_1 B)))))))
% 4.71/5.16 (assert (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat) (M2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_nat (@ F N2)) (@ F M2)) (@ (@ tptp.ord_less_nat N2) M2)))))
% 4.71/5.16 (assert (forall ((F (-> tptp.nat tptp.extended_enat)) (N2 tptp.nat) (M2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_le72135733267957522d_enat (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ F N2)) (@ F M2)) (@ (@ tptp.ord_less_nat N2) M2)))))
% 4.71/5.16 (assert (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat) (M2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_real (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_real (@ F N2)) (@ F M2)) (@ (@ tptp.ord_less_nat N2) M2)))))
% 4.71/5.16 (assert (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat) (M2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_int (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_int (@ F N2)) (@ F M2)) (@ (@ tptp.ord_less_nat N2) M2)))))
% 4.71/5.16 (assert (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N2) N4) (@ (@ tptp.ord_less_nat (@ F N2)) (@ F N4))))))
% 4.71/5.16 (assert (forall ((F (-> tptp.nat tptp.extended_enat)) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_le72135733267957522d_enat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N2) N4) (@ (@ tptp.ord_le72135733267957522d_enat (@ F N2)) (@ F N4))))))
% 4.71/5.16 (assert (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_real (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N2) N4) (@ (@ tptp.ord_less_real (@ F N2)) (@ F N4))))))
% 4.71/5.16 (assert (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_int (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N2) N4) (@ (@ tptp.ord_less_int (@ F N2)) (@ F N4))))))
% 4.71/5.16 (assert (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (@ (@ tptp.ord_less_eq_real (@ F N4)) (@ F N2))))))
% 4.71/5.16 (assert (forall ((F (-> tptp.nat tptp.set_nat)) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (@ (@ tptp.ord_less_eq_set_nat (@ F N4)) (@ F N2))))))
% 4.71/5.16 (assert (forall ((F (-> tptp.nat tptp.set_int)) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (@ (@ tptp.ord_less_eq_set_int (@ F N4)) (@ F N2))))))
% 4.71/5.16 (assert (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (@ (@ tptp.ord_less_eq_nat (@ F N4)) (@ F N2))))))
% 4.71/5.16 (assert (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (@ (@ tptp.ord_less_eq_int (@ F N4)) (@ F N2))))))
% 4.71/5.16 (assert (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (@ (@ tptp.ord_less_eq_real (@ F N2)) (@ F N4))))))
% 4.71/5.16 (assert (forall ((F (-> tptp.nat tptp.set_nat)) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (@ (@ tptp.ord_less_eq_set_nat (@ F N2)) (@ F N4))))))
% 4.71/5.16 (assert (forall ((F (-> tptp.nat tptp.set_int)) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (@ (@ tptp.ord_less_eq_set_int (@ F N2)) (@ F N4))))))
% 4.71/5.16 (assert (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (@ (@ tptp.ord_less_eq_nat (@ F N2)) (@ F N4))))))
% 4.71/5.16 (assert (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (@ (@ tptp.ord_less_eq_int (@ F N2)) (@ F N4))))))
% 4.71/5.16 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_nat M2) (@ tptp.suc N2)))))
% 4.71/5.16 (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))))
% 4.71/5.16 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat M2) (@ tptp.suc N2)) (@ (@ tptp.ord_less_eq_nat M2) N2))))
% 4.71/5.16 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ (@ tptp.ord_less_nat N2) (@ tptp.suc M2)) (= N2 M2)))))
% 4.71/5.16 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N2) (@ (@ tptp.ord_less_nat M2) N2))))
% 4.71/5.16 (assert (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ P J) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) N3) (=> (@ (@ tptp.ord_less_nat N3) J) (=> (@ P (@ tptp.suc N3)) (@ P N3))))) (@ P I))))))
% 4.71/5.16 (assert (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ P I) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) N3) (=> (@ (@ tptp.ord_less_nat N3) J) (=> (@ P N3) (@ P (@ tptp.suc N3)))))) (@ P J))))))
% 4.71/5.16 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N2) (@ (@ tptp.ord_less_nat M2) N2))))
% 4.71/5.16 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N2) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N2))))
% 4.71/5.16 (assert (forall ((F (-> tptp.nat tptp.nat)) (M2 tptp.nat) (K tptp.nat)) (=> (forall ((M3 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M3) N3) (@ (@ tptp.ord_less_nat (@ F M3)) (@ F N3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ F M2)) K)) (@ F (@ (@ tptp.plus_plus_nat M2) K))))))
% 4.71/5.16 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P N2) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat K3) N2) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) K3) (not (@ P I5)))) (@ P K3)))))))
% 4.71/5.16 (assert (= (lambda ((Y4 tptp.list_VEBT_VEBT) (Z2 tptp.list_VEBT_VEBT)) (= Y4 Z2)) (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))))))))
% 4.71/5.16 (assert (= (lambda ((Y4 tptp.list_int) (Z2 tptp.list_int)) (= Y4 Z2)) (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))))))))
% 4.71/5.16 (assert (= (lambda ((Y4 tptp.list_nat) (Z2 tptp.list_nat)) (= Y4 Z2)) (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))))))))
% 4.71/5.16 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.vEBT_VEBT Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (exists ((X6 tptp.vEBT_VEBT)) (@ (@ P I3) X6)))) (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)))))))))
% 4.71/5.16 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.int Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (exists ((X6 tptp.int)) (@ (@ P I3) X6)))) (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)))))))))
% 4.71/5.16 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (exists ((X6 tptp.nat)) (@ (@ P I3) X6)))) (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)))))))))
% 4.71/5.16 (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)))))
% 4.71/5.16 (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)))))
% 4.71/5.16 (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)))))
% 4.71/5.16 (assert (forall ((Xs tptp.list_Extended_enat) (A2 tptp.set_Extended_enat) (X tptp.extended_enat) (I tptp.nat)) (=> (@ (@ tptp.ord_le7203529160286727270d_enat (@ tptp.set_Extended_enat2 Xs)) A2) (=> (@ (@ tptp.member_Extended_enat X) A2) (@ (@ tptp.ord_le7203529160286727270d_enat (@ tptp.set_Extended_enat2 (@ (@ (@ tptp.list_u3071683517702156500d_enat Xs) I) X))) A2)))))
% 4.71/5.16 (assert (forall ((Xs tptp.list_real) (A2 tptp.set_real) (X tptp.real) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 Xs)) A2) (=> (@ (@ tptp.member_real X) A2) (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real Xs) I) X))) A2)))))
% 4.71/5.16 (assert (forall ((Xs tptp.list_set_nat) (A2 tptp.set_set_nat) (X tptp.set_nat) (I tptp.nat)) (=> (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.set_set_nat2 Xs)) A2) (=> (@ (@ tptp.member_set_nat X) A2) (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.set_set_nat2 (@ (@ (@ tptp.list_update_set_nat Xs) I) X))) A2)))))
% 4.71/5.16 (assert (forall ((Xs tptp.list_VEBT_VEBT) (A2 tptp.set_VEBT_VEBT) (X tptp.vEBT_VEBT) (I tptp.nat)) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) A2) (=> (@ (@ tptp.member_VEBT_VEBT X) A2) (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) X))) A2)))))
% 4.71/5.16 (assert (forall ((Xs tptp.list_nat) (A2 tptp.set_nat) (X tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) A2) (=> (@ (@ tptp.member_nat X) A2) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs) I) X))) A2)))))
% 4.71/5.16 (assert (forall ((Xs tptp.list_int) (A2 tptp.set_int) (X tptp.int) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) A2) (=> (@ (@ tptp.member_int X) A2) (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs) I) X))) A2)))))
% 4.71/5.16 (assert (forall ((Xs tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Xs)) (@ P X4))) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs) I3)))))))
% 4.71/5.16 (assert (forall ((Xs tptp.list_int) (P (-> tptp.int Bool))) (= (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) (@ tptp.set_int2 Xs)) (@ P X4))) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_int Xs)) (@ P (@ (@ tptp.nth_int Xs) I3)))))))
% 4.71/5.16 (assert (forall ((Xs tptp.list_nat) (P (-> tptp.nat Bool))) (= (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ tptp.set_nat2 Xs)) (@ P X4))) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs)) (@ P (@ (@ tptp.nth_nat Xs) I3)))))))
% 4.71/5.16 (assert (forall ((Xs tptp.list_Extended_enat) (P (-> tptp.extended_enat Bool)) (X tptp.extended_enat)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s3941691890525107288d_enat Xs)) (@ P (@ (@ tptp.nth_Extended_enat Xs) I4)))) (=> (@ (@ tptp.member_Extended_enat X) (@ tptp.set_Extended_enat2 Xs)) (@ P X)))))
% 4.71/5.16 (assert (forall ((Xs tptp.list_real) (P (-> tptp.real Bool)) (X 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 X) (@ tptp.set_real2 Xs)) (@ P X)))))
% 4.71/5.16 (assert (forall ((Xs tptp.list_set_nat) (P (-> tptp.set_nat Bool)) (X tptp.set_nat)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s3254054031482475050et_nat Xs)) (@ P (@ (@ tptp.nth_set_nat Xs) I4)))) (=> (@ (@ tptp.member_set_nat X) (@ tptp.set_set_nat2 Xs)) (@ P X)))))
% 4.71/5.16 (assert (forall ((Xs tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool)) (X tptp.vEBT_VEBT)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs) I4)))) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs)) (@ P X)))))
% 4.71/5.16 (assert (forall ((Xs tptp.list_int) (P (-> tptp.int Bool)) (X 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 X) (@ tptp.set_int2 Xs)) (@ P X)))))
% 4.71/5.16 (assert (forall ((Xs tptp.list_nat) (P (-> tptp.nat Bool)) (X 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 X) (@ tptp.set_nat2 Xs)) (@ P X)))))
% 4.71/5.16 (assert (forall ((X tptp.extended_enat) (Xs tptp.list_Extended_enat)) (= (@ (@ tptp.member_Extended_enat X) (@ tptp.set_Extended_enat2 Xs)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s3941691890525107288d_enat Xs)) (= (@ (@ tptp.nth_Extended_enat Xs) I3) X))))))
% 4.71/5.16 (assert (forall ((X tptp.real) (Xs tptp.list_real)) (= (@ (@ tptp.member_real X) (@ 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) X))))))
% 4.71/5.16 (assert (forall ((X tptp.set_nat) (Xs tptp.list_set_nat)) (= (@ (@ tptp.member_set_nat X) (@ tptp.set_set_nat2 Xs)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s3254054031482475050et_nat Xs)) (= (@ (@ tptp.nth_set_nat Xs) I3) X))))))
% 4.71/5.16 (assert (forall ((X tptp.vEBT_VEBT) (Xs tptp.list_VEBT_VEBT)) (= (@ (@ tptp.member_VEBT_VEBT X) (@ 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) X))))))
% 4.71/5.16 (assert (forall ((X tptp.int) (Xs tptp.list_int)) (= (@ (@ tptp.member_int X) (@ 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) X))))))
% 4.71/5.16 (assert (forall ((X tptp.nat) (Xs tptp.list_nat)) (= (@ (@ tptp.member_nat X) (@ 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) X))))))
% 4.71/5.16 (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))))))
% 4.71/5.16 (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))))))
% 4.71/5.16 (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))))))
% 4.71/5.16 (assert (forall ((N2 tptp.nat) (Xs tptp.list_Extended_enat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s3941691890525107288d_enat Xs)) (@ (@ tptp.member_Extended_enat (@ (@ tptp.nth_Extended_enat Xs) N2)) (@ tptp.set_Extended_enat2 Xs)))))
% 4.71/5.16 (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)))))
% 4.71/5.16 (assert (forall ((N2 tptp.nat) (Xs tptp.list_set_nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s3254054031482475050et_nat Xs)) (@ (@ tptp.member_set_nat (@ (@ tptp.nth_set_nat Xs) N2)) (@ tptp.set_set_nat2 Xs)))))
% 4.71/5.16 (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)))))
% 4.71/5.16 (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)))))
% 4.71/5.16 (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)))))
% 4.71/5.16 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y) X) (= (@ (@ tptp.ord_less_eq_real X) Y) (= X Y)))))
% 4.71/5.16 (assert (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X) (= (@ (@ tptp.ord_less_eq_set_nat X) Y) (= X Y)))))
% 4.71/5.16 (assert (forall ((Y tptp.set_int) (X tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y) X) (= (@ (@ tptp.ord_less_eq_set_int X) Y) (= X Y)))))
% 4.71/5.16 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= (@ (@ tptp.ord_less_eq_nat X) Y) (= X Y)))))
% 4.71/5.16 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= (@ (@ tptp.ord_less_eq_int X) Y) (= X Y)))))
% 4.71/5.16 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_eq_real X) Y)) (@ (@ tptp.ord_less_eq_real Y) X))))
% 4.71/5.16 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))))
% 4.71/5.16 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int X) Y)) (@ (@ tptp.ord_less_eq_int Y) X))))
% 4.71/5.16 (assert (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (= (@ F B2) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_real (@ F A)) C))))))
% 4.71/5.16 (assert (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (= (@ F B2) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 4.71/5.16 (assert (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (= (@ F B2) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 4.71/5.16 (assert (forall ((A tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (= (@ F B2) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_real (@ F A)) C))))))
% 4.71/5.16 (assert (forall ((A tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (= (@ F B2) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 4.71/5.16 (assert (forall ((A tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (= (@ F B2) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 4.71/5.16 (assert (forall ((A tptp.int) (B2 tptp.int) (F (-> tptp.int tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (= (@ F B2) C) (=> (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_real (@ F A)) C))))))
% 4.71/5.16 (assert (forall ((A tptp.int) (B2 tptp.int) (F (-> tptp.int tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (= (@ F B2) C) (=> (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 4.71/5.16 (assert (forall ((A tptp.int) (B2 tptp.int) (F (-> tptp.int tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (= (@ F B2) C) (=> (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 4.71/5.16 (assert (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.set_nat)) (C tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (= (@ F B2) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X5) Y3) (@ (@ tptp.ord_less_eq_set_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_set_nat (@ F A)) C))))))
% 4.71/5.16 (assert (forall ((A tptp.real) (F (-> tptp.real tptp.real)) (B2 tptp.real) (C tptp.real)) (=> (= A (@ F B2)) (=> (@ (@ tptp.ord_less_eq_real B2) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_real A) (@ F C)))))))
% 4.71/5.16 (assert (forall ((A tptp.nat) (F (-> tptp.real tptp.nat)) (B2 tptp.real) (C tptp.real)) (=> (= A (@ F B2)) (=> (@ (@ tptp.ord_less_eq_real B2) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat A) (@ F C)))))))
% 4.71/5.16 (assert (forall ((A tptp.int) (F (-> tptp.real tptp.int)) (B2 tptp.real) (C tptp.real)) (=> (= A (@ F B2)) (=> (@ (@ tptp.ord_less_eq_real B2) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int A) (@ F C)))))))
% 4.71/5.16 (assert (forall ((A tptp.real) (F (-> tptp.nat tptp.real)) (B2 tptp.nat) (C tptp.nat)) (=> (= A (@ F B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_real A) (@ F C)))))))
% 4.71/5.16 (assert (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B2 tptp.nat) (C tptp.nat)) (=> (= A (@ F B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat A) (@ F C)))))))
% 4.71/5.16 (assert (forall ((A tptp.int) (F (-> tptp.nat tptp.int)) (B2 tptp.nat) (C tptp.nat)) (=> (= A (@ F B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int A) (@ F C)))))))
% 4.71/5.16 (assert (forall ((A tptp.real) (F (-> tptp.int tptp.real)) (B2 tptp.int) (C tptp.int)) (=> (= A (@ F B2)) (=> (@ (@ tptp.ord_less_eq_int B2) C) (=> (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_real A) (@ F C)))))))
% 4.71/5.16 (assert (forall ((A tptp.nat) (F (-> tptp.int tptp.nat)) (B2 tptp.int) (C tptp.int)) (=> (= A (@ F B2)) (=> (@ (@ tptp.ord_less_eq_int B2) C) (=> (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat A) (@ F C)))))))
% 4.71/5.16 (assert (forall ((A tptp.int) (F (-> tptp.int tptp.int)) (B2 tptp.int) (C tptp.int)) (=> (= A (@ F B2)) (=> (@ (@ tptp.ord_less_eq_int B2) C) (=> (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int A) (@ F C)))))))
% 4.71/5.16 (assert (forall ((A tptp.set_nat) (F (-> tptp.real tptp.set_nat)) (B2 tptp.real) (C tptp.real)) (=> (= A (@ F B2)) (=> (@ (@ tptp.ord_less_eq_real B2) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X5) Y3) (@ (@ tptp.ord_less_eq_set_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_set_nat A) (@ F C)))))))
% 4.71/5.16 (assert (forall ((X tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real Y) X))))
% 4.71/5.16 (assert (forall ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X) Y) (@ (@ tptp.ord_less_eq_nat Y) X))))
% 4.71/5.16 (assert (forall ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_eq_int X) Y) (@ (@ tptp.ord_less_eq_int Y) X))))
% 4.71/5.16 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (= X Y) (@ (@ tptp.ord_less_eq_real X) Y))))
% 4.71/5.16 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (= X Y) (@ (@ tptp.ord_less_eq_set_nat X) Y))))
% 4.71/5.16 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (= X Y) (@ (@ tptp.ord_less_eq_set_int X) Y))))
% 4.71/5.16 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (= X Y) (@ (@ tptp.ord_less_eq_nat X) Y))))
% 4.71/5.16 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (= X Y) (@ (@ tptp.ord_less_eq_int X) Y))))
% 4.71/5.16 (assert (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_eq_real (@ F B2)) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_real (@ F A)) C))))))
% 4.71/5.16 (assert (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_eq_nat (@ F B2)) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 4.71/5.16 (assert (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_eq_int (@ F B2)) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 4.71/5.16 (assert (forall ((A tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ tptp.ord_less_eq_real (@ F B2)) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_real (@ F A)) C))))))
% 4.71/5.16 (assert (forall ((A tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ tptp.ord_less_eq_nat (@ F B2)) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 4.71/5.16 (assert (forall ((A tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ tptp.ord_less_eq_int (@ F B2)) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 4.71/5.16 (assert (forall ((A tptp.int) (B2 tptp.int) (F (-> tptp.int tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (@ (@ tptp.ord_less_eq_real (@ F B2)) C) (=> (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_real (@ F A)) C))))))
% 4.71/5.16 (assert (forall ((A tptp.int) (B2 tptp.int) (F (-> tptp.int tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (@ (@ tptp.ord_less_eq_nat (@ F B2)) C) (=> (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 4.71/5.16 (assert (forall ((A tptp.int) (B2 tptp.int) (F (-> tptp.int tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (@ (@ tptp.ord_less_eq_int (@ F B2)) C) (=> (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 4.71/5.16 (assert (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.set_nat)) (C tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_eq_set_nat (@ F B2)) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X5) Y3) (@ (@ tptp.ord_less_eq_set_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_set_nat (@ F A)) C))))))
% 4.71/5.16 (assert (forall ((A tptp.real) (F (-> tptp.real tptp.real)) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_real B2) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 4.71/5.16 (assert (forall ((A tptp.real) (F (-> tptp.nat tptp.real)) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 4.71/5.16 (assert (forall ((A tptp.real) (F (-> tptp.int tptp.real)) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_int B2) C) (=> (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 4.71/5.16 (assert (forall ((A tptp.nat) (F (-> tptp.real tptp.nat)) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_real B2) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 4.71/5.16 (assert (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 4.71/5.16 (assert (forall ((A tptp.nat) (F (-> tptp.int tptp.nat)) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_int B2) C) (=> (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 4.71/5.16 (assert (forall ((A tptp.int) (F (-> tptp.real tptp.int)) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_real B2) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 4.71/5.16 (assert (forall ((A tptp.int) (F (-> tptp.nat tptp.int)) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 4.71/5.16 (assert (forall ((A tptp.int) (F (-> tptp.int tptp.int)) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_int B2) C) (=> (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 4.71/5.16 (assert (forall ((A tptp.real) (F (-> tptp.set_nat tptp.real)) (B2 tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_set_nat B2) C) (=> (forall ((X5 tptp.set_nat) (Y3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 4.71/5.16 (assert (= (lambda ((Y4 tptp.real) (Z2 tptp.real)) (= Y4 Z2)) (lambda ((A3 tptp.real) (B3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A3) B3) (@ (@ tptp.ord_less_eq_real B3) A3)))))
% 4.71/5.16 (assert (= (lambda ((Y4 tptp.set_nat) (Z2 tptp.set_nat)) (= Y4 Z2)) (lambda ((A3 tptp.set_nat) (B3 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A3) B3) (@ (@ tptp.ord_less_eq_set_nat B3) A3)))))
% 4.71/5.16 (assert (= (lambda ((Y4 tptp.set_int) (Z2 tptp.set_int)) (= Y4 Z2)) (lambda ((A3 tptp.set_int) (B3 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A3) B3) (@ (@ tptp.ord_less_eq_set_int B3) A3)))))
% 4.71/5.16 (assert (= (lambda ((Y4 tptp.nat) (Z2 tptp.nat)) (= Y4 Z2)) (lambda ((A3 tptp.nat) (B3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A3) B3) (@ (@ tptp.ord_less_eq_nat B3) A3)))))
% 4.71/5.16 (assert (= (lambda ((Y4 tptp.int) (Z2 tptp.int)) (= Y4 Z2)) (lambda ((A3 tptp.int) (B3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A3) B3) (@ (@ tptp.ord_less_eq_int B3) A3)))))
% 4.71/5.16 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_eq_real B2) A) (= A B2)))))
% 4.71/5.16 (assert (forall ((A tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B2) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A) (= A B2)))))
% 4.71/5.16 (assert (forall ((A tptp.set_int) (B2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) B2) (=> (@ (@ tptp.ord_less_eq_set_int B2) A) (= A B2)))))
% 4.71/5.16 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ tptp.ord_less_eq_nat B2) A) (= A B2)))))
% 4.71/5.16 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (@ (@ tptp.ord_less_eq_int B2) A) (= A B2)))))
% 4.71/5.16 (assert (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real C))) (=> (@ (@ tptp.ord_less_eq_real B2) A) (=> (@ _let_1 B2) (@ _let_1 A))))))
% 4.71/5.16 (assert (forall ((B2 tptp.set_nat) (A tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat C))) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A) (=> (@ _let_1 B2) (@ _let_1 A))))))
% 4.71/5.16 (assert (forall ((B2 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 B2) A) (=> (@ _let_1 B2) (@ _let_1 A))))))
% 4.71/5.16 (assert (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B2) A) (=> (@ _let_1 B2) (@ _let_1 A))))))
% 4.71/5.16 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (=> (@ (@ tptp.ord_less_eq_int B2) A) (=> (@ _let_1 B2) (@ _let_1 A))))))
% 4.71/5.16 (assert (forall ((B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B2) A) (=> (@ (@ tptp.ord_less_eq_real A) B2) (= A B2)))))
% 4.71/5.16 (assert (forall ((B2 tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A) (=> (@ (@ tptp.ord_less_eq_set_nat A) B2) (= A B2)))))
% 4.71/5.16 (assert (forall ((B2 tptp.set_int) (A tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int B2) A) (=> (@ (@ tptp.ord_less_eq_set_int A) B2) (= A B2)))))
% 4.71/5.16 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B2) A) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (= A B2)))))
% 4.71/5.16 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B2) A) (=> (@ (@ tptp.ord_less_eq_int A) B2) (= A B2)))))
% 4.71/5.16 (assert (= (lambda ((Y4 tptp.real) (Z2 tptp.real)) (= Y4 Z2)) (lambda ((A3 tptp.real) (B3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real B3) A3) (@ (@ tptp.ord_less_eq_real A3) B3)))))
% 4.71/5.16 (assert (= (lambda ((Y4 tptp.set_nat) (Z2 tptp.set_nat)) (= Y4 Z2)) (lambda ((A3 tptp.set_nat) (B3 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat B3) A3) (@ (@ tptp.ord_less_eq_set_nat A3) B3)))))
% 4.71/5.16 (assert (= (lambda ((Y4 tptp.set_int) (Z2 tptp.set_int)) (= Y4 Z2)) (lambda ((A3 tptp.set_int) (B3 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int B3) A3) (@ (@ tptp.ord_less_eq_set_int A3) B3)))))
% 4.71/5.16 (assert (= (lambda ((Y4 tptp.nat) (Z2 tptp.nat)) (= Y4 Z2)) (lambda ((A3 tptp.nat) (B3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B3) A3) (@ (@ tptp.ord_less_eq_nat A3) B3)))))
% 4.71/5.16 (assert (= (lambda ((Y4 tptp.int) (Z2 tptp.int)) (= Y4 Z2)) (lambda ((A3 tptp.int) (B3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B3) A3) (@ (@ tptp.ord_less_eq_int A3) B3)))))
% 4.71/5.16 (assert (forall ((P (-> tptp.real tptp.real Bool)) (A tptp.real) (B2 tptp.real)) (=> (forall ((A4 tptp.real) (B4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A4) B4) (@ (@ P A4) B4))) (=> (forall ((A4 tptp.real) (B4 tptp.real)) (=> (@ (@ P B4) A4) (@ (@ P A4) B4))) (@ (@ P A) B2)))))
% 4.71/5.16 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B2 tptp.nat)) (=> (forall ((A4 tptp.nat) (B4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A4) B4) (@ (@ P A4) B4))) (=> (forall ((A4 tptp.nat) (B4 tptp.nat)) (=> (@ (@ P B4) A4) (@ (@ P A4) B4))) (@ (@ P A) B2)))))
% 4.71/5.16 (assert (forall ((P (-> tptp.int tptp.int Bool)) (A tptp.int) (B2 tptp.int)) (=> (forall ((A4 tptp.int) (B4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A4) B4) (@ (@ P A4) B4))) (=> (forall ((A4 tptp.int) (B4 tptp.int)) (=> (@ (@ P B4) A4) (@ (@ P A4) B4))) (@ (@ P A) B2)))))
% 4.71/5.16 (assert (forall ((X tptp.real) (Y tptp.real) (Z3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) Z3) (@ _let_1 Z3))))))
% 4.71/5.16 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z3 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_set_nat Y) Z3) (@ _let_1 Z3))))))
% 4.71/5.16 (assert (forall ((X tptp.set_int) (Y tptp.set_int) (Z3 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_set_int Y) Z3) (@ _let_1 Z3))))))
% 4.71/5.16 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_nat Y) Z3) (@ _let_1 Z3))))))
% 4.71/5.16 (assert (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z3) (@ _let_1 Z3))))))
% 4.71/5.16 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_real B2) C) (@ _let_1 C))))))
% 4.71/5.16 (assert (forall ((A tptp.set_nat) (B2 tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_set_nat B2) C) (@ _let_1 C))))))
% 4.71/5.16 (assert (forall ((A tptp.set_int) (B2 tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_set_int B2) C) (@ _let_1 C))))))
% 4.71/5.16 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (@ _let_1 C))))))
% 4.71/5.16 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_int B2) C) (@ _let_1 C))))))
% 4.71/5.16 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ (@ tptp.ord_less_eq_real Y) X) (= X Y)))))
% 4.71/5.16 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X) (= X Y)))))
% 4.71/5.16 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X) Y) (=> (@ (@ tptp.ord_less_eq_set_int Y) X) (= X Y)))))
% 4.71/5.16 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= X Y)))))
% 4.71/5.16 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= X Y)))))
% 4.71/5.16 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ _let_1 B2) (=> (= B2 C) (@ _let_1 C))))))
% 4.71/5.16 (assert (forall ((A tptp.set_nat) (B2 tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A))) (=> (@ _let_1 B2) (=> (= B2 C) (@ _let_1 C))))))
% 4.71/5.16 (assert (forall ((A tptp.set_int) (B2 tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A))) (=> (@ _let_1 B2) (=> (= B2 C) (@ _let_1 C))))))
% 4.71/5.16 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B2) (=> (= B2 C) (@ _let_1 C))))))
% 4.71/5.16 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 B2) (=> (= B2 C) (@ _let_1 C))))))
% 4.71/5.16 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (= A B2) (=> (@ (@ tptp.ord_less_eq_real B2) C) (@ (@ tptp.ord_less_eq_real A) C)))))
% 4.71/5.16 (assert (forall ((A tptp.set_nat) (B2 tptp.set_nat) (C tptp.set_nat)) (=> (= A B2) (=> (@ (@ tptp.ord_less_eq_set_nat B2) C) (@ (@ tptp.ord_less_eq_set_nat A) C)))))
% 4.71/5.16 (assert (forall ((A tptp.set_int) (B2 tptp.set_int) (C tptp.set_int)) (=> (= A B2) (=> (@ (@ tptp.ord_less_eq_set_int B2) C) (@ (@ tptp.ord_less_eq_set_int A) C)))))
% 4.71/5.16 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (= A B2) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (@ (@ tptp.ord_less_eq_nat A) C)))))
% 4.71/5.16 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (= A B2) (=> (@ (@ tptp.ord_less_eq_int B2) C) (@ (@ tptp.ord_less_eq_int A) C)))))
% 4.71/5.16 (assert (= (lambda ((Y4 tptp.real) (Z2 tptp.real)) (= Y4 Z2)) (lambda ((X4 tptp.real) (Y5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real X4) Y5) (@ (@ tptp.ord_less_eq_real Y5) X4)))))
% 4.71/5.16 (assert (= (lambda ((Y4 tptp.set_nat) (Z2 tptp.set_nat)) (= Y4 Z2)) (lambda ((X4 tptp.set_nat) (Y5 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat X4) Y5) (@ (@ tptp.ord_less_eq_set_nat Y5) X4)))))
% 4.71/5.16 (assert (= (lambda ((Y4 tptp.set_int) (Z2 tptp.set_int)) (= Y4 Z2)) (lambda ((X4 tptp.set_int) (Y5 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int X4) Y5) (@ (@ tptp.ord_less_eq_set_int Y5) X4)))))
% 4.71/5.16 (assert (= (lambda ((Y4 tptp.nat) (Z2 tptp.nat)) (= Y4 Z2)) (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X4) Y5) (@ (@ tptp.ord_less_eq_nat Y5) X4)))))
% 4.71/5.16 (assert (= (lambda ((Y4 tptp.int) (Z2 tptp.int)) (= Y4 Z2)) (lambda ((X4 tptp.int) (Y5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X4) Y5) (@ (@ tptp.ord_less_eq_int Y5) X4)))))
% 4.71/5.16 (assert (forall ((X tptp.real) (Y tptp.real) (Z3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_real Z3))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_real Y))) (let ((_let_6 (@ _let_5 Z3))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z3))) (=> (=> _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)))))))))))))))))))
% 4.71/5.16 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_nat Z3))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_nat Y))) (let ((_let_6 (@ _let_5 Z3))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z3))) (=> (=> _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)))))))))))))))))))
% 4.71/5.16 (assert (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_int Z3))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_int Y))) (let ((_let_6 (@ _let_5 Z3))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z3))) (=> (=> _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)))))))))))))))))))
% 4.71/5.16 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real A) B2)) (and (@ (@ tptp.ord_less_eq_real B2) A) (not (= B2 A))))))
% 4.71/5.16 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat A) B2)) (and (@ (@ tptp.ord_less_eq_nat B2) A) (not (= B2 A))))))
% 4.71/5.16 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int A) B2)) (and (@ (@ tptp.ord_less_eq_int B2) A) (not (= B2 A))))))
% 4.71/5.16 (assert (forall ((N2 tptp.nat) (Xs tptp.list_Extended_enat) (X tptp.extended_enat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s3941691890525107288d_enat Xs)) (@ (@ tptp.member_Extended_enat X) (@ tptp.set_Extended_enat2 (@ (@ (@ tptp.list_u3071683517702156500d_enat Xs) N2) X))))))
% 4.71/5.16 (assert (forall ((N2 tptp.nat) (Xs tptp.list_real) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_real Xs)) (@ (@ tptp.member_real X) (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real Xs) N2) X))))))
% 4.71/5.16 (assert (forall ((N2 tptp.nat) (Xs tptp.list_set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s3254054031482475050et_nat Xs)) (@ (@ tptp.member_set_nat X) (@ tptp.set_set_nat2 (@ (@ (@ tptp.list_update_set_nat Xs) N2) X))))))
% 4.71/5.16 (assert (forall ((N2 tptp.nat) (Xs tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) N2) X))))))
% 4.71/5.16 (assert (forall ((N2 tptp.nat) (Xs tptp.list_int) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_int Xs)) (@ (@ tptp.member_int X) (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs) N2) X))))))
% 4.71/5.16 (assert (forall ((N2 tptp.nat) (Xs tptp.list_nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.member_nat X) (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs) N2) X))))))
% 4.71/5.16 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))))
% 4.71/5.16 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X) Y) (not (@ (@ tptp.ord_le72135733267957522d_enat Y) X)))))
% 4.71/5.16 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (@ (@ tptp.ord_less_real Y) X)))))
% 4.71/5.16 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (@ (@ tptp.ord_less_int Y) X)))))
% 4.71/5.16 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (= Y X)))))
% 4.71/5.16 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X) Y) (not (= Y X)))))
% 4.71/5.16 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (= Y X)))))
% 4.71/5.16 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (= Y X)))))
% 4.71/5.16 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (= X Y)))))
% 4.71/5.16 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X) Y) (not (= X Y)))))
% 4.71/5.16 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (= X Y)))))
% 4.71/5.16 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (= X Y)))))
% 4.71/5.16 (assert (forall ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_nat X) Y) (= X Y) (@ (@ tptp.ord_less_nat Y) X))))
% 4.71/5.16 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (or (@ (@ tptp.ord_le72135733267957522d_enat X) Y) (= X Y) (@ (@ tptp.ord_le72135733267957522d_enat Y) X))))
% 4.71/5.16 (assert (forall ((X tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_real X) Y) (= X Y) (@ (@ tptp.ord_less_real Y) X))))
% 4.71/5.16 (assert (forall ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_int X) Y) (= X Y) (@ (@ tptp.ord_less_int Y) X))))
% 4.71/5.16 (assert (forall ((X tptp.nat) (Y tptp.nat) (P Bool)) (=> (@ (@ tptp.ord_less_nat X) Y) (=> (@ (@ tptp.ord_less_nat Y) X) P))))
% 4.71/5.16 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat) (P Bool)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X) Y) (=> (@ (@ tptp.ord_le72135733267957522d_enat Y) X) P))))
% 4.71/5.16 (assert (forall ((X tptp.real) (Y tptp.real) (P Bool)) (=> (@ (@ tptp.ord_less_real X) Y) (=> (@ (@ tptp.ord_less_real Y) X) P))))
% 4.71/5.16 (assert (forall ((X tptp.int) (Y tptp.int) (P Bool)) (=> (@ (@ tptp.ord_less_int X) Y) (=> (@ (@ tptp.ord_less_int Y) X) P))))
% 4.71/5.16 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))))
% 4.71/5.16 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X) Y) (not (@ (@ tptp.ord_le72135733267957522d_enat Y) X)))))
% 4.71/5.16 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (@ (@ tptp.ord_less_real Y) X)))))
% 4.71/5.16 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (@ (@ tptp.ord_less_int Y) X)))))
% 4.71/5.16 (assert (forall ((A tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (=> (@ (@ tptp.ord_less_nat (@ F B2)) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y3) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 4.71/5.16 (assert (forall ((A tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.extended_enat)) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_less_nat A) B2) (=> (@ (@ tptp.ord_le72135733267957522d_enat (@ F B2)) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y3) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_le72135733267957522d_enat (@ F A)) C))))))
% 4.71/5.16 (assert (forall ((A tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat A) B2) (=> (@ (@ tptp.ord_less_real (@ F B2)) 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))))))
% 4.71/5.16 (assert (forall ((A tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_nat A) B2) (=> (@ (@ tptp.ord_less_int (@ F B2)) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y3) (@ (@ tptp.ord_less_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 4.71/5.16 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (F (-> tptp.extended_enat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B2) (=> (@ (@ tptp.ord_less_nat (@ F B2)) C) (=> (forall ((X5 tptp.extended_enat) (Y3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y3) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 4.71/5.16 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (F (-> tptp.extended_enat tptp.extended_enat)) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B2) (=> (@ (@ tptp.ord_le72135733267957522d_enat (@ F B2)) C) (=> (forall ((X5 tptp.extended_enat) (Y3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y3) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_le72135733267957522d_enat (@ F A)) C))))))
% 4.71/5.16 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (F (-> tptp.extended_enat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B2) (=> (@ (@ tptp.ord_less_real (@ F B2)) C) (=> (forall ((X5 tptp.extended_enat) (Y3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 4.71/5.16 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (F (-> tptp.extended_enat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B2) (=> (@ (@ tptp.ord_less_int (@ F B2)) C) (=> (forall ((X5 tptp.extended_enat) (Y3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y3) (@ (@ tptp.ord_less_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 4.71/5.16 (assert (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.ord_less_nat (@ F B2)) C) (=> (forall ((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))))))
% 4.71/5.16 (assert (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.extended_enat)) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.ord_le72135733267957522d_enat (@ F B2)) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_le72135733267957522d_enat (@ F A)) C))))))
% 4.71/5.16 (assert (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_nat B2) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y3) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 4.71/5.16 (assert (forall ((A tptp.nat) (F (-> tptp.extended_enat tptp.nat)) (B2 tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B2) C) (=> (forall ((X5 tptp.extended_enat) (Y3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y3) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 4.71/5.16 (assert (forall ((A tptp.nat) (F (-> tptp.real tptp.nat)) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_real B2) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 4.71/5.16 (assert (forall ((A tptp.nat) (F (-> tptp.int tptp.nat)) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_int B2) C) (=> (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Y3) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 4.71/5.16 (assert (forall ((A tptp.extended_enat) (F (-> tptp.nat tptp.extended_enat)) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_nat B2) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y3) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 4.71/5.16 (assert (forall ((A tptp.extended_enat) (F (-> tptp.extended_enat tptp.extended_enat)) (B2 tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B2) C) (=> (forall ((X5 tptp.extended_enat) (Y3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y3) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 4.71/5.16 (assert (forall ((A tptp.extended_enat) (F (-> tptp.real tptp.extended_enat)) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_real B2) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 4.71/5.16 (assert (forall ((A tptp.extended_enat) (F (-> tptp.int tptp.extended_enat)) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_int B2) C) (=> (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Y3) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 4.71/5.16 (assert (forall ((A tptp.real) (F (-> tptp.nat tptp.real)) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_nat B2) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 4.71/5.16 (assert (forall ((A tptp.real) (F (-> tptp.extended_enat tptp.real)) (B2 tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B2) C) (=> (forall ((X5 tptp.extended_enat) (Y3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 4.71/5.16 (assert (forall ((X tptp.nat)) (not (@ (@ tptp.ord_less_nat X) X))))
% 4.71/5.16 (assert (forall ((X tptp.extended_enat)) (not (@ (@ tptp.ord_le72135733267957522d_enat X) X))))
% 4.71/5.16 (assert (forall ((X tptp.real)) (not (@ (@ tptp.ord_less_real X) X))))
% 4.71/5.16 (assert (forall ((X tptp.int)) (not (@ (@ tptp.ord_less_int X) X))))
% 4.71/5.16 (assert (forall ((A tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (=> (= (@ F B2) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y3) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 4.71/5.16 (assert (forall ((A tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.extended_enat)) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_less_nat A) B2) (=> (= (@ F B2) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y3) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_le72135733267957522d_enat (@ F A)) C))))))
% 4.71/5.16 (assert (forall ((A tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat A) B2) (=> (= (@ F B2) 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))))))
% 4.71/5.16 (assert (forall ((A tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_nat A) B2) (=> (= (@ F B2) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y3) (@ (@ tptp.ord_less_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 4.71/5.16 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (F (-> tptp.extended_enat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B2) (=> (= (@ F B2) C) (=> (forall ((X5 tptp.extended_enat) (Y3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y3) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 4.71/5.16 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (F (-> tptp.extended_enat tptp.extended_enat)) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B2) (=> (= (@ F B2) C) (=> (forall ((X5 tptp.extended_enat) (Y3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y3) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_le72135733267957522d_enat (@ F A)) C))))))
% 4.71/5.16 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (F (-> tptp.extended_enat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B2) (=> (= (@ F B2) C) (=> (forall ((X5 tptp.extended_enat) (Y3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 4.71/5.16 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (F (-> tptp.extended_enat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B2) (=> (= (@ F B2) C) (=> (forall ((X5 tptp.extended_enat) (Y3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y3) (@ (@ tptp.ord_less_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 4.71/5.16 (assert (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_real A) B2) (=> (= (@ F B2) C) (=> (forall ((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))))))
% 4.71/5.16 (assert (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.extended_enat)) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_less_real A) B2) (=> (= (@ F B2) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_le72135733267957522d_enat (@ F A)) C))))))
% 4.71/5.16 (assert (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B2 tptp.nat) (C tptp.nat)) (=> (= A (@ F B2)) (=> (@ (@ tptp.ord_less_nat B2) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y3) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_nat A) (@ F C)))))))
% 4.71/5.16 (assert (forall ((A tptp.extended_enat) (F (-> tptp.nat tptp.extended_enat)) (B2 tptp.nat) (C tptp.nat)) (=> (= A (@ F B2)) (=> (@ (@ tptp.ord_less_nat B2) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y3) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_le72135733267957522d_enat A) (@ F C)))))))
% 4.71/5.16 (assert (forall ((A tptp.real) (F (-> tptp.nat tptp.real)) (B2 tptp.nat) (C tptp.nat)) (=> (= A (@ F B2)) (=> (@ (@ tptp.ord_less_nat B2) 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)))))))
% 4.71/5.16 (assert (forall ((A tptp.int) (F (-> tptp.nat tptp.int)) (B2 tptp.nat) (C tptp.nat)) (=> (= A (@ F B2)) (=> (@ (@ tptp.ord_less_nat B2) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y3) (@ (@ tptp.ord_less_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_int A) (@ F C)))))))
% 4.71/5.16 (assert (forall ((A tptp.nat) (F (-> tptp.extended_enat tptp.nat)) (B2 tptp.extended_enat) (C tptp.extended_enat)) (=> (= A (@ F B2)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B2) C) (=> (forall ((X5 tptp.extended_enat) (Y3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y3) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_nat A) (@ F C)))))))
% 4.71/5.16 (assert (forall ((A tptp.extended_enat) (F (-> tptp.extended_enat tptp.extended_enat)) (B2 tptp.extended_enat) (C tptp.extended_enat)) (=> (= A (@ F B2)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B2) C) (=> (forall ((X5 tptp.extended_enat) (Y3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y3) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_le72135733267957522d_enat A) (@ F C)))))))
% 4.71/5.16 (assert (forall ((A tptp.real) (F (-> tptp.extended_enat tptp.real)) (B2 tptp.extended_enat) (C tptp.extended_enat)) (=> (= A (@ F B2)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B2) C) (=> (forall ((X5 tptp.extended_enat) (Y3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 4.71/5.16 (assert (forall ((A tptp.int) (F (-> tptp.extended_enat tptp.int)) (B2 tptp.extended_enat) (C tptp.extended_enat)) (=> (= A (@ F B2)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B2) C) (=> (forall ((X5 tptp.extended_enat) (Y3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y3) (@ (@ tptp.ord_less_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_int A) (@ F C)))))))
% 4.71/5.16 (assert (forall ((A tptp.nat) (F (-> tptp.real tptp.nat)) (B2 tptp.real) (C tptp.real)) (=> (= A (@ F B2)) (=> (@ (@ tptp.ord_less_real B2) C) (=> (forall ((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)))))))
% 4.71/5.16 (assert (forall ((A tptp.extended_enat) (F (-> tptp.real tptp.extended_enat)) (B2 tptp.real) (C tptp.real)) (=> (= A (@ F B2)) (=> (@ (@ tptp.ord_less_real B2) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_le72135733267957522d_enat A) (@ F C)))))))
% 4.71/5.16 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_nat Y) Z3) (@ _let_1 Z3))))))
% 4.71/5.16 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat) (Z3 tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_le72135733267957522d_enat Y) Z3) (@ _let_1 Z3))))))
% 4.71/5.16 (assert (forall ((X tptp.real) (Y tptp.real) (Z3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_real Y) Z3) (@ _let_1 Z3))))))
% 4.71/5.16 (assert (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_int Y) Z3) (@ _let_1 Z3))))))
% 4.71/5.16 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (not (@ (@ tptp.ord_less_nat B2) A)))))
% 4.71/5.16 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B2) (not (@ (@ tptp.ord_le72135733267957522d_enat B2) A)))))
% 4.71/5.16 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (not (@ (@ tptp.ord_less_real B2) A)))))
% 4.71/5.16 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B2) (not (@ (@ tptp.ord_less_int B2) A)))))
% 4.71/5.16 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_nat X) Y) (@ (@ tptp.ord_less_nat Y) X)))))
% 4.71/5.16 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (= (not (= X Y)) (or (@ (@ tptp.ord_le72135733267957522d_enat X) Y) (@ (@ tptp.ord_le72135733267957522d_enat Y) X)))))
% 4.71/5.16 (assert (forall ((X tptp.real) (Y tptp.real)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_real Y) X)))))
% 4.71/5.16 (assert (forall ((X tptp.int) (Y tptp.int)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_int X) Y) (@ (@ tptp.ord_less_int Y) X)))))
% 4.71/5.16 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))))
% 4.71/5.16 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X) Y) (not (@ (@ tptp.ord_le72135733267957522d_enat Y) X)))))
% 4.71/5.16 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (@ (@ tptp.ord_less_real Y) X)))))
% 4.71/5.16 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (@ (@ tptp.ord_less_int Y) X)))))
% 4.71/5.16 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X)))))
% 4.71/5.16 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_le72135733267957522d_enat X) Y)) (@ (@ tptp.ord_le72135733267957522d_enat Y) X)))))
% 4.71/5.16 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_real X) Y)) (@ (@ tptp.ord_less_real Y) X)))))
% 4.71/5.16 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_int Y) X)))))
% 4.71/5.16 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B2) A) (not (= A B2)))))
% 4.71/5.16 (assert (forall ((B2 tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B2) A) (not (= A B2)))))
% 4.71/5.16 (assert (forall ((B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B2) A) (not (= A B2)))))
% 4.71/5.16 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B2) A) (not (= A B2)))))
% 4.71/5.16 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (not (= A B2)))))
% 4.71/5.16 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B2) (not (= A B2)))))
% 4.71/5.16 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (not (= A B2)))))
% 4.71/5.16 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B2) (not (= A B2)))))
% 4.71/5.16 (assert (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ (@ tptp.ord_less_nat B2) A) (=> (@ _let_1 B2) (@ _let_1 A))))))
% 4.71/5.16 (assert (forall ((B2 tptp.extended_enat) (A tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat C))) (=> (@ (@ tptp.ord_le72135733267957522d_enat B2) A) (=> (@ _let_1 B2) (@ _let_1 A))))))
% 4.71/5.16 (assert (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C))) (=> (@ (@ tptp.ord_less_real B2) A) (=> (@ _let_1 B2) (@ _let_1 A))))))
% 4.71/5.16 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ (@ tptp.ord_less_int B2) A) (=> (@ _let_1 B2) (@ _let_1 A))))))
% 4.71/5.16 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (or (@ (@ tptp.ord_less_nat Y) X) (= X Y)))))
% 4.71/5.16 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (= (not (@ (@ tptp.ord_le72135733267957522d_enat X) Y)) (or (@ (@ tptp.ord_le72135733267957522d_enat Y) X) (= X Y)))))
% 4.71/5.16 (assert (forall ((X tptp.real) (Y tptp.real)) (= (not (@ (@ tptp.ord_less_real X) Y)) (or (@ (@ tptp.ord_less_real Y) X) (= X Y)))))
% 4.71/5.16 (assert (forall ((X tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_int X) Y)) (or (@ (@ tptp.ord_less_int Y) X) (= X Y)))))
% 4.71/5.16 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_nat B2) C) (@ _let_1 C))))))
% 4.71/5.16 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat A))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_le72135733267957522d_enat B2) C) (@ _let_1 C))))))
% 4.71/5.16 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_real B2) C) (@ _let_1 C))))))
% 4.71/5.16 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_int B2) C) (@ _let_1 C))))))
% 4.71/5.16 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B2 tptp.nat)) (=> (forall ((A4 tptp.nat) (B4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A4) B4) (@ (@ P A4) B4))) (=> (forall ((A4 tptp.nat)) (@ (@ P A4) A4)) (=> (forall ((A4 tptp.nat) (B4 tptp.nat)) (=> (@ (@ P B4) A4) (@ (@ P A4) B4))) (@ (@ P A) B2))))))
% 4.71/5.16 (assert (forall ((P (-> tptp.extended_enat tptp.extended_enat Bool)) (A tptp.extended_enat) (B2 tptp.extended_enat)) (=> (forall ((A4 tptp.extended_enat) (B4 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A4) B4) (@ (@ P A4) B4))) (=> (forall ((A4 tptp.extended_enat)) (@ (@ P A4) A4)) (=> (forall ((A4 tptp.extended_enat) (B4 tptp.extended_enat)) (=> (@ (@ P B4) A4) (@ (@ P A4) B4))) (@ (@ P A) B2))))))
% 4.71/5.16 (assert (forall ((P (-> tptp.real tptp.real Bool)) (A tptp.real) (B2 tptp.real)) (=> (forall ((A4 tptp.real) (B4 tptp.real)) (=> (@ (@ tptp.ord_less_real A4) B4) (@ (@ P A4) B4))) (=> (forall ((A4 tptp.real)) (@ (@ P A4) A4)) (=> (forall ((A4 tptp.real) (B4 tptp.real)) (=> (@ (@ P B4) A4) (@ (@ P A4) B4))) (@ (@ P A) B2))))))
% 4.71/5.16 (assert (forall ((P (-> tptp.int tptp.int Bool)) (A tptp.int) (B2 tptp.int)) (=> (forall ((A4 tptp.int) (B4 tptp.int)) (=> (@ (@ tptp.ord_less_int A4) B4) (@ (@ P A4) B4))) (=> (forall ((A4 tptp.int)) (@ (@ P A4) A4)) (=> (forall ((A4 tptp.int) (B4 tptp.int)) (=> (@ (@ P B4) A4) (@ (@ P A4) B4))) (@ (@ P A) B2))))))
% 4.71/5.16 (assert (= (lambda ((P2 (-> tptp.nat Bool))) (exists ((X7 tptp.nat)) (@ P2 X7))) (lambda ((P3 (-> tptp.nat Bool))) (exists ((N tptp.nat)) (and (@ P3 N) (forall ((M tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (@ P3 M)))))))))
% 4.71/5.16 (assert (= (lambda ((P2 (-> tptp.extended_enat Bool))) (exists ((X7 tptp.extended_enat)) (@ P2 X7))) (lambda ((P3 (-> tptp.extended_enat Bool))) (exists ((N tptp.extended_enat)) (and (@ P3 N) (forall ((M tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat M) N) (not (@ P3 M)))))))))
% 4.71/5.16 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))))
% 4.71/5.16 (assert (forall ((A tptp.extended_enat)) (not (@ (@ tptp.ord_le72135733267957522d_enat A) A))))
% 4.71/5.16 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real A) A))))
% 4.71/5.16 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int A) A))))
% 4.71/5.16 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B2) A) (not (@ (@ tptp.ord_less_nat A) B2)))))
% 4.71/5.16 (assert (forall ((B2 tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B2) A) (not (@ (@ tptp.ord_le72135733267957522d_enat A) B2)))))
% 4.71/5.16 (assert (forall ((B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B2) A) (not (@ (@ tptp.ord_less_real A) B2)))))
% 4.71/5.16 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B2) A) (not (@ (@ tptp.ord_less_int A) B2)))))
% 4.71/5.16 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_nat Y) X)))))
% 4.71/5.16 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (not (@ (@ tptp.ord_le72135733267957522d_enat X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_le72135733267957522d_enat Y) X)))))
% 4.71/5.16 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_real X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_real Y) X)))))
% 4.71/5.16 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_int Y) X)))))
% 4.71/5.16 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat Y) X)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (= X Y)))))
% 4.71/5.16 (assert (forall ((Y tptp.extended_enat) (X tptp.extended_enat)) (=> (not (@ (@ tptp.ord_le72135733267957522d_enat Y) X)) (= (not (@ (@ tptp.ord_le72135733267957522d_enat X) Y)) (= X Y)))))
% 4.71/5.16 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (not (@ (@ tptp.ord_less_real Y) X)) (= (not (@ (@ tptp.ord_less_real X) Y)) (= X Y)))))
% 4.71/5.16 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (not (@ (@ tptp.ord_less_int Y) X)) (= (not (@ (@ tptp.ord_less_int X) Y)) (= X Y)))))
% 4.71/5.16 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat)) (=> (forall ((X5 tptp.nat)) (=> (forall ((Y6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Y6) X5) (@ P Y6))) (@ P X5))) (@ P A))))
% 4.71/5.16 (assert (forall ((P (-> tptp.extended_enat Bool)) (A tptp.extended_enat)) (=> (forall ((X5 tptp.extended_enat)) (=> (forall ((Y6 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat Y6) X5) (@ P Y6))) (@ P X5))) (@ P A))))
% 4.71/5.16 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B2) (=> (= B2 C) (@ _let_1 C))))))
% 4.71/5.16 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat A))) (=> (@ _let_1 B2) (=> (= B2 C) (@ _let_1 C))))))
% 4.71/5.16 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B2) (=> (= B2 C) (@ _let_1 C))))))
% 4.71/5.16 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 B2) (=> (= B2 C) (@ _let_1 C))))))
% 4.71/5.16 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (= A B2) (=> (@ (@ tptp.ord_less_nat B2) C) (@ (@ tptp.ord_less_nat A) C)))))
% 4.71/5.16 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat)) (=> (= A B2) (=> (@ (@ tptp.ord_le72135733267957522d_enat B2) C) (@ (@ tptp.ord_le72135733267957522d_enat A) C)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (= A B2) (=> (@ (@ tptp.ord_less_real B2) C) (@ (@ tptp.ord_less_real A) C)))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (= A B2) (=> (@ (@ tptp.ord_less_int B2) C) (@ (@ tptp.ord_less_int A) C)))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (not (@ (@ tptp.ord_less_nat B2) A)))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B2) (not (@ (@ tptp.ord_le72135733267957522d_enat B2) A)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (not (@ (@ tptp.ord_less_real B2) A)))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B2) (not (@ (@ tptp.ord_less_int B2) A)))))
% 4.71/5.17 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (= X Y)))))
% 4.71/5.17 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X) Y) (not (= X Y)))))
% 4.71/5.17 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (= X Y)))))
% 4.71/5.17 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (= X Y)))))
% 4.71/5.17 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (exists ((Z tptp.real)) (and (@ (@ tptp.ord_less_real X) Z) (@ (@ tptp.ord_less_real Z) Y))))))
% 4.71/5.17 (assert (forall ((X tptp.nat)) (exists ((X_12 tptp.nat)) (@ (@ tptp.ord_less_nat X) X_12))))
% 4.71/5.17 (assert (forall ((X tptp.real)) (exists ((X_12 tptp.real)) (@ (@ tptp.ord_less_real X) X_12))))
% 4.71/5.17 (assert (forall ((X tptp.int)) (exists ((X_12 tptp.int)) (@ (@ tptp.ord_less_int X) X_12))))
% 4.71/5.17 (assert (forall ((X tptp.real)) (exists ((Y3 tptp.real)) (@ (@ tptp.ord_less_real Y3) X))))
% 4.71/5.17 (assert (forall ((X tptp.int)) (exists ((Y3 tptp.int)) (@ (@ tptp.ord_less_int Y3) X))))
% 4.71/5.17 (assert (forall ((I tptp.nat) (Xs tptp.list_VEBT_VEBT) (J tptp.nat) (X tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) X)) J))) (let ((_let_2 (= I J))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_VEBT_VEBT Xs) J)))))))))
% 4.71/5.17 (assert (forall ((I tptp.nat) (Xs tptp.list_int) (J tptp.nat) (X tptp.int)) (let ((_let_1 (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int Xs) I) X)) J))) (let ((_let_2 (= I J))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int Xs)) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_int Xs) J)))))))))
% 4.71/5.17 (assert (forall ((I tptp.nat) (Xs tptp.list_nat) (J tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs) I) X)) J))) (let ((_let_2 (= I J))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs)) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_nat Xs) J)))))))))
% 4.71/5.17 (assert (forall ((I tptp.nat) (Xs tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) X) Xs) (= (@ (@ tptp.nth_VEBT_VEBT Xs) I) X)))))
% 4.71/5.17 (assert (forall ((I tptp.nat) (Xs tptp.list_int) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int Xs)) (= (= (@ (@ (@ tptp.list_update_int Xs) I) X) Xs) (= (@ (@ tptp.nth_int Xs) I) X)))))
% 4.71/5.17 (assert (forall ((I tptp.nat) (Xs tptp.list_nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs)) (= (= (@ (@ (@ tptp.list_update_nat Xs) I) X) Xs) (= (@ (@ tptp.nth_nat Xs) I) X)))))
% 4.71/5.17 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X)))))
% 4.71/5.17 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (not (@ P N3)) (exists ((M5 tptp.nat)) (and (@ (@ tptp.ord_less_nat M5) N3) (not (@ P M5)))))) (@ P N2))))
% 4.71/5.17 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M5) N3) (@ P M5))) (@ P N3))) (@ P N2))))
% 4.71/5.17 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) N2))))
% 4.71/5.17 (assert (forall ((S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S) T) (not (= S T)))))
% 4.71/5.17 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) M2) (not (= M2 N2)))))
% 4.71/5.17 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) N2))))
% 4.71/5.17 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (not (= M2 N2)) (or (@ (@ tptp.ord_less_nat M2) N2) (@ (@ tptp.ord_less_nat N2) M2)))))
% 4.71/5.17 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B2 tptp.nat)) (=> (@ P K) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B2))) (exists ((X5 tptp.nat)) (and (@ P X5) (forall ((Y6 tptp.nat)) (=> (@ P Y6) (@ (@ tptp.ord_less_eq_nat Y6) X5)))))))))
% 4.71/5.17 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_nat N2) M2))))
% 4.71/5.17 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (= M2 N2)))))
% 4.71/5.17 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (= M2 N2) (@ (@ tptp.ord_less_eq_nat M2) N2))))
% 4.71/5.17 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J) (=> (@ (@ tptp.ord_less_eq_nat J) K) (@ _let_1 K))))))
% 4.71/5.17 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) N2)))
% 4.71/5.17 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat X) Y) (or (@ (@ tptp.ord_le72135733267957522d_enat X) Y) (= X Y)))))
% 4.71/5.17 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (or (@ (@ tptp.ord_less_real X) Y) (= X Y)))))
% 4.71/5.17 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (or (@ (@ tptp.ord_less_set_nat X) Y) (= X Y)))))
% 4.71/5.17 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X) Y) (or (@ (@ tptp.ord_less_set_int X) Y) (= X Y)))))
% 4.71/5.17 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (or (@ (@ tptp.ord_less_nat X) Y) (= X Y)))))
% 4.71/5.17 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (or (@ (@ tptp.ord_less_int X) Y) (= X Y)))))
% 4.71/5.17 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (or (@ (@ tptp.ord_le2932123472753598470d_enat X) Y) (@ (@ tptp.ord_le72135733267957522d_enat Y) X))))
% 4.71/5.17 (assert (forall ((X tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_real Y) X))))
% 4.71/5.17 (assert (forall ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X) Y) (@ (@ tptp.ord_less_nat Y) X))))
% 4.71/5.17 (assert (forall ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_eq_int X) Y) (@ (@ tptp.ord_less_int Y) X))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.extended_enat)) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_less_nat A) B2) (=> (@ (@ tptp.ord_le2932123472753598470d_enat (@ F B2)) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y3) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_le72135733267957522d_enat (@ F A)) C))))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (F (-> tptp.extended_enat tptp.extended_enat)) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B2) (=> (@ (@ tptp.ord_le2932123472753598470d_enat (@ F B2)) C) (=> (forall ((X5 tptp.extended_enat) (Y3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y3) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_le72135733267957522d_enat (@ F A)) C))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.extended_enat)) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.ord_le2932123472753598470d_enat (@ F B2)) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_le72135733267957522d_enat (@ F A)) C))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int) (F (-> tptp.int tptp.extended_enat)) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_less_int A) B2) (=> (@ (@ tptp.ord_le2932123472753598470d_enat (@ F B2)) C) (=> (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Y3) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_le72135733267957522d_enat (@ F A)) C))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat A) B2) (=> (@ (@ tptp.ord_less_eq_real (@ F B2)) C) (=> (forall ((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))))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (F (-> tptp.extended_enat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B2) (=> (@ (@ tptp.ord_less_eq_real (@ F B2)) C) (=> (forall ((X5 tptp.extended_enat) (Y3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.ord_less_eq_real (@ F B2)) C) (=> (forall ((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))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int) (F (-> tptp.int tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_int A) B2) (=> (@ (@ tptp.ord_less_eq_real (@ F B2)) C) (=> (forall ((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))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (=> (@ (@ tptp.ord_less_eq_nat (@ F B2)) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y3) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (F (-> tptp.extended_enat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B2) (=> (@ (@ tptp.ord_less_eq_nat (@ F B2)) C) (=> (forall ((X5 tptp.extended_enat) (Y3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y3) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (F (-> tptp.real tptp.extended_enat)) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_real B2) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X5) Y3) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (F (-> tptp.real tptp.real)) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_real B2) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (F (-> tptp.real tptp.nat)) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_real B2) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (F (-> tptp.real tptp.int)) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_real B2) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (F (-> tptp.nat tptp.extended_enat)) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (F (-> tptp.nat tptp.real)) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (F (-> tptp.nat tptp.int)) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (F (-> tptp.int tptp.extended_enat)) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_int B2) C) (=> (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y3) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (F (-> tptp.int tptp.real)) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_int B2) C) (=> (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.extended_enat)) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_le72135733267957522d_enat (@ F B2)) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X5) Y3) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_le72135733267957522d_enat (@ F A)) C))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_real (@ F B2)) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_nat (@ F B2)) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_int (@ F B2)) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.extended_enat)) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ tptp.ord_le72135733267957522d_enat (@ F B2)) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_le72135733267957522d_enat (@ F A)) C))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ tptp.ord_less_real (@ F B2)) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ tptp.ord_less_nat (@ F B2)) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ tptp.ord_less_int (@ F B2)) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int) (F (-> tptp.int tptp.extended_enat)) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (@ (@ tptp.ord_le72135733267957522d_enat (@ F B2)) C) (=> (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y3) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_le72135733267957522d_enat (@ F A)) C))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int) (F (-> tptp.int tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (@ (@ tptp.ord_less_real (@ F B2)) C) (=> (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (F (-> tptp.nat tptp.extended_enat)) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) (@ F B2)) (=> (@ (@ tptp.ord_less_nat B2) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y3) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_le72135733267957522d_enat A) (@ F C)))))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (F (-> tptp.extended_enat tptp.extended_enat)) (B2 tptp.extended_enat) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) (@ F B2)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B2) C) (=> (forall ((X5 tptp.extended_enat) (Y3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y3) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_le72135733267957522d_enat A) (@ F C)))))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (F (-> tptp.real tptp.extended_enat)) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) (@ F B2)) (=> (@ (@ tptp.ord_less_real B2) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_le72135733267957522d_enat A) (@ F C)))))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (F (-> tptp.int tptp.extended_enat)) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) (@ F B2)) (=> (@ (@ tptp.ord_less_int B2) C) (=> (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Y3) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_le72135733267957522d_enat A) (@ F C)))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (F (-> tptp.nat tptp.real)) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B2)) (=> (@ (@ tptp.ord_less_nat B2) C) (=> (forall ((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)))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (F (-> tptp.extended_enat tptp.real)) (B2 tptp.extended_enat) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B2)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B2) C) (=> (forall ((X5 tptp.extended_enat) (Y3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (F (-> tptp.real tptp.real)) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B2)) (=> (@ (@ tptp.ord_less_real B2) C) (=> (forall ((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)))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (F (-> tptp.int tptp.real)) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B2)) (=> (@ (@ tptp.ord_less_int B2) C) (=> (forall ((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)))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) (@ F B2)) (=> (@ (@ tptp.ord_less_nat B2) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y3) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_nat A) (@ F C)))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (F (-> tptp.extended_enat tptp.nat)) (B2 tptp.extended_enat) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_less_eq_nat A) (@ F B2)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B2) C) (=> (forall ((X5 tptp.extended_enat) (Y3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y3) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_nat A) (@ F C)))))))
% 4.71/5.17 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat) (Z3 tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Y) Z3) (@ _let_1 Z3))))))
% 4.71/5.17 (assert (forall ((X tptp.real) (Y tptp.real) (Z3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) Z3) (@ _let_1 Z3))))))
% 4.71/5.17 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z3 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_set_nat Y) Z3) (@ _let_1 Z3))))))
% 4.71/5.17 (assert (forall ((X tptp.set_int) (Y tptp.set_int) (Z3 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_set_int Y) Z3) (@ _let_1 Z3))))))
% 4.71/5.17 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_nat Y) Z3) (@ _let_1 Z3))))))
% 4.71/5.17 (assert (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z3) (@ _let_1 Z3))))))
% 4.71/5.17 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat) (Z3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat X) Y) (=> (@ (@ tptp.ord_le72135733267957522d_enat Y) Z3) (@ (@ tptp.ord_le72135733267957522d_enat X) Z3)))))
% 4.71/5.17 (assert (forall ((X tptp.real) (Y tptp.real) (Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ (@ tptp.ord_less_real Y) Z3) (@ (@ tptp.ord_less_real X) Z3)))))
% 4.71/5.17 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (=> (@ (@ tptp.ord_less_set_nat Y) Z3) (@ (@ tptp.ord_less_set_nat X) Z3)))))
% 4.71/5.17 (assert (forall ((X tptp.set_int) (Y tptp.set_int) (Z3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X) Y) (=> (@ (@ tptp.ord_less_set_int Y) Z3) (@ (@ tptp.ord_less_set_int X) Z3)))))
% 4.71/5.17 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (=> (@ (@ tptp.ord_less_nat Y) Z3) (@ (@ tptp.ord_less_nat X) Z3)))))
% 4.71/5.17 (assert (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (=> (@ (@ tptp.ord_less_int Y) Z3) (@ (@ tptp.ord_less_int X) Z3)))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (=> (not (= A B2)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B2) (@ (@ tptp.ord_le72135733267957522d_enat A) B2)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (not (= A B2)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (@ (@ tptp.ord_less_real A) B2)))))
% 4.71/5.17 (assert (forall ((A tptp.set_nat) (B2 tptp.set_nat)) (=> (not (= A B2)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B2) (@ (@ tptp.ord_less_set_nat A) B2)))))
% 4.71/5.17 (assert (forall ((A tptp.set_int) (B2 tptp.set_int)) (=> (not (= A B2)) (=> (@ (@ tptp.ord_less_eq_set_int A) B2) (@ (@ tptp.ord_less_set_int A) B2)))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (not (= A B2)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (@ (@ tptp.ord_less_nat A) B2)))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (not (= A B2)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (@ (@ tptp.ord_less_int A) B2)))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B2) (=> (not (= A B2)) (@ (@ tptp.ord_le72135733267957522d_enat A) B2)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (not (= A B2)) (@ (@ tptp.ord_less_real A) B2)))))
% 4.71/5.17 (assert (forall ((A tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B2) (=> (not (= A B2)) (@ (@ tptp.ord_less_set_nat A) B2)))))
% 4.71/5.17 (assert (forall ((A tptp.set_int) (B2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) B2) (=> (not (= A B2)) (@ (@ tptp.ord_less_set_int A) B2)))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (not (= A B2)) (@ (@ tptp.ord_less_nat A) B2)))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (not (= A B2)) (@ (@ tptp.ord_less_int A) B2)))))
% 4.71/5.17 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X) Y) (@ (@ tptp.ord_le2932123472753598470d_enat X) Y))))
% 4.71/5.17 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_eq_real X) Y))))
% 4.71/5.17 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat X) Y) (@ (@ tptp.ord_less_eq_set_nat X) Y))))
% 4.71/5.17 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int X) Y) (@ (@ tptp.ord_less_eq_set_int X) Y))))
% 4.71/5.17 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (@ (@ tptp.ord_less_eq_nat X) Y))))
% 4.71/5.17 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (@ (@ tptp.ord_less_eq_int X) Y))))
% 4.71/5.17 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (= (not (@ (@ tptp.ord_le72135733267957522d_enat X) Y)) (@ (@ tptp.ord_le2932123472753598470d_enat Y) X))))
% 4.71/5.17 (assert (forall ((X tptp.real) (Y tptp.real)) (= (not (@ (@ tptp.ord_less_real X) Y)) (@ (@ tptp.ord_less_eq_real Y) X))))
% 4.71/5.17 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))))
% 4.71/5.17 (assert (forall ((X tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_eq_int Y) X))))
% 4.71/5.17 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (= (not (@ (@ tptp.ord_le2932123472753598470d_enat X) Y)) (@ (@ tptp.ord_le72135733267957522d_enat Y) X))))
% 4.71/5.17 (assert (forall ((X tptp.real) (Y tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real X) Y)) (@ (@ tptp.ord_less_real Y) X))))
% 4.71/5.17 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X))))
% 4.71/5.17 (assert (forall ((X tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int X) Y)) (@ (@ tptp.ord_less_int Y) X))))
% 4.71/5.17 (assert (= tptp.ord_le72135733267957522d_enat (lambda ((X4 tptp.extended_enat) (Y5 tptp.extended_enat)) (and (@ (@ tptp.ord_le2932123472753598470d_enat X4) Y5) (not (= X4 Y5))))))
% 4.71/5.17 (assert (= tptp.ord_less_real (lambda ((X4 tptp.real) (Y5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real X4) Y5) (not (= X4 Y5))))))
% 4.71/5.17 (assert (= tptp.ord_less_set_nat (lambda ((X4 tptp.set_nat) (Y5 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat X4) Y5) (not (= X4 Y5))))))
% 4.71/5.17 (assert (= tptp.ord_less_set_int (lambda ((X4 tptp.set_int) (Y5 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int X4) Y5) (not (= X4 Y5))))))
% 4.71/5.17 (assert (= tptp.ord_less_nat (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X4) Y5) (not (= X4 Y5))))))
% 4.71/5.17 (assert (= tptp.ord_less_int (lambda ((X4 tptp.int) (Y5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X4) Y5) (not (= X4 Y5))))))
% 4.71/5.17 (assert (= tptp.ord_le2932123472753598470d_enat (lambda ((X4 tptp.extended_enat) (Y5 tptp.extended_enat)) (or (@ (@ tptp.ord_le72135733267957522d_enat X4) Y5) (= X4 Y5)))))
% 4.71/5.17 (assert (= tptp.ord_less_eq_real (lambda ((X4 tptp.real) (Y5 tptp.real)) (or (@ (@ tptp.ord_less_real X4) Y5) (= X4 Y5)))))
% 4.71/5.17 (assert (= tptp.ord_less_eq_set_nat (lambda ((X4 tptp.set_nat) (Y5 tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat X4) Y5) (= X4 Y5)))))
% 4.71/5.17 (assert (= tptp.ord_less_eq_set_int (lambda ((X4 tptp.set_int) (Y5 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int X4) Y5) (= X4 Y5)))))
% 4.71/5.17 (assert (= tptp.ord_less_eq_nat (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (or (@ (@ tptp.ord_less_nat X4) Y5) (= X4 Y5)))))
% 4.71/5.17 (assert (= tptp.ord_less_eq_int (lambda ((X4 tptp.int) (Y5 tptp.int)) (or (@ (@ tptp.ord_less_int X4) Y5) (= X4 Y5)))))
% 4.71/5.17 (assert (forall ((B2 tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B2) A) (@ (@ tptp.ord_le2932123472753598470d_enat B2) A))))
% 4.71/5.17 (assert (forall ((B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B2) A) (@ (@ tptp.ord_less_eq_real B2) A))))
% 4.71/5.17 (assert (forall ((B2 tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B2) A) (@ (@ tptp.ord_less_eq_set_nat B2) A))))
% 4.71/5.17 (assert (forall ((B2 tptp.set_int) (A tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int B2) A) (@ (@ tptp.ord_less_eq_set_int B2) A))))
% 4.71/5.17 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B2) A) (@ (@ tptp.ord_less_eq_nat B2) A))))
% 4.71/5.17 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B2) A) (@ (@ tptp.ord_less_eq_int B2) A))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B2) (@ (@ tptp.ord_le2932123472753598470d_enat A) B2))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (@ (@ tptp.ord_less_eq_real A) B2))))
% 4.71/5.17 (assert (forall ((A tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A) B2) (@ (@ tptp.ord_less_eq_set_nat A) B2))))
% 4.71/5.17 (assert (forall ((A tptp.set_int) (B2 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A) B2) (@ (@ tptp.ord_less_eq_set_int A) B2))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (@ (@ tptp.ord_less_eq_nat A) B2))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B2) (@ (@ tptp.ord_less_eq_int A) B2))))
% 4.71/5.17 (assert (= tptp.ord_le72135733267957522d_enat (lambda ((B3 tptp.extended_enat) (A3 tptp.extended_enat)) (and (@ (@ tptp.ord_le2932123472753598470d_enat B3) A3) (not (@ (@ tptp.ord_le2932123472753598470d_enat A3) B3))))))
% 4.71/5.17 (assert (= tptp.ord_less_real (lambda ((B3 tptp.real) (A3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real B3) A3) (not (@ (@ tptp.ord_less_eq_real A3) B3))))))
% 4.71/5.17 (assert (= tptp.ord_less_set_nat (lambda ((B3 tptp.set_nat) (A3 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat B3) A3) (not (@ (@ tptp.ord_less_eq_set_nat A3) B3))))))
% 4.71/5.17 (assert (= tptp.ord_less_set_int (lambda ((B3 tptp.set_int) (A3 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int B3) A3) (not (@ (@ tptp.ord_less_eq_set_int A3) B3))))))
% 4.71/5.17 (assert (= tptp.ord_less_nat (lambda ((B3 tptp.nat) (A3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B3) A3) (not (@ (@ tptp.ord_less_eq_nat A3) B3))))))
% 4.71/5.17 (assert (= tptp.ord_less_int (lambda ((B3 tptp.int) (A3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B3) A3) (not (@ (@ tptp.ord_less_eq_int A3) B3))))))
% 4.71/5.17 (assert (forall ((B2 tptp.extended_enat) (A tptp.extended_enat) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B2) A) (=> (@ (@ tptp.ord_le2932123472753598470d_enat C) B2) (@ (@ tptp.ord_le72135733267957522d_enat C) A)))))
% 4.71/5.17 (assert (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real B2) A) (=> (@ (@ tptp.ord_less_eq_real C) B2) (@ (@ tptp.ord_less_real C) A)))))
% 4.71/5.17 (assert (forall ((B2 tptp.set_nat) (A tptp.set_nat) (C tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B2) A) (=> (@ (@ tptp.ord_less_eq_set_nat C) B2) (@ (@ tptp.ord_less_set_nat C) A)))))
% 4.71/5.17 (assert (forall ((B2 tptp.set_int) (A tptp.set_int) (C tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int B2) A) (=> (@ (@ tptp.ord_less_eq_set_int C) B2) (@ (@ tptp.ord_less_set_int C) A)))))
% 4.71/5.17 (assert (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat B2) A) (=> (@ (@ tptp.ord_less_eq_nat C) B2) (@ (@ tptp.ord_less_nat C) A)))))
% 4.71/5.17 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int B2) A) (=> (@ (@ tptp.ord_less_eq_int C) B2) (@ (@ tptp.ord_less_int C) A)))))
% 4.71/5.17 (assert (forall ((B2 tptp.extended_enat) (A tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat C))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B2) A) (=> (@ _let_1 B2) (@ _let_1 A))))))
% 4.71/5.17 (assert (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C))) (=> (@ (@ tptp.ord_less_eq_real B2) A) (=> (@ _let_1 B2) (@ _let_1 A))))))
% 4.71/5.17 (assert (forall ((B2 tptp.set_nat) (A tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat C))) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A) (=> (@ _let_1 B2) (@ _let_1 A))))))
% 4.71/5.17 (assert (forall ((B2 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 B2) A) (=> (@ _let_1 B2) (@ _let_1 A))))))
% 4.71/5.17 (assert (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B2) A) (=> (@ _let_1 B2) (@ _let_1 A))))))
% 4.71/5.17 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ (@ tptp.ord_less_eq_int B2) A) (=> (@ _let_1 B2) (@ _let_1 A))))))
% 4.71/5.17 (assert (= tptp.ord_le72135733267957522d_enat (lambda ((B3 tptp.extended_enat) (A3 tptp.extended_enat)) (and (@ (@ tptp.ord_le2932123472753598470d_enat B3) A3) (not (= A3 B3))))))
% 4.71/5.17 (assert (= tptp.ord_less_real (lambda ((B3 tptp.real) (A3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real B3) A3) (not (= A3 B3))))))
% 4.71/5.17 (assert (= tptp.ord_less_set_nat (lambda ((B3 tptp.set_nat) (A3 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat B3) A3) (not (= A3 B3))))))
% 4.71/5.17 (assert (= tptp.ord_less_set_int (lambda ((B3 tptp.set_int) (A3 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int B3) A3) (not (= A3 B3))))))
% 4.71/5.17 (assert (= tptp.ord_less_nat (lambda ((B3 tptp.nat) (A3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B3) A3) (not (= A3 B3))))))
% 4.71/5.17 (assert (= tptp.ord_less_int (lambda ((B3 tptp.int) (A3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B3) A3) (not (= A3 B3))))))
% 4.71/5.17 (assert (= tptp.ord_le2932123472753598470d_enat (lambda ((B3 tptp.extended_enat) (A3 tptp.extended_enat)) (or (@ (@ tptp.ord_le72135733267957522d_enat B3) A3) (= A3 B3)))))
% 4.71/5.17 (assert (= tptp.ord_less_eq_real (lambda ((B3 tptp.real) (A3 tptp.real)) (or (@ (@ tptp.ord_less_real B3) A3) (= A3 B3)))))
% 4.71/5.17 (assert (= tptp.ord_less_eq_set_nat (lambda ((B3 tptp.set_nat) (A3 tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat B3) A3) (= A3 B3)))))
% 4.71/5.17 (assert (= tptp.ord_less_eq_set_int (lambda ((B3 tptp.set_int) (A3 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int B3) A3) (= A3 B3)))))
% 4.71/5.17 (assert (= tptp.ord_less_eq_nat (lambda ((B3 tptp.nat) (A3 tptp.nat)) (or (@ (@ tptp.ord_less_nat B3) A3) (= A3 B3)))))
% 4.71/5.17 (assert (= tptp.ord_less_eq_int (lambda ((B3 tptp.int) (A3 tptp.int)) (or (@ (@ tptp.ord_less_int B3) A3) (= A3 B3)))))
% 4.71/5.17 (assert (forall ((X tptp.real) (Y tptp.real) (Z3 tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (=> (forall ((W tptp.real)) (=> (@ (@ tptp.ord_less_real X) W) (=> (@ (@ tptp.ord_less_real W) Y) (@ (@ tptp.ord_less_eq_real W) Z3)))) (@ (@ tptp.ord_less_eq_real Y) Z3)))))
% 4.71/5.17 (assert (forall ((Z3 tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X) (=> (forall ((W tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) W) (=> (@ (@ tptp.ord_less_real W) X) (@ (@ tptp.ord_less_eq_real Y) W)))) (@ (@ tptp.ord_less_eq_real Y) Z3)))))
% 4.71/5.17 (assert (= tptp.ord_le72135733267957522d_enat (lambda ((A3 tptp.extended_enat) (B3 tptp.extended_enat)) (and (@ (@ tptp.ord_le2932123472753598470d_enat A3) B3) (not (@ (@ tptp.ord_le2932123472753598470d_enat B3) A3))))))
% 4.71/5.17 (assert (= tptp.ord_less_real (lambda ((A3 tptp.real) (B3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A3) B3) (not (@ (@ tptp.ord_less_eq_real B3) A3))))))
% 4.71/5.17 (assert (= tptp.ord_less_set_nat (lambda ((A3 tptp.set_nat) (B3 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A3) B3) (not (@ (@ tptp.ord_less_eq_set_nat B3) A3))))))
% 4.71/5.17 (assert (= tptp.ord_less_set_int (lambda ((A3 tptp.set_int) (B3 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A3) B3) (not (@ (@ tptp.ord_less_eq_set_int B3) A3))))))
% 4.71/5.17 (assert (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A3) B3) (not (@ (@ tptp.ord_less_eq_nat B3) A3))))))
% 4.71/5.17 (assert (= tptp.ord_less_int (lambda ((A3 tptp.int) (B3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A3) B3) (not (@ (@ tptp.ord_less_eq_int B3) A3))))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat A))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B2) C) (@ _let_1 C))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_real B2) C) (@ _let_1 C))))))
% 4.71/5.17 (assert (forall ((A tptp.set_nat) (B2 tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat A))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_set_nat B2) C) (@ _let_1 C))))))
% 4.71/5.17 (assert (forall ((A tptp.set_int) (B2 tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int A))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_set_int B2) C) (@ _let_1 C))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (@ _let_1 C))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_int B2) C) (@ _let_1 C))))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B2) (=> (@ (@ tptp.ord_le72135733267957522d_enat B2) C) (@ (@ tptp.ord_le72135733267957522d_enat A) C)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_real B2) C) (@ (@ tptp.ord_less_real A) C)))))
% 4.71/5.17 (assert (forall ((A tptp.set_nat) (B2 tptp.set_nat) (C tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B2) (=> (@ (@ tptp.ord_less_set_nat B2) C) (@ (@ tptp.ord_less_set_nat A) C)))))
% 4.71/5.17 (assert (forall ((A tptp.set_int) (B2 tptp.set_int) (C tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) B2) (=> (@ (@ tptp.ord_less_set_int B2) C) (@ (@ tptp.ord_less_set_int A) C)))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ tptp.ord_less_nat B2) C) (@ (@ tptp.ord_less_nat A) C)))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (@ (@ tptp.ord_less_int B2) C) (@ (@ tptp.ord_less_int A) C)))))
% 4.71/5.17 (assert (= tptp.ord_le72135733267957522d_enat (lambda ((A3 tptp.extended_enat) (B3 tptp.extended_enat)) (and (@ (@ tptp.ord_le2932123472753598470d_enat A3) B3) (not (= A3 B3))))))
% 4.71/5.17 (assert (= tptp.ord_less_real (lambda ((A3 tptp.real) (B3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A3) B3) (not (= A3 B3))))))
% 4.71/5.17 (assert (= tptp.ord_less_set_nat (lambda ((A3 tptp.set_nat) (B3 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A3) B3) (not (= A3 B3))))))
% 4.71/5.17 (assert (= tptp.ord_less_set_int (lambda ((A3 tptp.set_int) (B3 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A3) B3) (not (= A3 B3))))))
% 4.71/5.17 (assert (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A3) B3) (not (= A3 B3))))))
% 4.71/5.17 (assert (= tptp.ord_less_int (lambda ((A3 tptp.int) (B3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A3) B3) (not (= A3 B3))))))
% 4.71/5.17 (assert (= tptp.ord_le2932123472753598470d_enat (lambda ((A3 tptp.extended_enat) (B3 tptp.extended_enat)) (or (@ (@ tptp.ord_le72135733267957522d_enat A3) B3) (= A3 B3)))))
% 4.71/5.17 (assert (= tptp.ord_less_eq_real (lambda ((A3 tptp.real) (B3 tptp.real)) (or (@ (@ tptp.ord_less_real A3) B3) (= A3 B3)))))
% 4.71/5.17 (assert (= tptp.ord_less_eq_set_nat (lambda ((A3 tptp.set_nat) (B3 tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat A3) B3) (= A3 B3)))))
% 4.71/5.17 (assert (= tptp.ord_less_eq_set_int (lambda ((A3 tptp.set_int) (B3 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int A3) B3) (= A3 B3)))))
% 4.71/5.17 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (or (@ (@ tptp.ord_less_nat A3) B3) (= A3 B3)))))
% 4.71/5.17 (assert (= tptp.ord_less_eq_int (lambda ((A3 tptp.int) (B3 tptp.int)) (or (@ (@ tptp.ord_less_int A3) B3) (= A3 B3)))))
% 4.71/5.17 (assert (forall ((Y tptp.extended_enat) (X tptp.extended_enat)) (=> (not (@ (@ tptp.ord_le2932123472753598470d_enat Y) X)) (@ (@ tptp.ord_le72135733267957522d_enat X) Y))))
% 4.71/5.17 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (not (@ (@ tptp.ord_less_eq_real Y) X)) (@ (@ tptp.ord_less_real X) Y))))
% 4.71/5.17 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat Y) X)) (@ (@ tptp.ord_less_nat X) Y))))
% 4.71/5.17 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int Y) X)) (@ (@ tptp.ord_less_int X) Y))))
% 4.71/5.17 (assert (= tptp.ord_le72135733267957522d_enat (lambda ((X4 tptp.extended_enat) (Y5 tptp.extended_enat)) (and (@ (@ tptp.ord_le2932123472753598470d_enat X4) Y5) (not (@ (@ tptp.ord_le2932123472753598470d_enat Y5) X4))))))
% 4.71/5.17 (assert (= tptp.ord_less_real (lambda ((X4 tptp.real) (Y5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real X4) Y5) (not (@ (@ tptp.ord_less_eq_real Y5) X4))))))
% 4.71/5.17 (assert (= tptp.ord_less_set_nat (lambda ((X4 tptp.set_nat) (Y5 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat X4) Y5) (not (@ (@ tptp.ord_less_eq_set_nat Y5) X4))))))
% 4.71/5.17 (assert (= tptp.ord_less_set_int (lambda ((X4 tptp.set_int) (Y5 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int X4) Y5) (not (@ (@ tptp.ord_less_eq_set_int Y5) X4))))))
% 4.71/5.17 (assert (= tptp.ord_less_nat (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X4) Y5) (not (@ (@ tptp.ord_less_eq_nat Y5) X4))))))
% 4.71/5.17 (assert (= tptp.ord_less_int (lambda ((X4 tptp.int) (Y5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X4) Y5) (not (@ (@ tptp.ord_less_eq_int Y5) X4))))))
% 4.71/5.17 (assert (forall ((Y tptp.real) (Z3 tptp.real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y) (@ (@ tptp.ord_less_eq_real X5) Z3))) (@ (@ tptp.ord_less_eq_real Y) Z3))))
% 4.71/5.17 (assert (forall ((Z3 tptp.real) (Y tptp.real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X5) (@ (@ tptp.ord_less_eq_real Y) X5))) (@ (@ tptp.ord_less_eq_real Y) Z3))))
% 4.71/5.17 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat X) Y) (= (not (@ (@ tptp.ord_le72135733267957522d_enat X) Y)) (= X Y)))))
% 4.71/5.17 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (= (not (@ (@ tptp.ord_less_real X) Y)) (= X Y)))))
% 4.71/5.17 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (= (not (@ (@ tptp.ord_less_set_nat X) Y)) (= X Y)))))
% 4.71/5.17 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X) Y) (= (not (@ (@ tptp.ord_less_set_int X) Y)) (= X Y)))))
% 4.71/5.17 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (= (not (@ (@ tptp.ord_less_nat X) Y)) (= X Y)))))
% 4.71/5.17 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (= (not (@ (@ tptp.ord_less_int X) Y)) (= X Y)))))
% 4.71/5.17 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (not (@ (@ tptp.ord_le72135733267957522d_enat X) Y)) (= (@ (@ tptp.ord_le2932123472753598470d_enat X) Y) (= X Y)))))
% 4.71/5.17 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_real X) Y)) (= (@ (@ tptp.ord_less_eq_real X) Y) (= X Y)))))
% 4.71/5.17 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (not (@ (@ tptp.ord_less_set_nat X) Y)) (= (@ (@ tptp.ord_less_eq_set_nat X) Y) (= X Y)))))
% 4.71/5.17 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (not (@ (@ tptp.ord_less_set_int X) Y)) (= (@ (@ tptp.ord_less_eq_set_int X) Y) (= X Y)))))
% 4.71/5.17 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (= (@ (@ tptp.ord_less_eq_nat X) Y) (= X Y)))))
% 4.71/5.17 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (= (@ (@ tptp.ord_less_eq_int X) Y) (= X Y)))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (= (not (@ (@ tptp.ord_le72135733267957522d_enat A) B2)) (or (not (@ (@ tptp.ord_le2932123472753598470d_enat A) B2)) (= A B2)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (not (@ (@ tptp.ord_less_real A) B2)) (or (not (@ (@ tptp.ord_less_eq_real A) B2)) (= A B2)))))
% 4.71/5.17 (assert (forall ((A tptp.set_nat) (B2 tptp.set_nat)) (= (not (@ (@ tptp.ord_less_set_nat A) B2)) (or (not (@ (@ tptp.ord_less_eq_set_nat A) B2)) (= A B2)))))
% 4.71/5.17 (assert (forall ((A tptp.set_int) (B2 tptp.set_int)) (= (not (@ (@ tptp.ord_less_set_int A) B2)) (or (not (@ (@ tptp.ord_less_eq_set_int A) B2)) (= A B2)))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat A) B2)) (or (not (@ (@ tptp.ord_less_eq_nat A) B2)) (= A B2)))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (not (@ (@ tptp.ord_less_int A) B2)) (or (not (@ (@ tptp.ord_less_eq_int A) B2)) (= A B2)))))
% 4.71/5.17 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (not (@ (@ tptp.ord_le72135733267957522d_enat X) Y)) (@ (@ tptp.ord_le2932123472753598470d_enat Y) X))))
% 4.71/5.17 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_real X) Y)) (@ (@ tptp.ord_less_eq_real Y) X))))
% 4.71/5.17 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))))
% 4.71/5.17 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_eq_int Y) X))))
% 4.71/5.17 (assert (forall ((Y tptp.extended_enat) (X tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Y) X) (not (@ (@ tptp.ord_le72135733267957522d_enat X) Y)))))
% 4.71/5.17 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y) X) (not (@ (@ tptp.ord_less_real X) Y)))))
% 4.71/5.17 (assert (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X) (not (@ (@ tptp.ord_less_set_nat X) Y)))))
% 4.71/5.17 (assert (forall ((Y tptp.set_int) (X tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y) X) (not (@ (@ tptp.ord_less_set_int X) Y)))))
% 4.71/5.17 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (not (@ (@ tptp.ord_less_nat X) Y)))))
% 4.71/5.17 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (not (@ (@ tptp.ord_less_int X) Y)))))
% 4.71/5.17 (assert (forall ((F (-> tptp.nat tptp.nat)) (I tptp.nat) (J tptp.nat)) (=> (forall ((I4 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) J3) (@ (@ tptp.ord_less_nat (@ F I4)) (@ F J3)))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ F I)) (@ F J))))))
% 4.71/5.17 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (=> (not (= M2 N2)) (@ (@ tptp.ord_less_nat M2) N2)))))
% 4.71/5.17 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat M2) N2) (= M2 N2)) (@ (@ tptp.ord_less_eq_nat M2) N2))))
% 4.71/5.17 (assert (= tptp.ord_less_eq_nat (lambda ((M tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_nat M) N) (= M N)))))
% 4.71/5.17 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.vEBT_invar_vebt (@ tptp.vEBT_vebt_buildup N2)) N2))))
% 4.71/5.17 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat B2) A)) B2) (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))))
% 4.71/5.17 (assert (forall ((B2 tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real B2) A)) B2) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 4.71/5.17 (assert (forall ((B2 tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int B2) A)) B2) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) B2)) B2) (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B2)) B2) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B2)) B2) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat A) B2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real A) B2)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) B2))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int A) B2)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat B2) A)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real B2) A)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) B2))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int B2) A)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2))))
% 4.71/5.17 (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))))
% 4.71/5.17 (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))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (assert (forall ((B2 tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real B2) A)) B2) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))))
% 4.71/5.17 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat B2) A)) B2) (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat))))
% 4.71/5.17 (assert (forall ((B2 tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int B2) A)) B2) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) B2)) B2) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) B2)) B2) (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) B2)) B2) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.plus_plus_real A) B2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B2))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.plus_plus_nat A) B2)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B2))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.plus_plus_int A) B2)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B2))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.plus_plus_real B2) A)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B2))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.plus_plus_nat B2) A)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B2))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.plus_plus_int B2) A)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B2))))
% 4.71/5.17 (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))))
% 4.71/5.17 (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))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))))
% 4.71/5.17 (assert (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B2) A) (@ (@ tptp.plus_plus_nat C) A)) (= B2 C))))
% 4.71/5.17 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (= (= (@ (@ tptp.plus_plus_int B2) A) (@ (@ tptp.plus_plus_int C) A)) (= B2 C))))
% 4.71/5.17 (assert (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (= (= (@ (@ tptp.plus_plus_real B2) A) (@ (@ tptp.plus_plus_real C) A)) (= B2 C))))
% 4.71/5.17 (assert (forall ((N2 tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat N2) tptp.zero_z5237406670263579293d_enat) (= N2 tptp.zero_z5237406670263579293d_enat))))
% 4.71/5.17 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N2) tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat))))
% 4.71/5.17 (assert (forall ((N2 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= N2 tptp.zero_zero_nat))))
% 4.71/5.17 (assert (forall ((N2 tptp.extended_enat)) (= (not (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) N2)) (= N2 tptp.zero_z5237406670263579293d_enat))))
% 4.71/5.17 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_real A) B2)))))
% 4.71/5.17 (assert (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_nat A) B2)))))
% 4.71/5.17 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_int A) B2)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B2) C)) (@ (@ tptp.ord_less_eq_real A) B2))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B2) C)) (@ (@ tptp.ord_less_eq_nat A) B2))))
% 4.71/5.17 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B2) C)) (@ (@ tptp.ord_less_eq_int A) B2))))
% 4.71/5.17 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 4.71/5.17 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 4.71/5.17 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 4.71/5.17 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat)) (= (@ (@ tptp.plus_p3455044024723400733d_enat A) tptp.zero_z5237406670263579293d_enat) A)))
% 4.71/5.17 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.plus_plus_real A) A)) (= A tptp.zero_zero_real))))
% 4.71/5.17 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ (@ tptp.plus_plus_int A) A)) (= A tptp.zero_zero_int))))
% 4.71/5.17 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B2) A) A) (= B2 tptp.zero_zero_nat))))
% 4.71/5.17 (assert (forall ((B2 tptp.real) (A tptp.real)) (= (= (@ (@ tptp.plus_plus_real B2) A) A) (= B2 tptp.zero_zero_real))))
% 4.71/5.17 (assert (forall ((B2 tptp.int) (A tptp.int)) (= (= (@ (@ tptp.plus_plus_int B2) A) A) (= B2 tptp.zero_zero_int))))
% 4.71/5.17 (assert (forall ((B2 tptp.complex) (A tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex B2) A) A) (= B2 tptp.zero_zero_complex))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat A) B2) A) (= B2 tptp.zero_zero_nat))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) B2) A) (= B2 tptp.zero_zero_real))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) B2) A) (= B2 tptp.zero_zero_int))))
% 4.71/5.17 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex A) B2) A) (= B2 tptp.zero_zero_complex))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat B2) A)) (= B2 tptp.zero_zero_nat))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (= A (@ (@ tptp.plus_plus_real B2) A)) (= B2 tptp.zero_zero_real))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (= A (@ (@ tptp.plus_plus_int B2) A)) (= B2 tptp.zero_zero_int))))
% 4.71/5.17 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (= A (@ (@ tptp.plus_plus_complex B2) A)) (= B2 tptp.zero_zero_complex))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat A) B2)) (= B2 tptp.zero_zero_nat))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (= A (@ (@ tptp.plus_plus_real A) B2)) (= B2 tptp.zero_zero_real))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (= A (@ (@ tptp.plus_plus_int A) B2)) (= B2 tptp.zero_zero_int))))
% 4.71/5.17 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (= A (@ (@ tptp.plus_plus_complex A) B2)) (= B2 tptp.zero_zero_complex))))
% 4.71/5.17 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))
% 4.71/5.17 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (= (= (@ (@ tptp.plus_p3455044024723400733d_enat X) Y) tptp.zero_z5237406670263579293d_enat) (and (= X tptp.zero_z5237406670263579293d_enat) (= Y tptp.zero_z5237406670263579293d_enat)))))
% 4.71/5.17 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.plus_plus_nat X) Y)) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))
% 4.71/5.17 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (= (= tptp.zero_z5237406670263579293d_enat (@ (@ tptp.plus_p3455044024723400733d_enat X) Y)) (and (= X tptp.zero_z5237406670263579293d_enat) (= Y tptp.zero_z5237406670263579293d_enat)))))
% 4.71/5.17 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)))
% 4.71/5.17 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 4.71/5.17 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 4.71/5.17 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat)) (= (@ (@ tptp.plus_p3455044024723400733d_enat tptp.zero_z5237406670263579293d_enat) A) A)))
% 4.71/5.17 (assert (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (= (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_nat A) B2)))))
% 4.71/5.17 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_real A) B2)))))
% 4.71/5.17 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_int A) B2)))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B2) C)) (@ (@ tptp.ord_less_nat A) B2))))
% 4.71/5.17 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B2) C)) (@ (@ tptp.ord_less_real A) B2))))
% 4.71/5.17 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B2) C)) (@ (@ tptp.ord_less_int A) B2))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (assert (forall ((X tptp.nat)) (= (= tptp.zero_zero_nat X) (= X tptp.zero_zero_nat))))
% 4.71/5.17 (assert (forall ((X tptp.real)) (= (= tptp.zero_zero_real X) (= X tptp.zero_zero_real))))
% 4.71/5.17 (assert (forall ((X tptp.int)) (= (= tptp.zero_zero_int X) (= X tptp.zero_zero_int))))
% 4.71/5.17 (assert (forall ((X tptp.complex)) (= (= tptp.zero_zero_complex X) (= X tptp.zero_zero_complex))))
% 4.71/5.17 (assert (forall ((X tptp.extended_enat)) (= (= tptp.zero_z5237406670263579293d_enat X) (= X tptp.zero_z5237406670263579293d_enat))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B2) C))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B2) C))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_real B2) C))))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat A))) (= (@ (@ tptp.plus_p3455044024723400733d_enat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_p3455044024723400733d_enat B2) C))))))
% 4.71/5.17 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I J) (= K L)) (= (@ (@ tptp.plus_plus_nat I) K) (@ (@ tptp.plus_plus_nat J) L)))))
% 4.71/5.17 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (= I J) (= K L)) (= (@ (@ tptp.plus_plus_int I) K) (@ (@ tptp.plus_plus_int J) L)))))
% 4.71/5.17 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (= I J) (= K L)) (= (@ (@ tptp.plus_plus_real I) K) (@ (@ tptp.plus_plus_real J) L)))))
% 4.71/5.17 (assert (forall ((I tptp.extended_enat) (J tptp.extended_enat) (K tptp.extended_enat) (L tptp.extended_enat)) (=> (and (= I J) (= K L)) (= (@ (@ tptp.plus_p3455044024723400733d_enat I) K) (@ (@ tptp.plus_p3455044024723400733d_enat J) L)))))
% 4.71/5.17 (assert (forall ((A2 tptp.nat) (K tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_nat A2) B2) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B2)))))))
% 4.71/5.17 (assert (forall ((A2 tptp.int) (K tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_int A2) B2) (@ _let_1 (@ (@ tptp.plus_plus_int A) B2)))))))
% 4.71/5.17 (assert (forall ((A2 tptp.real) (K tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_real A2) B2) (@ _let_1 (@ (@ tptp.plus_plus_real A) B2)))))))
% 4.71/5.17 (assert (forall ((A2 tptp.extended_enat) (K tptp.extended_enat) (A tptp.extended_enat) (B2 tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.plus_p3455044024723400733d_enat A2) B2) (@ _let_1 (@ (@ tptp.plus_p3455044024723400733d_enat A) B2)))))))
% 4.71/5.17 (assert (forall ((B tptp.nat) (K tptp.nat) (B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (let ((_let_2 (@ tptp.plus_plus_nat K))) (=> (= B (@ _let_2 B2)) (= (@ _let_1 B) (@ _let_2 (@ _let_1 B2))))))))
% 4.71/5.17 (assert (forall ((B tptp.int) (K tptp.int) (B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (let ((_let_2 (@ tptp.plus_plus_int K))) (=> (= B (@ _let_2 B2)) (= (@ _let_1 B) (@ _let_2 (@ _let_1 B2))))))))
% 4.71/5.17 (assert (forall ((B tptp.real) (K tptp.real) (B2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (let ((_let_2 (@ tptp.plus_plus_real K))) (=> (= B (@ _let_2 B2)) (= (@ _let_1 B) (@ _let_2 (@ _let_1 B2))))))))
% 4.71/5.17 (assert (forall ((B tptp.extended_enat) (K tptp.extended_enat) (B2 tptp.extended_enat) (A tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat A))) (let ((_let_2 (@ tptp.plus_p3455044024723400733d_enat K))) (=> (= B (@ _let_2 B2)) (= (@ _let_1 B) (@ _let_2 (@ _let_1 B2))))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B2) C))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B2) C))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_real B2) C))))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat A))) (= (@ (@ tptp.plus_p3455044024723400733d_enat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_p3455044024723400733d_enat B2) C))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))))
% 4.71/5.17 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (= (= (@ (@ tptp.plus_plus_int B2) A) (@ (@ tptp.plus_plus_int C) A)) (= B2 C))))
% 4.71/5.17 (assert (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (= (= (@ (@ tptp.plus_plus_real B2) A) (@ (@ tptp.plus_plus_real C) A)) (= B2 C))))
% 4.71/5.17 (assert (= tptp.plus_plus_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.plus_plus_nat B3) A3))))
% 4.71/5.17 (assert (= tptp.plus_plus_int (lambda ((A3 tptp.int) (B3 tptp.int)) (@ (@ tptp.plus_plus_int B3) A3))))
% 4.71/5.17 (assert (= tptp.plus_plus_real (lambda ((A3 tptp.real) (B3 tptp.real)) (@ (@ tptp.plus_plus_real B3) A3))))
% 4.71/5.17 (assert (= tptp.plus_p3455044024723400733d_enat (lambda ((A3 tptp.extended_enat) (B3 tptp.extended_enat)) (@ (@ tptp.plus_p3455044024723400733d_enat B3) A3))))
% 4.71/5.17 (assert (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat B2))) (let ((_let_2 (@ tptp.plus_plus_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 4.71/5.17 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int B2))) (let ((_let_2 (@ tptp.plus_plus_int A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 4.71/5.17 (assert (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real B2))) (let ((_let_2 (@ tptp.plus_plus_real A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 4.71/5.17 (assert (forall ((B2 tptp.extended_enat) (A tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat B2))) (let ((_let_2 (@ tptp.plus_p3455044024723400733d_enat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (=> (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (=> (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (=> (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))))
% 4.71/5.17 (assert (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat B2) A) (@ (@ tptp.plus_plus_nat C) A)) (= B2 C))))
% 4.71/5.17 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (= (@ (@ tptp.plus_plus_int B2) A) (@ (@ tptp.plus_plus_int C) A)) (= B2 C))))
% 4.71/5.17 (assert (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (=> (= (@ (@ tptp.plus_plus_real B2) A) (@ (@ tptp.plus_plus_real C) A)) (= B2 C))))
% 4.71/5.17 (assert (forall ((X tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) X)))
% 4.71/5.17 (assert (forall ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X)))
% 4.71/5.17 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 4.71/5.17 (assert (forall ((N2 tptp.extended_enat)) (=> (not (= N2 tptp.zero_z5237406670263579293d_enat)) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) N2))))
% 4.71/5.17 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) tptp.zero_zero_nat))))
% 4.71/5.17 (assert (forall ((N2 tptp.extended_enat)) (not (@ (@ tptp.ord_le72135733267957522d_enat N2) tptp.zero_z5237406670263579293d_enat))))
% 4.71/5.17 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N2) (not (= N2 tptp.zero_zero_nat)))))
% 4.71/5.17 (assert (forall ((M2 tptp.extended_enat) (N2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat M2) N2) (not (= N2 tptp.zero_z5237406670263579293d_enat)))))
% 4.71/5.17 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (not (= N2 tptp.zero_zero_nat)))))
% 4.71/5.17 (assert (forall ((N2 tptp.extended_enat)) (= (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) N2) (not (= N2 tptp.zero_z5237406670263579293d_enat)))))
% 4.71/5.17 (assert (forall ((I tptp.extended_enat) (J tptp.extended_enat) (K tptp.extended_enat) (L tptp.extended_enat)) (=> (and (@ (@ tptp.ord_le2932123472753598470d_enat I) J) (= K L)) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.plus_p3455044024723400733d_enat I) K)) (@ (@ tptp.plus_p3455044024723400733d_enat J) L)))))
% 4.71/5.17 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I) J) (= K L)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 4.71/5.17 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I) J) (= K L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 4.71/5.17 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I) J) (= K L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 4.71/5.17 (assert (forall ((I tptp.extended_enat) (J tptp.extended_enat) (K tptp.extended_enat) (L tptp.extended_enat)) (=> (and (= I J) (@ (@ tptp.ord_le2932123472753598470d_enat K) L)) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.plus_p3455044024723400733d_enat I) K)) (@ (@ tptp.plus_p3455044024723400733d_enat J) L)))))
% 4.71/5.17 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (= I J) (@ (@ tptp.ord_less_eq_real K) L)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 4.71/5.17 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I J) (@ (@ tptp.ord_less_eq_nat K) L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 4.71/5.17 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (= I J) (@ (@ tptp.ord_less_eq_int K) L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 4.71/5.17 (assert (forall ((I tptp.extended_enat) (J tptp.extended_enat) (K tptp.extended_enat) (L tptp.extended_enat)) (=> (and (@ (@ tptp.ord_le2932123472753598470d_enat I) J) (@ (@ tptp.ord_le2932123472753598470d_enat K) L)) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.plus_p3455044024723400733d_enat I) K)) (@ (@ tptp.plus_p3455044024723400733d_enat J) L)))))
% 4.71/5.17 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I) J) (@ (@ tptp.ord_less_eq_real K) L)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 4.71/5.17 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat K) L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 4.71/5.17 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I) J) (@ (@ tptp.ord_less_eq_int K) L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat) (D tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B2) (=> (@ (@ tptp.ord_le2932123472753598470d_enat C) D) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) C)) (@ (@ tptp.plus_p3455044024723400733d_enat B2) D))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_eq_real C) D) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B2) D))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ tptp.ord_less_eq_nat C) D) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B2) D))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (@ (@ tptp.ord_less_eq_int C) D) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B2) D))))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat C))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B2) (@ (@ tptp.ord_le2932123472753598470d_enat (@ _let_1 A)) (@ _let_1 B2))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (=> (@ (@ tptp.ord_less_eq_real A) B2) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B2))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B2))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_eq_int A) B2) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B2))))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B2) (not (forall ((C2 tptp.extended_enat)) (not (= B2 (@ (@ tptp.plus_p3455044024723400733d_enat A) C2))))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (not (forall ((C2 tptp.nat)) (not (= B2 (@ (@ tptp.plus_plus_nat A) C2))))))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B2) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) C)) (@ (@ tptp.plus_p3455044024723400733d_enat B2) C)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B2) C)))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B2) C)))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B2) C)))))
% 4.71/5.17 (assert (= tptp.ord_le2932123472753598470d_enat (lambda ((A3 tptp.extended_enat) (B3 tptp.extended_enat)) (exists ((C3 tptp.extended_enat)) (= B3 (@ (@ tptp.plus_p3455044024723400733d_enat A3) C3))))))
% 4.71/5.17 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (exists ((C3 tptp.nat)) (= B3 (@ (@ tptp.plus_plus_nat A3) C3))))))
% 4.71/5.17 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (=> (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_real A) B2)))))
% 4.71/5.17 (assert (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_nat A) B2)))))
% 4.71/5.17 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_int A) B2)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B2) C)) (@ (@ tptp.ord_less_eq_real A) B2))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B2) C)) (@ (@ tptp.ord_less_eq_nat A) B2))))
% 4.71/5.17 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B2) C)) (@ (@ tptp.ord_less_eq_int A) B2))))
% 4.71/5.17 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)))
% 4.71/5.17 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 4.71/5.17 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 4.71/5.17 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat)) (= (@ (@ tptp.plus_p3455044024723400733d_enat tptp.zero_z5237406670263579293d_enat) A) A)))
% 4.71/5.17 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 4.71/5.17 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 4.71/5.17 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 4.71/5.17 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat)) (= (@ (@ tptp.plus_p3455044024723400733d_enat A) tptp.zero_z5237406670263579293d_enat) A)))
% 4.71/5.17 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 4.71/5.17 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 4.71/5.17 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)))
% 4.71/5.17 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I) J) (@ (@ tptp.ord_less_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 4.71/5.17 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_real I) J) (@ (@ tptp.ord_less_real K) L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 4.71/5.17 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I) J) (@ (@ tptp.ord_less_int K) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 4.71/5.17 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I J) (@ (@ tptp.ord_less_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 4.71/5.17 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (= I J) (@ (@ tptp.ord_less_real K) L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 4.71/5.17 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (= I J) (@ (@ tptp.ord_less_int K) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 4.71/5.17 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I) J) (= K L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 4.71/5.17 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_real I) J) (= K L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 4.71/5.17 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I) J) (= K L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (=> (@ (@ tptp.ord_less_nat C) D) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B2) D))))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat) (D tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B2) (=> (@ (@ tptp.ord_le72135733267957522d_enat C) D) (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) C)) (@ (@ tptp.plus_p3455044024723400733d_enat B2) D))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.ord_less_real C) D) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B2) D))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A) B2) (=> (@ (@ tptp.ord_less_int C) D) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B2) D))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_nat A) B2) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B2))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (=> (@ (@ tptp.ord_less_real A) B2) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B2))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_int A) B2) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B2))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B2) C)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B2) C)))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B2) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B2) C)))))
% 4.71/5.17 (assert (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_nat A) B2)))))
% 4.71/5.17 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_real A) B2)))))
% 4.71/5.17 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_int A) B2)))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B2) C)) (@ (@ tptp.ord_less_nat A) B2))))
% 4.71/5.17 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B2) C)) (@ (@ tptp.ord_less_real A) B2))))
% 4.71/5.17 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B2) C)) (@ (@ tptp.ord_less_int A) B2))))
% 4.71/5.17 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat X) tptp.zero_z5237406670263579293d_enat) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Y) tptp.zero_z5237406670263579293d_enat) (= (= (@ (@ tptp.plus_p3455044024723400733d_enat X) Y) tptp.zero_z5237406670263579293d_enat) (and (= X tptp.zero_z5237406670263579293d_enat) (= Y tptp.zero_z5237406670263579293d_enat)))))))
% 4.71/5.17 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (= (= (@ (@ tptp.plus_plus_real X) Y) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real)))))))
% 4.71/5.17 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat Y) tptp.zero_zero_nat) (= (= (@ (@ tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))))
% 4.71/5.17 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.zero_zero_int) (= (= (@ (@ tptp.plus_plus_int X) Y) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))))))
% 4.71/5.17 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_p3455044024723400733d_enat X) Y) tptp.zero_z5237406670263579293d_enat) (and (= X tptp.zero_z5237406670263579293d_enat) (= Y tptp.zero_z5237406670263579293d_enat))))))))
% 4.71/5.17 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_real X) Y) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real))))))))
% 4.71/5.17 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat))))))))
% 4.71/5.17 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_int X) Y) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int))))))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) tptp.zero_z5237406670263579293d_enat) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B2) tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) B2)) tptp.zero_z5237406670263579293d_enat)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) B2)) tptp.zero_zero_real)))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat B2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) B2)) tptp.zero_zero_nat)))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) B2)) tptp.zero_zero_int)))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_p3455044024723400733d_enat A) B2)))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_real A) B2)))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B2)))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_int A) B2)))))))
% 4.71/5.17 (assert (forall ((C tptp.extended_enat) (B2 tptp.extended_enat) (A tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat B2))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_p3455044024723400733d_enat A) C)))))))
% 4.71/5.17 (assert (forall ((C tptp.real) (B2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real B2))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_real A) C)))))))
% 4.71/5.17 (assert (forall ((C tptp.nat) (B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C)))))))
% 4.71/5.17 (assert (forall ((C tptp.int) (B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int B2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_int A) C)))))))
% 4.71/5.17 (assert (forall ((C tptp.extended_enat) (A tptp.extended_enat) (B2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat C) tptp.zero_z5237406670263579293d_enat) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B2) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) C)) B2)))))
% 4.71/5.17 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real A) B2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) B2)))))
% 4.71/5.17 (assert (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) B2)))))
% 4.71/5.17 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int A) B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) B2)))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat B2))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_p3455044024723400733d_enat A) C)))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real B2))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_real A) C)))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C)))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int B2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int A) C)))))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (C tptp.extended_enat) (B2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) tptp.zero_z5237406670263579293d_enat) (=> (@ (@ tptp.ord_le2932123472753598470d_enat C) B2) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) C)) B2)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real C) B2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) B2)))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat C) B2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) B2)))))
% 4.71/5.17 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int C) B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) B2)))))
% 4.71/5.17 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I) J) (@ (@ tptp.ord_less_real K) L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 4.71/5.17 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 4.71/5.17 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I) J) (@ (@ tptp.ord_less_int K) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 4.71/5.17 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_real I) J) (@ (@ tptp.ord_less_eq_real K) L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 4.71/5.17 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I) J) (@ (@ tptp.ord_less_eq_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 4.71/5.17 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I) J) (@ (@ tptp.ord_less_eq_int K) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_real C) D) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B2) D))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ tptp.ord_less_nat C) D) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B2) D))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (@ (@ tptp.ord_less_int C) D) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B2) D))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.ord_less_eq_real C) D) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B2) D))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (=> (@ (@ tptp.ord_less_eq_nat C) D) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B2) D))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A) B2) (=> (@ (@ tptp.ord_less_eq_int C) D) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B2) D))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat B2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C)))))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat B2))) (=> (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_p3455044024723400733d_enat A) C)))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real B2))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_real A) C)))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int A) C)))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (not (forall ((C2 tptp.nat)) (=> (= B2 (@ (@ tptp.plus_plus_nat A) C2)) (= C2 tptp.zero_zero_nat)))))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B2) (not (forall ((C2 tptp.extended_enat)) (=> (= B2 (@ (@ tptp.plus_p3455044024723400733d_enat A) C2)) (= C2 tptp.zero_z5237406670263579293d_enat)))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B2)))))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_p3455044024723400733d_enat A) B2)))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_real A) B2)))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_int A) B2)))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat B2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) B2)) tptp.zero_zero_nat)))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) tptp.zero_z5237406670263579293d_enat) (=> (@ (@ tptp.ord_le72135733267957522d_enat B2) tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) B2)) tptp.zero_z5237406670263579293d_enat)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real B2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B2)) tptp.zero_zero_real)))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B2)) tptp.zero_zero_int)))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) tptp.zero_z5237406670263579293d_enat) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B2) tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) B2)) tptp.zero_z5237406670263579293d_enat)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B2)) tptp.zero_zero_real)))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat B2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) B2)) tptp.zero_zero_nat)))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B2)) tptp.zero_zero_int)))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_p3455044024723400733d_enat A) B2)))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_real A) B2)))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B2)))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_int A) B2)))))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) tptp.zero_z5237406670263579293d_enat) (=> (@ (@ tptp.ord_le72135733267957522d_enat B2) tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) B2)) tptp.zero_z5237406670263579293d_enat)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real B2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B2)) tptp.zero_zero_real)))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat B2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) B2)) tptp.zero_zero_nat)))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B2)) tptp.zero_zero_int)))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) B2) (@ _let_1 (@ (@ tptp.plus_p3455044024723400733d_enat A) B2)))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B2) (@ _let_1 (@ (@ tptp.plus_plus_real A) B2)))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B2) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B2)))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B2) (@ _let_1 (@ (@ tptp.plus_plus_int A) B2)))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real B2) C) (@ (@ tptp.ord_less_real B2) (@ (@ tptp.plus_plus_real A) C))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (@ (@ tptp.ord_less_nat B2) (@ (@ tptp.plus_plus_nat A) C))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int B2) C) (@ (@ tptp.ord_less_int B2) (@ (@ tptp.plus_plus_int A) C))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real B2))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_real A) C)))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat B2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C)))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int A) C)))))))
% 4.71/5.17 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 4.71/5.17 (assert (forall ((A tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 4.71/5.17 (assert (forall ((N2 tptp.nat) (X tptp.nat)) (not (@ (@ tptp.vEBT_V5719532721284313246member (@ tptp.vEBT_vebt_buildup N2)) X))))
% 4.71/5.17 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (forall ((E tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.plus_plus_real Y) E)))) (@ (@ tptp.ord_less_eq_real X) Y))))
% 4.71/5.17 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real X) Y)) tptp.zero_zero_real) (or (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real)))))
% 4.71/5.17 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int X) Y)) tptp.zero_zero_int) (or (@ (@ tptp.ord_less_int X) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Y) tptp.zero_zero_int)))))
% 4.71/5.17 (assert (forall ((N2 tptp.nat)) (= (@ tptp.vEBT_VEBT_set_vebt (@ tptp.vEBT_vebt_buildup N2)) tptp.bot_bot_set_nat)))
% 4.71/5.17 (assert (forall ((A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat)) (=> (forall ((X5 tptp.extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat X5))) (=> (@ _let_1 A2) (@ _let_1 B)))) (@ (@ tptp.ord_le7203529160286727270d_enat A2) B))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_real) (B tptp.set_real)) (=> (forall ((X5 tptp.real)) (let ((_let_1 (@ tptp.member_real X5))) (=> (@ _let_1 A2) (@ _let_1 B)))) (@ (@ tptp.ord_less_eq_set_real A2) B))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_set_nat) (B tptp.set_set_nat)) (=> (forall ((X5 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X5))) (=> (@ _let_1 A2) (@ _let_1 B)))) (@ (@ tptp.ord_le6893508408891458716et_nat A2) B))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (=> (forall ((X5 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X5))) (=> (@ _let_1 A2) (@ _let_1 B)))) (@ (@ tptp.ord_less_eq_set_nat A2) B))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_int) (B tptp.set_int)) (=> (forall ((X5 tptp.int)) (let ((_let_1 (@ tptp.member_int X5))) (=> (@ _let_1 A2) (@ _let_1 B)))) (@ (@ tptp.ord_less_eq_set_int A2) B))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B) (=> (not (= A2 B)) (@ (@ tptp.ord_less_set_nat A2) B)))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B) (=> (not (= A2 B)) (@ (@ tptp.ord_less_set_int A2) B)))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B) (=> (@ (@ tptp.ord_less_eq_set_nat B) A2) (= A2 B)))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B) (=> (@ (@ tptp.ord_less_eq_set_int B) A2) (= A2 B)))))
% 4.71/5.17 (assert (forall ((N2 tptp.nat) (X tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ tptp.vEBT_vebt_buildup N2)) X))))
% 4.71/5.17 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (@ tptp.finite_finite_nat (@ tptp.vEBT_VEBT_set_vebt T)))))
% 4.71/5.17 (assert (= tptp.vEBT_V8194947554948674370ptions (lambda ((T2 tptp.vEBT_VEBT) (X4 tptp.nat)) (or (@ (@ tptp.vEBT_V5719532721284313246member T2) X4) (@ (@ tptp.vEBT_VEBT_membermima T2) X4)))))
% 4.71/5.17 (assert (forall ((P (-> tptp.list_nat Bool))) (= (= tptp.bot_bot_set_list_nat (@ tptp.collect_list_nat P)) (forall ((X4 tptp.list_nat)) (not (@ P X4))))))
% 4.71/5.17 (assert (forall ((P (-> tptp.set_nat Bool))) (= (= tptp.bot_bot_set_set_nat (@ tptp.collect_set_nat P)) (forall ((X4 tptp.set_nat)) (not (@ P X4))))))
% 4.71/5.17 (assert (forall ((P (-> tptp.extended_enat Bool))) (= (= tptp.bot_bo7653980558646680370d_enat (@ tptp.collec4429806609662206161d_enat P)) (forall ((X4 tptp.extended_enat)) (not (@ P X4))))))
% 4.71/5.17 (assert (forall ((P (-> tptp.real Bool))) (= (= tptp.bot_bot_set_real (@ tptp.collect_real P)) (forall ((X4 tptp.real)) (not (@ P X4))))))
% 4.71/5.17 (assert (forall ((P (-> tptp.nat Bool))) (= (= tptp.bot_bot_set_nat (@ tptp.collect_nat P)) (forall ((X4 tptp.nat)) (not (@ P X4))))))
% 4.71/5.17 (assert (forall ((P (-> tptp.int Bool))) (= (= tptp.bot_bot_set_int (@ tptp.collect_int P)) (forall ((X4 tptp.int)) (not (@ P X4))))))
% 4.71/5.17 (assert (forall ((P (-> tptp.list_nat Bool))) (= (= (@ tptp.collect_list_nat P) tptp.bot_bot_set_list_nat) (forall ((X4 tptp.list_nat)) (not (@ P X4))))))
% 4.71/5.17 (assert (forall ((P (-> tptp.set_nat Bool))) (= (= (@ tptp.collect_set_nat P) tptp.bot_bot_set_set_nat) (forall ((X4 tptp.set_nat)) (not (@ P X4))))))
% 4.71/5.17 (assert (forall ((P (-> tptp.extended_enat Bool))) (= (= (@ tptp.collec4429806609662206161d_enat P) tptp.bot_bo7653980558646680370d_enat) (forall ((X4 tptp.extended_enat)) (not (@ P X4))))))
% 4.71/5.17 (assert (forall ((P (-> tptp.real Bool))) (= (= (@ tptp.collect_real P) tptp.bot_bot_set_real) (forall ((X4 tptp.real)) (not (@ P X4))))))
% 4.71/5.17 (assert (forall ((P (-> tptp.nat Bool))) (= (= (@ tptp.collect_nat P) tptp.bot_bot_set_nat) (forall ((X4 tptp.nat)) (not (@ P X4))))))
% 4.71/5.17 (assert (forall ((P (-> tptp.int Bool))) (= (= (@ tptp.collect_int P) tptp.bot_bot_set_int) (forall ((X4 tptp.int)) (not (@ P X4))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_set_nat)) (= (forall ((X4 tptp.set_nat)) (not (@ (@ tptp.member_set_nat X4) A2))) (= A2 tptp.bot_bot_set_set_nat))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_Extended_enat)) (= (forall ((X4 tptp.extended_enat)) (not (@ (@ tptp.member_Extended_enat X4) A2))) (= A2 tptp.bot_bo7653980558646680370d_enat))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_real)) (= (forall ((X4 tptp.real)) (not (@ (@ tptp.member_real X4) A2))) (= A2 tptp.bot_bot_set_real))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_nat)) (= (forall ((X4 tptp.nat)) (not (@ (@ tptp.member_nat X4) A2))) (= A2 tptp.bot_bot_set_nat))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_int)) (= (forall ((X4 tptp.int)) (not (@ (@ tptp.member_int X4) A2))) (= A2 tptp.bot_bot_set_int))))
% 4.71/5.17 (assert (forall ((C tptp.set_nat)) (not (@ (@ tptp.member_set_nat C) tptp.bot_bot_set_set_nat))))
% 4.71/5.17 (assert (forall ((C tptp.extended_enat)) (not (@ (@ tptp.member_Extended_enat C) tptp.bot_bo7653980558646680370d_enat))))
% 4.71/5.17 (assert (forall ((C tptp.real)) (not (@ (@ tptp.member_real C) tptp.bot_bot_set_real))))
% 4.71/5.17 (assert (forall ((C tptp.nat)) (not (@ (@ tptp.member_nat C) tptp.bot_bot_set_nat))))
% 4.71/5.17 (assert (forall ((C tptp.int)) (not (@ (@ tptp.member_int C) tptp.bot_bot_set_int))))
% 4.71/5.17 (assert (forall ((Tree tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt Tree) N2) (=> (@ (@ tptp.vEBT_vebt_member Tree) X) (or (@ (@ tptp.vEBT_V5719532721284313246member Tree) X) (@ (@ tptp.vEBT_VEBT_membermima Tree) X))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_Extended_enat)) (@ (@ tptp.ord_le7203529160286727270d_enat tptp.bot_bo7653980558646680370d_enat) A2)))
% 4.71/5.17 (assert (forall ((A2 tptp.set_real)) (@ (@ tptp.ord_less_eq_set_real tptp.bot_bot_set_real) A2)))
% 4.71/5.17 (assert (forall ((A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat tptp.bot_bot_set_nat) A2)))
% 4.71/5.17 (assert (forall ((A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int tptp.bot_bot_set_int) A2)))
% 4.71/5.17 (assert (forall ((A2 tptp.set_Extended_enat)) (= (@ (@ tptp.ord_le7203529160286727270d_enat A2) tptp.bot_bo7653980558646680370d_enat) (= A2 tptp.bot_bo7653980558646680370d_enat))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real A2) tptp.bot_bot_set_real) (= A2 tptp.bot_bot_set_real))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A2) tptp.bot_bot_set_nat) (= A2 tptp.bot_bot_set_nat))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A2) tptp.bot_bot_set_int) (= A2 tptp.bot_bot_set_int))))
% 4.71/5.17 (assert (forall ((Xs tptp.list_VEBT_VEBT)) (@ tptp.finite5795047828879050333T_VEBT (@ tptp.set_VEBT_VEBT2 Xs))))
% 4.71/5.17 (assert (forall ((Xs tptp.list_nat)) (@ tptp.finite_finite_nat (@ tptp.set_nat2 Xs))))
% 4.71/5.17 (assert (forall ((Xs tptp.list_complex)) (@ tptp.finite3207457112153483333omplex (@ tptp.set_complex2 Xs))))
% 4.71/5.17 (assert (forall ((Xs tptp.list_int)) (@ tptp.finite_finite_int (@ tptp.set_int2 Xs))))
% 4.71/5.17 (assert (forall ((Xs tptp.list_Extended_enat)) (@ tptp.finite4001608067531595151d_enat (@ tptp.set_Extended_enat2 Xs))))
% 4.71/5.17 (assert (forall ((S2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S2) (=> (not (= S2 tptp.bot_bot_set_nat)) (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) S2) (not (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) S2) (@ (@ tptp.ord_less_nat Xa) X5))))))))))
% 4.71/5.17 (assert (forall ((S2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat S2) (=> (not (= S2 tptp.bot_bo7653980558646680370d_enat)) (exists ((X5 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X5) S2) (not (exists ((Xa tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat Xa) S2) (@ (@ tptp.ord_le72135733267957522d_enat Xa) X5))))))))))
% 4.71/5.17 (assert (forall ((S2 tptp.set_real)) (=> (@ tptp.finite_finite_real S2) (=> (not (= S2 tptp.bot_bot_set_real)) (exists ((X5 tptp.real)) (and (@ (@ tptp.member_real X5) S2) (not (exists ((Xa tptp.real)) (and (@ (@ tptp.member_real Xa) S2) (@ (@ tptp.ord_less_real Xa) X5))))))))))
% 4.71/5.17 (assert (forall ((S2 tptp.set_int)) (=> (@ tptp.finite_finite_int S2) (=> (not (= S2 tptp.bot_bot_set_int)) (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) S2) (not (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) S2) (@ (@ tptp.ord_less_int Xa) X5))))))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_Extended_enat)) (not (@ (@ tptp.ord_le2529575680413868914d_enat A2) tptp.bot_bo7653980558646680370d_enat))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_real)) (not (@ (@ tptp.ord_less_set_real A2) tptp.bot_bot_set_real))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_nat)) (not (@ (@ tptp.ord_less_set_nat A2) tptp.bot_bot_set_nat))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_int)) (not (@ (@ tptp.ord_less_set_int A2) tptp.bot_bot_set_int))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat C))) (=> (@ (@ tptp.ord_le2529575680413868914d_enat A2) B) (=> (@ _let_1 A2) (@ _let_1 B))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_real) (B tptp.set_real) (C tptp.real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ (@ tptp.ord_less_set_real A2) B) (=> (@ _let_1 A2) (@ _let_1 B))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_set_nat) (B tptp.set_set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ (@ tptp.ord_less_set_set_nat A2) B) (=> (@ _let_1 A2) (@ _let_1 B))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat) (C tptp.nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ (@ tptp.ord_less_set_nat A2) B) (=> (@ _let_1 A2) (@ _let_1 B))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_int) (B tptp.set_int) (C tptp.int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ (@ tptp.ord_less_set_int A2) B) (=> (@ _let_1 A2) (@ _let_1 B))))))
% 4.71/5.17 (assert (forall ((X8 tptp.set_nat)) (=> (not (= X8 tptp.bot_bot_set_nat)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) X8) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) X8) (@ (@ tptp.ord_less_nat X5) Xa))))) (not (@ tptp.finite_finite_nat X8))))))
% 4.71/5.17 (assert (forall ((X8 tptp.set_Extended_enat)) (=> (not (= X8 tptp.bot_bo7653980558646680370d_enat)) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) X8) (exists ((Xa tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat Xa) X8) (@ (@ tptp.ord_le72135733267957522d_enat X5) Xa))))) (not (@ tptp.finite4001608067531595151d_enat X8))))))
% 4.71/5.17 (assert (forall ((X8 tptp.set_real)) (=> (not (= X8 tptp.bot_bot_set_real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) X8) (exists ((Xa tptp.real)) (and (@ (@ tptp.member_real Xa) X8) (@ (@ tptp.ord_less_real X5) Xa))))) (not (@ tptp.finite_finite_real X8))))))
% 4.71/5.17 (assert (forall ((X8 tptp.set_int)) (=> (not (= X8 tptp.bot_bot_set_int)) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) X8) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) X8) (@ (@ tptp.ord_less_int X5) Xa))))) (not (@ tptp.finite_finite_int X8))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_set_nat)) (= (exists ((X4 tptp.set_nat)) (@ (@ tptp.member_set_nat X4) A2)) (not (= A2 tptp.bot_bot_set_set_nat)))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_Extended_enat)) (= (exists ((X4 tptp.extended_enat)) (@ (@ tptp.member_Extended_enat X4) A2)) (not (= A2 tptp.bot_bo7653980558646680370d_enat)))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_real)) (= (exists ((X4 tptp.real)) (@ (@ tptp.member_real X4) A2)) (not (= A2 tptp.bot_bot_set_real)))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_nat)) (= (exists ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) A2)) (not (= A2 tptp.bot_bot_set_nat)))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_int)) (= (exists ((X4 tptp.int)) (@ (@ tptp.member_int X4) A2)) (not (= A2 tptp.bot_bot_set_int)))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_set_nat)) (=> (forall ((Y3 tptp.set_nat)) (not (@ (@ tptp.member_set_nat Y3) A2))) (= A2 tptp.bot_bot_set_set_nat))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_Extended_enat)) (=> (forall ((Y3 tptp.extended_enat)) (not (@ (@ tptp.member_Extended_enat Y3) A2))) (= A2 tptp.bot_bo7653980558646680370d_enat))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_real)) (=> (forall ((Y3 tptp.real)) (not (@ (@ tptp.member_real Y3) A2))) (= A2 tptp.bot_bot_set_real))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_nat)) (=> (forall ((Y3 tptp.nat)) (not (@ (@ tptp.member_nat Y3) A2))) (= A2 tptp.bot_bot_set_nat))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_int)) (=> (forall ((Y3 tptp.int)) (not (@ (@ tptp.member_int Y3) A2))) (= A2 tptp.bot_bot_set_int))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_set_nat) (A tptp.set_nat)) (=> (= A2 tptp.bot_bot_set_set_nat) (not (@ (@ tptp.member_set_nat A) A2)))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_Extended_enat) (A tptp.extended_enat)) (=> (= A2 tptp.bot_bo7653980558646680370d_enat) (not (@ (@ tptp.member_Extended_enat A) A2)))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_real) (A tptp.real)) (=> (= A2 tptp.bot_bot_set_real) (not (@ (@ tptp.member_real A) A2)))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_nat) (A tptp.nat)) (=> (= A2 tptp.bot_bot_set_nat) (not (@ (@ tptp.member_nat A) A2)))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_int) (A tptp.int)) (=> (= A2 tptp.bot_bot_set_int) (not (@ (@ tptp.member_int A) A2)))))
% 4.71/5.17 (assert (forall ((A tptp.set_nat)) (not (@ (@ tptp.member_set_nat A) tptp.bot_bot_set_set_nat))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat)) (not (@ (@ tptp.member_Extended_enat A) tptp.bot_bo7653980558646680370d_enat))))
% 4.71/5.17 (assert (forall ((A tptp.real)) (not (@ (@ tptp.member_real A) tptp.bot_bot_set_real))))
% 4.71/5.17 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.member_nat A) tptp.bot_bot_set_nat))))
% 4.71/5.17 (assert (forall ((A tptp.int)) (not (@ (@ tptp.member_int A) tptp.bot_bot_set_int))))
% 4.71/5.17 (assert (forall ((A tptp.set_Extended_enat)) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A) tptp.bot_bo7653980558646680370d_enat) (= A tptp.bot_bo7653980558646680370d_enat))))
% 4.71/5.17 (assert (forall ((A tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A) tptp.bot_bot_set_real) (= A tptp.bot_bot_set_real))))
% 4.71/5.17 (assert (forall ((A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) tptp.bot_bot_set_nat) (= A tptp.bot_bot_set_nat))))
% 4.71/5.17 (assert (forall ((A tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) tptp.bot_bot_set_int) (= A tptp.bot_bot_set_int))))
% 4.71/5.17 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.bot_bot_nat) (= A tptp.bot_bot_nat))))
% 4.71/5.17 (assert (forall ((A tptp.set_Extended_enat)) (= (@ (@ tptp.ord_le7203529160286727270d_enat A) tptp.bot_bo7653980558646680370d_enat) (= A tptp.bot_bo7653980558646680370d_enat))))
% 4.71/5.17 (assert (forall ((A tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real A) tptp.bot_bot_set_real) (= A tptp.bot_bot_set_real))))
% 4.71/5.17 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A) tptp.bot_bot_set_nat) (= A tptp.bot_bot_set_nat))))
% 4.71/5.17 (assert (forall ((A tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A) tptp.bot_bot_set_int) (= A tptp.bot_bot_set_int))))
% 4.71/5.17 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.bot_bot_nat) (= A tptp.bot_bot_nat))))
% 4.71/5.17 (assert (forall ((A tptp.set_Extended_enat)) (@ (@ tptp.ord_le7203529160286727270d_enat tptp.bot_bo7653980558646680370d_enat) A)))
% 4.71/5.17 (assert (forall ((A tptp.set_real)) (@ (@ tptp.ord_less_eq_set_real tptp.bot_bot_set_real) A)))
% 4.71/5.17 (assert (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat tptp.bot_bot_set_nat) A)))
% 4.71/5.17 (assert (forall ((A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int tptp.bot_bot_set_int) A)))
% 4.71/5.17 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.bot_bot_nat) A)))
% 4.71/5.17 (assert (forall ((A tptp.set_Extended_enat)) (= (not (= A tptp.bot_bo7653980558646680370d_enat)) (@ (@ tptp.ord_le2529575680413868914d_enat tptp.bot_bo7653980558646680370d_enat) A))))
% 4.71/5.17 (assert (forall ((A tptp.set_real)) (= (not (= A tptp.bot_bot_set_real)) (@ (@ tptp.ord_less_set_real tptp.bot_bot_set_real) A))))
% 4.71/5.17 (assert (forall ((A tptp.set_nat)) (= (not (= A tptp.bot_bot_set_nat)) (@ (@ tptp.ord_less_set_nat tptp.bot_bot_set_nat) A))))
% 4.71/5.17 (assert (forall ((A tptp.set_int)) (= (not (= A tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_set_int tptp.bot_bot_set_int) A))))
% 4.71/5.17 (assert (forall ((A tptp.nat)) (= (not (= A tptp.bot_bot_nat)) (@ (@ tptp.ord_less_nat tptp.bot_bot_nat) A))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat)) (= (not (= A tptp.bot_bo4199563552545308370d_enat)) (@ (@ tptp.ord_le72135733267957522d_enat tptp.bot_bo4199563552545308370d_enat) A))))
% 4.71/5.17 (assert (forall ((A tptp.set_Extended_enat)) (not (@ (@ tptp.ord_le2529575680413868914d_enat A) tptp.bot_bo7653980558646680370d_enat))))
% 4.71/5.17 (assert (forall ((A tptp.set_real)) (not (@ (@ tptp.ord_less_set_real A) tptp.bot_bot_set_real))))
% 4.71/5.17 (assert (forall ((A tptp.set_nat)) (not (@ (@ tptp.ord_less_set_nat A) tptp.bot_bot_set_nat))))
% 4.71/5.17 (assert (forall ((A tptp.set_int)) (not (@ (@ tptp.ord_less_set_int A) tptp.bot_bot_set_int))))
% 4.71/5.17 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.bot_bot_nat))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat)) (not (@ (@ tptp.ord_le72135733267957522d_enat A) tptp.bot_bo4199563552545308370d_enat))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_VEBT_VEBT)) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (exists ((Xs2 tptp.list_VEBT_VEBT)) (= (@ tptp.set_VEBT_VEBT2 Xs2) A2)))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (exists ((Xs2 tptp.list_nat)) (= (@ tptp.set_nat2 Xs2) A2)))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A2) (exists ((Xs2 tptp.list_complex)) (= (@ tptp.set_complex2 Xs2) A2)))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (exists ((Xs2 tptp.list_int)) (= (@ tptp.set_int2 Xs2) A2)))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (exists ((Xs2 tptp.list_Extended_enat)) (= (@ tptp.set_Extended_enat2 Xs2) A2)))))
% 4.71/5.17 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_real X) Y)) (@ (@ tptp.ord_less_real Y) X)))))
% 4.71/5.17 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_int Y) X)))))
% 4.71/5.17 (assert (forall ((X2 tptp.real)) (exists ((X_12 tptp.real)) (@ (@ tptp.ord_less_real X2) X_12))))
% 4.71/5.17 (assert (forall ((X2 tptp.real)) (exists ((Y3 tptp.real)) (@ (@ tptp.ord_less_real Y3) X2))))
% 4.71/5.17 (assert (= tptp.ord_less_eq_set_nat (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat A5) B5) (= A5 B5)))))
% 4.71/5.17 (assert (= tptp.ord_less_eq_set_int (lambda ((A5 tptp.set_int) (B5 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int A5) B5) (= A5 B5)))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat) (C4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B) (=> (@ (@ tptp.ord_less_set_nat B) C4) (@ (@ tptp.ord_less_set_nat A2) C4)))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_int) (B tptp.set_int) (C4 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B) (=> (@ (@ tptp.ord_less_set_int B) C4) (@ (@ tptp.ord_less_set_int A2) C4)))))
% 4.71/5.17 (assert (= tptp.ord_less_set_nat (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A5) B5) (not (@ (@ tptp.ord_less_eq_set_nat B5) A5))))))
% 4.71/5.17 (assert (= tptp.ord_less_set_int (lambda ((A5 tptp.set_int) (B5 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A5) B5) (not (@ (@ tptp.ord_less_eq_set_int B5) A5))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat) (C4 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat A2))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_nat B) C4) (@ _let_1 C4))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_int) (B tptp.set_int) (C4 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int A2))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_int B) C4) (@ _let_1 C4))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A2) B) (@ (@ tptp.ord_less_eq_set_nat A2) B))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A2) B) (@ (@ tptp.ord_less_eq_set_int A2) B))))
% 4.71/5.17 (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 ((X4 tptp.real)) (=> (@ P X4) (@ Q X4))))))
% 4.71/5.17 (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 ((X4 tptp.list_nat)) (=> (@ P X4) (@ Q X4))))))
% 4.71/5.17 (assert (forall ((P (-> tptp.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.collect_set_nat P)) (@ tptp.collect_set_nat Q)) (forall ((X4 tptp.set_nat)) (=> (@ P X4) (@ Q X4))))))
% 4.71/5.17 (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 ((X4 tptp.nat)) (=> (@ P X4) (@ Q X4))))))
% 4.71/5.17 (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 ((X4 tptp.int)) (=> (@ P X4) (@ Q X4))))))
% 4.71/5.17 (assert (= (lambda ((Y4 tptp.set_nat) (Z2 tptp.set_nat)) (= Y4 Z2)) (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A5) B5) (@ (@ tptp.ord_less_eq_set_nat B5) A5)))))
% 4.71/5.17 (assert (= (lambda ((Y4 tptp.set_int) (Z2 tptp.set_int)) (= Y4 Z2)) (lambda ((A5 tptp.set_int) (B5 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A5) B5) (@ (@ tptp.ord_less_eq_set_int B5) A5)))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat) (C4 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A2))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_nat B) C4) (@ _let_1 C4))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_int) (B tptp.set_int) (C4 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A2))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_int B) C4) (@ _let_1 C4))))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (assert (forall ((P (-> tptp.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (=> (forall ((X5 tptp.set_nat)) (=> (@ P X5) (@ Q X5))) (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.collect_set_nat P)) (@ tptp.collect_set_nat Q)))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A2) A2)))
% 4.71/5.17 (assert (forall ((A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A2) A2)))
% 4.71/5.17 (assert (= tptp.ord_le7203529160286727270d_enat (lambda ((A5 tptp.set_Extended_enat) (B5 tptp.set_Extended_enat)) (forall ((T2 tptp.extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat T2))) (=> (@ _let_1 A5) (@ _let_1 B5)))))))
% 4.71/5.17 (assert (= tptp.ord_less_eq_set_real (lambda ((A5 tptp.set_real) (B5 tptp.set_real)) (forall ((T2 tptp.real)) (let ((_let_1 (@ tptp.member_real T2))) (=> (@ _let_1 A5) (@ _let_1 B5)))))))
% 4.71/5.17 (assert (= tptp.ord_le6893508408891458716et_nat (lambda ((A5 tptp.set_set_nat) (B5 tptp.set_set_nat)) (forall ((T2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat T2))) (=> (@ _let_1 A5) (@ _let_1 B5)))))))
% 4.71/5.17 (assert (= tptp.ord_less_eq_set_nat (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (forall ((T2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat T2))) (=> (@ _let_1 A5) (@ _let_1 B5)))))))
% 4.71/5.17 (assert (= tptp.ord_less_eq_set_int (lambda ((A5 tptp.set_int) (B5 tptp.set_int)) (forall ((T2 tptp.int)) (let ((_let_1 (@ tptp.member_int T2))) (=> (@ _let_1 A5) (@ _let_1 B5)))))))
% 4.71/5.17 (assert (= tptp.ord_less_set_nat (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A5) B5) (not (= A5 B5))))))
% 4.71/5.17 (assert (= tptp.ord_less_set_int (lambda ((A5 tptp.set_int) (B5 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A5) B5) (not (= A5 B5))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (=> (= A2 B) (@ (@ tptp.ord_less_eq_set_nat B) A2))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_int) (B tptp.set_int)) (=> (= A2 B) (@ (@ tptp.ord_less_eq_set_int B) A2))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (=> (= A2 B) (@ (@ tptp.ord_less_eq_set_nat A2) B))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_int) (B tptp.set_int)) (=> (= A2 B) (@ (@ tptp.ord_less_eq_set_int A2) B))))
% 4.71/5.17 (assert (= tptp.ord_le7203529160286727270d_enat (lambda ((A5 tptp.set_Extended_enat) (B5 tptp.set_Extended_enat)) (forall ((X4 tptp.extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat X4))) (=> (@ _let_1 A5) (@ _let_1 B5)))))))
% 4.71/5.17 (assert (= tptp.ord_less_eq_set_real (lambda ((A5 tptp.set_real) (B5 tptp.set_real)) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.member_real X4))) (=> (@ _let_1 A5) (@ _let_1 B5)))))))
% 4.71/5.17 (assert (= tptp.ord_le6893508408891458716et_nat (lambda ((A5 tptp.set_set_nat) (B5 tptp.set_set_nat)) (forall ((X4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X4))) (=> (@ _let_1 A5) (@ _let_1 B5)))))))
% 4.71/5.17 (assert (= tptp.ord_less_eq_set_nat (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (forall ((X4 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X4))) (=> (@ _let_1 A5) (@ _let_1 B5)))))))
% 4.71/5.17 (assert (= tptp.ord_less_eq_set_int (lambda ((A5 tptp.set_int) (B5 tptp.set_int)) (forall ((X4 tptp.int)) (let ((_let_1 (@ tptp.member_int X4))) (=> (@ _let_1 A5) (@ _let_1 B5)))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (=> (= A2 B) (not (=> (@ (@ tptp.ord_less_eq_set_nat A2) B) (not (@ (@ tptp.ord_less_eq_set_nat B) A2)))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_int) (B tptp.set_int)) (=> (= A2 B) (not (=> (@ (@ tptp.ord_less_eq_set_int A2) B) (not (@ (@ tptp.ord_less_eq_set_int B) A2)))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A2) B) (not (=> (@ (@ tptp.ord_less_eq_set_nat A2) B) (@ (@ tptp.ord_less_eq_set_nat B) A2))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A2) B) (not (=> (@ (@ tptp.ord_less_eq_set_int A2) B) (@ (@ tptp.ord_less_eq_set_int B) A2))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat C))) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) B) (=> (@ _let_1 A2) (@ _let_1 B))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_real) (B tptp.set_real) (C tptp.real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ (@ tptp.ord_less_eq_set_real A2) B) (=> (@ _let_1 A2) (@ _let_1 B))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_set_nat) (B tptp.set_set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A2) B) (=> (@ _let_1 A2) (@ _let_1 B))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat) (C tptp.nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B) (=> (@ _let_1 A2) (@ _let_1 B))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_int) (B tptp.set_int) (C tptp.int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ (@ tptp.ord_less_eq_set_int A2) B) (=> (@ _let_1 A2) (@ _let_1 B))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat) (X tptp.extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat X))) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) B) (=> (@ _let_1 A2) (@ _let_1 B))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_real) (B tptp.set_real) (X tptp.real)) (let ((_let_1 (@ tptp.member_real X))) (=> (@ (@ tptp.ord_less_eq_set_real A2) B) (=> (@ _let_1 A2) (@ _let_1 B))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_set_nat) (B tptp.set_set_nat) (X tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X))) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A2) B) (=> (@ _let_1 A2) (@ _let_1 B))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat) (X tptp.nat)) (let ((_let_1 (@ tptp.member_nat X))) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B) (=> (@ _let_1 A2) (@ _let_1 B))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_int) (B tptp.set_int) (X tptp.int)) (let ((_let_1 (@ tptp.member_int X))) (=> (@ (@ tptp.ord_less_eq_set_int A2) B) (=> (@ _let_1 A2) (@ _let_1 B))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (not (= A2 tptp.bot_bo7653980558646680370d_enat)) (exists ((X5 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X5) A2) (forall ((Xa tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat Xa) A2) (=> (@ (@ tptp.ord_le2932123472753598470d_enat X5) Xa) (= X5 Xa))))))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_real)) (=> (@ tptp.finite_finite_real A2) (=> (not (= A2 tptp.bot_bot_set_real)) (exists ((X5 tptp.real)) (and (@ (@ tptp.member_real X5) A2) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A2) (=> (@ (@ tptp.ord_less_eq_real X5) Xa) (= X5 Xa))))))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A2) (=> (not (= A2 tptp.bot_bot_set_set_nat)) (exists ((X5 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X5) A2) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_nat X5) Xa) (= X5 Xa))))))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_set_int)) (=> (@ tptp.finite6197958912794628473et_int A2) (=> (not (= A2 tptp.bot_bot_set_set_int)) (exists ((X5 tptp.set_int)) (and (@ (@ tptp.member_set_int X5) A2) (forall ((Xa tptp.set_int)) (=> (@ (@ tptp.member_set_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_int X5) Xa) (= X5 Xa))))))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (=> (not (= A2 tptp.bot_bot_set_nat)) (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) A2) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_nat X5) Xa) (= X5 Xa))))))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (=> (not (= A2 tptp.bot_bot_set_int)) (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) A2) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_int X5) Xa) (= X5 Xa))))))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (not (= A2 tptp.bot_bo7653980558646680370d_enat)) (exists ((X5 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X5) A2) (forall ((Xa tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat Xa) A2) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Xa) X5) (= X5 Xa))))))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_real)) (=> (@ tptp.finite_finite_real A2) (=> (not (= A2 tptp.bot_bot_set_real)) (exists ((X5 tptp.real)) (and (@ (@ tptp.member_real X5) A2) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A2) (=> (@ (@ tptp.ord_less_eq_real Xa) X5) (= X5 Xa))))))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A2) (=> (not (= A2 tptp.bot_bot_set_set_nat)) (exists ((X5 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X5) A2) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_nat Xa) X5) (= X5 Xa))))))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_set_int)) (=> (@ tptp.finite6197958912794628473et_int A2) (=> (not (= A2 tptp.bot_bot_set_set_int)) (exists ((X5 tptp.set_int)) (and (@ (@ tptp.member_set_int X5) A2) (forall ((Xa tptp.set_int)) (=> (@ (@ tptp.member_set_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_int Xa) X5) (= X5 Xa))))))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (=> (not (= A2 tptp.bot_bot_set_nat)) (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) A2) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_nat Xa) X5) (= X5 Xa))))))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (=> (not (= A2 tptp.bot_bot_set_int)) (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) A2) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_int Xa) X5) (= X5 Xa))))))))))
% 4.71/5.17 (assert (= tptp.finite_finite_nat (lambda ((N5 tptp.set_nat)) (exists ((M tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) N5) (@ (@ tptp.ord_less_eq_nat X4) M)))))))
% 4.71/5.17 (assert (forall ((S2 tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S2)) (forall ((M tptp.nat)) (exists ((N tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.member_nat N) S2)))))))
% 4.71/5.17 (assert (= tptp.finite_finite_nat (lambda ((N5 tptp.set_nat)) (exists ((M tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) N5) (@ (@ tptp.ord_less_nat X4) M)))))))
% 4.71/5.17 (assert (forall ((S2 tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S2)) (forall ((M tptp.nat)) (exists ((N tptp.nat)) (and (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.member_nat N) S2)))))))
% 4.71/5.17 (assert (forall ((N6 tptp.set_nat) (N2 tptp.nat)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) N6) (@ (@ tptp.ord_less_nat X5) N2))) (@ tptp.finite_finite_nat N6))))
% 4.71/5.17 (assert (forall ((K tptp.nat) (S2 tptp.set_nat)) (=> (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) M3) (exists ((N7 tptp.nat)) (and (@ (@ tptp.ord_less_nat M3) N7) (@ (@ tptp.member_nat N7) S2))))) (not (@ tptp.finite_finite_nat S2)))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat A2) (=> (forall ((A6 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A6) (=> (forall ((B6 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B6) A6) (@ P B6))) (@ P A6)))) (@ P A2)))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((A6 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A6) (=> (forall ((B6 tptp.set_complex)) (=> (@ (@ tptp.ord_less_set_complex B6) A6) (@ P B6))) (@ P A6)))) (@ P A2)))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((A6 tptp.set_int)) (=> (@ tptp.finite_finite_int A6) (=> (forall ((B6 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int B6) A6) (@ P B6))) (@ P A6)))) (@ P A2)))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (forall ((A6 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A6) (=> (forall ((B6 tptp.set_Extended_enat)) (=> (@ (@ tptp.ord_le2529575680413868914d_enat B6) A6) (@ P B6))) (@ P A6)))) (@ P A2)))))
% 4.71/5.17 (assert (forall ((S2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (not (= S2 tptp.bot_bot_set_complex)) (not (exists ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) S2) (@ (@ tptp.ord_less_nat (@ F X2)) (@ F (@ (@ tptp.lattic5364784637807008409ex_nat F) S2))))))))))
% 4.71/5.17 (assert (forall ((S2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat S2) (=> (not (= S2 tptp.bot_bo7653980558646680370d_enat)) (not (exists ((X2 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X2) S2) (@ (@ tptp.ord_less_nat (@ F X2)) (@ F (@ (@ tptp.lattic3845382081240766429at_nat F) S2))))))))))
% 4.71/5.17 (assert (forall ((S2 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real S2) (=> (not (= S2 tptp.bot_bot_set_real)) (not (exists ((X2 tptp.real)) (and (@ (@ tptp.member_real X2) S2) (@ (@ tptp.ord_less_nat (@ F X2)) (@ F (@ (@ tptp.lattic5055836439445974935al_nat F) S2))))))))))
% 4.71/5.17 (assert (forall ((S2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat S2) (=> (not (= S2 tptp.bot_bot_set_nat)) (not (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) S2) (@ (@ tptp.ord_less_nat (@ F X2)) (@ F (@ (@ tptp.lattic7446932960582359483at_nat F) S2))))))))))
% 4.71/5.17 (assert (forall ((S2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int S2) (=> (not (= S2 tptp.bot_bot_set_int)) (not (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) S2) (@ (@ tptp.ord_less_nat (@ F X2)) (@ F (@ (@ tptp.lattic8446286672483414039nt_nat F) S2))))))))))
% 4.71/5.17 (assert (forall ((S2 tptp.set_complex) (F (-> tptp.complex tptp.extended_enat))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (not (= S2 tptp.bot_bot_set_complex)) (not (exists ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) S2) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X2)) (@ F (@ (@ tptp.lattic7796887085614042845d_enat F) S2))))))))))
% 4.71/5.17 (assert (forall ((S2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.extended_enat))) (=> (@ tptp.finite4001608067531595151d_enat S2) (=> (not (= S2 tptp.bot_bo7653980558646680370d_enat)) (not (exists ((X2 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X2) S2) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X2)) (@ F (@ (@ tptp.lattic1996716550891908761d_enat F) S2))))))))))
% 4.71/5.17 (assert (forall ((S2 tptp.set_real) (F (-> tptp.real tptp.extended_enat))) (=> (@ tptp.finite_finite_real S2) (=> (not (= S2 tptp.bot_bot_set_real)) (not (exists ((X2 tptp.real)) (and (@ (@ tptp.member_real X2) S2) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X2)) (@ F (@ (@ tptp.lattic9066027731366277983d_enat F) S2))))))))))
% 4.71/5.17 (assert (forall ((S2 tptp.set_nat) (F (-> tptp.nat tptp.extended_enat))) (=> (@ tptp.finite_finite_nat S2) (=> (not (= S2 tptp.bot_bot_set_nat)) (not (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) S2) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X2)) (@ F (@ (@ tptp.lattic8926238025367240251d_enat F) S2))))))))))
% 4.71/5.17 (assert (forall ((S2 tptp.set_int) (F (-> tptp.int tptp.extended_enat))) (=> (@ tptp.finite_finite_int S2) (=> (not (= S2 tptp.bot_bot_set_int)) (not (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) S2) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X2)) (@ F (@ (@ tptp.lattic6042659972569420511d_enat F) S2))))))))))
% 4.71/5.17 (assert (= tptp.bot_bot_set_list_nat (@ tptp.collect_list_nat tptp.bot_bot_list_nat_o)))
% 4.71/5.17 (assert (= tptp.bot_bot_set_set_nat (@ tptp.collect_set_nat tptp.bot_bot_set_nat_o)))
% 4.71/5.17 (assert (= tptp.bot_bo7653980558646680370d_enat (@ tptp.collec4429806609662206161d_enat tptp.bot_bo1954855461789132331enat_o)))
% 4.71/5.17 (assert (= tptp.bot_bot_set_real (@ tptp.collect_real tptp.bot_bot_real_o)))
% 4.71/5.17 (assert (= tptp.bot_bot_set_nat (@ tptp.collect_nat tptp.bot_bot_nat_o)))
% 4.71/5.17 (assert (= tptp.bot_bot_set_int (@ tptp.collect_int tptp.bot_bot_int_o)))
% 4.71/5.17 (assert (= tptp.bot_bot_nat tptp.zero_zero_nat))
% 4.71/5.17 (assert (forall ((M7 tptp.set_list_VEBT_VEBT)) (=> (@ tptp.finite3004134309566078307T_VEBT M7) (exists ((N3 tptp.nat)) (forall ((X2 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member2936631157270082147T_VEBT X2) M7) (@ (@ tptp.ord_less_nat (@ tptp.size_s6755466524823107622T_VEBT X2)) N3)))))))
% 4.71/5.17 (assert (forall ((M7 tptp.set_list_int)) (=> (@ tptp.finite3922522038869484883st_int M7) (exists ((N3 tptp.nat)) (forall ((X2 tptp.list_int)) (=> (@ (@ tptp.member_list_int X2) M7) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_int X2)) N3)))))))
% 4.71/5.17 (assert (forall ((M7 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat M7) (exists ((N3 tptp.nat)) (forall ((X2 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat X2) M7) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_nat X2)) N3)))))))
% 4.71/5.17 (assert (forall ((P (-> tptp.nat Bool)) (X tptp.nat) (M7 tptp.nat)) (=> (@ P X) (=> (forall ((X5 tptp.nat)) (=> (@ P X5) (@ (@ tptp.ord_less_eq_nat X5) M7))) (not (forall ((M3 tptp.nat)) (=> (@ P M3) (not (forall ((X2 tptp.nat)) (=> (@ P X2) (@ (@ tptp.ord_less_eq_nat X2) M3)))))))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_Extended_enat) (A tptp.extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ (@ tptp.member_Extended_enat A) A2) (exists ((X5 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat A) X5) (forall ((Xa tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat Xa) A2) (=> (@ (@ tptp.ord_le2932123472753598470d_enat X5) Xa) (= X5 Xa))))))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_real) (A tptp.real)) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real A) A2) (exists ((X5 tptp.real)) (and (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_less_eq_real A) X5) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A2) (=> (@ (@ tptp.ord_less_eq_real X5) Xa) (= X5 Xa))))))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_set_nat) (A tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A2) (=> (@ (@ tptp.member_set_nat A) A2) (exists ((X5 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X5) A2) (@ (@ tptp.ord_less_eq_set_nat A) X5) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_nat X5) Xa) (= X5 Xa))))))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_set_int) (A tptp.set_int)) (=> (@ tptp.finite6197958912794628473et_int A2) (=> (@ (@ tptp.member_set_int A) A2) (exists ((X5 tptp.set_int)) (and (@ (@ tptp.member_set_int X5) A2) (@ (@ tptp.ord_less_eq_set_int A) X5) (forall ((Xa tptp.set_int)) (=> (@ (@ tptp.member_set_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_int X5) Xa) (= X5 Xa))))))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_nat) (A tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.member_nat A) A2) (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_less_eq_nat A) X5) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_nat X5) Xa) (= X5 Xa))))))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_int) (A tptp.int)) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int A) A2) (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_eq_int A) X5) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_int X5) Xa) (= X5 Xa))))))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_Extended_enat) (A tptp.extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ (@ tptp.member_Extended_enat A) A2) (exists ((X5 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat X5) A) (forall ((Xa tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat Xa) A2) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Xa) X5) (= X5 Xa))))))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_real) (A tptp.real)) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real A) A2) (exists ((X5 tptp.real)) (and (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_less_eq_real X5) A) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A2) (=> (@ (@ tptp.ord_less_eq_real Xa) X5) (= X5 Xa))))))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_set_nat) (A tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A2) (=> (@ (@ tptp.member_set_nat A) A2) (exists ((X5 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X5) A2) (@ (@ tptp.ord_less_eq_set_nat X5) A) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_nat Xa) X5) (= X5 Xa))))))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_set_int) (A tptp.set_int)) (=> (@ tptp.finite6197958912794628473et_int A2) (=> (@ (@ tptp.member_set_int A) A2) (exists ((X5 tptp.set_int)) (and (@ (@ tptp.member_set_int X5) A2) (@ (@ tptp.ord_less_eq_set_int X5) A) (forall ((Xa tptp.set_int)) (=> (@ (@ tptp.member_set_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_int Xa) X5) (= X5 Xa))))))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_nat) (A tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.member_nat A) A2) (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_less_eq_nat X5) A) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_nat Xa) X5) (= X5 Xa))))))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_int) (A tptp.int)) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int A) A2) (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_eq_int X5) A) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_int Xa) X5) (= X5 Xa))))))))))
% 4.71/5.17 (assert (@ tptp.finite3207457112153483333omplex tptp.bot_bot_set_complex))
% 4.71/5.17 (assert (@ tptp.finite4001608067531595151d_enat tptp.bot_bo7653980558646680370d_enat))
% 4.71/5.17 (assert (@ tptp.finite_finite_real tptp.bot_bot_set_real))
% 4.71/5.17 (assert (@ tptp.finite_finite_nat tptp.bot_bot_set_nat))
% 4.71/5.17 (assert (@ tptp.finite_finite_int tptp.bot_bot_set_int))
% 4.71/5.17 (assert (forall ((S2 tptp.set_complex)) (=> (not (@ tptp.finite3207457112153483333omplex S2)) (not (= S2 tptp.bot_bot_set_complex)))))
% 4.71/5.17 (assert (forall ((S2 tptp.set_Extended_enat)) (=> (not (@ tptp.finite4001608067531595151d_enat S2)) (not (= S2 tptp.bot_bo7653980558646680370d_enat)))))
% 4.71/5.17 (assert (forall ((S2 tptp.set_real)) (=> (not (@ tptp.finite_finite_real S2)) (not (= S2 tptp.bot_bot_set_real)))))
% 4.71/5.17 (assert (forall ((S2 tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat S2)) (not (= S2 tptp.bot_bot_set_nat)))))
% 4.71/5.17 (assert (forall ((S2 tptp.set_int)) (=> (not (@ tptp.finite_finite_int S2)) (not (= S2 tptp.bot_bot_set_int)))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_set_nat) (R (-> tptp.set_nat tptp.set_nat Bool))) (=> (@ tptp.finite1152437895449049373et_nat A2) (=> (forall ((X5 tptp.set_nat)) (not (@ (@ R X5) X5))) (=> (forall ((X5 tptp.set_nat) (Y3 tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ R X5))) (=> (@ _let_1 Y3) (=> (@ (@ R Y3) Z) (@ _let_1 Z))))) (=> (forall ((X5 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X5) A2) (exists ((Y6 tptp.set_nat)) (and (@ (@ tptp.member_set_nat Y6) A2) (@ (@ R X5) Y6))))) (= A2 tptp.bot_bot_set_set_nat)))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_complex) (R (-> tptp.complex tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X5 tptp.complex)) (not (@ (@ R X5) X5))) (=> (forall ((X5 tptp.complex) (Y3 tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ R X5))) (=> (@ _let_1 Y3) (=> (@ (@ R Y3) Z) (@ _let_1 Z))))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (exists ((Y6 tptp.complex)) (and (@ (@ tptp.member_complex Y6) A2) (@ (@ R X5) Y6))))) (= A2 tptp.bot_bot_set_complex)))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_Extended_enat) (R (-> tptp.extended_enat tptp.extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (forall ((X5 tptp.extended_enat)) (not (@ (@ R X5) X5))) (=> (forall ((X5 tptp.extended_enat) (Y3 tptp.extended_enat) (Z tptp.extended_enat)) (let ((_let_1 (@ R X5))) (=> (@ _let_1 Y3) (=> (@ (@ R Y3) Z) (@ _let_1 Z))))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) A2) (exists ((Y6 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat Y6) A2) (@ (@ R X5) Y6))))) (= A2 tptp.bot_bo7653980558646680370d_enat)))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_real) (R (-> tptp.real tptp.real Bool))) (=> (@ tptp.finite_finite_real A2) (=> (forall ((X5 tptp.real)) (not (@ (@ R X5) X5))) (=> (forall ((X5 tptp.real) (Y3 tptp.real) (Z tptp.real)) (let ((_let_1 (@ R X5))) (=> (@ _let_1 Y3) (=> (@ (@ R Y3) Z) (@ _let_1 Z))))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (exists ((Y6 tptp.real)) (and (@ (@ tptp.member_real Y6) A2) (@ (@ R X5) Y6))))) (= A2 tptp.bot_bot_set_real)))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_nat) (R (-> tptp.nat tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A2) (=> (forall ((X5 tptp.nat)) (not (@ (@ R X5) X5))) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ R X5))) (=> (@ _let_1 Y3) (=> (@ (@ R Y3) Z) (@ _let_1 Z))))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (exists ((Y6 tptp.nat)) (and (@ (@ tptp.member_nat Y6) A2) (@ (@ R X5) Y6))))) (= A2 tptp.bot_bot_set_nat)))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_int) (R (-> tptp.int tptp.int Bool))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X5 tptp.int)) (not (@ (@ R X5) X5))) (=> (forall ((X5 tptp.int) (Y3 tptp.int) (Z tptp.int)) (let ((_let_1 (@ R X5))) (=> (@ _let_1 Y3) (=> (@ (@ R Y3) Z) (@ _let_1 Z))))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (exists ((Y6 tptp.int)) (and (@ (@ tptp.member_int Y6) A2) (@ (@ R X5) Y6))))) (= A2 tptp.bot_bot_set_int)))))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_complex) (B tptp.set_complex)) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B) (=> (@ tptp.finite3207457112153483333omplex B) (@ tptp.finite3207457112153483333omplex A2)))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat)) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) B) (=> (@ tptp.finite4001608067531595151d_enat B) (@ tptp.finite4001608067531595151d_enat A2)))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B) (=> (@ tptp.finite_finite_nat B) (@ tptp.finite_finite_nat A2)))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B) (=> (@ tptp.finite_finite_int B) (@ tptp.finite_finite_int A2)))))
% 4.71/5.17 (assert (forall ((S2 tptp.set_complex) (T3 tptp.set_complex)) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (not (@ tptp.finite3207457112153483333omplex S2)) (not (@ tptp.finite3207457112153483333omplex T3))))))
% 4.71/5.17 (assert (forall ((S2 tptp.set_Extended_enat) (T3 tptp.set_Extended_enat)) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (not (@ tptp.finite4001608067531595151d_enat S2)) (not (@ tptp.finite4001608067531595151d_enat T3))))))
% 4.71/5.17 (assert (forall ((S2 tptp.set_nat) (T3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat S2) T3) (=> (not (@ tptp.finite_finite_nat S2)) (not (@ tptp.finite_finite_nat T3))))))
% 4.71/5.17 (assert (forall ((S2 tptp.set_int) (T3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int S2) T3) (=> (not (@ tptp.finite_finite_int S2)) (not (@ tptp.finite_finite_int T3))))))
% 4.71/5.17 (assert (forall ((B tptp.set_complex) (A2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex B) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B) (@ tptp.finite3207457112153483333omplex A2)))))
% 4.71/5.17 (assert (forall ((B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat B) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) B) (@ tptp.finite4001608067531595151d_enat A2)))))
% 4.71/5.17 (assert (forall ((B tptp.set_nat) (A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B) (@ tptp.finite_finite_nat A2)))))
% 4.71/5.17 (assert (forall ((B tptp.set_int) (A2 tptp.set_int)) (=> (@ tptp.finite_finite_int B) (=> (@ (@ tptp.ord_less_eq_set_int A2) B) (@ tptp.finite_finite_int A2)))))
% 4.71/5.17 (assert (forall ((S2 tptp.set_complex) (Y tptp.complex) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (not (= S2 tptp.bot_bot_set_complex)) (=> (@ (@ tptp.member_complex Y) S2) (@ (@ tptp.ord_less_eq_real (@ F (@ (@ tptp.lattic8794016678065449205x_real F) S2))) (@ F Y)))))))
% 4.71/5.17 (assert (forall ((S2 tptp.set_Extended_enat) (Y tptp.extended_enat) (F (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat S2) (=> (not (= S2 tptp.bot_bo7653980558646680370d_enat)) (=> (@ (@ tptp.member_Extended_enat Y) S2) (@ (@ tptp.ord_less_eq_real (@ F (@ (@ tptp.lattic1189837152898106425t_real F) S2))) (@ F Y)))))))
% 4.71/5.17 (assert (forall ((S2 tptp.set_real) (Y tptp.real) (F (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real S2) (=> (not (= S2 tptp.bot_bot_set_real)) (=> (@ (@ tptp.member_real Y) S2) (@ (@ tptp.ord_less_eq_real (@ F (@ (@ tptp.lattic8440615504127631091l_real F) S2))) (@ F Y)))))))
% 4.71/5.17 (assert (forall ((S2 tptp.set_nat) (Y tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat S2) (=> (not (= S2 tptp.bot_bot_set_nat)) (=> (@ (@ tptp.member_nat Y) S2) (@ (@ tptp.ord_less_eq_real (@ F (@ (@ tptp.lattic488527866317076247t_real F) S2))) (@ F Y)))))))
% 4.71/5.17 (assert (forall ((S2 tptp.set_int) (Y tptp.int) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int S2) (=> (not (= S2 tptp.bot_bot_set_int)) (=> (@ (@ tptp.member_int Y) S2) (@ (@ tptp.ord_less_eq_real (@ F (@ (@ tptp.lattic2675449441010098035t_real F) S2))) (@ F Y)))))))
% 4.71/5.17 (assert (forall ((S2 tptp.set_complex) (Y tptp.complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (not (= S2 tptp.bot_bot_set_complex)) (=> (@ (@ tptp.member_complex Y) S2) (@ (@ tptp.ord_less_eq_nat (@ F (@ (@ tptp.lattic5364784637807008409ex_nat F) S2))) (@ F Y)))))))
% 4.71/5.17 (assert (forall ((S2 tptp.set_Extended_enat) (Y tptp.extended_enat) (F (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat S2) (=> (not (= S2 tptp.bot_bo7653980558646680370d_enat)) (=> (@ (@ tptp.member_Extended_enat Y) S2) (@ (@ tptp.ord_less_eq_nat (@ F (@ (@ tptp.lattic3845382081240766429at_nat F) S2))) (@ F Y)))))))
% 4.71/5.17 (assert (forall ((S2 tptp.set_real) (Y tptp.real) (F (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real S2) (=> (not (= S2 tptp.bot_bot_set_real)) (=> (@ (@ tptp.member_real Y) S2) (@ (@ tptp.ord_less_eq_nat (@ F (@ (@ tptp.lattic5055836439445974935al_nat F) S2))) (@ F Y)))))))
% 4.71/5.17 (assert (forall ((S2 tptp.set_nat) (Y tptp.nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat S2) (=> (not (= S2 tptp.bot_bot_set_nat)) (=> (@ (@ tptp.member_nat Y) S2) (@ (@ tptp.ord_less_eq_nat (@ F (@ (@ tptp.lattic7446932960582359483at_nat F) S2))) (@ F Y)))))))
% 4.71/5.17 (assert (forall ((S2 tptp.set_int) (Y tptp.int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int S2) (=> (not (= S2 tptp.bot_bot_set_int)) (=> (@ (@ tptp.member_int Y) S2) (@ (@ tptp.ord_less_eq_nat (@ F (@ (@ tptp.lattic8446286672483414039nt_nat F) S2))) (@ F Y)))))))
% 4.71/5.17 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B2 tptp.nat)) (=> (forall ((A4 tptp.nat) (B4 tptp.nat)) (= (@ (@ P A4) B4) (@ (@ P B4) A4))) (=> (forall ((A4 tptp.nat)) (@ (@ P A4) tptp.zero_zero_nat)) (=> (forall ((A4 tptp.nat) (B4 tptp.nat)) (let ((_let_1 (@ P A4))) (=> (@ _let_1 B4) (@ _let_1 (@ (@ tptp.plus_plus_nat A4) B4))))) (@ (@ P A) B2))))))
% 4.71/5.17 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool)) (M2 tptp.nat)) (=> (forall ((K3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K3) (@ P K3))) (=> (forall ((K3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N2) (=> (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K3) I5) (@ P I5))) (@ P K3)))) (@ P M2)))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_set_nat)) (=> (forall ((X5 tptp.set_nat)) (not (@ (@ tptp.member_set_nat X5) A2))) (@ (@ tptp.ord_le6893508408891458716et_nat A2) tptp.bot_bot_set_set_nat))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_Extended_enat)) (=> (forall ((X5 tptp.extended_enat)) (not (@ (@ tptp.member_Extended_enat X5) A2))) (@ (@ tptp.ord_le7203529160286727270d_enat A2) tptp.bot_bo7653980558646680370d_enat))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_real)) (=> (forall ((X5 tptp.real)) (not (@ (@ tptp.member_real X5) A2))) (@ (@ tptp.ord_less_eq_set_real A2) tptp.bot_bot_set_real))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_nat)) (=> (forall ((X5 tptp.nat)) (not (@ (@ tptp.member_nat X5) A2))) (@ (@ tptp.ord_less_eq_set_nat A2) tptp.bot_bot_set_nat))))
% 4.71/5.17 (assert (forall ((A2 tptp.set_int)) (=> (forall ((X5 tptp.int)) (not (@ (@ tptp.member_int X5) A2))) (@ (@ tptp.ord_less_eq_set_int A2) tptp.bot_bot_set_int))))
% 4.71/5.17 (assert (forall ((X tptp.nat)) (=> (not (= X tptp.zero_zero_nat)) (not (forall ((N3 tptp.nat)) (not (= X (@ tptp.suc N3))))))))
% 4.71/5.17 (assert (forall ((X tptp.nat)) (=> (not (= X tptp.zero_zero_nat)) (=> (not (= X (@ tptp.suc tptp.zero_zero_nat))) (not (forall ((Va tptp.nat)) (not (= X (@ tptp.suc (@ tptp.suc Va))))))))))
% 4.71/5.17 (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))))))))
% 4.71/5.17 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (= (= B2 (@ (@ tptp.plus_plus_nat B2) A)) (= A tptp.zero_zero_nat))))
% 4.71/5.17 (assert (forall ((B2 tptp.real) (A tptp.real)) (= (= B2 (@ (@ tptp.plus_plus_real B2) A)) (= A tptp.zero_zero_real))))
% 4.71/5.17 (assert (forall ((B2 tptp.int) (A tptp.int)) (= (= B2 (@ (@ tptp.plus_plus_int B2) A)) (= A tptp.zero_zero_int))))
% 4.71/5.17 (assert (forall ((B2 tptp.complex) (A tptp.complex)) (= (= B2 (@ (@ tptp.plus_plus_complex B2) A)) (= A tptp.zero_zero_complex))))
% 4.71/5.17 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 4.71/5.17 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 4.71/5.17 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 4.71/5.17 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)))
% 4.71/5.17 (assert (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 4.71/5.17 (assert (not (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) tptp.zero_z5237406670263579293d_enat)))
% 4.71/5.17 (assert (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.zero_zero_real)))
% 4.71/5.17 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.zero_zero_int)))
% 4.71/5.17 (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)))))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (or (= A B2) (not (@ (@ tptp.ord_less_eq_real A) B2)) (not (@ (@ tptp.ord_less_eq_real B2) A)))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (or (= A B2) (not (@ (@ tptp.ord_less_eq_nat A) B2)) (not (@ (@ tptp.ord_less_eq_nat B2) A)))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int)) (or (= A B2) (not (@ (@ tptp.ord_less_eq_int A) B2)) (not (@ (@ tptp.ord_less_eq_int B2) A)))))
% 4.71/5.17 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real A) A)))
% 4.71/5.17 (assert (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A) A)))
% 4.71/5.17 (assert (forall ((A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A) A)))
% 4.71/5.17 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)))
% 4.71/5.17 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) A)))
% 4.71/5.17 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat)) (not (@ (@ tptp.ord_le72135733267957522d_enat A) A))))
% 4.71/5.17 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real A) A))))
% 4.71/5.17 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int A) A))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B2) C))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_real B2) C))))))
% 4.71/5.17 (assert (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) tptp.zero_z5237406670263579293d_enat))
% 4.71/5.17 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.zero_zero_real))
% 4.71/5.17 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 4.71/5.17 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.zero_zero_int))
% 4.71/5.17 (assert (forall ((B7 tptp.extended_enat) (A7 tptp.extended_enat)) (= (not (@ (@ tptp.ord_le2932123472753598470d_enat B7) A7)) (@ (@ tptp.ord_le72135733267957522d_enat A7) B7))))
% 4.71/5.17 (assert (forall ((B7 tptp.real) (A7 tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real B7) A7)) (@ (@ tptp.ord_less_real A7) B7))))
% 4.71/5.17 (assert (forall ((B7 tptp.nat) (A7 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat B7) A7)) (@ (@ tptp.ord_less_nat A7) B7))))
% 4.71/5.17 (assert (forall ((B7 tptp.int) (A7 tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int B7) A7)) (@ (@ tptp.ord_less_int A7) B7))))
% 4.71/5.17 (assert (forall ((P (-> tptp.list_nat Bool))) (= (= (@ tptp.collect_list_nat P) tptp.bot_bot_set_list_nat) (= P tptp.bot_bot_list_nat_o))))
% 4.71/5.17 (assert (forall ((P (-> tptp.set_nat Bool))) (= (= (@ tptp.collect_set_nat P) tptp.bot_bot_set_set_nat) (= P tptp.bot_bot_set_nat_o))))
% 4.71/5.17 (assert (forall ((P (-> tptp.extended_enat Bool))) (= (= (@ tptp.collec4429806609662206161d_enat P) tptp.bot_bo7653980558646680370d_enat) (= P tptp.bot_bo1954855461789132331enat_o))))
% 4.71/5.17 (assert (forall ((P (-> tptp.real Bool))) (= (= (@ tptp.collect_real P) tptp.bot_bot_set_real) (= P tptp.bot_bot_real_o))))
% 4.71/5.17 (assert (forall ((P (-> tptp.nat Bool))) (= (= (@ tptp.collect_nat P) tptp.bot_bot_set_nat) (= P tptp.bot_bot_nat_o))))
% 4.71/5.17 (assert (forall ((P (-> tptp.int Bool))) (= (= (@ tptp.collect_int P) tptp.bot_bot_set_int) (= P tptp.bot_bot_int_o))))
% 4.71/5.17 (assert (= tptp.bot_bot_set_nat_o (lambda ((X4 tptp.set_nat)) (@ (@ tptp.member_set_nat X4) tptp.bot_bot_set_set_nat))))
% 4.71/5.17 (assert (= tptp.bot_bo1954855461789132331enat_o (lambda ((X4 tptp.extended_enat)) (@ (@ tptp.member_Extended_enat X4) tptp.bot_bo7653980558646680370d_enat))))
% 4.71/5.17 (assert (= tptp.bot_bot_real_o (lambda ((X4 tptp.real)) (@ (@ tptp.member_real X4) tptp.bot_bot_set_real))))
% 4.71/5.17 (assert (= tptp.bot_bot_nat_o (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) tptp.bot_bot_set_nat))))
% 4.71/5.17 (assert (= tptp.bot_bot_int_o (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) tptp.bot_bot_set_int))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (P (-> tptp.extended_enat Bool))) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B2) (=> (@ P A) (=> (not (@ P B2)) (exists ((C2 tptp.extended_enat)) (and (@ (@ tptp.ord_le2932123472753598470d_enat A) C2) (@ (@ tptp.ord_le2932123472753598470d_enat C2) B2) (forall ((X2 tptp.extended_enat)) (=> (and (@ (@ tptp.ord_le2932123472753598470d_enat A) X2) (@ (@ tptp.ord_le72135733267957522d_enat X2) C2)) (@ P X2))) (forall ((D3 tptp.extended_enat)) (=> (forall ((X5 tptp.extended_enat)) (=> (and (@ (@ tptp.ord_le2932123472753598470d_enat A) X5) (@ (@ tptp.ord_le72135733267957522d_enat X5) D3)) (@ P X5))) (@ (@ tptp.ord_le2932123472753598470d_enat D3) C2))))))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (P (-> tptp.real Bool))) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ P A) (=> (not (@ P B2)) (exists ((C2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A) C2) (@ (@ tptp.ord_less_eq_real C2) B2) (forall ((X2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A) X2) (@ (@ tptp.ord_less_real X2) C2)) (@ P X2))) (forall ((D3 tptp.real)) (=> (forall ((X5 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A) X5) (@ (@ tptp.ord_less_real X5) D3)) (@ P X5))) (@ (@ tptp.ord_less_eq_real D3) C2))))))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat A) B2) (=> (@ P A) (=> (not (@ P B2)) (exists ((C2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A) C2) (@ (@ tptp.ord_less_eq_nat C2) B2) (forall ((X2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat A) X2) (@ (@ tptp.ord_less_nat X2) C2)) (@ P X2))) (forall ((D3 tptp.nat)) (=> (forall ((X5 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat A) X5) (@ (@ tptp.ord_less_nat X5) D3)) (@ P X5))) (@ (@ tptp.ord_less_eq_nat D3) C2))))))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int A) B2) (=> (@ P A) (=> (not (@ P B2)) (exists ((C2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A) C2) (@ (@ tptp.ord_less_eq_int C2) B2) (forall ((X2 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int A) X2) (@ (@ tptp.ord_less_int X2) C2)) (@ P X2))) (forall ((D3 tptp.int)) (=> (forall ((X5 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int A) X5) (@ (@ tptp.ord_less_int X5) D3)) (@ P X5))) (@ (@ tptp.ord_less_eq_int D3) C2))))))))))
% 4.71/5.17 (assert (forall ((T tptp.extended_enat)) (exists ((Z tptp.extended_enat)) (forall ((X2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z) X2) (not (@ (@ tptp.ord_le2932123472753598470d_enat X2) T)))))))
% 4.71/5.17 (assert (forall ((T tptp.real)) (exists ((Z tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X2) (not (@ (@ tptp.ord_less_eq_real X2) T)))))))
% 4.71/5.17 (assert (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z) X2) (not (@ (@ tptp.ord_less_eq_nat X2) T)))))))
% 4.71/5.17 (assert (forall ((T tptp.int)) (exists ((Z tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int Z) X2) (not (@ (@ tptp.ord_less_eq_int X2) T)))))))
% 4.71/5.17 (assert (forall ((T tptp.extended_enat)) (exists ((Z tptp.extended_enat)) (forall ((X2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z) X2) (@ (@ tptp.ord_le2932123472753598470d_enat T) X2))))))
% 4.71/5.17 (assert (forall ((T tptp.real)) (exists ((Z tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X2) (@ (@ tptp.ord_less_eq_real T) X2))))))
% 4.71/5.17 (assert (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z) X2) (@ (@ tptp.ord_less_eq_nat T) X2))))))
% 4.71/5.17 (assert (forall ((T tptp.int)) (exists ((Z tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int Z) X2) (@ (@ tptp.ord_less_eq_int T) X2))))))
% 4.71/5.17 (assert (forall ((T tptp.extended_enat)) (exists ((Z tptp.extended_enat)) (forall ((X2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X2) Z) (@ (@ tptp.ord_le2932123472753598470d_enat X2) T))))))
% 4.71/5.17 (assert (forall ((T tptp.real)) (exists ((Z tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Z) (@ (@ tptp.ord_less_eq_real X2) T))))))
% 4.71/5.17 (assert (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Z) (@ (@ tptp.ord_less_eq_nat X2) T))))))
% 4.71/5.17 (assert (forall ((T tptp.int)) (exists ((Z tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Z) (@ (@ tptp.ord_less_eq_int X2) T))))))
% 4.71/5.17 (assert (forall ((T tptp.extended_enat)) (exists ((Z tptp.extended_enat)) (forall ((X2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X2) Z) (not (@ (@ tptp.ord_le2932123472753598470d_enat T) X2)))))))
% 4.71/5.17 (assert (forall ((T tptp.real)) (exists ((Z tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Z) (not (@ (@ tptp.ord_less_eq_real T) X2)))))))
% 4.71/5.17 (assert (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Z) (not (@ (@ tptp.ord_less_eq_nat T) X2)))))))
% 4.71/5.17 (assert (forall ((T tptp.int)) (exists ((Z tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Z) (not (@ (@ tptp.ord_less_eq_int T) X2)))))))
% 4.71/5.17 (assert (forall ((X tptp.extended_enat) (Xs tptp.list_Extended_enat)) (=> (not (@ (@ tptp.member_Extended_enat X) (@ tptp.set_Extended_enat2 Xs))) (= (@ (@ tptp.count_101369445342291426d_enat Xs) X) tptp.zero_zero_nat))))
% 4.71/5.17 (assert (forall ((X tptp.real) (Xs tptp.list_real)) (=> (not (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs))) (= (@ (@ tptp.count_list_real Xs) X) tptp.zero_zero_nat))))
% 4.71/5.17 (assert (forall ((X tptp.set_nat) (Xs tptp.list_set_nat)) (=> (not (@ (@ tptp.member_set_nat X) (@ tptp.set_set_nat2 Xs))) (= (@ (@ tptp.count_list_set_nat Xs) X) tptp.zero_zero_nat))))
% 4.71/5.17 (assert (forall ((X tptp.vEBT_VEBT) (Xs tptp.list_VEBT_VEBT)) (=> (not (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs))) (= (@ (@ tptp.count_list_VEBT_VEBT Xs) X) tptp.zero_zero_nat))))
% 4.71/5.17 (assert (forall ((X tptp.int) (Xs tptp.list_int)) (=> (not (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs))) (= (@ (@ tptp.count_list_int Xs) X) tptp.zero_zero_nat))))
% 4.71/5.17 (assert (forall ((X tptp.nat) (Xs tptp.list_nat)) (=> (not (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs))) (= (@ (@ tptp.count_list_nat Xs) X) tptp.zero_zero_nat))))
% 4.71/5.17 (assert (let ((_let_1 (@ (@ tptp.vEBT_VEBT_high tptp.mi) tptp.na))) (let ((_let_2 (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_1))) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat tptp.mi) tptp.ma))) tptp.deg) tptp.treeList) tptp.summary)) tptp.xa) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat tptp.xa) (@ (@ tptp.ord_max_nat tptp.mi) tptp.ma)))) tptp.deg) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT tptp.treeList) _let_1) (@ (@ tptp.vEBT_vebt_insert _let_2) (@ (@ tptp.vEBT_VEBT_low tptp.mi) tptp.na)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_2)) (@ (@ tptp.vEBT_vebt_insert tptp.summary) _let_1)) tptp.summary))))))
% 4.71/5.17 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList2) Summary)) N2) (= Deg N2))))
% 4.71/5.17 (assert (forall ((Tree tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt Tree) (@ tptp.suc (@ tptp.suc N2))) (exists ((Info2 tptp.option4927543243414619207at_nat) (TreeList3 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (= Tree (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc (@ tptp.suc N2))) TreeList3) S3))))))
% 4.71/5.17 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) Deg) (=> (= Mi Ma) (and (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X_1))))) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_1))))))))
% 4.71/5.17 (assert (forall ((X tptp.set_Extended_enat)) (= (@ (@ tptp.ord_ma4205026669011143323d_enat X) tptp.bot_bo7653980558646680370d_enat) X)))
% 4.71/5.17 (assert (forall ((X tptp.set_real)) (= (@ (@ tptp.ord_max_set_real X) tptp.bot_bot_set_real) X)))
% 4.71/5.17 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.ord_max_set_nat X) tptp.bot_bot_set_nat) X)))
% 4.71/5.17 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.ord_max_set_int X) tptp.bot_bot_set_int) X)))
% 4.71/5.17 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.ord_max_nat X) tptp.bot_bot_nat) X)))
% 4.71/5.17 (assert (forall ((X tptp.set_Extended_enat)) (= (@ (@ tptp.ord_ma4205026669011143323d_enat tptp.bot_bo7653980558646680370d_enat) X) X)))
% 4.71/5.17 (assert (forall ((X tptp.set_real)) (= (@ (@ tptp.ord_max_set_real tptp.bot_bot_set_real) X) X)))
% 4.71/5.17 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.ord_max_set_nat tptp.bot_bot_set_nat) X) X)))
% 4.71/5.17 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.ord_max_set_int tptp.bot_bot_set_int) X) X)))
% 4.71/5.17 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.bot_bot_nat) X) X)))
% 4.71/5.17 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_max_nat (@ tptp.suc M2)) (@ tptp.suc N2)) (@ tptp.suc (@ (@ tptp.ord_max_nat M2) N2)))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (= (@ (@ tptp.ord_max_nat A) B2) tptp.zero_zero_nat) (and (= A tptp.zero_zero_nat) (= B2 tptp.zero_zero_nat)))))
% 4.71/5.17 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) A) A)))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.ord_max_nat A) B2)) (and (= A tptp.zero_zero_nat) (= B2 tptp.zero_zero_nat)))))
% 4.71/5.17 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat A) tptp.zero_zero_nat) A)))
% 4.71/5.17 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) N2) N2)))
% 4.71/5.17 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_max_nat N2) tptp.zero_zero_nat) N2)))
% 4.71/5.17 (assert (= (@ tptp.nat_triangle tptp.zero_zero_nat) tptp.zero_zero_nat))
% 4.71/5.17 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va2 tptp.list_VEBT_VEBT) (Vb tptp.vEBT_VEBT) (X tptp.nat)) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) tptp.zero_zero_nat) Va2) Vb)) X) (or (= X Mi) (= X Ma)))))
% 4.71/5.17 (assert (= tptp.ord_max_real (lambda ((A3 tptp.real) (B3 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_eq_real A3) B3)) B3) A3))))
% 4.71/5.17 (assert (= tptp.ord_max_set_nat (lambda ((A3 tptp.set_nat) (B3 tptp.set_nat)) (@ (@ (@ tptp.if_set_nat (@ (@ tptp.ord_less_eq_set_nat A3) B3)) B3) A3))))
% 4.71/5.17 (assert (= tptp.ord_max_set_int (lambda ((A3 tptp.set_int) (B3 tptp.set_int)) (@ (@ (@ tptp.if_set_int (@ (@ tptp.ord_less_eq_set_int A3) B3)) B3) A3))))
% 4.71/5.17 (assert (= tptp.ord_max_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_eq_nat A3) B3)) B3) A3))))
% 4.71/5.17 (assert (= tptp.ord_max_int (lambda ((A3 tptp.int) (B3 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int A3) B3)) B3) A3))))
% 4.71/5.17 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y) X) (= (@ (@ tptp.ord_max_real X) Y) X))))
% 4.71/5.17 (assert (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X) (= (@ (@ tptp.ord_max_set_nat X) Y) X))))
% 4.71/5.17 (assert (forall ((Y tptp.set_int) (X tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y) X) (= (@ (@ tptp.ord_max_set_int X) Y) X))))
% 4.71/5.17 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= (@ (@ tptp.ord_max_nat X) Y) X))))
% 4.71/5.17 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= (@ (@ tptp.ord_max_int X) Y) X))))
% 4.71/5.17 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (= (@ (@ tptp.ord_max_real X) Y) Y))))
% 4.71/5.17 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (= (@ (@ tptp.ord_max_set_nat X) Y) Y))))
% 4.71/5.17 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X) Y) (= (@ (@ tptp.ord_max_set_int X) Y) Y))))
% 4.71/5.17 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (= (@ (@ tptp.ord_max_nat X) Y) Y))))
% 4.71/5.17 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (= (@ (@ tptp.ord_max_int X) Y) Y))))
% 4.71/5.17 (assert (forall ((X tptp.real) (Y tptp.real) (Z3 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.ord_max_real X) Y)) Z3) (@ (@ tptp.ord_max_real (@ (@ tptp.plus_plus_real X) Z3)) (@ (@ tptp.plus_plus_real Y) Z3)))))
% 4.71/5.17 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat X) Y)) Z3) (@ (@ tptp.ord_max_nat (@ (@ tptp.plus_plus_nat X) Z3)) (@ (@ tptp.plus_plus_nat Y) Z3)))))
% 4.71/5.17 (assert (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.ord_max_int X) Y)) Z3) (@ (@ tptp.ord_max_int (@ (@ tptp.plus_plus_int X) Z3)) (@ (@ tptp.plus_plus_int Y) Z3)))))
% 4.71/5.17 (assert (forall ((X tptp.real) (Y tptp.real) (Z3 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real X))) (= (@ _let_1 (@ (@ tptp.ord_max_real Y) Z3)) (@ (@ tptp.ord_max_real (@ _let_1 Y)) (@ _let_1 Z3))))))
% 4.71/5.17 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat X))) (= (@ _let_1 (@ (@ tptp.ord_max_nat Y) Z3)) (@ (@ tptp.ord_max_nat (@ _let_1 Y)) (@ _let_1 Z3))))))
% 4.71/5.17 (assert (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X))) (= (@ _let_1 (@ (@ tptp.ord_max_int Y) Z3)) (@ (@ tptp.ord_max_int (@ _let_1 Y)) (@ _let_1 Z3))))))
% 4.71/5.17 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (Q3 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat M2) N2)) Q3) (@ (@ tptp.ord_max_nat (@ (@ tptp.plus_plus_nat M2) Q3)) (@ (@ tptp.plus_plus_nat N2) Q3)))))
% 4.71/5.17 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (Q3 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M2))) (= (@ _let_1 (@ (@ tptp.ord_max_nat N2) Q3)) (@ (@ tptp.ord_max_nat (@ _let_1 N2)) (@ _let_1 Q3))))))
% 4.71/5.17 (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))))
% 4.71/5.17 (assert (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Z) (not (@ (@ tptp.ord_less_nat T) X2)))))))
% 4.71/5.17 (assert (forall ((T tptp.extended_enat)) (exists ((Z tptp.extended_enat)) (forall ((X2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X2) Z) (not (@ (@ tptp.ord_le72135733267957522d_enat T) X2)))))))
% 4.71/5.17 (assert (forall ((T tptp.real)) (exists ((Z tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Z) (not (@ (@ tptp.ord_less_real T) X2)))))))
% 4.71/5.17 (assert (forall ((T tptp.int)) (exists ((Z tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Z) (not (@ (@ tptp.ord_less_int T) X2)))))))
% 4.71/5.17 (assert (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X2))) (=> (@ _let_1 Z) (@ _let_1 T)))))))
% 4.71/5.17 (assert (forall ((T tptp.extended_enat)) (exists ((Z tptp.extended_enat)) (forall ((X2 tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat X2))) (=> (@ _let_1 Z) (@ _let_1 T)))))))
% 4.71/5.17 (assert (forall ((T tptp.real)) (exists ((Z tptp.real)) (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X2))) (=> (@ _let_1 Z) (@ _let_1 T)))))))
% 4.71/5.17 (assert (forall ((T tptp.int)) (exists ((Z tptp.int)) (forall ((X2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X2))) (=> (@ _let_1 Z) (@ _let_1 T)))))))
% 4.71/5.17 (assert (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Z) (not (= X2 T)))))))
% 4.71/5.17 (assert (forall ((T tptp.extended_enat)) (exists ((Z tptp.extended_enat)) (forall ((X2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X2) Z) (not (= X2 T)))))))
% 4.71/5.17 (assert (forall ((T tptp.real)) (exists ((Z tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Z) (not (= X2 T)))))))
% 4.71/5.17 (assert (forall ((T tptp.int)) (exists ((Z tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Z) (not (= X2 T)))))))
% 4.71/5.17 (assert (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Z) (not (= X2 T)))))))
% 4.71/5.17 (assert (forall ((T tptp.extended_enat)) (exists ((Z tptp.extended_enat)) (forall ((X2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X2) Z) (not (= X2 T)))))))
% 4.71/5.17 (assert (forall ((T tptp.real)) (exists ((Z tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Z) (not (= X2 T)))))))
% 4.71/5.17 (assert (forall ((T tptp.int)) (exists ((Z tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Z) (not (= X2 T)))))))
% 4.71/5.17 (assert (forall ((P (-> tptp.nat Bool)) (P4 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q4 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z4) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z4) (= (@ Q X5) (@ Q4 X5))))) (exists ((Z tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Z) (= (or (@ P X2) (@ Q X2)) (or (@ P4 X2) (@ Q4 X2))))))))))
% 4.71/5.17 (assert (forall ((P (-> tptp.extended_enat Bool)) (P4 (-> tptp.extended_enat Bool)) (Q (-> tptp.extended_enat Bool)) (Q4 (-> tptp.extended_enat Bool))) (=> (exists ((Z4 tptp.extended_enat)) (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Z4) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z4 tptp.extended_enat)) (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Z4) (= (@ Q X5) (@ Q4 X5))))) (exists ((Z tptp.extended_enat)) (forall ((X2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X2) Z) (= (or (@ P X2) (@ Q X2)) (or (@ P4 X2) (@ Q4 X2))))))))))
% 4.71/5.17 (assert (forall ((P (-> tptp.real Bool)) (P4 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q4 (-> tptp.real Bool))) (=> (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z4) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z4) (= (@ Q X5) (@ Q4 X5))))) (exists ((Z tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Z) (= (or (@ P X2) (@ Q X2)) (or (@ P4 X2) (@ Q4 X2))))))))))
% 4.71/5.17 (assert (forall ((P (-> tptp.int Bool)) (P4 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q4 (-> tptp.int Bool))) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z4) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z4) (= (@ Q X5) (@ Q4 X5))))) (exists ((Z tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Z) (= (or (@ P X2) (@ Q X2)) (or (@ P4 X2) (@ Q4 X2))))))))))
% 4.71/5.17 (assert (forall ((P (-> tptp.nat Bool)) (P4 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q4 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z4) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z4) (= (@ Q X5) (@ Q4 X5))))) (exists ((Z tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Z) (= (and (@ P X2) (@ Q X2)) (and (@ P4 X2) (@ Q4 X2))))))))))
% 4.71/5.17 (assert (forall ((P (-> tptp.extended_enat Bool)) (P4 (-> tptp.extended_enat Bool)) (Q (-> tptp.extended_enat Bool)) (Q4 (-> tptp.extended_enat Bool))) (=> (exists ((Z4 tptp.extended_enat)) (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Z4) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z4 tptp.extended_enat)) (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Z4) (= (@ Q X5) (@ Q4 X5))))) (exists ((Z tptp.extended_enat)) (forall ((X2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X2) Z) (= (and (@ P X2) (@ Q X2)) (and (@ P4 X2) (@ Q4 X2))))))))))
% 4.71/5.17 (assert (forall ((P (-> tptp.real Bool)) (P4 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q4 (-> tptp.real Bool))) (=> (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z4) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z4) (= (@ Q X5) (@ Q4 X5))))) (exists ((Z tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Z) (= (and (@ P X2) (@ Q X2)) (and (@ P4 X2) (@ Q4 X2))))))))))
% 4.71/5.17 (assert (forall ((P (-> tptp.int Bool)) (P4 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q4 (-> tptp.int Bool))) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z4) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z4) (= (@ Q X5) (@ Q4 X5))))) (exists ((Z tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Z) (= (and (@ P X2) (@ Q X2)) (and (@ P4 X2) (@ Q4 X2))))))))))
% 4.71/5.17 (assert (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z) X2) (@ (@ tptp.ord_less_nat T) X2))))))
% 4.71/5.17 (assert (forall ((T tptp.extended_enat)) (exists ((Z tptp.extended_enat)) (forall ((X2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z) X2) (@ (@ tptp.ord_le72135733267957522d_enat T) X2))))))
% 4.71/5.17 (assert (forall ((T tptp.real)) (exists ((Z tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X2) (@ (@ tptp.ord_less_real T) X2))))))
% 4.71/5.17 (assert (forall ((T tptp.int)) (exists ((Z tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int Z) X2) (@ (@ tptp.ord_less_int T) X2))))))
% 4.71/5.17 (assert (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z) X2) (not (@ (@ tptp.ord_less_nat X2) T)))))))
% 4.71/5.17 (assert (forall ((T tptp.extended_enat)) (exists ((Z tptp.extended_enat)) (forall ((X2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z) X2) (not (@ (@ tptp.ord_le72135733267957522d_enat X2) T)))))))
% 4.71/5.17 (assert (forall ((T tptp.real)) (exists ((Z tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X2) (not (@ (@ tptp.ord_less_real X2) T)))))))
% 4.71/5.17 (assert (forall ((T tptp.int)) (exists ((Z tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int Z) X2) (not (@ (@ tptp.ord_less_int X2) T)))))))
% 4.71/5.17 (assert (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z) X2) (not (= X2 T)))))))
% 4.71/5.17 (assert (forall ((T tptp.extended_enat)) (exists ((Z tptp.extended_enat)) (forall ((X2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z) X2) (not (= X2 T)))))))
% 4.71/5.17 (assert (forall ((T tptp.real)) (exists ((Z tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X2) (not (= X2 T)))))))
% 4.71/5.17 (assert (forall ((T tptp.int)) (exists ((Z tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int Z) X2) (not (= X2 T)))))))
% 4.71/5.17 (assert (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z) X2) (not (= X2 T)))))))
% 4.71/5.17 (assert (forall ((T tptp.extended_enat)) (exists ((Z tptp.extended_enat)) (forall ((X2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z) X2) (not (= X2 T)))))))
% 4.71/5.17 (assert (forall ((T tptp.real)) (exists ((Z tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X2) (not (= X2 T)))))))
% 4.71/5.17 (assert (forall ((T tptp.int)) (exists ((Z tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int Z) X2) (not (= X2 T)))))))
% 4.71/5.17 (assert (forall ((P (-> tptp.nat Bool)) (P4 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q4 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X5) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X5) (= (@ Q X5) (@ Q4 X5))))) (exists ((Z tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z) X2) (= (or (@ P X2) (@ Q X2)) (or (@ P4 X2) (@ Q4 X2))))))))))
% 4.71/5.17 (assert (forall ((P (-> tptp.extended_enat Bool)) (P4 (-> tptp.extended_enat Bool)) (Q (-> tptp.extended_enat Bool)) (Q4 (-> tptp.extended_enat Bool))) (=> (exists ((Z4 tptp.extended_enat)) (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z4) X5) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z4 tptp.extended_enat)) (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z4) X5) (= (@ Q X5) (@ Q4 X5))))) (exists ((Z tptp.extended_enat)) (forall ((X2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z) X2) (= (or (@ P X2) (@ Q X2)) (or (@ P4 X2) (@ Q4 X2))))))))))
% 4.71/5.17 (assert (forall ((P (-> tptp.real Bool)) (P4 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q4 (-> tptp.real Bool))) (=> (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X5) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X5) (= (@ Q X5) (@ Q4 X5))))) (exists ((Z tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X2) (= (or (@ P X2) (@ Q X2)) (or (@ P4 X2) (@ Q4 X2))))))))))
% 4.71/5.17 (assert (forall ((P (-> tptp.int Bool)) (P4 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q4 (-> tptp.int Bool))) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X5) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X5) (= (@ Q X5) (@ Q4 X5))))) (exists ((Z tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int Z) X2) (= (or (@ P X2) (@ Q X2)) (or (@ P4 X2) (@ Q4 X2))))))))))
% 4.71/5.17 (assert (forall ((P (-> tptp.nat Bool)) (P4 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q4 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X5) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X5) (= (@ Q X5) (@ Q4 X5))))) (exists ((Z tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z) X2) (= (and (@ P X2) (@ Q X2)) (and (@ P4 X2) (@ Q4 X2))))))))))
% 4.71/5.17 (assert (forall ((P (-> tptp.extended_enat Bool)) (P4 (-> tptp.extended_enat Bool)) (Q (-> tptp.extended_enat Bool)) (Q4 (-> tptp.extended_enat Bool))) (=> (exists ((Z4 tptp.extended_enat)) (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z4) X5) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z4 tptp.extended_enat)) (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z4) X5) (= (@ Q X5) (@ Q4 X5))))) (exists ((Z tptp.extended_enat)) (forall ((X2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z) X2) (= (and (@ P X2) (@ Q X2)) (and (@ P4 X2) (@ Q4 X2))))))))))
% 4.71/5.17 (assert (forall ((P (-> tptp.real Bool)) (P4 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q4 (-> tptp.real Bool))) (=> (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X5) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X5) (= (@ Q X5) (@ Q4 X5))))) (exists ((Z tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X2) (= (and (@ P X2) (@ Q X2)) (and (@ P4 X2) (@ Q4 X2))))))))))
% 4.71/5.17 (assert (forall ((P (-> tptp.int Bool)) (P4 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q4 (-> tptp.int Bool))) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X5) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X5) (= (@ Q X5) (@ Q4 X5))))) (exists ((Z tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int Z) X2) (= (and (@ P X2) (@ Q X2)) (and (@ P4 X2) (@ Q4 X2))))))))))
% 4.71/5.17 (assert (forall ((A tptp.real)) (exists ((B4 tptp.real)) (or (@ (@ tptp.ord_less_real A) B4) (@ (@ tptp.ord_less_real B4) A)))))
% 4.71/5.17 (assert (forall ((Xs tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.count_list_VEBT_VEBT Xs) X)) (@ tptp.size_s6755466524823107622T_VEBT Xs))))
% 4.71/5.17 (assert (forall ((Xs tptp.list_int) (X tptp.int)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.count_list_int Xs) X)) (@ tptp.size_size_list_int Xs))))
% 4.71/5.17 (assert (forall ((Xs tptp.list_nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.count_list_nat Xs) X)) (@ tptp.size_size_list_nat Xs))))
% 4.71/5.17 (assert (forall ((V tptp.product_prod_nat_nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vb) Vc)) X))))
% 4.71/5.17 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B2) A) (= (@ (@ tptp.ord_max_nat A) B2) A))))
% 4.71/5.17 (assert (forall ((B2 tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B2) A) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B2) A))))
% 4.71/5.17 (assert (forall ((B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B2) A) (= (@ (@ tptp.ord_max_real A) B2) A))))
% 4.71/5.17 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B2) A) (= (@ (@ tptp.ord_max_int A) B2) A))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (= (@ (@ tptp.ord_max_nat A) B2) B2))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B2) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B2) B2))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (= (@ (@ tptp.ord_max_real A) B2) B2))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B2) (= (@ (@ tptp.ord_max_int A) B2) B2))))
% 4.71/5.17 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.ord_max_nat X) Y)) Z3) (and (@ (@ tptp.ord_less_nat X) Z3) (@ (@ tptp.ord_less_nat Y) Z3)))))
% 4.71/5.17 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat) (Z3 tptp.extended_enat)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.ord_ma741700101516333627d_enat X) Y)) Z3) (and (@ (@ tptp.ord_le72135733267957522d_enat X) Z3) (@ (@ tptp.ord_le72135733267957522d_enat Y) Z3)))))
% 4.71/5.17 (assert (forall ((X tptp.real) (Y tptp.real) (Z3 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.ord_max_real X) Y)) Z3) (and (@ (@ tptp.ord_less_real X) Z3) (@ (@ tptp.ord_less_real Y) Z3)))))
% 4.71/5.17 (assert (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.ord_max_int X) Y)) Z3) (and (@ (@ tptp.ord_less_int X) Z3) (@ (@ tptp.ord_less_int Y) Z3)))))
% 4.71/5.17 (assert (forall ((B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B2) A) (= (@ (@ tptp.ord_max_real A) B2) A))))
% 4.71/5.17 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B2) A) (= (@ (@ tptp.ord_max_nat A) B2) A))))
% 4.71/5.17 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B2) A) (= (@ (@ tptp.ord_max_int A) B2) A))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (= (@ (@ tptp.ord_max_real A) B2) B2))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (= (@ (@ tptp.ord_max_nat A) B2) B2))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (= (@ (@ tptp.ord_max_int A) B2) B2))))
% 4.71/5.17 (assert (forall ((B2 tptp.real) (C tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.ord_max_real B2) C)) A) (and (@ (@ tptp.ord_less_eq_real B2) A) (@ (@ tptp.ord_less_eq_real C) A)))))
% 4.71/5.17 (assert (forall ((B2 tptp.nat) (C tptp.nat) (A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat B2) C)) A) (and (@ (@ tptp.ord_less_eq_nat B2) A) (@ (@ tptp.ord_less_eq_nat C) A)))))
% 4.71/5.17 (assert (forall ((B2 tptp.int) (C tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int B2) C)) A) (and (@ (@ tptp.ord_less_eq_int B2) A) (@ (@ tptp.ord_less_eq_int C) A)))))
% 4.71/5.17 (assert (forall ((V tptp.product_prod_nat_nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT) (X tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Uy) Uz)) X))))
% 4.71/5.17 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) (@ tptp.suc tptp.zero_zero_nat)) Ts) S))) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X) _let_1))))
% 4.71/5.17 (assert (forall ((Uz tptp.product_prod_nat_nat) (Va2 tptp.nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz)) Va2) Vb) Vc)))))
% 4.71/5.17 (assert (forall ((C tptp.real) (B2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.ord_max_real A) B2))))))
% 4.71/5.17 (assert (forall ((C tptp.nat) (B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.ord_max_nat A) B2))))))
% 4.71/5.17 (assert (forall ((C tptp.int) (B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.ord_max_int A) B2))))))
% 4.71/5.17 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_real A) B2))))))
% 4.71/5.17 (assert (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_nat A) B2))))))
% 4.71/5.17 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_int A) B2))))))
% 4.71/5.17 (assert (= tptp.ord_less_eq_real (lambda ((A3 tptp.real) (B3 tptp.real)) (= (@ (@ tptp.ord_max_real A3) B3) B3))))
% 4.71/5.17 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (= (@ (@ tptp.ord_max_nat A3) B3) B3))))
% 4.71/5.17 (assert (= tptp.ord_less_eq_int (lambda ((A3 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.ord_max_int A3) B3) B3))))
% 4.71/5.17 (assert (= tptp.ord_less_eq_real (lambda ((B3 tptp.real) (A3 tptp.real)) (= (@ (@ tptp.ord_max_real A3) B3) A3))))
% 4.71/5.17 (assert (= tptp.ord_less_eq_nat (lambda ((B3 tptp.nat) (A3 tptp.nat)) (= (@ (@ tptp.ord_max_nat A3) B3) A3))))
% 4.71/5.17 (assert (= tptp.ord_less_eq_int (lambda ((B3 tptp.int) (A3 tptp.int)) (= (@ (@ tptp.ord_max_int A3) B3) A3))))
% 4.71/5.17 (assert (forall ((Z3 tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real Z3))) (= (@ _let_1 (@ (@ tptp.ord_max_real X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 4.71/5.17 (assert (forall ((Z3 tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat Z3))) (= (@ _let_1 (@ (@ tptp.ord_max_nat X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 4.71/5.17 (assert (forall ((Z3 tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int Z3))) (= (@ _let_1 (@ (@ tptp.ord_max_int X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 4.71/5.17 (assert (forall ((B2 tptp.real) (A tptp.real)) (@ (@ tptp.ord_less_eq_real B2) (@ (@ tptp.ord_max_real A) B2))))
% 4.71/5.17 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (@ (@ tptp.ord_less_eq_nat B2) (@ (@ tptp.ord_max_nat A) B2))))
% 4.71/5.17 (assert (forall ((B2 tptp.int) (A tptp.int)) (@ (@ tptp.ord_less_eq_int B2) (@ (@ tptp.ord_max_int A) B2))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.ord_max_real A) B2))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.ord_max_nat A) B2))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.ord_max_int A) B2))))
% 4.71/5.17 (assert (= tptp.ord_less_eq_real (lambda ((B3 tptp.real) (A3 tptp.real)) (= A3 (@ (@ tptp.ord_max_real A3) B3)))))
% 4.71/5.17 (assert (= tptp.ord_less_eq_nat (lambda ((B3 tptp.nat) (A3 tptp.nat)) (= A3 (@ (@ tptp.ord_max_nat A3) B3)))))
% 4.71/5.17 (assert (= tptp.ord_less_eq_int (lambda ((B3 tptp.int) (A3 tptp.int)) (= A3 (@ (@ tptp.ord_max_int A3) B3)))))
% 4.71/5.17 (assert (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B2) A) (=> (@ (@ tptp.ord_less_eq_real C) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.ord_max_real B2) C)) A)))))
% 4.71/5.17 (assert (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B2) A) (=> (@ (@ tptp.ord_less_eq_nat C) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat B2) C)) A)))))
% 4.71/5.17 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B2) A) (=> (@ (@ tptp.ord_less_eq_int C) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int B2) C)) A)))))
% 4.71/5.17 (assert (forall ((B2 tptp.real) (C tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.ord_max_real B2) C)) A) (not (=> (@ (@ tptp.ord_less_eq_real B2) A) (not (@ (@ tptp.ord_less_eq_real C) A)))))))
% 4.71/5.17 (assert (forall ((B2 tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat B2) C)) A) (not (=> (@ (@ tptp.ord_less_eq_nat B2) A) (not (@ (@ tptp.ord_less_eq_nat C) A)))))))
% 4.71/5.17 (assert (forall ((B2 tptp.int) (C tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int B2) C)) A) (not (=> (@ (@ tptp.ord_less_eq_int B2) A) (not (@ (@ tptp.ord_less_eq_int C) A)))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (= A (@ (@ tptp.ord_max_real A) B2)) (@ (@ tptp.ord_less_eq_real B2) A))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (= A (@ (@ tptp.ord_max_nat A) B2)) (@ (@ tptp.ord_less_eq_nat B2) A))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (= A (@ (@ tptp.ord_max_int A) B2)) (@ (@ tptp.ord_less_eq_int B2) A))))
% 4.71/5.17 (assert (forall ((B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B2) A) (= A (@ (@ tptp.ord_max_real A) B2)))))
% 4.71/5.17 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B2) A) (= A (@ (@ tptp.ord_max_nat A) B2)))))
% 4.71/5.17 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B2) A) (= A (@ (@ tptp.ord_max_int A) B2)))))
% 4.71/5.17 (assert (forall ((C tptp.real) (A tptp.real) (D tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real C) A) (=> (@ (@ tptp.ord_less_eq_real D) B2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.ord_max_real C) D)) (@ (@ tptp.ord_max_real A) B2))))))
% 4.71/5.17 (assert (forall ((C tptp.nat) (A tptp.nat) (D tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) A) (=> (@ (@ tptp.ord_less_eq_nat D) B2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat C) D)) (@ (@ tptp.ord_max_nat A) B2))))))
% 4.71/5.17 (assert (forall ((C tptp.int) (A tptp.int) (D tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C) A) (=> (@ (@ tptp.ord_less_eq_int D) B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int C) D)) (@ (@ tptp.ord_max_int A) B2))))))
% 4.71/5.17 (assert (forall ((C tptp.nat) (B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.ord_max_nat A) B2))))))
% 4.71/5.17 (assert (forall ((C tptp.extended_enat) (B2 tptp.extended_enat) (A tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat A) B2))))))
% 4.71/5.17 (assert (forall ((C tptp.real) (B2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.ord_max_real A) B2))))))
% 4.71/5.17 (assert (forall ((C tptp.int) (B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.ord_max_int A) B2))))))
% 4.71/5.17 (assert (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_nat A) B2))))))
% 4.71/5.17 (assert (forall ((C tptp.extended_enat) (A tptp.extended_enat) (B2 tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat A) B2))))))
% 4.71/5.17 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_real A) B2))))))
% 4.71/5.17 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_int A) B2))))))
% 4.71/5.17 (assert (= tptp.ord_less_nat (lambda ((B3 tptp.nat) (A3 tptp.nat)) (and (= A3 (@ (@ tptp.ord_max_nat A3) B3)) (not (= A3 B3))))))
% 4.71/5.17 (assert (= tptp.ord_le72135733267957522d_enat (lambda ((B3 tptp.extended_enat) (A3 tptp.extended_enat)) (and (= A3 (@ (@ tptp.ord_ma741700101516333627d_enat A3) B3)) (not (= A3 B3))))))
% 4.71/5.17 (assert (= tptp.ord_less_real (lambda ((B3 tptp.real) (A3 tptp.real)) (and (= A3 (@ (@ tptp.ord_max_real A3) B3)) (not (= A3 B3))))))
% 4.71/5.17 (assert (= tptp.ord_less_int (lambda ((B3 tptp.int) (A3 tptp.int)) (and (= A3 (@ (@ tptp.ord_max_int A3) B3)) (not (= A3 B3))))))
% 4.71/5.17 (assert (forall ((B2 tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.ord_max_nat B2) C)) A) (not (=> (@ (@ tptp.ord_less_nat B2) A) (not (@ (@ tptp.ord_less_nat C) A)))))))
% 4.71/5.17 (assert (forall ((B2 tptp.extended_enat) (C tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.ord_ma741700101516333627d_enat B2) C)) A) (not (=> (@ (@ tptp.ord_le72135733267957522d_enat B2) A) (not (@ (@ tptp.ord_le72135733267957522d_enat C) A)))))))
% 4.71/5.17 (assert (forall ((B2 tptp.real) (C tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.ord_max_real B2) C)) A) (not (=> (@ (@ tptp.ord_less_real B2) A) (not (@ (@ tptp.ord_less_real C) A)))))))
% 4.71/5.17 (assert (forall ((B2 tptp.int) (C tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.ord_max_int B2) C)) A) (not (=> (@ (@ tptp.ord_less_int B2) A) (not (@ (@ tptp.ord_less_int C) A)))))))
% 4.71/5.17 (assert (forall ((Z3 tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat Z3))) (= (@ _let_1 (@ (@ tptp.ord_max_nat X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 4.71/5.17 (assert (forall ((Z3 tptp.extended_enat) (X tptp.extended_enat) (Y tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat Z3))) (= (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 4.71/5.17 (assert (forall ((Z3 tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real Z3))) (= (@ _let_1 (@ (@ tptp.ord_max_real X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 4.71/5.17 (assert (forall ((Z3 tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_int Z3))) (= (@ _let_1 (@ (@ tptp.ord_max_int X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 4.71/5.17 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) tptp.zero_zero_nat) Ts) S))) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X) _let_1))))
% 4.71/5.17 (assert (forall ((X22 tptp.product_prod_nat_nat)) (= (@ tptp.size_s170228958280169651at_nat (@ tptp.some_P7363390416028606310at_nat X22)) (@ tptp.suc tptp.zero_zero_nat))))
% 4.71/5.17 (assert (forall ((X22 tptp.num)) (= (@ tptp.size_size_option_num (@ tptp.some_num X22)) (@ tptp.suc tptp.zero_zero_nat))))
% 4.71/5.17 (assert (forall ((M2 tptp.nat) (Xs tptp.list_VEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.nth_Pr744662078594809490T_VEBT (@ (@ tptp.enumerate_VEBT_VEBT N2) Xs)) M2) (@ (@ tptp.produc599794634098209291T_VEBT (@ (@ tptp.plus_plus_nat N2) M2)) (@ (@ tptp.nth_VEBT_VEBT Xs) M2))))))
% 4.71/5.17 (assert (forall ((M2 tptp.nat) (Xs tptp.list_int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_Pr3440142176431000676at_int (@ (@ tptp.enumerate_int N2) Xs)) M2) (@ (@ tptp.product_Pair_nat_int (@ (@ tptp.plus_plus_nat N2) M2)) (@ (@ tptp.nth_int Xs) M2))))))
% 4.71/5.17 (assert (forall ((M2 tptp.nat) (Xs tptp.list_nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_Pr7617993195940197384at_nat (@ (@ tptp.enumerate_nat N2) Xs)) M2) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat N2) M2)) (@ (@ tptp.nth_nat Xs) M2))))))
% 4.71/5.17 (assert (forall ((X tptp.product_prod_nat_nat) (P (-> tptp.product_prod_nat_nat Bool)) (Xs tptp.list_P6011104703257516679at_nat)) (= (= (@ tptp.some_P7363390416028606310at_nat X) (@ (@ tptp.find_P8199882355184865565at_nat P) Xs)) (exists ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs) I3))) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s5460976970255530739at_nat Xs)) (@ P _let_1) (= X _let_1) (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J2) I3) (not (@ P (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs) J2)))))))))))
% 4.71/5.17 (assert (forall ((X tptp.num) (P (-> tptp.num Bool)) (Xs tptp.list_num)) (= (= (@ tptp.some_num X) (@ (@ tptp.find_num P) Xs)) (exists ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_num Xs) I3))) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_num Xs)) (@ P _let_1) (= X _let_1) (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J2) I3) (not (@ P (@ (@ tptp.nth_num Xs) J2)))))))))))
% 4.71/5.17 (assert (forall ((X tptp.vEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool)) (Xs tptp.list_VEBT_VEBT)) (= (= (@ tptp.some_VEBT_VEBT X) (@ (@ tptp.find_VEBT_VEBT P) Xs)) (exists ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_VEBT_VEBT Xs) I3))) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ P _let_1) (= X _let_1) (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J2) I3) (not (@ P (@ (@ tptp.nth_VEBT_VEBT Xs) J2)))))))))))
% 4.71/5.17 (assert (forall ((X tptp.int) (P (-> tptp.int Bool)) (Xs tptp.list_int)) (= (= (@ tptp.some_int X) (@ (@ tptp.find_int P) Xs)) (exists ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_int Xs) I3))) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_int Xs)) (@ P _let_1) (= X _let_1) (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J2) I3) (not (@ P (@ (@ tptp.nth_int Xs) J2)))))))))))
% 4.71/5.17 (assert (forall ((X tptp.nat) (P (-> tptp.nat Bool)) (Xs tptp.list_nat)) (= (= (@ tptp.some_nat X) (@ (@ tptp.find_nat P) Xs)) (exists ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_nat Xs) I3))) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs)) (@ P _let_1) (= X _let_1) (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J2) I3) (not (@ P (@ (@ tptp.nth_nat Xs) J2)))))))))))
% 4.71/5.17 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool)) (Xs tptp.list_P6011104703257516679at_nat) (X tptp.product_prod_nat_nat)) (= (= (@ (@ tptp.find_P8199882355184865565at_nat P) Xs) (@ tptp.some_P7363390416028606310at_nat X)) (exists ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs) I3))) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s5460976970255530739at_nat Xs)) (@ P _let_1) (= X _let_1) (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J2) I3) (not (@ P (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs) J2)))))))))))
% 4.71/5.17 (assert (forall ((P (-> tptp.num Bool)) (Xs tptp.list_num) (X tptp.num)) (= (= (@ (@ tptp.find_num P) Xs) (@ tptp.some_num X)) (exists ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_num Xs) I3))) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_num Xs)) (@ P _let_1) (= X _let_1) (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J2) I3) (not (@ P (@ (@ tptp.nth_num Xs) J2)))))))))))
% 4.71/5.17 (assert (forall ((P (-> tptp.vEBT_VEBT Bool)) (Xs tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (= (= (@ (@ tptp.find_VEBT_VEBT P) Xs) (@ tptp.some_VEBT_VEBT X)) (exists ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_VEBT_VEBT Xs) I3))) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ P _let_1) (= X _let_1) (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J2) I3) (not (@ P (@ (@ tptp.nth_VEBT_VEBT Xs) J2)))))))))))
% 4.71/5.17 (assert (forall ((P (-> tptp.int Bool)) (Xs tptp.list_int) (X tptp.int)) (= (= (@ (@ tptp.find_int P) Xs) (@ tptp.some_int X)) (exists ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_int Xs) I3))) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_int Xs)) (@ P _let_1) (= X _let_1) (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J2) I3) (not (@ P (@ (@ tptp.nth_int Xs) J2)))))))))))
% 4.71/5.17 (assert (forall ((P (-> tptp.nat Bool)) (Xs tptp.list_nat) (X tptp.nat)) (= (= (@ (@ tptp.find_nat P) Xs) (@ tptp.some_nat X)) (exists ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_nat Xs) I3))) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs)) (@ P _let_1) (= X _let_1) (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J2) I3) (not (@ P (@ (@ tptp.nth_nat Xs) J2)))))))))))
% 4.71/5.17 (assert (=> (not (= tptp.mi tptp.ma)) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high tptp.ma) tptp.na) I5) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I5)) (@ (@ tptp.vEBT_VEBT_low tptp.ma) tptp.na))) (forall ((Y6 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high Y6) tptp.na) I5) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I5)) (@ (@ tptp.vEBT_VEBT_low Y6) tptp.na))) (and (@ (@ tptp.ord_less_nat tptp.mi) Y6) (@ (@ tptp.ord_less_eq_nat Y6) tptp.ma)))))))))
% 4.71/5.17 (assert (forall ((Xs tptp.list_P6011104703257516679at_nat) (Ys tptp.list_P6011104703257516679at_nat) (R2 tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.member6693912407220327184at_nat (@ (@ tptp.produc5943733680697469783at_nat Xs) Ys)) (@ tptp.listre4828114922151135584at_nat R2)) (exists ((Y5 tptp.product_prod_nat_nat) (N tptp.nat)) (and (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs) N)) Y5)) R2) (@ (@ tptp.ord_less_nat N) (@ tptp.size_s5460976970255530739at_nat Xs)) (= Ys (@ (@ (@ tptp.list_u6180841689913720943at_nat Xs) N) Y5)))))))
% 4.71/5.17 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT) (R2 tptp.set_Pr6192946355708809607T_VEBT)) (= (@ (@ tptp.member4439316823752958928T_VEBT (@ (@ tptp.produc3897820843166775703T_VEBT Xs) Ys)) (@ tptp.listrel1_VEBT_VEBT R2)) (exists ((Y5 tptp.vEBT_VEBT) (N tptp.nat)) (and (@ (@ tptp.member568628332442017744T_VEBT (@ (@ tptp.produc537772716801021591T_VEBT (@ (@ tptp.nth_VEBT_VEBT Xs) N)) Y5)) R2) (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= Ys (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) N) Y5)))))))
% 4.71/5.17 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int) (R2 tptp.set_Pr958786334691620121nt_int)) (= (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int Xs) Ys)) (@ tptp.listrel1_int R2)) (exists ((Y5 tptp.int) (N tptp.nat)) (and (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int (@ (@ tptp.nth_int Xs) N)) Y5)) R2) (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs)) (= Ys (@ (@ (@ tptp.list_update_int Xs) N) Y5)))))))
% 4.71/5.17 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat Xs) Ys)) (@ tptp.listrel1_nat R2)) (exists ((Y5 tptp.nat) (N tptp.nat)) (and (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.nth_nat Xs) N)) Y5)) R2) (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (= Ys (@ (@ (@ tptp.list_update_nat Xs) N) Y5)))))))
% 4.71/5.17 (assert (forall ((X (-> tptp.product_prod_nat_nat tptp.nat)) (X22 tptp.product_prod_nat_nat)) (= (@ (@ tptp.size_o8335143837870341156at_nat X) (@ tptp.some_P7363390416028606310at_nat X22)) (@ (@ tptp.plus_plus_nat (@ X X22)) (@ tptp.suc tptp.zero_zero_nat)))))
% 4.71/5.17 (assert (forall ((X (-> tptp.num tptp.nat)) (X22 tptp.num)) (= (@ (@ tptp.size_option_num X) (@ tptp.some_num X22)) (@ (@ tptp.plus_plus_nat (@ X X22)) (@ tptp.suc tptp.zero_zero_nat)))))
% 4.71/5.17 (assert (forall ((I tptp.nat) (N2 tptp.nat) (P (-> tptp.nat Bool)) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) N2) (=> (@ P X) (@ P (@ (@ tptp.nth_nat (@ (@ tptp.replicate_nat N2) X)) I))))))
% 4.71/5.17 (assert (forall ((I tptp.nat) (N2 tptp.nat) (P (-> tptp.int Bool)) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat I) N2) (=> (@ P X) (@ P (@ (@ tptp.nth_int (@ (@ tptp.replicate_int N2) X)) I))))))
% 4.71/5.17 (assert (forall ((I tptp.nat) (N2 tptp.nat) (P (-> tptp.vEBT_VEBT Bool)) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I) N2) (=> (@ P X) (@ P (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.replicate_VEBT_VEBT N2) X)) I))))))
% 4.71/5.17 (assert (forall ((V tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc V)))) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat X) X))) _let_1) TreeList2) Summary)))))
% 4.71/5.17 (assert (= tptp.gen_length_VEBT_VEBT (lambda ((N tptp.nat) (Xs3 tptp.list_VEBT_VEBT)) (@ (@ tptp.plus_plus_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs3)))))
% 4.71/5.17 (assert (= tptp.gen_length_int (lambda ((N tptp.nat) (Xs3 tptp.list_int)) (@ (@ tptp.plus_plus_nat N) (@ tptp.size_size_list_int Xs3)))))
% 4.71/5.17 (assert (= tptp.gen_length_nat (lambda ((N tptp.nat) (Xs3 tptp.list_nat)) (@ (@ tptp.plus_plus_nat N) (@ tptp.size_size_list_nat Xs3)))))
% 4.71/5.17 (assert (= (@ tptp.size_s6755466524823107622T_VEBT tptp.treeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)))
% 4.71/5.17 (assert (@ (@ tptp.ord_less_nat tptp.ma) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.deg)))
% 4.71/5.17 (assert (@ (@ tptp.ord_less_nat tptp.xa) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.deg)))
% 4.71/5.17 (assert (@ (@ tptp.ord_less_nat tptp.i) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)))
% 4.71/5.17 (assert (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 tptp.treeList)) (and (@ (@ tptp.vEBT_invar_vebt X2) tptp.na) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.ord_less_nat Xa) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.na)) (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_vebt_insert X2) Xa)) tptp.na)))))))
% 4.71/5.17 (assert (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (= (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I5)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions tptp.summary) I5)))))
% 4.71/5.17 (assert (forall ((Ma tptp.nat) (N2 tptp.nat) (M2 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) M2))) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high Ma) N2)) (@ _let_1 M2))))))
% 4.71/5.17 (assert (forall ((Tree tptp.vEBT_VEBT) (X tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member Tree) X) (=> (@ (@ tptp.vEBT_invar_vebt Tree) N2) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))))
% 4.71/5.17 (assert (forall ((M2 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat M2)) (@ tptp.numera1916890842035813515d_enat N2)) (@ (@ tptp.ord_less_eq_num M2) N2))))
% 4.71/5.17 (assert (forall ((M2 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M2)) (@ tptp.numeral_numeral_real N2)) (@ (@ tptp.ord_less_eq_num M2) N2))))
% 4.71/5.17 (assert (forall ((M2 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat M2)) (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.ord_less_eq_num M2) N2))))
% 4.71/5.17 (assert (forall ((M2 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M2)) (@ tptp.numeral_numeral_int N2)) (@ (@ tptp.ord_less_eq_num M2) N2))))
% 4.71/5.17 (assert (forall ((M2 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat M2)) (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.ord_less_num M2) N2))))
% 4.71/5.17 (assert (forall ((M2 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat M2)) (@ tptp.numera1916890842035813515d_enat N2)) (@ (@ tptp.ord_less_num M2) N2))))
% 4.71/5.17 (assert (forall ((M2 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M2)) (@ tptp.numeral_numeral_int N2)) (@ (@ tptp.ord_less_num M2) N2))))
% 4.71/5.17 (assert (forall ((M2 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M2)) (@ tptp.numeral_numeral_real N2)) (@ (@ tptp.ord_less_num M2) N2))))
% 4.71/5.17 (assert (forall ((M2 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat M2)) (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M2) N2)))))
% 4.71/5.17 (assert (forall ((M2 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.numera1916890842035813515d_enat M2)) (@ tptp.numera1916890842035813515d_enat N2)) (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.plus_plus_num M2) N2)))))
% 4.71/5.17 (assert (forall ((M2 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int M2)) (@ tptp.numeral_numeral_int N2)) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M2) N2)))))
% 4.71/5.17 (assert (forall ((M2 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real M2)) (@ tptp.numeral_numeral_real N2)) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M2) N2)))))
% 4.71/5.17 (assert (forall ((V tptp.num) (W2 tptp.num) (Z3 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat V)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat W2)) Z3)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num V) W2))) Z3))))
% 4.71/5.17 (assert (forall ((V tptp.num) (W2 tptp.num) (Z3 tptp.extended_enat)) (= (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.numera1916890842035813515d_enat V)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.numera1916890842035813515d_enat W2)) Z3)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.plus_plus_num V) W2))) Z3))))
% 4.71/5.17 (assert (forall ((V tptp.num) (W2 tptp.num) (Z3 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int V)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int W2)) Z3)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num V) W2))) Z3))))
% 4.71/5.17 (assert (forall ((V tptp.num) (W2 tptp.num) (Z3 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real V)) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real W2)) Z3)) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num V) W2))) Z3))))
% 4.71/5.17 (assert (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary))) (=> (or (= X Mi) (= X Ma)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X) _let_1))))))
% 4.71/5.17 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.vEBT_vebt_insert T) X)) X)))))
% 4.71/5.17 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (@ (@ tptp.ord_less_nat X) _let_1) (=> (@ (@ tptp.ord_less_nat Y) _let_1) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions T) X) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.vEBT_vebt_insert T) Y)) X))))))))
% 4.71/5.17 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (@ (@ tptp.ord_less_nat X) _let_1) (=> (@ (@ tptp.ord_less_nat Y) _let_1) (=> (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.vEBT_vebt_insert T) X)) Y) (or (@ (@ tptp.vEBT_vebt_member T) Y) (= X Y)))))))))
% 4.71/5.17 (assert (forall ((M2 tptp.nat) (X tptp.vEBT_VEBT) (N2 tptp.nat) (Y tptp.vEBT_VEBT)) (= (= (@ (@ tptp.replicate_VEBT_VEBT M2) X) (@ (@ tptp.replicate_VEBT_VEBT N2) Y)) (and (= M2 N2) (=> (not (= M2 tptp.zero_zero_nat)) (= X Y))))))
% 4.71/5.17 (assert (forall ((N2 tptp.nat) (X tptp.vEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ tptp.replicate_VEBT_VEBT N2) X)) N2)))
% 4.71/5.17 (assert (forall ((N2 tptp.nat) (X tptp.int)) (= (@ tptp.size_size_list_int (@ (@ tptp.replicate_int N2) X)) N2)))
% 4.71/5.17 (assert (forall ((N2 tptp.nat) (X tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.replicate_nat N2) X)) N2)))
% 4.71/5.17 (assert (forall ((N2 tptp.nat) (Xs tptp.list_VEBT_VEBT)) (= (@ tptp.size_s4762443039079500285T_VEBT (@ (@ tptp.enumerate_VEBT_VEBT N2) Xs)) (@ tptp.size_s6755466524823107622T_VEBT Xs))))
% 4.71/5.17 (assert (forall ((N2 tptp.nat) (Xs tptp.list_int)) (= (@ tptp.size_s2970893825323803983at_int (@ (@ tptp.enumerate_int N2) Xs)) (@ tptp.size_size_list_int Xs))))
% 4.71/5.17 (assert (forall ((N2 tptp.nat) (Xs tptp.list_nat)) (= (@ tptp.size_s5460976970255530739at_nat (@ (@ tptp.enumerate_nat N2) Xs)) (@ tptp.size_size_list_nat Xs))))
% 4.71/5.17 (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))))))
% 4.71/5.17 (assert (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_vebt_insert tptp.summary) X)) tptp.m))))
% 4.71/5.17 (assert (forall ((N2 tptp.num)) (= (@ tptp.suc (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num N2) tptp.one)))))
% 4.71/5.17 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat U))) (let ((_let_2 (@ tptp.numera1916890842035813515d_enat V))) (let ((_let_3 (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_le2932123472753598470d_enat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 4.71/5.17 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real U))) (let ((_let_2 (@ tptp.numeral_numeral_real V))) (let ((_let_3 (@ (@ tptp.ord_max_real _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_real _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 4.71/5.17 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat U))) (let ((_let_2 (@ tptp.numeral_numeral_nat V))) (let ((_let_3 (@ (@ tptp.ord_max_nat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_nat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 4.71/5.17 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int U))) (let ((_let_2 (@ tptp.numeral_numeral_int V))) (let ((_let_3 (@ (@ tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 4.71/5.17 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X))) (= (@ (@ tptp.ord_max_nat _let_1) tptp.zero_zero_nat) _let_1))))
% 4.71/5.17 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) tptp.zero_z5237406670263579293d_enat) _let_1))))
% 4.71/5.17 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X))) (= (@ (@ tptp.ord_max_int _let_1) tptp.zero_zero_int) _let_1))))
% 4.71/5.17 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X))) (= (@ (@ tptp.ord_max_real _let_1) tptp.zero_zero_real) _let_1))))
% 4.71/5.17 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X))) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) _let_1) _let_1))))
% 4.71/5.17 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) _let_1) _let_1))))
% 4.71/5.17 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X))) (= (@ (@ tptp.ord_max_int tptp.zero_zero_int) _let_1) _let_1))))
% 4.71/5.17 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X))) (= (@ (@ tptp.ord_max_real tptp.zero_zero_real) _let_1) _let_1))))
% 4.71/5.17 (assert (and (@ (@ tptp.ord_less_eq_nat tptp.mi) tptp.ma) (@ (@ tptp.ord_less_nat tptp.ma) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.deg))))
% 4.71/5.17 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 tptp.treeList)) (=> (@ (@ tptp.vEBT_invar_vebt X) tptp.na) (=> (@ (@ tptp.ord_less_nat Xa2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.na)) (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_vebt_insert X) Xa2)) tptp.na))))))
% 4.71/5.17 (assert (forall ((X tptp.extended_enat) (N2 tptp.nat) (Y tptp.extended_enat)) (= (@ (@ tptp.member_Extended_enat X) (@ tptp.set_Extended_enat2 (@ (@ tptp.replic7216382294607269926d_enat N2) Y))) (and (= X Y) (not (= N2 tptp.zero_zero_nat))))))
% 4.71/5.17 (assert (forall ((X tptp.real) (N2 tptp.nat) (Y tptp.real)) (= (@ (@ tptp.member_real X) (@ tptp.set_real2 (@ (@ tptp.replicate_real N2) Y))) (and (= X Y) (not (= N2 tptp.zero_zero_nat))))))
% 4.71/5.17 (assert (forall ((X tptp.set_nat) (N2 tptp.nat) (Y tptp.set_nat)) (= (@ (@ tptp.member_set_nat X) (@ tptp.set_set_nat2 (@ (@ tptp.replicate_set_nat N2) Y))) (and (= X Y) (not (= N2 tptp.zero_zero_nat))))))
% 4.71/5.17 (assert (forall ((X tptp.int) (N2 tptp.nat) (Y tptp.int)) (= (@ (@ tptp.member_int X) (@ tptp.set_int2 (@ (@ tptp.replicate_int N2) Y))) (and (= X Y) (not (= N2 tptp.zero_zero_nat))))))
% 4.71/5.17 (assert (forall ((X tptp.nat) (N2 tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.member_nat X) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N2) Y))) (and (= X Y) (not (= N2 tptp.zero_zero_nat))))))
% 4.71/5.17 (assert (forall ((X tptp.vEBT_VEBT) (N2 tptp.nat) (Y tptp.vEBT_VEBT)) (= (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N2) Y))) (and (= X Y) (not (= N2 tptp.zero_zero_nat))))))
% 4.71/5.17 (assert (forall ((N2 tptp.nat) (A tptp.int) (P (-> tptp.int Bool))) (= (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) (@ tptp.set_int2 (@ (@ tptp.replicate_int N2) A))) (@ P X4))) (and (@ P A) (not (= N2 tptp.zero_zero_nat))))))
% 4.71/5.17 (assert (forall ((N2 tptp.nat) (A tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N2) A))) (@ P X4))) (and (@ P A) (not (= N2 tptp.zero_zero_nat))))))
% 4.71/5.17 (assert (forall ((N2 tptp.nat) (A tptp.vEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (exists ((X4 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N2) A))) (@ P X4))) (and (@ P A) (not (= N2 tptp.zero_zero_nat))))))
% 4.71/5.17 (assert (forall ((N2 tptp.nat) (A tptp.int) (P (-> tptp.int Bool))) (= (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) (@ tptp.set_int2 (@ (@ tptp.replicate_int N2) A))) (@ P X4))) (or (@ P A) (= N2 tptp.zero_zero_nat)))))
% 4.71/5.17 (assert (forall ((N2 tptp.nat) (A tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N2) A))) (@ P X4))) (or (@ P A) (= N2 tptp.zero_zero_nat)))))
% 4.71/5.17 (assert (forall ((N2 tptp.nat) (A tptp.vEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N2) A))) (@ P X4))) (or (@ P A) (= N2 tptp.zero_zero_nat)))))
% 4.71/5.17 (assert (forall ((I tptp.nat) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) N2) (= (@ (@ tptp.nth_nat (@ (@ tptp.replicate_nat N2) X)) I) X))))
% 4.71/5.17 (assert (forall ((I tptp.nat) (N2 tptp.nat) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat I) N2) (= (@ (@ tptp.nth_int (@ (@ tptp.replicate_int N2) X)) I) X))))
% 4.71/5.17 (assert (forall ((I tptp.nat) (N2 tptp.nat) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I) N2) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.replicate_VEBT_VEBT N2) X)) I) X))))
% 4.71/5.17 (assert (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high tptp.mi) tptp.na)) (@ _let_1 tptp.m)) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_low tptp.mi) tptp.na)) (@ _let_1 tptp.na)))))
% 4.71/5.17 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (@ tptp.suc (@ tptp.suc N2)))))
% 4.71/5.17 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc N2)))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT) (R2 tptp.set_Pr6192946355708809607T_VEBT)) (=> (@ (@ tptp.member4439316823752958928T_VEBT (@ (@ tptp.produc3897820843166775703T_VEBT Xs) Ys)) (@ tptp.listrel1_VEBT_VEBT R2)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_s6755466524823107622T_VEBT Ys)))))
% 4.71/5.17 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int) (R2 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int Xs) Ys)) (@ tptp.listrel1_int R2)) (= (@ tptp.size_size_list_int Xs) (@ tptp.size_size_list_int Ys)))))
% 4.71/5.17 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat Xs) Ys)) (@ tptp.listrel1_nat R2)) (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys)))))
% 4.71/5.17 (assert (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)) (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))))
% 4.71/5.17 (assert (forall ((P (-> tptp.extended_enat Bool)) (Xs tptp.list_Extended_enat)) (= (= (@ (@ tptp.find_Extended_enat P) Xs) tptp.none_Extended_enat) (not (exists ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) (@ tptp.set_Extended_enat2 Xs)) (@ P X4)))))))
% 4.71/5.17 (assert (forall ((P (-> tptp.real Bool)) (Xs tptp.list_real)) (= (= (@ (@ tptp.find_real P) Xs) tptp.none_real) (not (exists ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) (@ tptp.set_real2 Xs)) (@ P X4)))))))
% 4.71/5.17 (assert (forall ((P (-> tptp.set_nat Bool)) (Xs tptp.list_set_nat)) (= (= (@ (@ tptp.find_set_nat P) Xs) tptp.none_set_nat) (not (exists ((X4 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X4) (@ tptp.set_set_nat2 Xs)) (@ P X4)))))))
% 4.71/5.17 (assert (forall ((P (-> tptp.vEBT_VEBT Bool)) (Xs tptp.list_VEBT_VEBT)) (= (= (@ (@ tptp.find_VEBT_VEBT P) Xs) tptp.none_VEBT_VEBT) (not (exists ((X4 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Xs)) (@ P X4)))))))
% 4.71/5.17 (assert (forall ((P (-> tptp.int Bool)) (Xs tptp.list_int)) (= (= (@ (@ tptp.find_int P) Xs) tptp.none_int) (not (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) (@ tptp.set_int2 Xs)) (@ P X4)))))))
% 4.71/5.17 (assert (forall ((P (-> tptp.nat Bool)) (Xs tptp.list_nat)) (= (= (@ (@ tptp.find_nat P) Xs) tptp.none_nat) (not (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) (@ tptp.set_nat2 Xs)) (@ P X4)))))))
% 4.71/5.17 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool)) (Xs tptp.list_P6011104703257516679at_nat)) (= (= (@ (@ tptp.find_P8199882355184865565at_nat P) Xs) tptp.none_P5556105721700978146at_nat) (not (exists ((X4 tptp.product_prod_nat_nat)) (and (@ (@ tptp.member8440522571783428010at_nat X4) (@ tptp.set_Pr5648618587558075414at_nat Xs)) (@ P X4)))))))
% 4.71/5.17 (assert (forall ((P (-> tptp.num Bool)) (Xs tptp.list_num)) (= (= (@ (@ tptp.find_num P) Xs) tptp.none_num) (not (exists ((X4 tptp.num)) (and (@ (@ tptp.member_num X4) (@ tptp.set_num2 Xs)) (@ P X4)))))))
% 4.71/5.17 (assert (forall ((P (-> tptp.extended_enat Bool)) (Xs tptp.list_Extended_enat)) (= (= tptp.none_Extended_enat (@ (@ tptp.find_Extended_enat P) Xs)) (not (exists ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) (@ tptp.set_Extended_enat2 Xs)) (@ P X4)))))))
% 4.71/5.17 (assert (forall ((P (-> tptp.real Bool)) (Xs tptp.list_real)) (= (= tptp.none_real (@ (@ tptp.find_real P) Xs)) (not (exists ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) (@ tptp.set_real2 Xs)) (@ P X4)))))))
% 4.71/5.17 (assert (forall ((P (-> tptp.set_nat Bool)) (Xs tptp.list_set_nat)) (= (= tptp.none_set_nat (@ (@ tptp.find_set_nat P) Xs)) (not (exists ((X4 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X4) (@ tptp.set_set_nat2 Xs)) (@ P X4)))))))
% 4.71/5.17 (assert (forall ((P (-> tptp.vEBT_VEBT Bool)) (Xs tptp.list_VEBT_VEBT)) (= (= tptp.none_VEBT_VEBT (@ (@ tptp.find_VEBT_VEBT P) Xs)) (not (exists ((X4 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Xs)) (@ P X4)))))))
% 4.71/5.17 (assert (forall ((P (-> tptp.int Bool)) (Xs tptp.list_int)) (= (= tptp.none_int (@ (@ tptp.find_int P) Xs)) (not (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) (@ tptp.set_int2 Xs)) (@ P X4)))))))
% 4.71/5.17 (assert (forall ((P (-> tptp.nat Bool)) (Xs tptp.list_nat)) (= (= tptp.none_nat (@ (@ tptp.find_nat P) Xs)) (not (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) (@ tptp.set_nat2 Xs)) (@ P X4)))))))
% 4.71/5.17 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool)) (Xs tptp.list_P6011104703257516679at_nat)) (= (= tptp.none_P5556105721700978146at_nat (@ (@ tptp.find_P8199882355184865565at_nat P) Xs)) (not (exists ((X4 tptp.product_prod_nat_nat)) (and (@ (@ tptp.member8440522571783428010at_nat X4) (@ tptp.set_Pr5648618587558075414at_nat Xs)) (@ P X4)))))))
% 4.71/5.17 (assert (forall ((P (-> tptp.num Bool)) (Xs tptp.list_num)) (= (= tptp.none_num (@ (@ tptp.find_num P) Xs)) (not (exists ((X4 tptp.num)) (and (@ (@ tptp.member_num X4) (@ tptp.set_num2 Xs)) (@ P X4)))))))
% 4.71/5.17 (assert (forall ((X tptp.nat) (N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat X) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M2))) (=> (@ _let_2 N2) (=> (@ _let_2 M2) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high X) N2)) (@ _let_1 M2)))))))))
% 4.71/5.17 (assert (forall ((X (-> tptp.product_prod_nat_nat tptp.nat))) (= (@ (@ tptp.size_o8335143837870341156at_nat X) tptp.none_P5556105721700978146at_nat) (@ tptp.suc tptp.zero_zero_nat))))
% 4.71/5.17 (assert (forall ((X (-> tptp.num tptp.nat))) (= (@ (@ tptp.size_option_num X) tptp.none_num) (@ tptp.suc tptp.zero_zero_nat))))
% 4.71/5.17 (assert (forall ((X tptp.nat) (N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat X) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M2))) (=> (@ _let_2 N2) (=> (@ _let_2 M2) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_low X) N2)) (@ _let_1 N2)))))))))
% 4.71/5.17 (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))))))
% 4.71/5.17 (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))))))
% 4.71/5.17 (assert (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary tptp.vEBT_VEBT) (M2 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) M2) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)) (=> (= M2 N2) (=> (= Deg (@ (@ tptp.plus_plus_nat N2) M2)) (=> (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))))))))))
% 4.71/5.17 (assert (= (@ tptp.numeral_numeral_nat tptp.one) (@ tptp.suc tptp.zero_zero_nat)))
% 4.71/5.17 (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))))
% 4.71/5.17 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_zero_complex (@ tptp.numera6690914467698888265omplex N2)))))
% 4.71/5.17 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_zero_nat (@ tptp.numeral_numeral_nat N2)))))
% 4.71/5.17 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_z5237406670263579293d_enat (@ tptp.numera1916890842035813515d_enat N2)))))
% 4.71/5.17 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_zero_int (@ tptp.numeral_numeral_int N2)))))
% 4.71/5.17 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_zero_real (@ tptp.numeral_numeral_real N2)))))
% 4.71/5.17 (assert (forall ((X tptp.produc4471711990508489141at_nat)) (not (forall ((F2 (-> tptp.nat tptp.nat tptp.nat)) (A4 tptp.nat) (B4 tptp.nat) (Acc tptp.nat)) (not (= X (@ (@ tptp.produc3209952032786966637at_nat F2) (@ (@ tptp.produc487386426758144856at_nat A4) (@ (@ tptp.product_Pair_nat_nat B4) Acc)))))))))
% 4.71/5.17 (assert (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary tptp.vEBT_VEBT) (M2 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) M2) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)) (=> (= M2 (@ tptp.suc N2)) (=> (= Deg (@ (@ tptp.plus_plus_nat N2) M2)) (=> (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))))))))))
% 4.71/5.17 (assert (= (@ tptp.size_size_num tptp.one) tptp.zero_zero_nat))
% 4.71/5.17 (assert (= (@ tptp.size_s170228958280169651at_nat tptp.none_P5556105721700978146at_nat) (@ tptp.suc tptp.zero_zero_nat)))
% 4.71/5.17 (assert (= (@ tptp.size_size_option_num tptp.none_num) (@ tptp.suc tptp.zero_zero_nat)))
% 4.71/5.17 (assert (forall ((Xs tptp.list_Extended_enat) (Ys tptp.list_Extended_enat) (P (-> tptp.extended_enat Bool)) (Q (-> tptp.extended_enat Bool))) (=> (= Xs Ys) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ tptp.set_Extended_enat2 Ys)) (= (@ P X5) (@ Q X5)))) (= (@ (@ tptp.find_Extended_enat P) Xs) (@ (@ tptp.find_Extended_enat Q) Ys))))))
% 4.71/5.17 (assert (forall ((Xs tptp.list_real) (Ys tptp.list_real) (P (-> tptp.real Bool)) (Q (-> tptp.real Bool))) (=> (= Xs Ys) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ tptp.set_real2 Ys)) (= (@ P X5) (@ Q X5)))) (= (@ (@ tptp.find_real P) Xs) (@ (@ tptp.find_real Q) Ys))))))
% 4.71/5.17 (assert (forall ((Xs tptp.list_set_nat) (Ys tptp.list_set_nat) (P (-> tptp.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (=> (= Xs Ys) (=> (forall ((X5 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X5) (@ tptp.set_set_nat2 Ys)) (= (@ P X5) (@ Q X5)))) (= (@ (@ tptp.find_set_nat P) Xs) (@ (@ tptp.find_set_nat Q) Ys))))))
% 4.71/5.17 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool)) (Q (-> tptp.vEBT_VEBT Bool))) (=> (= Xs Ys) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 Ys)) (= (@ P X5) (@ Q X5)))) (= (@ (@ tptp.find_VEBT_VEBT P) Xs) (@ (@ tptp.find_VEBT_VEBT Q) Ys))))))
% 4.71/5.17 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (= Xs Ys) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ tptp.set_int2 Ys)) (= (@ P X5) (@ Q X5)))) (= (@ (@ tptp.find_int P) Xs) (@ (@ tptp.find_int Q) Ys))))))
% 4.71/5.17 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat) (P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (= Xs Ys) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) (@ tptp.set_nat2 Ys)) (= (@ P X5) (@ Q X5)))) (= (@ (@ tptp.find_nat P) Xs) (@ (@ tptp.find_nat Q) Ys))))))
% 4.71/5.17 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat N2)) tptp.zero_z5237406670263579293d_enat))))
% 4.71/5.17 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N2)) tptp.zero_zero_real))))
% 4.71/5.17 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N2)) tptp.zero_zero_nat))))
% 4.71/5.17 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N2)) tptp.zero_zero_int))))
% 4.71/5.17 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ tptp.numera1916890842035813515d_enat N2))))
% 4.71/5.17 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N2))))
% 4.71/5.17 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N2))))
% 4.71/5.17 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N2))))
% 4.71/5.17 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N2)) tptp.zero_zero_nat))))
% 4.71/5.17 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat N2)) tptp.zero_z5237406670263579293d_enat))))
% 4.71/5.17 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N2)) tptp.zero_zero_int))))
% 4.71/5.17 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N2)) tptp.zero_zero_real))))
% 4.71/5.17 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N2))))
% 4.71/5.17 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ tptp.numera1916890842035813515d_enat N2))))
% 4.71/5.17 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N2))))
% 4.71/5.17 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N2))))
% 4.71/5.17 (assert (forall ((Xs tptp.list_Extended_enat) (N2 tptp.nat) (X tptp.extended_enat)) (=> (= (@ tptp.size_s3941691890525107288d_enat Xs) N2) (=> (forall ((Y3 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat Y3) (@ tptp.set_Extended_enat2 Xs)) (= Y3 X))) (= Xs (@ (@ tptp.replic7216382294607269926d_enat N2) X))))))
% 4.71/5.17 (assert (forall ((Xs tptp.list_real) (N2 tptp.nat) (X tptp.real)) (=> (= (@ tptp.size_size_list_real Xs) N2) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.member_real Y3) (@ tptp.set_real2 Xs)) (= Y3 X))) (= Xs (@ (@ tptp.replicate_real N2) X))))))
% 4.71/5.17 (assert (forall ((Xs tptp.list_set_nat) (N2 tptp.nat) (X tptp.set_nat)) (=> (= (@ tptp.size_s3254054031482475050et_nat Xs) N2) (=> (forall ((Y3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Y3) (@ tptp.set_set_nat2 Xs)) (= Y3 X))) (= Xs (@ (@ tptp.replicate_set_nat N2) X))))))
% 4.71/5.17 (assert (forall ((Xs tptp.list_VEBT_VEBT) (N2 tptp.nat) (X 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 X))) (= Xs (@ (@ tptp.replicate_VEBT_VEBT N2) X))))))
% 4.71/5.17 (assert (forall ((Xs tptp.list_int) (N2 tptp.nat) (X tptp.int)) (=> (= (@ tptp.size_size_list_int Xs) N2) (=> (forall ((Y3 tptp.int)) (=> (@ (@ tptp.member_int Y3) (@ tptp.set_int2 Xs)) (= Y3 X))) (= Xs (@ (@ tptp.replicate_int N2) X))))))
% 4.71/5.17 (assert (forall ((Xs tptp.list_nat) (N2 tptp.nat) (X tptp.nat)) (=> (= (@ tptp.size_size_list_nat Xs) N2) (=> (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.member_nat Y3) (@ tptp.set_nat2 Xs)) (= Y3 X))) (= Xs (@ (@ tptp.replicate_nat N2) X))))))
% 4.71/5.17 (assert (forall ((Xs tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 Xs)) (= X5 X))) (= (@ (@ tptp.replicate_VEBT_VEBT (@ tptp.size_s6755466524823107622T_VEBT Xs)) X) Xs))))
% 4.71/5.17 (assert (forall ((Xs tptp.list_int) (X tptp.int)) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ tptp.set_int2 Xs)) (= X5 X))) (= (@ (@ tptp.replicate_int (@ tptp.size_size_list_int Xs)) X) Xs))))
% 4.71/5.17 (assert (forall ((Xs tptp.list_nat) (X tptp.nat)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) (@ tptp.set_nat2 Xs)) (= X5 X))) (= (@ (@ tptp.replicate_nat (@ tptp.size_size_list_nat Xs)) X) Xs))))
% 4.71/5.17 (assert (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT) (X tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)) X))))
% 4.71/5.17 (assert (forall ((Uw tptp.nat) (Ux tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT)) (@ tptp.vEBT_VEBT_minNull (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw) Ux) Uy))))
% 4.71/5.17 (assert (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary tptp.vEBT_VEBT) (M2 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) M2) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _let_2 M2)) (=> (= M2 N2) (=> (= Deg (@ (@ tptp.plus_plus_nat N2) M2)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)) (= (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) X6)) (@ (@ 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))) M2)) (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)))))))))))))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (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))))
% 4.71/5.17 (assert (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary tptp.vEBT_VEBT) (M2 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) M2) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _let_2 M2)) (=> (= M2 (@ tptp.suc N2)) (=> (= Deg (@ (@ tptp.plus_plus_nat N2) M2)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)) (= (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) X6)) (@ (@ 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))) M2)) (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)))))))))))))))
% 4.71/5.17 (assert (= tptp.size_s6755466524823107622T_VEBT (@ tptp.gen_length_VEBT_VEBT tptp.zero_zero_nat)))
% 4.71/5.17 (assert (= tptp.size_size_list_int (@ tptp.gen_length_int tptp.zero_zero_nat)))
% 4.71/5.17 (assert (= tptp.size_size_list_nat (@ tptp.gen_length_nat tptp.zero_zero_nat)))
% 4.71/5.17 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real))))))
% 4.71/5.17 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int))))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_real X) _let_1) (@ (@ tptp.power_power_real Y) _let_1)) (= X Y))))))))
% 4.71/5.17 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_nat X) _let_1) (@ (@ tptp.power_power_nat Y) _let_1)) (= X Y))))))))
% 4.71/5.17 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_int X) _let_1) (@ (@ tptp.power_power_int Y) _let_1)) (= X Y))))))))
% 4.71/5.17 (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))))
% 4.71/5.17 (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))))
% 4.71/5.17 (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))))
% 4.71/5.17 (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))))
% 4.71/5.17 (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))))
% 4.71/5.17 (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))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B2) N2)) (@ (@ tptp.ord_less_eq_real A) B2))))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B2) N2)) (@ (@ tptp.ord_less_eq_nat A) B2))))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B2) N2)) (@ (@ tptp.ord_less_eq_int A) B2))))))))
% 4.71/5.17 (assert (forall ((X tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Mi tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3))) (let ((_let_5 (@ tptp.product_Pair_nat_nat Mi))) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (=> (@ (@ tptp.ord_less_nat Mi) X) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (not (= X Ma)) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 (@ (@ tptp.ord_max_nat X) Ma)))) Deg) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) _let_3) (@ (@ tptp.vEBT_vebt_insert _let_4) (@ (@ tptp.vEBT_VEBT_low X) _let_2)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_4)) (@ (@ tptp.vEBT_vebt_insert Summary) _let_3)) Summary))))))))))))))
% 4.71/5.17 (assert (forall ((Mi tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (X tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Mi) _let_2))) (let ((_let_4 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3))) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (=> (@ (@ tptp.ord_less_nat X) Mi) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (not (= X Ma)) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat X) (@ (@ tptp.ord_max_nat Mi) Ma)))) Deg) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) _let_3) (@ (@ tptp.vEBT_vebt_insert _let_4) (@ (@ tptp.vEBT_VEBT_low Mi) _let_2)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_4)) (@ (@ tptp.vEBT_vebt_insert Summary) _let_3)) Summary)))))))))))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (=> (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (and (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (or (= X Mi) (= X Ma) (and (@ (@ tptp.ord_less_nat X) Ma) (@ (@ tptp.ord_less_nat Mi) X) (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2)))))))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.divide_divide_nat (@ _let_1 (@ (@ tptp.plus_plus_nat A) B2))) (@ _let_1 A)) (@ _let_1 B2)))))
% 4.71/5.17 (assert (= tptp.vEBT_VEBT_high (lambda ((X4 tptp.nat) (N tptp.nat)) (@ (@ tptp.divide_divide_nat X4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 4.71/5.17 (assert (= (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.na))
% 4.71/5.17 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 4.71/5.17 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 4.71/5.17 (assert (forall ((A tptp.complex) (C tptp.complex) (B2 tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) C) (@ (@ tptp.divide1717551699836669952omplex B2) C)) (or (= C tptp.zero_zero_complex) (= A B2)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (= (@ (@ tptp.divide_divide_real A) C) (@ (@ tptp.divide_divide_real B2) C)) (or (= C tptp.zero_zero_real) (= A B2)))))
% 4.71/5.17 (assert (forall ((C tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex C))) (= (= (@ _let_1 A) (@ _let_1 B2)) (or (= C tptp.zero_zero_complex) (= A B2))))))
% 4.71/5.17 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (= (= (@ _let_1 A) (@ _let_1 B2)) (or (= C tptp.zero_zero_real) (= A B2))))))
% 4.71/5.17 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 4.71/5.17 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 4.71/5.17 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 4.71/5.17 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 4.71/5.17 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B2) tptp.zero_zero_complex) (or (= A tptp.zero_zero_complex) (= B2 tptp.zero_zero_complex)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (= (@ (@ tptp.divide_divide_real A) B2) tptp.zero_zero_real) (or (= A tptp.zero_zero_real) (= B2 tptp.zero_zero_real)))))
% 4.71/5.17 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex tptp.zero_zero_complex) A) tptp.zero_zero_complex)))
% 4.71/5.17 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 4.71/5.17 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 4.71/5.17 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real tptp.zero_zero_real) A) tptp.zero_zero_real)))
% 4.71/5.17 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_8040749407984259932d_enat tptp.zero_z5237406670263579293d_enat) (@ tptp.suc N2)) tptp.zero_z5237406670263579293d_enat)))
% 4.71/5.17 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.suc N2)) tptp.zero_zero_nat)))
% 4.71/5.17 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.suc N2)) tptp.zero_zero_real)))
% 4.71/5.17 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.suc N2)) tptp.zero_zero_complex)))
% 4.71/5.17 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.suc N2)) tptp.zero_zero_int)))
% 4.71/5.17 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_8040749407984259932d_enat tptp.zero_z5237406670263579293d_enat) (@ tptp.numeral_numeral_nat K)) tptp.zero_z5237406670263579293d_enat)))
% 4.71/5.17 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_nat)))
% 4.71/5.17 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_real)))
% 4.71/5.17 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_complex)))
% 4.71/5.17 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_int)))
% 4.71/5.17 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 4.71/5.17 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 4.71/5.17 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 4.71/5.17 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 4.71/5.17 (assert (forall ((X tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.power_power_nat X) M2) _let_1) (or (= M2 tptp.zero_zero_nat) (= X _let_1))))))
% 4.71/5.17 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.power_power_nat _let_1) N2) _let_1))))
% 4.71/5.17 (assert (forall ((X tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat X) N2)) (or (@ _let_1 X) (= N2 tptp.zero_zero_nat))))))
% 4.71/5.17 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList2) Summary))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat Deg) _let_2))) (=> (@ (@ tptp.vEBT_invar_vebt _let_1) N2) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_2) Deg)) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) (@ (@ tptp.vEBT_VEBT_high X) _let_3))) (@ (@ tptp.vEBT_VEBT_low X) _let_3)) (@ (@ tptp.vEBT_V8194947554948674370ptions _let_1) X)))))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) B2)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B2) C)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A) B2)) tptp.zero_zero_real) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ _let_1 B2)))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B2) C))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real A) B2)) (or (and (@ _let_1 A) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real)))))))
% 4.71/5.17 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_real X) Y)))))))
% 4.71/5.17 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))))
% 4.71/5.17 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))))
% 4.71/5.17 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X) Y))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B2) C)) (@ (@ tptp.divide_divide_real A) C))))))
% 4.71/5.17 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X) Y))))))
% 4.71/5.17 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))))
% 4.71/5.17 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))))
% 4.71/5.17 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_real X) Y)))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A) B2)) tptp.zero_zero_real) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_real B2) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ _let_1 B2)))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B2) C)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B2)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B2) A)) (not (= C tptp.zero_zero_real))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real A) B2)) (or (and (@ _let_1 A) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B2) tptp.zero_zero_real)))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B2) C))))))
% 4.71/5.17 (assert (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real B2) A) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B2) C))))))
% 4.71/5.17 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))))
% 4.71/5.17 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X) Y))))))
% 4.71/5.17 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ _let_1 (@ (@ tptp.divide_divide_real X) Y)))))))
% 4.71/5.17 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B2) C)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B2)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B2) A))))))
% 4.71/5.17 (assert (forall ((X tptp.real) (Y tptp.real) (W2 tptp.real) (Z3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ _let_1 W2) (=> (@ (@ tptp.ord_less_real W2) Z3) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Z3)) (@ (@ tptp.divide_divide_real Y) W2)))))))))
% 4.71/5.17 (assert (forall ((X tptp.real) (Y tptp.real) (W2 tptp.real) (Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) Y) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) W2) (=> (@ (@ tptp.ord_less_eq_real W2) Z3) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Z3)) (@ (@ tptp.divide_divide_real Y) W2))))))))
% 4.71/5.17 (assert (forall ((Y tptp.real) (X tptp.real) (W2 tptp.real) (Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) W2) (=> (@ (@ tptp.ord_less_eq_real W2) Z3) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Z3)) (@ (@ tptp.divide_divide_real Y) W2))))))))
% 4.71/5.17 (assert (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real X) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.plus_plus_real _let_1) _let_1) X))))
% 4.71/5.17 (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))))))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X))) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) Y)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B2) N2))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B2) N2))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B2) N2))))))
% 4.71/5.17 (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))))))
% 4.71/5.17 (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))))))
% 4.71/5.17 (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))))))
% 4.71/5.17 (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))))))
% 4.71/5.17 (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))))))
% 4.71/5.17 (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))))))
% 4.71/5.17 (assert (forall ((I tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) I) (=> (@ (@ tptp.ord_less_nat (@ _let_1 M2)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M2) N2))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (N2 tptp.nat) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B2) N2)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B2) (@ (@ tptp.ord_less_real A) B2)))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (N2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B2) N2)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B2) (@ (@ tptp.ord_less_nat A) B2)))))
% 4.71/5.17 (assert (forall ((A tptp.int) (N2 tptp.nat) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B2) N2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B2) (@ (@ tptp.ord_less_int A) B2)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (N2 tptp.nat) (B2 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 B2) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= A B2))))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (N2 tptp.nat) (B2 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 B2) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= A B2))))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (N2 tptp.nat) (B2 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 B2) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= A B2))))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (N2 tptp.nat) (B2 tptp.real)) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) _let_1)) (@ (@ tptp.power_power_real B2) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B2) (@ (@ tptp.ord_less_eq_real A) B2))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (N2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) _let_1)) (@ (@ tptp.power_power_nat B2) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B2) (@ (@ tptp.ord_less_eq_nat A) B2))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (N2 tptp.nat) (B2 tptp.int)) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) _let_1)) (@ (@ tptp.power_power_int B2) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B2) (@ (@ tptp.ord_less_eq_int A) B2))))))
% 4.71/5.17 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.power_8040749407984259932d_enat tptp.zero_z5237406670263579293d_enat) N2) tptp.zero_z5237406670263579293d_enat))))
% 4.71/5.17 (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))))
% 4.71/5.17 (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))))
% 4.71/5.17 (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))))
% 4.71/5.17 (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))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (assert (forall ((I tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)))) (=> (@ _let_1 I) (@ _let_1 (@ (@ tptp.power_power_nat I) N2))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (N2 tptp.nat) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (= (@ (@ tptp.power_power_real A) N2) (@ (@ tptp.power_power_real B2) N2)) (=> (@ _let_1 A) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= A B2))))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (N2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (= (@ (@ tptp.power_power_nat A) N2) (@ (@ tptp.power_power_nat B2) N2)) (=> (@ _let_1 A) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= A B2))))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (N2 tptp.nat) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (= (@ (@ tptp.power_power_int A) N2) (@ (@ tptp.power_power_int B2) N2)) (=> (@ _let_1 A) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= A B2))))))))
% 4.71/5.17 (assert (forall ((N2 tptp.nat) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= (= (@ (@ tptp.power_power_real A) N2) (@ (@ tptp.power_power_real B2) N2)) (= A B2))))))))
% 4.71/5.17 (assert (forall ((N2 tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= (= (@ (@ tptp.power_power_nat A) N2) (@ (@ tptp.power_power_nat B2) N2)) (= A B2))))))))
% 4.71/5.17 (assert (forall ((N2 tptp.nat) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= (= (@ (@ tptp.power_power_int A) N2) (@ (@ tptp.power_power_int B2) N2)) (= A B2))))))))
% 4.71/5.17 (assert (= (@ (@ tptp.power_8040749407984259932d_enat tptp.zero_z5237406670263579293d_enat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_z5237406670263579293d_enat))
% 4.71/5.17 (assert (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 4.71/5.17 (assert (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_real))
% 4.71/5.17 (assert (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_complex))
% 4.71/5.17 (assert (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 4.71/5.17 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))
% 4.71/5.17 (assert (forall ((K tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K) (@ (@ tptp.ord_less_eq_nat M2) (@ (@ tptp.power_power_nat K) M2)))))
% 4.71/5.17 (assert (forall ((M2 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 M2) _let_1)) (@ (@ tptp.power_power_nat N2) _let_1)) (@ (@ tptp.ord_less_eq_nat M2) N2)))))
% 4.71/5.17 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat M2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) N2) (@ (@ tptp.ord_less_eq_nat M2) N2))))
% 4.71/5.17 (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))))))
% 4.71/5.17 (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))))))
% 4.71/5.17 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_real X) _let_2) (@ (@ tptp.power_power_real Y) _let_2)) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= X Y))))))))
% 4.71/5.17 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_nat X) _let_2) (@ (@ tptp.power_power_nat Y) _let_2)) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= X Y))))))))
% 4.71/5.17 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_int X) _let_2) (@ (@ tptp.power_power_int Y) _let_2)) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= X Y))))))))
% 4.71/5.17 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_eq_real X) Y))))))
% 4.71/5.17 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat X) _let_1)) (@ (@ tptp.power_power_nat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y) (@ (@ tptp.ord_less_eq_nat X) Y))))))
% 4.71/5.17 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (@ (@ tptp.ord_less_eq_int X) Y))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B2) N2)))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B2) N2)))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_int A) B2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B2) N2)))))))
% 4.71/5.17 (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))))
% 4.71/5.17 (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))))
% 4.71/5.17 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_real X) Y))))))
% 4.71/5.17 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat X) _let_1)) (@ (@ tptp.power_power_nat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y) (@ (@ tptp.ord_less_nat X) Y))))))
% 4.71/5.17 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (@ (@ tptp.ord_less_int X) Y))))))
% 4.71/5.17 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))))))
% 4.71/5.17 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))))))
% 4.71/5.17 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real))))))
% 4.71/5.17 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int))))))
% 4.71/5.17 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) tptp.zero_zero_real)))))
% 4.71/5.17 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))) tptp.zero_zero_int)))))
% 4.71/5.17 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) (or (not (= X tptp.zero_zero_real)) (not (= Y tptp.zero_zero_real)))))))
% 4.71/5.17 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))) (or (not (= X tptp.zero_zero_int)) (not (= Y tptp.zero_zero_int)))))))
% 4.71/5.17 (assert (forall ((X tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Mi tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high X) _let_1))) (=> (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) Deg) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low X) _let_1)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X))))))))
% 4.71/5.17 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat M2) M2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)))
% 4.71/5.17 (assert (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc M2))) _let_1) (@ tptp.suc (@ (@ tptp.divide_divide_nat M2) _let_1))))))
% 4.71/5.17 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) Deg) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (or (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) (@ (@ tptp.vEBT_VEBT_high X) _let_1))) (@ (@ tptp.vEBT_VEBT_low X) _let_1)) (= X Mi) (= X Ma)))))))
% 4.71/5.17 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N2) (= (@ (@ tptp.divide_divide_nat M2) N2) tptp.zero_zero_nat))))
% 4.71/5.17 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.divide_divide_nat M2) (@ tptp.suc tptp.zero_zero_nat)) M2)))
% 4.71/5.17 (assert (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (M2 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))) M2)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2)))))
% 4.71/5.17 (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)))))))
% 4.71/5.17 (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))))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (M2 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 M2))) (@ _let_1 N2)) (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N2))))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (M2 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 M2))) (@ _let_1 N2)) (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N2))))))))
% 4.71/5.17 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 4.71/5.17 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 4.71/5.17 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 4.71/5.17 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 4.71/5.17 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.one_one_complex) A)))
% 4.71/5.17 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.one_one_nat) A)))
% 4.71/5.17 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.one_one_int) A)))
% 4.71/5.17 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.one_one_real) A)))
% 4.71/5.17 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B2) tptp.one_one_complex) (and (not (= B2 tptp.zero_zero_complex)) (= A B2)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (= (@ (@ tptp.divide_divide_real A) B2) tptp.one_one_real) (and (not (= B2 tptp.zero_zero_real)) (= A B2)))))
% 4.71/5.17 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))))
% 4.71/5.17 (assert (forall ((A tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat A) A) tptp.one_one_nat))))
% 4.71/5.17 (assert (forall ((A tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int A) A) tptp.one_one_int))))
% 4.71/5.17 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) A) tptp.one_one_real))))
% 4.71/5.17 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (= tptp.one_one_complex (@ (@ tptp.divide1717551699836669952omplex A) B2)) (and (not (= B2 tptp.zero_zero_complex)) (= A B2)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (= tptp.one_one_real (@ (@ tptp.divide_divide_real A) B2)) (and (not (= B2 tptp.zero_zero_real)) (= A B2)))))
% 4.71/5.17 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))))
% 4.71/5.17 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) A) tptp.one_one_real))))
% 4.71/5.17 (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)))))))
% 4.71/5.17 (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)))))))
% 4.71/5.17 (assert (forall ((B2 tptp.real) (A tptp.real)) (= (= (@ (@ tptp.divide_divide_real B2) A) tptp.one_one_real) (and (not (= A tptp.zero_zero_real)) (= A B2)))))
% 4.71/5.17 (assert (forall ((B2 tptp.real) (A tptp.real)) (= (= tptp.one_one_real (@ (@ tptp.divide_divide_real B2) A)) (and (not (= A tptp.zero_zero_real)) (= A B2)))))
% 4.71/5.17 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.divide_divide_real tptp.one_one_real) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 4.71/5.17 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) (= A tptp.zero_zero_real))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (= (= (@ _let_1 M2) (@ _let_1 N2)) (= M2 N2))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (= (= (@ _let_1 M2) (@ _let_1 N2)) (= M2 N2))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (= (= (@ _let_1 M2) (@ _let_1 N2)) (= M2 N2))))))
% 4.71/5.17 (assert (= (@ (@ tptp.ord_max_real tptp.one_one_real) tptp.zero_zero_real) tptp.one_one_real))
% 4.71/5.17 (assert (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.one_on7984719198319812577d_enat) tptp.zero_z5237406670263579293d_enat) tptp.one_on7984719198319812577d_enat))
% 4.71/5.17 (assert (= (@ (@ tptp.ord_max_nat tptp.one_one_nat) tptp.zero_zero_nat) tptp.one_one_nat))
% 4.71/5.17 (assert (= (@ (@ tptp.ord_max_int tptp.one_one_int) tptp.zero_zero_int) tptp.one_one_int))
% 4.71/5.17 (assert (= (@ (@ tptp.ord_max_real tptp.zero_zero_real) tptp.one_one_real) tptp.one_one_real))
% 4.71/5.17 (assert (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) tptp.one_on7984719198319812577d_enat) tptp.one_on7984719198319812577d_enat))
% 4.71/5.17 (assert (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) tptp.one_one_nat) tptp.one_one_nat))
% 4.71/5.17 (assert (= (@ (@ tptp.ord_max_int tptp.zero_zero_int) tptp.one_one_int) tptp.one_one_int))
% 4.71/5.17 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat N2) tptp.one_one_nat) (= N2 tptp.zero_zero_nat))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (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))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B2) A)) (@ (@ tptp.ord_less_real A) B2)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B2) A)) (@ (@ tptp.ord_less_real B2) A)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B2) A)) tptp.one_one_real) (@ (@ tptp.ord_less_real B2) A)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B2) A)) tptp.one_one_real) (@ _let_1 B2))))))
% 4.71/5.17 (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))))
% 4.71/5.17 (assert (forall ((B2 tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B2) (= (@ (@ tptp.ord_less_nat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))))
% 4.71/5.17 (assert (forall ((B2 tptp.real) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B2))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B2) (= (@ (@ tptp.ord_less_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))))
% 4.71/5.17 (assert (forall ((B2 tptp.int) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B2))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B2) (= (@ (@ tptp.ord_less_int (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B2) A)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real A) B2)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B2) A)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real B2) A)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B2) A)) (@ (@ tptp.ord_less_eq_real B2) A)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B2) A)) (@ (@ tptp.ord_less_eq_real A) B2)))))
% 4.71/5.17 (assert (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 4.71/5.17 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 4.71/5.17 (assert (= (@ (@ tptp.plus_p3455044024723400733d_enat tptp.one_on7984719198319812577d_enat) tptp.one_on7984719198319812577d_enat) (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))))
% 4.71/5.17 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))
% 4.71/5.17 (assert (= (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))
% 4.71/5.17 (assert (forall ((B2 tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2) (=> (@ (@ tptp.ord_less_nat B2) tptp.one_one_nat) (= (@ (@ tptp.ord_less_nat (@ _let_1 M2)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat N2) M2)))))))
% 4.71/5.17 (assert (forall ((B2 tptp.real) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B2))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B2) (=> (@ (@ tptp.ord_less_real B2) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ _let_1 M2)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat N2) M2)))))))
% 4.71/5.17 (assert (forall ((B2 tptp.int) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_int B2) tptp.one_one_int) (= (@ (@ tptp.ord_less_int (@ _let_1 M2)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat N2) M2)))))))
% 4.71/5.17 (assert (forall ((B2 tptp.real) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B2))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B2) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))))
% 4.71/5.17 (assert (forall ((B2 tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B2) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))))
% 4.71/5.17 (assert (forall ((B2 tptp.int) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B2))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B2) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))))
% 4.71/5.17 (assert (= (@ tptp.suc tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (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))))
% 4.71/5.17 (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))))
% 4.71/5.17 (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))))
% 4.71/5.17 (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))))
% 4.71/5.17 (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))))
% 4.71/5.17 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_le72135733267957522d_enat tptp.one_on7984719198319812577d_enat) (@ tptp.numera1916890842035813515d_enat N2)) (@ (@ tptp.ord_less_num tptp.one) N2))))
% 4.71/5.17 (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))))
% 4.71/5.17 (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))))
% 4.71/5.17 (assert (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 4.71/5.17 (assert (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 4.71/5.17 (assert (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 4.71/5.17 (assert (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 4.71/5.17 (assert (forall ((B2 tptp.real) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B2))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B2) (=> (@ (@ tptp.ord_less_real B2) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 M2)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat N2) M2)))))))
% 4.71/5.17 (assert (forall ((B2 tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2) (=> (@ (@ tptp.ord_less_nat B2) tptp.one_one_nat) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M2)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat N2) M2)))))))
% 4.71/5.17 (assert (forall ((B2 tptp.int) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_int B2) tptp.one_one_int) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 M2)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat N2) M2)))))))
% 4.71/5.17 (assert (forall ((X tptp.nat)) (= (= tptp.one_one_nat X) (= X tptp.one_one_nat))))
% 4.71/5.17 (assert (forall ((X tptp.int)) (= (= tptp.one_one_int X) (= X tptp.one_one_int))))
% 4.71/5.17 (assert (forall ((X tptp.complex)) (= (= tptp.one_one_complex X) (= X tptp.one_one_complex))))
% 4.71/5.17 (assert (forall ((X tptp.real)) (= (= tptp.one_one_real X) (= X tptp.one_one_real))))
% 4.71/5.17 (assert (@ (@ tptp.ord_less_eq_real tptp.one_one_real) tptp.one_one_real))
% 4.71/5.17 (assert (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.one_one_nat))
% 4.71/5.17 (assert (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.one_one_int))
% 4.71/5.17 (assert (not (= tptp.zero_zero_nat tptp.one_one_nat)))
% 4.71/5.17 (assert (not (= tptp.zero_zero_real tptp.one_one_real)))
% 4.71/5.17 (assert (not (= tptp.zero_zero_int tptp.one_one_int)))
% 4.71/5.17 (assert (not (= tptp.zero_zero_complex tptp.one_one_complex)))
% 4.71/5.17 (assert (not (= tptp.zero_z5237406670263579293d_enat tptp.one_on7984719198319812577d_enat)))
% 4.71/5.17 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.one_one_nat)))
% 4.71/5.17 (assert (not (@ (@ tptp.ord_le72135733267957522d_enat tptp.one_on7984719198319812577d_enat) tptp.one_on7984719198319812577d_enat)))
% 4.71/5.17 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) tptp.one_one_real)))
% 4.71/5.17 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.one_one_int)))
% 4.71/5.17 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (=> (not (= B2 tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat B2) A)) B2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) B2)) tptp.one_one_nat)))))
% 4.71/5.17 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (not (= B2 tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int B2) A)) B2) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) B2)) tptp.one_one_int)))))
% 4.71/5.17 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (=> (not (= B2 tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B2)) B2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) B2)) tptp.one_one_nat)))))
% 4.71/5.17 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (not (= B2 tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B2)) B2) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) B2)) tptp.one_one_int)))))
% 4.71/5.17 (assert (not (@ (@ tptp.ord_le2932123472753598470d_enat tptp.one_on7984719198319812577d_enat) tptp.zero_z5237406670263579293d_enat)))
% 4.71/5.17 (assert (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) tptp.zero_zero_real)))
% 4.71/5.17 (assert (not (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 4.71/5.17 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.zero_zero_int)))
% 4.71/5.17 (assert (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) tptp.one_on7984719198319812577d_enat))
% 4.71/5.17 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.one_one_real))
% 4.71/5.17 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 4.71/5.17 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 4.71/5.17 (assert (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) tptp.one_on7984719198319812577d_enat))
% 4.71/5.17 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.one_one_real))
% 4.71/5.17 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 4.71/5.17 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 4.71/5.17 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 4.71/5.17 (assert (not (@ (@ tptp.ord_le72135733267957522d_enat tptp.one_on7984719198319812577d_enat) tptp.zero_z5237406670263579293d_enat)))
% 4.71/5.17 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) tptp.zero_zero_real)))
% 4.71/5.17 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.zero_zero_int)))
% 4.71/5.17 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 4.71/5.17 (assert (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) tptp.one_on7984719198319812577d_enat))
% 4.71/5.17 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.one_one_real))
% 4.71/5.17 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 4.71/5.17 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 4.71/5.17 (assert (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) tptp.one_on7984719198319812577d_enat))
% 4.71/5.17 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.one_one_real))
% 4.71/5.17 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 4.71/5.17 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.one_on7984719198319812577d_enat) (@ tptp.numera1916890842035813515d_enat N2))))
% 4.71/5.17 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.numeral_numeral_real N2))))
% 4.71/5.17 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N2))))
% 4.71/5.17 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.numeral_numeral_int N2))))
% 4.71/5.17 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N2)) tptp.one_one_nat))))
% 4.71/5.17 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat N2)) tptp.one_on7984719198319812577d_enat))))
% 4.71/5.17 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N2)) tptp.one_one_int))))
% 4.71/5.17 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N2)) tptp.one_one_real))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) (@ (@ tptp.plus_plus_nat B2) tptp.one_one_nat)))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B2) (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) tptp.one_on7984719198319812577d_enat)) (@ (@ tptp.plus_p3455044024723400733d_enat B2) tptp.one_on7984719198319812577d_enat)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) tptp.one_one_real)) (@ (@ tptp.plus_plus_real B2) tptp.one_one_real)))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B2) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) (@ (@ tptp.plus_plus_int B2) tptp.one_one_int)))))
% 4.71/5.17 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat))))
% 4.71/5.17 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real A) tptp.one_one_real))))
% 4.71/5.17 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int A) tptp.one_one_int))))
% 4.71/5.17 (assert (forall ((B2 tptp.complex) (A tptp.complex)) (=> (not (= B2 tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B2) tptp.one_one_complex) (= A B2)))))
% 4.71/5.17 (assert (forall ((B2 tptp.real) (A tptp.real)) (=> (not (= B2 tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real A) B2) tptp.one_one_real) (= A B2)))))
% 4.71/5.17 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex X))) (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)))))
% 4.71/5.17 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X))) (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))))
% 4.71/5.17 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.plus_p3455044024723400733d_enat tptp.one_on7984719198319812577d_enat) _let_1) (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) tptp.one_on7984719198319812577d_enat)))))
% 4.71/5.17 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X))) (= (@ (@ tptp.plus_plus_int tptp.one_one_int) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))
% 4.71/5.17 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X))) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))))
% 4.71/5.17 (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))))))
% 4.71/5.17 (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))))))
% 4.71/5.17 (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))))))
% 4.71/5.17 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (= (= (@ (@ tptp.divide_divide_nat M2) N2) M2) (= N2 tptp.one_one_nat)))))
% 4.71/5.17 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M2) N2)) M2)))))
% 4.71/5.17 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 4.71/5.17 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 4.71/5.17 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 4.71/5.17 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 4.71/5.17 (assert (= tptp.one_one_nat (@ tptp.suc tptp.zero_zero_nat)))
% 4.71/5.17 (assert (= tptp.suc (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))
% 4.71/5.17 (assert (= (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.suc))
% 4.71/5.17 (assert (= tptp.suc (@ tptp.plus_plus_nat tptp.one_one_nat)))
% 4.71/5.17 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat)))
% 4.71/5.17 (assert (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.plus_p3455044024723400733d_enat tptp.one_on7984719198319812577d_enat) tptp.one_on7984719198319812577d_enat)))
% 4.71/5.17 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real)))
% 4.71/5.17 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int)))
% 4.71/5.17 (assert (forall ((B2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B2) A)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ _let_1 B2)) (and (@ _let_1 tptp.zero_zero_real) (@ (@ tptp.ord_less_real B2) A)))))))
% 4.71/5.17 (assert (forall ((B2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B2) A)) tptp.one_one_real) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_real B2) A)) (and (@ _let_1 tptp.zero_zero_real) (@ _let_1 B2)) (= A tptp.zero_zero_real))))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) B2)) (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real)))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) B2)) (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real))) B2))))
% 4.71/5.17 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8040749407984259932d_enat tptp.zero_z5237406670263579293d_enat) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_on7984719198319812577d_enat)) (=> (not _let_2) (= _let_1 tptp.zero_z5237406670263579293d_enat)))))))
% 4.71/5.17 (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)))))))
% 4.71/5.17 (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)))))))
% 4.71/5.17 (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)))))))
% 4.71/5.17 (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)))))))
% 4.71/5.17 (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)))))))
% 4.71/5.17 (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)))))))
% 4.71/5.17 (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)))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (M2 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 M2)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M2) N2))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (M2 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 M2)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M2) N2))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (M2 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 M2)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M2) N2))))))
% 4.71/5.17 (assert (forall ((N2 tptp.nat) (N6 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat N2) N6) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_nat (@ _let_1 N2)) (@ _let_1 N6)))))))
% 4.71/5.17 (assert (forall ((N2 tptp.nat) (N6 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat N2) N6) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (@ (@ tptp.ord_less_real (@ _let_1 N2)) (@ _let_1 N6)))))))
% 4.71/5.17 (assert (forall ((N2 tptp.nat) (N6 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat N2) N6) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (@ (@ tptp.ord_less_int (@ _let_1 N2)) (@ _let_1 N6)))))))
% 4.71/5.17 (assert (forall ((N2 tptp.nat) (N6 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N6) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A) (@ (@ tptp.ord_less_eq_real (@ _let_1 N2)) (@ _let_1 N6)))))))
% 4.71/5.17 (assert (forall ((N2 tptp.nat) (N6 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N6) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N2)) (@ _let_1 N6)))))))
% 4.71/5.17 (assert (forall ((N2 tptp.nat) (N6 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N6) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A) (@ (@ tptp.ord_less_eq_int (@ _let_1 N2)) (@ _let_1 N6)))))))
% 4.71/5.17 (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))))))
% 4.71/5.17 (assert (forall ((B2 tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B2) A)) tptp.one_one_real) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real B2) A)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real A) B2)) (= A tptp.zero_zero_real)))))
% 4.71/5.17 (assert (forall ((B2 tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B2) A)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real A) B2)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B2) A))))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (assert (forall ((N2 tptp.nat) (N6 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat N2) N6) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ _let_1 N6)) (@ _let_1 N2))))))))
% 4.71/5.17 (assert (forall ((N2 tptp.nat) (N6 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat N2) N6) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ _let_1 N6)) (@ _let_1 N2))))))))
% 4.71/5.17 (assert (forall ((N2 tptp.nat) (N6 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat N2) N6) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ _let_1 N6)) (@ _let_1 N2))))))))
% 4.71/5.17 (assert (forall ((N2 tptp.nat) (N6 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N6) (=> (@ (@ 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 N6)) (@ _let_1 N2))))))))
% 4.71/5.17 (assert (forall ((N2 tptp.nat) (N6 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N6) (=> (@ (@ 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 N6)) (@ _let_1 N2))))))))
% 4.71/5.17 (assert (forall ((N2 tptp.nat) (N6 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N6) (=> (@ (@ 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 N6)) (@ _let_1 N2))))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (M2 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 M2)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M2) N2))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (M2 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 M2)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M2) N2))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (M2 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 M2)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M2) N2))))))
% 4.71/5.17 (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))))))
% 4.71/5.17 (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))))))
% 4.71/5.17 (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))))))
% 4.71/5.17 (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)))))))
% 4.71/5.17 (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)))))))
% 4.71/5.17 (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)))))))
% 4.71/5.17 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 4.71/5.17 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M2) K)) (@ (@ tptp.divide_divide_nat N2) K)))))
% 4.71/5.17 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M2) N2)) M2)))
% 4.71/5.17 (assert (forall ((B2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ _let_1 B2) (=> (@ _let_1 K) (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (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)))))))))))
% 4.71/5.17 (assert (forall ((B2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B2) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) K) (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (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))))))))))
% 4.71/5.17 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.divide_divide_nat M2) N2) tptp.zero_zero_nat) (or (@ (@ tptp.ord_less_nat M2) N2) (= N2 tptp.zero_zero_nat)))))
% 4.71/5.17 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M2) N2)) (@ (@ tptp.divide_divide_nat (@ tptp.suc M2)) N2))))
% 4.71/5.17 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N2)) (@ _let_1 M2)))))))
% 4.71/5.17 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.divide_divide_nat M2) N2)) (and (@ (@ tptp.ord_less_eq_nat N2) M2) (@ _let_1 N2))))))
% 4.71/5.17 (assert (forall ((M2 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 M2) N2)) tptp.zero_zero_nat)) (not (= (@ _let_1 M2) tptp.zero_zero_nat))))))
% 4.71/5.17 (assert (forall ((M2 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 M2) N2)) tptp.zero_zero_int)) (not (= (@ _let_1 M2) tptp.zero_zero_int))))))
% 4.71/5.17 (assert (forall ((M2 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 M2) N2)) tptp.zero_zero_nat)) (not (= (@ _let_1 N2) tptp.zero_zero_nat))))))
% 4.71/5.17 (assert (forall ((M2 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 M2) N2)) tptp.zero_zero_int)) (not (= (@ _let_1 N2) tptp.zero_zero_int))))))
% 4.71/5.17 (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))))))
% 4.71/5.17 (assert (= tptp.vEBT_VEBT_bit_concat (lambda ((H tptp.nat) (L2 tptp.nat) (D4 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) D4))) L2))))
% 4.71/5.17 (assert (forall ((X tptp.nat) (N2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_nat X) _let_1) (= (@ (@ tptp.vEBT_VEBT_low (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat Y) _let_1)) X)) N2) X)))))
% 4.71/5.17 (assert (forall ((X tptp.nat) (N2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_nat X) _let_1) (= (@ (@ tptp.vEBT_VEBT_high (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat Y) _let_1)) X)) N2) Y)))))
% 4.71/5.17 (assert (forall ((A1 tptp.vEBT_VEBT) (A22 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt A1) A22) (=> (=> (exists ((A4 Bool) (B4 Bool)) (= A1 (@ (@ tptp.vEBT_Leaf A4) B4))) (not (= A22 (@ tptp.suc tptp.zero_zero_nat)))) (=> (forall ((TreeList3 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M3 tptp.nat) (Deg2 tptp.nat)) (=> (= A1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList3) Summary2)) (=> (= A22 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 Summary2) M3) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M3)) (=> (= M3 N3) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M3)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) 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) (Summary2 tptp.vEBT_VEBT) (M3 tptp.nat) (Deg2 tptp.nat)) (=> (= A1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList3) Summary2)) (=> (= A22 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 Summary2) M3) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M3)) (=> (= M3 (@ tptp.suc N3)) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M3)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) 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) (Summary2 tptp.vEBT_VEBT) (M3 tptp.nat) (Deg2 tptp.nat) (Mi2 tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (= Mi2 Ma2))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (= A1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Deg2) TreeList3) Summary2)) (=> (= A22 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 Summary2) M3) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ _let_2 M3)) (=> (= M3 N3) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M3)) (=> (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M3)) (= (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I5)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I5)))) (=> (=> _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 Mi2) Ma2) (=> (@ (@ tptp.ord_less_nat Ma2) (@ _let_2 Deg2)) (not (=> (not _let_1) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M3)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma2) N3) I5) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I5)) (@ (@ tptp.vEBT_VEBT_low Ma2) N3))) (forall ((X2 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X2) N3) I5) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I5)) (@ (@ tptp.vEBT_VEBT_low X2) N3))) (and (@ (@ tptp.ord_less_nat Mi2) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma2))))))))))))))))))))))) (not (forall ((TreeList3 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M3 tptp.nat) (Deg2 tptp.nat) (Mi2 tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (= Mi2 Ma2))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (= A1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Deg2) TreeList3) Summary2)) (=> (= A22 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 Summary2) M3) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ _let_2 M3)) (=> (= M3 (@ tptp.suc N3)) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M3)) (=> (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M3)) (= (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I5)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I5)))) (=> (=> _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 Mi2) Ma2) (=> (@ (@ tptp.ord_less_nat Ma2) (@ _let_2 Deg2)) (not (=> (not _let_1) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M3)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma2) N3) I5) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I5)) (@ (@ tptp.vEBT_VEBT_low Ma2) N3))) (forall ((X2 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X2) N3) I5) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I5)) (@ (@ tptp.vEBT_VEBT_low X2) N3))) (and (@ (@ tptp.ord_less_nat Mi2) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma2)))))))))))))))))))))))))))))))
% 4.71/5.17 (assert (= tptp.vEBT_invar_vebt (lambda ((A12 tptp.vEBT_VEBT) (A23 tptp.nat)) (or (and (exists ((A3 Bool) (B3 Bool)) (= A12 (@ (@ tptp.vEBT_Leaf A3) B3))) (= A23 (@ tptp.suc tptp.zero_zero_nat))) (exists ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary3 tptp.vEBT_VEBT)) (and (= A12 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A23) TreeList) Summary3)) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X4) N))) (@ (@ tptp.vEBT_invar_vebt Summary3) N) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= A23 (@ (@ tptp.plus_plus_nat N) N)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) X6))) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X6))))))) (exists ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc N))) (and (= A12 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A23) TreeList) Summary3)) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X4) N))) (@ (@ tptp.vEBT_invar_vebt Summary3) _let_1) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (= A23 (@ (@ tptp.plus_plus_nat N) _let_1)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) X6))) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X6)))))))) (exists ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary3 tptp.vEBT_VEBT) (Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (= Mi3 Ma3))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (and (= A12 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) A23) TreeList) Summary3)) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X4) N))) (@ (@ tptp.vEBT_invar_vebt Summary3) N) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ _let_2 N)) (= A23 (@ (@ 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 ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I3)))) (=> _let_1 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X6)))))) (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ _let_2 A23)) (=> (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 Ma3) N) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) (@ (@ tptp.vEBT_VEBT_low Ma3) N))) (forall ((X4 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X4) N) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) (@ (@ tptp.vEBT_VEBT_low X4) N))) (and (@ (@ tptp.ord_less_nat Mi3) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma3)))))))))))) (exists ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary3 tptp.vEBT_VEBT) (Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (= Mi3 Ma3))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ tptp.suc N))) (and (= A12 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) A23) TreeList) Summary3)) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X4) N))) (@ (@ tptp.vEBT_invar_vebt Summary3) _let_3) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ _let_2 _let_3)) (= A23 (@ (@ 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 ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I3)))) (=> _let_1 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X6)))))) (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ _let_2 A23)) (=> (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 Ma3) N) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) (@ (@ tptp.vEBT_VEBT_low Ma3) N))) (forall ((X4 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X4) N) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) (@ (@ tptp.vEBT_VEBT_low X4) N))) (and (@ (@ tptp.ord_less_nat Mi3) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma3)))))))))))))))))
% 4.71/5.17 (assert (forall ((M2 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat M2)) (@ tptp.numera1916890842035813515d_enat N2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat M2)) (@ tptp.numeral_numeral_nat N2)))))
% 4.71/5.17 (assert (forall ((M2 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat M2)) (@ tptp.numera1916890842035813515d_enat N2)) (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat M2)) (@ tptp.numeral_numeral_nat N2)))))
% 4.71/5.17 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 4.71/5.17 (assert (forall ((A Bool) (B2 Bool)) (not (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_Leaf A) B2)) tptp.zero_zero_nat))))
% 4.71/5.17 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (= N2 tptp.one_one_nat) (exists ((A4 Bool) (B4 Bool)) (= T (@ (@ tptp.vEBT_Leaf A4) B4)))))))
% 4.71/5.17 (assert (forall ((T tptp.vEBT_VEBT)) (=> (@ (@ tptp.vEBT_invar_vebt T) tptp.one_one_nat) (exists ((A4 Bool) (B4 Bool)) (= T (@ (@ tptp.vEBT_Leaf A4) B4))))))
% 4.71/5.17 (assert (forall ((T tptp.vEBT_VEBT)) (= (@ (@ tptp.vEBT_invar_vebt T) tptp.one_one_nat) (exists ((A3 Bool) (B3 Bool)) (= T (@ (@ tptp.vEBT_Leaf A3) B3))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (= (= (@ (@ tptp.times_times_nat A) C) (@ (@ tptp.times_times_nat B2) C)) (or (= C tptp.zero_zero_nat) (= A B2)))))
% 4.71/5.17 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (= (@ (@ tptp.times_times_int A) C) (@ (@ tptp.times_times_int B2) C)) (or (= C tptp.zero_zero_int) (= A B2)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (= (@ (@ tptp.times_times_real A) C) (@ (@ tptp.times_times_real B2) C)) (or (= C tptp.zero_zero_real) (= A B2)))))
% 4.71/5.17 (assert (forall ((A tptp.complex) (C tptp.complex) (B2 tptp.complex)) (= (= (@ (@ tptp.times_times_complex A) C) (@ (@ tptp.times_times_complex B2) C)) (or (= C tptp.zero_zero_complex) (= A B2)))))
% 4.71/5.17 (assert (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (= (= (@ _let_1 A) (@ _let_1 B2)) (or (= C tptp.zero_zero_nat) (= A B2))))))
% 4.71/5.17 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (= (@ _let_1 A) (@ _let_1 B2)) (or (= C tptp.zero_zero_int) (= A B2))))))
% 4.71/5.17 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (= (@ _let_1 A) (@ _let_1 B2)) (or (= C tptp.zero_zero_real) (= A B2))))))
% 4.71/5.17 (assert (forall ((C tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C))) (= (= (@ _let_1 A) (@ _let_1 B2)) (or (= C tptp.zero_zero_complex) (= A B2))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (= (@ (@ tptp.times_times_nat A) B2) tptp.zero_zero_nat) (or (= A tptp.zero_zero_nat) (= B2 tptp.zero_zero_nat)))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (= (@ (@ tptp.times_times_int A) B2) tptp.zero_zero_int) (or (= A tptp.zero_zero_int) (= B2 tptp.zero_zero_int)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (= (@ (@ tptp.times_times_real A) B2) tptp.zero_zero_real) (or (= A tptp.zero_zero_real) (= B2 tptp.zero_zero_real)))))
% 4.71/5.17 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (= (@ (@ tptp.times_times_complex A) B2) tptp.zero_zero_complex) (or (= A tptp.zero_zero_complex) (= B2 tptp.zero_zero_complex)))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (= (= (@ (@ tptp.times_7803423173614009249d_enat A) B2) tptp.zero_z5237406670263579293d_enat) (or (= A tptp.zero_z5237406670263579293d_enat) (= B2 tptp.zero_z5237406670263579293d_enat)))))
% 4.71/5.17 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 4.71/5.17 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 4.71/5.17 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 4.71/5.17 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat A) tptp.zero_z5237406670263579293d_enat) tptp.zero_z5237406670263579293d_enat)))
% 4.71/5.17 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 4.71/5.17 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 4.71/5.17 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.zero_zero_real) A) tptp.zero_zero_real)))
% 4.71/5.17 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.zero_zero_complex) A) tptp.zero_zero_complex)))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat tptp.zero_z5237406670263579293d_enat) A) tptp.zero_z5237406670263579293d_enat)))
% 4.71/5.17 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)))
% 4.71/5.17 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.one_one_int) A)))
% 4.71/5.17 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.one_one_real) A)))
% 4.71/5.17 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.one_one_complex) A)))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat A) tptp.one_on7984719198319812577d_enat) A)))
% 4.71/5.17 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)))
% 4.71/5.17 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)))
% 4.71/5.17 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A) A)))
% 4.71/5.17 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.one_one_complex) A) A)))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat tptp.one_on7984719198319812577d_enat) A) A)))
% 4.71/5.17 (assert (forall ((B2 tptp.complex) (C tptp.complex) (A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex B2) C)) A) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex B2) A)) C))))
% 4.71/5.17 (assert (forall ((B2 tptp.real) (C tptp.real) (A tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real B2) C)) A) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real B2) A)) C))))
% 4.71/5.17 (assert (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (= (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_times_complex B2) C))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (= (@ (@ tptp.divide_divide_real (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_times_real B2) C))))))
% 4.71/5.17 (assert (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) (@ (@ tptp.divide1717551699836669952omplex B2) C)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) C)) B2))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (= (@ (@ tptp.divide_divide_real A) (@ (@ tptp.divide_divide_real B2) C)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) C)) B2))))
% 4.71/5.17 (assert (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ (@ tptp.divide1717551699836669952omplex B2) C)) (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 B2)) C)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.divide_divide_real B2) C)) (@ (@ tptp.divide_divide_real (@ _let_1 B2)) C)))))
% 4.71/5.17 (assert (forall ((M2 tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.times_times_nat M2) K) (@ (@ tptp.times_times_nat N2) K)) (or (= M2 N2) (= K tptp.zero_zero_nat)))))
% 4.71/5.17 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (= (@ _let_1 M2) (@ _let_1 N2)) (or (= M2 N2) (= K tptp.zero_zero_nat))))))
% 4.71/5.17 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.times_times_nat M2) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 4.71/5.17 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.times_times_nat M2) N2) tptp.zero_zero_nat) (or (= M2 tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat)))))
% 4.71/5.17 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (= tptp.one_one_nat (@ (@ tptp.times_times_nat M2) N2)) (and (= M2 tptp.one_one_nat) (= N2 tptp.one_one_nat)))))
% 4.71/5.17 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.times_times_nat M2) N2) tptp.one_one_nat) (and (= M2 tptp.one_one_nat) (= N2 tptp.one_one_nat)))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (assert (forall ((C tptp.int) (B2 tptp.int)) (= (= C (@ (@ tptp.times_times_int B2) C)) (or (= C tptp.zero_zero_int) (= B2 tptp.one_one_int)))))
% 4.71/5.17 (assert (forall ((C tptp.real) (B2 tptp.real)) (= (= C (@ (@ tptp.times_times_real B2) C)) (or (= C tptp.zero_zero_real) (= B2 tptp.one_one_real)))))
% 4.71/5.17 (assert (forall ((C tptp.complex) (B2 tptp.complex)) (= (= C (@ (@ tptp.times_times_complex B2) C)) (or (= C tptp.zero_zero_complex) (= B2 tptp.one_one_complex)))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (assert (forall ((C tptp.int) (B2 tptp.int)) (= (= C (@ (@ tptp.times_times_int C) B2)) (or (= C tptp.zero_zero_int) (= B2 tptp.one_one_int)))))
% 4.71/5.17 (assert (forall ((C tptp.real) (B2 tptp.real)) (= (= C (@ (@ tptp.times_times_real C) B2)) (or (= C tptp.zero_zero_real) (= B2 tptp.one_one_real)))))
% 4.71/5.17 (assert (forall ((C tptp.complex) (B2 tptp.complex)) (= (= C (@ (@ tptp.times_times_complex C) B2)) (or (= C tptp.zero_zero_complex) (= B2 tptp.one_one_complex)))))
% 4.71/5.17 (assert (forall ((X tptp.int) (Y tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y)) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))))
% 4.71/5.17 (assert (forall ((X tptp.real) (Y tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y)) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real)))))
% 4.71/5.17 (assert (forall ((C tptp.complex) (A tptp.complex) (B2 tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex C) B2)) (@ (@ tptp.divide1717551699836669952omplex A) B2)))))
% 4.71/5.17 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real C) B2)) (@ (@ tptp.divide_divide_real A) B2)))))
% 4.71/5.17 (assert (forall ((B2 tptp.complex) (A tptp.complex)) (=> (not (= B2 tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) B2)) B2) A))))
% 4.71/5.17 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (=> (not (= B2 tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) B2)) B2) A))))
% 4.71/5.17 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (not (= B2 tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) B2)) B2) A))))
% 4.71/5.17 (assert (forall ((B2 tptp.real) (A tptp.real)) (=> (not (= B2 tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) B2)) B2) A))))
% 4.71/5.17 (assert (forall ((C tptp.complex) (A tptp.complex) (B2 tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B2) C)) (@ (@ tptp.divide1717551699836669952omplex A) B2)))))
% 4.71/5.17 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) C)) (@ (@ tptp.divide_divide_real A) B2)))))
% 4.71/5.17 (assert (forall ((C tptp.complex) (A tptp.complex) (B2 tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex C) A)) (@ (@ tptp.times_times_complex B2) C)) (@ (@ tptp.divide1717551699836669952omplex A) B2)))))
% 4.71/5.17 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real C) A)) (@ (@ tptp.times_times_real B2) C)) (@ (@ tptp.divide_divide_real A) B2)))))
% 4.71/5.17 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) B2)) A) B2))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) B2)) A) B2))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) B2)) A) B2))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) B2)) A) B2))))
% 4.71/5.17 (assert (forall ((C tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C))) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.divide1717551699836669952omplex A) B2))))))
% 4.71/5.17 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.divide_divide_real A) B2))))))
% 4.71/5.17 (assert (forall ((C tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C))) (let ((_let_2 (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 A)) (@ _let_1 B2)))) (let ((_let_3 (= C tptp.zero_zero_complex))) (and (=> _let_3 (= _let_2 tptp.zero_zero_complex)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide1717551699836669952omplex A) B2)))))))))
% 4.71/5.17 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (let ((_let_2 (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ _let_1 B2)))) (let ((_let_3 (= C tptp.zero_zero_real))) (and (=> _let_3 (= _let_2 tptp.zero_zero_real)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_real A) B2)))))))))
% 4.71/5.17 (assert (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 A)) (@ _let_1 B2)))) (let ((_let_3 (= C tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_nat A) B2)))))))))
% 4.71/5.17 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (let ((_let_2 (@ (@ tptp.divide_divide_int (@ _let_1 A)) (@ _let_1 B2)))) (let ((_let_3 (= C tptp.zero_zero_int))) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_int A) B2)))))))))
% 4.71/5.17 (assert (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (=> (not (= C tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B2) C)) (@ (@ tptp.divide_divide_nat A) B2)))))
% 4.71/5.17 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (=> (not (= C tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) C)) (@ (@ tptp.divide_divide_int A) B2)))))
% 4.71/5.17 (assert (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (not (= C tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.divide_divide_nat A) B2))))))
% 4.71/5.17 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (not (= C tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.divide_divide_int A) B2))))))
% 4.71/5.17 (assert (forall ((A tptp.complex) (B2 tptp.complex) (V tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex V))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B2)) _let_1) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) _let_1)) (@ (@ tptp.times_times_complex B2) _let_1))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat V))) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B2)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) _let_1)) (@ (@ tptp.times_times_nat B2) _let_1))))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (V tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat V))) (= (@ (@ tptp.times_7803423173614009249d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) B2)) _let_1) (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.times_7803423173614009249d_enat A) _let_1)) (@ (@ tptp.times_7803423173614009249d_enat B2) _let_1))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int V))) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B2)) _let_1) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) _let_1)) (@ (@ tptp.times_times_int B2) _let_1))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real V))) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B2)) _let_1) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) _let_1)) (@ (@ tptp.times_times_real B2) _let_1))))))
% 4.71/5.17 (assert (forall ((V tptp.num) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B2) C)) (@ (@ tptp.plus_plus_complex (@ _let_1 B2)) (@ _let_1 C))))))
% 4.71/5.17 (assert (forall ((V tptp.num) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B2) C)) (@ (@ tptp.plus_plus_nat (@ _let_1 B2)) (@ _let_1 C))))))
% 4.71/5.17 (assert (forall ((V tptp.num) (B2 tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat V)))) (= (@ _let_1 (@ (@ tptp.plus_p3455044024723400733d_enat B2) C)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ _let_1 B2)) (@ _let_1 C))))))
% 4.71/5.17 (assert (forall ((V tptp.num) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B2) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B2)) (@ _let_1 C))))))
% 4.71/5.17 (assert (forall ((V tptp.num) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B2) C)) (@ (@ tptp.plus_plus_real (@ _let_1 B2)) (@ _let_1 C))))))
% 4.71/5.17 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.times_times_nat M2) N2)) (and (= M2 _let_1) (= N2 _let_1))))))
% 4.71/5.17 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.times_times_nat M2) N2) _let_1) (and (= M2 _let_1) (= N2 _let_1))))))
% 4.71/5.17 (assert (forall ((M2 tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat M2) K)) (@ (@ tptp.times_times_nat N2) K)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat M2) N2)))))
% 4.71/5.17 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.times_times_nat M2) N2)) (and (@ _let_1 M2) (@ _let_1 N2))))))
% 4.71/5.17 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M2))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.plus_plus_nat M2) (@ _let_1 N2))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.divide_divide_real B2) _let_1)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) _let_1)) B2)))))
% 4.71/5.17 (assert (forall ((B2 tptp.real) (W2 tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B2) _let_1)) A) (@ (@ tptp.ord_less_eq_real B2) (@ (@ tptp.times_times_real A) _let_1))))))
% 4.71/5.17 (assert (forall ((B2 tptp.complex) (W2 tptp.num) (A tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W2))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B2) _let_1) A) (and (=> (not _let_2) (= B2 (@ (@ tptp.times_times_complex A) _let_1))) (=> _let_2 (= A tptp.zero_zero_complex))))))))
% 4.71/5.17 (assert (forall ((B2 tptp.real) (W2 tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B2) _let_1) A) (and (=> (not _let_2) (= B2 (@ (@ tptp.times_times_real A) _let_1))) (=> _let_2 (= A tptp.zero_zero_real))))))))
% 4.71/5.17 (assert (forall ((A tptp.complex) (B2 tptp.complex) (W2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W2))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= A (@ (@ tptp.divide1717551699836669952omplex B2) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex A) _let_1) B2)) (=> _let_2 (= A tptp.zero_zero_complex))))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= A (@ (@ tptp.divide_divide_real B2) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real A) _let_1) B2)) (=> _let_2 (= A tptp.zero_zero_real))))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.divide_divide_real B2) _let_1)) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) _let_1)) B2)))))
% 4.71/5.17 (assert (forall ((B2 tptp.real) (W2 tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B2) _let_1)) A) (@ (@ tptp.ord_less_real B2) (@ (@ tptp.times_times_real A) _let_1))))))
% 4.71/5.17 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) (@ (@ tptp.times_times_complex A) B2)) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) B2)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) (@ (@ tptp.times_times_real A) B2)) (@ (@ tptp.divide_divide_real tptp.one_one_real) B2)))))
% 4.71/5.17 (assert (forall ((B2 tptp.complex) (A tptp.complex)) (=> (not (= B2 tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex B2) (@ (@ tptp.times_times_complex A) B2)) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) A)))))
% 4.71/5.17 (assert (forall ((B2 tptp.real) (A tptp.real)) (=> (not (= B2 tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real B2) (@ (@ tptp.times_times_real A) B2)) (@ (@ tptp.divide_divide_real tptp.one_one_real) A)))))
% 4.71/5.17 (assert (forall ((B2 tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (not (= B2 tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B2) C)) A)) B2) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B2))))))
% 4.71/5.17 (assert (forall ((B2 tptp.int) (C tptp.int) (A tptp.int)) (=> (not (= B2 tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) C)) A)) B2) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B2))))))
% 4.71/5.17 (assert (forall ((B2 tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (not (= B2 tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C) B2)) A)) B2) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B2))))))
% 4.71/5.17 (assert (forall ((B2 tptp.int) (C tptp.int) (A tptp.int)) (=> (not (= B2 tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C) B2)) A)) B2) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B2))))))
% 4.71/5.17 (assert (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (not (= B2 tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat B2) C))) B2) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B2))))))
% 4.71/5.17 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B2 tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int B2) C))) B2) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B2))))))
% 4.71/5.17 (assert (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (not (= B2 tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat C) B2))) B2) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B2))))))
% 4.71/5.17 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B2 tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int C) B2))) B2) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B2))))))
% 4.71/5.17 (assert (forall ((M2 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 M2) N2)) (and (@ _let_1 M2) (@ _let_1 N2))))))
% 4.71/5.17 (assert (forall ((M2 tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M2) K)) (@ (@ tptp.times_times_nat N2) K)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_eq_nat M2) N2)))))
% 4.71/5.17 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat M2) N2)) N2) M2))))
% 4.71/5.17 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N2) M2)) N2) M2))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_times_nat B2) C))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_times_int B2) C))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_times_real B2) C))))))
% 4.71/5.17 (assert (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_times_complex B2) C))))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.times_7803423173614009249d_enat A))) (= (@ (@ tptp.times_7803423173614009249d_enat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_7803423173614009249d_enat B2) C))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_times_nat B2) C))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_times_int B2) C))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_times_real B2) C))))))
% 4.71/5.17 (assert (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_times_complex B2) C))))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.times_7803423173614009249d_enat A))) (= (@ (@ tptp.times_7803423173614009249d_enat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_7803423173614009249d_enat B2) C))))))
% 4.71/5.17 (assert (= tptp.times_times_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.times_times_nat B3) A3))))
% 4.71/5.17 (assert (= tptp.times_times_int (lambda ((A3 tptp.int) (B3 tptp.int)) (@ (@ tptp.times_times_int B3) A3))))
% 4.71/5.17 (assert (= tptp.times_times_real (lambda ((A3 tptp.real) (B3 tptp.real)) (@ (@ tptp.times_times_real B3) A3))))
% 4.71/5.17 (assert (= tptp.times_times_complex (lambda ((A3 tptp.complex) (B3 tptp.complex)) (@ (@ tptp.times_times_complex B3) A3))))
% 4.71/5.17 (assert (= tptp.times_7803423173614009249d_enat (lambda ((A3 tptp.extended_enat) (B3 tptp.extended_enat)) (@ (@ tptp.times_7803423173614009249d_enat B3) A3))))
% 4.71/5.17 (assert (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat B2))) (let ((_let_2 (@ tptp.times_times_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 4.71/5.17 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int B2))) (let ((_let_2 (@ tptp.times_times_int A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 4.71/5.17 (assert (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real B2))) (let ((_let_2 (@ tptp.times_times_real A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 4.71/5.17 (assert (forall ((B2 tptp.complex) (A tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex B2))) (let ((_let_2 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 4.71/5.17 (assert (forall ((B2 tptp.extended_enat) (A tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.times_7803423173614009249d_enat B2))) (let ((_let_2 (@ tptp.times_7803423173614009249d_enat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 4.71/5.17 (assert (forall ((X21 Bool) (X222 Bool)) (= (@ tptp.size_size_VEBT_VEBT (@ (@ tptp.vEBT_Leaf X21) X222)) tptp.zero_zero_nat)))
% 4.71/5.17 (assert (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (=> (not (= C tptp.zero_zero_nat)) (= (= (@ (@ tptp.times_times_nat A) C) (@ (@ tptp.times_times_nat B2) C)) (= A B2)))))
% 4.71/5.17 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (=> (not (= C tptp.zero_zero_int)) (= (= (@ (@ tptp.times_times_int A) C) (@ (@ tptp.times_times_int B2) C)) (= A B2)))))
% 4.71/5.17 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (= (@ (@ tptp.times_times_real A) C) (@ (@ tptp.times_times_real B2) C)) (= A B2)))))
% 4.71/5.17 (assert (forall ((C tptp.complex) (A tptp.complex) (B2 tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (= (@ (@ tptp.times_times_complex A) C) (@ (@ tptp.times_times_complex B2) C)) (= A B2)))))
% 4.71/5.17 (assert (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (not (= C tptp.zero_zero_nat)) (= (= (@ _let_1 A) (@ _let_1 B2)) (= A B2))))))
% 4.71/5.17 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (not (= C tptp.zero_zero_int)) (= (= (@ _let_1 A) (@ _let_1 B2)) (= A B2))))))
% 4.71/5.17 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (not (= C tptp.zero_zero_real)) (= (= (@ _let_1 A) (@ _let_1 B2)) (= A B2))))))
% 4.71/5.17 (assert (forall ((C tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C))) (=> (not (= C tptp.zero_zero_complex)) (= (= (@ _let_1 A) (@ _let_1 B2)) (= A B2))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (not (= B2 tptp.zero_zero_nat)) (not (= (@ (@ tptp.times_times_nat A) B2) tptp.zero_zero_nat))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (not (= B2 tptp.zero_zero_int)) (not (= (@ (@ tptp.times_times_int A) B2) tptp.zero_zero_int))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B2 tptp.zero_zero_real)) (not (= (@ (@ tptp.times_times_real A) B2) tptp.zero_zero_real))))))
% 4.71/5.17 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B2 tptp.zero_zero_complex)) (not (= (@ (@ tptp.times_times_complex A) B2) tptp.zero_zero_complex))))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (=> (not (= A tptp.zero_z5237406670263579293d_enat)) (=> (not (= B2 tptp.zero_z5237406670263579293d_enat)) (not (= (@ (@ tptp.times_7803423173614009249d_enat A) B2) tptp.zero_z5237406670263579293d_enat))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (= (@ (@ tptp.times_times_nat A) B2) tptp.zero_zero_nat) (or (= A tptp.zero_zero_nat) (= B2 tptp.zero_zero_nat)))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (= (@ (@ tptp.times_times_int A) B2) tptp.zero_zero_int) (or (= A tptp.zero_zero_int) (= B2 tptp.zero_zero_int)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (= (@ (@ tptp.times_times_real A) B2) tptp.zero_zero_real) (or (= A tptp.zero_zero_real) (= B2 tptp.zero_zero_real)))))
% 4.71/5.17 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (=> (= (@ (@ tptp.times_times_complex A) B2) tptp.zero_zero_complex) (or (= A tptp.zero_zero_complex) (= B2 tptp.zero_zero_complex)))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (=> (= (@ (@ tptp.times_7803423173614009249d_enat A) B2) tptp.zero_z5237406670263579293d_enat) (or (= A tptp.zero_z5237406670263579293d_enat) (= B2 tptp.zero_z5237406670263579293d_enat)))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (not (= (@ (@ tptp.times_times_nat A) B2) tptp.zero_zero_nat)) (and (not (= A tptp.zero_zero_nat)) (not (= B2 tptp.zero_zero_nat))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (not (= (@ (@ tptp.times_times_int A) B2) tptp.zero_zero_int)) (and (not (= A tptp.zero_zero_int)) (not (= B2 tptp.zero_zero_int))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (not (= (@ (@ tptp.times_times_real A) B2) tptp.zero_zero_real)) (and (not (= A tptp.zero_zero_real)) (not (= B2 tptp.zero_zero_real))))))
% 4.71/5.17 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (=> (not (= (@ (@ tptp.times_times_complex A) B2) tptp.zero_zero_complex)) (and (not (= A tptp.zero_zero_complex)) (not (= B2 tptp.zero_zero_complex))))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (=> (not (= (@ (@ tptp.times_7803423173614009249d_enat A) B2) tptp.zero_z5237406670263579293d_enat)) (and (not (= A tptp.zero_z5237406670263579293d_enat)) (not (= B2 tptp.zero_z5237406670263579293d_enat))))))
% 4.71/5.17 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)))
% 4.71/5.17 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)))
% 4.71/5.17 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A) A)))
% 4.71/5.17 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.one_one_complex) A) A)))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat tptp.one_on7984719198319812577d_enat) A) A)))
% 4.71/5.17 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)))
% 4.71/5.17 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.one_one_int) A)))
% 4.71/5.17 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.one_one_real) A)))
% 4.71/5.17 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.one_one_complex) A)))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat A) tptp.one_on7984719198319812577d_enat) A)))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat B2))) (let ((_let_2 (@ tptp.times_times_nat A))) (= (and (not (= A B2)) (not (= C D))) (not (= (@ (@ tptp.plus_plus_nat (@ _let_2 C)) (@ _let_1 D)) (@ (@ tptp.plus_plus_nat (@ _let_2 D)) (@ _let_1 C)))))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.times_times_int B2))) (let ((_let_2 (@ tptp.times_times_int A))) (= (and (not (= A B2)) (not (= C D))) (not (= (@ (@ tptp.plus_plus_int (@ _let_2 C)) (@ _let_1 D)) (@ (@ tptp.plus_plus_int (@ _let_2 D)) (@ _let_1 C)))))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.times_times_real B2))) (let ((_let_2 (@ tptp.times_times_real A))) (= (and (not (= A B2)) (not (= C D))) (not (= (@ (@ tptp.plus_plus_real (@ _let_2 C)) (@ _let_1 D)) (@ (@ tptp.plus_plus_real (@ _let_2 D)) (@ _let_1 C)))))))))
% 4.71/5.17 (assert (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex) (D tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex B2))) (let ((_let_2 (@ tptp.times_times_complex A))) (= (and (not (= A B2)) (not (= C D))) (not (= (@ (@ tptp.plus_plus_complex (@ _let_2 C)) (@ _let_1 D)) (@ (@ tptp.plus_plus_complex (@ _let_2 D)) (@ _let_1 C)))))))))
% 4.71/5.17 (assert (forall ((W2 tptp.nat) (Y tptp.nat) (X tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat X))) (let ((_let_2 (@ tptp.times_times_nat W2))) (= (= (@ (@ tptp.plus_plus_nat (@ _let_2 Y)) (@ _let_1 Z3)) (@ (@ tptp.plus_plus_nat (@ _let_2 Z3)) (@ _let_1 Y))) (or (= W2 X) (= Y Z3)))))))
% 4.71/5.17 (assert (forall ((W2 tptp.int) (Y tptp.int) (X tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int X))) (let ((_let_2 (@ tptp.times_times_int W2))) (= (= (@ (@ tptp.plus_plus_int (@ _let_2 Y)) (@ _let_1 Z3)) (@ (@ tptp.plus_plus_int (@ _let_2 Z3)) (@ _let_1 Y))) (or (= W2 X) (= Y Z3)))))))
% 4.71/5.17 (assert (forall ((W2 tptp.real) (Y tptp.real) (X tptp.real) (Z3 tptp.real)) (let ((_let_1 (@ tptp.times_times_real X))) (let ((_let_2 (@ tptp.times_times_real W2))) (= (= (@ (@ tptp.plus_plus_real (@ _let_2 Y)) (@ _let_1 Z3)) (@ (@ tptp.plus_plus_real (@ _let_2 Z3)) (@ _let_1 Y))) (or (= W2 X) (= Y Z3)))))))
% 4.71/5.17 (assert (forall ((W2 tptp.complex) (Y tptp.complex) (X tptp.complex) (Z3 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex X))) (let ((_let_2 (@ tptp.times_times_complex W2))) (= (= (@ (@ tptp.plus_plus_complex (@ _let_2 Y)) (@ _let_1 Z3)) (@ (@ tptp.plus_plus_complex (@ _let_2 Z3)) (@ _let_1 Y))) (or (= W2 X) (= Y Z3)))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (E2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) E2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B2) E2)) C)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B2)) E2)) C))))
% 4.71/5.17 (assert (forall ((A tptp.int) (E2 tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) E2)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B2)) E2)) C))))
% 4.71/5.17 (assert (forall ((A tptp.real) (E2 tptp.real) (B2 tptp.real) (C tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B2) E2)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B2)) E2)) C))))
% 4.71/5.17 (assert (forall ((A tptp.complex) (E2 tptp.complex) (B2 tptp.complex) (C tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) E2)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex B2) E2)) C)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B2)) E2)) C))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (E2 tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat)) (= (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.times_7803423173614009249d_enat A) E2)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.times_7803423173614009249d_enat B2) E2)) C)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.times_7803423173614009249d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) B2)) E2)) C))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B2)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B2) C)))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B2)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) C)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B2)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) C)))))
% 4.71/5.17 (assert (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B2)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B2) C)))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) B2)) C) (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.times_7803423173614009249d_enat A) C)) (@ (@ tptp.times_7803423173614009249d_enat B2) C)))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B2) C)) (@ (@ tptp.plus_plus_nat (@ _let_1 B2)) (@ _let_1 C))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B2) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B2)) (@ _let_1 C))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B2) C)) (@ (@ tptp.plus_plus_real (@ _let_1 B2)) (@ _let_1 C))))))
% 4.71/5.17 (assert (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B2) C)) (@ (@ tptp.plus_plus_complex (@ _let_1 B2)) (@ _let_1 C))))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.times_7803423173614009249d_enat A))) (= (@ _let_1 (@ (@ tptp.plus_p3455044024723400733d_enat B2) C)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ _let_1 B2)) (@ _let_1 C))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B2)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B2) C)))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B2)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) C)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B2)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) C)))))
% 4.71/5.17 (assert (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B2)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B2) C)))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) B2)) C) (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.times_7803423173614009249d_enat A) C)) (@ (@ tptp.times_7803423173614009249d_enat B2) C)))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B2) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B2)) (@ _let_1 C))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B2) C)) (@ (@ tptp.plus_plus_real (@ _let_1 B2)) (@ _let_1 C))))))
% 4.71/5.17 (assert (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B2) C)) (@ (@ tptp.plus_plus_complex (@ _let_1 B2)) (@ _let_1 C))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B2)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) C)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B2)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) C)))))
% 4.71/5.17 (assert (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B2)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B2) C)))))
% 4.71/5.17 (assert (forall ((X tptp.complex) (Y tptp.complex) (Z3 tptp.complex) (W2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide1717551699836669952omplex Z3) W2)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex X) Z3)) (@ (@ tptp.times_times_complex Y) W2)))))
% 4.71/5.17 (assert (forall ((X tptp.real) (Y tptp.real) (Z3 tptp.real) (W2 tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real Z3) W2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real X) Z3)) (@ (@ tptp.times_times_real Y) W2)))))
% 4.71/5.17 (assert (forall ((X tptp.complex) (Y tptp.complex) (Z3 tptp.complex) (W2 tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide1717551699836669952omplex Z3) W2)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex X) W2)) (@ (@ tptp.times_times_complex Y) Z3)))))
% 4.71/5.17 (assert (forall ((X tptp.real) (Y tptp.real) (Z3 tptp.real) (W2 tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real Z3) W2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real X) W2)) (@ (@ tptp.times_times_real Y) Z3)))))
% 4.71/5.17 (assert (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (= (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_times_complex C) B2))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (= (@ (@ tptp.divide_divide_real (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_times_real C) B2))))))
% 4.71/5.17 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (= (@ _let_1 M2) (@ _let_1 N2)) (= M2 N2)))))
% 4.71/5.17 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) N2) tptp.zero_zero_nat)))
% 4.71/5.17 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I)) (@ _let_1 J))))))
% 4.71/5.17 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I) K)) (@ (@ tptp.times_times_nat J) K)))))
% 4.71/5.17 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ (@ tptp.ord_less_eq_nat K) L) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I) K)) (@ (@ tptp.times_times_nat J) L))))))
% 4.71/5.17 (assert (forall ((M2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat M2) (@ (@ tptp.times_times_nat M2) M2))))
% 4.71/5.17 (assert (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M2))) (@ (@ tptp.ord_less_eq_nat M2) (@ _let_1 (@ _let_1 M2))))))
% 4.71/5.17 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N2)) (@ (@ tptp.plus_plus_nat (@ _let_1 M2)) (@ _let_1 N2))))))
% 4.71/5.17 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat M2) N2)) K) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat M2) K)) (@ (@ tptp.times_times_nat N2) K)))))
% 4.71/5.17 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) N2) N2)))
% 4.71/5.17 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.times_times_nat N2) tptp.one_one_nat) N2)))
% 4.71/5.17 (assert (forall ((Uu Bool) (Uv Bool) (Uw tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.vEBT_Leaf Uu) Uv)) Uw))))
% 4.71/5.17 (assert (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf false) false)))
% 4.71/5.17 (assert (forall ((Uv Bool)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf true) Uv)))))
% 4.71/5.17 (assert (forall ((Uu Bool)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf Uu) true)))))
% 4.71/5.17 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (Q3 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.ord_max_nat M2) N2)) Q3) (@ (@ tptp.ord_max_nat (@ (@ tptp.times_times_nat M2) Q3)) (@ (@ tptp.times_times_nat N2) Q3)))))
% 4.71/5.17 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (Q3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M2))) (= (@ _let_1 (@ (@ tptp.ord_max_nat N2) Q3)) (@ (@ tptp.ord_max_nat (@ _let_1 N2)) (@ _let_1 Q3))))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat) (D tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B2) (=> (@ (@ tptp.ord_le2932123472753598470d_enat C) D) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.times_7803423173614009249d_enat A) C)) (@ (@ tptp.times_7803423173614009249d_enat B2) D)))))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_eq_real C) D) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) D)))))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ tptp.ord_less_eq_nat C) D) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B2) D)))))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (@ (@ tptp.ord_less_eq_int C) D) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) D)))))))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat) (D tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B2) (=> (@ (@ tptp.ord_le2932123472753598470d_enat C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.times_7803423173614009249d_enat A) C)) (@ (@ tptp.times_7803423173614009249d_enat B2) D)))))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_eq_real C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) D)))))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ tptp.ord_less_eq_nat C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B2) D)))))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (@ (@ tptp.ord_less_eq_int C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) D)))))))))
% 4.71/5.17 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) A))))
% 4.71/5.17 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) A))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (@ _let_1 A) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real))) (@ _let_1 (@ (@ tptp.times_times_real A) B2))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (@ _let_1 A) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int))) (@ _let_1 (@ (@ tptp.times_times_int A) B2))))))
% 4.71/5.17 (assert (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_eq_real B2) A) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B2)))))))
% 4.71/5.17 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int B2) A) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B2)))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B2))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) B2))))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.times_7803423173614009249d_enat C))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B2) (=> (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) C) (@ (@ tptp.ord_le2932123472753598470d_enat (@ _let_1 A)) (@ _let_1 B2)))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B2)))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B2)))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B2)))))))
% 4.71/5.17 (assert (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B2) A) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) C))))))
% 4.71/5.17 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B2) A) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) C))))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B2) (=> (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) C) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.times_7803423173614009249d_enat A) C)) (@ (@ tptp.times_7803423173614009249d_enat B2) C))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) C))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B2) C))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) C))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B2)) tptp.zero_zero_real) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ _let_1 B2)))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B2)) tptp.zero_zero_int) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (@ _let_1 B2)))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ _let_1 B2))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B2)) tptp.zero_zero_real)))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_nat B2) tptp.zero_zero_nat)) (and (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (@ _let_1 B2))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) B2)) tptp.zero_zero_nat)))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (@ _let_1 B2))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B2)) tptp.zero_zero_int)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_real A) B2)))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_nat A) B2)))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_int A) B2)))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B2)) tptp.zero_zero_real)))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat B2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) B2)) tptp.zero_zero_nat)))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B2)) tptp.zero_zero_int)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B2)) tptp.zero_zero_real)))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) B2)) tptp.zero_zero_nat)))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B2)) tptp.zero_zero_int)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real B2) A)) tptp.zero_zero_real)))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat B2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat B2) A)) tptp.zero_zero_nat)))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int B2) A)) tptp.zero_zero_int)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.times_times_real A) B2)) (or (and (@ _let_1 A) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real)))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.times_times_int A) B2)) (or (and (@ _let_1 A) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int)))))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.times_7803423173614009249d_enat C))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B2) (=> (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) C) (@ (@ tptp.ord_le2932123472753598470d_enat (@ _let_1 A)) (@ _let_1 B2)))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B2)))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B2)))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B2)))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real B2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B2))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) B2))))))
% 4.71/5.17 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) A)) tptp.zero_zero_real))))
% 4.71/5.17 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) A)) tptp.zero_zero_int))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) B2)) tptp.zero_zero_real) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_real B2) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ _let_1 B2)))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) B2)) tptp.zero_zero_int) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (@ _let_1 B2)))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) B2)) tptp.zero_zero_nat)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B2) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) B2)) tptp.zero_zero_real)))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) B2)) tptp.zero_zero_int)))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat B2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) B2)) tptp.zero_zero_nat)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real B2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) B2)) tptp.zero_zero_real)))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) B2)) tptp.zero_zero_int)))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_nat A) B2)))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_real A) B2)))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_int A) B2)))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat B2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat B2) A)) tptp.zero_zero_nat)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real B2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real B2) A)) tptp.zero_zero_real)))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int B2) A)) tptp.zero_zero_int)))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.times_times_real A) B2)) (or (and (@ _let_1 A) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B2) tptp.zero_zero_real)))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.times_times_int A) B2)) (or (and (@ _let_1 A) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int)))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 (@ (@ tptp.times_times_nat A) B2)) (=> (@ _let_1 A) (@ _let_1 B2))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ (@ tptp.times_times_real A) B2)) (=> (@ _let_1 A) (@ _let_1 B2))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.times_times_int A) B2)) (=> (@ _let_1 A) (@ _let_1 B2))))))
% 4.71/5.17 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 (@ (@ tptp.times_times_nat B2) A)) (=> (@ _let_1 A) (@ _let_1 B2))))))
% 4.71/5.17 (assert (forall ((B2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ (@ tptp.times_times_real B2) A)) (=> (@ _let_1 A) (@ _let_1 B2))))))
% 4.71/5.17 (assert (forall ((B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.times_times_int B2) A)) (=> (@ _let_1 A) (@ _let_1 B2))))))
% 4.71/5.17 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_real B2) A))))))
% 4.71/5.17 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_int B2) A))))))
% 4.71/5.17 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_real A) B2))))))
% 4.71/5.17 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_int A) B2))))))
% 4.71/5.17 (assert (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real B2) A) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B2)))))))
% 4.71/5.17 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int B2) A) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B2)))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat A) B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B2)))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B2)))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int A) B2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B2)))))))
% 4.71/5.17 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B2)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B2)) (and (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B2) A)))))))
% 4.71/5.17 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B2)) (or (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B2)) (and (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B2) A)))))))
% 4.71/5.17 (assert (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real B2) A) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) C))))))
% 4.71/5.17 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int B2) A) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) C))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B2) C))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) C))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) C))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) C)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B2)) (and (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B2) A))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) C)) (or (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B2)) (and (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B2) A))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat A) B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B2)))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B2)))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int A) B2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B2)))))))
% 4.71/5.17 (assert (forall ((R2 tptp.nat) (A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat R2))) (=> (not (= R2 tptp.zero_zero_nat)) (=> (and (= A B2) (not (= C D))) (not (= (@ (@ tptp.plus_plus_nat A) (@ _let_1 C)) (@ (@ tptp.plus_plus_nat B2) (@ _let_1 D)))))))))
% 4.71/5.17 (assert (forall ((R2 tptp.int) (A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.times_times_int R2))) (=> (not (= R2 tptp.zero_zero_int)) (=> (and (= A B2) (not (= C D))) (not (= (@ (@ tptp.plus_plus_int A) (@ _let_1 C)) (@ (@ tptp.plus_plus_int B2) (@ _let_1 D)))))))))
% 4.71/5.17 (assert (forall ((R2 tptp.real) (A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.times_times_real R2))) (=> (not (= R2 tptp.zero_zero_real)) (=> (and (= A B2) (not (= C D))) (not (= (@ (@ tptp.plus_plus_real A) (@ _let_1 C)) (@ (@ tptp.plus_plus_real B2) (@ _let_1 D)))))))))
% 4.71/5.17 (assert (forall ((R2 tptp.complex) (A tptp.complex) (B2 tptp.complex) (C tptp.complex) (D tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex R2))) (=> (not (= R2 tptp.zero_zero_complex)) (=> (and (= A B2) (not (= C D))) (not (= (@ (@ tptp.plus_plus_complex A) (@ _let_1 C)) (@ (@ tptp.plus_plus_complex B2) (@ _let_1 D)))))))))
% 4.71/5.17 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 M2) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.times_times_nat M2) N2)))))))
% 4.71/5.17 (assert (forall ((M2 tptp.real) (N2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 M2) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.times_times_real M2) N2)))))))
% 4.71/5.17 (assert (forall ((M2 tptp.int) (N2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 M2) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.times_times_int M2) N2)))))))
% 4.71/5.17 (assert (forall ((Y tptp.complex) (Z3 tptp.complex) (X tptp.complex) (W2 tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z3 tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex X) Y) (@ (@ tptp.divide1717551699836669952omplex W2) Z3)) (= (@ (@ tptp.times_times_complex X) Z3) (@ (@ tptp.times_times_complex W2) Y)))))))
% 4.71/5.17 (assert (forall ((Y tptp.real) (Z3 tptp.real) (X tptp.real) (W2 tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z3 tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real X) Y) (@ (@ tptp.divide_divide_real W2) Z3)) (= (@ (@ tptp.times_times_real X) Z3) (@ (@ tptp.times_times_real W2) Y)))))))
% 4.71/5.17 (assert (forall ((B2 tptp.complex) (C tptp.complex) (A tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B2) C) A) (and (=> (not _let_1) (= B2 (@ (@ tptp.times_times_complex A) C))) (=> _let_1 (= A tptp.zero_zero_complex)))))))
% 4.71/5.17 (assert (forall ((B2 tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B2) C) A) (and (=> (not _let_1) (= B2 (@ (@ tptp.times_times_real A) C))) (=> _let_1 (= A tptp.zero_zero_real)))))))
% 4.71/5.17 (assert (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= A (@ (@ tptp.divide1717551699836669952omplex B2) C)) (and (=> (not _let_1) (= (@ (@ tptp.times_times_complex A) C) B2)) (=> _let_1 (= A tptp.zero_zero_complex)))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= A (@ (@ tptp.divide_divide_real B2) C)) (and (=> (not _let_1) (= (@ (@ tptp.times_times_real A) C) B2)) (=> _let_1 (= A tptp.zero_zero_real)))))))
% 4.71/5.17 (assert (forall ((C tptp.complex) (B2 tptp.complex) (A tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (=> (= B2 (@ (@ tptp.times_times_complex A) C)) (= (@ (@ tptp.divide1717551699836669952omplex B2) C) A)))))
% 4.71/5.17 (assert (forall ((C tptp.real) (B2 tptp.real) (A tptp.real)) (=> (not (= C tptp.zero_zero_real)) (=> (= B2 (@ (@ tptp.times_times_real A) C)) (= (@ (@ tptp.divide_divide_real B2) C) A)))))
% 4.71/5.17 (assert (forall ((C tptp.complex) (A tptp.complex) (B2 tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (=> (= (@ (@ tptp.times_times_complex A) C) B2) (= A (@ (@ tptp.divide1717551699836669952omplex B2) C))))))
% 4.71/5.17 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (not (= C tptp.zero_zero_real)) (=> (= (@ (@ tptp.times_times_real A) C) B2) (= A (@ (@ tptp.divide_divide_real B2) C))))))
% 4.71/5.17 (assert (forall ((C tptp.complex) (B2 tptp.complex) (A tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex B2) C) A) (= B2 (@ (@ tptp.times_times_complex A) C))))))
% 4.71/5.17 (assert (forall ((C tptp.real) (B2 tptp.real) (A tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real B2) C) A) (= B2 (@ (@ tptp.times_times_real A) C))))))
% 4.71/5.17 (assert (forall ((C tptp.complex) (A tptp.complex) (B2 tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (= A (@ (@ tptp.divide1717551699836669952omplex B2) C)) (= (@ (@ tptp.times_times_complex A) C) B2)))))
% 4.71/5.17 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (= A (@ (@ tptp.divide_divide_real B2) C)) (= (@ (@ tptp.times_times_real A) C) B2)))))
% 4.71/5.17 (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))))))
% 4.71/5.17 (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))))))
% 4.71/5.17 (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))))))
% 4.71/5.17 (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))))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8040749407984259932d_enat A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_7803423173614009249d_enat A) (@ _let_1 N2))))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (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)))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8040749407984259932d_enat A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_7803423173614009249d_enat (@ _let_1 N2)) A)))))
% 4.71/5.17 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M2)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M2) N2)))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N2)) (@ (@ tptp.times_times_nat (@ _let_1 M2)) (@ _let_1 N2))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N2)) (@ (@ tptp.times_times_int (@ _let_1 M2)) (@ _let_1 N2))))))
% 4.71/5.17 (assert (forall ((A tptp.real) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N2)) (@ (@ tptp.times_times_real (@ _let_1 M2)) (@ _let_1 N2))))))
% 4.71/5.17 (assert (forall ((A tptp.complex) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N2)) (@ (@ tptp.times_times_complex (@ _let_1 M2)) (@ _let_1 N2))))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8040749407984259932d_enat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N2)) (@ (@ tptp.times_7803423173614009249d_enat (@ _let_1 M2)) (@ _let_1 N2))))))
% 4.71/5.17 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat I) K)) (@ (@ tptp.times_times_nat J) K))))))
% 4.71/5.17 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat (@ _let_1 I)) (@ _let_1 J)))))))
% 4.71/5.17 (assert (= (@ tptp.vEBT_vebt_buildup tptp.zero_zero_nat) (@ (@ tptp.vEBT_Leaf false) false)))
% 4.71/5.17 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M2)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M2) N2)))))
% 4.71/5.17 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.suc M2)) N2) (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.times_times_nat M2) N2)))))
% 4.71/5.17 (assert (forall ((Uu Bool) (Uv Bool) (D tptp.nat)) (= (@ (@ tptp.vEBT_VEBT_valid (@ (@ tptp.vEBT_Leaf Uu) Uv)) D) (= D tptp.one_one_nat))))
% 4.71/5.17 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (= M2 (@ (@ tptp.times_times_nat M2) N2)) (or (= N2 tptp.one_one_nat) (= M2 tptp.zero_zero_nat)))))
% 4.71/5.17 (assert (forall ((M2 tptp.nat) (I tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.times_times_nat I) N2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M2) N2)) I))))
% 4.71/5.17 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M2) N2)) N2)) M2)))
% 4.71/5.17 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat N2) (@ (@ tptp.divide_divide_nat M2) N2))) M2)))
% 4.71/5.17 (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)))))))
% 4.71/5.17 (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)))))))
% 4.71/5.17 (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)))))))
% 4.71/5.17 (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)))))))
% 4.71/5.17 (assert (forall ((A tptp.extended_enat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_8040749407984259932d_enat A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N2))) (@ (@ tptp.times_7803423173614009249d_enat A) (@ (@ tptp.power_8040749407984259932d_enat (@ _let_2 N2)) _let_1)))))))
% 4.71/5.17 (assert (forall ((M2 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 M2)) (@ _let_1 N2))))))
% 4.71/5.17 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (not (= (@ _let_1 M2) (@ tptp.suc (@ _let_1 N2)))))))
% 4.71/5.17 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A4 Bool) (B4 Bool) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A4) B4)) X5)))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT) (Ux2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2)) Ux2)))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList3) S3)) X5)))))))))
% 4.71/5.17 (assert (forall ((A Bool) (B2 Bool)) (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_Leaf A) B2)) (@ tptp.suc tptp.zero_zero_nat))))
% 4.71/5.17 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.ord_less_eq_real C) D) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) D))))))))
% 4.71/5.17 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (=> (@ (@ tptp.ord_less_eq_nat C) D) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B2) D))))))))
% 4.71/5.17 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A) B2) (=> (@ (@ tptp.ord_less_eq_int C) D) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) D))))))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_real C) D) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) D))))))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ tptp.ord_less_nat C) D) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B2) D))))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (@ (@ tptp.ord_less_int C) D) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) D))))))))
% 4.71/5.18 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) C)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B2)))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B2) C)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat A) B2)))))
% 4.71/5.18 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) C)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) B2)))))
% 4.71/5.18 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B2))))))
% 4.71/5.18 (assert (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat A) B2))))))
% 4.71/5.18 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B2)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) B2))))))
% 4.71/5.18 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_real A) B2))))))
% 4.71/5.18 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_int A) B2))))))
% 4.71/5.18 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_real B2) A))))))
% 4.71/5.18 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_int B2) A))))))
% 4.71/5.18 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) C)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B2)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B2) A))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) C)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B2)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B2) A))))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.ord_less_real C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) D)))))))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat A) B2) (=> (@ (@ tptp.ord_less_nat C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B2) D)))))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int A) B2) (=> (@ (@ tptp.ord_less_int C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) D)))))))))
% 4.71/5.18 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) C)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B2)))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B2) C)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat A) B2)))))
% 4.71/5.18 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) C)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B2)))))
% 4.71/5.18 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B2)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B2)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B2) A)))))))
% 4.71/5.18 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B2)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B2)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B2) A)))))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.ord_less_real C) D) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) D))))))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (=> (@ (@ tptp.ord_less_nat C) D) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B2) D))))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A) B2) (=> (@ (@ tptp.ord_less_int C) D) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) D))))))))
% 4.71/5.18 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B2)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B2))))))
% 4.71/5.18 (assert (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B2)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat A) B2))))))
% 4.71/5.18 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B2))))))
% 4.71/5.18 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) C)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B2)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B2) A))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) C)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) B2)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B2) A))))))
% 4.71/5.18 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B2)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B2)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B2) A)))))))
% 4.71/5.18 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B2)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) B2)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B2) A)))))))
% 4.71/5.18 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Y) X)) X)))))))
% 4.71/5.18 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int Y) X)) X)))))))
% 4.71/5.18 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X) Y)) X)))))))
% 4.71/5.18 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X) Y)) X)))))))
% 4.71/5.18 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) tptp.one_on7984719198319812577d_enat) (=> (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) B2) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B2) tptp.one_on7984719198319812577d_enat) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.times_7803423173614009249d_enat A) B2)) tptp.one_on7984719198319812577d_enat))))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B2) (=> (@ (@ tptp.ord_less_eq_real B2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B2)) tptp.one_one_real))))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B2) (=> (@ (@ tptp.ord_less_eq_nat B2) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) B2)) tptp.one_one_nat))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_eq_int B2) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B2)) tptp.one_one_int))))))
% 4.71/5.18 (assert (forall ((C tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat C) tptp.one_on7984719198319812577d_enat) (=> (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) A) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.times_7803423173614009249d_enat A) C)) A)))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y))) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real)))))
% 4.71/5.18 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y))) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))))
% 4.71/5.18 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y)))))
% 4.71/5.18 (assert (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y)))))
% 4.71/5.18 (assert (forall ((X tptp.nat) (A Bool) (B2 Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A))) (let ((_let_2 (@ _let_1 B2))) (let ((_let_3 (@ (@ tptp.vEBT_vebt_insert _let_2) X))) (let ((_let_4 (= X tptp.one_one_nat))) (let ((_let_5 (= X tptp.zero_zero_nat))) (and (=> _let_5 (= _let_3 (@ (@ tptp.vEBT_Leaf true) B2))) (=> (not _let_5) (and (=> _let_4 (= _let_3 (@ _let_1 true))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 4.71/5.18 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y))) (or (not (= X tptp.zero_zero_real)) (not (= Y tptp.zero_zero_real))))))
% 4.71/5.18 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y))) (or (not (= X tptp.zero_zero_int)) (not (= Y tptp.zero_zero_int))))))
% 4.71/5.18 (assert (forall ((X tptp.real) (Y tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y))) tptp.zero_zero_real))))
% 4.71/5.18 (assert (forall ((X tptp.int) (Y tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y))) tptp.zero_zero_int))))
% 4.71/5.18 (assert (forall ((B2 tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ _let_1 C))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B2) C)) A) (and (=> _let_4 (@ (@ tptp.ord_less_real B2) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_real _let_3) B2)) (=> (not _let_2) (@ _let_1 A))))))))))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_1 (@ (@ tptp.divide_divide_real B2) C)) (and (=> _let_4 (@ (@ tptp.ord_less_real _let_3) B2)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_real B2) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_real))))))))))))
% 4.71/5.18 (assert (forall ((C tptp.real) (B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B2) C)) A) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) B2)))))
% 4.71/5.18 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.divide_divide_real B2) C)) (@ (@ tptp.ord_less_real B2) (@ (@ tptp.times_times_real A) C))))))
% 4.71/5.18 (assert (forall ((C tptp.real) (B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B2) C)) A) (@ (@ tptp.ord_less_real B2) (@ (@ tptp.times_times_real A) C))))))
% 4.71/5.18 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.divide_divide_real B2) C)) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) B2)))))
% 4.71/5.18 (assert (forall ((Y tptp.real) (X tptp.real) (Z3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.times_times_real Z3) Y)) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y)) Z3)))))
% 4.71/5.18 (assert (forall ((Y tptp.real) (Z3 tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real Z3) Y)) X) (@ (@ tptp.ord_less_real Z3) (@ (@ tptp.divide_divide_real X) Y))))))
% 4.71/5.18 (assert (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real B2) A) (=> (@ _let_2 C) (=> (@ _let_2 (@ (@ tptp.times_times_real A) B2)) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B2)))))))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B2)) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B2))))))))
% 4.71/5.18 (assert (= (@ tptp.vEBT_vebt_buildup (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.vEBT_Leaf false) false)))
% 4.71/5.18 (assert (forall ((B2 tptp.complex) (C tptp.complex) (W2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W2))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B2) C) _let_1) (and (=> (not _let_2) (= B2 (@ (@ tptp.times_times_complex _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))))
% 4.71/5.18 (assert (forall ((B2 tptp.real) (C tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B2) C) _let_1) (and (=> (not _let_2) (= B2 (@ (@ tptp.times_times_real _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))))
% 4.71/5.18 (assert (forall ((W2 tptp.num) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W2))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= _let_1 (@ (@ tptp.divide1717551699836669952omplex B2) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex _let_1) C) B2)) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))))
% 4.71/5.18 (assert (forall ((W2 tptp.num) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= _let_1 (@ (@ tptp.divide_divide_real B2) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real _let_1) C) B2)) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))))
% 4.71/5.18 (assert (forall ((A Bool) (B2 Bool) (X tptp.nat)) (let ((_let_1 (= X tptp.one_one_nat))) (let ((_let_2 (= X tptp.zero_zero_nat))) (= (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.vEBT_Leaf A) B2)) X) (and (=> _let_2 A) (=> (not _let_2) (and (=> _let_1 B2) _let_1))))))))
% 4.71/5.18 (assert (forall ((Z3 tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z3 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X) Z3)) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.times_times_complex Y) Z3))) Z3)))))
% 4.71/5.18 (assert (forall ((Z3 tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z3 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X) Z3)) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real Y) Z3))) Z3)))))
% 4.71/5.18 (assert (forall ((Z3 tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z3 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.divide1717551699836669952omplex Y) Z3)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex X) Z3)) Y)) Z3)))))
% 4.71/5.18 (assert (forall ((Z3 tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z3 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real X) (@ (@ tptp.divide_divide_real Y) Z3)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) Z3)) Y)) Z3)))))
% 4.71/5.18 (assert (forall ((Y tptp.complex) (Z3 tptp.complex) (X tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex Z3) (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.times_times_complex Z3) Y))) Y)))))
% 4.71/5.18 (assert (forall ((Y tptp.real) (Z3 tptp.real) (X tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real Z3) (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real Z3) Y))) Y)))))
% 4.71/5.18 (assert (forall ((Y tptp.complex) (X tptp.complex) (Z3 tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X) Y)) Z3) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.times_times_complex Z3) Y))) Y)))))
% 4.71/5.18 (assert (forall ((Y tptp.real) (X tptp.real) (Z3 tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X) Y)) Z3) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real Z3) Y))) Y)))))
% 4.71/5.18 (assert (forall ((Y tptp.complex) (Z3 tptp.complex) (X tptp.complex) (W2 tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z3 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide1717551699836669952omplex W2) Z3)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex X) Z3)) (@ (@ tptp.times_times_complex W2) Y))) (@ (@ tptp.times_times_complex Y) Z3)))))))
% 4.71/5.18 (assert (forall ((Y tptp.real) (Z3 tptp.real) (X tptp.real) (W2 tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z3 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real W2) Z3)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) Z3)) (@ (@ tptp.times_times_real W2) Y))) (@ (@ tptp.times_times_real Y) Z3)))))))
% 4.71/5.18 (assert (forall ((Z3 tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.divide1717551699836669952omplex B2) Z3)))) (let ((_let_2 (= Z3 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) Z3)) B2)) Z3))))))))
% 4.71/5.18 (assert (forall ((Z3 tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real A) (@ (@ tptp.divide_divide_real B2) Z3)))) (let ((_let_2 (= Z3 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) Z3)) B2)) Z3))))))))
% 4.71/5.18 (assert (forall ((Z3 tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex A) Z3)) B2))) (let ((_let_2 (= Z3 tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 B2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.times_times_complex B2) Z3))) Z3))))))))
% 4.71/5.18 (assert (forall ((Z3 tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real A) Z3)) B2))) (let ((_let_2 (= Z3 tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 B2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) (@ (@ tptp.times_times_real B2) Z3))) Z3))))))))
% 4.71/5.18 (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)))))))
% 4.71/5.18 (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)))))))
% 4.71/5.18 (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)))))))
% 4.71/5.18 (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))))))
% 4.71/5.18 (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))))))
% 4.71/5.18 (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))))))
% 4.71/5.18 (assert (forall ((A Bool) (B2 Bool) (X tptp.nat)) (let ((_let_1 (= X tptp.one_one_nat))) (let ((_let_2 (= X tptp.zero_zero_nat))) (= (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.vEBT_Leaf A) B2)) X) (and (=> _let_2 A) (=> (not _let_2) (and (=> _let_1 B2) _let_1))))))))
% 4.71/5.18 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)))) (=> (@ _let_1 N2) (=> (@ _let_1 M2) (@ _let_1 (@ (@ tptp.times_times_nat M2) N2)))))))
% 4.71/5.18 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M2) (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat M2) N2))))))
% 4.71/5.18 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M2) (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat N2) M2))))))
% 4.71/5.18 (assert (forall ((X tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull X)) (=> (forall ((Uv2 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf true) Uv2)))) (=> (forall ((Uu2 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf Uu2) true)))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc2))))))))))
% 4.71/5.18 (assert (forall ((Q3 tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q3) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M2) Q3)) N2) (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.times_times_nat N2) Q3))))))
% 4.71/5.18 (assert (forall ((X tptp.vEBT_VEBT)) (=> (@ tptp.vEBT_VEBT_minNull X) (=> (not (= X (@ (@ tptp.vEBT_Leaf false) false))) (not (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2)))))))))
% 4.71/5.18 (assert (forall ((A tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (exists ((R3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (= (@ (@ tptp.power_power_real R3) (@ tptp.suc N2)) A))))))
% 4.71/5.18 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (forall ((Z tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (=> (@ (@ tptp.ord_less_real Z) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Z) X)) Y)))) (@ (@ tptp.ord_less_eq_real X) Y))))
% 4.71/5.18 (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))))))
% 4.71/5.18 (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))))))
% 4.71/5.18 (assert (forall ((C tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real C) (@ (@ tptp.times_times_real B2) C)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real tptp.one_one_real) B2)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B2) tptp.one_one_real))))))
% 4.71/5.18 (assert (forall ((C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int C) (@ (@ tptp.times_times_int B2) C)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int tptp.one_one_int) B2)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B2) tptp.one_one_int))))))
% 4.71/5.18 (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))))))
% 4.71/5.18 (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))))))
% 4.71/5.18 (assert (forall ((C tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real C) (@ (@ tptp.times_times_real C) B2)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real tptp.one_one_real) B2)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B2) tptp.one_one_real))))))
% 4.71/5.18 (assert (forall ((C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int C) (@ (@ tptp.times_times_int C) B2)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int tptp.one_one_int) B2)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B2) tptp.one_one_int))))))
% 4.71/5.18 (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))))))
% 4.71/5.18 (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))))))
% 4.71/5.18 (assert (forall ((C tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real C) (@ (@ tptp.times_times_real B2) C)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) B2)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B2) tptp.one_one_real))))))
% 4.71/5.18 (assert (forall ((C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.times_times_int B2) C)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) B2)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B2) tptp.one_one_int))))))
% 4.71/5.18 (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))))))
% 4.71/5.18 (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))))))
% 4.71/5.18 (assert (forall ((C tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real C) (@ (@ tptp.times_times_real C) B2)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) B2)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B2) tptp.one_one_real))))))
% 4.71/5.18 (assert (forall ((C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.times_times_int C) B2)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) B2)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B2) tptp.one_one_int))))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B2)) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B2))))))))
% 4.71/5.18 (assert (forall ((Y tptp.real) (Z3 tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Z3) Y)) X) (@ (@ tptp.ord_less_eq_real Z3) (@ (@ tptp.divide_divide_real X) Y))))))
% 4.71/5.18 (assert (forall ((Y tptp.real) (X tptp.real) (Z3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.times_times_real Z3) Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) Z3)))))
% 4.71/5.18 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.divide_divide_real B2) C)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) B2)))))
% 4.71/5.18 (assert (forall ((C tptp.real) (B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B2) C)) A) (@ (@ tptp.ord_less_eq_real B2) (@ (@ tptp.times_times_real A) C))))))
% 4.71/5.18 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.divide_divide_real B2) C)) (@ (@ tptp.ord_less_eq_real B2) (@ (@ tptp.times_times_real A) C))))))
% 4.71/5.18 (assert (forall ((C tptp.real) (B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B2) C)) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) B2)))))
% 4.71/5.18 (assert (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (=> (@ (@ tptp.ord_less_eq_real B2) A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B2)) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B2))))))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_1 (@ (@ tptp.divide_divide_real B2) C)) (and (=> _let_4 (@ (@ tptp.ord_less_eq_real _let_3) B2)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_real B2) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_real))))))))))))
% 4.71/5.18 (assert (forall ((B2 tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.times_times_real A) C))) (let ((_let_3 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B2) C)) A) (and (=> _let_3 (@ (@ tptp.ord_less_eq_real B2) _let_2)) (=> (not _let_3) (and (=> _let_1 (@ (@ tptp.ord_less_eq_real _let_2) B2)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A)))))))))))
% 4.71/5.18 (assert (forall ((X tptp.real) (A tptp.real) (Y tptp.real) (U tptp.real) (V tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real X) A) (=> (@ (@ tptp.ord_less_eq_real Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_real U) V) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real U) X)) (@ (@ tptp.times_times_real V) Y))) A)))))))))
% 4.71/5.18 (assert (forall ((X tptp.int) (A tptp.int) (Y tptp.int) (U tptp.int) (V tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int X) A) (=> (@ (@ tptp.ord_less_eq_int Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_int U) V) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U) X)) (@ (@ tptp.times_times_int V) Y))) A)))))))))
% 4.71/5.18 (assert (forall ((B2 tptp.real) (C tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ _let_2 C))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B2) C)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_real B2) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real _let_4) B2)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))))
% 4.71/5.18 (assert (forall ((W2 tptp.num) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (let ((_let_2 (@ tptp.ord_less_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B2) C)) (and (=> _let_5 (@ (@ tptp.ord_less_real _let_4) B2)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real B2) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))))
% 4.71/5.18 (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))))))
% 4.71/5.18 (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))))))
% 4.71/5.18 (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))))))
% 4.71/5.18 (assert (forall ((Z3 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) Z3) (@ (@ tptp.plus_plus_complex Z3) Z3))))
% 4.71/5.18 (assert (forall ((Z3 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z3) (@ (@ tptp.plus_plus_nat Z3) Z3))))
% 4.71/5.18 (assert (forall ((Z3 tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))) Z3) (@ (@ tptp.plus_p3455044024723400733d_enat Z3) Z3))))
% 4.71/5.18 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Z3) (@ (@ tptp.plus_plus_int Z3) Z3))))
% 4.71/5.18 (assert (forall ((Z3 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) Z3) (@ (@ tptp.plus_plus_real Z3) Z3))))
% 4.71/5.18 (assert (forall ((Z3 tptp.complex)) (= (@ (@ tptp.times_times_complex Z3) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_complex Z3) Z3))))
% 4.71/5.18 (assert (forall ((Z3 tptp.nat)) (= (@ (@ tptp.times_times_nat Z3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_nat Z3) Z3))))
% 4.71/5.18 (assert (forall ((Z3 tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat Z3) (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_p3455044024723400733d_enat Z3) Z3))))
% 4.71/5.18 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.times_times_int Z3) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_int Z3) Z3))))
% 4.71/5.18 (assert (forall ((Z3 tptp.real)) (= (@ (@ tptp.times_times_real Z3) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real Z3) Z3))))
% 4.71/5.18 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex A))) (= (@ _let_1 (@ _let_1 B2)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) A)) B2)))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ _let_1 (@ _let_1 B2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)) B2)))))
% 4.71/5.18 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat A))) (= (@ _let_1 (@ _let_1 B2)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))) A)) B2)))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ _let_1 (@ _let_1 B2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)) B2)))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ _let_1 (@ _let_1 B2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) A)) B2)))))
% 4.71/5.18 (assert (forall ((N2 tptp.nat) (Q3 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 Q3)) M2) (=> (@ (@ tptp.ord_less_nat M2) (@ _let_1 (@ tptp.suc Q3))) (= (@ (@ tptp.divide_divide_nat M2) N2) Q3))))))
% 4.71/5.18 (assert (forall ((Q3 tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q3) (= (@ (@ tptp.ord_less_eq_nat M2) (@ (@ tptp.divide_divide_nat N2) Q3)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M2) Q3)) N2)))))
% 4.71/5.18 (assert (forall ((P (-> tptp.nat Bool)) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (= N2 tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.divide_divide_nat M2) N2)) (and (=> _let_1 (@ P tptp.zero_zero_nat)) (=> (not _let_1) (forall ((I3 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J2) N2) (=> (= M2 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N2) I3)) J2)) (@ P I3))))))))))
% 4.71/5.18 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M2) N2)) N2))))))
% 4.71/5.18 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.times_times_nat N2) (@ (@ tptp.divide_divide_nat M2) N2)))))))
% 4.71/5.18 (assert (forall ((X tptp.vEBT_VEBT) (Y Bool)) (let ((_let_1 (not Y))) (=> (= (@ tptp.vEBT_VEBT_minNull X) Y) (=> (=> (= X (@ (@ tptp.vEBT_Leaf false) false)) _let_1) (=> (=> (exists ((Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf true) Uv2))) Y) (=> (=> (exists ((Uu2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) true))) Y) (=> (=> (exists ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2))) _let_1) (not (=> (exists ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc2))) Y))))))))))
% 4.71/5.18 (assert (forall ((X tptp.real) (A tptp.real) (Y tptp.real) (U tptp.real) (V tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real X) A) (=> (@ (@ tptp.ord_less_real Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_real U) V) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real U) X)) (@ (@ tptp.times_times_real V) Y))) A)))))))))
% 4.71/5.18 (assert (forall ((X tptp.int) (A tptp.int) (Y tptp.int) (U tptp.int) (V tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int X) A) (=> (@ (@ tptp.ord_less_int Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_int U) V) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U) X)) (@ (@ tptp.times_times_int V) Y))) A)))))))))
% 4.71/5.18 (assert (forall ((B2 tptp.real) (C tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B2) C)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_real B2) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_real _let_3) B2)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1))))))))))))
% 4.71/5.18 (assert (forall ((W2 tptp.num) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (let ((_let_2 (@ tptp.ord_less_eq_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B2) C)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_real _let_4) B2)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_real B2) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))))
% 4.71/5.18 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X)) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y) _let_2)))))))
% 4.71/5.18 (assert (forall ((P (-> tptp.nat Bool)) (M2 tptp.nat) (N2 tptp.nat)) (= (@ P (@ (@ tptp.divide_divide_nat M2) 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)) M2) (@ (@ tptp.ord_less_nat M2) (@ _let_1 (@ tptp.suc Q5))) (@ P Q5))))))))
% 4.71/5.18 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A4 Bool) (B4 Bool) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A4) B4)) X5)))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2)) X5)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2)) X5)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2)) X5)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList3) Summary2)) X5)))))))))))
% 4.71/5.18 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A4 Bool) (B4 Bool) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A4) B4)) X5)))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts2) S3)) X5)))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S3)) X5)))) (=> (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc (@ tptp.suc V2))) TreeList3) Summary2)) X5)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList3) Summary2)) X5)))))))))))
% 4.71/5.18 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (Uv2 Bool) (Uw2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) Uv2)) Uw2)))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT) (Uz2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2)) Uz2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2)) X5)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList3) Vc2)) X5)))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList3) Vd)) X5)))))))))))
% 4.71/5.18 (assert (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex X) Y)) _let_2) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex X) _let_2)) (@ (@ tptp.power_power_complex Y) _let_2))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X)) Y)))))))
% 4.71/5.18 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat X) Y)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat X) _let_1)) (@ (@ tptp.power_power_nat Y) _let_1))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat _let_1) X)) Y))))))
% 4.71/5.18 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_8040749407984259932d_enat (@ (@ tptp.plus_p3455044024723400733d_enat X) Y)) _let_2) (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.power_8040749407984259932d_enat X) _let_2)) (@ (@ tptp.power_8040749407984259932d_enat Y) _let_2))) (@ (@ tptp.times_7803423173614009249d_enat (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat _let_1)) X)) Y)))))))
% 4.71/5.18 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int X) Y)) _let_2) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_2)) (@ (@ tptp.power_power_int Y) _let_2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int _let_1)) X)) Y)))))))
% 4.71/5.18 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X) Y)) _let_2) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X)) Y)))))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (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))))))
% 4.71/5.18 (assert (forall ((U tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (= (@ (@ tptp.power_power_real U) (@ tptp.numeral_numeral_nat _let_1)) (@ (@ tptp.times_times_real X) Y)) (=> (@ _let_2 X) (=> (@ _let_2 Y) (@ (@ tptp.ord_less_eq_real U) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) Y)) (@ tptp.numeral_numeral_real _let_1))))))))))
% 4.71/5.18 (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))))))
% 4.71/5.18 (assert (forall ((N2 tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (exists ((R3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (= (@ (@ tptp.power_power_real R3) N2) A)))))))
% 4.71/5.18 (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 ((Y6 tptp.real)) (=> (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y6) (= (@ (@ tptp.power_power_real Y6) N2) A)) (= Y6 X5)))))))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (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))))
% 4.71/5.18 (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))))
% 4.71/5.18 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M2)) (@ _let_1 N2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_eq_nat M2) N2))))))
% 4.71/5.18 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 M2)) (@ _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 M2) N2)))))))))
% 4.71/5.18 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M2)) (@ _let_1 N2)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat M2) N2))))))
% 4.71/5.18 (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)))))))
% 4.71/5.18 (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)))))))
% 4.71/5.18 (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))))))
% 4.71/5.18 (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))))))
% 4.71/5.18 (assert (forall ((K tptp.nat) (M2 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 M2)) (@ _let_1 N2)) (@ (@ tptp.divide_divide_nat M2) N2))))))
% 4.71/5.18 (assert (forall ((K tptp.nat) (M2 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 M2)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M2) N2))))))
% 4.71/5.18 (assert (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (= (@ _let_1 (@ (@ tptp.times_times_nat B2) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B2)) C))))))
% 4.71/5.18 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (= (@ _let_1 (@ (@ tptp.times_times_int B2) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B2)) C))))))
% 4.71/5.18 (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))))
% 4.71/5.18 (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))))
% 4.71/5.18 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (= (@ _let_1 M2) (@ _let_1 N2)) (or (= K tptp.zero_zero_nat) (= M2 N2))))))
% 4.71/5.18 (assert (forall ((I tptp.nat) (U tptp.nat) (J tptp.nat) (K tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) K)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat I) J)) U)) K))))
% 4.71/5.18 (assert (forall ((K tptp.nat) (M2 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 M2)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M2) N2))))))
% 4.71/5.18 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ _let_1 M2) (@ _let_1 N2)) (= M2 N2))))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) B2) (= (@ (@ tptp.divide_divide_nat A) B2) tptp.zero_zero_nat)))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) B2) (= (@ (@ tptp.divide_divide_int A) B2) tptp.zero_zero_int)))))
% 4.71/5.18 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_nat B2) A) (@ _let_1 (@ (@ tptp.divide_divide_nat A) B2)))))))
% 4.71/5.18 (assert (forall ((B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_int B2) A) (@ _let_1 (@ (@ tptp.divide_divide_int A) B2)))))))
% 4.71/5.18 (assert (forall ((Z3 tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z3) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X) Z3)) (@ (@ tptp.times_times_real Y) Z3)) (@ (@ tptp.ord_less_eq_real X) Y)))))
% 4.71/5.18 (assert (forall ((Z3 tptp.int) (X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z3) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X) Z3)) (@ (@ tptp.times_times_int Y) Z3)) (@ (@ tptp.ord_less_eq_int X) Y)))))
% 4.71/5.18 (assert (forall ((Z3 tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.times_times_real Z3))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z3) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_real X) Y))))))
% 4.71/5.18 (assert (forall ((Z3 tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.times_times_int Z3))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z3) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_int X) Y))))))
% 4.71/5.18 (assert (forall ((Q3 tptp.nat) (R2 tptp.nat)) (= (@ tptp.unique6322359934112328802ux_nat (@ (@ tptp.product_Pair_nat_nat Q3) R2)) (= R2 tptp.zero_zero_nat))))
% 4.71/5.18 (assert (forall ((Q3 tptp.int) (R2 tptp.int)) (= (@ tptp.unique6319869463603278526ux_int (@ (@ tptp.product_Pair_int_int Q3) R2)) (= R2 tptp.zero_zero_int))))
% 4.71/5.18 (assert (= tptp.vEBT_VEBT_low (lambda ((X4 tptp.nat) (N tptp.nat)) (@ (@ tptp.modulo_modulo_nat X4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 4.71/5.18 (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))))))))
% 4.71/5.18 (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))))))))
% 4.71/5.18 (assert (forall ((N2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.member_nat (@ tptp.suc N2)) (@ tptp.nat_set_decode X)) (@ (@ tptp.member_nat N2) (@ tptp.nat_set_decode (@ (@ tptp.divide_divide_nat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 4.71/5.18 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_insert X) Xa2) Y) (=> (forall ((A4 Bool) (B4 Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A4))) (let ((_let_2 (@ _let_1 B4))) (let ((_let_3 (= Xa2 tptp.one_one_nat))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_2) (not (and (=> _let_4 (= Y (@ (@ tptp.vEBT_Leaf true) B4))) (=> (not _let_4) (and (=> _let_3 (= Y (@ _let_1 true))) (=> (not _let_3) (= Y _let_2)))))))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts2) S3))) (=> (= X _let_1) (not (= Y _let_1))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S3))) (=> (= X _let_1) (not (= Y _let_1))))) (=> (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc V2)))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Summary2)) (not (= Y (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Xa2) Xa2))) _let_1) TreeList3) Summary2)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_5 (@ (@ _let_4 Mi2) Xa2))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_6))) (=> (= X _let_2) (not (= Y (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_4 Xa2) Mi2)) (@ (@ tptp.ord_max_nat _let_5) Ma2)))) _let_1) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList3) _let_6) (@ (@ tptp.vEBT_vebt_insert _let_7) (@ (@ tptp.vEBT_VEBT_low _let_5) _let_3)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_7)) (@ (@ tptp.vEBT_vebt_insert Summary2) _let_6)) Summary2))) _let_2))))))))))))))))))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_VEBT_VEBT)) (= (@ tptp.size_s6639371672096860321T_VEBT (@ (@ tptp.produc662631939642741121T_VEBT Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_int Xs)) (@ tptp.size_s6755466524823107622T_VEBT Ys)))))
% 4.71/5.18 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int)) (= (@ tptp.size_s5157815400016825771nt_int (@ (@ tptp.product_int_int Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_int Xs)) (@ tptp.size_size_list_int Ys)))))
% 4.71/5.18 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_nat)) (= (@ tptp.size_s7647898544948552527nt_nat (@ (@ tptp.product_int_nat Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_int Xs)) (@ tptp.size_size_list_nat Ys)))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_int)) (= (@ tptp.size_s2970893825323803983at_int (@ (@ tptp.product_nat_int Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs)) (@ tptp.size_size_list_int Ys)))))
% 4.71/5.18 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (= (@ tptp.size_s5460976970255530739at_nat (@ (@ tptp.product_nat_nat Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs)) (@ tptp.size_size_list_nat Ys)))))
% 4.71/5.18 (assert (forall ((Z3 tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z3) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real X) Z3)) (@ (@ tptp.times_times_real Y) Z3)) (@ (@ tptp.ord_less_real X) Y)))))
% 4.71/5.18 (assert (forall ((Z3 tptp.int) (X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z3) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int X) Z3)) (@ (@ tptp.times_times_int Y) Z3)) (@ (@ tptp.ord_less_int X) Y)))))
% 4.71/5.18 (assert (= tptp.vEBT_VEBT_set_vebt (lambda ((T2 tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_vebt_member T2)))))
% 4.71/5.18 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat M2) tptp.one_one_nat) (= M2 tptp.one_one_nat))))
% 4.71/5.18 (assert (forall ((P (-> tptp.real Bool)) (Q (-> tptp.real Bool))) (= (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((X4 tptp.real)) (or (@ P X4) (@ Q X4))))) (and (@ tptp.finite_finite_real (@ tptp.collect_real P)) (@ tptp.finite_finite_real (@ tptp.collect_real Q))))))
% 4.71/5.18 (assert (forall ((P (-> tptp.list_nat Bool)) (Q (-> tptp.list_nat Bool))) (= (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (or (@ P X4) (@ Q X4))))) (and (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat P)) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat Q))))))
% 4.71/5.18 (assert (forall ((P (-> tptp.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (= (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (or (@ P X4) (@ Q X4))))) (and (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat P)) (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat Q))))))
% 4.71/5.18 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (= (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (or (@ P X4) (@ Q X4))))) (and (@ tptp.finite_finite_nat (@ tptp.collect_nat P)) (@ tptp.finite_finite_nat (@ tptp.collect_nat Q))))))
% 4.71/5.18 (assert (forall ((P (-> tptp.complex Bool)) (Q (-> tptp.complex Bool))) (= (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (or (@ P X4) (@ Q X4))))) (and (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex P)) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex Q))))))
% 4.71/5.18 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (= (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((X4 tptp.int)) (or (@ P X4) (@ Q X4))))) (and (@ tptp.finite_finite_int (@ tptp.collect_int P)) (@ tptp.finite_finite_int (@ tptp.collect_int Q))))))
% 4.71/5.18 (assert (forall ((P (-> tptp.extended_enat Bool)) (Q (-> tptp.extended_enat Bool))) (= (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (or (@ P X4) (@ Q X4))))) (and (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat P)) (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat Q))))))
% 4.71/5.18 (assert (forall ((P (-> tptp.real Bool)) (Q (-> tptp.real Bool))) (=> (or (@ tptp.finite_finite_real (@ tptp.collect_real P)) (@ tptp.finite_finite_real (@ tptp.collect_real Q))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((X4 tptp.real)) (and (@ P X4) (@ Q X4))))))))
% 4.71/5.18 (assert (forall ((P (-> tptp.list_nat Bool)) (Q (-> tptp.list_nat Bool))) (=> (or (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat P)) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat Q))) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (and (@ P X4) (@ Q X4))))))))
% 4.71/5.18 (assert (forall ((P (-> tptp.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (=> (or (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat P)) (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat Q))) (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (and (@ P X4) (@ Q X4))))))))
% 4.71/5.18 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (or (@ tptp.finite_finite_nat (@ tptp.collect_nat P)) (@ tptp.finite_finite_nat (@ tptp.collect_nat Q))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ P X4) (@ Q X4))))))))
% 4.71/5.18 (assert (forall ((P (-> tptp.complex Bool)) (Q (-> tptp.complex Bool))) (=> (or (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex P)) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex Q))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (and (@ P X4) (@ Q X4))))))))
% 4.71/5.18 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (or (@ tptp.finite_finite_int (@ tptp.collect_int P)) (@ tptp.finite_finite_int (@ tptp.collect_int Q))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ P X4) (@ Q X4))))))))
% 4.71/5.18 (assert (forall ((P (-> tptp.extended_enat Bool)) (Q (-> tptp.extended_enat Bool))) (=> (or (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat P)) (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat Q))) (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (and (@ P X4) (@ Q X4))))))))
% 4.71/5.18 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))))
% 4.71/5.18 (assert (forall ((A tptp.real)) (= (@ (@ tptp.dvd_dvd_real tptp.zero_zero_real) A) (= A tptp.zero_zero_real))))
% 4.71/5.18 (assert (forall ((A tptp.int)) (= (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) A) (= A tptp.zero_zero_int))))
% 4.71/5.18 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.dvd_dvd_complex tptp.zero_zero_complex) A) (= A tptp.zero_zero_complex))))
% 4.71/5.18 (assert (forall ((A tptp.extended_enat)) (= (@ (@ tptp.dvd_dv3785147216227455552d_enat tptp.zero_z5237406670263579293d_enat) A) (= A tptp.zero_z5237406670263579293d_enat))))
% 4.71/5.18 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) tptp.zero_zero_nat)))
% 4.71/5.18 (assert (forall ((A tptp.real)) (@ (@ tptp.dvd_dvd_real A) tptp.zero_zero_real)))
% 4.71/5.18 (assert (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int A) tptp.zero_zero_int)))
% 4.71/5.18 (assert (forall ((A tptp.complex)) (@ (@ tptp.dvd_dvd_complex A) tptp.zero_zero_complex)))
% 4.71/5.18 (assert (forall ((A tptp.extended_enat)) (@ (@ tptp.dvd_dv3785147216227455552d_enat A) tptp.zero_z5237406670263579293d_enat)))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B2) A)) (@ _let_1 B2)))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B2) A)) (@ _let_1 B2)))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B2) A)) (@ _let_1 B2)))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat A) B2)) (@ _let_1 B2)))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) B2)) (@ _let_1 B2)))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real A) B2)) (@ _let_1 B2)))))
% 4.71/5.18 (assert (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.dvd_dvd_nat M2) _let_1) (= M2 _let_1)))))
% 4.71/5.18 (assert (forall ((K tptp.nat)) (@ (@ tptp.dvd_dvd_nat (@ tptp.suc tptp.zero_zero_nat)) K)))
% 4.71/5.18 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) A) tptp.zero_zero_nat)))
% 4.71/5.18 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) A) tptp.zero_zero_int)))
% 4.71/5.18 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.zero_zero_nat) A)))
% 4.71/5.18 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.zero_zero_int) A)))
% 4.71/5.18 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 4.71/5.18 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 4.71/5.18 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 4.71/5.18 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B2) (=> (@ _let_1 C) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat B2) A)) (@ (@ tptp.divide_divide_nat C) A)) (@ (@ tptp.dvd_dvd_nat B2) C)))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B2) (=> (@ _let_1 C) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int B2) A)) (@ (@ tptp.divide_divide_int C) A)) (@ (@ tptp.dvd_dvd_int B2) C)))))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B2)) B2) (@ (@ tptp.modulo_modulo_nat A) B2))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B2)) B2) (@ (@ tptp.modulo_modulo_int A) B2))))
% 4.71/5.18 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat B2) A)) B2) (@ (@ tptp.modulo_modulo_nat A) B2))))
% 4.71/5.18 (assert (forall ((B2 tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int B2) A)) B2) (@ (@ tptp.modulo_modulo_int A) B2))))
% 4.71/5.18 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M2)) (@ _let_1 N2)) (or (= K tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat M2) N2))))))
% 4.71/5.18 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N2) (= (@ (@ tptp.modulo_modulo_nat M2) N2) M2))))
% 4.71/5.18 (assert (forall ((A2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A2) (@ tptp.finite6551019134538273531omplex (@ tptp.collect_set_complex (lambda ((B5 tptp.set_complex)) (@ (@ tptp.ord_le211207098394363844omplex B5) A2)))))))
% 4.71/5.18 (assert (forall ((A2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (@ tptp.finite5468666774076196335d_enat (@ tptp.collec2260605976452661553d_enat (lambda ((B5 tptp.set_Extended_enat)) (@ (@ tptp.ord_le7203529160286727270d_enat B5) A2)))))))
% 4.71/5.18 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat (lambda ((B5 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat B5) A2)))))))
% 4.71/5.18 (assert (forall ((A2 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (@ tptp.finite6197958912794628473et_int (@ tptp.collect_set_int (lambda ((B5 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int B5) A2)))))))
% 4.71/5.18 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) K))))))
% 4.71/5.18 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) K))))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat B2) A)) (@ (@ tptp.times_times_nat C) A)) (@ (@ tptp.dvd_dvd_nat B2) C)))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int B2) A)) (@ (@ tptp.times_times_int C) A)) (@ (@ tptp.dvd_dvd_int B2) C)))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 B2)) (@ _let_1 C)) (@ (@ tptp.dvd_dvd_nat B2) C))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 B2)) (@ _let_1 C)) (@ (@ tptp.dvd_dvd_int B2) C))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) C)) (or (= C tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int A) B2)))))
% 4.71/5.18 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) C)) (or (= C tptp.zero_zero_real) (@ (@ tptp.dvd_dvd_real A) B2)))))
% 4.71/5.18 (assert (forall ((A tptp.complex) (C tptp.complex) (B2 tptp.complex)) (= (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B2) C)) (or (= C tptp.zero_zero_complex) (@ (@ tptp.dvd_dvd_complex A) B2)))))
% 4.71/5.18 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 A)) (@ _let_1 B2)) (or (= C tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int A) B2))))))
% 4.71/5.18 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (@ (@ tptp.dvd_dvd_real (@ _let_1 A)) (@ _let_1 B2)) (or (= C tptp.zero_zero_real) (@ (@ tptp.dvd_dvd_real A) B2))))))
% 4.71/5.18 (assert (forall ((C tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C))) (= (@ (@ tptp.dvd_dvd_complex (@ _let_1 A)) (@ _let_1 B2)) (or (= C tptp.zero_zero_complex) (@ (@ tptp.dvd_dvd_complex A) B2))))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B2)) tptp.one_one_nat)))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B2)) tptp.one_one_int)))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B2) (@ (@ tptp.times_times_nat C) A))) (@ _let_1 B2)))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B2) (@ (@ tptp.times_times_int C) A))) (@ _let_1 B2)))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B2) (@ (@ tptp.times_times_real C) A))) (@ _let_1 B2)))))
% 4.71/5.18 (assert (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B2) (@ (@ tptp.times_times_complex C) A))) (@ _let_1 B2)))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C) A)) B2)) (@ _let_1 B2)))))
% 4.71/5.18 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C) A)) B2)) (@ _let_1 B2)))))
% 4.71/5.18 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real C) A)) B2)) (@ _let_1 B2)))))
% 4.71/5.18 (assert (forall ((A tptp.complex) (C tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex C) A)) B2)) (@ _let_1 B2)))))
% 4.71/5.18 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat B2) A)) B2) tptp.zero_zero_nat)))
% 4.71/5.18 (assert (forall ((B2 tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int B2) A)) B2) tptp.zero_zero_int)))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B2)) B2) tptp.zero_zero_nat)))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B2)) B2) tptp.zero_zero_int)))
% 4.71/5.18 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)))
% 4.71/5.18 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.one_one_int) tptp.zero_zero_int)))
% 4.71/5.18 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)))
% 4.71/5.18 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.one_one_int) tptp.zero_zero_int)))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B2) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat B2) A)) A) B2))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B2) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int B2) A)) A) B2))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B2) (= (@ (@ tptp.times_times_nat A) (@ (@ tptp.divide_divide_nat B2) A)) B2))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B2) (= (@ (@ tptp.times_times_int A) (@ (@ tptp.divide_divide_int B2) A)) B2))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat A) B2)) tptp.one_one_nat)))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int A) B2)) tptp.one_one_int)))))
% 4.71/5.18 (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))))
% 4.71/5.18 (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))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (assert (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B2)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) C)) (@ (@ tptp.divide_divide_nat B2) C))))))))
% 4.71/5.18 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B2)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B2) C))))))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) B2)) B2) tptp.zero_zero_nat)))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) B2)) B2) tptp.zero_zero_int)))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) B2)) B2) tptp.zero_zero_nat)))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) B2)) B2) tptp.zero_zero_int)))
% 4.71/5.18 (assert (forall ((B2 tptp.nat) (C tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B2) C)) A)) B2) (@ (@ tptp.modulo_modulo_nat A) B2))))
% 4.71/5.18 (assert (forall ((B2 tptp.int) (C tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) C)) A)) B2) (@ (@ tptp.modulo_modulo_int A) B2))))
% 4.71/5.18 (assert (forall ((C tptp.nat) (B2 tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C) B2)) A)) B2) (@ (@ tptp.modulo_modulo_nat A) B2))))
% 4.71/5.18 (assert (forall ((C tptp.int) (B2 tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C) B2)) A)) B2) (@ (@ tptp.modulo_modulo_int A) B2))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat B2) C))) B2) (@ (@ tptp.modulo_modulo_nat A) B2))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int B2) C))) B2) (@ (@ tptp.modulo_modulo_int A) B2))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat C) B2))) B2) (@ (@ tptp.modulo_modulo_nat A) B2))))
% 4.71/5.18 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int C) B2))) B2) (@ (@ tptp.modulo_modulo_int A) B2))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B2) (= (@ (@ tptp.modulo_modulo_nat B2) A) tptp.zero_zero_nat))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B2) (= (@ (@ tptp.modulo_modulo_int B2) A) tptp.zero_zero_int))))
% 4.71/5.18 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat M2) (@ tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)))
% 4.71/5.18 (assert (= (@ tptp.nat_set_decode tptp.zero_zero_nat) tptp.bot_bot_set_nat))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat B2) A)) A) B2))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int B2) A)) A) B2))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat B2) (@ (@ tptp.divide_divide_nat tptp.one_one_nat) A)) (@ (@ tptp.divide_divide_nat B2) A)))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (@ (@ tptp.times_times_int B2) (@ (@ tptp.divide_divide_int tptp.one_one_int) A)) (@ (@ tptp.divide_divide_int B2) A)))))
% 4.71/5.18 (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))))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (assert (forall ((N2 tptp.nat) (A tptp.nat) (B2 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 B2) N2)) (@ (@ tptp.dvd_dvd_nat A) B2)))))
% 4.71/5.18 (assert (forall ((N2 tptp.nat) (A tptp.int) (B2 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 B2) N2)) (@ (@ tptp.dvd_dvd_int A) B2)))))
% 4.71/5.18 (assert (forall ((N2 tptp.nat) (K tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N2) K)) M2))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M2)) N2))))
% 4.71/5.18 (assert (forall ((K tptp.nat) (N2 tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K) N2)) M2))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M2)) N2))))
% 4.71/5.18 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat M2) (@ (@ tptp.times_times_nat N2) K)))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M2)) N2))))
% 4.71/5.18 (assert (forall ((M2 tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat M2) (@ (@ tptp.times_times_nat K) N2)))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M2)) N2))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat A) B2)) (= (@ _let_1 A) (@ _let_1 B2))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) B2)) (= (@ _let_1 A) (@ _let_1 B2))))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_nat A) B2))) (not (= (not (@ _let_1 A)) (not (@ _let_1 B2))))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_int A) B2))) (not (= (not (@ _let_1 A)) (not (@ _let_1 B2))))))))
% 4.71/5.18 (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)))))))
% 4.71/5.18 (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))))))
% 4.71/5.18 (assert (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc M2))) _let_1) (@ (@ tptp.modulo_modulo_nat M2) _let_1)))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.member_nat tptp.zero_zero_nat) (@ tptp.nat_set_decode X)) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X)))))
% 4.71/5.18 (assert (forall ((A tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.numeral_numeral_nat W2))) (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)))))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (W2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.numeral_numeral_nat W2))) (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)))))))))
% 4.71/5.18 (assert (forall ((A tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W2))) (= (@ (@ 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))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W2))) (= (@ (@ 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))))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (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))))))
% 4.71/5.18 (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))))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat M2) M2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat)))
% 4.71/5.18 (assert (forall ((A tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.numeral_numeral_nat W2))) (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)))))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (W2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.numeral_numeral_nat W2))) (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)))))))))
% 4.71/5.18 (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))))))
% 4.71/5.18 (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))))))
% 4.71/5.18 (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))))))
% 4.71/5.18 (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))))))
% 4.71/5.18 (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))))))
% 4.71/5.18 (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))))))
% 4.71/5.18 (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))))))
% 4.71/5.18 (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))))))
% 4.71/5.18 (assert (forall ((M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat M2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (= _let_1 tptp.one_one_nat)))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (assert (forall ((A tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W2))) (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)))))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W2))) (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)))))))))
% 4.71/5.18 (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))))))))))
% 4.71/5.18 (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))))))))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_set_real (@ tptp.collect_real (lambda ((C3 tptp.real)) (@ (@ tptp.dvd_dvd_real C3) A)))) (@ tptp.collect_real (lambda ((C3 tptp.real)) (@ (@ tptp.dvd_dvd_real C3) B2)))) (and (@ (@ tptp.dvd_dvd_real A) B2) (not (@ (@ tptp.dvd_dvd_real B2) A))))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_set_nat (@ tptp.collect_nat (lambda ((C3 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C3) A)))) (@ tptp.collect_nat (lambda ((C3 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C3) B2)))) (and (@ (@ tptp.dvd_dvd_nat A) B2) (not (@ (@ tptp.dvd_dvd_nat B2) A))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_set_int (@ tptp.collect_int (lambda ((C3 tptp.int)) (@ (@ tptp.dvd_dvd_int C3) A)))) (@ tptp.collect_int (lambda ((C3 tptp.int)) (@ (@ tptp.dvd_dvd_int C3) B2)))) (and (@ (@ tptp.dvd_dvd_int A) B2) (not (@ (@ tptp.dvd_dvd_int B2) A))))))
% 4.71/5.18 (assert (= tptp.ord_le2529575680413868914d_enat (lambda ((A5 tptp.set_Extended_enat) (B5 tptp.set_Extended_enat)) (@ (@ tptp.ord_le8499522857272258027enat_o (lambda ((X4 tptp.extended_enat)) (@ (@ tptp.member_Extended_enat X4) A5))) (lambda ((X4 tptp.extended_enat)) (@ (@ tptp.member_Extended_enat X4) B5))))))
% 4.71/5.18 (assert (= tptp.ord_less_set_real (lambda ((A5 tptp.set_real) (B5 tptp.set_real)) (@ (@ tptp.ord_less_real_o (lambda ((X4 tptp.real)) (@ (@ tptp.member_real X4) A5))) (lambda ((X4 tptp.real)) (@ (@ tptp.member_real X4) B5))))))
% 4.71/5.18 (assert (= tptp.ord_less_set_set_nat (lambda ((A5 tptp.set_set_nat) (B5 tptp.set_set_nat)) (@ (@ tptp.ord_less_set_nat_o (lambda ((X4 tptp.set_nat)) (@ (@ tptp.member_set_nat X4) A5))) (lambda ((X4 tptp.set_nat)) (@ (@ tptp.member_set_nat X4) B5))))))
% 4.71/5.18 (assert (= tptp.ord_less_set_nat (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (@ (@ tptp.ord_less_nat_o (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) A5))) (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) B5))))))
% 4.71/5.18 (assert (= tptp.ord_less_set_int (lambda ((A5 tptp.set_int) (B5 tptp.set_int)) (@ (@ tptp.ord_less_int_o (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) A5))) (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) B5))))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat A) B2) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat B2) A))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int A) B2) tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int B2) A))))
% 4.71/5.18 (assert (= tptp.dvd_dvd_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat B3) A3) tptp.zero_zero_nat))))
% 4.71/5.18 (assert (= tptp.dvd_dvd_int (lambda ((A3 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.modulo_modulo_int B3) A3) tptp.zero_zero_int))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) B2) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat B2) A))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) B2) tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int B2) A))))
% 4.71/5.18 (assert (= tptp.bot_bot_set_list_nat (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) false))))
% 4.71/5.18 (assert (= tptp.bot_bot_set_set_nat (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) false))))
% 4.71/5.18 (assert (= tptp.bot_bo7653980558646680370d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) false))))
% 4.71/5.18 (assert (= tptp.bot_bot_set_real (@ tptp.collect_real (lambda ((X4 tptp.real)) false))))
% 4.71/5.18 (assert (= tptp.bot_bot_set_nat (@ tptp.collect_nat (lambda ((X4 tptp.nat)) false))))
% 4.71/5.18 (assert (= tptp.bot_bot_set_int (@ tptp.collect_int (lambda ((X4 tptp.int)) false))))
% 4.71/5.18 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) A)))
% 4.71/5.18 (assert (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int A) A)))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B2) (=> (@ (@ tptp.dvd_dvd_nat B2) C) (@ _let_1 C))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B2) (=> (@ (@ tptp.dvd_dvd_int B2) C) (@ _let_1 C))))))
% 4.71/5.18 (assert (forall ((C tptp.nat) (B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C))) (=> (@ _let_1 B2) (= (@ _let_1 (@ (@ tptp.modulo_modulo_nat A) B2)) (@ _let_1 A))))))
% 4.71/5.18 (assert (forall ((C tptp.int) (B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (@ _let_1 B2) (= (@ _let_1 (@ (@ tptp.modulo_modulo_int A) B2)) (@ _let_1 A))))))
% 4.71/5.18 (assert (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C))) (=> (@ _let_1 (@ (@ tptp.modulo_modulo_nat A) B2)) (=> (@ _let_1 B2) (@ _let_1 A))))))
% 4.71/5.18 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (@ _let_1 (@ (@ tptp.modulo_modulo_int A) B2)) (=> (@ _let_1 B2) (@ _let_1 A))))))
% 4.71/5.18 (assert (forall ((P (-> tptp.real Bool))) (=> (not (@ tptp.finite_finite_real (@ tptp.collect_real P))) (exists ((X_12 tptp.real)) (@ P X_12)))))
% 4.71/5.18 (assert (forall ((P (-> tptp.list_nat Bool))) (=> (not (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat P))) (exists ((X_12 tptp.list_nat)) (@ P X_12)))))
% 4.71/5.18 (assert (forall ((P (-> tptp.set_nat Bool))) (=> (not (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat P))) (exists ((X_12 tptp.set_nat)) (@ P X_12)))))
% 4.71/5.18 (assert (forall ((P (-> tptp.nat Bool))) (=> (not (@ tptp.finite_finite_nat (@ tptp.collect_nat P))) (exists ((X_12 tptp.nat)) (@ P X_12)))))
% 4.71/5.18 (assert (forall ((P (-> tptp.complex Bool))) (=> (not (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex P))) (exists ((X_12 tptp.complex)) (@ P X_12)))))
% 4.71/5.18 (assert (forall ((P (-> tptp.int Bool))) (=> (not (@ tptp.finite_finite_int (@ tptp.collect_int P))) (exists ((X_12 tptp.int)) (@ P X_12)))))
% 4.71/5.18 (assert (forall ((P (-> tptp.extended_enat Bool))) (=> (not (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat P))) (exists ((X_12 tptp.extended_enat)) (@ P X_12)))))
% 4.71/5.18 (assert (forall ((A2 tptp.set_real) (B tptp.set_nat) (R (-> tptp.real tptp.nat Bool))) (=> (not (@ tptp.finite_finite_real A2)) (=> (@ tptp.finite_finite_nat B) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) B) (@ (@ R X5) Xa))))) (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) B) (not (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((A3 tptp.real)) (and (@ (@ tptp.member_real A3) A2) (@ (@ R A3) X5)))))))))))))
% 4.71/5.18 (assert (forall ((A2 tptp.set_real) (B tptp.set_complex) (R (-> tptp.real tptp.complex Bool))) (=> (not (@ tptp.finite_finite_real A2)) (=> (@ tptp.finite3207457112153483333omplex B) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) B) (@ (@ R X5) Xa))))) (exists ((X5 tptp.complex)) (and (@ (@ tptp.member_complex X5) B) (not (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((A3 tptp.real)) (and (@ (@ tptp.member_real A3) A2) (@ (@ R A3) X5)))))))))))))
% 4.71/5.18 (assert (forall ((A2 tptp.set_real) (B tptp.set_int) (R (-> tptp.real tptp.int Bool))) (=> (not (@ tptp.finite_finite_real A2)) (=> (@ tptp.finite_finite_int B) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) B) (@ (@ R X5) Xa))))) (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) B) (not (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((A3 tptp.real)) (and (@ (@ tptp.member_real A3) A2) (@ (@ R A3) X5)))))))))))))
% 4.71/5.18 (assert (forall ((A2 tptp.set_real) (B tptp.set_Extended_enat) (R (-> tptp.real tptp.extended_enat Bool))) (=> (not (@ tptp.finite_finite_real A2)) (=> (@ tptp.finite4001608067531595151d_enat B) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (exists ((Xa tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat Xa) B) (@ (@ R X5) Xa))))) (exists ((X5 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X5) B) (not (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((A3 tptp.real)) (and (@ (@ tptp.member_real A3) A2) (@ (@ R A3) X5)))))))))))))
% 4.71/5.18 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat) (R (-> tptp.nat tptp.nat Bool))) (=> (not (@ tptp.finite_finite_nat A2)) (=> (@ tptp.finite_finite_nat B) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) B) (@ (@ R X5) Xa))))) (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) B) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A3 tptp.nat)) (and (@ (@ tptp.member_nat A3) A2) (@ (@ R A3) X5)))))))))))))
% 4.71/5.18 (assert (forall ((A2 tptp.set_nat) (B tptp.set_complex) (R (-> tptp.nat tptp.complex Bool))) (=> (not (@ tptp.finite_finite_nat A2)) (=> (@ tptp.finite3207457112153483333omplex B) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) B) (@ (@ R X5) Xa))))) (exists ((X5 tptp.complex)) (and (@ (@ tptp.member_complex X5) B) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A3 tptp.nat)) (and (@ (@ tptp.member_nat A3) A2) (@ (@ R A3) X5)))))))))))))
% 4.71/5.18 (assert (forall ((A2 tptp.set_nat) (B tptp.set_int) (R (-> tptp.nat tptp.int Bool))) (=> (not (@ tptp.finite_finite_nat A2)) (=> (@ tptp.finite_finite_int B) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) B) (@ (@ R X5) Xa))))) (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) B) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A3 tptp.nat)) (and (@ (@ tptp.member_nat A3) A2) (@ (@ R A3) X5)))))))))))))
% 4.71/5.18 (assert (forall ((A2 tptp.set_nat) (B tptp.set_Extended_enat) (R (-> tptp.nat tptp.extended_enat Bool))) (=> (not (@ tptp.finite_finite_nat A2)) (=> (@ tptp.finite4001608067531595151d_enat B) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (exists ((Xa tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat Xa) B) (@ (@ R X5) Xa))))) (exists ((X5 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X5) B) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A3 tptp.nat)) (and (@ (@ tptp.member_nat A3) A2) (@ (@ R A3) X5)))))))))))))
% 4.71/5.18 (assert (forall ((A2 tptp.set_complex) (B tptp.set_nat) (R (-> tptp.complex tptp.nat Bool))) (=> (not (@ tptp.finite3207457112153483333omplex A2)) (=> (@ tptp.finite_finite_nat B) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) B) (@ (@ R X5) Xa))))) (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) B) (not (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((A3 tptp.complex)) (and (@ (@ tptp.member_complex A3) A2) (@ (@ R A3) X5)))))))))))))
% 4.71/5.18 (assert (forall ((A2 tptp.set_complex) (B tptp.set_complex) (R (-> tptp.complex tptp.complex Bool))) (=> (not (@ tptp.finite3207457112153483333omplex A2)) (=> (@ tptp.finite3207457112153483333omplex B) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) B) (@ (@ R X5) Xa))))) (exists ((X5 tptp.complex)) (and (@ (@ tptp.member_complex X5) B) (not (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((A3 tptp.complex)) (and (@ (@ tptp.member_complex A3) A2) (@ (@ R A3) X5)))))))))))))
% 4.71/5.18 (assert (forall ((R tptp.set_Extended_enat) (S2 tptp.set_Extended_enat)) (= (@ (@ tptp.ord_le100613205991271927enat_o (lambda ((X4 tptp.extended_enat)) (@ (@ tptp.member_Extended_enat X4) R))) (lambda ((X4 tptp.extended_enat)) (@ (@ tptp.member_Extended_enat X4) S2))) (@ (@ tptp.ord_le7203529160286727270d_enat R) S2))))
% 4.71/5.18 (assert (forall ((R tptp.set_real) (S2 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_real_o (lambda ((X4 tptp.real)) (@ (@ tptp.member_real X4) R))) (lambda ((X4 tptp.real)) (@ (@ tptp.member_real X4) S2))) (@ (@ tptp.ord_less_eq_set_real R) S2))))
% 4.71/5.18 (assert (forall ((R tptp.set_set_nat) (S2 tptp.set_set_nat)) (= (@ (@ tptp.ord_le3964352015994296041_nat_o (lambda ((X4 tptp.set_nat)) (@ (@ tptp.member_set_nat X4) R))) (lambda ((X4 tptp.set_nat)) (@ (@ tptp.member_set_nat X4) S2))) (@ (@ tptp.ord_le6893508408891458716et_nat R) S2))))
% 4.71/5.18 (assert (forall ((R tptp.set_nat) (S2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_nat_o (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) R))) (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) S2))) (@ (@ tptp.ord_less_eq_set_nat R) S2))))
% 4.71/5.18 (assert (forall ((R tptp.set_int) (S2 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_int_o (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) R))) (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) S2))) (@ (@ tptp.ord_less_eq_set_int R) S2))))
% 4.71/5.18 (assert (= tptp.ord_le7203529160286727270d_enat (lambda ((A5 tptp.set_Extended_enat) (B5 tptp.set_Extended_enat)) (@ (@ tptp.ord_le100613205991271927enat_o (lambda ((X4 tptp.extended_enat)) (@ (@ tptp.member_Extended_enat X4) A5))) (lambda ((X4 tptp.extended_enat)) (@ (@ tptp.member_Extended_enat X4) B5))))))
% 4.71/5.18 (assert (= tptp.ord_less_eq_set_real (lambda ((A5 tptp.set_real) (B5 tptp.set_real)) (@ (@ tptp.ord_less_eq_real_o (lambda ((X4 tptp.real)) (@ (@ tptp.member_real X4) A5))) (lambda ((X4 tptp.real)) (@ (@ tptp.member_real X4) B5))))))
% 4.71/5.18 (assert (= tptp.ord_le6893508408891458716et_nat (lambda ((A5 tptp.set_set_nat) (B5 tptp.set_set_nat)) (@ (@ tptp.ord_le3964352015994296041_nat_o (lambda ((X4 tptp.set_nat)) (@ (@ tptp.member_set_nat X4) A5))) (lambda ((X4 tptp.set_nat)) (@ (@ tptp.member_set_nat X4) B5))))))
% 4.71/5.18 (assert (= tptp.ord_less_eq_set_nat (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat_o (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) A5))) (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) B5))))))
% 4.71/5.18 (assert (= tptp.ord_less_eq_set_int (lambda ((A5 tptp.set_int) (B5 tptp.set_int)) (@ (@ tptp.ord_less_eq_int_o (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) A5))) (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) B5))))))
% 4.71/5.18 (assert (forall ((A2 tptp.set_Extended_enat) (P (-> tptp.extended_enat Bool))) (@ (@ tptp.ord_le7203529160286727270d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) A2) (@ P X4))))) A2)))
% 4.71/5.18 (assert (forall ((A2 tptp.set_real) (P (-> tptp.real Bool))) (@ (@ tptp.ord_less_eq_set_real (@ tptp.collect_real (lambda ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) A2) (@ P X4))))) A2)))
% 4.71/5.18 (assert (forall ((A2 tptp.set_list_nat) (P (-> tptp.list_nat Bool))) (@ (@ tptp.ord_le6045566169113846134st_nat (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (and (@ (@ tptp.member_list_nat X4) A2) (@ P X4))))) A2)))
% 4.71/5.18 (assert (forall ((A2 tptp.set_set_nat) (P (-> tptp.set_nat Bool))) (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X4) A2) (@ P X4))))) A2)))
% 4.71/5.18 (assert (forall ((A2 tptp.set_nat) (P (-> tptp.nat Bool))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A2) (@ P X4))))) A2)))
% 4.71/5.18 (assert (forall ((A2 tptp.set_int) (P (-> tptp.int Bool))) (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A2) (@ P X4))))) A2)))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.collect_real (lambda ((C3 tptp.real)) (@ (@ tptp.dvd_dvd_real C3) A)))) (@ tptp.collect_real (lambda ((C3 tptp.real)) (@ (@ tptp.dvd_dvd_real C3) B2)))) (@ (@ tptp.dvd_dvd_real A) B2))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat (lambda ((C3 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C3) A)))) (@ tptp.collect_nat (lambda ((C3 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C3) B2)))) (@ (@ tptp.dvd_dvd_nat A) B2))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int (lambda ((C3 tptp.int)) (@ (@ tptp.dvd_dvd_int C3) A)))) (@ tptp.collect_int (lambda ((C3 tptp.int)) (@ (@ tptp.dvd_dvd_int C3) B2)))) (@ (@ tptp.dvd_dvd_int A) B2))))
% 4.71/5.18 (assert (forall ((X8 tptp.set_Extended_enat) (P (-> tptp.extended_enat Bool))) (@ (@ tptp.ord_le7203529160286727270d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) X8) (@ P X4))))) X8)))
% 4.71/5.18 (assert (forall ((X8 tptp.set_real) (P (-> tptp.real Bool))) (@ (@ tptp.ord_less_eq_set_real (@ tptp.collect_real (lambda ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) X8) (@ P X4))))) X8)))
% 4.71/5.18 (assert (forall ((X8 tptp.set_list_nat) (P (-> tptp.list_nat Bool))) (@ (@ tptp.ord_le6045566169113846134st_nat (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (and (@ (@ tptp.member_list_nat X4) X8) (@ P X4))))) X8)))
% 4.71/5.18 (assert (forall ((X8 tptp.set_set_nat) (P (-> tptp.set_nat Bool))) (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X4) X8) (@ P X4))))) X8)))
% 4.71/5.18 (assert (forall ((X8 tptp.set_nat) (P (-> tptp.nat Bool))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) X8) (@ P X4))))) X8)))
% 4.71/5.18 (assert (forall ((X8 tptp.set_int) (P (-> tptp.int Bool))) (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) X8) (@ P X4))))) X8)))
% 4.71/5.18 (assert (forall ((X tptp.extended_enat) (Z5 tptp.set_Extended_enat) (X8 tptp.set_Extended_enat) (P (-> tptp.extended_enat Bool))) (=> (@ (@ tptp.member_Extended_enat X) Z5) (=> (@ (@ tptp.ord_le7203529160286727270d_enat Z5) (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) X8) (@ P X4))))) (@ P X)))))
% 4.71/5.18 (assert (forall ((X tptp.real) (Z5 tptp.set_real) (X8 tptp.set_real) (P (-> tptp.real Bool))) (=> (@ (@ tptp.member_real X) Z5) (=> (@ (@ tptp.ord_less_eq_set_real Z5) (@ tptp.collect_real (lambda ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) X8) (@ P X4))))) (@ P X)))))
% 4.71/5.18 (assert (forall ((X tptp.list_nat) (Z5 tptp.set_list_nat) (X8 tptp.set_list_nat) (P (-> tptp.list_nat Bool))) (=> (@ (@ tptp.member_list_nat X) Z5) (=> (@ (@ tptp.ord_le6045566169113846134st_nat Z5) (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (and (@ (@ tptp.member_list_nat X4) X8) (@ P X4))))) (@ P X)))))
% 4.71/5.18 (assert (forall ((X tptp.set_nat) (Z5 tptp.set_set_nat) (X8 tptp.set_set_nat) (P (-> tptp.set_nat Bool))) (=> (@ (@ tptp.member_set_nat X) Z5) (=> (@ (@ tptp.ord_le6893508408891458716et_nat Z5) (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X4) X8) (@ P X4))))) (@ P X)))))
% 4.71/5.18 (assert (forall ((X tptp.nat) (Z5 tptp.set_nat) (X8 tptp.set_nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.member_nat X) Z5) (=> (@ (@ tptp.ord_less_eq_set_nat Z5) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) X8) (@ P X4))))) (@ P X)))))
% 4.71/5.18 (assert (forall ((X tptp.int) (Z5 tptp.set_int) (X8 tptp.set_int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.member_int X) Z5) (=> (@ (@ tptp.ord_less_eq_set_int Z5) (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) X8) (@ P X4))))) (@ P X)))))
% 4.71/5.18 (assert (= (lambda ((H tptp.nat)) tptp.zero_zero_nat) (@ tptp.times_times_nat tptp.zero_zero_nat)))
% 4.71/5.18 (assert (= (lambda ((H tptp.int)) tptp.zero_zero_int) (@ tptp.times_times_int tptp.zero_zero_int)))
% 4.71/5.18 (assert (= (lambda ((H tptp.real)) tptp.zero_zero_real) (@ tptp.times_times_real tptp.zero_zero_real)))
% 4.71/5.18 (assert (= (lambda ((H tptp.complex)) tptp.zero_zero_complex) (@ tptp.times_times_complex tptp.zero_zero_complex)))
% 4.71/5.18 (assert (= (lambda ((H tptp.extended_enat)) tptp.zero_z5237406670263579293d_enat) (@ tptp.times_7803423173614009249d_enat tptp.zero_z5237406670263579293d_enat)))
% 4.71/5.18 (assert (= (lambda ((X4 tptp.nat)) X4) (@ tptp.times_times_nat tptp.one_one_nat)))
% 4.71/5.18 (assert (= (lambda ((X4 tptp.int)) X4) (@ tptp.times_times_int tptp.one_one_int)))
% 4.71/5.18 (assert (= (lambda ((X4 tptp.real)) X4) (@ tptp.times_times_real tptp.one_one_real)))
% 4.71/5.18 (assert (= (lambda ((X4 tptp.complex)) X4) (@ tptp.times_times_complex tptp.one_one_complex)))
% 4.71/5.18 (assert (= (lambda ((X4 tptp.extended_enat)) X4) (@ tptp.times_7803423173614009249d_enat tptp.one_on7984719198319812577d_enat)))
% 4.71/5.18 (assert (= tptp.ord_max_real (lambda ((A3 tptp.real) (B3 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_eq_real A3) B3)) B3) A3))))
% 4.71/5.18 (assert (= tptp.ord_max_set_nat (lambda ((A3 tptp.set_nat) (B3 tptp.set_nat)) (@ (@ (@ tptp.if_set_nat (@ (@ tptp.ord_less_eq_set_nat A3) B3)) B3) A3))))
% 4.71/5.18 (assert (= tptp.ord_max_set_int (lambda ((A3 tptp.set_int) (B3 tptp.set_int)) (@ (@ (@ tptp.if_set_int (@ (@ tptp.ord_less_eq_set_int A3) B3)) B3) A3))))
% 4.71/5.18 (assert (= tptp.ord_max_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_eq_nat A3) B3)) B3) A3))))
% 4.71/5.18 (assert (= tptp.ord_max_int (lambda ((A3 tptp.int) (B3 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int A3) B3)) B3) A3))))
% 4.71/5.18 (assert (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((D4 tptp.nat)) (@ (@ tptp.dvd_dvd_nat D4) M2)))))))
% 4.71/5.18 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (= (@ (@ tptp.modulo_modulo_nat A) B2) tptp.zero_zero_nat))))
% 4.71/5.18 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (= (@ (@ tptp.modulo_modulo_int A) B2) tptp.zero_zero_int))))
% 4.71/5.18 (assert (= tptp.bot_bot_nat_nat_o (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X4) Y5)) tptp.bot_bo2099793752762293965at_nat))))
% 4.71/5.18 (assert (= tptp.bot_bo1565574316222977092_nat_o (lambda ((X4 tptp.vEBT_VEBT) (Y5 tptp.nat)) (@ (@ tptp.member373505688050248522BT_nat (@ (@ tptp.produc738532404422230701BT_nat X4) Y5)) tptp.bot_bo1642239108664514429BT_nat))))
% 4.71/5.18 (assert (= tptp.bot_bot_int_int_o (lambda ((X4 tptp.int) (Y5 tptp.int)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X4) Y5)) tptp.bot_bo1796632182523588997nt_int))))
% 4.71/5.18 (assert (= tptp.bot_bo4898103413517107610_nat_o (lambda ((X4 tptp.product_prod_nat_nat) (Y5 tptp.product_prod_nat_nat)) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X4) Y5)) tptp.bot_bo5327735625951526323at_nat))))
% 4.71/5.18 (assert (forall ((P (-> tptp.nat Bool)) (I tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (and (@ P K2) (@ (@ tptp.ord_less_nat K2) I)))))))
% 4.71/5.18 (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)))))))
% 4.71/5.18 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.modulo_modulo_nat M2) N2)) (not (@ (@ tptp.dvd_dvd_nat N2) M2)))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.modulo_modulo_nat (@ _let_1 (@ (@ tptp.modulo_modulo_nat B2) C))) C) (@ (@ tptp.modulo_modulo_nat (@ _let_1 B2)) C)))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.modulo_modulo_int (@ _let_1 (@ (@ tptp.modulo_modulo_int B2) C))) C) (@ (@ tptp.modulo_modulo_int (@ _let_1 B2)) C)))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) C)) B2)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B2)) C))))
% 4.71/5.18 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) C)) B2)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B2)) C))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (C tptp.nat) (A7 tptp.nat) (B2 tptp.nat) (B7 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) C) (@ (@ tptp.modulo_modulo_nat A7) C)) (=> (= (@ (@ tptp.modulo_modulo_nat B2) C) (@ (@ tptp.modulo_modulo_nat B7) C)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B2)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A7) B7)) C))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (C tptp.int) (A7 tptp.int) (B2 tptp.int) (B7 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A7) C)) (=> (= (@ (@ tptp.modulo_modulo_int B2) C) (@ (@ tptp.modulo_modulo_int B7) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B2)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A7) B7)) C))))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) C)) (@ (@ tptp.modulo_modulo_nat B2) C))) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B2)) C))))
% 4.71/5.18 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) C)) (@ (@ tptp.modulo_modulo_int B2) C))) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B2)) C))))
% 4.71/5.18 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))))
% 4.71/5.18 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real tptp.zero_zero_real) A) (= A tptp.zero_zero_real))))
% 4.71/5.18 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) A) (= A tptp.zero_zero_int))))
% 4.71/5.18 (assert (forall ((A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex tptp.zero_zero_complex) A) (= A tptp.zero_zero_complex))))
% 4.71/5.18 (assert (forall ((A tptp.extended_enat)) (=> (@ (@ tptp.dvd_dv3785147216227455552d_enat tptp.zero_z5237406670263579293d_enat) A) (= A tptp.zero_z5237406670263579293d_enat))))
% 4.71/5.18 (assert (= tptp.dvd_dvd_real (lambda ((A3 tptp.real) (B3 tptp.real)) (=> (= A3 tptp.zero_zero_real) (= B3 tptp.zero_zero_real)))))
% 4.71/5.18 (assert (= tptp.dvd_dvd_complex (lambda ((A3 tptp.complex) (B3 tptp.complex)) (=> (= A3 tptp.zero_zero_complex) (= B3 tptp.zero_zero_complex)))))
% 4.71/5.18 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M2) N2)))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc M2))) N2))))
% 4.71/5.18 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M2) N2))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M2)) N2))))
% 4.71/5.18 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) A) (not (forall ((K3 tptp.nat)) (not (= A (@ (@ tptp.times_times_nat B2) K3))))))))
% 4.71/5.18 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B2) A) (not (forall ((K3 tptp.int)) (not (= A (@ (@ tptp.times_times_int B2) K3))))))))
% 4.71/5.18 (assert (forall ((B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real B2) A) (not (forall ((K3 tptp.real)) (not (= A (@ (@ tptp.times_times_real B2) K3))))))))
% 4.71/5.18 (assert (forall ((B2 tptp.complex) (A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex B2) A) (not (forall ((K3 tptp.complex)) (not (= A (@ (@ tptp.times_times_complex B2) K3))))))))
% 4.71/5.18 (assert (forall ((B2 tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.dvd_dv3785147216227455552d_enat B2) A) (not (forall ((K3 tptp.extended_enat)) (not (= A (@ (@ tptp.times_7803423173614009249d_enat B2) K3))))))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat) (K tptp.nat)) (=> (= A (@ (@ tptp.times_times_nat B2) K)) (@ (@ tptp.dvd_dvd_nat B2) A))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int) (K tptp.int)) (=> (= A (@ (@ tptp.times_times_int B2) K)) (@ (@ tptp.dvd_dvd_int B2) A))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real) (K tptp.real)) (=> (= A (@ (@ tptp.times_times_real B2) K)) (@ (@ tptp.dvd_dvd_real B2) A))))
% 4.71/5.18 (assert (forall ((A tptp.complex) (B2 tptp.complex) (K tptp.complex)) (=> (= A (@ (@ tptp.times_times_complex B2) K)) (@ (@ tptp.dvd_dvd_complex B2) A))))
% 4.71/5.18 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (K tptp.extended_enat)) (=> (= A (@ (@ tptp.times_7803423173614009249d_enat B2) K)) (@ (@ tptp.dvd_dv3785147216227455552d_enat B2) A))))
% 4.71/5.18 (assert (= tptp.dvd_dvd_nat (lambda ((B3 tptp.nat) (A3 tptp.nat)) (exists ((K2 tptp.nat)) (= A3 (@ (@ tptp.times_times_nat B3) K2))))))
% 4.71/5.18 (assert (= tptp.dvd_dvd_int (lambda ((B3 tptp.int) (A3 tptp.int)) (exists ((K2 tptp.int)) (= A3 (@ (@ tptp.times_times_int B3) K2))))))
% 4.71/5.18 (assert (= tptp.dvd_dvd_real (lambda ((B3 tptp.real) (A3 tptp.real)) (exists ((K2 tptp.real)) (= A3 (@ (@ tptp.times_times_real B3) K2))))))
% 4.71/5.18 (assert (= tptp.dvd_dvd_complex (lambda ((B3 tptp.complex) (A3 tptp.complex)) (exists ((K2 tptp.complex)) (= A3 (@ (@ tptp.times_times_complex B3) K2))))))
% 4.71/5.18 (assert (= tptp.dvd_dv3785147216227455552d_enat (lambda ((B3 tptp.extended_enat) (A3 tptp.extended_enat)) (exists ((K2 tptp.extended_enat)) (= A3 (@ (@ tptp.times_7803423173614009249d_enat B3) K2))))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_nat B2) C))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_int B2) C))))))
% 4.71/5.18 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_real B2) C))))))
% 4.71/5.18 (assert (forall ((A tptp.complex) (C tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_complex B2) C))))))
% 4.71/5.18 (assert (forall ((A tptp.extended_enat) (C tptp.extended_enat) (B2 tptp.extended_enat)) (let ((_let_1 (@ tptp.dvd_dv3785147216227455552d_enat A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_7803423173614009249d_enat B2) C))))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_nat B2) C))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_int B2) C))))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_real B2) C))))))
% 4.71/5.18 (assert (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_complex B2) C))))))
% 4.71/5.18 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.dvd_dv3785147216227455552d_enat A))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_7803423173614009249d_enat B2) C))))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B2)) C) (@ (@ tptp.dvd_dvd_nat A) C))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B2)) C) (@ (@ tptp.dvd_dvd_int A) C))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) B2)) C) (@ (@ tptp.dvd_dvd_real A) C))))
% 4.71/5.18 (assert (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.times_times_complex A) B2)) C) (@ (@ tptp.dvd_dvd_complex A) C))))
% 4.71/5.18 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat)) (=> (@ (@ tptp.dvd_dv3785147216227455552d_enat (@ (@ tptp.times_7803423173614009249d_enat A) B2)) C) (@ (@ tptp.dvd_dv3785147216227455552d_enat A) C))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat A) B2))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int A) B2))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real)) (@ (@ tptp.dvd_dvd_real A) (@ (@ tptp.times_times_real A) B2))))
% 4.71/5.18 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (@ (@ tptp.dvd_dvd_complex A) (@ (@ tptp.times_times_complex A) B2))))
% 4.71/5.18 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (@ (@ tptp.dvd_dv3785147216227455552d_enat A) (@ (@ tptp.times_7803423173614009249d_enat A) B2))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B2) (=> (@ (@ tptp.dvd_dvd_nat C) D) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B2) D))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B2) (=> (@ (@ tptp.dvd_dvd_int C) D) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) D))))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.dvd_dvd_real A) B2) (=> (@ (@ tptp.dvd_dvd_real C) D) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) D))))))
% 4.71/5.18 (assert (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex) (D tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex A) B2) (=> (@ (@ tptp.dvd_dvd_complex C) D) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B2) D))))))
% 4.71/5.18 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat) (D tptp.extended_enat)) (=> (@ (@ tptp.dvd_dv3785147216227455552d_enat A) B2) (=> (@ (@ tptp.dvd_dv3785147216227455552d_enat C) D) (@ (@ tptp.dvd_dv3785147216227455552d_enat (@ (@ tptp.times_7803423173614009249d_enat A) C)) (@ (@ tptp.times_7803423173614009249d_enat B2) D))))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B2)) C) (@ (@ tptp.dvd_dvd_nat B2) C))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B2)) C) (@ (@ tptp.dvd_dvd_int B2) C))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) B2)) C) (@ (@ tptp.dvd_dvd_real B2) C))))
% 4.71/5.18 (assert (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.times_times_complex A) B2)) C) (@ (@ tptp.dvd_dvd_complex B2) C))))
% 4.71/5.18 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat)) (=> (@ (@ tptp.dvd_dv3785147216227455552d_enat (@ (@ tptp.times_7803423173614009249d_enat A) B2)) C) (@ (@ tptp.dvd_dv3785147216227455552d_enat B2) C))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat B2) A))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int B2) A))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real)) (@ (@ tptp.dvd_dvd_real A) (@ (@ tptp.times_times_real B2) A))))
% 4.71/5.18 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (@ (@ tptp.dvd_dvd_complex A) (@ (@ tptp.times_times_complex B2) A))))
% 4.71/5.18 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (@ (@ tptp.dvd_dv3785147216227455552d_enat A) (@ (@ tptp.times_7803423173614009249d_enat B2) A))))
% 4.71/5.18 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat tptp.one_one_nat) A)))
% 4.71/5.18 (assert (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int tptp.one_one_int) A)))
% 4.71/5.18 (assert (forall ((A tptp.complex)) (@ (@ tptp.dvd_dvd_complex tptp.one_one_complex) A)))
% 4.71/5.18 (assert (forall ((A tptp.real)) (@ (@ tptp.dvd_dvd_real tptp.one_one_real) A)))
% 4.71/5.18 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat B2))) (=> (@ _let_1 tptp.one_one_nat) (@ _let_1 A)))))
% 4.71/5.18 (assert (forall ((B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int B2))) (=> (@ _let_1 tptp.one_one_int) (@ _let_1 A)))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B2) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (@ _let_1 tptp.one_one_nat))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B2) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (@ _let_1 tptp.one_one_int))))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B2) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B2) C)) (@ _let_1 C))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B2) (= (@ _let_1 (@ (@ tptp.plus_plus_int B2) C)) (@ _let_1 C))))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 B2) (= (@ _let_1 (@ (@ tptp.plus_plus_real B2) C)) (@ _let_1 C))))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 C) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B2) C)) (@ _let_1 B2))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 C) (= (@ _let_1 (@ (@ tptp.plus_plus_int B2) C)) (@ _let_1 B2))))))
% 4.71/5.18 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 C) (= (@ _let_1 (@ (@ tptp.plus_plus_real B2) C)) (@ _let_1 B2))))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat B2) C)))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int B2) C)))))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_real B2) C)))))))
% 4.71/5.18 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.dvd_dv3785147216227455552d_enat A))) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_p3455044024723400733d_enat B2) C)))))))
% 4.71/5.18 (assert (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= (= (@ (@ tptp.divide_divide_nat A) C) (@ (@ tptp.divide_divide_nat B2) C)) (= A B2)))))))
% 4.71/5.18 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= (= (@ (@ tptp.divide_divide_int A) C) (@ (@ tptp.divide_divide_int B2) C)) (= A B2)))))))
% 4.71/5.18 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real C))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= (= (@ (@ tptp.divide_divide_real A) C) (@ (@ tptp.divide_divide_real B2) C)) (= A B2)))))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C))) (=> (= (@ (@ tptp.divide_divide_nat A) C) (@ (@ tptp.divide_divide_nat B2) C)) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= A B2)))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (= (@ (@ tptp.divide_divide_int A) C) (@ (@ tptp.divide_divide_int B2) C)) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= A B2)))))))
% 4.71/5.18 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real C))) (=> (= (@ (@ tptp.divide_divide_real A) C) (@ (@ tptp.divide_divide_real B2) C)) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= A B2)))))))
% 4.71/5.18 (assert (forall ((D tptp.nat) (B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat D) B2) (=> (@ (@ tptp.dvd_dvd_nat B2) A) (= (@ (@ tptp.divide_divide_nat (@ _let_1 D)) (@ (@ tptp.divide_divide_nat B2) D)) (@ _let_1 B2)))))))
% 4.71/5.18 (assert (forall ((D tptp.int) (B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int D) B2) (=> (@ (@ tptp.dvd_dvd_int B2) A) (= (@ (@ tptp.divide_divide_int (@ _let_1 D)) (@ (@ tptp.divide_divide_int B2) D)) (@ _let_1 B2)))))))
% 4.71/5.18 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M2) N2)) M2)))
% 4.71/5.18 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))))
% 4.71/5.18 (assert (forall ((A tptp.nat)) (let ((_let_1 (not (= A tptp.zero_zero_nat)))) (= _let_1 (and (@ (@ tptp.dvd_dvd_nat A) tptp.zero_zero_nat) _let_1)))))
% 4.71/5.18 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))))
% 4.71/5.18 (assert (forall ((A tptp.nat)) (not (and (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (not (= tptp.zero_zero_nat A))))))
% 4.71/5.18 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) tptp.zero_zero_nat)))
% 4.71/5.18 (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)))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (assert (= tptp.vEBT_set_vebt (lambda ((T2 tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_V8194947554948674370ptions T2)))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.nat_set_decode M2)) (@ tptp.nat_set_decode N2)) (@ (@ tptp.ord_less_eq_nat M2) N2))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat A) B2)) A))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.modulo_modulo_int A) B2)) A))))
% 4.71/5.18 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2) (@ (@ tptp.ord_less_nat (@ (@ tptp.modulo_modulo_nat A) B2)) B2))))
% 4.71/5.18 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (@ (@ tptp.ord_less_int (@ (@ tptp.modulo_modulo_int A) B2)) B2))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat A) B2) A) (= (@ (@ tptp.divide_divide_nat A) B2) tptp.zero_zero_nat))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int A) B2) A) (= (@ (@ tptp.divide_divide_int A) B2) tptp.zero_zero_int))))
% 4.71/5.18 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int B2) C)) (not (forall ((D5 tptp.int)) (not (= B2 (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int C) D5)))))))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B2)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) C)) (@ (@ tptp.divide_divide_nat B2) C))) (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) C)) (@ (@ tptp.modulo_modulo_nat B2) C))) C)))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B2)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B2) C))) (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) C)) (@ (@ tptp.modulo_modulo_int B2) C))) C)))))
% 4.71/5.18 (assert (not (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) tptp.one_one_nat)))
% 4.71/5.18 (assert (not (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) tptp.one_one_int)))
% 4.71/5.18 (assert (forall ((D tptp.nat) (S tptp.nat)) (exists ((Z 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) Z) (= _let_1 _let_1)))))))
% 4.71/5.18 (assert (forall ((D tptp.extended_enat) (S tptp.extended_enat)) (exists ((Z tptp.extended_enat)) (forall ((X2 tptp.extended_enat)) (let ((_let_1 (not (@ (@ tptp.dvd_dv3785147216227455552d_enat D) (@ (@ tptp.plus_p3455044024723400733d_enat X2) S))))) (=> (@ (@ tptp.ord_le72135733267957522d_enat X2) Z) (= _let_1 _let_1)))))))
% 4.71/5.18 (assert (forall ((D tptp.real) (S tptp.real)) (exists ((Z 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) Z) (= _let_1 _let_1)))))))
% 4.71/5.18 (assert (forall ((D tptp.int) (S tptp.int)) (exists ((Z 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) Z) (= _let_1 _let_1)))))))
% 4.71/5.18 (assert (forall ((D tptp.nat) (S tptp.nat)) (exists ((Z 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) Z) (= _let_1 _let_1)))))))
% 4.71/5.18 (assert (forall ((D tptp.extended_enat) (S tptp.extended_enat)) (exists ((Z tptp.extended_enat)) (forall ((X2 tptp.extended_enat)) (let ((_let_1 (@ (@ tptp.dvd_dv3785147216227455552d_enat D) (@ (@ tptp.plus_p3455044024723400733d_enat X2) S)))) (=> (@ (@ tptp.ord_le72135733267957522d_enat X2) Z) (= _let_1 _let_1)))))))
% 4.71/5.18 (assert (forall ((D tptp.real) (S tptp.real)) (exists ((Z 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) Z) (= _let_1 _let_1)))))))
% 4.71/5.18 (assert (forall ((D tptp.int) (S tptp.int)) (exists ((Z 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) Z) (= _let_1 _let_1)))))))
% 4.71/5.18 (assert (forall ((D tptp.nat) (S tptp.nat)) (exists ((Z 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 Z) X2) (= _let_1 _let_1)))))))
% 4.71/5.18 (assert (forall ((D tptp.extended_enat) (S tptp.extended_enat)) (exists ((Z tptp.extended_enat)) (forall ((X2 tptp.extended_enat)) (let ((_let_1 (not (@ (@ tptp.dvd_dv3785147216227455552d_enat D) (@ (@ tptp.plus_p3455044024723400733d_enat X2) S))))) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z) X2) (= _let_1 _let_1)))))))
% 4.71/5.18 (assert (forall ((D tptp.real) (S tptp.real)) (exists ((Z 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 Z) X2) (= _let_1 _let_1)))))))
% 4.71/5.18 (assert (forall ((D tptp.int) (S tptp.int)) (exists ((Z 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 Z) X2) (= _let_1 _let_1)))))))
% 4.71/5.18 (assert (forall ((D tptp.nat) (S tptp.nat)) (exists ((Z tptp.nat)) (forall ((X2 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X2) S)))) (=> (@ (@ tptp.ord_less_nat Z) X2) (= _let_1 _let_1)))))))
% 4.71/5.18 (assert (forall ((D tptp.extended_enat) (S tptp.extended_enat)) (exists ((Z tptp.extended_enat)) (forall ((X2 tptp.extended_enat)) (let ((_let_1 (@ (@ tptp.dvd_dv3785147216227455552d_enat D) (@ (@ tptp.plus_p3455044024723400733d_enat X2) S)))) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z) X2) (= _let_1 _let_1)))))))
% 4.71/5.18 (assert (forall ((D tptp.real) (S tptp.real)) (exists ((Z tptp.real)) (forall ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X2) S)))) (=> (@ (@ tptp.ord_less_real Z) X2) (= _let_1 _let_1)))))))
% 4.71/5.18 (assert (forall ((D tptp.int) (S tptp.int)) (exists ((Z tptp.int)) (forall ((X2 tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X2) S)))) (=> (@ (@ tptp.ord_less_int Z) X2) (= _let_1 _let_1)))))))
% 4.71/5.18 (assert (forall ((B2 tptp.complex) (A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex B2) A) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B2) tptp.zero_zero_complex) (= A tptp.zero_zero_complex)))))
% 4.71/5.18 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) A) (= (= (@ (@ tptp.divide_divide_nat A) B2) tptp.zero_zero_nat) (= A tptp.zero_zero_nat)))))
% 4.71/5.18 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B2) A) (= (= (@ (@ tptp.divide_divide_int A) B2) tptp.zero_zero_int) (= A tptp.zero_zero_int)))))
% 4.71/5.18 (assert (forall ((B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real B2) A) (= (= (@ (@ tptp.divide_divide_real A) B2) tptp.zero_zero_real) (= A tptp.zero_zero_real)))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (= (@ (@ tptp.times_times_nat B2) A) (@ (@ tptp.times_times_nat C) A)) (= B2 C)))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (= (@ (@ tptp.times_times_int B2) A) (@ (@ tptp.times_times_int C) A)) (= B2 C)))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C))))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B2)) C) (@ (@ tptp.dvd_dvd_nat B2) C)))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B2)) C) (@ (@ tptp.dvd_dvd_int B2) C)))))
% 4.71/5.18 (assert (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.times_times_nat B2) C)) (@ _let_1 C))))))
% 4.71/5.18 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.times_times_int B2) C)) (@ _let_1 C))))))
% 4.71/5.18 (assert (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B2)) C) (@ (@ tptp.dvd_dvd_nat A) C)))))
% 4.71/5.18 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B2)) C) (@ (@ tptp.dvd_dvd_int A) C)))))
% 4.71/5.18 (assert (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.times_times_nat C) B2)) (@ _let_1 C))))))
% 4.71/5.18 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.times_times_int C) B2)) (@ _let_1 C))))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B2)) tptp.one_one_nat) (and (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat)))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B2)) tptp.one_one_int) (and (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int)))))
% 4.71/5.18 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M2) N2)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M2)) N2))) (let ((_let_3 (= _let_1 N2))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 4.71/5.18 (assert (forall ((N2 tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.nat_set_decode N2))))
% 4.71/5.18 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat) (P5 tptp.nat) (M2 tptp.nat)) (=> (@ P N2) (=> (@ (@ tptp.ord_less_nat N2) P5) (=> (@ (@ tptp.ord_less_nat M2) P5) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N3) P5) (=> (@ P N3) (@ P (@ (@ tptp.modulo_modulo_nat (@ tptp.suc N3)) P5))))) (@ P M2)))))))
% 4.71/5.18 (assert (forall ((C tptp.nat) (B2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat C) B2) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat B2) C)) A) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat B2) A)) C)))))
% 4.71/5.18 (assert (forall ((C tptp.int) (B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int C) B2) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int B2) C)) A) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int B2) A)) C)))))
% 4.71/5.18 (assert (forall ((C tptp.nat) (B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) B2) (= (@ _let_1 (@ (@ tptp.divide_divide_nat B2) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B2)) C))))))
% 4.71/5.18 (assert (forall ((C tptp.int) (B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.dvd_dvd_int C) B2) (= (@ _let_1 (@ (@ tptp.divide_divide_int B2) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B2)) C))))))
% 4.71/5.18 (assert (forall ((C tptp.nat) (B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) B2) (=> (@ (@ tptp.dvd_dvd_nat B2) A) (= (@ _let_1 (@ (@ tptp.divide_divide_nat B2) C)) (@ (@ tptp.times_times_nat (@ _let_1 B2)) C)))))))
% 4.71/5.18 (assert (forall ((C tptp.int) (B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int C) B2) (=> (@ (@ tptp.dvd_dvd_int B2) A) (= (@ _let_1 (@ (@ tptp.divide_divide_int B2) C)) (@ (@ tptp.times_times_int (@ _let_1 B2)) C)))))))
% 4.71/5.18 (assert (forall ((B2 tptp.nat) (C tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (let ((_let_2 (@ (@ tptp.times_times_nat B2) C))) (=> (@ (@ tptp.dvd_dvd_nat _let_2) A) (= (@ _let_1 _let_2) (@ (@ tptp.divide_divide_nat (@ _let_1 B2)) C)))))))
% 4.71/5.18 (assert (forall ((B2 tptp.int) (C tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (let ((_let_2 (@ (@ tptp.times_times_int B2) C))) (=> (@ (@ tptp.dvd_dvd_int _let_2) A) (= (@ _let_1 _let_2) (@ (@ tptp.divide_divide_int (@ _let_1 B2)) C)))))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) C)) B2) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.divide_divide_nat B2) C)))))
% 4.71/5.18 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) B2) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.divide_divide_int B2) C)))))
% 4.71/5.18 (assert (forall ((B2 tptp.nat) (A tptp.nat) (D tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) A) (=> (@ (@ tptp.dvd_dvd_nat D) C) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B2)) (@ (@ tptp.divide_divide_nat C) D)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B2) D)))))))
% 4.71/5.18 (assert (forall ((B2 tptp.int) (A tptp.int) (D tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B2) A) (=> (@ (@ tptp.dvd_dvd_int D) C) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B2)) (@ (@ tptp.divide_divide_int C) D)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) D)))))))
% 4.71/5.18 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (M2 tptp.nat) (N2 tptp.nat)) (=> (forall ((M3 tptp.nat)) (@ (@ P M3) tptp.zero_zero_nat)) (=> (forall ((M3 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (=> (@ (@ P N3) (@ (@ tptp.modulo_modulo_nat M3) N3)) (@ (@ P M3) N3)))) (@ (@ P M2) N2)))))
% 4.71/5.18 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_nat (@ (@ tptp.modulo_modulo_nat M2) N2)) N2))))
% 4.71/5.18 (assert (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.divide_divide_nat C) B2)) (@ _let_1 C))))))
% 4.71/5.18 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.divide_divide_int C) B2)) (@ _let_1 C))))))
% 4.71/5.18 (assert (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat A) B2)) C) (@ (@ tptp.dvd_dvd_nat A) C)))))
% 4.71/5.18 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int A) B2)) C) (@ (@ tptp.dvd_dvd_int A) C)))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (= (@ (@ tptp.divide_divide_nat B2) A) (@ (@ tptp.divide_divide_nat C) A)) (= B2 C)))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (= (@ (@ tptp.divide_divide_int B2) A) (@ (@ tptp.divide_divide_int C) A)) (= B2 C)))))
% 4.71/5.18 (assert (forall ((C tptp.nat) (B2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat C) B2) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B2)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) C)) (@ (@ tptp.divide_divide_nat B2) C))))))
% 4.71/5.18 (assert (forall ((C tptp.int) (B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int C) B2) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B2)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B2) C))))))
% 4.71/5.18 (assert (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat C) A) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B2)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) C)) (@ (@ tptp.divide_divide_nat B2) C))))))
% 4.71/5.18 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int C) A) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B2)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B2) C))))))
% 4.71/5.18 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M2) (@ tptp.suc N2))) N2)))
% 4.71/5.18 (assert (forall ((M2 tptp.nat) (D tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M2) D) tptp.zero_zero_nat) (exists ((Q2 tptp.nat)) (= M2 (@ (@ tptp.times_times_nat D) Q2))))))
% 4.71/5.18 (assert (forall ((X tptp.nat) (Y tptp.nat) (N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X) Y) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X) N2)) (@ (@ tptp.power_power_nat Y) M2))))))
% 4.71/5.18 (assert (forall ((X tptp.real) (Y tptp.real) (N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_real X) Y) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.power_power_real X) N2)) (@ (@ tptp.power_power_real Y) M2))))))
% 4.71/5.18 (assert (forall ((X tptp.complex) (Y tptp.complex) (N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_complex X) Y) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.power_power_complex X) N2)) (@ (@ tptp.power_power_complex Y) M2))))))
% 4.71/5.18 (assert (forall ((X tptp.int) (Y tptp.int) (N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int X) Y) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int X) N2)) (@ (@ tptp.power_power_int Y) M2))))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (N2 tptp.nat) (B2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 N2)) B2) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.dvd_dvd_nat (@ _let_1 M2)) B2))))))
% 4.71/5.18 (assert (forall ((A tptp.real) (N2 tptp.nat) (B2 tptp.real) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.dvd_dvd_real (@ _let_1 N2)) B2) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.dvd_dvd_real (@ _let_1 M2)) B2))))))
% 4.71/5.18 (assert (forall ((A tptp.complex) (N2 tptp.nat) (B2 tptp.complex) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (@ (@ tptp.dvd_dvd_complex (@ _let_1 N2)) B2) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.dvd_dvd_complex (@ _let_1 M2)) B2))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (N2 tptp.nat) (B2 tptp.int) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.dvd_dvd_int (@ _let_1 N2)) B2) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.dvd_dvd_int (@ _let_1 M2)) B2))))))
% 4.71/5.18 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.dvd_dvd_nat (@ _let_1 M2)) (@ _let_1 N2))))))
% 4.71/5.18 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.dvd_dvd_real (@ _let_1 M2)) (@ _let_1 N2))))))
% 4.71/5.18 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.dvd_dvd_complex (@ _let_1 M2)) (@ _let_1 N2))))))
% 4.71/5.18 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.dvd_dvd_int (@ _let_1 M2)) (@ _let_1 N2))))))
% 4.71/5.18 (assert (forall ((X tptp.nat) (N2 tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat X) N2) (@ (@ tptp.modulo_modulo_nat Y) N2)) (exists ((Q1 tptp.nat) (Q22 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N2))) (= (@ (@ tptp.plus_plus_nat X) (@ _let_1 Q1)) (@ (@ tptp.plus_plus_nat Y) (@ _let_1 Q22))))))))
% 4.71/5.18 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N2) (=> (@ (@ tptp.dvd_dvd_nat M2) N2) (@ _let_1 M2))))))
% 4.71/5.18 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_nat M2) N2) (not (@ (@ tptp.dvd_dvd_nat N2) M2))))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (exists ((D5 tptp.nat) (X5 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ tptp.times_times_nat B2))) (let ((_let_3 (@ tptp.dvd_dvd_nat D5))) (and (@ _let_3 A) (@ _let_3 B2) (or (= (@ _let_1 X5) (@ (@ tptp.plus_plus_nat (@ _let_2 Y3)) D5)) (= (@ _let_2 X5) (@ (@ tptp.plus_plus_nat (@ _let_1 Y3)) D5))))))))))
% 4.71/5.18 (assert (forall ((D tptp.nat) (A tptp.nat) (B2 tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ tptp.times_times_nat B2))) (let ((_let_3 (@ tptp.dvd_dvd_nat D))) (=> (@ _let_3 A) (=> (@ _let_3 B2) (=> (or (= (@ _let_1 X) (@ (@ tptp.plus_plus_nat (@ _let_2 Y)) D)) (= (@ _let_2 X) (@ (@ 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) B2))) (let ((_let_3 (@ tptp.times_times_nat _let_2))) (let ((_let_4 (@ tptp.dvd_dvd_nat D))) (and (@ _let_4 A) (@ _let_4 _let_2) (or (= (@ _let_1 X5) (@ (@ tptp.plus_plus_nat (@ _let_3 Y3)) D)) (= (@ _let_3 X5) (@ (@ tptp.plus_plus_nat (@ _let_1 Y3)) D)))))))))))))))))
% 4.71/5.18 (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))))))))))
% 4.71/5.18 (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))))))))))
% 4.71/5.18 (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))))))))
% 4.71/5.18 (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))))))))
% 4.71/5.18 (assert (forall ((A2 tptp.set_complex) (N2 tptp.nat)) (=> (@ tptp.finite3207457112153483333omplex A2) (@ tptp.finite8712137658972009173omplex (@ tptp.collect_list_complex (lambda ((Xs3 tptp.list_complex)) (and (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs3)) A2) (= (@ tptp.size_s3451745648224563538omplex Xs3) N2))))))))
% 4.71/5.18 (assert (forall ((A2 tptp.set_Extended_enat) (N2 tptp.nat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (@ tptp.finite1862508098717546133d_enat (@ tptp.collec8433460942617342167d_enat (lambda ((Xs3 tptp.list_Extended_enat)) (and (@ (@ tptp.ord_le7203529160286727270d_enat (@ tptp.set_Extended_enat2 Xs3)) A2) (= (@ tptp.size_s3941691890525107288d_enat Xs3) N2))))))))
% 4.71/5.18 (assert (forall ((A2 tptp.set_VEBT_VEBT) (N2 tptp.nat)) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (@ tptp.finite3004134309566078307T_VEBT (@ tptp.collec5608196760682091941T_VEBT (lambda ((Xs3 tptp.list_VEBT_VEBT)) (and (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs3)) A2) (= (@ tptp.size_s6755466524823107622T_VEBT Xs3) N2))))))))
% 4.71/5.18 (assert (forall ((A2 tptp.set_nat) (N2 tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((Xs3 tptp.list_nat)) (and (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs3)) A2) (= (@ tptp.size_size_list_nat Xs3) N2))))))))
% 4.71/5.18 (assert (forall ((A2 tptp.set_int) (N2 tptp.nat)) (=> (@ tptp.finite_finite_int A2) (@ tptp.finite3922522038869484883st_int (@ tptp.collect_list_int (lambda ((Xs3 tptp.list_int)) (and (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs3)) A2) (= (@ tptp.size_size_list_int Xs3) N2))))))))
% 4.71/5.18 (assert (forall ((Va2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_1))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_2))) (let ((_let_8 (@ tptp.vEBT_vebt_buildup _let_2))) (let ((_let_9 (@ (@ tptp.dvd_dvd_nat _let_1) _let_2))) (and (=> _let_9 (= _let_8 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_9) (= _let_8 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4))))))))))))))))
% 4.71/5.18 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.modulo_modulo_nat A) B2)))))
% 4.71/5.18 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.modulo_modulo_int A) B2)))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) B2) (= (@ (@ tptp.modulo_modulo_nat A) B2) A)))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) B2) (= (@ (@ tptp.modulo_modulo_int A) B2) A)))))
% 4.71/5.18 (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))))
% 4.71/5.18 (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))))
% 4.71/5.18 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat tptp.one)) tptp.zero_zero_nat)))
% 4.71/5.18 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N2)) (@ tptp.numeral_numeral_int tptp.one)) tptp.zero_zero_int)))
% 4.71/5.18 (assert (forall ((A2 tptp.set_complex) (N2 tptp.nat)) (=> (@ tptp.finite3207457112153483333omplex A2) (@ tptp.finite8712137658972009173omplex (@ tptp.collect_list_complex (lambda ((Xs3 tptp.list_complex)) (and (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs3)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s3451745648224563538omplex Xs3)) N2))))))))
% 4.71/5.18 (assert (forall ((A2 tptp.set_Extended_enat) (N2 tptp.nat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (@ tptp.finite1862508098717546133d_enat (@ tptp.collec8433460942617342167d_enat (lambda ((Xs3 tptp.list_Extended_enat)) (and (@ (@ tptp.ord_le7203529160286727270d_enat (@ tptp.set_Extended_enat2 Xs3)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s3941691890525107288d_enat Xs3)) N2))))))))
% 4.71/5.18 (assert (forall ((A2 tptp.set_VEBT_VEBT) (N2 tptp.nat)) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (@ tptp.finite3004134309566078307T_VEBT (@ tptp.collec5608196760682091941T_VEBT (lambda ((Xs3 tptp.list_VEBT_VEBT)) (and (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs3)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT Xs3)) N2))))))))
% 4.71/5.18 (assert (forall ((A2 tptp.set_nat) (N2 tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((Xs3 tptp.list_nat)) (and (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs3)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs3)) N2))))))))
% 4.71/5.18 (assert (forall ((A2 tptp.set_int) (N2 tptp.nat)) (=> (@ tptp.finite_finite_int A2) (@ tptp.finite3922522038869484883st_int (@ tptp.collect_list_int (lambda ((Xs3 tptp.list_int)) (and (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs3)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs3)) N2))))))))
% 4.71/5.18 (assert (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B2) (@ (@ tptp.divide_divide_nat A) B2))) (@ (@ tptp.modulo_modulo_nat A) B2))) C) (@ (@ tptp.plus_plus_nat A) C))))
% 4.71/5.18 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) (@ (@ tptp.divide_divide_int A) B2))) (@ (@ tptp.modulo_modulo_int A) B2))) C) (@ (@ tptp.plus_plus_int A) C))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B2)) B2)) (@ (@ tptp.modulo_modulo_nat A) B2))) C) (@ (@ tptp.plus_plus_nat A) C))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B2)) B2)) (@ (@ tptp.modulo_modulo_int A) B2))) C) (@ (@ tptp.plus_plus_int A) C))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= A (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B2)) B2)) (@ (@ tptp.modulo_modulo_nat A) B2)))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B2)) B2)) (@ (@ tptp.modulo_modulo_int A) B2)))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B2)) B2)) (@ (@ tptp.modulo_modulo_nat A) B2)) A)))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B2)) B2)) (@ (@ tptp.modulo_modulo_int A) B2)) A)))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) B2)) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B2)) B2)) A)))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) B2)) (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B2)) B2)) A)))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) B2)) (@ (@ tptp.times_times_nat B2) (@ (@ tptp.divide_divide_nat A) B2))) A)))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) B2)) (@ (@ tptp.times_times_int B2) (@ (@ tptp.divide_divide_int A) B2))) A)))
% 4.71/5.18 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B2) (@ (@ tptp.divide_divide_nat A) B2))) (@ (@ tptp.modulo_modulo_nat A) B2)) A)))
% 4.71/5.18 (assert (forall ((B2 tptp.int) (A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) (@ (@ tptp.divide_divide_int A) B2))) (@ (@ tptp.modulo_modulo_int A) B2)) A)))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.divide_divide_nat (@ _let_1 B2)) C) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.divide_divide_nat B2) C))) (@ (@ tptp.divide_divide_nat (@ _let_1 (@ (@ tptp.modulo_modulo_nat B2) C))) C))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.divide_divide_int (@ _let_1 B2)) C) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.divide_divide_int B2) C))) (@ (@ tptp.divide_divide_int (@ _let_1 (@ (@ tptp.modulo_modulo_int B2) C))) C))))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (not (=> (not (= A tptp.zero_zero_nat)) (forall ((C2 tptp.nat)) (not (= B2 (@ (@ tptp.times_times_nat A) C2)))))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (not (=> (not (= A tptp.zero_zero_int)) (forall ((C2 tptp.int)) (not (= B2 (@ (@ tptp.times_times_int A) C2)))))))))
% 4.71/5.18 (assert (forall ((P (-> tptp.nat Bool)) (L tptp.nat)) (= (exists ((X4 tptp.nat)) (@ P (@ (@ tptp.times_times_nat L) X4))) (exists ((X4 tptp.nat)) (and (@ (@ tptp.dvd_dvd_nat L) (@ (@ tptp.plus_plus_nat X4) tptp.zero_zero_nat)) (@ P X4))))))
% 4.71/5.18 (assert (forall ((P (-> tptp.int Bool)) (L tptp.int)) (= (exists ((X4 tptp.int)) (@ P (@ (@ tptp.times_times_int L) X4))) (exists ((X4 tptp.int)) (and (@ (@ tptp.dvd_dvd_int L) (@ (@ tptp.plus_plus_int X4) tptp.zero_zero_int)) (@ P X4))))))
% 4.71/5.18 (assert (forall ((P (-> tptp.real Bool)) (L tptp.real)) (= (exists ((X4 tptp.real)) (@ P (@ (@ tptp.times_times_real L) X4))) (exists ((X4 tptp.real)) (and (@ (@ tptp.dvd_dvd_real L) (@ (@ tptp.plus_plus_real X4) tptp.zero_zero_real)) (@ P X4))))))
% 4.71/5.18 (assert (forall ((P (-> tptp.complex Bool)) (L tptp.complex)) (= (exists ((X4 tptp.complex)) (@ P (@ (@ tptp.times_times_complex L) X4))) (exists ((X4 tptp.complex)) (and (@ (@ tptp.dvd_dvd_complex L) (@ (@ tptp.plus_plus_complex X4) tptp.zero_zero_complex)) (@ P X4))))))
% 4.71/5.18 (assert (forall ((P (-> tptp.extended_enat Bool)) (L tptp.extended_enat)) (= (exists ((X4 tptp.extended_enat)) (@ P (@ (@ tptp.times_7803423173614009249d_enat L) X4))) (exists ((X4 tptp.extended_enat)) (and (@ (@ tptp.dvd_dv3785147216227455552d_enat L) (@ (@ tptp.plus_p3455044024723400733d_enat X4) tptp.zero_z5237406670263579293d_enat)) (@ P X4))))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B2) (= (= (@ (@ tptp.divide_divide_nat B2) A) C) (= B2 (@ (@ tptp.times_times_nat C) A)))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int A) B2) (= (= (@ (@ tptp.divide_divide_int B2) A) C) (= B2 (@ (@ tptp.times_times_int C) A)))))))
% 4.71/5.18 (assert (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (not (= B2 tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) A) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat A) B2)) C) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat C) B2)))))))
% 4.71/5.18 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B2 tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B2) A) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int A) B2)) C) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int C) B2)))))))
% 4.71/5.18 (assert (forall ((C tptp.nat) (B2 tptp.nat) (A tptp.nat)) (=> (not (= C tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat C) B2) (= (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.divide_divide_nat B2) C)) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) C)) B2))))))
% 4.71/5.18 (assert (forall ((C tptp.int) (B2 tptp.int) (A tptp.int)) (=> (not (= C tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int C) B2) (= (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.divide_divide_int B2) C)) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) B2))))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat) (D tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (not (= C tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B2) (=> (@ (@ tptp.dvd_dvd_nat C) D) (= (= (@ (@ tptp.divide_divide_nat B2) A) (@ (@ tptp.divide_divide_nat D) C)) (= (@ (@ tptp.times_times_nat B2) C) (@ (@ tptp.times_times_nat A) D)))))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int) (D tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (not (= C tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int A) B2) (=> (@ (@ tptp.dvd_dvd_int C) D) (= (= (@ (@ tptp.divide_divide_int B2) A) (@ (@ tptp.divide_divide_int D) C)) (= (@ (@ tptp.times_times_int B2) C) (@ (@ tptp.times_times_int A) D)))))))))
% 4.71/5.18 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (= (= (@ (@ tptp.divide_divide_nat A) B2) tptp.zero_zero_nat) (= A tptp.zero_zero_nat)))))
% 4.71/5.18 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (= (= (@ (@ tptp.divide_divide_int A) B2) tptp.zero_zero_int) (= A tptp.zero_zero_int)))))
% 4.71/5.18 (assert (forall ((B2 tptp.nat) (C tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat C) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.times_times_nat B2) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B2)) C)))))))
% 4.71/5.18 (assert (forall ((B2 tptp.int) (C tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int C) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.times_times_int B2) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B2)) C)))))))
% 4.71/5.18 (assert (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.divide_divide_nat B2) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B2)) C))))))
% 4.71/5.18 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.dvd_dvd_int C) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.divide_divide_int B2) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B2)) C))))))
% 4.71/5.18 (assert (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B2)) C) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) C)) B2)))))
% 4.71/5.18 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B2)) C) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) C)) B2)))))
% 4.71/5.18 (assert (forall ((C tptp.nat) (B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat B2) A) (= (@ _let_1 (@ (@ tptp.times_times_nat B2) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B2)) C)))))))
% 4.71/5.18 (assert (forall ((C tptp.int) (B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int C) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int B2) A) (= (@ _let_1 (@ (@ tptp.times_times_int B2) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B2)) C)))))))
% 4.71/5.18 (assert (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (= (= A (@ (@ tptp.divide_divide_nat C) B2)) (= (@ (@ tptp.times_times_nat A) B2) C)))))
% 4.71/5.18 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (= (= A (@ (@ tptp.divide_divide_int C) B2)) (= (@ (@ tptp.times_times_int A) B2) C)))))
% 4.71/5.18 (assert (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (= (= (@ (@ tptp.divide_divide_nat A) B2) C) (= A (@ (@ tptp.times_times_nat C) B2))))))
% 4.71/5.18 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (= (= (@ (@ tptp.divide_divide_int A) B2) C) (= A (@ (@ tptp.times_times_int C) B2))))))
% 4.71/5.18 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M2) N2)) N2))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (assert (forall ((A2 tptp.nat) (B tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (= (@ (@ tptp.modulo_modulo_nat A2) N2) tptp.zero_zero_nat) (=> (= (@ (@ tptp.modulo_modulo_nat B) N2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat A2) N2)) (@ (@ tptp.divide_divide_nat B) N2))))))))
% 4.71/5.18 (assert (forall ((M2 tptp.nat) (Q3 tptp.nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M2) Q3) (@ (@ tptp.modulo_modulo_nat N2) Q3)) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (not (forall ((S3 tptp.nat)) (not (= M2 (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.times_times_nat Q3) S3))))))))))
% 4.71/5.18 (assert (forall ((M2 tptp.nat) (Q3 tptp.nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M2) Q3) (@ (@ tptp.modulo_modulo_nat N2) Q3)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (not (forall ((S3 tptp.nat)) (not (= N2 (@ (@ tptp.plus_plus_nat M2) (@ (@ tptp.times_times_nat Q3) S3))))))))))
% 4.71/5.18 (assert (forall ((X tptp.nat) (N2 tptp.nat) (Y tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat X) N2) (@ (@ tptp.modulo_modulo_nat Y) N2)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (exists ((Q2 tptp.nat)) (= X (@ (@ tptp.plus_plus_nat Y) (@ (@ tptp.times_times_nat N2) Q2))))))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (Q3 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat M2))) (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 M2) N2)) Q3))) (@ _let_1 N2)))))))
% 4.71/5.18 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M2)) (@ _let_1 N2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.dvd_dvd_nat M2) N2))))))
% 4.71/5.18 (assert (forall ((K tptp.nat) (M2 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 M2)) (@ _let_1 N2)) (@ (@ tptp.dvd_dvd_nat M2) N2))))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (exists ((D5 tptp.nat) (X5 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat D5))) (and (@ _let_1 A) (@ _let_1 B2) (= (@ (@ tptp.times_times_nat A) X5) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B2) Y3)) D5))))))))
% 4.71/5.18 (assert (forall ((X tptp.nat) (Y tptp.vEBT_VEBT)) (let ((_let_1 (not (= Y (@ (@ tptp.vEBT_Leaf false) false))))) (=> (= (@ tptp.vEBT_vebt_buildup X) Y) (=> (=> (= X tptp.zero_zero_nat) _let_1) (=> (=> (= X (@ tptp.suc tptp.zero_zero_nat)) _let_1) (not (forall ((Va tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_1))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_2))) (let ((_let_8 (@ (@ tptp.dvd_dvd_nat _let_1) _let_2))) (=> (= X _let_2) (not (and (=> _let_8 (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_8) (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4)))))))))))))))))))))))
% 4.71/5.18 (assert (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 4.71/5.18 (assert (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 4.71/5.18 (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 ((B4 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat tptp.one_one_nat))) (=> (not (= B4 tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B4) tptp.one_one_nat) (=> (= (@ _let_1 A) B4) (=> (= (@ _let_1 B4) A) (=> (= (@ (@ tptp.times_times_nat A) B4) tptp.one_one_nat) (not (= (@ (@ tptp.divide_divide_nat C) A) (@ (@ tptp.times_times_nat C) B4)))))))))))))))
% 4.71/5.18 (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 ((B4 tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int tptp.one_one_int))) (=> (not (= B4 tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B4) tptp.one_one_int) (=> (= (@ _let_1 A) B4) (=> (= (@ _let_1 B4) A) (=> (= (@ (@ tptp.times_times_int A) B4) tptp.one_one_int) (not (= (@ (@ tptp.divide_divide_int C) A) (@ (@ tptp.times_times_int C) B4)))))))))))))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (= (@ (@ tptp.divide_divide_nat A) (@ (@ tptp.times_times_nat A) B2)) (@ (@ tptp.divide_divide_nat tptp.one_one_nat) B2))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (= (@ (@ tptp.divide_divide_int A) (@ (@ tptp.times_times_int A) B2)) (@ (@ tptp.divide_divide_int tptp.one_one_int) B2))))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (= (@ (@ tptp.divide_divide_nat A) (@ (@ tptp.times_times_nat B2) A)) (@ (@ tptp.divide_divide_nat tptp.one_one_nat) B2))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (= (@ (@ tptp.divide_divide_int A) (@ (@ tptp.times_times_int B2) A)) (@ (@ tptp.divide_divide_int tptp.one_one_int) B2))))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (not (@ _let_1 A)) (=> (not (@ _let_1 B2)) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B2)))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (not (@ _let_1 A)) (=> (not (@ _let_1 B2)) (@ _let_1 (@ (@ tptp.plus_plus_int A) B2)))))))
% 4.71/5.18 (assert (forall ((X tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat X))) (=> (not (= X tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M2)) (@ _let_1 N2)) (or (@ (@ tptp.dvd_dvd_nat X) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat M2) N2)))))))
% 4.71/5.18 (assert (forall ((X tptp.int) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X))) (=> (not (= X tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 M2)) (@ _let_1 N2)) (or (@ (@ tptp.dvd_dvd_int X) tptp.one_one_int) (@ (@ tptp.ord_less_eq_nat M2) N2)))))))
% 4.71/5.18 (assert (forall ((N2 tptp.nat) (X tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X tptp.one_one_nat)) (@ (@ tptp.dvd_dvd_nat X) (@ (@ tptp.power_power_nat X) N2)))))
% 4.71/5.18 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X tptp.one_one_real)) (@ (@ tptp.dvd_dvd_real X) (@ (@ tptp.power_power_real X) N2)))))
% 4.71/5.18 (assert (forall ((N2 tptp.nat) (X tptp.complex)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X tptp.one_one_complex)) (@ (@ tptp.dvd_dvd_complex X) (@ (@ tptp.power_power_complex X) N2)))))
% 4.71/5.18 (assert (forall ((N2 tptp.nat) (X tptp.int)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X tptp.one_one_int)) (@ (@ tptp.dvd_dvd_int X) (@ (@ tptp.power_power_int X) N2)))))
% 4.71/5.18 (assert (forall ((P (-> tptp.nat Bool)) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (= N2 tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.modulo_modulo_nat M2) N2)) (and (=> _let_1 (@ P M2)) (=> (not _let_1) (forall ((I3 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J2) N2) (=> (= M2 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N2) I3)) J2)) (@ P J2))))))))))
% 4.71/5.18 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat M2) N2)) M2) (= N2 tptp.one_one_nat)))))
% 4.71/5.18 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat N2) M2)) M2) (= N2 tptp.one_one_nat)))))
% 4.71/5.18 (assert (forall ((I tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M2)) (@ _let_1 N2)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) I) (@ (@ tptp.ord_less_eq_nat M2) N2))))))
% 4.71/5.18 (assert (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat A))) (let ((_let_2 (@ tptp.times_times_nat B2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (= (@ _let_1 (@ _let_2 C)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat A) B2)) C))) (@ _let_1 B2))))))))
% 4.71/5.18 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ tptp.times_times_int B2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (= (@ _let_1 (@ _let_2 C)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A) B2)) C))) (@ _let_1 B2))))))))
% 4.71/5.18 (assert (forall ((N2 tptp.nat) (Xs tptp.list_P6011104703257516679at_nat) (Ys tptp.list_P6011104703257516679at_nat)) (let ((_let_1 (@ tptp.size_s5460976970255530739at_nat Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_s5460976970255530739at_nat Xs)) _let_1)) (= (@ (@ tptp.nth_Pr6744343527793145070at_nat (@ (@ tptp.produc3544356994491977349at_nat Xs) Ys)) N2) (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_Pr7617993195940197384at_nat Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 4.71/5.18 (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))))))))
% 4.71/5.18 (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))))))))
% 4.71/5.18 (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))))))))
% 4.71/5.18 (assert (forall ((N2 tptp.nat) (Xs tptp.list_int) (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_int Xs)) _let_1)) (= (@ (@ tptp.nth_Pr3474266648193625910T_VEBT (@ (@ tptp.produc662631939642741121T_VEBT Xs) Ys)) N2) (@ (@ tptp.produc3329399203697025711T_VEBT (@ (@ tptp.nth_int Xs) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 4.71/5.18 (assert (forall ((N2 tptp.nat) (Xs tptp.list_int) (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_int Xs)) _let_1)) (= (@ (@ tptp.nth_Pr4439495888332055232nt_int (@ (@ tptp.product_int_int Xs) Ys)) N2) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.nth_int Xs) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_int Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 4.71/5.18 (assert (forall ((N2 tptp.nat) (Xs tptp.list_int) (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_int Xs)) _let_1)) (= (@ (@ tptp.nth_Pr8617346907841251940nt_nat (@ (@ tptp.product_int_nat Xs) Ys)) N2) (@ (@ tptp.product_Pair_int_nat (@ (@ tptp.nth_int Xs) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_nat Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 4.71/5.18 (assert (forall ((N2 tptp.nat) (Xs tptp.list_nat) (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_nat Xs)) _let_1)) (= (@ (@ tptp.nth_Pr744662078594809490T_VEBT (@ (@ tptp.produc7156399406898700509T_VEBT Xs) Ys)) N2) (@ (@ tptp.produc599794634098209291T_VEBT (@ (@ tptp.nth_nat Xs) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 4.71/5.18 (assert (forall ((N2 tptp.nat) (Xs tptp.list_nat) (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_nat Xs)) _let_1)) (= (@ (@ tptp.nth_Pr3440142176431000676at_int (@ (@ tptp.product_nat_int Xs) Ys)) N2) (@ (@ tptp.product_Pair_nat_int (@ (@ tptp.nth_nat Xs) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_int Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 4.71/5.18 (assert (forall ((N2 tptp.nat) (Xs tptp.list_nat) (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_nat Xs)) _let_1)) (= (@ (@ tptp.nth_Pr7617993195940197384at_nat (@ (@ tptp.product_nat_nat Xs) Ys)) N2) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.nth_nat Xs) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_nat Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 4.71/5.18 (assert (forall ((N2 tptp.nat) (A tptp.real) (B2 tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B2) N2))))))
% 4.71/5.18 (assert (forall ((N2 tptp.nat) (A tptp.int) (B2 tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B2) N2))))))
% 4.71/5.18 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M2) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.times_times_nat M2) N2))) M2) tptp.one_one_nat))))
% 4.71/5.18 (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))))
% 4.71/5.18 (assert (forall ((K tptp.nat) (M2 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 M2)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M2) N2))))))
% 4.71/5.18 (assert (forall ((M2 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 M2) A)) (or (@ _let_1 A) (= M2 tptp.zero_zero_nat))))))
% 4.71/5.18 (assert (forall ((M2 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 M2) A)) (or (@ _let_1 A) (= M2 tptp.zero_zero_nat))))))
% 4.71/5.18 (assert (forall ((M2 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 M2) A)) (and (@ _let_1 A) (not (= M2 tptp.zero_zero_nat)))))))
% 4.71/5.18 (assert (forall ((M2 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 M2) A)) (and (@ _let_1 A) (not (= M2 tptp.zero_zero_nat)))))))
% 4.71/5.18 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B2)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2) (=> (@ (@ tptp.ord_less_nat _let_2) B2) (= _let_2 (@ _let_1 B2))))))))
% 4.71/5.18 (assert (forall ((B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B2)))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_int _let_2) B2) (= _let_2 (@ _let_1 B2))))))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (assert (forall ((Uy tptp.option4927543243414619207at_nat) (V tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (= (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ (@ (@ tptp.vEBT_Node Uy) _let_1) TreeList2) S)) X) (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) _let_4))))))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (N2 tptp.nat) (M2 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 M2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M2)))) _let_2))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (N2 tptp.nat) (M2 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 M2)) (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M2)))) _let_2))))))
% 4.71/5.18 (assert (forall ((A tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)) (not (forall ((B4 tptp.nat)) (not (= A (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B4)) tptp.one_one_nat))))))))
% 4.71/5.18 (assert (forall ((A tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)) (not (forall ((B4 tptp.int)) (not (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B4)) tptp.one_one_int))))))))
% 4.71/5.18 (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))))))))
% 4.71/5.18 (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))))))))
% 4.71/5.18 (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))))))
% 4.71/5.18 (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))))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (assert (forall ((A2 tptp.nat) (B tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B) (=> (@ (@ 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 B) N2) tptp.zero_zero_nat)) tptp.one_one_nat) tptp.zero_zero_nat))) (@ (@ tptp.divide_divide_nat B) N2))))))
% 4.71/5.18 (assert (forall ((V tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Vd2)) X) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) _let_4))))))))
% 4.71/5.18 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (let ((_let_2 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.modulo_modulo_nat A) _let_3)) B2) (= (@ _let_2 (@ _let_1 _let_3)) (@ _let_1 B2)))))))))
% 4.71/5.18 (assert (forall ((B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (let ((_let_2 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.modulo_modulo_int A) _let_3)) B2) (= (@ _let_2 (@ _let_1 _let_3)) (@ _let_1 B2)))))))))
% 4.71/5.18 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Ma) X)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat X) Mi)))) (= (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList2) Summary)) X) (=> (not (= X Mi)) (=> (not (= X Ma)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) _let_4))))))))))))))))
% 4.71/5.18 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (V tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList2) Vc)) X) (or (= X Mi) (= X Ma) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) _let_4)))))))))
% 4.71/5.18 (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))))))))
% 4.71/5.18 (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))))))))
% 4.71/5.18 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2) Y) (=> (forall ((A4 Bool) (B4 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A4) B4)) (= Y (not (and (=> _let_2 A4) (=> (not _let_2) (and (=> _let_1 B4) _let_1))))))))) (=> (=> (exists ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2))) Y) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((S3 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ 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 Xa2) _let_1))) _let_3))))))))))))))
% 4.71/5.18 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2) (=> (forall ((A4 Bool) (B4 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A4) B4)) (not (and (=> _let_2 A4) (=> (not _let_2) (and (=> _let_1 B4) _let_1)))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((S3 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ 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 Xa2) _let_1))) _let_3))))))))))))
% 4.71/5.18 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2)) (=> (forall ((A4 Bool) (B4 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A4) B4)) (and (=> _let_2 A4) (=> (not _let_2) (and (=> _let_1 B4) _let_1))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2)))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((S3 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ 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 Xa2) _let_1))) _let_3))))))))))))
% 4.71/5.18 (assert (forall ((M2 tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat X))) (let ((_let_2 (@ _let_1 M2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_plus_nat _let_2) M2))))))))))
% 4.71/5.18 (assert (forall ((M2 tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int X))) (let ((_let_2 (@ _let_1 M2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) M2)))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_plus_int _let_2) M2))))))))))
% 4.71/5.18 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_membermima X) Xa2) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList3) Vc2))) (not (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3)))))))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vd tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList3) Vd))) (not (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3)))))))))))))
% 4.71/5.18 (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))))))))
% 4.71/5.18 (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))))))))
% 4.71/5.18 (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))))))))
% 4.71/5.18 (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))))))))
% 4.71/5.18 (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))))))))
% 4.71/5.18 (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))))))))
% 4.71/5.18 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member X) Xa2) (=> (forall ((A4 Bool) (B4 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A4) B4)) (not (and (=> _let_2 A4) (=> (not _let_2) (and (=> _let_1 B4) _let_1)))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList3) Summary2))) (not (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))))))
% 4.71/5.18 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X) Xa2) Y) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) Y) (=> (=> (exists ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2))) Y) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (= Y (not (or (= Xa2 Mi2) (= Xa2 Ma2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList3) Vc2))) (= Y (not (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vd tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList3) Vd))) (= Y (not (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))
% 4.71/5.18 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_membermima X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2)))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (or (= Xa2 Mi2) (= Xa2 Ma2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList3) Vc2))) (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vd tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList3) Vd))) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))
% 4.71/5.18 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList2) Summary))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ tptp.if_nat (@ (@ tptp.ord_less_nat X) Mi)))) (let ((_let_5 (@ (@ _let_4 Mi) X))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_6))) (= (@ (@ tptp.vEBT_vebt_insert _let_2) X) (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (not (or (= X Mi) (= X Ma))))) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_4 X) Mi)) (@ (@ tptp.ord_max_nat _let_5) Ma)))) _let_1) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) _let_6) (@ (@ tptp.vEBT_vebt_insert _let_7) (@ (@ tptp.vEBT_VEBT_low _let_5) _let_3)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_7)) (@ (@ tptp.vEBT_vebt_insert Summary) _let_6)) Summary))) _let_2)))))))))))
% 4.71/5.18 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_vebt_member X) Xa2)) (=> (forall ((A4 Bool) (B4 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A4) B4)) (and (=> _let_2 A4) (=> (not _let_2) (and (=> _let_1 B4) _let_1))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList3) Summary2))) (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))))))))
% 4.71/5.18 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_vebt_member X) Xa2) Y) (=> (forall ((A4 Bool) (B4 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A4) B4)) (= Y (not (and (=> _let_2 A4) (=> (not _let_2) (and (=> _let_1 B4) _let_1))))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) Y) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) Y) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) Y) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList3) Summary2))) (= Y (not (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))))))))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (let ((_let_2 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2) (=> (@ (@ tptp.ord_less_eq_nat B2) (@ (@ tptp.modulo_modulo_nat A) _let_3)) (= (@ (@ tptp.plus_plus_nat (@ _let_2 (@ _let_1 _let_3))) tptp.one_one_nat) (@ _let_1 B2))))))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (let ((_let_2 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_eq_int B2) (@ (@ tptp.modulo_modulo_int A) _let_3)) (= (@ (@ tptp.plus_plus_int (@ _let_2 (@ _let_1 _let_3))) tptp.one_one_int) (@ _let_1 B2))))))))))
% 4.71/5.18 (assert (forall ((N2 tptp.nat) (C tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z6 tptp.complex)) (= (@ (@ tptp.power_power_complex Z6) N2) C)))))))
% 4.71/5.18 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((Z6 tptp.real)) (= (@ (@ tptp.power_power_real Z6) N2) tptp.one_one_real)))))))
% 4.71/5.18 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z6 tptp.complex)) (= (@ (@ tptp.power_power_complex Z6) N2) tptp.one_one_complex)))))))
% 4.71/5.18 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_insert X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A4 Bool) (B4 Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A4))) (let ((_let_2 (@ _let_1 B4))) (let ((_let_3 (= Xa2 tptp.one_one_nat))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_2) (=> (and (=> _let_4 (= Y (@ (@ tptp.vEBT_Leaf true) B4))) (=> (not _let_4) (and (=> _let_3 (= Y (@ _let_1 true))) (=> (not _let_3) (= Y _let_2))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2)))))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts2) S3))) (=> (= X _let_1) (=> (= Y _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S3))) (=> (= X _let_1) (=> (= Y _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc V2)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Summary2))) (=> (= X _let_2) (=> (= Y (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Xa2) Xa2))) _let_1) TreeList3) Summary2)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2)))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_5 (@ (@ _let_4 Mi2) Xa2))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_6))) (=> (= X _let_2) (=> (= Y (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_4 Xa2) Mi2)) (@ (@ tptp.ord_max_nat _let_5) Ma2)))) _let_1) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList3) _let_6) (@ (@ tptp.vEBT_vebt_insert _let_7) (@ (@ tptp.vEBT_VEBT_low _let_5) _let_3)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_7)) (@ (@ tptp.vEBT_vebt_insert Summary2) _let_6)) Summary2))) _let_2)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))))
% 4.71/5.18 (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))))))))
% 4.71/5.18 (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))))))))
% 4.71/5.18 (assert (forall ((I6 tptp.set_real) (X (-> tptp.real tptp.nat)) (Y (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I6) (not (= (@ X I3) tptp.one_one_nat)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I6) (not (= (@ Y I3) tptp.one_one_nat)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I6) (not (= (@ (@ tptp.times_times_nat (@ X I3)) (@ Y I3)) tptp.one_one_nat))))))))))
% 4.71/5.18 (assert (forall ((I6 tptp.set_nat) (X (-> tptp.nat tptp.nat)) (Y (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I6) (not (= (@ X I3) tptp.one_one_nat)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I6) (not (= (@ Y I3) tptp.one_one_nat)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I6) (not (= (@ (@ tptp.times_times_nat (@ X I3)) (@ Y I3)) tptp.one_one_nat))))))))))
% 4.71/5.18 (assert (forall ((I6 tptp.set_complex) (X (-> tptp.complex tptp.nat)) (Y (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I3 tptp.complex)) (and (@ (@ tptp.member_complex I3) I6) (not (= (@ X I3) tptp.one_one_nat)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I3 tptp.complex)) (and (@ (@ tptp.member_complex I3) I6) (not (= (@ Y I3) tptp.one_one_nat)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I3 tptp.complex)) (and (@ (@ tptp.member_complex I3) I6) (not (= (@ (@ tptp.times_times_nat (@ X I3)) (@ Y I3)) tptp.one_one_nat))))))))))
% 4.71/5.18 (assert (forall ((I6 tptp.set_int) (X (-> tptp.int tptp.nat)) (Y (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.member_int I3) I6) (not (= (@ X I3) tptp.one_one_nat)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.member_int I3) I6) (not (= (@ Y I3) tptp.one_one_nat)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.member_int I3) I6) (not (= (@ (@ tptp.times_times_nat (@ X I3)) (@ Y I3)) tptp.one_one_nat))))))))))
% 4.71/5.18 (assert (forall ((I6 tptp.set_Extended_enat) (X (-> tptp.extended_enat tptp.nat)) (Y (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I3 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I3) I6) (not (= (@ X I3) tptp.one_one_nat)))))) (=> (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I3 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I3) I6) (not (= (@ Y I3) tptp.one_one_nat)))))) (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I3 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I3) I6) (not (= (@ (@ tptp.times_times_nat (@ X I3)) (@ Y I3)) tptp.one_one_nat))))))))))
% 4.71/5.18 (assert (forall ((I6 tptp.set_real) (X (-> tptp.real tptp.int)) (Y (-> tptp.real tptp.int))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I6) (not (= (@ X I3) tptp.one_one_int)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I6) (not (= (@ Y I3) tptp.one_one_int)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I6) (not (= (@ (@ tptp.times_times_int (@ X I3)) (@ Y I3)) tptp.one_one_int))))))))))
% 4.71/5.18 (assert (forall ((I6 tptp.set_nat) (X (-> tptp.nat tptp.int)) (Y (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I6) (not (= (@ X I3) tptp.one_one_int)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I6) (not (= (@ Y I3) tptp.one_one_int)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I6) (not (= (@ (@ tptp.times_times_int (@ X I3)) (@ Y I3)) tptp.one_one_int))))))))))
% 4.71/5.18 (assert (forall ((I6 tptp.set_complex) (X (-> tptp.complex tptp.int)) (Y (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I3 tptp.complex)) (and (@ (@ tptp.member_complex I3) I6) (not (= (@ X I3) tptp.one_one_int)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I3 tptp.complex)) (and (@ (@ tptp.member_complex I3) I6) (not (= (@ Y I3) tptp.one_one_int)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I3 tptp.complex)) (and (@ (@ tptp.member_complex I3) I6) (not (= (@ (@ tptp.times_times_int (@ X I3)) (@ Y I3)) tptp.one_one_int))))))))))
% 4.71/5.18 (assert (forall ((I6 tptp.set_int) (X (-> tptp.int tptp.int)) (Y (-> tptp.int tptp.int))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.member_int I3) I6) (not (= (@ X I3) tptp.one_one_int)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.member_int I3) I6) (not (= (@ Y I3) tptp.one_one_int)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.member_int I3) I6) (not (= (@ (@ tptp.times_times_int (@ X I3)) (@ Y I3)) tptp.one_one_int))))))))))
% 4.71/5.18 (assert (forall ((I6 tptp.set_Extended_enat) (X (-> tptp.extended_enat tptp.int)) (Y (-> tptp.extended_enat tptp.int))) (=> (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I3 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I3) I6) (not (= (@ X I3) tptp.one_one_int)))))) (=> (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I3 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I3) I6) (not (= (@ Y I3) tptp.one_one_int)))))) (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I3 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I3) I6) (not (= (@ (@ tptp.times_times_int (@ X I3)) (@ Y I3)) tptp.one_one_int))))))))))
% 4.71/5.18 (assert (forall ((I6 tptp.set_real) (X (-> tptp.real tptp.nat)) (Y (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I6) (not (= (@ X I3) tptp.zero_zero_nat)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I6) (not (= (@ Y I3) tptp.zero_zero_nat)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I6) (not (= (@ (@ tptp.plus_plus_nat (@ X I3)) (@ Y I3)) tptp.zero_zero_nat))))))))))
% 4.71/5.18 (assert (forall ((I6 tptp.set_nat) (X (-> tptp.nat tptp.nat)) (Y (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I6) (not (= (@ X I3) tptp.zero_zero_nat)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I6) (not (= (@ Y I3) tptp.zero_zero_nat)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I6) (not (= (@ (@ tptp.plus_plus_nat (@ X I3)) (@ Y I3)) tptp.zero_zero_nat))))))))))
% 4.71/5.18 (assert (forall ((I6 tptp.set_complex) (X (-> tptp.complex tptp.nat)) (Y (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I3 tptp.complex)) (and (@ (@ tptp.member_complex I3) I6) (not (= (@ X I3) tptp.zero_zero_nat)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I3 tptp.complex)) (and (@ (@ tptp.member_complex I3) I6) (not (= (@ Y I3) tptp.zero_zero_nat)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I3 tptp.complex)) (and (@ (@ tptp.member_complex I3) I6) (not (= (@ (@ tptp.plus_plus_nat (@ X I3)) (@ Y I3)) tptp.zero_zero_nat))))))))))
% 4.71/5.18 (assert (forall ((I6 tptp.set_int) (X (-> tptp.int tptp.nat)) (Y (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.member_int I3) I6) (not (= (@ X I3) tptp.zero_zero_nat)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.member_int I3) I6) (not (= (@ Y I3) tptp.zero_zero_nat)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.member_int I3) I6) (not (= (@ (@ tptp.plus_plus_nat (@ X I3)) (@ Y I3)) tptp.zero_zero_nat))))))))))
% 4.71/5.18 (assert (forall ((I6 tptp.set_Extended_enat) (X (-> tptp.extended_enat tptp.nat)) (Y (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I3 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I3) I6) (not (= (@ X I3) tptp.zero_zero_nat)))))) (=> (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I3 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I3) I6) (not (= (@ Y I3) tptp.zero_zero_nat)))))) (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I3 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I3) I6) (not (= (@ (@ tptp.plus_plus_nat (@ X I3)) (@ Y I3)) tptp.zero_zero_nat))))))))))
% 4.71/5.18 (assert (forall ((I6 tptp.set_real) (X (-> tptp.real tptp.real)) (Y (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I6) (not (= (@ X I3) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I6) (not (= (@ Y I3) tptp.zero_zero_real)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I6) (not (= (@ (@ tptp.plus_plus_real (@ X I3)) (@ Y I3)) tptp.zero_zero_real))))))))))
% 4.71/5.18 (assert (forall ((I6 tptp.set_nat) (X (-> tptp.nat tptp.real)) (Y (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I6) (not (= (@ X I3) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I6) (not (= (@ Y I3) tptp.zero_zero_real)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I6) (not (= (@ (@ tptp.plus_plus_real (@ X I3)) (@ Y I3)) tptp.zero_zero_real))))))))))
% 4.71/5.18 (assert (forall ((I6 tptp.set_complex) (X (-> tptp.complex tptp.real)) (Y (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I3 tptp.complex)) (and (@ (@ tptp.member_complex I3) I6) (not (= (@ X I3) tptp.zero_zero_real)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I3 tptp.complex)) (and (@ (@ tptp.member_complex I3) I6) (not (= (@ Y I3) tptp.zero_zero_real)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I3 tptp.complex)) (and (@ (@ tptp.member_complex I3) I6) (not (= (@ (@ tptp.plus_plus_real (@ X I3)) (@ Y I3)) tptp.zero_zero_real))))))))))
% 4.71/5.18 (assert (forall ((I6 tptp.set_int) (X (-> tptp.int tptp.real)) (Y (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.member_int I3) I6) (not (= (@ X I3) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.member_int I3) I6) (not (= (@ Y I3) tptp.zero_zero_real)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.member_int I3) I6) (not (= (@ (@ tptp.plus_plus_real (@ X I3)) (@ Y I3)) tptp.zero_zero_real))))))))))
% 4.71/5.18 (assert (forall ((I6 tptp.set_Extended_enat) (X (-> tptp.extended_enat tptp.real)) (Y (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I3 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I3) I6) (not (= (@ X I3) tptp.zero_zero_real)))))) (=> (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I3 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I3) I6) (not (= (@ Y I3) tptp.zero_zero_real)))))) (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I3 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I3) I6) (not (= (@ (@ tptp.plus_plus_real (@ X I3)) (@ Y I3)) tptp.zero_zero_real))))))))))
% 4.71/5.18 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_vebt_member X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A4 Bool) (B4 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A4) B4))) (let ((_let_2 (= Xa2 tptp.one_one_nat))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_1) (=> (= Y (and (=> _let_3 A4) (=> (not _let_3) (and (=> _let_2 B4) _let_2)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_7 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (= X _let_2) (=> (= Y (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_7 (=> _let_7 (and _let_6 (=> _let_6 (and (=> _let_5 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5)))))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))))
% 4.71/5.18 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_vebt_member X) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A4 Bool) (B4 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A4) B4))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (and (=> _let_2 A4) (=> (not _let_2) (and (=> _let_1 B4) _let_1))))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Summary2))) (=> (= X _let_7) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_7) Xa2)) (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))))))))))))
% 4.71/5.18 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member X) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A4 Bool) (B4 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A4) B4))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (=> _let_2 A4) (=> (not _let_2) (and (=> _let_1 B4) _let_1)))))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Summary2))) (=> (= X _let_7) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_7) Xa2)) (not (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))))))))))
% 4.71/5.18 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat M2) N2) (=> (@ (@ tptp.dvd_dvd_nat N2) M2) (= M2 N2)))))
% 4.71/5.18 (assert (forall ((M2 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 M2) A)) (not (= (@ _let_1 A) (= M2 tptp.zero_zero_nat)))))))
% 4.71/5.18 (assert (forall ((M2 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 M2) A)) (not (= (@ _let_1 A) (= M2 tptp.zero_zero_nat)))))))
% 4.71/5.18 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A4 Bool) (B4 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A4) B4))) (let ((_let_2 (= Xa2 tptp.one_one_nat))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_1) (=> (= Y (and (=> _let_3 A4) (=> (not _let_3) (and (=> _let_2 B4) _let_2)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (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 Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (= X _let_2) (=> (= Y (and (=> _let_5 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))
% 4.71/5.18 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A4 Bool) (B4 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A4) B4))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (=> _let_2 A4) (=> (not _let_2) (and (=> _let_1 B4) _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 Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList3) S3))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (not (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))
% 4.71/5.18 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A4 Bool) (B4 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A4) B4))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (and (=> _let_2 A4) (=> (not _let_2) (and (=> _let_1 B4) _let_1))))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (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 Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList3) S3))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))
% 4.71/5.18 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (=> (= X _let_1) (=> (= Y (or (= Xa2 Mi2) (= Xa2 Ma2))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Vc2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (= X _let_2) (=> (= Y (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_5 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Vd))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (= X _let_2) (=> (= Y (and (=> _let_5 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))
% 4.71/5.18 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_membermima X) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)) (or (= Xa2 Mi2) (= Xa2 Ma2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Vc2))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4)))))))))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Vd))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))))
% 4.71/5.18 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_membermima X) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Vc2))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (not (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Vd))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (not (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4)))))))))))))))))
% 4.71/5.18 (assert (= (@ tptp.arcosh_real tptp.one_one_real) tptp.zero_zero_real))
% 4.71/5.18 (assert (= (@ tptp.arsinh_real tptp.zero_zero_real) tptp.zero_zero_real))
% 4.71/5.18 (assert (= (@ tptp.artanh_real tptp.zero_zero_real) tptp.zero_zero_real))
% 4.71/5.18 (assert (forall ((X tptp.nat) (Y tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.accp_nat tptp.vEBT_v4011308405150292612up_rel))) (let ((_let_3 (= Y (@ (@ tptp.vEBT_Leaf false) false)))) (=> (= (@ tptp.vEBT_vebt_buildup X) Y) (=> (@ _let_2 X) (=> (=> (= X tptp.zero_zero_nat) (=> _let_3 (not (@ _let_2 tptp.zero_zero_nat)))) (=> (=> (= X _let_1) (=> _let_3 (not (@ _let_2 _let_1)))) (not (forall ((Va tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) _let_2))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_2))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1))) (let ((_let_8 (@ (@ tptp.dvd_dvd_nat _let_2) _let_1))) (=> (= X _let_1) (=> (and (=> _let_8 (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_8) (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4))))) (not (@ (@ tptp.accp_nat tptp.vEBT_v4011308405150292612up_rel) _let_1)))))))))))))))))))))))
% 4.71/5.18 (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)))))))
% 4.71/5.18 (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)))))))
% 4.71/5.18 (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))))))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (M2 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 M2))) _let_4)) (or (@ (@ tptp.ord_less_nat N2) M2) (= _let_4 tptp.zero_zero_nat) (and (@ (@ tptp.ord_less_eq_nat M2) N2) (@ _let_3 (@ (@ tptp.divide_divide_nat A) (@ _let_2 (@ (@ tptp.minus_minus_nat N2) M2)))))))))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (M2 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 M2))) _let_4)) (or (@ (@ tptp.ord_less_nat N2) M2) (= _let_4 tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_nat M2) N2) (@ _let_3 (@ (@ tptp.divide_divide_int A) (@ _let_2 (@ (@ tptp.minus_minus_nat N2) M2)))))))))))))
% 4.71/5.18 (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))))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) A) tptp.zero_zero_complex)))
% 4.71/5.18 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) A) tptp.zero_zero_int)))
% 4.71/5.18 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) A) tptp.zero_zero_real)))
% 4.71/5.18 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) tptp.zero_zero_complex) A)))
% 4.71/5.18 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) tptp.zero_zero_int) A)))
% 4.71/5.18 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) tptp.zero_zero_real) A)))
% 4.71/5.18 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 4.71/5.18 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) tptp.zero_zero_complex) A)))
% 4.71/5.18 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) tptp.zero_zero_nat) A)))
% 4.71/5.18 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) tptp.zero_zero_int) A)))
% 4.71/5.18 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) tptp.zero_zero_real) A)))
% 4.71/5.18 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) A) tptp.zero_zero_complex)))
% 4.71/5.18 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) A) tptp.zero_zero_nat)))
% 4.71/5.18 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) A) tptp.zero_zero_int)))
% 4.71/5.18 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) A) tptp.zero_zero_real)))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B2)) B2) A)))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B2)) B2) A)))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B2)) B2) A)))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B2)) B2) A)))
% 4.71/5.18 (assert (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.minus_minus_nat A) B2)))))
% 4.71/5.18 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (= (@ (@ tptp.minus_minus_int (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.minus_minus_int A) B2)))))
% 4.71/5.18 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (= (@ (@ tptp.minus_minus_real (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.minus_minus_real A) B2)))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B2)) A) B2)))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B2)) A) B2)))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B2)) A) B2)))
% 4.71/5.18 (assert (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B2) C)) (@ (@ tptp.minus_minus_nat A) B2))))
% 4.71/5.18 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B2) C)) (@ (@ tptp.minus_minus_int A) B2))))
% 4.71/5.18 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B2) C)) (@ (@ tptp.minus_minus_real A) B2))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B2)) B2) A)))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B2)) B2) A)))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B2)) B2) A)))
% 4.71/5.18 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M2)) (@ tptp.suc N2)) (@ (@ tptp.minus_minus_nat M2) N2))))
% 4.71/5.18 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat (@ tptp.suc M2)) N2)) (@ tptp.suc K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat M2) N2)) K))))
% 4.71/5.18 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) N2) tptp.zero_zero_nat)))
% 4.71/5.18 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat M2) M2) tptp.zero_zero_nat)))
% 4.71/5.18 (assert (forall ((I tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat I) N2) (= (@ _let_1 (@ _let_1 I)) I)))))
% 4.71/5.18 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ _let_1 (@ (@ tptp.plus_plus_nat J) K))))))
% 4.71/5.18 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.zero_n3304061248610475627l_real P)) (@ tptp.zero_n3304061248610475627l_real Q)) (=> P Q))))
% 4.71/5.18 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)) (=> P Q))))
% 4.71/5.18 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)) (=> P Q))))
% 4.71/5.18 (assert (= (@ tptp.zero_n3304061248610475627l_real false) tptp.zero_zero_real))
% 4.71/5.18 (assert (= (@ tptp.zero_n1201886186963655149omplex false) tptp.zero_zero_complex))
% 4.71/5.18 (assert (= (@ tptp.zero_n1046097342994218471d_enat false) tptp.zero_z5237406670263579293d_enat))
% 4.71/5.18 (assert (= (@ tptp.zero_n2687167440665602831ol_nat false) tptp.zero_zero_nat))
% 4.71/5.18 (assert (= (@ tptp.zero_n2684676970156552555ol_int false) tptp.zero_zero_int))
% 4.71/5.18 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n3304061248610475627l_real P) tptp.zero_zero_real) (not P))))
% 4.71/5.18 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n1201886186963655149omplex P) tptp.zero_zero_complex) (not P))))
% 4.71/5.18 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n1046097342994218471d_enat P) tptp.zero_z5237406670263579293d_enat) (not P))))
% 4.71/5.18 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P) tptp.zero_zero_nat) (not P))))
% 4.71/5.18 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P) tptp.zero_zero_int) (not P))))
% 4.71/5.18 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.zero_n1046097342994218471d_enat P)) (@ tptp.zero_n1046097342994218471d_enat Q)) (and (not P) Q))))
% 4.71/5.18 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_real (@ tptp.zero_n3304061248610475627l_real P)) (@ tptp.zero_n3304061248610475627l_real Q)) (and (not P) Q))))
% 4.71/5.18 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)) (and (not P) Q))))
% 4.71/5.18 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)) (and (not P) Q))))
% 4.71/5.18 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n1201886186963655149omplex P) tptp.one_one_complex) P)))
% 4.71/5.18 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n3304061248610475627l_real P) tptp.one_one_real) P)))
% 4.71/5.18 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P) tptp.one_one_nat) P)))
% 4.71/5.18 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P) tptp.one_one_int) P)))
% 4.71/5.18 (assert (= (@ tptp.zero_n1201886186963655149omplex true) tptp.one_one_complex))
% 4.71/5.18 (assert (= (@ tptp.zero_n3304061248610475627l_real true) tptp.one_one_real))
% 4.71/5.18 (assert (= (@ tptp.zero_n2687167440665602831ol_nat true) tptp.one_one_nat))
% 4.71/5.18 (assert (= (@ tptp.zero_n2684676970156552555ol_int true) tptp.one_one_int))
% 4.71/5.18 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_ri631733984087533419it_int N2) tptp.zero_zero_int) tptp.zero_zero_int)))
% 4.71/5.18 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n2687167440665602831ol_nat (or P Q)) (@ (@ tptp.ord_max_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)))))
% 4.71/5.18 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n2684676970156552555ol_int (or P Q)) (@ (@ tptp.ord_max_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real A) B2)) (@ (@ tptp.ord_less_eq_real B2) A))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int A) B2)) (@ (@ tptp.ord_less_eq_int B2) A))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real A) B2)) (@ (@ tptp.ord_less_real B2) A))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int A) B2)) (@ (@ tptp.ord_less_int B2) A))))
% 4.71/5.18 (assert (forall ((B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B2) A) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B2)) B2) A))))
% 4.71/5.18 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B2) A) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat A) B2)) B2) A))))
% 4.71/5.18 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B2) A) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B2)) B2) A))))
% 4.71/5.18 (assert (forall ((B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B2) A) (= (@ (@ tptp.plus_plus_real B2) (@ (@ tptp.minus_minus_real A) B2)) A))))
% 4.71/5.18 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B2) A) (= (@ (@ tptp.plus_plus_nat B2) (@ (@ tptp.minus_minus_nat A) B2)) A))))
% 4.71/5.18 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B2) A) (= (@ (@ tptp.plus_plus_int B2) (@ (@ tptp.minus_minus_int A) B2)) A))))
% 4.71/5.18 (assert (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) tptp.one_one_complex) tptp.zero_zero_complex))
% 4.71/5.18 (assert (= (@ (@ tptp.minus_minus_int tptp.one_one_int) tptp.one_one_int) tptp.zero_zero_int))
% 4.71/5.18 (assert (= (@ (@ tptp.minus_minus_real tptp.one_one_real) tptp.one_one_real) tptp.zero_zero_real))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.plus_plus_nat A) B2)) tptp.zero_zero_nat)))
% 4.71/5.18 (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))))))
% 4.71/5.18 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int A) B2)) C) (@ (@ tptp.minus_minus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B2) C))))))))
% 4.71/5.18 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.zero_n3304061248610475627l_real P)) P)))
% 4.71/5.18 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.zero_n2687167440665602831ol_nat P)) P)))
% 4.71/5.18 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.zero_n2684676970156552555ol_int P)) P)))
% 4.71/5.18 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) M2)) (@ (@ tptp.ord_less_nat M2) N2))))
% 4.71/5.18 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ (@ tptp.minus_minus_nat M2) N2) tptp.zero_zero_nat))))
% 4.71/5.18 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.minus_minus_nat M2) N2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat M2) N2))))
% 4.71/5.18 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_real (@ tptp.zero_n3304061248610475627l_real P)) tptp.one_one_real) (not P))))
% 4.71/5.18 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.zero_n2687167440665602831ol_nat P)) tptp.one_one_nat) (not P))))
% 4.71/5.18 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_int (@ tptp.zero_n2684676970156552555ol_int P)) tptp.one_one_int) (not P))))
% 4.71/5.18 (assert (forall ((P Bool)) (= (@ tptp.zero_n1201886186963655149omplex (not P)) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.zero_n1201886186963655149omplex P)))))
% 4.71/5.18 (assert (forall ((P Bool)) (= (@ tptp.zero_n3304061248610475627l_real (not P)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ tptp.zero_n3304061248610475627l_real P)))))
% 4.71/5.18 (assert (forall ((P Bool)) (= (@ tptp.zero_n2684676970156552555ol_int (not P)) (@ (@ tptp.minus_minus_int tptp.one_one_int) (@ tptp.zero_n2684676970156552555ol_int P)))))
% 4.71/5.18 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat I) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat I) K)) J)))))
% 4.71/5.18 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J) K)) I) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J) I)) K)))))
% 4.71/5.18 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I))) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ _let_1 (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K))))))
% 4.71/5.18 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N2)) tptp.one_one_nat) N2)))
% 4.71/5.18 (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)))))))
% 4.71/5.18 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N2)) tptp.one_one_int) tptp.one_one_int)))
% 4.71/5.18 (assert (= (@ tptp.nat_set_encode tptp.bot_bot_set_nat) tptp.zero_zero_nat))
% 4.71/5.18 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (= (@ tptp.nat_set_decode (@ tptp.nat_set_encode A2)) A2))))
% 4.71/5.18 (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))))
% 4.71/5.18 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc (@ (@ tptp.minus_minus_nat J) K))) I) (@ (@ tptp.minus_minus_nat (@ tptp.suc J)) (@ (@ tptp.plus_plus_nat K) I))))))
% 4.71/5.18 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat I) (@ tptp.suc (@ (@ tptp.minus_minus_nat J) K))) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat I) K)) (@ tptp.suc J))))))
% 4.71/5.18 (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))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.minus_minus_int A) B2)) (@ _let_1 (@ (@ tptp.plus_plus_int A) B2))))))
% 4.71/5.18 (assert (forall ((B2 Bool)) (= (@ (@ tptp.divide_divide_nat (@ tptp.zero_n2687167440665602831ol_nat B2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat)))
% 4.71/5.18 (assert (forall ((B2 Bool)) (= (@ (@ tptp.divide_divide_int (@ tptp.zero_n2684676970156552555ol_int B2)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int)))
% 4.71/5.18 (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))))
% 4.71/5.18 (assert (forall ((M2 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 M2) N2)) (or (@ (@ tptp.ord_less_nat M2) N2) (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N2)))))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (assert (forall ((P5 Bool) (Q3 Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P5) (@ tptp.zero_n2687167440665602831ol_nat Q3)) (= P5 Q3))))
% 4.71/5.18 (assert (forall ((P5 Bool) (Q3 Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P5) (@ tptp.zero_n2684676970156552555ol_int Q3)) (= P5 Q3))))
% 4.71/5.18 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ (@ tptp.minus_minus_nat (@ _let_1 K)) J)))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat A))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 C)) B2) (@ (@ tptp.minus_minus_nat (@ _let_1 B2)) C)))))
% 4.71/5.18 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (= (@ (@ tptp.minus_minus_int (@ _let_1 C)) B2) (@ (@ tptp.minus_minus_int (@ _let_1 B2)) C)))))
% 4.71/5.18 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (= (@ (@ tptp.minus_minus_real (@ _let_1 C)) B2) (@ (@ tptp.minus_minus_real (@ _let_1 B2)) C)))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B2) (@ (@ tptp.minus_minus_int C) D)) (= (= A B2) (= C D)))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A) B2) (@ (@ tptp.minus_minus_real C) D)) (= (= A B2) (= C D)))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n1201886186963655149omplex (and P Q)) (@ (@ tptp.times_times_complex (@ tptp.zero_n1201886186963655149omplex P)) (@ tptp.zero_n1201886186963655149omplex Q)))))
% 4.71/5.18 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n1046097342994218471d_enat (and P Q)) (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.zero_n1046097342994218471d_enat P)) (@ tptp.zero_n1046097342994218471d_enat Q)))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real) (D tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_eq_real D) C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B2) D))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int) (D tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (@ (@ tptp.ord_less_eq_int D) C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B2) D))))))
% 4.71/5.18 (assert (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real C))) (=> (@ (@ tptp.ord_less_eq_real B2) A) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B2))))))
% 4.71/5.18 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int C))) (=> (@ (@ tptp.ord_less_eq_int B2) A) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B2))))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B2) C)))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B2) C)))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A) B2) (@ (@ tptp.minus_minus_real C) D)) (= (@ (@ tptp.ord_less_eq_real A) B2) (@ (@ tptp.ord_less_eq_real C) D)))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B2) (@ (@ tptp.minus_minus_int C) D)) (= (@ (@ tptp.ord_less_eq_int A) B2) (@ (@ tptp.ord_less_eq_int C) D)))))
% 4.71/5.18 (assert (= (lambda ((Y4 tptp.complex) (Z2 tptp.complex)) (= Y4 Z2)) (lambda ((A3 tptp.complex) (B3 tptp.complex)) (= (@ (@ tptp.minus_minus_complex A3) B3) tptp.zero_zero_complex))))
% 4.71/5.18 (assert (= (lambda ((Y4 tptp.int) (Z2 tptp.int)) (= Y4 Z2)) (lambda ((A3 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.minus_minus_int A3) B3) tptp.zero_zero_int))))
% 4.71/5.18 (assert (= (lambda ((Y4 tptp.real) (Z2 tptp.real)) (= Y4 Z2)) (lambda ((A3 tptp.real) (B3 tptp.real)) (= (@ (@ tptp.minus_minus_real A3) B3) tptp.zero_zero_real))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real) (D tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.ord_less_real D) C) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B2) D))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int) (D tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B2) (=> (@ (@ tptp.ord_less_int D) C) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B2) D))))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A) B2) (@ (@ tptp.minus_minus_real C) D)) (= (@ (@ tptp.ord_less_real A) B2) (@ (@ tptp.ord_less_real C) D)))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B2) (@ (@ tptp.minus_minus_int C) D)) (= (@ (@ tptp.ord_less_int A) B2) (@ (@ tptp.ord_less_int C) D)))))
% 4.71/5.18 (assert (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real C))) (=> (@ (@ tptp.ord_less_real B2) A) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B2))))))
% 4.71/5.18 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int C))) (=> (@ (@ tptp.ord_less_int B2) A) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B2))))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B2) C)))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B2) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B2) C)))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat B2) C)) (@ (@ tptp.minus_minus_nat (@ _let_1 B2)) (@ _let_1 C))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B2) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B2)) (@ _let_1 C))))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B2) C)) (@ (@ tptp.minus_minus_real (@ _let_1 B2)) (@ _let_1 C))))))
% 4.71/5.18 (assert (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ (@ tptp.minus_minus_complex B2) C)) (@ (@ tptp.minus_minus_complex (@ _let_1 B2)) (@ _let_1 C))))))
% 4.71/5.18 (assert (forall ((B2 tptp.nat) (C tptp.nat) (A tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat B2) C)) A) (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat B2) A)) (@ (@ tptp.times_times_nat C) A)))))
% 4.71/5.18 (assert (forall ((B2 tptp.int) (C tptp.int) (A tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B2) C)) A) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int B2) A)) (@ (@ tptp.times_times_int C) A)))))
% 4.71/5.18 (assert (forall ((B2 tptp.real) (C tptp.real) (A tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B2) C)) A) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real B2) A)) (@ (@ tptp.times_times_real C) A)))))
% 4.71/5.18 (assert (forall ((B2 tptp.complex) (C tptp.complex) (A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex B2) C)) A) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex B2) A)) (@ (@ tptp.times_times_complex C) A)))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B2) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B2)) (@ _let_1 C))))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B2) C)) (@ (@ tptp.minus_minus_real (@ _let_1 B2)) (@ _let_1 C))))))
% 4.71/5.18 (assert (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ (@ tptp.minus_minus_complex B2) C)) (@ (@ tptp.minus_minus_complex (@ _let_1 B2)) (@ _let_1 C))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B2)) C) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) C)))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B2)) C) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) C)))))
% 4.71/5.18 (assert (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex A) B2)) C) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B2) C)))))
% 4.71/5.18 (assert (forall ((A2 tptp.int) (K tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_int A2) B2) (@ _let_1 (@ (@ tptp.minus_minus_int A) B2)))))))
% 4.71/5.18 (assert (forall ((A2 tptp.real) (K tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_real A2) B2) (@ _let_1 (@ (@ tptp.minus_minus_real A) B2)))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (= (= (@ (@ tptp.minus_minus_int A) B2) C) (= A (@ (@ tptp.plus_plus_int C) B2)))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (= (= (@ (@ tptp.minus_minus_real A) B2) C) (= A (@ (@ tptp.plus_plus_real C) B2)))))
% 4.71/5.18 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (= A (@ (@ tptp.minus_minus_int C) B2)) (= (@ (@ tptp.plus_plus_int A) B2) C))))
% 4.71/5.18 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (= A (@ (@ tptp.minus_minus_real C) B2)) (= (@ (@ tptp.plus_plus_real A) B2) C))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B2) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B2)) C)))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B2) C)) (@ (@ tptp.minus_minus_real (@ _let_1 B2)) C)))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.minus_minus_int B2) C)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C)) B2))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (= (@ (@ tptp.minus_minus_real A) (@ (@ tptp.minus_minus_real B2) C)) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) C)) B2))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B2)) C) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C)) B2))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B2)) C) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) C)) B2))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B2) C)) (@ (@ tptp.minus_minus_int (@ _let_1 C)) B2)))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B2) C)) (@ (@ tptp.minus_minus_real (@ _let_1 C)) B2)))))
% 4.71/5.18 (assert (forall ((C tptp.nat) (B2 tptp.nat) (A tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat C) B2) A) (= C (@ (@ tptp.minus_minus_nat A) B2)))))
% 4.71/5.18 (assert (forall ((C tptp.int) (B2 tptp.int) (A tptp.int)) (=> (= (@ (@ tptp.plus_plus_int C) B2) A) (= C (@ (@ tptp.minus_minus_int A) B2)))))
% 4.71/5.18 (assert (forall ((C tptp.real) (B2 tptp.real) (A tptp.real)) (=> (= (@ (@ tptp.plus_plus_real C) B2) A) (= C (@ (@ tptp.minus_minus_real A) B2)))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat A))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B2) C))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (= (@ (@ tptp.minus_minus_int (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B2) C))))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (= (@ (@ tptp.minus_minus_real (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_real B2) C))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int) (D tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B2) D)) (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B2)) (@ (@ tptp.minus_minus_int C) D)))))
% 4.71/5.18 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real) (D tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B2) D)) (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B2)) (@ (@ tptp.minus_minus_real C) D)))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real A) B2)) C) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B2) C)))))
% 4.71/5.18 (assert (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z3) (@ _let_1 (@ (@ tptp.minus_minus_int Y) Z3)))))))
% 4.71/5.18 (assert (forall ((X tptp.real) (Y tptp.real) (Z3 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z3) (@ _let_1 (@ (@ tptp.minus_minus_real Y) Z3)))))))
% 4.71/5.18 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (I tptp.nat)) (=> (@ P K) (=> (forall ((N3 tptp.nat)) (=> (@ P (@ tptp.suc N3)) (@ P N3))) (@ P (@ (@ tptp.minus_minus_nat K) I))))))
% 4.71/5.18 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat M2) tptp.zero_zero_nat) M2)))
% 4.71/5.18 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.minus_minus_nat M2) N2) tptp.zero_zero_nat) (=> (= (@ (@ tptp.minus_minus_nat N2) M2) tptp.zero_zero_nat) (= M2 N2)))))
% 4.71/5.18 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (L tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (let ((_let_2 (@ tptp.ord_less_nat M2))) (=> (@ _let_2 N2) (=> (@ _let_2 L) (@ (@ tptp.ord_less_nat (@ _let_1 N2)) (@ _let_1 M2))))))))
% 4.71/5.18 (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))))
% 4.71/5.18 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M2) (=> (@ _let_1 N2) (= (= (@ (@ tptp.minus_minus_nat M2) K) (@ (@ tptp.minus_minus_nat N2) K)) (= M2 N2)))))))
% 4.71/5.18 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M2) (=> (@ _let_1 N2) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M2) K)) (@ (@ tptp.minus_minus_nat N2) K)) (@ (@ tptp.ord_less_eq_nat M2) N2)))))))
% 4.71/5.18 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M2))) (let ((_let_2 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_2 M2) (=> (@ _let_2 N2) (= (@ (@ tptp.minus_minus_nat (@ _let_1 K)) (@ (@ tptp.minus_minus_nat N2) K)) (@ _let_1 N2))))))))
% 4.71/5.18 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M2) L)) (@ (@ tptp.minus_minus_nat N2) L)))))
% 4.71/5.18 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M2) N2)) M2)))
% 4.71/5.18 (assert (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B2))) (let ((_let_2 (@ tptp.minus_minus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) C) (=> (@ _let_1 C) (= (@ (@ tptp.ord_less_eq_nat (@ _let_2 A)) (@ _let_2 B2)) (@ _let_1 A))))))))
% 4.71/5.18 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (L tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N2)) (@ _let_1 M2))))))
% 4.71/5.18 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 M2)) (@ _let_1 N2)) (@ (@ tptp.minus_minus_nat M2) N2)))))
% 4.71/5.18 (assert (forall ((M2 tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M2) K)) (@ (@ tptp.plus_plus_nat N2) K)) (@ (@ tptp.minus_minus_nat M2) N2))))
% 4.71/5.18 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N2) M2)) N2) M2)))
% 4.71/5.18 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M2) N2)) N2) M2)))
% 4.71/5.18 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N2)) (@ (@ tptp.minus_minus_nat (@ _let_1 M2)) (@ _let_1 N2))))))
% 4.71/5.18 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M2) N2)) K) (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat M2) K)) (@ (@ tptp.times_times_nat N2) K)))))
% 4.71/5.18 (assert (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.ord_max_int X) Y)) Z3) (@ (@ tptp.ord_max_int (@ (@ tptp.minus_minus_int X) Z3)) (@ (@ tptp.minus_minus_int Y) Z3)))))
% 4.71/5.18 (assert (forall ((X tptp.real) (Y tptp.real) (Z3 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.ord_max_real X) Y)) Z3) (@ (@ tptp.ord_max_real (@ (@ tptp.minus_minus_real X) Z3)) (@ (@ tptp.minus_minus_real Y) Z3)))))
% 4.71/5.18 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 M2) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N2)))))))
% 4.71/5.18 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.zero_n3304061248610475627l_real P))))
% 4.71/5.18 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.zero_n2687167440665602831ol_nat P))))
% 4.71/5.18 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.zero_n2684676970156552555ol_int P))))
% 4.71/5.18 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_real (@ tptp.zero_n3304061248610475627l_real P)) tptp.one_one_real)))
% 4.71/5.18 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_nat (@ tptp.zero_n2687167440665602831ol_nat P)) tptp.one_one_nat)))
% 4.71/5.18 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_int (@ tptp.zero_n2684676970156552555ol_int P)) tptp.one_one_int)))
% 4.71/5.18 (assert (forall ((P (-> tptp.real Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n3304061248610475627l_real P5)) (not (or (and P5 (not (@ P tptp.one_one_real))) (and (not P5) (not (@ P tptp.zero_zero_real))))))))
% 4.71/5.18 (assert (forall ((P (-> tptp.complex Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n1201886186963655149omplex P5)) (not (or (and P5 (not (@ P tptp.one_one_complex))) (and (not P5) (not (@ P tptp.zero_zero_complex))))))))
% 4.71/5.18 (assert (forall ((P (-> tptp.extended_enat Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n1046097342994218471d_enat P5)) (not (or (and P5 (not (@ P tptp.one_on7984719198319812577d_enat))) (and (not P5) (not (@ P tptp.zero_z5237406670263579293d_enat))))))))
% 4.71/5.18 (assert (forall ((P (-> tptp.nat Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n2687167440665602831ol_nat P5)) (not (or (and P5 (not (@ P tptp.one_one_nat))) (and (not P5) (not (@ P tptp.zero_zero_nat))))))))
% 4.71/5.18 (assert (forall ((P (-> tptp.int Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n2684676970156552555ol_int P5)) (not (or (and P5 (not (@ P tptp.one_one_int))) (and (not P5) (not (@ P tptp.zero_zero_int))))))))
% 4.71/5.18 (assert (forall ((P (-> tptp.real Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n3304061248610475627l_real P5)) (and (=> P5 (@ P tptp.one_one_real)) (=> (not P5) (@ P tptp.zero_zero_real))))))
% 4.71/5.18 (assert (forall ((P (-> tptp.complex Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n1201886186963655149omplex P5)) (and (=> P5 (@ P tptp.one_one_complex)) (=> (not P5) (@ P tptp.zero_zero_complex))))))
% 4.71/5.18 (assert (forall ((P (-> tptp.extended_enat Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n1046097342994218471d_enat P5)) (and (=> P5 (@ P tptp.one_on7984719198319812577d_enat)) (=> (not P5) (@ P tptp.zero_z5237406670263579293d_enat))))))
% 4.71/5.18 (assert (forall ((P (-> tptp.nat Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n2687167440665602831ol_nat P5)) (and (=> P5 (@ P tptp.one_one_nat)) (=> (not P5) (@ P tptp.zero_zero_nat))))))
% 4.71/5.18 (assert (forall ((P (-> tptp.int Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n2684676970156552555ol_int P5)) (and (=> P5 (@ P tptp.one_one_int)) (=> (not P5) (@ P tptp.zero_zero_int))))))
% 4.71/5.18 (assert (= tptp.zero_n3304061248610475627l_real (lambda ((P6 Bool)) (@ (@ (@ tptp.if_real P6) tptp.one_one_real) tptp.zero_zero_real))))
% 4.71/5.18 (assert (= tptp.zero_n1201886186963655149omplex (lambda ((P6 Bool)) (@ (@ (@ tptp.if_complex P6) tptp.one_one_complex) tptp.zero_zero_complex))))
% 4.71/5.18 (assert (= tptp.zero_n1046097342994218471d_enat (lambda ((P6 Bool)) (@ (@ (@ tptp.if_Extended_enat P6) tptp.one_on7984719198319812577d_enat) tptp.zero_z5237406670263579293d_enat))))
% 4.71/5.18 (assert (= tptp.zero_n2687167440665602831ol_nat (lambda ((P6 Bool)) (@ (@ (@ tptp.if_nat P6) tptp.one_one_nat) tptp.zero_zero_nat))))
% 4.71/5.18 (assert (= tptp.zero_n2684676970156552555ol_int (lambda ((P6 Bool)) (@ (@ (@ tptp.if_int P6) tptp.one_one_int) tptp.zero_zero_int))))
% 4.71/5.18 (assert (= tptp.ord_less_eq_real (lambda ((A3 tptp.real) (B3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A3) B3)) tptp.zero_zero_real))))
% 4.71/5.18 (assert (= tptp.ord_less_eq_int (lambda ((A3 tptp.int) (B3 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A3) B3)) tptp.zero_zero_int))))
% 4.71/5.18 (assert (= tptp.ord_less_real (lambda ((A3 tptp.real) (B3 tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A3) B3)) tptp.zero_zero_real))))
% 4.71/5.18 (assert (= tptp.ord_less_int (lambda ((A3 tptp.int) (B3 tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A3) B3)) tptp.zero_zero_int))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_nat A) B2))) (=> _let_1 (=> _let_1 (= (= (@ (@ tptp.minus_minus_nat B2) A) C) (= B2 (@ (@ tptp.plus_plus_nat C) A))))))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (= (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.minus_minus_nat B2) A)) B2))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (= (@ (@ tptp.minus_minus_nat C) (@ (@ tptp.minus_minus_nat B2) A)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat C) A)) B2)))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B2) C)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B2) A)) C)))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B2) A)) C) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B2) C)) A)))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (= (@ (@ tptp.minus_minus_nat (@ _let_1 B2)) A) (@ _let_1 (@ (@ tptp.minus_minus_nat B2) A)))))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat B2) A)) (@ (@ tptp.minus_minus_nat (@ _let_1 B2)) A))))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (= (@ (@ tptp.ord_less_eq_nat C) (@ (@ tptp.minus_minus_nat B2) A)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat C) A)) B2)))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (@ (@ tptp.ord_less_eq_nat C) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B2) C)) A)))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B2) A)) A) B2))))
% 4.71/5.18 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.minus_minus_real C) B2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) B2)) C))))
% 4.71/5.18 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.minus_minus_int C) B2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) B2)) C))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) B2)) C) (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.plus_plus_real C) B2)))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) B2)) C) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.plus_plus_int C) B2)))))
% 4.71/5.18 (assert (forall ((I 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 I) K)) N2))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real N2) K)) J)))))))))
% 4.71/5.18 (assert (forall ((I 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 I) K)) N2))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat N2) K)) J)))))))))
% 4.71/5.18 (assert (forall ((I 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 I) K)) N2))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int N2) K)) J)))))))))
% 4.71/5.18 (assert (forall ((I tptp.real) (K tptp.real) (N2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I) K)) N2) (@ (@ tptp.ord_less_eq_real I) (@ (@ tptp.minus_minus_real N2) K)))))
% 4.71/5.18 (assert (forall ((I tptp.nat) (K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) N2) (@ (@ tptp.ord_less_eq_nat I) (@ (@ tptp.minus_minus_nat N2) K)))))
% 4.71/5.18 (assert (forall ((I tptp.int) (K tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K)) N2) (@ (@ tptp.ord_less_eq_int I) (@ (@ tptp.minus_minus_int N2) K)))))
% 4.71/5.18 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.minus_minus_real C) B2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B2)) C))))
% 4.71/5.18 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ (@ tptp.minus_minus_int C) B2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B2)) C))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) B2)) C) (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real C) B2)))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) B2)) C) (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int C) B2)))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat A) B2)) (= (@ (@ tptp.plus_plus_nat B2) (@ (@ tptp.minus_minus_nat A) B2)) A))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (not (@ (@ tptp.ord_less_real A) B2)) (= (@ (@ tptp.plus_plus_real B2) (@ (@ tptp.minus_minus_real A) B2)) A))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (not (@ (@ tptp.ord_less_int A) B2)) (= (@ (@ tptp.plus_plus_int B2) (@ (@ tptp.minus_minus_int A) B2)) A))))
% 4.71/5.18 (assert (forall ((A tptp.int) (E2 tptp.int) (C tptp.int) (B2 tptp.int) (D tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E2)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) E2)) D)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B2)) E2)) C) D))))
% 4.71/5.18 (assert (forall ((A tptp.real) (E2 tptp.real) (C tptp.real) (B2 tptp.real) (D tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E2)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B2) E2)) D)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B2)) E2)) C) D))))
% 4.71/5.18 (assert (forall ((A tptp.complex) (E2 tptp.complex) (C tptp.complex) (B2 tptp.complex) (D tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) E2)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex B2) E2)) D)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex A) B2)) E2)) C) D))))
% 4.71/5.18 (assert (forall ((A tptp.int) (E2 tptp.int) (C tptp.int) (B2 tptp.int) (D tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E2)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) E2)) D)) (= C (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B2) A)) E2)) D)))))
% 4.71/5.18 (assert (forall ((A tptp.real) (E2 tptp.real) (C tptp.real) (B2 tptp.real) (D tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E2)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B2) E2)) D)) (= C (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B2) A)) E2)) D)))))
% 4.71/5.18 (assert (forall ((A tptp.complex) (E2 tptp.complex) (C tptp.complex) (B2 tptp.complex) (D tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) E2)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex B2) E2)) D)) (= C (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex B2) A)) E2)) D)))))
% 4.71/5.18 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X) Y)) (@ (@ tptp.minus_minus_int X) Y)))))
% 4.71/5.18 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.minus_minus_real X) Y)))))
% 4.71/5.18 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X) X)) (@ (@ tptp.times_times_complex Y) Y)) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex X) Y)) (@ (@ tptp.minus_minus_complex X) Y)))))
% 4.71/5.18 (assert (forall ((X tptp.int) (Y tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int X))) (= (@ (@ tptp.minus_minus_int (@ _let_1 Y)) (@ (@ tptp.times_times_int A) B2)) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_minus_int Y) B2))) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) A)) B2))))))
% 4.71/5.18 (assert (forall ((X tptp.real) (Y tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real X))) (= (@ (@ tptp.minus_minus_real (@ _let_1 Y)) (@ (@ tptp.times_times_real A) B2)) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_minus_real Y) B2))) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X) A)) B2))))))
% 4.71/5.18 (assert (forall ((X tptp.complex) (Y tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex X))) (= (@ (@ tptp.minus_minus_complex (@ _let_1 Y)) (@ (@ tptp.times_times_complex A) B2)) (@ (@ tptp.plus_plus_complex (@ _let_1 (@ (@ tptp.minus_minus_complex Y) B2))) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X) A)) B2))))))
% 4.71/5.18 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (@ (@ tptp.dvd_dvd_nat B2) (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.modulo_modulo_nat A) B2)))))
% 4.71/5.18 (assert (forall ((B2 tptp.int) (A tptp.int)) (@ (@ tptp.dvd_dvd_int B2) (@ (@ tptp.minus_minus_int A) (@ (@ tptp.modulo_modulo_int A) B2)))))
% 4.71/5.18 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M2) N2)) (@ tptp.suc M2))))
% 4.71/5.18 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M2))) (=> (@ (@ tptp.ord_less_nat N2) M2) (= (@ tptp.suc (@ _let_1 (@ tptp.suc N2))) (@ _let_1 N2))))))
% 4.71/5.18 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N2) (=> (@ _let_1 M2) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M2) N2)) M2))))))
% 4.71/5.18 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M2)) N2) (@ tptp.suc (@ (@ tptp.minus_minus_nat M2) N2))))))
% 4.71/5.18 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M2) (=> (@ _let_1 N2) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M2) K)) (@ (@ tptp.minus_minus_nat N2) K)) (@ (@ tptp.ord_less_nat M2) N2)))))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (=> (@ (@ tptp.ord_less_eq_nat C) A) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat A) C)) (@ (@ tptp.minus_minus_nat B2) C))))))
% 4.71/5.18 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat N2) (@ (@ tptp.plus_plus_nat N2) M2)) tptp.zero_zero_nat)))
% 4.71/5.18 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (=> (@ tptp.finite_finite_nat B) (= (= (@ tptp.nat_set_encode A2) (@ tptp.nat_set_encode B)) (= A2 B))))))
% 4.71/5.18 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M2) N2)) (= (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.minus_minus_nat M2) N2)) M2))))
% 4.71/5.18 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (= (@ (@ tptp.ord_less_nat I) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) J))))
% 4.71/5.18 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (= (@ (@ tptp.minus_minus_nat J) I) K) (= J (@ (@ tptp.plus_plus_nat K) I))))))
% 4.71/5.18 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J) I)) K) (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J) K)) I)))))
% 4.71/5.18 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I))) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ _let_1 (@ (@ tptp.minus_minus_nat J) K)))))))
% 4.71/5.18 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.ord_less_eq_nat I) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) J)))))
% 4.71/5.18 (assert (forall ((J tptp.nat) (K tptp.nat) (I tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat J) K)) I) (@ (@ tptp.ord_less_eq_nat J) (@ (@ tptp.plus_plus_nat I) K)))))
% 4.71/5.18 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M2))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.minus_minus_nat (@ _let_1 tptp.one_one_nat)) N2)))))
% 4.71/5.18 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat M2))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M2)) (or (@ (@ tptp.ord_less_nat N2) M2) (@ _let_1 N2))))))
% 4.71/5.18 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ _let_1 N2) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M2)))))))
% 4.71/5.18 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N2)) (=> (@ _let_1 M2) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (@ _let_1 N2)))))))
% 4.71/5.18 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N2)) (=> (@ _let_1 N2) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (@ _let_1 M2)))))))
% 4.71/5.18 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M2) N2)) (= (@ (@ tptp.modulo_modulo_nat M2) N2) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M2) N2)) N2)))))
% 4.71/5.18 (assert (= tptp.modulo_modulo_nat (lambda ((M tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat M) N)) M) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M) N)) N)))))
% 4.71/5.18 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (= (@ (@ tptp.modulo_modulo_nat M2) N2) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M2) N2)) N2)))))
% 4.71/5.18 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat N2) M2)) M2) (@ (@ tptp.ord_max_nat N2) M2))))
% 4.71/5.18 (assert (forall ((A tptp.real) (E2 tptp.real) (C tptp.real) (B2 tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E2)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B2) E2)) D)) (@ (@ tptp.ord_less_eq_real C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B2) A)) E2)) D)))))
% 4.71/5.18 (assert (forall ((A tptp.int) (E2 tptp.int) (C tptp.int) (B2 tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E2)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) E2)) D)) (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B2) A)) E2)) D)))))
% 4.71/5.18 (assert (forall ((A tptp.real) (E2 tptp.real) (C tptp.real) (B2 tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E2)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B2) E2)) D)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B2)) E2)) C)) D))))
% 4.71/5.18 (assert (forall ((A tptp.int) (E2 tptp.int) (C tptp.int) (B2 tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E2)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) E2)) D)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B2)) E2)) C)) D))))
% 4.71/5.18 (assert (forall ((A tptp.real) (E2 tptp.real) (C tptp.real) (B2 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 B2) E2)) D)) (@ (@ tptp.ord_less_real C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B2) A)) E2)) D)))))
% 4.71/5.18 (assert (forall ((A tptp.int) (E2 tptp.int) (C tptp.int) (B2 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 B2) E2)) D)) (@ (@ tptp.ord_less_int C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B2) A)) E2)) D)))))
% 4.71/5.18 (assert (forall ((A tptp.real) (E2 tptp.real) (C tptp.real) (B2 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 B2) E2)) D)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B2)) E2)) C)) D))))
% 4.71/5.18 (assert (forall ((A tptp.int) (E2 tptp.int) (C tptp.int) (B2 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 B2) E2)) D)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B2)) E2)) C)) D))))
% 4.71/5.18 (assert (forall ((Z3 tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z3 tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex X) Z3)) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex X) (@ (@ tptp.times_times_complex Y) Z3))) Z3)))))
% 4.71/5.18 (assert (forall ((Z3 tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z3 tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real X) Z3)) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X) (@ (@ tptp.times_times_real Y) Z3))) Z3)))))
% 4.71/5.18 (assert (forall ((Z3 tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z3 tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex X) (@ (@ tptp.divide1717551699836669952omplex Y) Z3)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X) Z3)) Y)) Z3)))))
% 4.71/5.18 (assert (forall ((Z3 tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z3 tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real X) (@ (@ tptp.divide_divide_real Y) Z3)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z3)) Y)) Z3)))))
% 4.71/5.18 (assert (forall ((Y tptp.complex) (Z3 tptp.complex) (X tptp.complex) (W2 tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z3 tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide1717551699836669952omplex W2) Z3)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X) Z3)) (@ (@ tptp.times_times_complex W2) Y))) (@ (@ tptp.times_times_complex Y) Z3)))))))
% 4.71/5.18 (assert (forall ((Y tptp.real) (Z3 tptp.real) (X tptp.real) (W2 tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z3 tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real W2) Z3)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z3)) (@ (@ tptp.times_times_real W2) Y))) (@ (@ tptp.times_times_real Y) Z3)))))))
% 4.71/5.18 (assert (forall ((Z3 tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex A) (@ (@ tptp.divide1717551699836669952omplex B2) Z3)))) (let ((_let_2 (= Z3 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) Z3)) B2)) Z3))))))))
% 4.71/5.18 (assert (forall ((Z3 tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real A) (@ (@ tptp.divide_divide_real B2) Z3)))) (let ((_let_2 (= Z3 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) Z3)) B2)) Z3))))))))
% 4.71/5.18 (assert (forall ((X tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X) X)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X) tptp.one_one_int)) (@ (@ tptp.minus_minus_int X) tptp.one_one_int)))))
% 4.71/5.18 (assert (forall ((X tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) X)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)) (@ (@ tptp.minus_minus_real X) tptp.one_one_real)))))
% 4.71/5.18 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X) X)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex X) tptp.one_one_complex)) (@ (@ tptp.minus_minus_complex X) tptp.one_one_complex)))))
% 4.71/5.18 (assert (forall ((D tptp.int) (D6 tptp.int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D6) (forall ((X2 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_int X2) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X2) (@ (@ tptp.times_times_int K4) D6))) T)))))))))
% 4.71/5.18 (assert (forall ((D tptp.real) (D6 tptp.real) (T tptp.real)) (=> (@ (@ tptp.dvd_dvd_real D) D6) (forall ((X2 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_real X2) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real X2) (@ (@ tptp.times_times_real K4) D6))) T)))))))))
% 4.71/5.18 (assert (forall ((D tptp.complex) (D6 tptp.complex) (T tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex D) D6) (forall ((X2 tptp.complex) (K4 tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_complex X2) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex X2) (@ (@ tptp.times_times_complex K4) D6))) T)))))))))
% 4.71/5.18 (assert (forall ((D tptp.int) (D6 tptp.int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D6) (forall ((X2 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (= (@ _let_1 (@ (@ tptp.plus_plus_int X2) T)) (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X2) (@ (@ tptp.times_times_int K4) D6))) T))))))))
% 4.71/5.18 (assert (forall ((D tptp.real) (D6 tptp.real) (T tptp.real)) (=> (@ (@ tptp.dvd_dvd_real D) D6) (forall ((X2 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real D))) (= (@ _let_1 (@ (@ tptp.plus_plus_real X2) T)) (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real X2) (@ (@ tptp.times_times_real K4) D6))) T))))))))
% 4.71/5.18 (assert (forall ((D tptp.complex) (D6 tptp.complex) (T tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex D) D6) (forall ((X2 tptp.complex) (K4 tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex D))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex X2) T)) (@ _let_1 (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex X2) (@ (@ tptp.times_times_complex K4) D6))) T))))))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.times_times_nat B2) (@ (@ tptp.divide_divide_nat A) B2))) (@ (@ tptp.modulo_modulo_nat A) B2))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.times_times_int B2) (@ (@ tptp.divide_divide_int A) B2))) (@ (@ tptp.modulo_modulo_int A) B2))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.modulo_modulo_nat A) B2)) (@ (@ tptp.times_times_nat B2) (@ (@ tptp.divide_divide_nat A) B2)))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.modulo_modulo_int A) B2)) (@ (@ tptp.times_times_int B2) (@ (@ tptp.divide_divide_int A) B2)))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.modulo_modulo_nat A) B2)) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B2)) B2))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.modulo_modulo_int A) B2)) (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B2)) B2))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B2)) B2)) (@ (@ tptp.modulo_modulo_nat A) B2))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B2)) B2)) (@ (@ tptp.modulo_modulo_int A) B2))))
% 4.71/5.18 (assert (forall ((M2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.power_power_int K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (= (@ (@ tptp.divide_divide_int (@ _let_1 M2)) K) (@ _let_1 (@ (@ tptp.minus_minus_nat M2) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 4.71/5.18 (assert (forall ((N2 tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I))) N2))))
% 4.71/5.18 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat) (B2 tptp.nat)) (= (@ P (@ (@ tptp.minus_minus_nat A) B2)) (not (or (and (@ (@ tptp.ord_less_nat A) B2) (not (@ P tptp.zero_zero_nat))) (exists ((D4 tptp.nat)) (and (= A (@ (@ tptp.plus_plus_nat B2) D4)) (not (@ P D4)))))))))
% 4.71/5.18 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat) (B2 tptp.nat)) (= (@ P (@ (@ tptp.minus_minus_nat A) B2)) (and (=> (@ (@ tptp.ord_less_nat A) B2) (@ P tptp.zero_zero_nat)) (forall ((D4 tptp.nat)) (=> (= A (@ (@ tptp.plus_plus_nat B2) D4)) (@ P D4)))))))
% 4.71/5.18 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J) K)) I) (@ (@ tptp.ord_less_nat J) (@ (@ tptp.plus_plus_nat I) K))))))
% 4.71/5.18 (assert (forall ((I tptp.nat) (J tptp.nat) (U tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.minus_minus_nat M2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I)) U)) N2))))))
% 4.71/5.18 (assert (forall ((J tptp.nat) (I tptp.nat) (U tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M2)) (@ (@ 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 I) J)) U)) M2)) N2)))))
% 4.71/5.18 (assert (forall ((I tptp.nat) (J tptp.nat) (U tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.ord_less_eq_nat M2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I)) U)) N2))))))
% 4.71/5.18 (assert (forall ((J tptp.nat) (I tptp.nat) (U tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M2)) (@ (@ 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 I) J)) U)) M2)) N2)))))
% 4.71/5.18 (assert (forall ((I tptp.nat) (J tptp.nat) (U tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (= M2 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I)) U)) N2))))))
% 4.71/5.18 (assert (forall ((J tptp.nat) (I tptp.nat) (U tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I) J)) U)) M2) N2)))))
% 4.71/5.18 (assert (forall ((N2 tptp.nat) (M2 tptp.nat) (Q3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (= (= (@ (@ tptp.modulo_modulo_nat M2) Q3) (@ (@ tptp.modulo_modulo_nat N2) Q3)) (@ (@ tptp.dvd_dvd_nat Q3) (@ (@ tptp.minus_minus_nat M2) N2))))))
% 4.71/5.18 (assert (forall ((A2 tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat A2)) (= (@ tptp.nat_set_encode A2) tptp.zero_zero_nat))))
% 4.71/5.18 (assert (forall ((M2 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 M2))) (= (@ (@ 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) M2)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N2))))))))
% 4.71/5.18 (assert (forall ((M2 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 M2))) (= (@ (@ 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) M2)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N2))))))))
% 4.71/5.18 (assert (forall ((Y tptp.real) (Z3 tptp.real) (X tptp.real) (W2 tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z3 tptp.zero_zero_real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real W2) Z3)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z3)) (@ (@ tptp.times_times_real W2) Y))) (@ (@ tptp.times_times_real Y) Z3))) tptp.zero_zero_real))))))
% 4.71/5.18 (assert (forall ((Y tptp.real) (Z3 tptp.real) (X tptp.real) (W2 tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z3 tptp.zero_zero_real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real W2) Z3)) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z3)) (@ (@ tptp.times_times_real W2) Y))) (@ (@ tptp.times_times_real Y) Z3))) tptp.zero_zero_real))))))
% 4.71/5.18 (assert (forall ((A tptp.complex) (N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (not (= A tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N2)) (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 M2)) (@ _let_1 N2))))))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N2)) (@ (@ tptp.divide_divide_nat (@ _let_1 M2)) (@ _let_1 N2))))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N2)) (@ (@ tptp.divide_divide_int (@ _let_1 M2)) (@ _let_1 N2))))))))
% 4.71/5.18 (assert (forall ((A tptp.real) (N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N2)) (@ (@ tptp.divide_divide_real (@ _let_1 M2)) (@ _let_1 N2))))))))
% 4.71/5.18 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M2)) N2) (@ (@ tptp.minus_minus_nat M2) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))))))
% 4.71/5.18 (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))))))
% 4.71/5.18 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (not (@ (@ tptp.ord_less_nat M2) N2)) (= (@ (@ tptp.divide_divide_nat M2) N2) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M2) N2)) N2)))))))
% 4.71/5.18 (assert (= tptp.divide_divide_nat (lambda ((M tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_nat (or (@ (@ tptp.ord_less_nat M) N) (= N tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M) N)) N))))))
% 4.71/5.18 (assert (= tptp.plus_plus_nat (lambda ((M tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_nat (= M tptp.zero_zero_nat)) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)) N))))))
% 4.71/5.18 (assert (forall ((J tptp.nat) (I tptp.nat) (U tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M2)) (@ (@ 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 I) J)) U)) M2)) N2)))))
% 4.71/5.18 (assert (forall ((I tptp.nat) (J tptp.nat) (U tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I)) U)) N2))))))
% 4.71/5.18 (assert (= tptp.times_times_nat (lambda ((M tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_nat (= M tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)) N))))))
% 4.71/5.18 (assert (forall ((Q3 tptp.nat) (N2 tptp.nat) (R2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat R2) M2))) (let ((_let_2 (@ tptp.dvd_dvd_nat M2))) (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)))))))))))
% 4.71/5.18 (assert (forall ((R2 tptp.nat) (N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat R2) N2) (=> (@ (@ tptp.ord_less_eq_nat R2) M2) (=> (@ (@ tptp.dvd_dvd_nat N2) (@ (@ tptp.minus_minus_nat M2) R2)) (= (@ (@ tptp.modulo_modulo_nat M2) N2) R2))))))
% 4.71/5.18 (assert (forall ((U tptp.real) (V tptp.real) (R2 tptp.real) (S tptp.real)) (=> (@ (@ tptp.ord_less_eq_real U) V) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) R2) (=> (@ (@ tptp.ord_less_eq_real R2) S) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real U) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real R2) (@ (@ tptp.minus_minus_real V) U))) S))) V))))))
% 4.71/5.18 (assert (forall ((N2 tptp.nat) (M2 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) M2)) tptp.zero_zero_nat))))))
% 4.71/5.18 (assert (forall ((N2 tptp.nat) (M2 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) M2)) tptp.zero_zero_int))))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 M2)) (@ _let_1 N2)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N2) M2))) (=> (not (= A tptp.zero_zero_nat)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N2)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M2))))))))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (let ((_let_2 (@ (@ tptp.divide_divide_int (@ _let_1 M2)) (@ _let_1 N2)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N2) M2))) (=> (not (= A tptp.zero_zero_int)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N2)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M2))))))))))))
% 4.71/5.18 (assert (= tptp.power_power_nat (lambda ((P6 tptp.nat) (M tptp.nat)) (@ (@ (@ tptp.if_nat (= M tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.times_times_nat P6) (@ (@ tptp.power_power_nat P6) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)))))))
% 4.71/5.18 (assert (= tptp.power_power_int (lambda ((P6 tptp.int) (M tptp.nat)) (@ (@ (@ tptp.if_int (= M tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ tptp.times_times_int P6) (@ (@ tptp.power_power_int P6) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)))))))
% 4.71/5.18 (assert (= tptp.power_power_real (lambda ((P6 tptp.real) (M tptp.nat)) (@ (@ (@ tptp.if_real (= M tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.times_times_real P6) (@ (@ tptp.power_power_real P6) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)))))))
% 4.71/5.18 (assert (= tptp.power_power_complex (lambda ((P6 tptp.complex) (M tptp.nat)) (@ (@ (@ tptp.if_complex (= M tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.times_times_complex P6) (@ (@ tptp.power_power_complex P6) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)))))))
% 4.71/5.18 (assert (= tptp.power_8040749407984259932d_enat (lambda ((P6 tptp.extended_enat) (M tptp.nat)) (@ (@ (@ tptp.if_Extended_enat (= M tptp.zero_zero_nat)) tptp.one_on7984719198319812577d_enat) (@ (@ tptp.times_7803423173614009249d_enat P6) (@ (@ tptp.power_8040749407984259932d_enat P6) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)))))))
% 4.71/5.18 (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))))))
% 4.71/5.18 (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))))))
% 4.71/5.18 (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))))))
% 4.71/5.18 (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))))))
% 4.71/5.18 (assert (forall ((N2 tptp.nat) (A tptp.extended_enat)) (let ((_let_1 (@ tptp.power_8040749407984259932d_enat A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_7803423173614009249d_enat (@ _let_1 (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))) A) (@ _let_1 N2))))))
% 4.71/5.18 (assert (forall ((K tptp.nat) (M2 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 M2) N2)) (@ (@ tptp.minus_minus_nat (@ _let_1 M2)) (@ _let_1 N2)))))))
% 4.71/5.18 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (= (@ (@ tptp.divide_divide_nat M2) N2) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M2) N2)) N2)))))))
% 4.71/5.18 (assert (= (@ tptp.size_num tptp.one) tptp.zero_zero_nat))
% 4.71/5.18 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat)) (=> (forall ((A4 tptp.nat)) (=> (= (@ (@ tptp.divide_divide_nat A4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A4) (@ P A4))) (=> (forall ((A4 tptp.nat) (B4 Bool)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat B4)) (@ (@ tptp.times_times_nat _let_1) A4)))) (=> (@ P A4) (=> (= (@ (@ tptp.divide_divide_nat _let_2) _let_1) A4) (@ P _let_2)))))) (@ P A)))))
% 4.71/5.18 (assert (forall ((P (-> tptp.int Bool)) (A tptp.int)) (=> (forall ((A4 tptp.int)) (=> (= (@ (@ tptp.divide_divide_int A4) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A4) (@ P A4))) (=> (forall ((A4 tptp.int) (B4 Bool)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int B4)) (@ (@ tptp.times_times_int _let_1) A4)))) (=> (@ P A4) (=> (= (@ (@ tptp.divide_divide_int _let_2) _let_1) A4) (@ P _let_2)))))) (@ P A)))))
% 4.71/5.18 (assert (forall ((M2 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 M2))) (= (@ (@ tptp.modulo_modulo_nat _let_2) (@ _let_1 N2)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat M2) N2))) _let_2))))))
% 4.71/5.18 (assert (forall ((M2 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 M2))) (= (@ (@ tptp.modulo_modulo_int _let_2) (@ _let_1 N2)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat M2) N2))) _let_2))))))
% 4.71/5.18 (assert (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex X) Y)) _let_2) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex X) _let_2)) (@ (@ tptp.power_power_complex Y) _let_2))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X)) Y)))))))
% 4.71/5.18 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int X) Y)) _let_2) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_2)) (@ (@ tptp.power_power_int Y) _let_2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int _let_1)) X)) Y)))))))
% 4.71/5.18 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) Y)) _let_2) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X)) Y)))))))
% 4.71/5.18 (assert (forall ((M2 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 M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) 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) M2)))) _let_2)))))))
% 4.71/5.18 (assert (forall ((M2 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 M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) 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) M2)))) _let_2)))))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B2)))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2) (=> (@ (@ tptp.ord_less_eq_nat B2) _let_2) (= (@ (@ tptp.minus_minus_nat _let_2) B2) (@ _let_1 B2)))))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B2)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_eq_int B2) _let_2) (= (@ (@ tptp.minus_minus_int _let_2) B2) (@ _let_1 B2)))))))))
% 4.71/5.18 (assert (forall ((M2 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 M2)) tptp.one_one_nat)) (@ _let_2 N2))) (@ (@ tptp.ord_less_eq_nat M2) N2))))))
% 4.71/5.18 (assert (forall ((M2 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 M2)) tptp.one_one_int)) (@ _let_2 N2))) (@ (@ tptp.ord_less_eq_nat M2) N2))))))
% 4.71/5.18 (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))))))))
% 4.71/5.18 (assert (forall ((M2 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 M2)) tptp.one_one_nat)) _let_3)) (or (= _let_3 tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat M2) N2))))))))
% 4.71/5.18 (assert (forall ((M2 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 M2)) tptp.one_one_int)) _let_3)) (or (= _let_3 tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_nat M2) N2))))))))
% 4.71/5.18 (assert (forall ((L tptp.num) (R2 tptp.int) (Q3 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q3))) (let ((_let_2 (@ (@ tptp.unique5024387138958732305ep_int L) (@ (@ tptp.product_Pair_int_int Q3) R2)))) (let ((_let_3 (@ tptp.numeral_numeral_int L))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_3) R2))) (and (=> _let_4 (= _let_2 (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R2) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.product_Pair_int_int _let_1) R2))))))))))
% 4.71/5.18 (assert (forall ((L tptp.num) (R2 tptp.nat) (Q3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q3))) (let ((_let_2 (@ (@ tptp.unique5026877609467782581ep_nat L) (@ (@ tptp.product_Pair_nat_nat Q3) R2)))) (let ((_let_3 (@ tptp.numeral_numeral_nat L))) (let ((_let_4 (@ (@ tptp.ord_less_eq_nat _let_3) R2))) (and (=> _let_4 (= _let_2 (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R2) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.product_Pair_nat_nat _let_1) R2))))))))))
% 4.71/5.18 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.vEBT_VEBT_set_vebt T)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_nat))))))
% 4.71/5.18 (assert (= tptp.artanh_real (lambda ((X4 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X4)) (@ (@ tptp.minus_minus_real tptp.one_one_real) X4)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 4.71/5.18 (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))))))))))
% 4.71/5.18 (assert (forall ((X tptp.set_Extended_enat) (Y tptp.set_Extended_enat)) (= (= (@ (@ tptp.minus_925952699566721837d_enat X) Y) tptp.bot_bo7653980558646680370d_enat) (@ (@ tptp.ord_le7203529160286727270d_enat X) Y))))
% 4.71/5.18 (assert (forall ((X tptp.set_real) (Y tptp.set_real)) (= (= (@ (@ tptp.minus_minus_set_real X) Y) tptp.bot_bot_set_real) (@ (@ tptp.ord_less_eq_set_real X) Y))))
% 4.71/5.18 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (= (@ (@ tptp.minus_minus_set_nat X) Y) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat X) Y))))
% 4.71/5.18 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (= (@ (@ tptp.minus_minus_set_int X) Y) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int X) Y))))
% 4.71/5.18 (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)))))))
% 4.71/5.18 (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)))))))
% 4.71/5.18 (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))))))))
% 4.71/5.18 (assert (forall ((A tptp.int)) (= (@ tptp.uminus_uminus_int (@ tptp.uminus_uminus_int A)) A)))
% 4.71/5.18 (assert (forall ((A tptp.real)) (= (@ tptp.uminus_uminus_real (@ tptp.uminus_uminus_real A)) A)))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (= (@ tptp.uminus_uminus_int A) (@ tptp.uminus_uminus_int B2)) (= A B2))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (= (@ tptp.uminus_uminus_real A) (@ tptp.uminus_uminus_real B2)) (= A B2))))
% 4.71/5.18 (assert (forall ((A2 tptp.set_Extended_enat)) (= (@ (@ tptp.minus_925952699566721837d_enat A2) A2) tptp.bot_bo7653980558646680370d_enat)))
% 4.71/5.18 (assert (forall ((A2 tptp.set_real)) (= (@ (@ tptp.minus_minus_set_real A2) A2) tptp.bot_bot_set_real)))
% 4.71/5.18 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int A2) A2) tptp.bot_bot_set_int)))
% 4.71/5.18 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat A2) A2) tptp.bot_bot_set_nat)))
% 4.71/5.18 (assert (forall ((A2 tptp.set_Extended_enat)) (= (@ (@ tptp.minus_925952699566721837d_enat tptp.bot_bo7653980558646680370d_enat) A2) tptp.bot_bo7653980558646680370d_enat)))
% 4.71/5.18 (assert (forall ((A2 tptp.set_real)) (= (@ (@ tptp.minus_minus_set_real tptp.bot_bot_set_real) A2) tptp.bot_bot_set_real)))
% 4.71/5.18 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int tptp.bot_bot_set_int) A2) tptp.bot_bot_set_int)))
% 4.71/5.18 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat tptp.bot_bot_set_nat) A2) tptp.bot_bot_set_nat)))
% 4.71/5.18 (assert (forall ((A2 tptp.set_Extended_enat)) (= (@ (@ tptp.minus_925952699566721837d_enat A2) tptp.bot_bo7653980558646680370d_enat) A2)))
% 4.71/5.18 (assert (forall ((A2 tptp.set_real)) (= (@ (@ tptp.minus_minus_set_real A2) tptp.bot_bot_set_real) A2)))
% 4.71/5.18 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int A2) tptp.bot_bot_set_int) A2)))
% 4.71/5.18 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat A2) tptp.bot_bot_set_nat) A2)))
% 4.71/5.18 (assert (forall ((B tptp.set_complex) (A2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex B) (= (@ tptp.finite3207457112153483333omplex (@ (@ tptp.minus_811609699411566653omplex A2) B)) (@ tptp.finite3207457112153483333omplex A2)))))
% 4.71/5.18 (assert (forall ((B tptp.set_int) (A2 tptp.set_int)) (=> (@ tptp.finite_finite_int B) (= (@ tptp.finite_finite_int (@ (@ tptp.minus_minus_set_int A2) B)) (@ tptp.finite_finite_int A2)))))
% 4.71/5.18 (assert (forall ((B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat B) (= (@ tptp.finite4001608067531595151d_enat (@ (@ tptp.minus_925952699566721837d_enat A2) B)) (@ tptp.finite4001608067531595151d_enat A2)))))
% 4.71/5.18 (assert (forall ((B tptp.set_nat) (A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B) (= (@ tptp.finite_finite_nat (@ (@ tptp.minus_minus_set_nat A2) B)) (@ tptp.finite_finite_nat A2)))))
% 4.71/5.18 (assert (forall ((A2 tptp.set_complex) (B tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A2) (@ tptp.finite3207457112153483333omplex (@ (@ tptp.minus_811609699411566653omplex A2) B)))))
% 4.71/5.18 (assert (forall ((A2 tptp.set_int) (B tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (@ tptp.finite_finite_int (@ (@ tptp.minus_minus_set_int A2) B)))))
% 4.71/5.18 (assert (forall ((A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (@ tptp.finite4001608067531595151d_enat (@ (@ tptp.minus_925952699566721837d_enat A2) B)))))
% 4.71/5.18 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (@ tptp.finite_finite_nat (@ (@ tptp.minus_minus_set_nat A2) B)))))
% 4.71/5.18 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat A2)) (@ tptp.uminus5710092332889474511et_nat B)) (@ (@ tptp.ord_less_eq_set_nat B) A2))))
% 4.71/5.18 (assert (forall ((A2 tptp.set_int) (B tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int A2)) (@ tptp.uminus1532241313380277803et_int B)) (@ (@ tptp.ord_less_eq_set_int B) A2))))
% 4.71/5.18 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat B)) (@ tptp.uminus5710092332889474511et_nat A2)))))
% 4.71/5.18 (assert (forall ((A2 tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B) (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int B)) (@ tptp.uminus1532241313380277803et_int A2)))))
% 4.71/5.18 (assert (forall ((W2 tptp.int) (Z3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int W2) (@ (@ tptp.minus_minus_int Z3) tptp.one_one_int)) (@ (@ tptp.ord_less_int W2) Z3))))
% 4.71/5.18 (assert (forall ((W2 tptp.int) (Z3 tptp.int)) (= (@ (@ tptp.ord_less_int W2) (@ (@ tptp.plus_plus_int Z3) tptp.one_one_int)) (@ (@ tptp.ord_less_eq_int W2) Z3))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 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) B2)))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 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) B2)))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 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) B2)))))))
% 4.71/5.18 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat X)) (@ tptp.uminus5710092332889474511et_nat Y)) (@ (@ tptp.ord_less_eq_set_nat Y) X))))
% 4.71/5.18 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int X)) (@ tptp.uminus1532241313380277803et_int Y)) (@ (@ tptp.ord_less_eq_set_int Y) X))))
% 4.71/5.18 (assert (forall ((B2 tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B2)) (@ tptp.uminus_uminus_real A)) (@ (@ tptp.ord_less_eq_real A) B2))))
% 4.71/5.18 (assert (forall ((B2 tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int B2)) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_eq_int A) B2))))
% 4.71/5.18 (assert (forall ((A tptp.int)) (= (= (@ tptp.uminus_uminus_int A) A) (= A tptp.zero_zero_int))))
% 4.71/5.18 (assert (forall ((A tptp.real)) (= (= (@ tptp.uminus_uminus_real A) A) (= A tptp.zero_zero_real))))
% 4.71/5.18 (assert (forall ((A tptp.int)) (= (= A (@ tptp.uminus_uminus_int A)) (= A tptp.zero_zero_int))))
% 4.71/5.18 (assert (forall ((A tptp.real)) (= (= A (@ tptp.uminus_uminus_real A)) (= A tptp.zero_zero_real))))
% 4.71/5.18 (assert (forall ((A tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 4.71/5.18 (assert (forall ((A tptp.int)) (= (= (@ tptp.uminus_uminus_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 4.71/5.18 (assert (forall ((A tptp.real)) (= (= (@ tptp.uminus_uminus_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 4.71/5.18 (assert (forall ((A tptp.complex)) (= (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex A)) (= tptp.zero_zero_complex A))))
% 4.71/5.18 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ tptp.uminus_uminus_int A)) (= tptp.zero_zero_int A))))
% 4.71/5.18 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ tptp.uminus_uminus_real A)) (= tptp.zero_zero_real A))))
% 4.71/5.18 (assert (= (@ tptp.uminus1482373934393186551omplex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 4.71/5.18 (assert (= (@ tptp.uminus_uminus_int tptp.zero_zero_int) tptp.zero_zero_int))
% 4.71/5.18 (assert (= (@ tptp.uminus_uminus_real tptp.zero_zero_real) tptp.zero_zero_real))
% 4.71/5.18 (assert (forall ((B2 tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B2)) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_int A) B2))))
% 4.71/5.18 (assert (forall ((B2 tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B2)) (@ tptp.uminus_uminus_real A)) (@ (@ tptp.ord_less_real A) B2))))
% 4.71/5.18 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) B2) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.times_times_complex A) B2)))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int A)) B2) (@ tptp.uminus_uminus_int (@ (@ tptp.times_times_int A) B2)))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real A)) B2) (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real A) B2)))))
% 4.71/5.18 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B2)) (@ (@ tptp.times_times_complex A) B2))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B2)) (@ (@ tptp.times_times_int A) B2))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B2)) (@ (@ tptp.times_times_real A) B2))))
% 4.71/5.18 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ tptp.uminus1482373934393186551omplex B2)) (@ tptp.uminus1482373934393186551omplex (@ _let_1 B2))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ tptp.uminus_uminus_int B2)) (@ tptp.uminus_uminus_int (@ _let_1 B2))))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ tptp.uminus_uminus_real B2)) (@ tptp.uminus_uminus_real (@ _let_1 B2))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int A) B2)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B2)))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real A) B2)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B2)))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) (@ (@ tptp.plus_plus_int A) B2)) B2)))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.plus_plus_real A) B2)) B2)))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B2)) B2)))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) B2)) B2)))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.minus_minus_int A) B2)) (@ (@ tptp.minus_minus_int B2) A))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.minus_minus_real A) B2)) (@ (@ tptp.minus_minus_real B2) A))))
% 4.71/5.18 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int X))) (= (@ _let_1 (@ tptp.uminus_uminus_int Y)) (@ _let_1 Y)))))
% 4.71/5.18 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real X))) (= (@ _let_1 (@ tptp.uminus_uminus_real Y)) (@ _let_1 Y)))))
% 4.71/5.18 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.uminus_uminus_int X)) Y) (@ (@ tptp.dvd_dvd_int X) Y))))
% 4.71/5.18 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.dvd_dvd_real (@ tptp.uminus_uminus_real X)) Y) (@ (@ tptp.dvd_dvd_real X) Y))))
% 4.71/5.18 (assert (forall ((A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat)) (= (= (@ (@ tptp.minus_925952699566721837d_enat A2) B) tptp.bot_bo7653980558646680370d_enat) (@ (@ tptp.ord_le7203529160286727270d_enat A2) B))))
% 4.71/5.18 (assert (forall ((A2 tptp.set_real) (B tptp.set_real)) (= (= (@ (@ tptp.minus_minus_set_real A2) B) tptp.bot_bot_set_real) (@ (@ tptp.ord_less_eq_set_real A2) B))))
% 4.71/5.18 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (= (= (@ (@ tptp.minus_minus_set_nat A2) B) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat A2) B))))
% 4.71/5.18 (assert (forall ((A2 tptp.set_int) (B tptp.set_int)) (= (= (@ (@ tptp.minus_minus_set_int A2) B) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int A2) B))))
% 4.71/5.18 (assert (forall ((I tptp.extended_enat) (L tptp.extended_enat) (U tptp.extended_enat)) (= (@ (@ tptp.member_Extended_enat I) (@ (@ tptp.set_or5403411693681687835d_enat L) U)) (and (@ (@ tptp.ord_le2932123472753598470d_enat L) I) (@ (@ tptp.ord_le2932123472753598470d_enat I) U)))))
% 4.71/5.18 (assert (forall ((I tptp.set_nat) (L tptp.set_nat) (U tptp.set_nat)) (= (@ (@ tptp.member_set_nat I) (@ (@ tptp.set_or4548717258645045905et_nat L) U)) (and (@ (@ tptp.ord_less_eq_set_nat L) I) (@ (@ tptp.ord_less_eq_set_nat I) U)))))
% 4.71/5.18 (assert (forall ((I tptp.set_int) (L tptp.set_int) (U tptp.set_int)) (= (@ (@ tptp.member_set_int I) (@ (@ tptp.set_or370866239135849197et_int L) U)) (and (@ (@ tptp.ord_less_eq_set_int L) I) (@ (@ tptp.ord_less_eq_set_int I) U)))))
% 4.71/5.18 (assert (forall ((I tptp.nat) (L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.member_nat I) (@ (@ tptp.set_or1269000886237332187st_nat L) U)) (and (@ (@ tptp.ord_less_eq_nat L) I) (@ (@ tptp.ord_less_eq_nat I) U)))))
% 4.71/5.18 (assert (forall ((I tptp.int) (L tptp.int) (U tptp.int)) (= (@ (@ tptp.member_int I) (@ (@ tptp.set_or1266510415728281911st_int L) U)) (and (@ (@ tptp.ord_less_eq_int L) I) (@ (@ tptp.ord_less_eq_int I) U)))))
% 4.71/5.18 (assert (forall ((I tptp.real) (L tptp.real) (U tptp.real)) (= (@ (@ tptp.member_real I) (@ (@ tptp.set_or1222579329274155063t_real L) U)) (and (@ (@ tptp.ord_less_eq_real L) I) (@ (@ tptp.ord_less_eq_real I) U)))))
% 4.71/5.18 (assert (forall ((L tptp.set_nat) (H2 tptp.set_nat) (L3 tptp.set_nat) (H3 tptp.set_nat)) (= (= (@ (@ tptp.set_or4548717258645045905et_nat L) H2) (@ (@ tptp.set_or4548717258645045905et_nat L3) H3)) (or (and (= L L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_set_nat L) H2)) (not (@ (@ tptp.ord_less_eq_set_nat L3) H3)))))))
% 4.71/5.18 (assert (forall ((L tptp.set_int) (H2 tptp.set_int) (L3 tptp.set_int) (H3 tptp.set_int)) (= (= (@ (@ tptp.set_or370866239135849197et_int L) H2) (@ (@ tptp.set_or370866239135849197et_int L3) H3)) (or (and (= L L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_set_int L) H2)) (not (@ (@ tptp.ord_less_eq_set_int L3) H3)))))))
% 4.71/5.18 (assert (forall ((L tptp.nat) (H2 tptp.nat) (L3 tptp.nat) (H3 tptp.nat)) (= (= (@ (@ tptp.set_or1269000886237332187st_nat L) H2) (@ (@ tptp.set_or1269000886237332187st_nat L3) H3)) (or (and (= L L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_nat L) H2)) (not (@ (@ tptp.ord_less_eq_nat L3) H3)))))))
% 4.71/5.18 (assert (forall ((L tptp.int) (H2 tptp.int) (L3 tptp.int) (H3 tptp.int)) (= (= (@ (@ tptp.set_or1266510415728281911st_int L) H2) (@ (@ tptp.set_or1266510415728281911st_int L3) H3)) (or (and (= L L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_int L) H2)) (not (@ (@ tptp.ord_less_eq_int L3) H3)))))))
% 4.71/5.18 (assert (forall ((L tptp.real) (H2 tptp.real) (L3 tptp.real) (H3 tptp.real)) (= (= (@ (@ tptp.set_or1222579329274155063t_real L) H2) (@ (@ tptp.set_or1222579329274155063t_real L3) H3)) (or (and (= L L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_real L) H2)) (not (@ (@ tptp.ord_less_eq_real L3) H3)))))))
% 4.71/5.18 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 4.71/5.18 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N2) tptp.zero_zero_int) tptp.zero_zero_int)))
% 4.71/5.18 (assert (forall ((L tptp.nat) (U tptp.nat)) (@ tptp.finite_finite_nat (@ (@ tptp.set_or1269000886237332187st_nat L) U))))
% 4.71/5.18 (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))))
% 4.71/5.18 (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))))
% 4.71/5.18 (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))))
% 4.71/5.18 (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))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (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))))
% 4.71/5.18 (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))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (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)))))
% 4.71/5.18 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) A) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))))
% 4.71/5.18 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) A) (@ (@ tptp.ord_less_real tptp.zero_zero_real) A))))
% 4.71/5.18 (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))))
% 4.71/5.18 (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))))
% 4.71/5.18 (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))))
% 4.71/5.18 (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))))
% 4.71/5.18 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)))
% 4.71/5.18 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)))
% 4.71/5.18 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)))
% 4.71/5.18 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) (@ tptp.uminus1482373934393186551omplex A)) tptp.zero_zero_complex)))
% 4.71/5.18 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ tptp.uminus_uminus_int A)) tptp.zero_zero_int)))
% 4.71/5.18 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real)))
% 4.71/5.18 (assert (forall ((B2 tptp.complex)) (= (@ (@ tptp.minus_minus_complex tptp.zero_zero_complex) B2) (@ tptp.uminus1482373934393186551omplex B2))))
% 4.71/5.18 (assert (forall ((B2 tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) B2) (@ tptp.uminus_uminus_int B2))))
% 4.71/5.18 (assert (forall ((B2 tptp.real)) (= (@ (@ tptp.minus_minus_real tptp.zero_zero_real) B2) (@ tptp.uminus_uminus_real B2))))
% 4.71/5.18 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex tptp.zero_zero_complex) A) (@ tptp.uminus1482373934393186551omplex A))))
% 4.71/5.18 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) A) (@ tptp.uminus_uminus_int A))))
% 4.71/5.18 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real tptp.zero_zero_real) A) (@ tptp.uminus_uminus_real A))))
% 4.71/5.18 (assert (forall ((M2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.numeral_numeral_int M2))) (= (@ (@ 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)))))))
% 4.71/5.18 (assert (forall ((M2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N2))) (let ((_let_2 (@ tptp.numeral_numeral_real M2))) (= (@ (@ 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)))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B2) (@ (@ tptp.minus_minus_int B2) A))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) B2) (@ (@ tptp.minus_minus_real B2) A))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ tptp.uminus_uminus_int B2)) (@ (@ tptp.plus_plus_int A) B2))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.minus_minus_real A) (@ tptp.uminus_uminus_real B2)) (@ (@ tptp.plus_plus_real A) B2))))
% 4.71/5.18 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex X) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex X))))
% 4.71/5.18 (assert (forall ((X tptp.real)) (= (@ (@ tptp.divide_divide_real X) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real X))))
% 4.71/5.18 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (= (= (@ (@ tptp.set_or5403411693681687835d_enat A) B2) tptp.bot_bo7653980558646680370d_enat) (not (@ (@ tptp.ord_le2932123472753598470d_enat A) B2)))))
% 4.71/5.18 (assert (forall ((A tptp.set_nat) (B2 tptp.set_nat)) (= (= (@ (@ tptp.set_or4548717258645045905et_nat A) B2) tptp.bot_bot_set_set_nat) (not (@ (@ tptp.ord_less_eq_set_nat A) B2)))))
% 4.71/5.18 (assert (forall ((A tptp.set_int) (B2 tptp.set_int)) (= (= (@ (@ tptp.set_or370866239135849197et_int A) B2) tptp.bot_bot_set_set_int) (not (@ (@ tptp.ord_less_eq_set_int A) B2)))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (= (@ (@ tptp.set_or1269000886237332187st_nat A) B2) tptp.bot_bot_set_nat) (not (@ (@ tptp.ord_less_eq_nat A) B2)))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (= (@ (@ tptp.set_or1266510415728281911st_int A) B2) tptp.bot_bot_set_int) (not (@ (@ tptp.ord_less_eq_int A) B2)))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (= (@ (@ tptp.set_or1222579329274155063t_real A) B2) tptp.bot_bot_set_real) (not (@ (@ tptp.ord_less_eq_real A) B2)))))
% 4.71/5.18 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (= (= tptp.bot_bo7653980558646680370d_enat (@ (@ tptp.set_or5403411693681687835d_enat A) B2)) (not (@ (@ tptp.ord_le2932123472753598470d_enat A) B2)))))
% 4.71/5.18 (assert (forall ((A tptp.set_nat) (B2 tptp.set_nat)) (= (= tptp.bot_bot_set_set_nat (@ (@ tptp.set_or4548717258645045905et_nat A) B2)) (not (@ (@ tptp.ord_less_eq_set_nat A) B2)))))
% 4.71/5.18 (assert (forall ((A tptp.set_int) (B2 tptp.set_int)) (= (= tptp.bot_bot_set_set_int (@ (@ tptp.set_or370866239135849197et_int A) B2)) (not (@ (@ tptp.ord_less_eq_set_int A) B2)))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (= tptp.bot_bot_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A) B2)) (not (@ (@ tptp.ord_less_eq_nat A) B2)))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (= tptp.bot_bot_set_int (@ (@ tptp.set_or1266510415728281911st_int A) B2)) (not (@ (@ tptp.ord_less_eq_int A) B2)))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (= tptp.bot_bot_set_real (@ (@ tptp.set_or1222579329274155063t_real A) B2)) (not (@ (@ tptp.ord_less_eq_real A) B2)))))
% 4.71/5.18 (assert (forall ((A tptp.set_nat) (B2 tptp.set_nat) (C tptp.set_nat) (D tptp.set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.set_or4548717258645045905et_nat A) B2)) (@ (@ tptp.set_or4548717258645045905et_nat C) D)) (or (not (@ (@ tptp.ord_less_eq_set_nat A) B2)) (and (@ (@ tptp.ord_less_eq_set_nat C) A) (@ (@ tptp.ord_less_eq_set_nat B2) D))))))
% 4.71/5.18 (assert (forall ((A tptp.set_int) (B2 tptp.set_int) (C tptp.set_int) (D tptp.set_int)) (= (@ (@ tptp.ord_le4403425263959731960et_int (@ (@ tptp.set_or370866239135849197et_int A) B2)) (@ (@ tptp.set_or370866239135849197et_int C) D)) (or (not (@ (@ tptp.ord_less_eq_set_int A) B2)) (and (@ (@ tptp.ord_less_eq_set_int C) A) (@ (@ tptp.ord_less_eq_set_int B2) D))))))
% 4.71/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A) B2)) (@ (@ tptp.set_or1269000886237332187st_nat C) D)) (or (not (@ (@ tptp.ord_less_eq_nat A) B2)) (and (@ (@ tptp.ord_less_eq_nat C) A) (@ (@ tptp.ord_less_eq_nat B2) D))))))
% 4.71/5.18 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.set_or1266510415728281911st_int A) B2)) (@ (@ tptp.set_or1266510415728281911st_int C) D)) (or (not (@ (@ tptp.ord_less_eq_int A) B2)) (and (@ (@ tptp.ord_less_eq_int C) A) (@ (@ tptp.ord_less_eq_int B2) D))))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.set_or1222579329274155063t_real A) B2)) (@ (@ tptp.set_or1222579329274155063t_real C) D)) (or (not (@ (@ tptp.ord_less_eq_real A) B2)) (and (@ (@ tptp.ord_less_eq_real C) A) (@ (@ tptp.ord_less_eq_real B2) D))))))
% 4.71/5.18 (assert (forall ((B2 tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B2) A) (= (@ (@ tptp.set_or5403411693681687835d_enat A) B2) tptp.bot_bo7653980558646680370d_enat))))
% 4.71/5.18 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B2) A) (= (@ (@ tptp.set_or1269000886237332187st_nat A) B2) tptp.bot_bot_set_nat))))
% 4.71/5.18 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B2) A) (= (@ (@ tptp.set_or1266510415728281911st_int A) B2) tptp.bot_bot_set_int))))
% 4.71/5.18 (assert (forall ((B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B2) A) (= (@ (@ tptp.set_or1222579329274155063t_real A) B2) tptp.bot_bot_set_real))))
% 4.71/5.18 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (not (@ tptp.finite_finite_real (@ (@ tptp.set_or1222579329274155063t_real A) B2))) (@ (@ tptp.ord_less_real A) B2))))
% 4.71/5.18 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 4.71/5.18 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int tptp.zero_zero_nat) A) tptp.zero_zero_int)))
% 4.71/5.18 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N2)) tptp.one_one_nat) tptp.one_one_nat)))
% 4.71/5.18 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) tptp.one_one_int) tptp.one_one_int)))
% 4.71/5.18 (assert (= (@ tptp.ln_ln_real tptp.one_one_real) tptp.zero_zero_real))
% 4.71/5.18 (assert (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.zero_zero_complex))
% 4.71/5.18 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 4.71/5.18 (assert (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 4.71/5.18 (assert (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.one_one_complex) tptp.zero_zero_complex))
% 4.71/5.18 (assert (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int) tptp.zero_zero_int))
% 4.71/5.18 (assert (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real) tptp.zero_zero_real))
% 4.71/5.18 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ (@ tptp.minus_minus_complex _let_1) _let_1) tptp.zero_zero_complex)))
% 4.71/5.18 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.minus_minus_int _let_1) _let_1) tptp.zero_zero_int)))
% 4.71/5.18 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ (@ tptp.minus_minus_real _let_1) _let_1) tptp.zero_zero_real)))
% 4.71/5.18 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int)))
% 4.71/5.18 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real U))) (let ((_let_2 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V)))) (let ((_let_3 (@ (@ tptp.ord_max_real _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_real _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 4.96/5.18 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int U))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))) (let ((_let_3 (@ (@ tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 4.96/5.18 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real U)))) (let ((_let_2 (@ tptp.numeral_numeral_real V))) (let ((_let_3 (@ (@ tptp.ord_max_real _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_real _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 4.96/5.18 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int U)))) (let ((_let_2 (@ tptp.numeral_numeral_int V))) (let ((_let_3 (@ (@ tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 4.96/5.18 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real U)))) (let ((_let_2 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V)))) (let ((_let_3 (@ (@ tptp.ord_max_real _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_real _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 4.96/5.18 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int U)))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))) (let ((_let_3 (@ (@ tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 4.96/5.18 (assert (forall ((N2 tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) tptp.one_one_nat) tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat))))
% 4.96/5.18 (assert (forall ((N2 tptp.nat)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N2) tptp.one_one_int) tptp.zero_zero_int) (= N2 tptp.zero_zero_nat))))
% 4.96/5.18 (assert (forall ((V tptp.num) (W2 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 W2))) Y)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num V) W2)))) Y))))
% 4.96/5.18 (assert (forall ((V tptp.num) (W2 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 W2))) Y)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num V) W2)))) Y))))
% 4.96/5.18 (assert (forall ((M2 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ (@ tptp.ord_less_eq_num N2) M2))))
% 4.96/5.18 (assert (forall ((M2 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ (@ tptp.ord_less_eq_num N2) M2))))
% 4.96/5.18 (assert (forall ((M2 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ (@ tptp.ord_less_num N2) M2))))
% 4.96/5.18 (assert (forall ((M2 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ (@ tptp.ord_less_num N2) M2))))
% 4.96/5.18 (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)))))
% 4.96/5.18 (assert (forall ((M2 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2)))) (not (= M2 tptp.one)))))
% 4.96/5.18 (assert (forall ((M2 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2)))) (not (= M2 tptp.one)))))
% 4.96/5.18 (assert (forall ((A tptp.real) (B2 tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.divide_divide_real B2) _let_1)) (@ (@ tptp.ord_less_eq_real B2) (@ (@ tptp.times_times_real A) _let_1))))))
% 4.96/5.18 (assert (forall ((B2 tptp.real) (W2 tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B2) _let_1)) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) _let_1)) B2)))))
% 4.96/5.18 (assert (forall ((B2 tptp.complex) (W2 tptp.num) (A tptp.complex)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W2)))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B2) _let_1) A) (and (=> (not _let_2) (= B2 (@ (@ tptp.times_times_complex A) _let_1))) (=> _let_2 (= A tptp.zero_zero_complex))))))))
% 4.96/5.18 (assert (forall ((B2 tptp.real) (W2 tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B2) _let_1) A) (and (=> (not _let_2) (= B2 (@ (@ tptp.times_times_real A) _let_1))) (=> _let_2 (= A tptp.zero_zero_real))))))))
% 4.96/5.18 (assert (forall ((A tptp.complex) (B2 tptp.complex) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W2)))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= A (@ (@ tptp.divide1717551699836669952omplex B2) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex A) _let_1) B2)) (=> _let_2 (= A tptp.zero_zero_complex))))))))
% 4.96/5.18 (assert (forall ((A tptp.real) (B2 tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= A (@ (@ tptp.divide_divide_real B2) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real A) _let_1) B2)) (=> _let_2 (= A tptp.zero_zero_real))))))))
% 4.96/5.18 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.uminus_uminus_int tptp.one_one_int)) (not (= M2 tptp.one)))))
% 4.96/5.18 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) (@ tptp.uminus_uminus_real tptp.one_one_real)) (not (= M2 tptp.one)))))
% 4.96/5.18 (assert (forall ((A tptp.real) (B2 tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.divide_divide_real B2) _let_1)) (@ (@ tptp.ord_less_real B2) (@ (@ tptp.times_times_real A) _let_1))))))
% 4.96/5.18 (assert (forall ((B2 tptp.real) (W2 tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B2) _let_1)) A) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) _let_1)) B2)))))
% 4.96/5.18 (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)))))
% 4.96/5.18 (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)))))
% 4.96/5.18 (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))))))
% 4.96/5.18 (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))))))
% 4.96/5.18 (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))))))
% 4.96/5.18 (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))))))
% 4.96/5.18 (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))))))
% 4.96/5.18 (assert (forall ((M2 tptp.nat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat V))) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M2)))) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M2)) _let_1)))))
% 4.96/5.18 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat M2))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc (@ tptp.suc N2)))) (@ _let_1 (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N2))))))
% 4.96/5.18 (assert (forall ((M2 tptp.nat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat V))) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M2)))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M2)) _let_1)))))
% 4.96/5.18 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat M2))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc (@ tptp.suc N2)))) (@ _let_1 (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N2))))))
% 4.96/5.18 (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))))))
% 4.96/5.18 (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))))))
% 4.96/5.18 (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))))))
% 4.96/5.18 (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)))))))
% 4.96/5.18 (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))))
% 4.96/5.18 (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))))
% 4.96/5.18 (assert (forall ((M2 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 M2) _let_1) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat N2) M2))) _let_1)))))
% 4.96/5.18 (assert (forall ((M2 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 M2) _let_1) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat N2) M2))) _let_1)))))
% 4.96/5.18 (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)))))
% 4.96/5.18 (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))))))
% 4.96/5.18 (assert (forall ((L tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) L) (@ tptp.uminus_uminus_int L))))
% 4.96/5.18 (assert (forall ((K tptp.int)) (= (@ (@ tptp.minus_minus_int K) tptp.zero_zero_int) K)))
% 4.96/5.18 (assert (forall ((Z1 tptp.int) (Z22 tptp.int) (W2 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int Z1) Z22)) W2) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int Z1) W2)) (@ (@ tptp.times_times_int Z22) W2)))))
% 4.96/5.18 (assert (forall ((W2 tptp.int) (Z1 tptp.int) (Z22 tptp.int)) (let ((_let_1 (@ tptp.times_times_int W2))) (= (@ _let_1 (@ (@ tptp.minus_minus_int Z1) Z22)) (@ (@ tptp.minus_minus_int (@ _let_1 Z1)) (@ _let_1 Z22))))))
% 4.96/5.18 (assert (forall ((I tptp.int) (K tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int I) K) (=> (@ P (@ (@ tptp.minus_minus_int K) tptp.one_one_int)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.ord_less_int I4) K) (=> (@ P I4) (@ P (@ (@ tptp.minus_minus_int I4) tptp.one_one_int))))) (@ P I))))))
% 4.96/5.18 (assert (forall ((K tptp.int) (M2 tptp.int) (N2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (=> (@ (@ tptp.dvd_dvd_int (@ _let_1 M2)) (@ _let_1 N2)) (=> (not (= K tptp.zero_zero_int)) (@ (@ tptp.dvd_dvd_int M2) N2))))))
% 4.96/5.18 (assert (forall ((Z3 tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int Z3) N2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N2) (@ (@ tptp.ord_less_eq_int Z3) N2)))))
% 4.96/5.18 (assert (forall ((M2 tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M2) (=> (@ (@ tptp.ord_less_int M2) N2) (not (@ (@ tptp.dvd_dvd_int N2) M2))))))
% 4.96/5.18 (assert (forall ((M2 tptp.int) (N2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 M2) (=> (@ _let_1 N2) (=> (@ (@ tptp.dvd_dvd_int M2) N2) (=> (@ (@ tptp.dvd_dvd_int N2) M2) (= M2 N2))))))))
% 4.96/5.18 (assert (forall ((K tptp.int) (N2 tptp.int) (M2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int K))) (= (@ _let_1 (@ (@ tptp.plus_plus_int N2) (@ (@ tptp.times_times_int K) M2))) (@ _let_1 N2)))))
% 4.96/5.18 (assert (forall ((A tptp.int) (D tptp.int) (X tptp.int) (T tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X))) (let ((_let_2 (@ tptp.dvd_dvd_int A))) (=> (@ _let_2 D) (= (@ _let_2 (@ _let_1 T)) (@ _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.times_times_int C) D))) T))))))))
% 4.96/5.18 (assert (forall ((I tptp.int)) (=> (not (= I tptp.zero_zero_int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((D4 tptp.int)) (@ (@ tptp.dvd_dvd_int D4) I)))))))
% 4.96/5.18 (assert (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat Y)) X) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat X)) Y))))
% 4.96/5.18 (assert (forall ((Y tptp.set_int) (X tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int Y)) X) (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int X)) Y))))
% 4.96/5.18 (assert (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) (@ tptp.uminus5710092332889474511et_nat X)) (@ (@ tptp.ord_less_eq_set_nat X) (@ tptp.uminus5710092332889474511et_nat Y)))))
% 4.96/5.18 (assert (forall ((Y tptp.set_int) (X tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y) (@ tptp.uminus1532241313380277803et_int X)) (@ (@ tptp.ord_less_eq_set_int X) (@ tptp.uminus1532241313380277803et_int Y)))))
% 4.96/5.18 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat Y)) (@ tptp.uminus5710092332889474511et_nat X)))))
% 4.96/5.18 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X) Y) (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int Y)) (@ tptp.uminus1532241313380277803et_int X)))))
% 4.96/5.18 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (=> (@ (@ tptp.ord_less_int I) J) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (@ (@ tptp.ord_less_int (@ _let_1 I)) (@ _let_1 J)))))))
% 4.96/5.18 (assert (forall ((W2 tptp.int) (Z3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int W2) tptp.one_one_int)) Z3) (@ (@ tptp.ord_less_int W2) Z3))))
% 4.96/5.18 (assert (forall ((K tptp.int) (I tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int K) I) (=> (@ P (@ (@ tptp.plus_plus_int K) tptp.one_one_int)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.ord_less_int K) I4) (=> (@ P I4) (@ P (@ (@ tptp.plus_plus_int I4) tptp.one_one_int))))) (@ P I))))))
% 4.96/5.18 (assert (forall ((Z3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z3) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) Z3)))))
% 4.96/5.18 (assert (forall ((W2 tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int W2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int Z3) tptp.one_one_int)) (or (@ _let_1 Z3) (= W2 Z3))))))
% 4.96/5.18 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) Z3)) Z3)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Z3) tptp.zero_zero_int))))
% 4.96/5.18 (assert (forall ((M2 tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M2) (= (= (@ (@ tptp.times_times_int M2) N2) tptp.one_one_int) (and (= M2 tptp.one_one_int) (= N2 tptp.one_one_int))))))
% 4.96/5.18 (assert (forall ((W2 tptp.int) (Z3 tptp.int)) (=> (@ (@ tptp.ord_less_int W2) Z3) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int W2) tptp.one_one_int)) Z3))))
% 4.96/5.18 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z3) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z3))))
% 4.96/5.18 (assert (forall ((Z3 tptp.int)) (not (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) Z3)) Z3) tptp.zero_zero_int))))
% 4.96/5.18 (assert (forall ((M2 tptp.int) (N2 tptp.int)) (=> (= (@ (@ tptp.times_times_int M2) N2) tptp.one_one_int) (or (= M2 tptp.one_one_int) (= M2 (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 4.96/5.18 (assert (forall ((M2 tptp.int) (N2 tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (= (@ (@ tptp.times_times_int M2) N2) tptp.one_one_int) (or (and (= M2 tptp.one_one_int) (= N2 tptp.one_one_int)) (and (= M2 _let_1) (= N2 _let_1)))))))
% 4.96/5.18 (assert (forall ((L tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) L) tptp.zero_zero_int)))
% 4.96/5.18 (assert (forall ((K tptp.int)) (= (@ (@ tptp.times_times_int K) tptp.zero_zero_int) tptp.zero_zero_int)))
% 4.96/5.18 (assert (forall ((Z1 tptp.int) (Z22 tptp.int) (W2 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int Z1) Z22)) W2) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Z1) W2)) (@ (@ tptp.times_times_int Z22) W2)))))
% 4.96/5.18 (assert (forall ((W2 tptp.int) (Z1 tptp.int) (Z22 tptp.int)) (let ((_let_1 (@ tptp.times_times_int W2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int Z1) Z22)) (@ (@ tptp.plus_plus_int (@ _let_1 Z1)) (@ _let_1 Z22))))))
% 4.96/5.18 (assert (= (@ tptp.uminus_uminus_int tptp.zero_zero_int) tptp.zero_zero_int))
% 4.96/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (= A (@ tptp.uminus_uminus_int B2)) (= B2 (@ tptp.uminus_uminus_int A)))))
% 4.96/5.18 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (= A (@ tptp.uminus_uminus_real B2)) (= B2 (@ tptp.uminus_uminus_real A)))))
% 4.96/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (= (@ tptp.uminus_uminus_int A) B2) (= (@ tptp.uminus_uminus_int B2) A))))
% 4.96/5.18 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (= (@ tptp.uminus_uminus_real A) B2) (= (@ tptp.uminus_uminus_real B2) A))))
% 4.96/5.18 (assert (forall ((N2 tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat (@ _let_1 A)) (@ _let_1 B2))) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B2))))))
% 4.96/5.18 (assert (forall ((N2 tptp.nat) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ _let_1 A)) (@ _let_1 B2))) (@ _let_1 (@ (@ tptp.plus_plus_int A) B2))))))
% 4.96/5.18 (assert (forall ((N2 tptp.nat) (A tptp.nat) (B2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat M2))) (let ((_let_2 (@ tptp.bit_se2925701944663578781it_nat N2))) (=> (= (@ _let_2 A) (@ _let_2 B2)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ _let_1 A) (@ _let_1 B2))))))))
% 4.96/5.18 (assert (forall ((N2 tptp.nat) (A tptp.int) (B2 tptp.int) (M2 tptp.nat)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int M2))) (let ((_let_2 (@ tptp.bit_se2923211474154528505it_int N2))) (=> (= (@ _let_2 A) (@ _let_2 B2)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ _let_1 A) (@ _let_1 B2))))))))
% 4.96/5.18 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (Q3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.bit_se2925701944663578781it_nat M2) Q3)) (@ (@ tptp.bit_se2925701944663578781it_nat N2) Q3)))))
% 4.96/5.18 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.bit_se2925701944663578781it_nat N2) M2)) M2)))
% 4.96/5.18 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int M2) K)) (@ (@ tptp.bit_se2923211474154528505it_int N2) K)))))
% 4.96/5.18 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B2)) (@ tptp.uminus_uminus_real A)))))
% 4.96/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int B2)) (@ tptp.uminus_uminus_int A)))))
% 4.96/5.18 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) B2) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B2)) A))))
% 4.96/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) B2) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int B2)) A))))
% 4.96/5.18 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ tptp.uminus_uminus_real B2)) (@ (@ tptp.ord_less_eq_real B2) (@ tptp.uminus_uminus_real A)))))
% 4.96/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ tptp.uminus_uminus_int B2)) (@ (@ tptp.ord_less_eq_int B2) (@ tptp.uminus_uminus_int A)))))
% 4.96/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B2) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B2)) (@ tptp.uminus_uminus_int A)))))
% 4.96/5.18 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B2)) (@ tptp.uminus_uminus_real A)))))
% 4.96/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) B2) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B2)) A))))
% 4.96/5.18 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) B2) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B2)) A))))
% 4.96/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ tptp.uminus_uminus_int B2)) (@ (@ tptp.ord_less_int B2) (@ tptp.uminus_uminus_int A)))))
% 4.96/5.18 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ tptp.uminus_uminus_real B2)) (@ (@ tptp.ord_less_real B2) (@ tptp.uminus_uminus_real A)))))
% 4.96/5.18 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (= (@ (@ tptp.times_times_complex A) A) (@ (@ tptp.times_times_complex B2) B2)) (or (= A B2) (= A (@ tptp.uminus1482373934393186551omplex B2))))))
% 4.96/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (= (@ (@ tptp.times_times_int A) A) (@ (@ tptp.times_times_int B2) B2)) (or (= A B2) (= A (@ tptp.uminus_uminus_int B2))))))
% 4.96/5.18 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (= (@ (@ tptp.times_times_real A) A) (@ (@ tptp.times_times_real B2) B2)) (or (= A B2) (= A (@ tptp.uminus_uminus_real B2))))))
% 4.96/5.18 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) B2) (@ (@ tptp.times_times_complex A) (@ tptp.uminus1482373934393186551omplex B2)))))
% 4.96/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int A)) B2) (@ (@ tptp.times_times_int A) (@ tptp.uminus_uminus_int B2)))))
% 4.96/5.18 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real A)) B2) (@ (@ tptp.times_times_real A) (@ tptp.uminus_uminus_real B2)))))
% 4.96/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int A) B2)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int B2)) (@ tptp.uminus_uminus_int A)))))
% 4.96/5.18 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real A) B2)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real B2)) (@ tptp.uminus_uminus_real A)))))
% 4.96/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int A) B2)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int B2)) (@ tptp.uminus_uminus_int A)))))
% 4.96/5.18 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real A) B2)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real B2)) (@ tptp.uminus_uminus_real A)))))
% 4.96/5.18 (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))))))
% 4.96/5.18 (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))))))
% 4.96/5.18 (assert (forall ((B2 tptp.int) (A tptp.int)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int B2)) A) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int A)) B2))))
% 4.96/5.18 (assert (forall ((B2 tptp.real) (A tptp.real)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real B2)) A) (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real A)) B2))))
% 4.96/5.18 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (= (@ tptp.uminus_uminus_real (@ _let_1 B2)) (@ _let_1 (@ tptp.uminus_uminus_real B2))))))
% 4.96/5.18 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B2)) (@ (@ tptp.divide_divide_real A) B2))))
% 4.96/5.18 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) B2)) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real A)) B2))))
% 4.96/5.18 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (not (@ tptp.finite3207457112153483333omplex S2)) (not (@ tptp.finite3207457112153483333omplex (@ (@ tptp.minus_811609699411566653omplex S2) T3)))))))
% 4.96/5.18 (assert (forall ((T3 tptp.set_int) (S2 tptp.set_int)) (=> (@ tptp.finite_finite_int T3) (=> (not (@ tptp.finite_finite_int S2)) (not (@ tptp.finite_finite_int (@ (@ tptp.minus_minus_set_int S2) T3)))))))
% 4.96/5.18 (assert (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (not (@ tptp.finite4001608067531595151d_enat S2)) (not (@ tptp.finite4001608067531595151d_enat (@ (@ tptp.minus_925952699566721837d_enat S2) T3)))))))
% 4.96/5.18 (assert (forall ((T3 tptp.set_nat) (S2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat T3) (=> (not (@ tptp.finite_finite_nat S2)) (not (@ tptp.finite_finite_nat (@ (@ tptp.minus_minus_set_nat S2) T3)))))))
% 4.96/5.18 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat) (C4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B) (=> (@ (@ tptp.ord_less_eq_set_nat B) C4) (= (@ (@ tptp.minus_minus_set_nat B) (@ (@ tptp.minus_minus_set_nat C4) A2)) A2)))))
% 4.96/5.18 (assert (forall ((A2 tptp.set_int) (B tptp.set_int) (C4 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B) (=> (@ (@ tptp.ord_less_eq_set_int B) C4) (= (@ (@ tptp.minus_minus_set_int B) (@ (@ tptp.minus_minus_set_int C4) A2)) A2)))))
% 4.96/5.18 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A2) B)) A2)))
% 4.96/5.18 (assert (forall ((A2 tptp.set_int) (B tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A2) B)) A2)))
% 4.96/5.18 (assert (forall ((A2 tptp.set_nat) (C4 tptp.set_nat) (D6 tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) C4) (=> (@ (@ tptp.ord_less_eq_set_nat D6) B) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A2) B)) (@ (@ tptp.minus_minus_set_nat C4) D6))))))
% 4.96/5.18 (assert (forall ((A2 tptp.set_int) (C4 tptp.set_int) (D6 tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) C4) (=> (@ (@ tptp.ord_less_eq_set_int D6) B) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A2) B)) (@ (@ tptp.minus_minus_set_int C4) D6))))))
% 4.96/5.18 (assert (forall ((A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat)) (=> (@ (@ tptp.ord_le2529575680413868914d_enat A2) B) (exists ((B4 tptp.extended_enat)) (@ (@ tptp.member_Extended_enat B4) (@ (@ tptp.minus_925952699566721837d_enat B) A2))))))
% 4.96/5.18 (assert (forall ((A2 tptp.set_real) (B tptp.set_real)) (=> (@ (@ tptp.ord_less_set_real A2) B) (exists ((B4 tptp.real)) (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real B) A2))))))
% 4.96/5.18 (assert (forall ((A2 tptp.set_set_nat) (B tptp.set_set_nat)) (=> (@ (@ tptp.ord_less_set_set_nat A2) B) (exists ((B4 tptp.set_nat)) (@ (@ tptp.member_set_nat B4) (@ (@ tptp.minus_2163939370556025621et_nat B) A2))))))
% 4.96/5.18 (assert (forall ((A2 tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A2) B) (exists ((B4 tptp.int)) (@ (@ tptp.member_int B4) (@ (@ tptp.minus_minus_set_int B) A2))))))
% 4.96/5.18 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A2) B) (exists ((B4 tptp.nat)) (@ (@ tptp.member_nat B4) (@ (@ tptp.minus_minus_set_nat B) A2))))))
% 4.96/5.18 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N tptp.nat) (K2 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 K2) _let_1))) _let_1)))))
% 4.96/5.18 (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))))))
% 4.96/5.18 (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)))))))
% 4.96/5.18 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (not (@ tptp.finite_finite_real (@ (@ tptp.set_or1222579329274155063t_real A) B2))))))
% 4.96/5.18 (assert (forall ((N2 tptp.nat) (A tptp.int) (B2 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 B2)) (= (@ _let_1 A) (@ _let_1 B2)))))))
% 4.96/5.18 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int M2))) (let ((_let_2 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ _let_2 A)) (@ (@ (@ (@ tptp.if_int_int (@ (@ tptp.ord_less_eq_nat N2) M2)) _let_2) _let_1) A))))))
% 4.96/5.18 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ P M))) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ P X4))))))
% 4.96/5.18 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M) N2) (@ P M))) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ P X4))))))
% 4.96/5.18 (assert (forall ((M2 tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M2)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))))
% 4.96/5.18 (assert (forall ((M2 tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))))
% 4.96/5.18 (assert (forall ((M2 tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) (@ tptp.numeral_numeral_real N2))))
% 4.96/5.18 (assert (forall ((M2 tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.numeral_numeral_int N2))))
% 4.96/5.18 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))))))
% 4.96/5.18 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_zero_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))))
% 4.96/5.18 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_zero_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))))
% 4.96/5.18 (assert (forall ((M2 tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))))
% 4.96/5.18 (assert (forall ((M2 tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M2)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))))
% 4.96/5.18 (assert (forall ((M2 tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.numeral_numeral_int N2))))
% 4.96/5.18 (assert (forall ((M2 tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) (@ tptp.numeral_numeral_real N2))))
% 4.96/5.18 (assert (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 4.96/5.18 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 4.96/5.18 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 4.96/5.18 (assert (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 4.96/5.18 (assert (not (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))
% 4.96/5.18 (assert (not (= tptp.zero_zero_int (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 4.96/5.18 (assert (not (= tptp.zero_zero_real (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 4.96/5.18 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) B2) (= (@ (@ tptp.plus_plus_complex A) B2) tptp.zero_zero_complex))))
% 4.96/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (= (@ tptp.uminus_uminus_int A) B2) (= (@ (@ tptp.plus_plus_int A) B2) tptp.zero_zero_int))))
% 4.96/5.18 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (= (@ tptp.uminus_uminus_real A) B2) (= (@ (@ tptp.plus_plus_real A) B2) tptp.zero_zero_real))))
% 4.96/5.18 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (= A (@ tptp.uminus1482373934393186551omplex B2)) (= (@ (@ tptp.plus_plus_complex A) B2) tptp.zero_zero_complex))))
% 4.96/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (= A (@ tptp.uminus_uminus_int B2)) (= (@ (@ tptp.plus_plus_int A) B2) tptp.zero_zero_int))))
% 4.96/5.18 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (= A (@ tptp.uminus_uminus_real B2)) (= (@ (@ tptp.plus_plus_real A) B2) tptp.zero_zero_real))))
% 4.96/5.18 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (=> (= (@ (@ tptp.plus_plus_complex A) B2) tptp.zero_zero_complex) (= (@ tptp.uminus1482373934393186551omplex A) B2))))
% 4.96/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (= (@ (@ tptp.plus_plus_int A) B2) tptp.zero_zero_int) (= (@ tptp.uminus_uminus_int A) B2))))
% 4.96/5.18 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (= (@ (@ tptp.plus_plus_real A) B2) tptp.zero_zero_real) (= (@ tptp.uminus_uminus_real A) B2))))
% 4.96/5.18 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)))
% 4.96/5.18 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)))
% 4.96/5.18 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)))
% 4.96/5.18 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex A) B2) tptp.zero_zero_complex) (= B2 (@ tptp.uminus1482373934393186551omplex A)))))
% 4.96/5.18 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) B2) tptp.zero_zero_int) (= B2 (@ tptp.uminus_uminus_int A)))))
% 4.96/5.18 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) B2) tptp.zero_zero_real) (= B2 (@ tptp.uminus_uminus_real A)))))
% 4.96/5.18 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 4.96/5.18 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 4.96/5.18 (assert (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 4.96/5.18 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 4.96/5.18 (assert (forall ((B2 tptp.complex) (A tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (=> (not (= B2 tptp.zero_zero_complex)) (= (@ tptp.uminus1482373934393186551omplex (@ _let_1 B2)) (@ _let_1 (@ tptp.uminus1482373934393186551omplex B2)))))))
% 4.96/5.18 (assert (forall ((B2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (=> (not (= B2 tptp.zero_zero_real)) (= (@ tptp.uminus_uminus_real (@ _let_1 B2)) (@ _let_1 (@ tptp.uminus_uminus_real B2)))))))
% 4.96/5.18 (assert (forall ((B2 tptp.complex) (A tptp.complex)) (=> (not (= B2 tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B2)) (@ (@ tptp.divide1717551699836669952omplex A) B2)))))
% 4.96/5.18 (assert (forall ((B2 tptp.real) (A tptp.real)) (=> (not (= B2 tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B2)) (@ (@ tptp.divide_divide_real A) B2)))))
% 4.96/5.18 (assert (forall ((X tptp.complex)) (= (= (@ (@ tptp.times_times_complex X) X) tptp.one_one_complex) (or (= X tptp.one_one_complex) (= X (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))))
% 4.96/5.18 (assert (forall ((X tptp.int)) (= (= (@ (@ tptp.times_times_int X) X) tptp.one_one_int) (or (= X tptp.one_one_int) (= X (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 4.96/5.18 (assert (forall ((X tptp.real)) (= (= (@ (@ tptp.times_times_real X) X) tptp.one_one_real) (or (= X tptp.one_one_real) (= X (@ tptp.uminus_uminus_real tptp.one_one_real))))))
% 4.96/5.18 (assert (forall ((B tptp.int) (K tptp.int) (B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (=> (= B (@ (@ tptp.plus_plus_int K) B2)) (= (@ _let_1 B) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int K)) (@ _let_1 B2)))))))
% 4.96/5.18 (assert (forall ((B tptp.real) (K tptp.real) (B2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (=> (= B (@ (@ tptp.plus_plus_real K) B2)) (= (@ _let_1 B) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real K)) (@ _let_1 B2)))))))
% 4.96/5.18 (assert (= tptp.minus_minus_int (lambda ((A3 tptp.int) (B3 tptp.int)) (@ (@ tptp.plus_plus_int A3) (@ tptp.uminus_uminus_int B3)))))
% 4.96/5.18 (assert (= tptp.minus_minus_real (lambda ((A3 tptp.real) (B3 tptp.real)) (@ (@ tptp.plus_plus_real A3) (@ tptp.uminus_uminus_real B3)))))
% 4.96/5.18 (assert (= tptp.minus_minus_int (lambda ((A3 tptp.int) (B3 tptp.int)) (@ (@ tptp.plus_plus_int A3) (@ tptp.uminus_uminus_int B3)))))
% 4.96/5.18 (assert (= tptp.minus_minus_real (lambda ((A3 tptp.real) (B3 tptp.real)) (@ (@ tptp.plus_plus_real A3) (@ tptp.uminus_uminus_real B3)))))
% 4.96/5.18 (assert (forall ((N2 tptp.nat) (M2 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 M2))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N2) M2))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 4.96/5.18 (assert (forall ((N2 tptp.nat) (M2 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 M2))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N2) M2))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 4.96/5.18 (assert (forall ((N2 tptp.nat) (M2 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 M2))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N2) M2))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 4.96/5.18 (assert (forall ((N2 tptp.nat) (M2 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 M2))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N2) M2))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 4.96/5.18 (assert (forall ((N2 tptp.nat) (M2 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 M2))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N2) M2))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 4.96/5.18 (assert (forall ((N2 tptp.nat) (M2 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 M2))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N2) M2))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 4.96/5.18 (assert (forall ((B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int B2) A) (= (@ _let_1 (@ tptp.uminus_uminus_int B2)) (@ tptp.uminus_uminus_int (@ _let_1 B2)))))))
% 4.96/5.18 (assert (forall ((B2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (=> (@ (@ tptp.dvd_dvd_real B2) A) (= (@ _let_1 (@ tptp.uminus_uminus_real B2)) (@ tptp.uminus_uminus_real (@ _let_1 B2)))))))
% 4.96/5.18 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B2) A) (= (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) B2) (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int A) B2))))))
% 4.96/5.18 (assert (forall ((B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real B2) A) (= (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real A)) B2) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) B2))))))
% 4.96/5.18 (assert (forall ((A2 tptp.set_Extended_enat)) (= (@ (@ tptp.ord_le7203529160286727270d_enat A2) (@ tptp.uminus417252749190364093d_enat A2)) (= A2 tptp.bot_bo7653980558646680370d_enat))))
% 4.96/5.18 (assert (forall ((A2 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real A2) (@ tptp.uminus612125837232591019t_real A2)) (= A2 tptp.bot_bot_set_real))))
% 4.96/5.18 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A2) (@ tptp.uminus5710092332889474511et_nat A2)) (= A2 tptp.bot_bot_set_nat))))
% 4.96/5.18 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A2) (@ tptp.uminus1532241313380277803et_int A2)) (= A2 tptp.bot_bot_set_int))))
% 4.96/5.18 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat) (D tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat C))) (= (@ (@ tptp.ord_le2529575680413868914d_enat (@ (@ tptp.set_or5403411693681687835d_enat A) B2)) (@ (@ tptp.set_or5403411693681687835d_enat C) D)) (and (or (not (@ (@ tptp.ord_le2932123472753598470d_enat A) B2)) (and (@ _let_1 A) (@ (@ tptp.ord_le2932123472753598470d_enat B2) D) (or (@ (@ tptp.ord_le72135733267957522d_enat C) A) (@ (@ tptp.ord_le72135733267957522d_enat B2) D)))) (@ _let_1 D))))))
% 4.96/5.18 (assert (forall ((A tptp.set_nat) (B2 tptp.set_nat) (C tptp.set_nat) (D tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat C))) (= (@ (@ tptp.ord_less_set_set_nat (@ (@ tptp.set_or4548717258645045905et_nat A) B2)) (@ (@ tptp.set_or4548717258645045905et_nat C) D)) (and (or (not (@ (@ tptp.ord_less_eq_set_nat A) B2)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_set_nat B2) D) (or (@ (@ tptp.ord_less_set_nat C) A) (@ (@ tptp.ord_less_set_nat B2) D)))) (@ _let_1 D))))))
% 4.96/5.18 (assert (forall ((A tptp.set_int) (B2 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) B2)) (@ (@ tptp.set_or370866239135849197et_int C) D)) (and (or (not (@ (@ tptp.ord_less_eq_set_int A) B2)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_set_int B2) D) (or (@ (@ tptp.ord_less_set_int C) A) (@ (@ tptp.ord_less_set_int B2) D)))) (@ _let_1 D))))))
% 4.96/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (= (@ (@ tptp.ord_less_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A) B2)) (@ (@ tptp.set_or1269000886237332187st_nat C) D)) (and (or (not (@ (@ tptp.ord_less_eq_nat A) B2)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_nat B2) D) (or (@ (@ tptp.ord_less_nat C) A) (@ (@ tptp.ord_less_nat B2) D)))) (@ _let_1 D))))))
% 4.96/5.18 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (= (@ (@ tptp.ord_less_set_int (@ (@ tptp.set_or1266510415728281911st_int A) B2)) (@ (@ tptp.set_or1266510415728281911st_int C) D)) (and (or (not (@ (@ tptp.ord_less_eq_int A) B2)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_int B2) D) (or (@ (@ tptp.ord_less_int C) A) (@ (@ tptp.ord_less_int B2) D)))) (@ _let_1 D))))))
% 4.96/5.18 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real C))) (= (@ (@ tptp.ord_less_set_real (@ (@ tptp.set_or1222579329274155063t_real A) B2)) (@ (@ tptp.set_or1222579329274155063t_real C) D)) (and (or (not (@ (@ tptp.ord_less_eq_real A) B2)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real B2) D) (or (@ (@ tptp.ord_less_real C) A) (@ (@ tptp.ord_less_real B2) D)))) (@ _let_1 D))))))
% 4.96/5.18 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) (@ tptp.suc N2)) (= (@ _let_1 (@ (@ tptp.bit_ri631733984087533419it_int N2) A)) (@ _let_1 A))))))
% 4.96/5.18 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) tptp.zero_zero_real)))
% 4.96/5.18 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) tptp.zero_zero_int)))
% 4.96/5.18 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))))
% 4.96/5.18 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))))
% 4.96/5.18 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) tptp.zero_zero_int)))
% 4.96/5.18 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) tptp.zero_zero_real)))
% 4.96/5.18 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))))
% 4.96/5.18 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))))
% 4.96/5.18 (assert (not (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 4.96/5.18 (assert (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 4.96/5.18 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 4.96/5.18 (assert (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 4.96/5.18 (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)))))
% 4.96/5.18 (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)))))
% 4.96/5.18 (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)))))
% 4.96/5.18 (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)))))
% 4.96/5.18 (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)))))
% 4.96/5.18 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 4.96/5.18 (assert (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 4.96/5.18 (assert (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 4.96/5.18 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 4.96/5.18 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))))))
% 4.96/5.18 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))))))
% 4.96/5.18 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M2)) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 4.96/5.18 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M2)) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 4.96/5.18 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 4.96/5.18 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 4.96/5.18 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real M2))))
% 4.96/5.18 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M2))))
% 4.96/5.18 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) tptp.one_one_real)))
% 4.96/5.18 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) tptp.one_one_int)))
% 4.96/5.18 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))))))
% 4.96/5.18 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))))))
% 4.96/5.18 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))))))
% 4.96/5.18 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))))))
% 4.96/5.18 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M2)) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 4.96/5.18 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M2)) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 4.96/5.18 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M2))))
% 4.96/5.18 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real M2))))
% 4.96/5.18 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) tptp.one_one_int)))
% 4.96/5.18 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) tptp.one_one_real)))
% 4.96/5.18 (assert (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= A (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex B2) C))) (and (=> (not _let_1) (= (@ (@ tptp.times_times_complex A) C) (@ tptp.uminus1482373934393186551omplex B2))) (=> _let_1 (= A tptp.zero_zero_complex)))))))
% 4.96/5.18 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= A (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B2) C))) (and (=> (not _let_1) (= (@ (@ tptp.times_times_real A) C) (@ tptp.uminus_uminus_real B2))) (=> _let_1 (= A tptp.zero_zero_real)))))))
% 4.96/5.18 (assert (forall ((B2 tptp.complex) (C tptp.complex) (A tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex B2) C)) A) (and (=> (not _let_1) (= (@ tptp.uminus1482373934393186551omplex B2) (@ (@ tptp.times_times_complex A) C))) (=> _let_1 (= A tptp.zero_zero_complex)))))))
% 4.96/5.18 (assert (forall ((B2 tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B2) C)) A) (and (=> (not _let_1) (= (@ tptp.uminus_uminus_real B2) (@ (@ tptp.times_times_real A) C))) (=> _let_1 (= A tptp.zero_zero_real)))))))
% 4.96/5.18 (assert (forall ((B2 tptp.complex) (A tptp.complex) (C tptp.complex)) (=> (not (= B2 tptp.zero_zero_complex)) (= (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B2)) C) (= (@ tptp.uminus1482373934393186551omplex A) (@ (@ tptp.times_times_complex C) B2))))))
% 4.96/5.18 (assert (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (=> (not (= B2 tptp.zero_zero_real)) (= (= (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) B2)) C) (= (@ tptp.uminus_uminus_real A) (@ (@ tptp.times_times_real C) B2))))))
% 4.96/5.18 (assert (forall ((B2 tptp.complex) (C tptp.complex) (A tptp.complex)) (=> (not (= B2 tptp.zero_zero_complex)) (= (= C (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B2))) (= (@ (@ tptp.times_times_complex C) B2) (@ tptp.uminus1482373934393186551omplex A))))))
% 4.96/5.18 (assert (forall ((B2 tptp.real) (C tptp.real) (A tptp.real)) (=> (not (= B2 tptp.zero_zero_real)) (= (= C (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) B2))) (= (@ (@ tptp.times_times_real C) B2) (@ tptp.uminus_uminus_real A))))))
% 4.96/5.18 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B2) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (and (not (= B2 tptp.zero_zero_complex)) (= A (@ tptp.uminus1482373934393186551omplex B2))))))
% 4.96/5.18 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (= (@ (@ tptp.divide_divide_real A) B2) (@ tptp.uminus_uminus_real tptp.one_one_real)) (and (not (= B2 tptp.zero_zero_real)) (= A (@ tptp.uminus_uminus_real B2))))))
% 4.96/5.18 (assert (forall ((N2 tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2)) (@ tptp.suc (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2))))))
% 4.96/5.18 (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))))))))
% 4.96/5.18 (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))))))
% 4.96/5.18 (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))))
% 4.96/5.18 (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))))
% 4.96/5.18 (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)))))
% 4.96/5.18 (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)))))
% 4.96/5.18 (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)))))
% 4.96/5.18 (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)))))
% 4.96/5.18 (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)))))
% 4.96/5.18 (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)))))
% 4.96/5.18 (assert (forall ((N6 tptp.set_nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N6) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ tptp.finite_finite_nat N6))))
% 4.96/5.18 (assert (forall ((C tptp.real) (B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B2) C))) A) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B2)) (@ (@ tptp.times_times_real A) C))))))
% 4.96/5.18 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B2) C))) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ tptp.uminus_uminus_real B2))))))
% 4.96/5.18 (assert (forall ((C tptp.real) (B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B2) C))) A) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ tptp.uminus_uminus_real B2))))))
% 4.96/5.18 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B2) C))) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B2)) (@ (@ tptp.times_times_real A) C))))))
% 4.96/5.18 (assert (forall ((B2 tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ tptp.uminus_uminus_real B2))) (let ((_let_4 (@ (@ tptp.times_times_real A) C))) (let ((_let_5 (@ _let_1 C))) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B2) C))) A) (and (=> _let_5 (@ (@ tptp.ord_less_real _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_real _let_4) _let_3)) (=> (not _let_2) (@ _let_1 A)))))))))))))
% 4.96/5.18 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ tptp.uminus_uminus_real B2))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_1 (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B2) C))) (and (=> _let_5 (@ (@ tptp.ord_less_real _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_real _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_real)))))))))))))
% 4.96/5.18 (assert (forall ((B2 tptp.complex) (C tptp.complex) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W2)))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B2) C) _let_1) (and (=> (not _let_2) (= B2 (@ (@ tptp.times_times_complex _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))))
% 4.96/5.18 (assert (forall ((B2 tptp.real) (C tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B2) C) _let_1) (and (=> (not _let_2) (= B2 (@ (@ tptp.times_times_real _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))))
% 4.96/5.18 (assert (forall ((W2 tptp.num) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W2)))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= _let_1 (@ (@ tptp.divide1717551699836669952omplex B2) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex _let_1) C) B2)) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))))
% 4.96/5.18 (assert (forall ((W2 tptp.num) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= _let_1 (@ (@ tptp.divide_divide_real B2) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real _let_1) C) B2)) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))))
% 4.96/5.18 (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))))
% 4.96/5.18 (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))))
% 4.96/5.18 (assert (forall ((Z3 tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) Z3))) B2))) (let ((_let_2 (= Z3 tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 B2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ (@ tptp.times_times_complex B2) Z3))) Z3))))))))
% 4.96/5.18 (assert (forall ((Z3 tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) Z3))) B2))) (let ((_let_2 (= Z3 tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 B2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.times_times_real B2) Z3))) Z3))))))))
% 4.96/5.18 (assert (forall ((Z3 tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z3 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex X) Z3))) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex X)) (@ (@ tptp.times_times_complex Y) Z3))) Z3)))))
% 4.96/5.18 (assert (forall ((Z3 tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z3 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real X) Z3))) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real X)) (@ (@ tptp.times_times_real Y) Z3))) Z3)))))
% 4.96/5.18 (assert (forall ((Z3 tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) Z3))) B2))) (let ((_let_2 (= Z3 tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 (@ tptp.uminus1482373934393186551omplex B2))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ (@ tptp.times_times_complex B2) Z3))) Z3))))))))
% 4.96/5.18 (assert (forall ((Z3 tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) Z3))) B2))) (let ((_let_2 (= Z3 tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_real B2))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.times_times_real B2) Z3))) Z3))))))))
% 4.96/5.18 (assert (forall ((Z3 tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex A) Z3)) B2))) (let ((_let_2 (= Z3 tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 (@ tptp.uminus1482373934393186551omplex B2))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex A) (@ (@ tptp.times_times_complex B2) Z3))) Z3))))))))
% 4.96/5.18 (assert (forall ((Z3 tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real A) Z3)) B2))) (let ((_let_2 (= Z3 tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_real B2))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real A) (@ (@ tptp.times_times_real B2) Z3))) Z3))))))))
% 4.96/5.18 (assert (forall ((Z3 tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z3 tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex X) Z3))) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex X)) (@ (@ tptp.times_times_complex Y) Z3))) Z3)))))
% 4.96/5.18 (assert (forall ((Z3 tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z3 tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real X) Z3))) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X)) (@ (@ tptp.times_times_real Y) Z3))) Z3)))))
% 4.96/5.18 (assert (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one)) (@ tptp.suc (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat)))))
% 4.96/5.18 (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))))
% 4.96/5.18 (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))))))
% 4.96/5.18 (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))))))
% 4.96/5.18 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) M2) M2))))
% 4.96/5.18 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.bit_se2925701944663578781it_nat N2) M2)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))
% 4.96/5.18 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) M2) M2) (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 4.96/5.18 (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)))))
% 4.96/5.18 (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)))))
% 4.96/5.18 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ tptp.uminus_uminus_real B2))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_1 (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B2) C))) (and (=> _let_5 (@ (@ tptp.ord_less_eq_real _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_eq_real _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_real)))))))))))))
% 4.96/5.18 (assert (forall ((B2 tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_2 (@ tptp.uminus_uminus_real B2))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B2) C))) A) (and (=> _let_4 (@ (@ tptp.ord_less_eq_real _let_2) _let_3)) (=> (not _let_4) (and (=> _let_1 (@ (@ tptp.ord_less_eq_real _let_3) _let_2)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A))))))))))))
% 4.96/5.18 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B2) C))) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B2)) (@ (@ tptp.times_times_real A) C))))))
% 4.96/5.18 (assert (forall ((C tptp.real) (B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B2) C))) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ tptp.uminus_uminus_real B2))))))
% 4.96/5.18 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B2) C))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ tptp.uminus_uminus_real B2))))))
% 4.96/5.18 (assert (forall ((C tptp.real) (B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B2) C))) A) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B2)) (@ (@ tptp.times_times_real A) C))))))
% 4.96/5.18 (assert (forall ((B2 tptp.real) (C tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ _let_2 C))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B2) C)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_real B2) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real _let_4) B2)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))))
% 4.96/5.18 (assert (forall ((W2 tptp.num) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (let ((_let_2 (@ tptp.ord_less_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B2) C)) (and (=> _let_5 (@ (@ tptp.ord_less_real _let_4) B2)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real B2) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))))
% 4.96/5.18 (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)))))
% 4.96/5.18 (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)))))
% 4.96/5.18 (assert (forall ((M2 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 M2))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat tptp.one)) _let_1)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M2)) (@ tptp.numeral_numeral_nat Q3)) tptp.zero_zero_nat)))))
% 4.96/5.18 (assert (forall ((M2 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 M2))) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int tptp.one)) _let_1)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M2)) (@ tptp.numeral_numeral_int Q3)) tptp.zero_zero_int)))))
% 4.96/5.18 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M2)))) N2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M2)) N2))))
% 4.96/5.18 (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)))))))
% 4.96/5.18 (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)))))))
% 4.96/5.18 (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)))))))
% 4.96/5.18 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M2)))) N2) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M2)) N2))))
% 4.96/5.18 (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))))
% 4.96/5.18 (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))))
% 4.96/5.18 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.bit_se2925701944663578781it_nat N2) M2)) M2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) M2))))
% 4.96/5.18 (assert (forall ((B2 tptp.real) (C tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B2) C)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_real B2) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_real _let_3) B2)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1))))))))))))
% 4.96/5.18 (assert (forall ((W2 tptp.num) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (let ((_let_2 (@ tptp.ord_less_eq_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B2) C)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_real _let_4) B2)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_real B2) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))))
% 4.96/5.18 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))))
% 4.96/5.18 (assert (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) X) (=> (@ (@ tptp.ord_less_eq_int X) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int)))))
% 4.96/5.18 (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))))
% 4.96/5.18 (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))))
% 4.96/5.18 (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))))
% 4.96/5.18 (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))))))
% 4.96/5.18 (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))))))
% 4.96/5.18 (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))))))))))
% 4.96/5.18 (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))))))))))
% 4.96/5.18 (assert (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ (@ tptp.modulo_modulo_nat M2) (@ 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))))))))
% 4.96/5.18 (assert (forall ((M2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (let ((_let_2 (@ tptp.bit1 M2))) (let ((_let_3 (@ tptp.unique5052692396658037445od_int _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_num M2) 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)))))))))))))
% 4.96/5.18 (assert (forall ((M2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (let ((_let_2 (@ tptp.bit1 M2))) (let ((_let_3 (@ tptp.unique5055182867167087721od_nat _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_num M2) 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)))))))))))))
% 4.96/5.18 (assert (forall ((M2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (let ((_let_2 (@ tptp.bit0 M2))) (let ((_let_3 (@ tptp.unique5052692396658037445od_int _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_eq_num M2) 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)))))))))))))
% 4.96/5.18 (assert (forall ((M2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (let ((_let_2 (@ tptp.bit0 M2))) (let ((_let_3 (@ tptp.unique5055182867167087721od_nat _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_eq_num M2) 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)))))))))))))
% 4.96/5.18 (assert (= tptp.unique5024387138958732305ep_int (lambda ((L2 tptp.num) (__flatten_var_0 tptp.product_prod_int_int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q5 tptp.int) (R4 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) R4)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R4) _let_2))) (@ (@ tptp.product_Pair_int_int _let_1) R4)))))) __flatten_var_0))))
% 4.96/5.18 (assert (= tptp.unique5026877609467782581ep_nat (lambda ((L2 tptp.num) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q5 tptp.nat) (R4 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) R4)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R4) _let_2))) (@ (@ tptp.product_Pair_nat_nat _let_1) R4)))))) __flatten_var_0))))
% 4.96/5.18 (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))))
% 4.96/5.18 (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))))
% 4.96/5.18 (assert (= tptp.unique5052692396658037445od_int (lambda ((M tptp.num) (N tptp.num)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_num M) N)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int M))) (@ (@ tptp.unique5024387138958732305ep_int N) (@ (@ tptp.unique5052692396658037445od_int M) (@ tptp.bit0 N)))))))
% 4.96/5.18 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M tptp.num) (N tptp.num)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_num M) N)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.unique5026877609467782581ep_nat N) (@ (@ tptp.unique5055182867167087721od_nat M) (@ tptp.bit0 N)))))))
% 4.96/5.18 (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)))))))
% 4.96/5.18 (assert (forall ((X tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X))) (let ((_let_2 (@ _let_1 A2))) (= (@ _let_1 _let_2) _let_2)))))
% 4.96/5.18 (assert (forall ((X tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int X))) (let ((_let_2 (@ _let_1 A2))) (= (@ _let_1 _let_2) _let_2)))))
% 4.96/5.18 (assert (forall ((X tptp.real) (A2 tptp.set_real)) (let ((_let_1 (@ tptp.insert_real X))) (let ((_let_2 (@ _let_1 A2))) (= (@ _let_1 _let_2) _let_2)))))
% 4.96/5.18 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (A2 tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat A))) (= (@ _let_1 (@ (@ tptp.insert_Extended_enat B2) A2)) (or (= A B2) (@ _let_1 A2))))))
% 4.96/5.18 (assert (forall ((A tptp.real) (B2 tptp.real) (A2 tptp.set_real)) (let ((_let_1 (@ tptp.member_real A))) (= (@ _let_1 (@ (@ tptp.insert_real B2) A2)) (or (= A B2) (@ _let_1 A2))))))
% 4.96/5.18 (assert (forall ((A tptp.set_nat) (B2 tptp.set_nat) (A2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat A))) (= (@ _let_1 (@ (@ tptp.insert_set_nat B2) A2)) (or (= A B2) (@ _let_1 A2))))))
% 4.96/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat A))) (= (@ _let_1 (@ (@ tptp.insert_nat B2) A2)) (or (= A B2) (@ _let_1 A2))))))
% 4.96/5.18 (assert (forall ((A tptp.int) (B2 tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ tptp.member_int A))) (= (@ _let_1 (@ (@ tptp.insert_int B2) A2)) (or (= A B2) (@ _let_1 A2))))))
% 4.96/5.18 (assert (forall ((A tptp.extended_enat) (B tptp.set_Extended_enat) (B2 tptp.extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat A))) (=> (=> (not (@ _let_1 B)) (= A B2)) (@ _let_1 (@ (@ tptp.insert_Extended_enat B2) B))))))
% 4.96/5.18 (assert (forall ((A tptp.real) (B tptp.set_real) (B2 tptp.real)) (let ((_let_1 (@ tptp.member_real A))) (=> (=> (not (@ _let_1 B)) (= A B2)) (@ _let_1 (@ (@ tptp.insert_real B2) B))))))
% 4.96/5.18 (assert (forall ((A tptp.set_nat) (B tptp.set_set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat A))) (=> (=> (not (@ _let_1 B)) (= A B2)) (@ _let_1 (@ (@ tptp.insert_set_nat B2) B))))))
% 4.96/5.18 (assert (forall ((A tptp.nat) (B tptp.set_nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat A))) (=> (=> (not (@ _let_1 B)) (= A B2)) (@ _let_1 (@ (@ tptp.insert_nat B2) B))))))
% 4.96/5.18 (assert (forall ((A tptp.int) (B tptp.set_int) (B2 tptp.int)) (let ((_let_1 (@ tptp.member_int A))) (=> (=> (not (@ _let_1 B)) (= A B2)) (@ _let_1 (@ (@ tptp.insert_int B2) B))))))
% 4.96/5.18 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ (@ tptp.minus_minus_set_nat A2) B))) (= (@ (@ tptp.minus_minus_set_nat _let_1) B) _let_1))))
% 4.96/5.18 (assert (forall ((C tptp.extended_enat) (A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat C))) (= (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) B)) (and (@ _let_1 A2) (not (@ _let_1 B)))))))
% 4.96/5.18 (assert (forall ((C tptp.real) (A2 tptp.set_real) (B tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) B)) (and (@ _let_1 A2) (not (@ _let_1 B)))))))
% 4.96/5.18 (assert (forall ((C tptp.set_nat) (A2 tptp.set_set_nat) (B tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (= (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A2) B)) (and (@ _let_1 A2) (not (@ _let_1 B)))))))
% 4.96/5.18 (assert (forall ((C tptp.int) (A2 tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B)) (and (@ _let_1 A2) (not (@ _let_1 B)))))))
% 4.96/5.18 (assert (forall ((C tptp.nat) (A2 tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B)) (and (@ _let_1 A2) (not (@ _let_1 B)))))))
% 4.96/5.18 (assert (forall ((C tptp.extended_enat) (A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat C))) (=> (@ _let_1 A2) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) B)))))))
% 4.96/5.18 (assert (forall ((C tptp.real) (A2 tptp.set_real) (B tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ _let_1 A2) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) B)))))))
% 4.96/5.18 (assert (forall ((C tptp.set_nat) (A2 tptp.set_set_nat) (B tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 A2) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A2) B)))))))
% 4.96/5.18 (assert (forall ((C tptp.int) (A2 tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 A2) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B)))))))
% 4.96/5.18 (assert (forall ((C tptp.nat) (A2 tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 A2) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B)))))))
% 4.96/5.18 (assert (forall ((C tptp.extended_enat) (A2 tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat C))) (=> (not (@ _let_1 A2)) (@ _let_1 (@ tptp.uminus417252749190364093d_enat A2))))))
% 4.96/5.18 (assert (forall ((C tptp.real) (A2 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (=> (not (@ _let_1 A2)) (@ _let_1 (@ tptp.uminus612125837232591019t_real A2))))))
% 4.96/5.18 (assert (forall ((C tptp.set_nat) (A2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (not (@ _let_1 A2)) (@ _let_1 (@ tptp.uminus613421341184616069et_nat A2))))))
% 4.96/5.18 (assert (forall ((C tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (not (@ _let_1 A2)) (@ _let_1 (@ tptp.uminus5710092332889474511et_nat A2))))))
% 4.96/5.18 (assert (forall ((C tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (not (@ _let_1 A2)) (@ _let_1 (@ tptp.uminus1532241313380277803et_int A2))))))
% 4.96/5.18 (assert (forall ((C tptp.extended_enat) (A2 tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat C))) (= (@ _let_1 (@ tptp.uminus417252749190364093d_enat A2)) (not (@ _let_1 A2))))))
% 4.96/5.18 (assert (forall ((C tptp.real) (A2 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (= (@ _let_1 (@ tptp.uminus612125837232591019t_real A2)) (not (@ _let_1 A2))))))
% 4.96/5.18 (assert (forall ((C tptp.set_nat) (A2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (= (@ _let_1 (@ tptp.uminus613421341184616069et_nat A2)) (not (@ _let_1 A2))))))
% 4.96/5.18 (assert (forall ((C tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (= (@ _let_1 (@ tptp.uminus5710092332889474511et_nat A2)) (not (@ _let_1 A2))))))
% 4.96/5.18 (assert (forall ((C tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (= (@ _let_1 (@ tptp.uminus1532241313380277803et_int A2)) (not (@ _let_1 A2))))))
% 4.96/5.18 (assert (forall ((L tptp.int) (U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or1266510415728281911st_int L) U))))
% 4.96/5.18 (assert (forall ((A tptp.set_nat)) (@ (@ tptp.member_set_nat A) (@ (@ tptp.insert_set_nat A) tptp.bot_bot_set_set_nat))))
% 4.96/5.18 (assert (forall ((A tptp.extended_enat)) (@ (@ tptp.member_Extended_enat A) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat))))
% 4.96/5.18 (assert (forall ((A tptp.real)) (@ (@ tptp.member_real A) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))
% 4.96/5.18 (assert (forall ((A tptp.nat)) (@ (@ tptp.member_nat A) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))
% 4.96/5.18 (assert (forall ((A tptp.int)) (@ (@ tptp.member_int A) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))
% 4.96/5.18 (assert (forall ((A tptp.real) (A2 tptp.set_real)) (= (@ tptp.finite_finite_real (@ (@ tptp.insert_real A) A2)) (@ tptp.finite_finite_real A2))))
% 4.96/5.18 (assert (forall ((A tptp.nat) (A2 tptp.set_nat)) (= (@ tptp.finite_finite_nat (@ (@ tptp.insert_nat A) A2)) (@ tptp.finite_finite_nat A2))))
% 4.96/5.18 (assert (forall ((A tptp.complex) (A2 tptp.set_complex)) (= (@ tptp.finite3207457112153483333omplex (@ (@ tptp.insert_complex A) A2)) (@ tptp.finite3207457112153483333omplex A2))))
% 4.96/5.18 (assert (forall ((A tptp.int) (A2 tptp.set_int)) (= (@ tptp.finite_finite_int (@ (@ tptp.insert_int A) A2)) (@ tptp.finite_finite_int A2))))
% 4.96/5.18 (assert (forall ((A tptp.extended_enat) (A2 tptp.set_Extended_enat)) (= (@ tptp.finite4001608067531595151d_enat (@ (@ tptp.insert_Extended_enat A) A2)) (@ tptp.finite4001608067531595151d_enat A2))))
% 4.96/5.18 (assert (forall ((X tptp.extended_enat) (A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat)) (= (@ (@ tptp.ord_le7203529160286727270d_enat (@ (@ tptp.insert_Extended_enat X) A2)) B) (and (@ (@ tptp.member_Extended_enat X) B) (@ (@ tptp.ord_le7203529160286727270d_enat A2) B)))))
% 4.96/5.18 (assert (forall ((X tptp.real) (A2 tptp.set_real) (B tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.insert_real X) A2)) B) (and (@ (@ tptp.member_real X) B) (@ (@ tptp.ord_less_eq_set_real A2) B)))))
% 4.96/5.18 (assert (forall ((X tptp.set_nat) (A2 tptp.set_set_nat) (B tptp.set_set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.insert_set_nat X) A2)) B) (and (@ (@ tptp.member_set_nat X) B) (@ (@ tptp.ord_le6893508408891458716et_nat A2) B)))))
% 4.96/5.18 (assert (forall ((X tptp.nat) (A2 tptp.set_nat) (B tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.insert_nat X) A2)) B) (and (@ (@ tptp.member_nat X) B) (@ (@ tptp.ord_less_eq_set_nat A2) B)))))
% 4.96/5.18 (assert (forall ((X tptp.int) (A2 tptp.set_int) (B tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.insert_int X) A2)) B) (and (@ (@ tptp.member_int X) B) (@ (@ tptp.ord_less_eq_set_int A2) B)))))
% 4.96/5.18 (assert (forall ((X tptp.extended_enat) (B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat)) (=> (@ (@ tptp.member_Extended_enat X) B) (= (@ (@ tptp.minus_925952699566721837d_enat (@ (@ tptp.insert_Extended_enat X) A2)) B) (@ (@ tptp.minus_925952699566721837d_enat A2) B)))))
% 4.96/5.18 (assert (forall ((X tptp.real) (B tptp.set_real) (A2 tptp.set_real)) (=> (@ (@ tptp.member_real X) B) (= (@ (@ tptp.minus_minus_set_real (@ (@ tptp.insert_real X) A2)) B) (@ (@ tptp.minus_minus_set_real A2) B)))))
% 4.96/5.18 (assert (forall ((X tptp.set_nat) (B tptp.set_set_nat) (A2 tptp.set_set_nat)) (=> (@ (@ tptp.member_set_nat X) B) (= (@ (@ tptp.minus_2163939370556025621et_nat (@ (@ tptp.insert_set_nat X) A2)) B) (@ (@ tptp.minus_2163939370556025621et_nat A2) B)))))
% 4.96/5.18 (assert (forall ((X tptp.int) (B tptp.set_int) (A2 tptp.set_int)) (=> (@ (@ tptp.member_int X) B) (= (@ (@ tptp.minus_minus_set_int (@ (@ tptp.insert_int X) A2)) B) (@ (@ tptp.minus_minus_set_int A2) B)))))
% 4.96/5.18 (assert (forall ((X tptp.nat) (B tptp.set_nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.member_nat X) B) (= (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.insert_nat X) A2)) B) (@ (@ tptp.minus_minus_set_nat A2) B)))))
% 4.96/5.18 (assert (forall ((X tptp.extended_enat) (A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.minus_925952699566721837d_enat A2))) (=> (not (@ (@ tptp.member_Extended_enat X) A2)) (= (@ _let_1 (@ (@ tptp.insert_Extended_enat X) B)) (@ _let_1 B))))))
% 4.96/5.18 (assert (forall ((X tptp.real) (A2 tptp.set_real) (B tptp.set_real)) (let ((_let_1 (@ tptp.minus_minus_set_real A2))) (=> (not (@ (@ tptp.member_real X) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X) B)) (@ _let_1 B))))))
% 4.96/5.18 (assert (forall ((X tptp.set_nat) (A2 tptp.set_set_nat) (B tptp.set_set_nat)) (let ((_let_1 (@ tptp.minus_2163939370556025621et_nat A2))) (=> (not (@ (@ tptp.member_set_nat X) A2)) (= (@ _let_1 (@ (@ tptp.insert_set_nat X) B)) (@ _let_1 B))))))
% 4.96/5.18 (assert (forall ((X tptp.int) (A2 tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.minus_minus_set_int A2))) (=> (not (@ (@ tptp.member_int X) A2)) (= (@ _let_1 (@ (@ tptp.insert_int X) B)) (@ _let_1 B))))))
% 4.96/5.18 (assert (forall ((X tptp.nat) (A2 tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat A2))) (=> (not (@ (@ tptp.member_nat X) A2)) (= (@ _let_1 (@ (@ tptp.insert_nat X) B)) (@ _let_1 B))))))
% 4.96/5.18 (assert (forall ((A tptp.list_nat)) (= (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (= X4 A))) (@ (@ tptp.insert_list_nat A) tptp.bot_bot_set_list_nat))))
% 4.96/5.18 (assert (forall ((A tptp.set_nat)) (= (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (= X4 A))) (@ (@ tptp.insert_set_nat A) tptp.bot_bot_set_set_nat))))
% 4.96/5.18 (assert (forall ((A tptp.extended_enat)) (= (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (= X4 A))) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat))))
% 4.96/5.18 (assert (forall ((A tptp.real)) (= (@ tptp.collect_real (lambda ((X4 tptp.real)) (= X4 A))) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))
% 4.96/5.18 (assert (forall ((A tptp.nat)) (= (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (= X4 A))) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))
% 4.96/5.18 (assert (forall ((A tptp.int)) (= (@ tptp.collect_int (lambda ((X4 tptp.int)) (= X4 A))) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))
% 4.96/5.18 (assert (forall ((A tptp.list_nat)) (= (@ tptp.collect_list_nat (@ (lambda ((Y4 tptp.list_nat) (Z2 tptp.list_nat)) (= Y4 Z2)) A)) (@ (@ tptp.insert_list_nat A) tptp.bot_bot_set_list_nat))))
% 4.96/5.18 (assert (forall ((A tptp.set_nat)) (= (@ tptp.collect_set_nat (@ (lambda ((Y4 tptp.set_nat) (Z2 tptp.set_nat)) (= Y4 Z2)) A)) (@ (@ tptp.insert_set_nat A) tptp.bot_bot_set_set_nat))))
% 4.96/5.18 (assert (forall ((A tptp.extended_enat)) (= (@ tptp.collec4429806609662206161d_enat (@ (lambda ((Y4 tptp.extended_enat) (Z2 tptp.extended_enat)) (= Y4 Z2)) A)) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat))))
% 4.96/5.18 (assert (forall ((A tptp.real)) (= (@ tptp.collect_real (@ (lambda ((Y4 tptp.real) (Z2 tptp.real)) (= Y4 Z2)) A)) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))
% 4.96/5.18 (assert (forall ((A tptp.nat)) (= (@ tptp.collect_nat (@ (lambda ((Y4 tptp.nat) (Z2 tptp.nat)) (= Y4 Z2)) A)) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))
% 4.96/5.18 (assert (forall ((A tptp.int)) (= (@ tptp.collect_int (@ (lambda ((Y4 tptp.int) (Z2 tptp.int)) (= Y4 Z2)) A)) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))
% 4.96/5.18 (assert (forall ((A tptp.int) (B2 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) B2)))))))
% 4.96/5.18 (assert (forall ((A tptp.extended_enat) (A2 tptp.set_Extended_enat) (B2 tptp.extended_enat)) (let ((_let_1 (@ (@ tptp.insert_Extended_enat B2) tptp.bot_bo7653980558646680370d_enat))) (= (= (@ (@ tptp.insert_Extended_enat A) A2) _let_1) (and (= A B2) (@ (@ tptp.ord_le7203529160286727270d_enat A2) _let_1))))))
% 4.96/5.18 (assert (forall ((A tptp.real) (A2 tptp.set_real) (B2 tptp.real)) (let ((_let_1 (@ (@ tptp.insert_real B2) tptp.bot_bot_set_real))) (= (= (@ (@ tptp.insert_real A) A2) _let_1) (and (= A B2) (@ (@ tptp.ord_less_eq_set_real A2) _let_1))))))
% 4.96/5.18 (assert (forall ((A tptp.nat) (A2 tptp.set_nat) (B2 tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat B2) tptp.bot_bot_set_nat))) (= (= (@ (@ tptp.insert_nat A) A2) _let_1) (and (= A B2) (@ (@ tptp.ord_less_eq_set_nat A2) _let_1))))))
% 4.96/5.18 (assert (forall ((A tptp.int) (A2 tptp.set_int) (B2 tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int B2) tptp.bot_bot_set_int))) (= (= (@ (@ tptp.insert_int A) A2) _let_1) (and (= A B2) (@ (@ tptp.ord_less_eq_set_int A2) _let_1))))))
% 4.96/5.18 (assert (forall ((B2 tptp.extended_enat) (A tptp.extended_enat) (A2 tptp.set_Extended_enat)) (let ((_let_1 (@ (@ tptp.insert_Extended_enat B2) tptp.bot_bo7653980558646680370d_enat))) (= (= _let_1 (@ (@ tptp.insert_Extended_enat A) A2)) (and (= A B2) (@ (@ tptp.ord_le7203529160286727270d_enat A2) _let_1))))))
% 4.96/5.18 (assert (forall ((B2 tptp.real) (A tptp.real) (A2 tptp.set_real)) (let ((_let_1 (@ (@ tptp.insert_real B2) tptp.bot_bot_set_real))) (= (= _let_1 (@ (@ tptp.insert_real A) A2)) (and (= A B2) (@ (@ tptp.ord_less_eq_set_real A2) _let_1))))))
% 4.96/5.18 (assert (forall ((B2 tptp.nat) (A tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.insert_nat B2) tptp.bot_bot_set_nat))) (= (= _let_1 (@ (@ tptp.insert_nat A) A2)) (and (= A B2) (@ (@ tptp.ord_less_eq_set_nat A2) _let_1))))))
% 4.96/5.18 (assert (forall ((B2 tptp.int) (A tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ (@ tptp.insert_int B2) tptp.bot_bot_set_int))) (= (= _let_1 (@ (@ tptp.insert_int A) A2)) (and (= A B2) (@ (@ tptp.ord_less_eq_set_int A2) _let_1))))))
% 4.96/5.18 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat)) (= (= (@ (@ tptp.set_or5403411693681687835d_enat A) B2) (@ (@ tptp.insert_Extended_enat C) tptp.bot_bo7653980558646680370d_enat)) (and (= A B2) (= B2 C)))))
% 4.96/5.18 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (= (= (@ (@ tptp.set_or1269000886237332187st_nat A) B2) (@ (@ tptp.insert_nat C) tptp.bot_bot_set_nat)) (and (= A B2) (= B2 C)))))
% 4.96/5.18 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (= (= (@ (@ tptp.set_or1266510415728281911st_int A) B2) (@ (@ tptp.insert_int C) tptp.bot_bot_set_int)) (and (= A B2) (= B2 C)))))
% 4.96/5.18 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (= (= (@ (@ tptp.set_or1222579329274155063t_real A) B2) (@ (@ tptp.insert_real C) tptp.bot_bot_set_real)) (and (= A B2) (= B2 C)))))
% 4.96/5.18 (assert (forall ((A tptp.extended_enat)) (= (@ (@ tptp.set_or5403411693681687835d_enat A) A) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat))))
% 4.96/5.18 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat A) A) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))
% 4.96/5.18 (assert (forall ((A tptp.int)) (= (@ (@ tptp.set_or1266510415728281911st_int A) A) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))
% 4.96/5.18 (assert (forall ((A tptp.real)) (= (@ (@ tptp.set_or1222579329274155063t_real A) A) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))
% 4.96/5.18 (assert (forall ((A tptp.extended_enat) (A2 tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.insert_Extended_enat A))) (= (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ _let_1 tptp.bot_bo7653980558646680370d_enat))) (@ _let_1 A2)))))
% 4.96/5.18 (assert (forall ((A tptp.real) (A2 tptp.set_real)) (let ((_let_1 (@ tptp.insert_real A))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ _let_1 tptp.bot_bot_set_real))) (@ _let_1 A2)))))
% 4.96/5.18 (assert (forall ((A tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ _let_1 tptp.bot_bot_set_int))) (@ _let_1 A2)))))
% 4.96/5.18 (assert (forall ((A tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) (@ _let_1 tptp.bot_bot_set_nat))) (@ _let_1 A2)))))
% 4.96/5.18 (assert (forall ((A2 tptp.set_real) (A tptp.real) (B tptp.set_real)) (let ((_let_1 (@ tptp.minus_minus_set_real A2))) (= (@ tptp.finite_finite_real (@ _let_1 (@ (@ tptp.insert_real A) B))) (@ tptp.finite_finite_real (@ _let_1 B))))))
% 4.96/5.18 (assert (forall ((A2 tptp.set_complex) (A tptp.complex) (B tptp.set_complex)) (let ((_let_1 (@ tptp.minus_811609699411566653omplex A2))) (= (@ tptp.finite3207457112153483333omplex (@ _let_1 (@ (@ tptp.insert_complex A) B))) (@ tptp.finite3207457112153483333omplex (@ _let_1 B))))))
% 4.96/5.18 (assert (forall ((A2 tptp.set_int) (A tptp.int) (B tptp.set_int)) (let ((_let_1 (@ tptp.minus_minus_set_int A2))) (= (@ tptp.finite_finite_int (@ _let_1 (@ (@ tptp.insert_int A) B))) (@ tptp.finite_finite_int (@ _let_1 B))))))
% 4.96/5.18 (assert (forall ((A2 tptp.set_Extended_enat) (A tptp.extended_enat) (B tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.minus_925952699566721837d_enat A2))) (= (@ tptp.finite4001608067531595151d_enat (@ _let_1 (@ (@ tptp.insert_Extended_enat A) B))) (@ tptp.finite4001608067531595151d_enat (@ _let_1 B))))))
% 4.96/5.18 (assert (forall ((A2 tptp.set_nat) (A tptp.nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat A2))) (= (@ tptp.finite_finite_nat (@ _let_1 (@ (@ tptp.insert_nat A) B))) (@ tptp.finite_finite_nat (@ _let_1 B))))))
% 4.96/5.18 (assert (= (@ tptp.pred_numeral tptp.one) tptp.zero_zero_nat))
% 4.96/5.18 (assert (forall ((K tptp.num) (N2 tptp.nat)) (= (= (@ tptp.numeral_numeral_nat K) (@ tptp.suc N2)) (= (@ tptp.pred_numeral K) N2))))
% 4.96/5.18 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (= (@ tptp.suc N2) (@ tptp.numeral_numeral_nat K)) (= N2 (@ tptp.pred_numeral K)))))
% 4.96/5.18 (assert (forall ((A2 tptp.set_set_nat) (B2 tptp.set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat A2) (@ tptp.uminus613421341184616069et_nat (@ (@ tptp.insert_set_nat B2) tptp.bot_bot_set_set_nat))) (not (@ (@ tptp.member_set_nat B2) A2)))))
% 4.96/5.18 (assert (forall ((A2 tptp.set_Extended_enat) (B2 tptp.extended_enat)) (= (@ (@ tptp.ord_le7203529160286727270d_enat A2) (@ tptp.uminus417252749190364093d_enat (@ (@ tptp.insert_Extended_enat B2) tptp.bot_bo7653980558646680370d_enat))) (not (@ (@ tptp.member_Extended_enat B2) A2)))))
% 4.96/5.18 (assert (forall ((A2 tptp.set_real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real A2) (@ tptp.uminus612125837232591019t_real (@ (@ tptp.insert_real B2) tptp.bot_bot_set_real))) (not (@ (@ tptp.member_real B2) A2)))))
% 4.96/5.18 (assert (forall ((A2 tptp.set_nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat A2) (@ tptp.uminus5710092332889474511et_nat (@ (@ tptp.insert_nat B2) tptp.bot_bot_set_nat))) (not (@ (@ tptp.member_nat B2) A2)))))
% 4.96/5.18 (assert (forall ((A2 tptp.set_int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int A2) (@ tptp.uminus1532241313380277803et_int (@ (@ tptp.insert_int B2) tptp.bot_bot_set_int))) (not (@ (@ tptp.member_int B2) A2)))))
% 4.96/5.18 (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))))
% 4.96/5.18 (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)))))
% 4.96/5.18 (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))))
% 4.96/5.18 (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)))))
% 4.96/5.18 (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)))))
% 4.96/5.18 (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))))
% 4.96/5.18 (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))))))
% 4.96/5.18 (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)))))
% 4.96/5.18 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int M2) tptp.one) (@ (@ tptp.product_Pair_int_int (@ tptp.numeral_numeral_int M2)) tptp.zero_zero_int))))
% 4.96/5.18 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat M2) tptp.one) (@ (@ tptp.product_Pair_nat_nat (@ tptp.numeral_numeral_nat M2)) tptp.zero_zero_nat))))
% 4.96/5.18 (assert (forall ((N2 tptp.nat) (X tptp.vEBT_VEBT)) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N2) X)) (@ (@ tptp.insert_VEBT_VEBT X) tptp.bot_bo8194388402131092736T_VEBT)))))
% 4.96/5.18 (assert (forall ((N2 tptp.nat) (X tptp.extended_enat)) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ tptp.set_Extended_enat2 (@ (@ tptp.replic7216382294607269926d_enat N2) X)) (@ (@ tptp.insert_Extended_enat X) tptp.bot_bo7653980558646680370d_enat)))))
% 4.96/5.18 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ tptp.set_real2 (@ (@ tptp.replicate_real N2) X)) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real)))))
% 4.96/5.18 (assert (forall ((N2 tptp.nat) (X tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N2) X)) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat)))))
% 4.96/5.18 (assert (forall ((N2 tptp.nat) (X tptp.int)) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ tptp.set_int2 (@ (@ tptp.replicate_int N2) X)) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int)))))
% 4.96/5.18 (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)))))
% 4.96/5.18 (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)))))
% 4.96/5.18 (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)))))
% 4.96/5.18 (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)))))
% 4.96/5.18 (assert (forall ((M2 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int (@ tptp.bit1 M2)) (@ tptp.bit0 N2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q5 tptp.int) (R4 tptp.int)) (@ (@ tptp.product_Pair_int_int Q5) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) R4)) tptp.one_one_int)))) (@ (@ tptp.unique5052692396658037445od_int M2) N2)))))
% 4.96/5.18 (assert (forall ((M2 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat (@ tptp.bit1 M2)) (@ tptp.bit0 N2)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q5 tptp.nat) (R4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Q5) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) R4)) tptp.one_one_nat)))) (@ (@ tptp.unique5055182867167087721od_nat M2) N2)))))
% 4.96/5.18 (assert (= tptp.minus_925952699566721837d_enat (lambda ((A5 tptp.set_Extended_enat) (B5 tptp.set_Extended_enat)) (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat X4))) (and (@ _let_1 A5) (not (@ _let_1 B5)))))))))
% 4.96/5.18 (assert (= tptp.minus_minus_set_real (lambda ((A5 tptp.set_real) (B5 tptp.set_real)) (@ tptp.collect_real (lambda ((X4 tptp.real)) (let ((_let_1 (@ tptp.member_real X4))) (and (@ _let_1 A5) (not (@ _let_1 B5)))))))))
% 4.96/5.18 (assert (= tptp.minus_7954133019191499631st_nat (lambda ((A5 tptp.set_list_nat) (B5 tptp.set_list_nat)) (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (let ((_let_1 (@ tptp.member_list_nat X4))) (and (@ _let_1 A5) (not (@ _let_1 B5)))))))))
% 4.96/5.18 (assert (= tptp.minus_2163939370556025621et_nat (lambda ((A5 tptp.set_set_nat) (B5 tptp.set_set_nat)) (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X4))) (and (@ _let_1 A5) (not (@ _let_1 B5)))))))))
% 4.96/5.18 (assert (= tptp.minus_minus_set_int (lambda ((A5 tptp.set_int) (B5 tptp.set_int)) (@ tptp.collect_int (lambda ((X4 tptp.int)) (let ((_let_1 (@ tptp.member_int X4))) (and (@ _let_1 A5) (not (@ _let_1 B5)))))))))
% 4.96/5.18 (assert (= tptp.minus_minus_set_nat (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X4))) (and (@ _let_1 A5) (not (@ _let_1 B5)))))))))
% 4.96/5.18 (assert (= tptp.minus_925952699566721837d_enat (lambda ((A5 tptp.set_Extended_enat) (B5 tptp.set_Extended_enat)) (@ tptp.collec4429806609662206161d_enat (@ (@ tptp.minus_2020553357622893040enat_o (lambda ((X4 tptp.extended_enat)) (@ (@ tptp.member_Extended_enat X4) A5))) (lambda ((X4 tptp.extended_enat)) (@ (@ tptp.member_Extended_enat X4) B5)))))))
% 4.96/5.18 (assert (= tptp.minus_minus_set_real (lambda ((A5 tptp.set_real) (B5 tptp.set_real)) (@ tptp.collect_real (@ (@ tptp.minus_minus_real_o (lambda ((X4 tptp.real)) (@ (@ tptp.member_real X4) A5))) (lambda ((X4 tptp.real)) (@ (@ tptp.member_real X4) B5)))))))
% 4.96/5.18 (assert (= tptp.minus_7954133019191499631st_nat (lambda ((A5 tptp.set_list_nat) (B5 tptp.set_list_nat)) (@ tptp.collect_list_nat (@ (@ tptp.minus_1139252259498527702_nat_o (lambda ((X4 tptp.list_nat)) (@ (@ tptp.member_list_nat X4) A5))) (lambda ((X4 tptp.list_nat)) (@ (@ tptp.member_list_nat X4) B5)))))))
% 4.96/5.18 (assert (= tptp.minus_2163939370556025621et_nat (lambda ((A5 tptp.set_set_nat) (B5 tptp.set_set_nat)) (@ tptp.collect_set_nat (@ (@ tptp.minus_6910147592129066416_nat_o (lambda ((X4 tptp.set_nat)) (@ (@ tptp.member_set_nat X4) A5))) (lambda ((X4 tptp.set_nat)) (@ (@ tptp.member_set_nat X4) B5)))))))
% 4.96/5.18 (assert (= tptp.minus_minus_set_int (lambda ((A5 tptp.set_int) (B5 tptp.set_int)) (@ tptp.collect_int (@ (@ tptp.minus_minus_int_o (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) A5))) (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) B5)))))))
% 4.96/5.18 (assert (= tptp.minus_minus_set_nat (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (@ tptp.collect_nat (@ (@ tptp.minus_minus_nat_o (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) A5))) (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) B5)))))))
% 4.96/5.18 (assert (forall ((X tptp.extended_enat) (B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat)) (let ((_let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) B))) (let ((_let_2 (@ tptp.insert_Extended_enat X))) (let ((_let_3 (@ (@ tptp.minus_925952699566721837d_enat (@ _let_2 A2)) B))) (let ((_let_4 (@ (@ tptp.member_Extended_enat X) B))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 4.96/5.18 (assert (forall ((X tptp.real) (B tptp.set_real) (A2 tptp.set_real)) (let ((_let_1 (@ (@ tptp.minus_minus_set_real A2) B))) (let ((_let_2 (@ tptp.insert_real X))) (let ((_let_3 (@ (@ tptp.minus_minus_set_real (@ _let_2 A2)) B))) (let ((_let_4 (@ (@ tptp.member_real X) B))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 4.96/5.18 (assert (forall ((X tptp.set_nat) (B tptp.set_set_nat) (A2 tptp.set_set_nat)) (let ((_let_1 (@ (@ tptp.minus_2163939370556025621et_nat A2) B))) (let ((_let_2 (@ tptp.insert_set_nat X))) (let ((_let_3 (@ (@ tptp.minus_2163939370556025621et_nat (@ _let_2 A2)) B))) (let ((_let_4 (@ (@ tptp.member_set_nat X) B))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 4.96/5.18 (assert (forall ((X tptp.int) (B tptp.set_int) (A2 tptp.set_int)) (let ((_let_1 (@ (@ tptp.minus_minus_set_int A2) B))) (let ((_let_2 (@ tptp.insert_int X))) (let ((_let_3 (@ (@ tptp.minus_minus_set_int (@ _let_2 A2)) B))) (let ((_let_4 (@ (@ tptp.member_int X) B))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 4.96/5.18 (assert (forall ((X tptp.nat) (B tptp.set_nat) (A2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.minus_minus_set_nat A2) B))) (let ((_let_2 (@ tptp.insert_nat X))) (let ((_let_3 (@ (@ tptp.minus_minus_set_nat (@ _let_2 A2)) B))) (let ((_let_4 (@ (@ tptp.member_nat X) B))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 4.96/5.18 (assert (forall ((C tptp.extended_enat) (A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat C))) (=> (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) B)) (not (@ _let_1 B))))))
% 4.96/5.18 (assert (forall ((C tptp.real) (A2 tptp.set_real) (B tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) B)) (not (@ _let_1 B))))))
% 4.96/5.18 (assert (forall ((C tptp.set_nat) (A2 tptp.set_set_nat) (B tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A2) B)) (not (@ _let_1 B))))))
% 4.96/5.18 (assert (forall ((C tptp.int) (A2 tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B)) (not (@ _let_1 B))))))
% 4.96/5.18 (assert (forall ((C tptp.nat) (A2 tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B)) (not (@ _let_1 B))))))
% 4.96/5.18 (assert (forall ((C tptp.extended_enat) (A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat C))) (=> (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) B)) (@ _let_1 A2)))))
% 4.96/5.18 (assert (forall ((C tptp.real) (A2 tptp.set_real) (B tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) B)) (@ _let_1 A2)))))
% 4.96/5.18 (assert (forall ((C tptp.set_nat) (A2 tptp.set_set_nat) (B tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A2) B)) (@ _let_1 A2)))))
% 4.96/5.18 (assert (forall ((C tptp.int) (A2 tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B)) (@ _let_1 A2)))))
% 4.96/5.18 (assert (forall ((C tptp.nat) (A2 tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B)) (@ _let_1 A2)))))
% 4.96/5.18 (assert (forall ((C tptp.extended_enat) (A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat C))) (=> (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) B)) (not (=> (@ _let_1 A2) (@ _let_1 B)))))))
% 4.96/5.18 (assert (forall ((C tptp.real) (A2 tptp.set_real) (B tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) B)) (not (=> (@ _let_1 A2) (@ _let_1 B)))))))
% 4.96/5.18 (assert (forall ((C tptp.set_nat) (A2 tptp.set_set_nat) (B tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A2) B)) (not (=> (@ _let_1 A2) (@ _let_1 B)))))))
% 4.96/5.18 (assert (forall ((C tptp.int) (A2 tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B)) (not (=> (@ _let_1 A2) (@ _let_1 B)))))))
% 4.96/5.18 (assert (forall ((C tptp.nat) (A2 tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B)) (not (=> (@ _let_1 A2) (@ _let_1 B)))))))
% 4.96/5.18 (assert (forall ((P (-> tptp.int Bool)) (K tptp.int) (I 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 I))))))
% 4.96/5.18 (assert (forall ((I tptp.int) (K tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_int I) 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 I))))))
% 4.96/5.18 (assert (forall ((K tptp.int) (M2 tptp.int) (N2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int K))) (=> (@ _let_1 (@ (@ tptp.minus_minus_int M2) N2)) (=> (@ _let_1 N2) (@ _let_1 M2))))))
% 4.96/5.18 (assert (forall ((C tptp.extended_enat) (A2 tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat C))) (=> (@ _let_1 (@ tptp.uminus417252749190364093d_enat A2)) (not (@ _let_1 A2))))))
% 4.96/5.18 (assert (forall ((C tptp.real) (A2 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ _let_1 (@ tptp.uminus612125837232591019t_real A2)) (not (@ _let_1 A2))))))
% 4.96/5.18 (assert (forall ((C tptp.set_nat) (A2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 (@ tptp.uminus613421341184616069et_nat A2)) (not (@ _let_1 A2))))))
% 4.96/5.18 (assert (forall ((C tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ tptp.uminus5710092332889474511et_nat A2)) (not (@ _let_1 A2))))))
% 4.96/5.18 (assert (forall ((C tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ tptp.uminus1532241313380277803et_int A2)) (not (@ _let_1 A2))))))
% 4.96/5.18 (assert (= tptp.uminus417252749190364093d_enat (lambda ((A5 tptp.set_Extended_enat)) (@ tptp.collec4429806609662206161d_enat (@ tptp.uminus6636779312473996640enat_o (lambda ((X4 tptp.extended_enat)) (@ (@ tptp.member_Extended_enat X4) A5)))))))
% 4.96/5.18 (assert (= tptp.uminus612125837232591019t_real (lambda ((A5 tptp.set_real)) (@ tptp.collect_real (@ tptp.uminus_uminus_real_o (lambda ((X4 tptp.real)) (@ (@ tptp.member_real X4) A5)))))))
% 4.96/5.18 (assert (= tptp.uminus3195874150345416415st_nat (lambda ((A5 tptp.set_list_nat)) (@ tptp.collect_list_nat (@ tptp.uminus5770388063884162150_nat_o (lambda ((X4 tptp.list_nat)) (@ (@ tptp.member_list_nat X4) A5)))))))
% 4.96/5.18 (assert (= tptp.uminus613421341184616069et_nat (lambda ((A5 tptp.set_set_nat)) (@ tptp.collect_set_nat (@ tptp.uminus6401447641752708672_nat_o (lambda ((X4 tptp.set_nat)) (@ (@ tptp.member_set_nat X4) A5)))))))
% 4.96/5.18 (assert (= tptp.uminus5710092332889474511et_nat (lambda ((A5 tptp.set_nat)) (@ tptp.collect_nat (@ tptp.uminus_uminus_nat_o (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) A5)))))))
% 4.96/5.18 (assert (= tptp.uminus1532241313380277803et_int (lambda ((A5 tptp.set_int)) (@ tptp.collect_int (@ tptp.uminus_uminus_int_o (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) A5)))))))
% 4.96/5.18 (assert (forall ((P (-> tptp.real Bool))) (= (@ tptp.collect_real (lambda ((X4 tptp.real)) (not (@ P X4)))) (@ tptp.uminus612125837232591019t_real (@ tptp.collect_real P)))))
% 4.96/5.18 (assert (forall ((P (-> tptp.list_nat Bool))) (= (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (not (@ P X4)))) (@ tptp.uminus3195874150345416415st_nat (@ tptp.collect_list_nat P)))))
% 4.96/5.18 (assert (forall ((P (-> tptp.set_nat Bool))) (= (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (not (@ P X4)))) (@ tptp.uminus613421341184616069et_nat (@ tptp.collect_set_nat P)))))
% 4.96/5.18 (assert (forall ((P (-> tptp.nat Bool))) (= (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (not (@ P X4)))) (@ tptp.uminus5710092332889474511et_nat (@ tptp.collect_nat P)))))
% 4.96/5.18 (assert (forall ((P (-> tptp.int Bool))) (= (@ tptp.collect_int (lambda ((X4 tptp.int)) (not (@ P X4)))) (@ tptp.uminus1532241313380277803et_int (@ tptp.collect_int P)))))
% 4.96/5.18 (assert (= tptp.uminus417252749190364093d_enat (lambda ((A5 tptp.set_Extended_enat)) (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (not (@ (@ tptp.member_Extended_enat X4) A5)))))))
% 4.96/5.18 (assert (= tptp.uminus612125837232591019t_real (lambda ((A5 tptp.set_real)) (@ tptp.collect_real (lambda ((X4 tptp.real)) (not (@ (@ tptp.member_real X4) A5)))))))
% 4.96/5.18 (assert (= tptp.uminus3195874150345416415st_nat (lambda ((A5 tptp.set_list_nat)) (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (not (@ (@ tptp.member_list_nat X4) A5)))))))
% 4.96/5.18 (assert (= tptp.uminus613421341184616069et_nat (lambda ((A5 tptp.set_set_nat)) (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (not (@ (@ tptp.member_set_nat X4) A5)))))))
% 4.96/5.18 (assert (= tptp.uminus5710092332889474511et_nat (lambda ((A5 tptp.set_nat)) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (not (@ (@ tptp.member_nat X4) A5)))))))
% 4.96/5.18 (assert (= tptp.uminus1532241313380277803et_int (lambda ((A5 tptp.set_int)) (@ tptp.collect_int (lambda ((X4 tptp.int)) (not (@ (@ tptp.member_int X4) A5)))))))
% 4.96/5.18 (assert (= tptp.insert_Extended_enat (lambda ((A3 tptp.extended_enat) (B5 tptp.set_Extended_enat)) (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (or (= X4 A3) (@ (@ tptp.member_Extended_enat X4) B5)))))))
% 4.96/5.18 (assert (= tptp.insert_real (lambda ((A3 tptp.real) (B5 tptp.set_real)) (@ tptp.collect_real (lambda ((X4 tptp.real)) (or (= X4 A3) (@ (@ tptp.member_real X4) B5)))))))
% 4.96/5.18 (assert (= tptp.insert_list_nat (lambda ((A3 tptp.list_nat) (B5 tptp.set_list_nat)) (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (or (= X4 A3) (@ (@ tptp.member_list_nat X4) B5)))))))
% 4.96/5.18 (assert (= tptp.insert_set_nat (lambda ((A3 tptp.set_nat) (B5 tptp.set_set_nat)) (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (or (= X4 A3) (@ (@ tptp.member_set_nat X4) B5)))))))
% 4.96/5.18 (assert (= tptp.insert_nat (lambda ((A3 tptp.nat) (B5 tptp.set_nat)) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (or (= X4 A3) (@ (@ tptp.member_nat X4) B5)))))))
% 4.96/5.18 (assert (= tptp.insert_int (lambda ((A3 tptp.int) (B5 tptp.set_int)) (@ tptp.collect_int (lambda ((X4 tptp.int)) (or (= X4 A3) (@ (@ tptp.member_int X4) B5)))))))
% 4.96/5.18 (assert (forall ((A tptp.real) (P (-> tptp.real Bool))) (= (@ (@ tptp.insert_real A) (@ tptp.collect_real P)) (@ tptp.collect_real (lambda ((U2 tptp.real)) (=> (not (= U2 A)) (@ P U2)))))))
% 4.96/5.18 (assert (forall ((A tptp.list_nat) (P (-> tptp.list_nat Bool))) (= (@ (@ tptp.insert_list_nat A) (@ tptp.collect_list_nat P)) (@ tptp.collect_list_nat (lambda ((U2 tptp.list_nat)) (=> (not (= U2 A)) (@ P U2)))))))
% 4.96/5.18 (assert (forall ((A tptp.set_nat) (P (-> tptp.set_nat Bool))) (= (@ (@ tptp.insert_set_nat A) (@ tptp.collect_set_nat P)) (@ tptp.collect_set_nat (lambda ((U2 tptp.set_nat)) (=> (not (= U2 A)) (@ P U2)))))))
% 4.96/5.18 (assert (forall ((A tptp.nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.insert_nat A) (@ tptp.collect_nat P)) (@ tptp.collect_nat (lambda ((U2 tptp.nat)) (=> (not (= U2 A)) (@ P U2)))))))
% 4.96/5.18 (assert (forall ((A tptp.int) (P (-> tptp.int Bool))) (= (@ (@ tptp.insert_int A) (@ tptp.collect_int P)) (@ tptp.collect_int (lambda ((U2 tptp.int)) (=> (not (= U2 A)) (@ P U2)))))))
% 4.96/5.18 (assert (forall ((A tptp.extended_enat) (A2 tptp.set_Extended_enat)) (=> (@ (@ tptp.member_Extended_enat A) A2) (exists ((B8 tptp.set_Extended_enat)) (and (= A2 (@ (@ tptp.insert_Extended_enat A) B8)) (not (@ (@ tptp.member_Extended_enat A) B8)))))))
% 4.96/5.18 (assert (forall ((A tptp.real) (A2 tptp.set_real)) (=> (@ (@ tptp.member_real A) A2) (exists ((B8 tptp.set_real)) (and (= A2 (@ (@ tptp.insert_real A) B8)) (not (@ (@ tptp.member_real A) B8)))))))
% 4.96/5.18 (assert (forall ((A tptp.set_nat) (A2 tptp.set_set_nat)) (=> (@ (@ tptp.member_set_nat A) A2) (exists ((B8 tptp.set_set_nat)) (and (= A2 (@ (@ tptp.insert_set_nat A) B8)) (not (@ (@ tptp.member_set_nat A) B8)))))))
% 4.96/5.18 (assert (forall ((A tptp.nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.member_nat A) A2) (exists ((B8 tptp.set_nat)) (and (= A2 (@ (@ tptp.insert_nat A) B8)) (not (@ (@ tptp.member_nat A) B8)))))))
% 4.96/5.18 (assert (forall ((A tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.member_int A) A2) (exists ((B8 tptp.set_int)) (and (= A2 (@ (@ tptp.insert_int A) B8)) (not (@ (@ tptp.member_int A) B8)))))))
% 4.96/5.18 (assert (forall ((X tptp.nat) (Y tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X))) (let ((_let_2 (@ tptp.insert_nat Y))) (= (@ _let_1 (@ _let_2 A2)) (@ _let_2 (@ _let_1 A2)))))))
% 4.96/5.18 (assert (forall ((X tptp.int) (Y tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int X))) (let ((_let_2 (@ tptp.insert_int Y))) (= (@ _let_1 (@ _let_2 A2)) (@ _let_2 (@ _let_1 A2)))))))
% 4.96/5.18 (assert (forall ((X tptp.real) (Y tptp.real) (A2 tptp.set_real)) (let ((_let_1 (@ tptp.insert_real X))) (let ((_let_2 (@ tptp.insert_real Y))) (= (@ _let_1 (@ _let_2 A2)) (@ _let_2 (@ _let_1 A2)))))))
% 4.96/5.18 (assert (forall ((A tptp.extended_enat) (A2 tptp.set_Extended_enat) (B2 tptp.extended_enat) (B tptp.set_Extended_enat)) (let ((_let_1 (= A B2))) (=> (not (@ (@ tptp.member_Extended_enat A) A2)) (=> (not (@ (@ tptp.member_Extended_enat B2) B)) (= (= (@ (@ tptp.insert_Extended_enat A) A2) (@ (@ tptp.insert_Extended_enat B2) B)) (and (=> _let_1 (= A2 B)) (=> (not _let_1) (exists ((C5 tptp.set_Extended_enat)) (and (= A2 (@ (@ tptp.insert_Extended_enat B2) C5)) (not (@ (@ tptp.member_Extended_enat B2) C5)) (= B (@ (@ tptp.insert_Extended_enat A) C5)) (not (@ (@ tptp.member_Extended_enat A) C5))))))))))))
% 4.96/5.18 (assert (forall ((A tptp.real) (A2 tptp.set_real) (B2 tptp.real) (B tptp.set_real)) (let ((_let_1 (= A B2))) (=> (not (@ (@ tptp.member_real A) A2)) (=> (not (@ (@ tptp.member_real B2) B)) (= (= (@ (@ tptp.insert_real A) A2) (@ (@ tptp.insert_real B2) B)) (and (=> _let_1 (= A2 B)) (=> (not _let_1) (exists ((C5 tptp.set_real)) (and (= A2 (@ (@ tptp.insert_real B2) C5)) (not (@ (@ tptp.member_real B2) C5)) (= B (@ (@ tptp.insert_real A) C5)) (not (@ (@ tptp.member_real A) C5))))))))))))
% 4.96/5.19 (assert (forall ((A tptp.set_nat) (A2 tptp.set_set_nat) (B2 tptp.set_nat) (B tptp.set_set_nat)) (let ((_let_1 (= A B2))) (=> (not (@ (@ tptp.member_set_nat A) A2)) (=> (not (@ (@ tptp.member_set_nat B2) B)) (= (= (@ (@ tptp.insert_set_nat A) A2) (@ (@ tptp.insert_set_nat B2) B)) (and (=> _let_1 (= A2 B)) (=> (not _let_1) (exists ((C5 tptp.set_set_nat)) (and (= A2 (@ (@ tptp.insert_set_nat B2) C5)) (not (@ (@ tptp.member_set_nat B2) C5)) (= B (@ (@ tptp.insert_set_nat A) C5)) (not (@ (@ tptp.member_set_nat A) C5))))))))))))
% 4.96/5.19 (assert (forall ((A tptp.nat) (A2 tptp.set_nat) (B2 tptp.nat) (B tptp.set_nat)) (let ((_let_1 (= A B2))) (=> (not (@ (@ tptp.member_nat A) A2)) (=> (not (@ (@ tptp.member_nat B2) B)) (= (= (@ (@ tptp.insert_nat A) A2) (@ (@ tptp.insert_nat B2) B)) (and (=> _let_1 (= A2 B)) (=> (not _let_1) (exists ((C5 tptp.set_nat)) (and (= A2 (@ (@ tptp.insert_nat B2) C5)) (not (@ (@ tptp.member_nat B2) C5)) (= B (@ (@ tptp.insert_nat A) C5)) (not (@ (@ tptp.member_nat A) C5))))))))))))
% 4.96/5.19 (assert (forall ((A tptp.int) (A2 tptp.set_int) (B2 tptp.int) (B tptp.set_int)) (let ((_let_1 (= A B2))) (=> (not (@ (@ tptp.member_int A) A2)) (=> (not (@ (@ tptp.member_int B2) B)) (= (= (@ (@ tptp.insert_int A) A2) (@ (@ tptp.insert_int B2) B)) (and (=> _let_1 (= A2 B)) (=> (not _let_1) (exists ((C5 tptp.set_int)) (and (= A2 (@ (@ tptp.insert_int B2) C5)) (not (@ (@ tptp.member_int B2) C5)) (= B (@ (@ tptp.insert_int A) C5)) (not (@ (@ tptp.member_int A) C5))))))))))))
% 4.96/5.19 (assert (forall ((A tptp.extended_enat) (A2 tptp.set_Extended_enat)) (=> (@ (@ tptp.member_Extended_enat A) A2) (= (@ (@ tptp.insert_Extended_enat A) A2) A2))))
% 4.96/5.19 (assert (forall ((A tptp.real) (A2 tptp.set_real)) (=> (@ (@ tptp.member_real A) A2) (= (@ (@ tptp.insert_real A) A2) A2))))
% 4.96/5.19 (assert (forall ((A tptp.set_nat) (A2 tptp.set_set_nat)) (=> (@ (@ tptp.member_set_nat A) A2) (= (@ (@ tptp.insert_set_nat A) A2) A2))))
% 4.96/5.19 (assert (forall ((A tptp.nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.member_nat A) A2) (= (@ (@ tptp.insert_nat A) A2) A2))))
% 4.96/5.19 (assert (forall ((A tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.member_int A) A2) (= (@ (@ tptp.insert_int A) A2) A2))))
% 4.96/5.19 (assert (forall ((X tptp.extended_enat) (A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.insert_Extended_enat X))) (let ((_let_2 (@ tptp.member_Extended_enat X))) (=> (not (@ _let_2 A2)) (=> (not (@ _let_2 B)) (= (= (@ _let_1 A2) (@ _let_1 B)) (= A2 B))))))))
% 4.96/5.19 (assert (forall ((X tptp.real) (A2 tptp.set_real) (B tptp.set_real)) (let ((_let_1 (@ tptp.insert_real X))) (let ((_let_2 (@ tptp.member_real X))) (=> (not (@ _let_2 A2)) (=> (not (@ _let_2 B)) (= (= (@ _let_1 A2) (@ _let_1 B)) (= A2 B))))))))
% 4.96/5.19 (assert (forall ((X tptp.set_nat) (A2 tptp.set_set_nat) (B tptp.set_set_nat)) (let ((_let_1 (@ tptp.insert_set_nat X))) (let ((_let_2 (@ tptp.member_set_nat X))) (=> (not (@ _let_2 A2)) (=> (not (@ _let_2 B)) (= (= (@ _let_1 A2) (@ _let_1 B)) (= A2 B))))))))
% 4.96/5.19 (assert (forall ((X tptp.nat) (A2 tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X))) (let ((_let_2 (@ tptp.member_nat X))) (=> (not (@ _let_2 A2)) (=> (not (@ _let_2 B)) (= (= (@ _let_1 A2) (@ _let_1 B)) (= A2 B))))))))
% 4.96/5.19 (assert (forall ((X tptp.int) (A2 tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.insert_int X))) (let ((_let_2 (@ tptp.member_int X))) (=> (not (@ _let_2 A2)) (=> (not (@ _let_2 B)) (= (= (@ _let_1 A2) (@ _let_1 B)) (= A2 B))))))))
% 4.96/5.19 (assert (forall ((X tptp.extended_enat) (A2 tptp.set_Extended_enat)) (=> (@ (@ tptp.member_Extended_enat X) A2) (not (forall ((B8 tptp.set_Extended_enat)) (=> (= A2 (@ (@ tptp.insert_Extended_enat X) B8)) (@ (@ tptp.member_Extended_enat X) B8)))))))
% 4.96/5.19 (assert (forall ((X tptp.real) (A2 tptp.set_real)) (=> (@ (@ tptp.member_real X) A2) (not (forall ((B8 tptp.set_real)) (=> (= A2 (@ (@ tptp.insert_real X) B8)) (@ (@ tptp.member_real X) B8)))))))
% 4.96/5.19 (assert (forall ((X tptp.set_nat) (A2 tptp.set_set_nat)) (=> (@ (@ tptp.member_set_nat X) A2) (not (forall ((B8 tptp.set_set_nat)) (=> (= A2 (@ (@ tptp.insert_set_nat X) B8)) (@ (@ tptp.member_set_nat X) B8)))))))
% 4.96/5.19 (assert (forall ((X tptp.nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.member_nat X) A2) (not (forall ((B8 tptp.set_nat)) (=> (= A2 (@ (@ tptp.insert_nat X) B8)) (@ (@ tptp.member_nat X) B8)))))))
% 4.96/5.19 (assert (forall ((X tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.member_int X) A2) (not (forall ((B8 tptp.set_int)) (=> (= A2 (@ (@ tptp.insert_int X) B8)) (@ (@ tptp.member_int X) B8)))))))
% 4.96/5.19 (assert (forall ((A tptp.extended_enat) (B tptp.set_Extended_enat) (B2 tptp.extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.insert_Extended_enat B2) B))))))
% 4.96/5.19 (assert (forall ((A tptp.real) (B tptp.set_real) (B2 tptp.real)) (let ((_let_1 (@ tptp.member_real A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.insert_real B2) B))))))
% 4.96/5.19 (assert (forall ((A tptp.set_nat) (B tptp.set_set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.insert_set_nat B2) B))))))
% 4.96/5.19 (assert (forall ((A tptp.nat) (B tptp.set_nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.insert_nat B2) B))))))
% 4.96/5.19 (assert (forall ((A tptp.int) (B tptp.set_int) (B2 tptp.int)) (let ((_let_1 (@ tptp.member_int A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.insert_int B2) B))))))
% 4.96/5.19 (assert (forall ((A tptp.extended_enat) (B tptp.set_Extended_enat)) (@ (@ tptp.member_Extended_enat A) (@ (@ tptp.insert_Extended_enat A) B))))
% 4.96/5.19 (assert (forall ((A tptp.real) (B tptp.set_real)) (@ (@ tptp.member_real A) (@ (@ tptp.insert_real A) B))))
% 4.96/5.19 (assert (forall ((A tptp.set_nat) (B tptp.set_set_nat)) (@ (@ tptp.member_set_nat A) (@ (@ tptp.insert_set_nat A) B))))
% 4.96/5.19 (assert (forall ((A tptp.nat) (B tptp.set_nat)) (@ (@ tptp.member_nat A) (@ (@ tptp.insert_nat A) B))))
% 4.96/5.19 (assert (forall ((A tptp.int) (B tptp.set_int)) (@ (@ tptp.member_int A) (@ (@ tptp.insert_int A) B))))
% 4.96/5.19 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (A2 tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat A))) (=> (@ _let_1 (@ (@ tptp.insert_Extended_enat B2) A2)) (=> (not (= A B2)) (@ _let_1 A2))))))
% 4.96/5.19 (assert (forall ((A tptp.real) (B2 tptp.real) (A2 tptp.set_real)) (let ((_let_1 (@ tptp.member_real A))) (=> (@ _let_1 (@ (@ tptp.insert_real B2) A2)) (=> (not (= A B2)) (@ _let_1 A2))))))
% 4.96/5.19 (assert (forall ((A tptp.set_nat) (B2 tptp.set_nat) (A2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat A))) (=> (@ _let_1 (@ (@ tptp.insert_set_nat B2) A2)) (=> (not (= A B2)) (@ _let_1 A2))))))
% 4.96/5.19 (assert (forall ((A tptp.nat) (B2 tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat A))) (=> (@ _let_1 (@ (@ tptp.insert_nat B2) A2)) (=> (not (= A B2)) (@ _let_1 A2))))))
% 4.96/5.19 (assert (forall ((A tptp.int) (B2 tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ tptp.member_int A))) (=> (@ _let_1 (@ (@ tptp.insert_int B2) A2)) (=> (not (= A B2)) (@ _let_1 A2))))))
% 4.96/5.19 (assert (forall ((K tptp.int) (I tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_int K) I) (=> (@ 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 I))))))
% 4.96/5.19 (assert (forall ((B2 tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.member_set_nat B2) (@ (@ tptp.insert_set_nat A) tptp.bot_bot_set_set_nat)) (= B2 A))))
% 4.96/5.19 (assert (forall ((B2 tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B2) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat)) (= B2 A))))
% 4.96/5.19 (assert (forall ((B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real)) (= B2 A))))
% 4.96/5.19 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.member_nat B2) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat)) (= B2 A))))
% 4.96/5.19 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int)) (= B2 A))))
% 4.96/5.19 (assert (forall ((B2 tptp.set_nat) (A tptp.set_nat)) (= (@ (@ tptp.member_set_nat B2) (@ (@ tptp.insert_set_nat A) tptp.bot_bot_set_set_nat)) (= B2 A))))
% 4.96/5.19 (assert (forall ((B2 tptp.extended_enat) (A tptp.extended_enat)) (= (@ (@ tptp.member_Extended_enat B2) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat)) (= B2 A))))
% 4.96/5.19 (assert (forall ((B2 tptp.real) (A tptp.real)) (= (@ (@ tptp.member_real B2) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real)) (= B2 A))))
% 4.96/5.19 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (= (@ (@ tptp.member_nat B2) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat)) (= B2 A))))
% 4.96/5.19 (assert (forall ((B2 tptp.int) (A tptp.int)) (= (@ (@ tptp.member_int B2) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int)) (= B2 A))))
% 4.96/5.19 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat) (D tptp.extended_enat)) (= (= (@ (@ tptp.insert_Extended_enat A) (@ (@ tptp.insert_Extended_enat B2) tptp.bot_bo7653980558646680370d_enat)) (@ (@ tptp.insert_Extended_enat C) (@ (@ tptp.insert_Extended_enat D) tptp.bot_bo7653980558646680370d_enat))) (or (and (= A C) (= B2 D)) (and (= A D) (= B2 C))))))
% 4.96/5.19 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (= (= (@ (@ tptp.insert_real A) (@ (@ tptp.insert_real B2) tptp.bot_bot_set_real)) (@ (@ tptp.insert_real C) (@ (@ tptp.insert_real D) tptp.bot_bot_set_real))) (or (and (= A C) (= B2 D)) (and (= A D) (= B2 C))))))
% 4.96/5.19 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (= (= (@ (@ tptp.insert_nat A) (@ (@ tptp.insert_nat B2) tptp.bot_bot_set_nat)) (@ (@ tptp.insert_nat C) (@ (@ tptp.insert_nat D) tptp.bot_bot_set_nat))) (or (and (= A C) (= B2 D)) (and (= A D) (= B2 C))))))
% 4.96/5.19 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (= (= (@ (@ tptp.insert_int A) (@ (@ tptp.insert_int B2) tptp.bot_bot_set_int)) (@ (@ tptp.insert_int C) (@ (@ tptp.insert_int D) tptp.bot_bot_set_int))) (or (and (= A C) (= B2 D)) (and (= A D) (= B2 C))))))
% 4.96/5.19 (assert (forall ((A tptp.extended_enat) (A2 tptp.set_Extended_enat)) (not (= (@ (@ tptp.insert_Extended_enat A) A2) tptp.bot_bo7653980558646680370d_enat))))
% 4.96/5.19 (assert (forall ((A tptp.real) (A2 tptp.set_real)) (not (= (@ (@ tptp.insert_real A) A2) tptp.bot_bot_set_real))))
% 4.96/5.19 (assert (forall ((A tptp.nat) (A2 tptp.set_nat)) (not (= (@ (@ tptp.insert_nat A) A2) tptp.bot_bot_set_nat))))
% 4.96/5.19 (assert (forall ((A tptp.int) (A2 tptp.set_int)) (not (= (@ (@ tptp.insert_int A) A2) tptp.bot_bot_set_int))))
% 4.96/5.19 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (=> (= (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat) (@ (@ tptp.insert_Extended_enat B2) tptp.bot_bo7653980558646680370d_enat)) (= A B2))))
% 4.96/5.19 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (= (@ (@ tptp.insert_real A) tptp.bot_bot_set_real) (@ (@ tptp.insert_real B2) tptp.bot_bot_set_real)) (= A B2))))
% 4.96/5.19 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (= (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat) (@ (@ tptp.insert_nat B2) tptp.bot_bot_set_nat)) (= A B2))))
% 4.96/5.19 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (= (@ (@ tptp.insert_int A) tptp.bot_bot_set_int) (@ (@ tptp.insert_int B2) tptp.bot_bot_set_int)) (= A B2))))
% 4.96/5.19 (assert (forall ((X tptp.extended_enat) (A2 tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.insert_Extended_enat X))) (= (@ tptp.uminus417252749190364093d_enat (@ _let_1 A2)) (@ (@ tptp.minus_925952699566721837d_enat (@ tptp.uminus417252749190364093d_enat A2)) (@ _let_1 tptp.bot_bo7653980558646680370d_enat))))))
% 4.96/5.19 (assert (forall ((X tptp.real) (A2 tptp.set_real)) (let ((_let_1 (@ tptp.insert_real X))) (= (@ tptp.uminus612125837232591019t_real (@ _let_1 A2)) (@ (@ tptp.minus_minus_set_real (@ tptp.uminus612125837232591019t_real A2)) (@ _let_1 tptp.bot_bot_set_real))))))
% 4.96/5.19 (assert (forall ((X tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int X))) (= (@ tptp.uminus1532241313380277803et_int (@ _let_1 A2)) (@ (@ tptp.minus_minus_set_int (@ tptp.uminus1532241313380277803et_int A2)) (@ _let_1 tptp.bot_bot_set_int))))))
% 4.96/5.19 (assert (forall ((X tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X))) (= (@ tptp.uminus5710092332889474511et_nat (@ _let_1 A2)) (@ (@ tptp.minus_minus_set_nat (@ tptp.uminus5710092332889474511et_nat A2)) (@ _let_1 tptp.bot_bot_set_nat))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (A tptp.extended_enat) (B tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.insert_Extended_enat A))) (let ((_let_2 (@ tptp.minus_925952699566721837d_enat A2))) (= (@ _let_2 (@ _let_1 B)) (@ (@ tptp.minus_925952699566721837d_enat (@ _let_2 B)) (@ _let_1 tptp.bot_bo7653980558646680370d_enat)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (A tptp.real) (B tptp.set_real)) (let ((_let_1 (@ tptp.insert_real A))) (let ((_let_2 (@ tptp.minus_minus_set_real A2))) (= (@ _let_2 (@ _let_1 B)) (@ (@ tptp.minus_minus_set_real (@ _let_2 B)) (@ _let_1 tptp.bot_bot_set_real)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (A tptp.int) (B tptp.set_int)) (let ((_let_1 (@ tptp.insert_int A))) (let ((_let_2 (@ tptp.minus_minus_set_int A2))) (= (@ _let_2 (@ _let_1 B)) (@ (@ tptp.minus_minus_set_int (@ _let_2 B)) (@ _let_1 tptp.bot_bot_set_int)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (A tptp.nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat A))) (let ((_let_2 (@ tptp.minus_minus_set_nat A2))) (= (@ _let_2 (@ _let_1 B)) (@ (@ tptp.minus_minus_set_nat (@ _let_2 B)) (@ _let_1 tptp.bot_bot_set_nat)))))))
% 4.96/5.19 (assert (forall ((A tptp.set_nat) (A2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.insert_set_nat A))) (=> (@ (@ tptp.member_set_nat A) A2) (= (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A2) (@ _let_1 tptp.bot_bot_set_set_nat))) A2)))))
% 4.96/5.19 (assert (forall ((A tptp.extended_enat) (A2 tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.insert_Extended_enat A))) (=> (@ (@ tptp.member_Extended_enat A) A2) (= (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ _let_1 tptp.bot_bo7653980558646680370d_enat))) A2)))))
% 4.96/5.19 (assert (forall ((A tptp.real) (A2 tptp.set_real)) (let ((_let_1 (@ tptp.insert_real A))) (=> (@ (@ tptp.member_real A) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ _let_1 tptp.bot_bot_set_real))) A2)))))
% 4.96/5.19 (assert (forall ((A tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int A))) (=> (@ (@ tptp.member_int A) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ _let_1 tptp.bot_bot_set_int))) A2)))))
% 4.96/5.19 (assert (forall ((A tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat A))) (=> (@ (@ tptp.member_nat A) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) (@ _let_1 tptp.bot_bot_set_nat))) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (A tptp.extended_enat) (B tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.insert_Extended_enat A))) (let ((_let_2 (@ tptp.minus_925952699566721837d_enat A2))) (= (@ _let_2 (@ _let_1 B)) (@ (@ tptp.minus_925952699566721837d_enat (@ _let_2 (@ _let_1 tptp.bot_bo7653980558646680370d_enat))) B))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (A tptp.real) (B tptp.set_real)) (let ((_let_1 (@ tptp.insert_real A))) (let ((_let_2 (@ tptp.minus_minus_set_real A2))) (= (@ _let_2 (@ _let_1 B)) (@ (@ tptp.minus_minus_set_real (@ _let_2 (@ _let_1 tptp.bot_bot_set_real))) B))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (A tptp.int) (B tptp.set_int)) (let ((_let_1 (@ tptp.insert_int A))) (let ((_let_2 (@ tptp.minus_minus_set_int A2))) (= (@ _let_2 (@ _let_1 B)) (@ (@ tptp.minus_minus_set_int (@ _let_2 (@ _let_1 tptp.bot_bot_set_int))) B))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (A tptp.nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat A))) (let ((_let_2 (@ tptp.minus_minus_set_nat A2))) (= (@ _let_2 (@ _let_1 B)) (@ (@ tptp.minus_minus_set_nat (@ _let_2 (@ _let_1 tptp.bot_bot_set_nat))) B))))))
% 4.96/5.19 (assert (forall ((X tptp.set_nat) (A2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.insert_set_nat X))) (=> (not (@ (@ tptp.member_set_nat X) A2)) (= (@ (@ tptp.minus_2163939370556025621et_nat (@ _let_1 A2)) (@ _let_1 tptp.bot_bot_set_set_nat)) A2)))))
% 4.96/5.19 (assert (forall ((X tptp.extended_enat) (A2 tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.insert_Extended_enat X))) (=> (not (@ (@ tptp.member_Extended_enat X) A2)) (= (@ (@ tptp.minus_925952699566721837d_enat (@ _let_1 A2)) (@ _let_1 tptp.bot_bo7653980558646680370d_enat)) A2)))))
% 4.96/5.19 (assert (forall ((X tptp.real) (A2 tptp.set_real)) (let ((_let_1 (@ tptp.insert_real X))) (=> (not (@ (@ tptp.member_real X) A2)) (= (@ (@ tptp.minus_minus_set_real (@ _let_1 A2)) (@ _let_1 tptp.bot_bot_set_real)) A2)))))
% 4.96/5.19 (assert (forall ((X tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int X))) (=> (not (@ (@ tptp.member_int X) A2)) (= (@ (@ tptp.minus_minus_set_int (@ _let_1 A2)) (@ _let_1 tptp.bot_bot_set_int)) A2)))))
% 4.96/5.19 (assert (forall ((X tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X))) (=> (not (@ (@ tptp.member_nat X) A2)) (= (@ (@ tptp.minus_minus_set_nat (@ _let_1 A2)) (@ _let_1 tptp.bot_bot_set_nat)) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (A tptp.real)) (=> (@ tptp.finite_finite_real A2) (@ tptp.finite_finite_real (@ (@ tptp.insert_real A) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (A tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (@ tptp.finite_finite_nat (@ (@ tptp.insert_nat A) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (A tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex A2) (@ tptp.finite3207457112153483333omplex (@ (@ tptp.insert_complex A) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (A tptp.int)) (=> (@ tptp.finite_finite_int A2) (@ tptp.finite_finite_int (@ (@ tptp.insert_int A) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (A tptp.extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (@ tptp.finite4001608067531595151d_enat (@ (@ tptp.insert_Extended_enat A) A2)))))
% 4.96/5.19 (assert (forall ((C4 tptp.set_real) (D6 tptp.set_real) (A tptp.real)) (let ((_let_1 (@ tptp.insert_real A))) (=> (@ (@ tptp.ord_less_eq_set_real C4) D6) (@ (@ tptp.ord_less_eq_set_real (@ _let_1 C4)) (@ _let_1 D6))))))
% 4.96/5.19 (assert (forall ((C4 tptp.set_nat) (D6 tptp.set_nat) (A tptp.nat)) (let ((_let_1 (@ tptp.insert_nat A))) (=> (@ (@ tptp.ord_less_eq_set_nat C4) D6) (@ (@ tptp.ord_less_eq_set_nat (@ _let_1 C4)) (@ _let_1 D6))))))
% 4.96/5.19 (assert (forall ((C4 tptp.set_int) (D6 tptp.set_int) (A tptp.int)) (let ((_let_1 (@ tptp.insert_int A))) (=> (@ (@ tptp.ord_less_eq_set_int C4) D6) (@ (@ tptp.ord_less_eq_set_int (@ _let_1 C4)) (@ _let_1 D6))))))
% 4.96/5.19 (assert (forall ((X tptp.extended_enat) (A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.ord_le7203529160286727270d_enat A2))) (=> (not (@ (@ tptp.member_Extended_enat X) A2)) (= (@ _let_1 (@ (@ tptp.insert_Extended_enat X) B)) (@ _let_1 B))))))
% 4.96/5.19 (assert (forall ((X tptp.real) (A2 tptp.set_real) (B tptp.set_real)) (let ((_let_1 (@ tptp.ord_less_eq_set_real A2))) (=> (not (@ (@ tptp.member_real X) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X) B)) (@ _let_1 B))))))
% 4.96/5.19 (assert (forall ((X tptp.set_nat) (A2 tptp.set_set_nat) (B tptp.set_set_nat)) (let ((_let_1 (@ tptp.ord_le6893508408891458716et_nat A2))) (=> (not (@ (@ tptp.member_set_nat X) A2)) (= (@ _let_1 (@ (@ tptp.insert_set_nat X) B)) (@ _let_1 B))))))
% 4.96/5.19 (assert (forall ((X tptp.nat) (A2 tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A2))) (=> (not (@ (@ tptp.member_nat X) A2)) (= (@ _let_1 (@ (@ tptp.insert_nat X) B)) (@ _let_1 B))))))
% 4.96/5.19 (assert (forall ((X tptp.int) (A2 tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A2))) (=> (not (@ (@ tptp.member_int X) A2)) (= (@ _let_1 (@ (@ tptp.insert_int X) B)) (@ _let_1 B))))))
% 4.96/5.19 (assert (forall ((B tptp.set_real) (A tptp.real)) (@ (@ tptp.ord_less_eq_set_real B) (@ (@ tptp.insert_real A) B))))
% 4.96/5.19 (assert (forall ((B tptp.set_nat) (A tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat B) (@ (@ tptp.insert_nat A) B))))
% 4.96/5.19 (assert (forall ((B tptp.set_int) (A tptp.int)) (@ (@ tptp.ord_less_eq_set_int B) (@ (@ tptp.insert_int A) B))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (B tptp.set_real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_set_real A2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.insert_real B2) B))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.insert_nat B2) B))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (B tptp.set_int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.insert_int B2) B))))))
% 4.96/5.19 (assert (forall ((X tptp.extended_enat) (A2 tptp.set_Extended_enat) (X8 tptp.set_Extended_enat)) (=> (@ (@ tptp.member_Extended_enat X) A2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat X8) A2) (@ (@ tptp.ord_le7203529160286727270d_enat (@ (@ tptp.insert_Extended_enat X) X8)) A2)))))
% 4.96/5.19 (assert (forall ((X tptp.real) (A2 tptp.set_real) (X8 tptp.set_real)) (=> (@ (@ tptp.member_real X) A2) (=> (@ (@ tptp.ord_less_eq_set_real X8) A2) (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.insert_real X) X8)) A2)))))
% 4.96/5.19 (assert (forall ((X tptp.set_nat) (A2 tptp.set_set_nat) (X8 tptp.set_set_nat)) (=> (@ (@ tptp.member_set_nat X) A2) (=> (@ (@ tptp.ord_le6893508408891458716et_nat X8) A2) (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.insert_set_nat X) X8)) A2)))))
% 4.96/5.19 (assert (forall ((X tptp.nat) (A2 tptp.set_nat) (X8 tptp.set_nat)) (=> (@ (@ tptp.member_nat X) A2) (=> (@ (@ tptp.ord_less_eq_set_nat X8) A2) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.insert_nat X) X8)) A2)))))
% 4.96/5.19 (assert (forall ((X tptp.int) (A2 tptp.set_int) (X8 tptp.set_int)) (=> (@ (@ tptp.member_int X) A2) (=> (@ (@ tptp.ord_less_eq_set_int X8) A2) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.insert_int X) X8)) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat) (X tptp.extended_enat) (C4 tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.minus_925952699566721837d_enat B))) (let ((_let_2 (@ tptp.ord_le7203529160286727270d_enat A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_Extended_enat X) C4))) (and (@ _let_2 (@ _let_1 C4)) (not (@ (@ tptp.member_Extended_enat X) A2))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (B tptp.set_real) (X tptp.real) (C4 tptp.set_real)) (let ((_let_1 (@ tptp.minus_minus_set_real B))) (let ((_let_2 (@ tptp.ord_less_eq_set_real A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_real X) C4))) (and (@ _let_2 (@ _let_1 C4)) (not (@ (@ tptp.member_real X) A2))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_set_nat) (B tptp.set_set_nat) (X tptp.set_nat) (C4 tptp.set_set_nat)) (let ((_let_1 (@ tptp.minus_2163939370556025621et_nat B))) (let ((_let_2 (@ tptp.ord_le6893508408891458716et_nat A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_set_nat X) C4))) (and (@ _let_2 (@ _let_1 C4)) (not (@ (@ tptp.member_set_nat X) A2))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat) (X tptp.nat) (C4 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat B))) (let ((_let_2 (@ tptp.ord_less_eq_set_nat A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_nat X) C4))) (and (@ _let_2 (@ _let_1 C4)) (not (@ (@ tptp.member_nat X) A2))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (B tptp.set_int) (X tptp.int) (C4 tptp.set_int)) (let ((_let_1 (@ tptp.minus_minus_set_int B))) (let ((_let_2 (@ tptp.ord_less_eq_set_int A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_int X) C4))) (and (@ _let_2 (@ _let_1 C4)) (not (@ (@ tptp.member_int X) A2))))))))
% 4.96/5.19 (assert (forall ((P (-> tptp.list_nat Bool)) (A tptp.list_nat)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (and (= X4 A) (@ P X4)))) (@ (@ tptp.insert_list_nat A) tptp.bot_bot_set_list_nat))) (=> (not _let_1) (= (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (and (= X4 A) (@ P X4)))) tptp.bot_bot_set_list_nat))))))
% 4.96/5.19 (assert (forall ((P (-> tptp.set_nat Bool)) (A tptp.set_nat)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (and (= X4 A) (@ P X4)))) (@ (@ tptp.insert_set_nat A) tptp.bot_bot_set_set_nat))) (=> (not _let_1) (= (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (and (= X4 A) (@ P X4)))) tptp.bot_bot_set_set_nat))))))
% 4.96/5.19 (assert (forall ((P (-> tptp.extended_enat Bool)) (A tptp.extended_enat)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (and (= X4 A) (@ P X4)))) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat))) (=> (not _let_1) (= (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (and (= X4 A) (@ P X4)))) tptp.bot_bo7653980558646680370d_enat))))))
% 4.96/5.19 (assert (forall ((P (-> tptp.real Bool)) (A tptp.real)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collect_real (lambda ((X4 tptp.real)) (and (= X4 A) (@ P X4)))) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))) (=> (not _let_1) (= (@ tptp.collect_real (lambda ((X4 tptp.real)) (and (= X4 A) (@ P X4)))) tptp.bot_bot_set_real))))))
% 4.96/5.19 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (= X4 A) (@ P X4)))) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))) (=> (not _let_1) (= (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (= X4 A) (@ P X4)))) tptp.bot_bot_set_nat))))))
% 4.96/5.19 (assert (forall ((P (-> tptp.int Bool)) (A tptp.int)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (= X4 A) (@ P X4)))) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))) (=> (not _let_1) (= (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (= X4 A) (@ P X4)))) tptp.bot_bot_set_int))))))
% 4.96/5.19 (assert (forall ((P (-> tptp.list_nat Bool)) (A tptp.list_nat)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (and (= A X4) (@ P X4)))) (@ (@ tptp.insert_list_nat A) tptp.bot_bot_set_list_nat))) (=> (not _let_1) (= (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (and (= A X4) (@ P X4)))) tptp.bot_bot_set_list_nat))))))
% 4.96/5.19 (assert (forall ((P (-> tptp.set_nat Bool)) (A tptp.set_nat)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (and (= A X4) (@ P X4)))) (@ (@ tptp.insert_set_nat A) tptp.bot_bot_set_set_nat))) (=> (not _let_1) (= (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (and (= A X4) (@ P X4)))) tptp.bot_bot_set_set_nat))))))
% 4.96/5.19 (assert (forall ((P (-> tptp.extended_enat Bool)) (A tptp.extended_enat)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (and (= A X4) (@ P X4)))) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat))) (=> (not _let_1) (= (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (and (= A X4) (@ P X4)))) tptp.bot_bo7653980558646680370d_enat))))))
% 4.96/5.19 (assert (forall ((P (-> tptp.real Bool)) (A tptp.real)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collect_real (lambda ((X4 tptp.real)) (and (= A X4) (@ P X4)))) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))) (=> (not _let_1) (= (@ tptp.collect_real (lambda ((X4 tptp.real)) (and (= A X4) (@ P X4)))) tptp.bot_bot_set_real))))))
% 4.96/5.19 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (= A X4) (@ P X4)))) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))) (=> (not _let_1) (= (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (= A X4) (@ P X4)))) tptp.bot_bot_set_nat))))))
% 4.96/5.19 (assert (forall ((P (-> tptp.int Bool)) (A tptp.int)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (= A X4) (@ P X4)))) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))) (=> (not _let_1) (= (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (= A X4) (@ P X4)))) tptp.bot_bot_set_int))))))
% 4.96/5.19 (assert (forall ((A tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A) (=> (not (= A tptp.bot_bot_set_complex)) (not (forall ((A6 tptp.set_complex)) (=> (exists ((A4 tptp.complex)) (= A (@ (@ tptp.insert_complex A4) A6))) (not (@ tptp.finite3207457112153483333omplex A6)))))))))
% 4.96/5.19 (assert (forall ((A tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A) (=> (not (= A tptp.bot_bo7653980558646680370d_enat)) (not (forall ((A6 tptp.set_Extended_enat)) (=> (exists ((A4 tptp.extended_enat)) (= A (@ (@ tptp.insert_Extended_enat A4) A6))) (not (@ tptp.finite4001608067531595151d_enat A6)))))))))
% 4.96/5.19 (assert (forall ((A tptp.set_real)) (=> (@ tptp.finite_finite_real A) (=> (not (= A tptp.bot_bot_set_real)) (not (forall ((A6 tptp.set_real)) (=> (exists ((A4 tptp.real)) (= A (@ (@ tptp.insert_real A4) A6))) (not (@ tptp.finite_finite_real A6)))))))))
% 4.96/5.19 (assert (forall ((A tptp.set_nat)) (=> (@ tptp.finite_finite_nat A) (=> (not (= A tptp.bot_bot_set_nat)) (not (forall ((A6 tptp.set_nat)) (=> (exists ((A4 tptp.nat)) (= A (@ (@ tptp.insert_nat A4) A6))) (not (@ tptp.finite_finite_nat A6)))))))))
% 4.96/5.19 (assert (forall ((A tptp.set_int)) (=> (@ tptp.finite_finite_int A) (=> (not (= A tptp.bot_bot_set_int)) (not (forall ((A6 tptp.set_int)) (=> (exists ((A4 tptp.int)) (= A (@ (@ tptp.insert_int A4) A6))) (not (@ tptp.finite_finite_int A6)))))))))
% 4.96/5.19 (assert (= tptp.finite3207457112153483333omplex (lambda ((A3 tptp.set_complex)) (or (= A3 tptp.bot_bot_set_complex) (exists ((A5 tptp.set_complex) (B3 tptp.complex)) (and (= A3 (@ (@ tptp.insert_complex B3) A5)) (@ tptp.finite3207457112153483333omplex A5)))))))
% 4.96/5.19 (assert (= tptp.finite4001608067531595151d_enat (lambda ((A3 tptp.set_Extended_enat)) (or (= A3 tptp.bot_bo7653980558646680370d_enat) (exists ((A5 tptp.set_Extended_enat) (B3 tptp.extended_enat)) (and (= A3 (@ (@ tptp.insert_Extended_enat B3) A5)) (@ tptp.finite4001608067531595151d_enat A5)))))))
% 4.96/5.19 (assert (= tptp.finite_finite_real (lambda ((A3 tptp.set_real)) (or (= A3 tptp.bot_bot_set_real) (exists ((A5 tptp.set_real) (B3 tptp.real)) (and (= A3 (@ (@ tptp.insert_real B3) A5)) (@ tptp.finite_finite_real A5)))))))
% 4.96/5.19 (assert (= tptp.finite_finite_nat (lambda ((A3 tptp.set_nat)) (or (= A3 tptp.bot_bot_set_nat) (exists ((A5 tptp.set_nat) (B3 tptp.nat)) (and (= A3 (@ (@ tptp.insert_nat B3) A5)) (@ tptp.finite_finite_nat A5)))))))
% 4.96/5.19 (assert (= tptp.finite_finite_int (lambda ((A3 tptp.set_int)) (or (= A3 tptp.bot_bot_set_int) (exists ((A5 tptp.set_int) (B3 tptp.int)) (and (= A3 (@ (@ tptp.insert_int B3) A5)) (@ tptp.finite_finite_int A5)))))))
% 4.96/5.19 (assert (forall ((F3 tptp.set_set_nat) (P (-> tptp.set_set_nat Bool))) (=> (@ tptp.finite1152437895449049373et_nat F3) (=> (@ P tptp.bot_bot_set_set_nat) (=> (forall ((X5 tptp.set_nat) (F4 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat F4) (=> (not (@ (@ tptp.member_set_nat X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_set_nat X5) F4)))))) (@ P F3))))))
% 4.96/5.19 (assert (forall ((F3 tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex F3) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((X5 tptp.complex) (F4 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex F4) (=> (not (@ (@ tptp.member_complex X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_complex X5) F4)))))) (@ P F3))))))
% 4.96/5.19 (assert (forall ((F3 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat F3) (=> (@ P tptp.bot_bo7653980558646680370d_enat) (=> (forall ((X5 tptp.extended_enat) (F4 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat F4) (=> (not (@ (@ tptp.member_Extended_enat X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_Extended_enat X5) F4)))))) (@ P F3))))))
% 4.96/5.19 (assert (forall ((F3 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real F3) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((X5 tptp.real) (F4 tptp.set_real)) (=> (@ tptp.finite_finite_real F4) (=> (not (@ (@ tptp.member_real X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_real X5) F4)))))) (@ P F3))))))
% 4.96/5.19 (assert (forall ((F3 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat F3) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((X5 tptp.nat) (F4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat F4) (=> (not (@ (@ tptp.member_nat X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_nat X5) F4)))))) (@ P F3))))))
% 4.96/5.19 (assert (forall ((F3 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int F3) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((X5 tptp.int) (F4 tptp.set_int)) (=> (@ tptp.finite_finite_int F4) (=> (not (@ (@ tptp.member_int X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_int X5) F4)))))) (@ P F3))))))
% 4.96/5.19 (assert (forall ((F3 tptp.set_set_nat) (P (-> tptp.set_set_nat Bool))) (=> (@ tptp.finite1152437895449049373et_nat F3) (=> (not (= F3 tptp.bot_bot_set_set_nat)) (=> (forall ((X5 tptp.set_nat)) (@ P (@ (@ tptp.insert_set_nat X5) tptp.bot_bot_set_set_nat))) (=> (forall ((X5 tptp.set_nat) (F4 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat F4) (=> (not (= F4 tptp.bot_bot_set_set_nat)) (=> (not (@ (@ tptp.member_set_nat X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_set_nat X5) F4))))))) (@ P F3)))))))
% 4.96/5.19 (assert (forall ((F3 tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex F3) (=> (not (= F3 tptp.bot_bot_set_complex)) (=> (forall ((X5 tptp.complex)) (@ P (@ (@ tptp.insert_complex X5) tptp.bot_bot_set_complex))) (=> (forall ((X5 tptp.complex) (F4 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex F4) (=> (not (= F4 tptp.bot_bot_set_complex)) (=> (not (@ (@ tptp.member_complex X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_complex X5) F4))))))) (@ P F3)))))))
% 4.96/5.19 (assert (forall ((F3 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat F3) (=> (not (= F3 tptp.bot_bo7653980558646680370d_enat)) (=> (forall ((X5 tptp.extended_enat)) (@ P (@ (@ tptp.insert_Extended_enat X5) tptp.bot_bo7653980558646680370d_enat))) (=> (forall ((X5 tptp.extended_enat) (F4 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat F4) (=> (not (= F4 tptp.bot_bo7653980558646680370d_enat)) (=> (not (@ (@ tptp.member_Extended_enat X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_Extended_enat X5) F4))))))) (@ P F3)))))))
% 4.96/5.19 (assert (forall ((F3 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real F3) (=> (not (= F3 tptp.bot_bot_set_real)) (=> (forall ((X5 tptp.real)) (@ P (@ (@ tptp.insert_real X5) tptp.bot_bot_set_real))) (=> (forall ((X5 tptp.real) (F4 tptp.set_real)) (=> (@ tptp.finite_finite_real F4) (=> (not (= F4 tptp.bot_bot_set_real)) (=> (not (@ (@ tptp.member_real X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_real X5) F4))))))) (@ P F3)))))))
% 4.96/5.19 (assert (forall ((F3 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat F3) (=> (not (= F3 tptp.bot_bot_set_nat)) (=> (forall ((X5 tptp.nat)) (@ P (@ (@ tptp.insert_nat X5) tptp.bot_bot_set_nat))) (=> (forall ((X5 tptp.nat) (F4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat F4) (=> (not (= F4 tptp.bot_bot_set_nat)) (=> (not (@ (@ tptp.member_nat X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_nat X5) F4))))))) (@ P F3)))))))
% 4.96/5.19 (assert (forall ((F3 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int F3) (=> (not (= F3 tptp.bot_bot_set_int)) (=> (forall ((X5 tptp.int)) (@ P (@ (@ tptp.insert_int X5) tptp.bot_bot_set_int))) (=> (forall ((X5 tptp.int) (F4 tptp.set_int)) (=> (@ tptp.finite_finite_int F4) (=> (not (= F4 tptp.bot_bot_set_int)) (=> (not (@ (@ tptp.member_int X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_int X5) F4))))))) (@ P F3)))))))
% 4.96/5.19 (assert (forall ((P (-> tptp.set_set_nat Bool)) (A2 tptp.set_set_nat)) (=> (forall ((A6 tptp.set_set_nat)) (=> (not (@ tptp.finite1152437895449049373et_nat A6)) (@ P A6))) (=> (@ P tptp.bot_bot_set_set_nat) (=> (forall ((X5 tptp.set_nat) (F4 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat F4) (=> (not (@ (@ tptp.member_set_nat X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_set_nat X5) F4)))))) (@ P A2))))))
% 4.96/5.19 (assert (forall ((P (-> tptp.set_complex Bool)) (A2 tptp.set_complex)) (=> (forall ((A6 tptp.set_complex)) (=> (not (@ tptp.finite3207457112153483333omplex A6)) (@ P A6))) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((X5 tptp.complex) (F4 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex F4) (=> (not (@ (@ tptp.member_complex X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_complex X5) F4)))))) (@ P A2))))))
% 4.96/5.19 (assert (forall ((P (-> tptp.set_Extended_enat Bool)) (A2 tptp.set_Extended_enat)) (=> (forall ((A6 tptp.set_Extended_enat)) (=> (not (@ tptp.finite4001608067531595151d_enat A6)) (@ P A6))) (=> (@ P tptp.bot_bo7653980558646680370d_enat) (=> (forall ((X5 tptp.extended_enat) (F4 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat F4) (=> (not (@ (@ tptp.member_Extended_enat X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_Extended_enat X5) F4)))))) (@ P A2))))))
% 4.96/5.19 (assert (forall ((P (-> tptp.set_real Bool)) (A2 tptp.set_real)) (=> (forall ((A6 tptp.set_real)) (=> (not (@ tptp.finite_finite_real A6)) (@ P A6))) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((X5 tptp.real) (F4 tptp.set_real)) (=> (@ tptp.finite_finite_real F4) (=> (not (@ (@ tptp.member_real X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_real X5) F4)))))) (@ P A2))))))
% 4.96/5.19 (assert (forall ((P (-> tptp.set_nat Bool)) (A2 tptp.set_nat)) (=> (forall ((A6 tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat A6)) (@ P A6))) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((X5 tptp.nat) (F4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat F4) (=> (not (@ (@ tptp.member_nat X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_nat X5) F4)))))) (@ P A2))))))
% 4.96/5.19 (assert (forall ((P (-> tptp.set_int Bool)) (A2 tptp.set_int)) (=> (forall ((A6 tptp.set_int)) (=> (not (@ tptp.finite_finite_int A6)) (@ P A6))) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((X5 tptp.int) (F4 tptp.set_int)) (=> (@ tptp.finite_finite_int F4) (=> (not (@ (@ tptp.member_int X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_int X5) F4)))))) (@ P A2))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_complex) (A tptp.complex)) (=> (not (@ tptp.finite3207457112153483333omplex S2)) (not (@ tptp.finite3207457112153483333omplex (@ (@ tptp.minus_811609699411566653omplex S2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex)))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_Extended_enat) (A tptp.extended_enat)) (=> (not (@ tptp.finite4001608067531595151d_enat S2)) (not (@ tptp.finite4001608067531595151d_enat (@ (@ tptp.minus_925952699566721837d_enat S2) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat)))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_real) (A tptp.real)) (=> (not (@ tptp.finite_finite_real S2)) (not (@ tptp.finite_finite_real (@ (@ tptp.minus_minus_set_real S2) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real)))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_int) (A tptp.int)) (=> (not (@ tptp.finite_finite_int S2)) (not (@ tptp.finite_finite_int (@ (@ tptp.minus_minus_set_int S2) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int)))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_nat) (A tptp.nat)) (=> (not (@ tptp.finite_finite_nat S2)) (not (@ tptp.finite_finite_nat (@ (@ tptp.minus_minus_set_nat S2) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat)))))))
% 4.96/5.19 (assert (forall ((X8 (-> tptp.set_complex Bool)) (A2 tptp.set_complex)) (=> (@ X8 A2) (=> (forall ((A6 tptp.set_complex)) (=> (@ X8 A6) (exists ((X2 tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_811609699411566653omplex A6) (@ (@ tptp.insert_complex X2) tptp.bot_bot_set_complex)))) (and (@ (@ tptp.member_complex X2) A6) (or (@ X8 _let_1) (not (@ tptp.finite3207457112153483333omplex _let_1)))))))) (not (@ tptp.finite3207457112153483333omplex A2))))))
% 4.96/5.19 (assert (forall ((X8 (-> tptp.set_Extended_enat Bool)) (A2 tptp.set_Extended_enat)) (=> (@ X8 A2) (=> (forall ((A6 tptp.set_Extended_enat)) (=> (@ X8 A6) (exists ((X2 tptp.extended_enat)) (let ((_let_1 (@ (@ tptp.minus_925952699566721837d_enat A6) (@ (@ tptp.insert_Extended_enat X2) tptp.bot_bo7653980558646680370d_enat)))) (and (@ (@ tptp.member_Extended_enat X2) A6) (or (@ X8 _let_1) (not (@ tptp.finite4001608067531595151d_enat _let_1)))))))) (not (@ tptp.finite4001608067531595151d_enat A2))))))
% 4.96/5.19 (assert (forall ((X8 (-> tptp.set_real Bool)) (A2 tptp.set_real)) (=> (@ X8 A2) (=> (forall ((A6 tptp.set_real)) (=> (@ X8 A6) (exists ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_set_real A6) (@ (@ tptp.insert_real X2) tptp.bot_bot_set_real)))) (and (@ (@ tptp.member_real X2) A6) (or (@ X8 _let_1) (not (@ tptp.finite_finite_real _let_1)))))))) (not (@ tptp.finite_finite_real A2))))))
% 4.96/5.19 (assert (forall ((X8 (-> tptp.set_int Bool)) (A2 tptp.set_int)) (=> (@ X8 A2) (=> (forall ((A6 tptp.set_int)) (=> (@ X8 A6) (exists ((X2 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_set_int A6) (@ (@ tptp.insert_int X2) tptp.bot_bot_set_int)))) (and (@ (@ tptp.member_int X2) A6) (or (@ X8 _let_1) (not (@ tptp.finite_finite_int _let_1)))))))) (not (@ tptp.finite_finite_int A2))))))
% 4.96/5.19 (assert (forall ((X8 (-> tptp.set_nat Bool)) (A2 tptp.set_nat)) (=> (@ X8 A2) (=> (forall ((A6 tptp.set_nat)) (=> (@ X8 A6) (exists ((X2 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_set_nat A6) (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat)))) (and (@ (@ tptp.member_nat X2) A6) (or (@ X8 _let_1) (not (@ tptp.finite_finite_nat _let_1)))))))) (not (@ tptp.finite_finite_nat A2))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_set_nat) (P (-> tptp.set_set_nat Bool))) (=> (@ tptp.finite1152437895449049373et_nat A2) (=> (@ P A2) (=> (forall ((A4 tptp.set_nat) (A6 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A6) (=> (@ (@ tptp.member_set_nat A4) A6) (=> (@ P A6) (@ P (@ (@ tptp.minus_2163939370556025621et_nat A6) (@ (@ tptp.insert_set_nat A4) tptp.bot_bot_set_set_nat))))))) (@ P tptp.bot_bot_set_set_nat))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ P A2) (=> (forall ((A4 tptp.complex) (A6 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A6) (=> (@ (@ tptp.member_complex A4) A6) (=> (@ P A6) (@ P (@ (@ tptp.minus_811609699411566653omplex A6) (@ (@ tptp.insert_complex A4) tptp.bot_bot_set_complex))))))) (@ P tptp.bot_bot_set_complex))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ P A2) (=> (forall ((A4 tptp.extended_enat) (A6 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A6) (=> (@ (@ tptp.member_Extended_enat A4) A6) (=> (@ P A6) (@ P (@ (@ tptp.minus_925952699566721837d_enat A6) (@ (@ tptp.insert_Extended_enat A4) tptp.bot_bo7653980558646680370d_enat))))))) (@ P tptp.bot_bo7653980558646680370d_enat))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real A2) (=> (@ P A2) (=> (forall ((A4 tptp.real) (A6 tptp.set_real)) (=> (@ tptp.finite_finite_real A6) (=> (@ (@ tptp.member_real A4) A6) (=> (@ P A6) (@ P (@ (@ tptp.minus_minus_set_real A6) (@ (@ tptp.insert_real A4) tptp.bot_bot_set_real))))))) (@ P tptp.bot_bot_set_real))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int A2) (=> (@ P A2) (=> (forall ((A4 tptp.int) (A6 tptp.set_int)) (=> (@ tptp.finite_finite_int A6) (=> (@ (@ tptp.member_int A4) A6) (=> (@ P A6) (@ P (@ (@ tptp.minus_minus_set_int A6) (@ (@ tptp.insert_int A4) tptp.bot_bot_set_int))))))) (@ P tptp.bot_bot_set_int))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat A2) (=> (@ P A2) (=> (forall ((A4 tptp.nat) (A6 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A6) (=> (@ (@ tptp.member_nat A4) A6) (=> (@ P A6) (@ P (@ (@ tptp.minus_minus_set_nat A6) (@ (@ tptp.insert_nat A4) tptp.bot_bot_set_nat))))))) (@ P tptp.bot_bot_set_nat))))))
% 4.96/5.19 (assert (forall ((X8 tptp.set_Extended_enat) (A tptp.extended_enat)) (let ((_let_1 (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat))) (= (@ (@ tptp.ord_le7203529160286727270d_enat X8) _let_1) (or (= X8 tptp.bot_bo7653980558646680370d_enat) (= X8 _let_1))))))
% 4.96/5.19 (assert (forall ((X8 tptp.set_real) (A tptp.real)) (let ((_let_1 (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))) (= (@ (@ tptp.ord_less_eq_set_real X8) _let_1) (or (= X8 tptp.bot_bot_set_real) (= X8 _let_1))))))
% 4.96/5.19 (assert (forall ((X8 tptp.set_nat) (A tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))) (= (@ (@ tptp.ord_less_eq_set_nat X8) _let_1) (or (= X8 tptp.bot_bot_set_nat) (= X8 _let_1))))))
% 4.96/5.19 (assert (forall ((X8 tptp.set_int) (A tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))) (= (@ (@ tptp.ord_less_eq_set_int X8) _let_1) (or (= X8 tptp.bot_bot_set_int) (= X8 _let_1))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (X tptp.extended_enat)) (let ((_let_1 (@ (@ tptp.insert_Extended_enat X) tptp.bot_bo7653980558646680370d_enat))) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) _let_1) (or (= A2 tptp.bot_bo7653980558646680370d_enat) (= A2 _let_1))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (X tptp.real)) (let ((_let_1 (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))) (=> (@ (@ tptp.ord_less_eq_set_real A2) _let_1) (or (= A2 tptp.bot_bot_set_real) (= A2 _let_1))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))) (=> (@ (@ tptp.ord_less_eq_set_nat A2) _let_1) (or (= A2 tptp.bot_bot_set_nat) (= A2 _let_1))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (X tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))) (=> (@ (@ tptp.ord_less_eq_set_int A2) _let_1) (or (= A2 tptp.bot_bot_set_int) (= A2 _let_1))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (X tptp.extended_enat) (B tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.insert_Extended_enat X))) (=> (@ (@ tptp.ord_le7203529160286727270d_enat (@ (@ tptp.minus_925952699566721837d_enat A2) (@ _let_1 tptp.bot_bo7653980558646680370d_enat))) B) (@ (@ tptp.ord_le7203529160286727270d_enat A2) (@ _let_1 B))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (X tptp.real) (B tptp.set_real)) (let ((_let_1 (@ tptp.insert_real X))) (=> (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.minus_minus_set_real A2) (@ _let_1 tptp.bot_bot_set_real))) B) (@ (@ tptp.ord_less_eq_set_real A2) (@ _let_1 B))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (X tptp.nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X))) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A2) (@ _let_1 tptp.bot_bot_set_nat))) B) (@ (@ tptp.ord_less_eq_set_nat A2) (@ _let_1 B))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (X tptp.int) (B tptp.set_int)) (let ((_let_1 (@ tptp.insert_int X))) (=> (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A2) (@ _let_1 tptp.bot_bot_set_int))) B) (@ (@ tptp.ord_less_eq_set_int A2) (@ _let_1 B))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_set_nat) (X tptp.set_nat) (B tptp.set_set_nat)) (let ((_let_1 (@ tptp.ord_le6893508408891458716et_nat A2))) (let ((_let_2 (@ (@ tptp.member_set_nat X) A2))) (let ((_let_3 (@ tptp.insert_set_nat X))) (= (@ _let_1 (@ _let_3 B)) (and (=> _let_2 (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.minus_2163939370556025621et_nat A2) (@ _let_3 tptp.bot_bot_set_set_nat))) B)) (=> (not _let_2) (@ _let_1 B)))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (X tptp.extended_enat) (B tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.ord_le7203529160286727270d_enat A2))) (let ((_let_2 (@ (@ tptp.member_Extended_enat X) A2))) (let ((_let_3 (@ tptp.insert_Extended_enat X))) (= (@ _let_1 (@ _let_3 B)) (and (=> _let_2 (@ (@ tptp.ord_le7203529160286727270d_enat (@ (@ tptp.minus_925952699566721837d_enat A2) (@ _let_3 tptp.bot_bo7653980558646680370d_enat))) B)) (=> (not _let_2) (@ _let_1 B)))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (X tptp.real) (B tptp.set_real)) (let ((_let_1 (@ tptp.ord_less_eq_set_real A2))) (let ((_let_2 (@ (@ tptp.member_real X) A2))) (let ((_let_3 (@ tptp.insert_real X))) (= (@ _let_1 (@ _let_3 B)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.minus_minus_set_real A2) (@ _let_3 tptp.bot_bot_set_real))) B)) (=> (not _let_2) (@ _let_1 B)))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (X tptp.nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A2))) (let ((_let_2 (@ (@ tptp.member_nat X) A2))) (let ((_let_3 (@ tptp.insert_nat X))) (= (@ _let_1 (@ _let_3 B)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A2) (@ _let_3 tptp.bot_bot_set_nat))) B)) (=> (not _let_2) (@ _let_1 B)))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (X tptp.int) (B tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A2))) (let ((_let_2 (@ (@ tptp.member_int X) A2))) (let ((_let_3 (@ tptp.insert_int X))) (= (@ _let_1 (@ _let_3 B)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A2) (@ _let_3 tptp.bot_bot_set_int))) B)) (=> (not _let_2) (@ _let_1 B)))))))))
% 4.96/5.19 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (=> (= A B2) (= (@ (@ tptp.set_or5403411693681687835d_enat A) B2) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat)))))
% 4.96/5.19 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (= A B2) (= (@ (@ tptp.set_or1269000886237332187st_nat A) B2) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat)))))
% 4.96/5.19 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (= A B2) (= (@ (@ tptp.set_or1266510415728281911st_int A) B2) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int)))))
% 4.96/5.19 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (= A B2) (= (@ (@ tptp.set_or1222579329274155063t_real A) B2) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real)))))
% 4.96/5.19 (assert (= tptp.numeral_numeral_nat (lambda ((K2 tptp.num)) (@ tptp.suc (@ tptp.pred_numeral K2)))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_complex) (P (-> tptp.set_complex Bool)) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((X5 tptp.complex) (S4 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex S4) (=> (forall ((Y6 tptp.complex)) (=> (@ (@ tptp.member_complex Y6) S4) (@ (@ tptp.ord_less_eq_real (@ F Y6)) (@ F X5)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_complex X5) S4)))))) (@ P S2))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool)) (F (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat S2) (=> (@ P tptp.bot_bo7653980558646680370d_enat) (=> (forall ((X5 tptp.extended_enat) (S4 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat S4) (=> (forall ((Y6 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat Y6) S4) (@ (@ tptp.ord_less_eq_real (@ F Y6)) (@ F X5)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_Extended_enat X5) S4)))))) (@ P S2))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_real) (P (-> tptp.set_real Bool)) (F (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real S2) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((X5 tptp.real) (S4 tptp.set_real)) (=> (@ tptp.finite_finite_real S4) (=> (forall ((Y6 tptp.real)) (=> (@ (@ tptp.member_real Y6) S4) (@ (@ tptp.ord_less_eq_real (@ F Y6)) (@ F X5)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_real X5) S4)))))) (@ P S2))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_nat) (P (-> tptp.set_nat Bool)) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat S2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((X5 tptp.nat) (S4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S4) (=> (forall ((Y6 tptp.nat)) (=> (@ (@ tptp.member_nat Y6) S4) (@ (@ tptp.ord_less_eq_real (@ F Y6)) (@ F X5)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_nat X5) S4)))))) (@ P S2))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_int) (P (-> tptp.set_int Bool)) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int S2) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((X5 tptp.int) (S4 tptp.set_int)) (=> (@ tptp.finite_finite_int S4) (=> (forall ((Y6 tptp.int)) (=> (@ (@ tptp.member_int Y6) S4) (@ (@ tptp.ord_less_eq_real (@ F Y6)) (@ F X5)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_int X5) S4)))))) (@ P S2))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_complex) (P (-> tptp.set_complex Bool)) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((X5 tptp.complex) (S4 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex S4) (=> (forall ((Y6 tptp.complex)) (=> (@ (@ tptp.member_complex Y6) S4) (@ (@ tptp.ord_less_eq_nat (@ F Y6)) (@ F X5)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_complex X5) S4)))))) (@ P S2))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool)) (F (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat S2) (=> (@ P tptp.bot_bo7653980558646680370d_enat) (=> (forall ((X5 tptp.extended_enat) (S4 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat S4) (=> (forall ((Y6 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat Y6) S4) (@ (@ tptp.ord_less_eq_nat (@ F Y6)) (@ F X5)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_Extended_enat X5) S4)))))) (@ P S2))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_real) (P (-> tptp.set_real Bool)) (F (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real S2) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((X5 tptp.real) (S4 tptp.set_real)) (=> (@ tptp.finite_finite_real S4) (=> (forall ((Y6 tptp.real)) (=> (@ (@ tptp.member_real Y6) S4) (@ (@ tptp.ord_less_eq_nat (@ F Y6)) (@ F X5)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_real X5) S4)))))) (@ P S2))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_nat) (P (-> tptp.set_nat Bool)) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat S2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((X5 tptp.nat) (S4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S4) (=> (forall ((Y6 tptp.nat)) (=> (@ (@ tptp.member_nat Y6) S4) (@ (@ tptp.ord_less_eq_nat (@ F Y6)) (@ F X5)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_nat X5) S4)))))) (@ P S2))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_int) (P (-> tptp.set_int Bool)) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int S2) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((X5 tptp.int) (S4 tptp.set_int)) (=> (@ tptp.finite_finite_int S4) (=> (forall ((Y6 tptp.int)) (=> (@ (@ tptp.member_int Y6) S4) (@ (@ tptp.ord_less_eq_nat (@ F Y6)) (@ F X5)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_int X5) S4)))))) (@ P S2))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat A2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((B4 tptp.nat) (A6 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A6) (=> (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A6) (@ (@ tptp.ord_less_nat X2) B4))) (=> (@ P A6) (@ P (@ (@ tptp.insert_nat B4) A6)))))) (@ P A2))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ P tptp.bot_bo7653980558646680370d_enat) (=> (forall ((B4 tptp.extended_enat) (A6 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A6) (=> (forall ((X2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X2) A6) (@ (@ tptp.ord_le72135733267957522d_enat X2) B4))) (=> (@ P A6) (@ P (@ (@ tptp.insert_Extended_enat B4) A6)))))) (@ P A2))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real A2) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((B4 tptp.real) (A6 tptp.set_real)) (=> (@ tptp.finite_finite_real A6) (=> (forall ((X2 tptp.real)) (=> (@ (@ tptp.member_real X2) A6) (@ (@ tptp.ord_less_real X2) B4))) (=> (@ P A6) (@ P (@ (@ tptp.insert_real B4) A6)))))) (@ P A2))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int A2) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((B4 tptp.int) (A6 tptp.set_int)) (=> (@ tptp.finite_finite_int A6) (=> (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) A6) (@ (@ tptp.ord_less_int X2) B4))) (=> (@ P A6) (@ P (@ (@ tptp.insert_int B4) A6)))))) (@ P A2))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat A2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((B4 tptp.nat) (A6 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A6) (=> (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A6) (@ (@ tptp.ord_less_nat B4) X2))) (=> (@ P A6) (@ P (@ (@ tptp.insert_nat B4) A6)))))) (@ P A2))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ P tptp.bot_bo7653980558646680370d_enat) (=> (forall ((B4 tptp.extended_enat) (A6 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A6) (=> (forall ((X2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X2) A6) (@ (@ tptp.ord_le72135733267957522d_enat B4) X2))) (=> (@ P A6) (@ P (@ (@ tptp.insert_Extended_enat B4) A6)))))) (@ P A2))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real A2) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((B4 tptp.real) (A6 tptp.set_real)) (=> (@ tptp.finite_finite_real A6) (=> (forall ((X2 tptp.real)) (=> (@ (@ tptp.member_real X2) A6) (@ (@ tptp.ord_less_real B4) X2))) (=> (@ P A6) (@ P (@ (@ tptp.insert_real B4) A6)))))) (@ P A2))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int A2) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((B4 tptp.int) (A6 tptp.set_int)) (=> (@ tptp.finite_finite_int A6) (=> (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) A6) (@ (@ tptp.ord_less_int B4) X2))) (=> (@ P A6) (@ P (@ (@ tptp.insert_int B4) A6)))))) (@ P A2))))))
% 4.96/5.19 (assert (forall ((F3 tptp.set_set_nat) (A2 tptp.set_set_nat) (P (-> tptp.set_set_nat Bool))) (=> (@ tptp.finite1152437895449049373et_nat F3) (=> (@ (@ tptp.ord_le6893508408891458716et_nat F3) A2) (=> (@ P tptp.bot_bot_set_set_nat) (=> (forall ((A4 tptp.set_nat) (F4 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat A4))) (=> (@ tptp.finite1152437895449049373et_nat F4) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_le6893508408891458716et_nat F4) A2) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_set_nat A4) F4))))))))) (@ P F3)))))))
% 4.96/5.19 (assert (forall ((F3 tptp.set_complex) (A2 tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex F3) (=> (@ (@ tptp.ord_le211207098394363844omplex F3) A2) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((A4 tptp.complex) (F4 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex A4))) (=> (@ tptp.finite3207457112153483333omplex F4) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_le211207098394363844omplex F4) A2) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_complex A4) F4))))))))) (@ P F3)))))))
% 4.96/5.19 (assert (forall ((F3 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat F3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat F3) A2) (=> (@ P tptp.bot_bo7653980558646680370d_enat) (=> (forall ((A4 tptp.extended_enat) (F4 tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat A4))) (=> (@ tptp.finite4001608067531595151d_enat F4) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat F4) A2) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_Extended_enat A4) F4))))))))) (@ P F3)))))))
% 4.96/5.19 (assert (forall ((F3 tptp.set_real) (A2 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real F3) (=> (@ (@ tptp.ord_less_eq_set_real F3) A2) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((A4 tptp.real) (F4 tptp.set_real)) (let ((_let_1 (@ tptp.member_real A4))) (=> (@ tptp.finite_finite_real F4) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_less_eq_set_real F4) A2) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_real A4) F4))))))))) (@ P F3)))))))
% 4.96/5.19 (assert (forall ((F3 tptp.set_nat) (A2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat F3) (=> (@ (@ tptp.ord_less_eq_set_nat F3) A2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((A4 tptp.nat) (F4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat A4))) (=> (@ tptp.finite_finite_nat F4) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_less_eq_set_nat F4) A2) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_nat A4) F4))))))))) (@ P F3)))))))
% 4.96/5.19 (assert (forall ((F3 tptp.set_int) (A2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int F3) (=> (@ (@ tptp.ord_less_eq_set_int F3) A2) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((A4 tptp.int) (F4 tptp.set_int)) (let ((_let_1 (@ tptp.member_int A4))) (=> (@ tptp.finite_finite_int F4) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_less_eq_set_int F4) A2) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_int A4) F4))))))))) (@ P F3)))))))
% 4.96/5.19 (assert (forall ((F3 tptp.set_set_nat) (A2 tptp.set_set_nat) (P (-> tptp.set_set_nat Bool))) (=> (@ tptp.finite1152437895449049373et_nat F3) (=> (@ (@ tptp.ord_le6893508408891458716et_nat F3) A2) (=> (@ P tptp.bot_bot_set_set_nat) (=> (forall ((A4 tptp.set_nat) (F4 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat A4))) (=> (@ tptp.finite1152437895449049373et_nat F4) (=> (@ _let_1 A2) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_set_nat A4) F4)))))))) (@ P F3)))))))
% 4.96/5.19 (assert (forall ((F3 tptp.set_complex) (A2 tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex F3) (=> (@ (@ tptp.ord_le211207098394363844omplex F3) A2) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((A4 tptp.complex) (F4 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex A4))) (=> (@ tptp.finite3207457112153483333omplex F4) (=> (@ _let_1 A2) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_complex A4) F4)))))))) (@ P F3)))))))
% 4.96/5.19 (assert (forall ((F3 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat F3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat F3) A2) (=> (@ P tptp.bot_bo7653980558646680370d_enat) (=> (forall ((A4 tptp.extended_enat) (F4 tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat A4))) (=> (@ tptp.finite4001608067531595151d_enat F4) (=> (@ _let_1 A2) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_Extended_enat A4) F4)))))))) (@ P F3)))))))
% 4.96/5.19 (assert (forall ((F3 tptp.set_real) (A2 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real F3) (=> (@ (@ tptp.ord_less_eq_set_real F3) A2) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((A4 tptp.real) (F4 tptp.set_real)) (let ((_let_1 (@ tptp.member_real A4))) (=> (@ tptp.finite_finite_real F4) (=> (@ _let_1 A2) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_real A4) F4)))))))) (@ P F3)))))))
% 4.96/5.19 (assert (forall ((F3 tptp.set_nat) (A2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat F3) (=> (@ (@ tptp.ord_less_eq_set_nat F3) A2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((A4 tptp.nat) (F4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat A4))) (=> (@ tptp.finite_finite_nat F4) (=> (@ _let_1 A2) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_nat A4) F4)))))))) (@ P F3)))))))
% 4.96/5.19 (assert (forall ((F3 tptp.set_int) (A2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int F3) (=> (@ (@ tptp.ord_less_eq_set_int F3) A2) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((A4 tptp.int) (F4 tptp.set_int)) (let ((_let_1 (@ tptp.member_int A4))) (=> (@ tptp.finite_finite_int F4) (=> (@ _let_1 A2) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_int A4) F4)))))))) (@ P F3)))))))
% 4.96/5.19 (assert (forall ((B tptp.set_set_nat) (P (-> tptp.set_set_nat Bool))) (=> (@ tptp.finite1152437895449049373et_nat B) (=> (@ P tptp.bot_bot_set_set_nat) (=> (forall ((A6 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A6) (=> (not (= A6 tptp.bot_bot_set_set_nat)) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A6) B) (=> (forall ((X2 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X2) A6) (@ P (@ (@ tptp.minus_2163939370556025621et_nat A6) (@ (@ tptp.insert_set_nat X2) tptp.bot_bot_set_set_nat))))) (@ P A6)))))) (@ P B))))))
% 4.96/5.19 (assert (forall ((B tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex B) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((A6 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A6) (=> (not (= A6 tptp.bot_bot_set_complex)) (=> (@ (@ tptp.ord_le211207098394363844omplex A6) B) (=> (forall ((X2 tptp.complex)) (=> (@ (@ tptp.member_complex X2) A6) (@ P (@ (@ tptp.minus_811609699411566653omplex A6) (@ (@ tptp.insert_complex X2) tptp.bot_bot_set_complex))))) (@ P A6)))))) (@ P B))))))
% 4.96/5.19 (assert (forall ((B tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat B) (=> (@ P tptp.bot_bo7653980558646680370d_enat) (=> (forall ((A6 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A6) (=> (not (= A6 tptp.bot_bo7653980558646680370d_enat)) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A6) B) (=> (forall ((X2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X2) A6) (@ P (@ (@ tptp.minus_925952699566721837d_enat A6) (@ (@ tptp.insert_Extended_enat X2) tptp.bot_bo7653980558646680370d_enat))))) (@ P A6)))))) (@ P B))))))
% 4.96/5.19 (assert (forall ((B tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real B) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((A6 tptp.set_real)) (=> (@ tptp.finite_finite_real A6) (=> (not (= A6 tptp.bot_bot_set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A6) B) (=> (forall ((X2 tptp.real)) (=> (@ (@ tptp.member_real X2) A6) (@ P (@ (@ tptp.minus_minus_set_real A6) (@ (@ tptp.insert_real X2) tptp.bot_bot_set_real))))) (@ P A6)))))) (@ P B))))))
% 4.96/5.19 (assert (forall ((B tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat B) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((A6 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A6) (=> (not (= A6 tptp.bot_bot_set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A6) B) (=> (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A6) (@ P (@ (@ tptp.minus_minus_set_nat A6) (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat))))) (@ P A6)))))) (@ P B))))))
% 4.96/5.19 (assert (forall ((B tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int B) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((A6 tptp.set_int)) (=> (@ tptp.finite_finite_int A6) (=> (not (= A6 tptp.bot_bot_set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A6) B) (=> (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) A6) (@ P (@ (@ tptp.minus_minus_set_int A6) (@ (@ tptp.insert_int X2) tptp.bot_bot_set_int))))) (@ P A6)))))) (@ P B))))))
% 4.96/5.19 (assert (forall ((P (-> tptp.set_set_nat Bool)) (B tptp.set_set_nat)) (let ((_let_1 (@ P B))) (=> (@ P tptp.bot_bot_set_set_nat) (=> (=> (not (@ tptp.finite1152437895449049373et_nat B)) _let_1) (=> (forall ((A6 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A6) (=> (not (= A6 tptp.bot_bot_set_set_nat)) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A6) B) (=> (forall ((X2 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X2) A6) (@ P (@ (@ tptp.minus_2163939370556025621et_nat A6) (@ (@ tptp.insert_set_nat X2) tptp.bot_bot_set_set_nat))))) (@ P A6)))))) _let_1))))))
% 4.96/5.19 (assert (forall ((P (-> tptp.set_complex Bool)) (B tptp.set_complex)) (let ((_let_1 (@ P B))) (=> (@ P tptp.bot_bot_set_complex) (=> (=> (not (@ tptp.finite3207457112153483333omplex B)) _let_1) (=> (forall ((A6 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A6) (=> (not (= A6 tptp.bot_bot_set_complex)) (=> (@ (@ tptp.ord_le211207098394363844omplex A6) B) (=> (forall ((X2 tptp.complex)) (=> (@ (@ tptp.member_complex X2) A6) (@ P (@ (@ tptp.minus_811609699411566653omplex A6) (@ (@ tptp.insert_complex X2) tptp.bot_bot_set_complex))))) (@ P A6)))))) _let_1))))))
% 4.96/5.19 (assert (forall ((P (-> tptp.set_Extended_enat Bool)) (B tptp.set_Extended_enat)) (let ((_let_1 (@ P B))) (=> (@ P tptp.bot_bo7653980558646680370d_enat) (=> (=> (not (@ tptp.finite4001608067531595151d_enat B)) _let_1) (=> (forall ((A6 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A6) (=> (not (= A6 tptp.bot_bo7653980558646680370d_enat)) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A6) B) (=> (forall ((X2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X2) A6) (@ P (@ (@ tptp.minus_925952699566721837d_enat A6) (@ (@ tptp.insert_Extended_enat X2) tptp.bot_bo7653980558646680370d_enat))))) (@ P A6)))))) _let_1))))))
% 4.96/5.19 (assert (forall ((P (-> tptp.set_real Bool)) (B tptp.set_real)) (let ((_let_1 (@ P B))) (=> (@ P tptp.bot_bot_set_real) (=> (=> (not (@ tptp.finite_finite_real B)) _let_1) (=> (forall ((A6 tptp.set_real)) (=> (@ tptp.finite_finite_real A6) (=> (not (= A6 tptp.bot_bot_set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A6) B) (=> (forall ((X2 tptp.real)) (=> (@ (@ tptp.member_real X2) A6) (@ P (@ (@ tptp.minus_minus_set_real A6) (@ (@ tptp.insert_real X2) tptp.bot_bot_set_real))))) (@ P A6)))))) _let_1))))))
% 4.96/5.19 (assert (forall ((P (-> tptp.set_nat Bool)) (B tptp.set_nat)) (let ((_let_1 (@ P B))) (=> (@ P tptp.bot_bot_set_nat) (=> (=> (not (@ tptp.finite_finite_nat B)) _let_1) (=> (forall ((A6 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A6) (=> (not (= A6 tptp.bot_bot_set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A6) B) (=> (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A6) (@ P (@ (@ tptp.minus_minus_set_nat A6) (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat))))) (@ P A6)))))) _let_1))))))
% 4.96/5.19 (assert (forall ((P (-> tptp.set_int Bool)) (B tptp.set_int)) (let ((_let_1 (@ P B))) (=> (@ P tptp.bot_bot_set_int) (=> (=> (not (@ tptp.finite_finite_int B)) _let_1) (=> (forall ((A6 tptp.set_int)) (=> (@ tptp.finite_finite_int A6) (=> (not (= A6 tptp.bot_bot_set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A6) B) (=> (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) A6) (@ P (@ (@ tptp.minus_minus_set_int A6) (@ (@ tptp.insert_int X2) tptp.bot_bot_set_int))))) (@ P A6)))))) _let_1))))))
% 4.96/5.19 (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)))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((T4 tptp.set_complex)) (=> (@ (@ tptp.ord_less_set_complex T4) S2) (=> (@ P T4) (exists ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) (@ (@ tptp.minus_811609699411566653omplex S2) T4)) (@ P (@ (@ tptp.insert_complex X2) T4))))))) (@ P S2))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat S2) (=> (@ P tptp.bot_bo7653980558646680370d_enat) (=> (forall ((T4 tptp.set_Extended_enat)) (=> (@ (@ tptp.ord_le2529575680413868914d_enat T4) S2) (=> (@ P T4) (exists ((X2 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X2) (@ (@ tptp.minus_925952699566721837d_enat S2) T4)) (@ P (@ (@ tptp.insert_Extended_enat X2) T4))))))) (@ P S2))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real S2) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((T4 tptp.set_real)) (=> (@ (@ tptp.ord_less_set_real T4) S2) (=> (@ P T4) (exists ((X2 tptp.real)) (and (@ (@ tptp.member_real X2) (@ (@ tptp.minus_minus_set_real S2) T4)) (@ P (@ (@ tptp.insert_real X2) T4))))))) (@ P S2))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int S2) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((T4 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int T4) S2) (=> (@ P T4) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.minus_minus_set_int S2) T4)) (@ P (@ (@ tptp.insert_int X2) T4))))))) (@ P S2))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat S2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((T4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat T4) S2) (=> (@ P T4) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) (@ (@ tptp.minus_minus_set_nat S2) T4)) (@ P (@ (@ tptp.insert_nat X2) T4))))))) (@ P S2))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_set_nat) (X tptp.set_nat) (B tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat X))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_set_nat X))) (let ((_let_4 (@ _let_1 B))) (let ((_let_5 (@ tptp.ord_less_set_set_nat A2))) (= (@ _let_5 (@ _let_3 B)) (and (=> _let_4 (@ _let_5 B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_set_nat (@ (@ tptp.minus_2163939370556025621et_nat A2) (@ _let_3 tptp.bot_bot_set_set_nat))) B)) (=> (not _let_2) (@ (@ tptp.ord_le6893508408891458716et_nat A2) B)))))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (X tptp.extended_enat) (B tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat X))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_Extended_enat X))) (let ((_let_4 (@ _let_1 B))) (let ((_let_5 (@ tptp.ord_le2529575680413868914d_enat A2))) (= (@ _let_5 (@ _let_3 B)) (and (=> _let_4 (@ _let_5 B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_le2529575680413868914d_enat (@ (@ tptp.minus_925952699566721837d_enat A2) (@ _let_3 tptp.bot_bo7653980558646680370d_enat))) B)) (=> (not _let_2) (@ (@ tptp.ord_le7203529160286727270d_enat A2) B)))))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (X tptp.real) (B tptp.set_real)) (let ((_let_1 (@ tptp.member_real X))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_real X))) (let ((_let_4 (@ _let_1 B))) (let ((_let_5 (@ tptp.ord_less_set_real A2))) (= (@ _let_5 (@ _let_3 B)) (and (=> _let_4 (@ _let_5 B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_real (@ (@ tptp.minus_minus_set_real A2) (@ _let_3 tptp.bot_bot_set_real))) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_real A2) B)))))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (X tptp.nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat X))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_nat X))) (let ((_let_4 (@ _let_1 B))) (let ((_let_5 (@ tptp.ord_less_set_nat A2))) (= (@ _let_5 (@ _let_3 B)) (and (=> _let_4 (@ _let_5 B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_nat (@ (@ tptp.minus_minus_set_nat A2) (@ _let_3 tptp.bot_bot_set_nat))) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_nat A2) B)))))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (X tptp.int) (B tptp.set_int)) (let ((_let_1 (@ tptp.member_int X))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_int X))) (let ((_let_4 (@ _let_1 B))) (let ((_let_5 (@ tptp.ord_less_set_int A2))) (= (@ _let_5 (@ _let_3 B)) (and (=> _let_4 (@ _let_5 B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_int (@ (@ tptp.minus_minus_set_int A2) (@ _let_3 tptp.bot_bot_set_int))) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_int A2) B)))))))))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ (@ tptp.insert_nat M2) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N2)) (@ (@ tptp.set_or1269000886237332187st_nat M2) N2)))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.insert_nat _let_2) (@ _let_1 N2))))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ (@ tptp.set_or1269000886237332187st_nat M2) N2) (@ (@ tptp.insert_nat M2) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N2))))))
% 4.96/5.19 (assert (forall ((Xs tptp.list_real) (I tptp.nat) (X tptp.real)) (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real Xs) I) X))) (@ (@ tptp.insert_real X) (@ tptp.set_real2 Xs)))))
% 4.96/5.19 (assert (forall ((Xs tptp.list_VEBT_VEBT) (I tptp.nat) (X tptp.vEBT_VEBT)) (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) X))) (@ (@ tptp.insert_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs)))))
% 4.96/5.19 (assert (forall ((Xs tptp.list_nat) (I tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs) I) X))) (@ (@ tptp.insert_nat X) (@ tptp.set_nat2 Xs)))))
% 4.96/5.19 (assert (forall ((Xs tptp.list_int) (I tptp.nat) (X tptp.int)) (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs) I) X))) (@ (@ tptp.insert_int X) (@ tptp.set_int2 Xs)))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat) (X tptp.vEBT_VEBT)) (= (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT (@ tptp.suc N2)) X)) (@ (@ tptp.insert_VEBT_VEBT X) tptp.bot_bo8194388402131092736T_VEBT))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat) (X tptp.extended_enat)) (= (@ tptp.set_Extended_enat2 (@ (@ tptp.replic7216382294607269926d_enat (@ tptp.suc N2)) X)) (@ (@ tptp.insert_Extended_enat X) tptp.bot_bo7653980558646680370d_enat))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat) (X tptp.real)) (= (@ tptp.set_real2 (@ (@ tptp.replicate_real (@ tptp.suc N2)) X)) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat) (X tptp.nat)) (= (@ tptp.set_nat2 (@ (@ tptp.replicate_nat (@ tptp.suc N2)) X)) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat) (X tptp.int)) (= (@ tptp.set_int2 (@ (@ tptp.replicate_int (@ tptp.suc N2)) X)) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat) (X tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N2) X)))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.bot_bo8194388402131092736T_VEBT)) (=> (not _let_2) (= _let_1 (@ (@ tptp.insert_VEBT_VEBT X) tptp.bot_bo8194388402131092736T_VEBT))))))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat) (X tptp.extended_enat)) (let ((_let_1 (@ tptp.set_Extended_enat2 (@ (@ tptp.replic7216382294607269926d_enat N2) X)))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.bot_bo7653980558646680370d_enat)) (=> (not _let_2) (= _let_1 (@ (@ tptp.insert_Extended_enat X) tptp.bot_bo7653980558646680370d_enat))))))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.set_real2 (@ (@ tptp.replicate_real N2) X)))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.bot_bot_set_real)) (=> (not _let_2) (= _let_1 (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))))))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N2) X)))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.bot_bot_set_nat)) (=> (not _let_2) (= _let_1 (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))))))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat) (X tptp.int)) (let ((_let_1 (@ tptp.set_int2 (@ (@ tptp.replicate_int N2) X)))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.bot_bot_set_int)) (=> (not _let_2) (= _let_1 (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))))))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.nat_set_decode Z3))) (=> (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)) Z3)) (@ (@ tptp.insert_nat N2) _let_1))))))
% 4.96/5.19 (assert (= tptp.unique5026877609467782581ep_nat (lambda ((L2 tptp.num) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q5 tptp.nat) (R4 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) R4)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R4) _let_2))) (@ (@ tptp.product_Pair_nat_nat _let_1) R4)))))) __flatten_var_0))))
% 4.96/5.19 (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))))
% 4.96/5.19 (assert (= tptp.divmod_nat (lambda ((M tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (or (= N tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat M) N))) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) M)) (@ (@ 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 M) N)) N))))))
% 4.96/5.19 (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)))))))
% 4.96/5.19 (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)))))))
% 4.96/5.19 (assert (= tptp.ring_17405671764205052669omplex (lambda ((K2 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.divide_divide_int K2) _let_2))))) (@ (@ (@ tptp.if_complex (= K2 tptp.zero_zero_int)) tptp.zero_zero_complex) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int)) (@ tptp.uminus1482373934393186551omplex (@ tptp.ring_17405671764205052669omplex (@ tptp.uminus_uminus_int K2)))) (@ (@ (@ tptp.if_complex (= (@ (@ tptp.modulo_modulo_int K2) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_plus_complex _let_3) tptp.one_one_complex))))))))))
% 4.96/5.19 (assert (= tptp.ring_1_of_int_int (lambda ((K2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_int _let_1) (@ tptp.ring_1_of_int_int (@ (@ tptp.divide_divide_int K2) _let_1))))) (@ (@ (@ tptp.if_int (= K2 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int (@ tptp.ring_1_of_int_int (@ tptp.uminus_uminus_int K2)))) (@ (@ (@ tptp.if_int (= (@ (@ tptp.modulo_modulo_int K2) _let_1) tptp.zero_zero_int)) _let_2) (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)))))))))
% 4.96/5.19 (assert (= tptp.ring_1_of_int_real (lambda ((K2 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int K2) _let_2))))) (@ (@ (@ tptp.if_real (= K2 tptp.zero_zero_int)) tptp.zero_zero_real) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int)) (@ tptp.uminus_uminus_real (@ tptp.ring_1_of_int_real (@ tptp.uminus_uminus_int K2)))) (@ (@ (@ tptp.if_real (= (@ (@ tptp.modulo_modulo_int K2) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_plus_real _let_3) tptp.one_one_real))))))))))
% 4.96/5.19 (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)))))))
% 4.96/5.19 (assert (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_int A) _let_1)))))
% 4.96/5.19 (assert (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N2)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)))))
% 4.96/5.19 (assert (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 4.96/5.19 (assert (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N2)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)) A))))
% 4.96/5.19 (assert (forall ((W2 tptp.int) (Z3 tptp.int)) (= (= (@ tptp.ring_1_of_int_real W2) (@ tptp.ring_1_of_int_real Z3)) (= W2 Z3))))
% 4.96/5.19 (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)))))
% 4.96/5.19 (assert (forall ((P Bool)) (= (@ tptp.ring_1_of_int_real (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n3304061248610475627l_real P))))
% 4.96/5.19 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n2684676970156552555ol_int P))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))))
% 4.96/5.19 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit tptp.zero_zero_nat) K) L) L)))
% 4.96/5.19 (assert (forall ((Z3 tptp.int)) (= (= (@ tptp.ring_1_of_int_int Z3) tptp.zero_zero_int) (= Z3 tptp.zero_zero_int))))
% 4.96/5.19 (assert (forall ((Z3 tptp.int)) (= (= (@ tptp.ring_17405671764205052669omplex Z3) tptp.zero_zero_complex) (= Z3 tptp.zero_zero_int))))
% 4.96/5.19 (assert (forall ((Z3 tptp.int)) (= (= (@ tptp.ring_1_of_int_real Z3) tptp.zero_zero_real) (= Z3 tptp.zero_zero_int))))
% 4.96/5.19 (assert (forall ((Z3 tptp.int)) (= (= tptp.zero_zero_int (@ tptp.ring_1_of_int_int Z3)) (= Z3 tptp.zero_zero_int))))
% 4.96/5.19 (assert (forall ((Z3 tptp.int)) (= (= tptp.zero_zero_complex (@ tptp.ring_17405671764205052669omplex Z3)) (= Z3 tptp.zero_zero_int))))
% 4.96/5.19 (assert (forall ((Z3 tptp.int)) (= (= tptp.zero_zero_real (@ tptp.ring_1_of_int_real Z3)) (= Z3 tptp.zero_zero_int))))
% 4.96/5.19 (assert (= (@ tptp.ring_1_of_int_int tptp.zero_zero_int) tptp.zero_zero_int))
% 4.96/5.19 (assert (= (@ tptp.ring_17405671764205052669omplex tptp.zero_zero_int) tptp.zero_zero_complex))
% 4.96/5.19 (assert (= (@ tptp.ring_1_of_int_real tptp.zero_zero_int) tptp.zero_zero_real))
% 4.96/5.19 (assert (forall ((W2 tptp.int) (Z3 tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real W2)) (@ tptp.ring_1_of_int_real Z3)) (@ (@ tptp.ord_less_eq_int W2) Z3))))
% 4.96/5.19 (assert (forall ((W2 tptp.int) (Z3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int W2)) (@ tptp.ring_1_of_int_int Z3)) (@ (@ tptp.ord_less_eq_int W2) Z3))))
% 4.96/5.19 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int K))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))))
% 4.96/5.19 (assert (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_real (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_real K))))
% 4.96/5.19 (assert (forall ((Z3 tptp.int) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (= (@ tptp.ring_1_of_int_int Z3) _let_1) (= Z3 _let_1)))))
% 4.96/5.19 (assert (forall ((Z3 tptp.int) (N2 tptp.num)) (= (= (@ tptp.ring_1_of_int_real Z3) (@ tptp.numeral_numeral_real N2)) (= Z3 (@ tptp.numeral_numeral_int N2)))))
% 4.96/5.19 (assert (forall ((W2 tptp.int) (Z3 tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real W2)) (@ tptp.ring_1_of_int_real Z3)) (@ (@ tptp.ord_less_int W2) Z3))))
% 4.96/5.19 (assert (forall ((W2 tptp.int) (Z3 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int W2)) (@ tptp.ring_1_of_int_int Z3)) (@ (@ tptp.ord_less_int W2) Z3))))
% 4.96/5.19 (assert (= (@ tptp.ring_1_of_int_int tptp.one_one_int) tptp.one_one_int))
% 4.96/5.19 (assert (= (@ tptp.ring_17405671764205052669omplex tptp.one_one_int) tptp.one_one_complex))
% 4.96/5.19 (assert (= (@ tptp.ring_1_of_int_real tptp.one_one_int) tptp.one_one_real))
% 4.96/5.19 (assert (forall ((Z3 tptp.int)) (= (= (@ tptp.ring_1_of_int_int Z3) tptp.one_one_int) (= Z3 tptp.one_one_int))))
% 4.96/5.19 (assert (forall ((Z3 tptp.int)) (= (= (@ tptp.ring_17405671764205052669omplex Z3) tptp.one_one_complex) (= Z3 tptp.one_one_int))))
% 4.96/5.19 (assert (forall ((Z3 tptp.int)) (= (= (@ tptp.ring_1_of_int_real Z3) tptp.one_one_real) (= Z3 tptp.one_one_int))))
% 4.96/5.19 (assert (forall ((W2 tptp.int) (Z3 tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.times_times_int W2) Z3)) (@ (@ tptp.times_times_int (@ tptp.ring_1_of_int_int W2)) (@ tptp.ring_1_of_int_int Z3)))))
% 4.96/5.19 (assert (forall ((W2 tptp.int) (Z3 tptp.int)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int W2) Z3)) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real W2)) (@ tptp.ring_1_of_int_real Z3)))))
% 4.96/5.19 (assert (forall ((W2 tptp.int) (Z3 tptp.int)) (= (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.times_times_int W2) Z3)) (@ (@ tptp.times_times_complex (@ tptp.ring_17405671764205052669omplex W2)) (@ tptp.ring_17405671764205052669omplex Z3)))))
% 4.96/5.19 (assert (forall ((W2 tptp.int) (Z3 tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.plus_plus_int W2) Z3)) (@ (@ tptp.plus_plus_int (@ tptp.ring_1_of_int_int W2)) (@ tptp.ring_1_of_int_int Z3)))))
% 4.96/5.19 (assert (forall ((W2 tptp.int) (Z3 tptp.int)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int W2) Z3)) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real W2)) (@ tptp.ring_1_of_int_real Z3)))))
% 4.96/5.19 (assert (forall ((Z3 tptp.int)) (= (@ tptp.ring_1_of_int_int (@ tptp.uminus_uminus_int Z3)) (@ tptp.uminus_uminus_int (@ tptp.ring_1_of_int_int Z3)))))
% 4.96/5.19 (assert (forall ((Z3 tptp.int)) (= (@ tptp.ring_1_of_int_real (@ tptp.uminus_uminus_int Z3)) (@ tptp.uminus_uminus_real (@ tptp.ring_1_of_int_real Z3)))))
% 4.96/5.19 (assert (= (@ tptp.bit_se2000444600071755411sk_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 4.96/5.19 (assert (= (@ tptp.bit_se2002935070580805687sk_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 4.96/5.19 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.bit_se2000444600071755411sk_int N2) tptp.zero_zero_int) (= N2 tptp.zero_zero_nat))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.bit_se2002935070580805687sk_nat N2) tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat))))
% 4.96/5.19 (assert (forall ((W2 tptp.int) (Z3 tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.minus_minus_int W2) Z3)) (@ (@ tptp.minus_minus_int (@ tptp.ring_1_of_int_int W2)) (@ tptp.ring_1_of_int_int Z3)))))
% 4.96/5.19 (assert (forall ((W2 tptp.int) (Z3 tptp.int)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.minus_minus_int W2) Z3)) (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real W2)) (@ tptp.ring_1_of_int_real Z3)))))
% 4.96/5.19 (assert (forall ((Z3 tptp.int) (N2 tptp.nat)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.power_power_int Z3) N2)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real Z3)) N2))))
% 4.96/5.19 (assert (forall ((Z3 tptp.int) (N2 tptp.nat)) (= (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.power_power_int Z3) N2)) (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex Z3)) N2))))
% 4.96/5.19 (assert (forall ((Z3 tptp.int) (N2 tptp.nat)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.power_power_int Z3) N2)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int Z3)) N2))))
% 4.96/5.19 (assert (forall ((B2 tptp.int) (W2 tptp.nat) (X tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B2)) W2) (@ tptp.ring_1_of_int_real X)) (= (@ (@ tptp.power_power_int B2) W2) X))))
% 4.96/5.19 (assert (forall ((B2 tptp.int) (W2 tptp.nat) (X tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex B2)) W2) (@ tptp.ring_17405671764205052669omplex X)) (= (@ (@ tptp.power_power_int B2) W2) X))))
% 4.96/5.19 (assert (forall ((B2 tptp.int) (W2 tptp.nat) (X tptp.int)) (= (= (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B2)) W2) (@ tptp.ring_1_of_int_int X)) (= (@ (@ tptp.power_power_int B2) W2) X))))
% 4.96/5.19 (assert (forall ((X tptp.int) (B2 tptp.int) (W2 tptp.nat)) (= (= (@ tptp.ring_1_of_int_real X) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B2)) W2)) (= X (@ (@ tptp.power_power_int B2) W2)))))
% 4.96/5.19 (assert (forall ((X tptp.int) (B2 tptp.int) (W2 tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex X) (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex B2)) W2)) (= X (@ (@ tptp.power_power_int B2) W2)))))
% 4.96/5.19 (assert (forall ((X tptp.int) (B2 tptp.int) (W2 tptp.nat)) (= (= (@ tptp.ring_1_of_int_int X) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B2)) W2)) (= X (@ (@ tptp.power_power_int B2) W2)))))
% 4.96/5.19 (assert (= (@ tptp.bit_se2000444600071755411sk_int (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_int))
% 4.96/5.19 (assert (= (@ tptp.bit_se2002935070580805687sk_nat (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat))
% 4.96/5.19 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ring_1_of_int_real Z3)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z3))))
% 4.96/5.19 (assert (forall ((Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z3)) (@ _let_1 Z3)))))
% 4.96/5.19 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z3)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_int Z3) tptp.zero_zero_int))))
% 4.96/5.19 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int Z3)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int Z3) tptp.zero_zero_int))))
% 4.96/5.19 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.ring_1_of_int_real Z3)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z3))))
% 4.96/5.19 (assert (forall ((Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z3)) (@ _let_1 Z3)))))
% 4.96/5.19 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z3)) tptp.zero_zero_real) (@ (@ tptp.ord_less_int Z3) tptp.zero_zero_int))))
% 4.96/5.19 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int Z3)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Z3) tptp.zero_zero_int))))
% 4.96/5.19 (assert (forall ((N2 tptp.num) (Z3 tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N2)) (@ tptp.ring_1_of_int_real Z3)) (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N2)) Z3))))
% 4.96/5.19 (assert (forall ((N2 tptp.num) (Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z3)) (@ _let_1 Z3)))))
% 4.96/5.19 (assert (forall ((Z3 tptp.int) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z3)) (@ tptp.numeral_numeral_real N2)) (@ (@ tptp.ord_less_eq_int Z3) (@ tptp.numeral_numeral_int N2)))))
% 4.96/5.19 (assert (forall ((Z3 tptp.int) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int Z3)) _let_1) (@ (@ tptp.ord_less_eq_int Z3) _let_1)))))
% 4.96/5.19 (assert (forall ((Z3 tptp.int) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int Z3)) _let_1) (@ (@ tptp.ord_less_int Z3) _let_1)))))
% 4.96/5.19 (assert (forall ((Z3 tptp.int) (N2 tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z3)) (@ tptp.numeral_numeral_real N2)) (@ (@ tptp.ord_less_int Z3) (@ tptp.numeral_numeral_int N2)))))
% 4.96/5.19 (assert (forall ((N2 tptp.num) (Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z3)) (@ _let_1 Z3)))))
% 4.96/5.19 (assert (forall ((N2 tptp.num) (Z3 tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N2)) (@ tptp.ring_1_of_int_real Z3)) (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N2)) Z3))))
% 4.96/5.19 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.ring_1_of_int_real Z3)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z3))))
% 4.96/5.19 (assert (forall ((Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.one_one_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z3)) (@ _let_1 Z3)))))
% 4.96/5.19 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z3)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_int Z3) tptp.one_one_int))))
% 4.96/5.19 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int Z3)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int Z3) tptp.one_one_int))))
% 4.96/5.19 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z3)) tptp.one_one_real) (@ (@ tptp.ord_less_int Z3) tptp.one_one_int))))
% 4.96/5.19 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int Z3)) tptp.one_one_int) (@ (@ tptp.ord_less_int Z3) tptp.one_one_int))))
% 4.96/5.19 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.ring_1_of_int_real Z3)) (@ (@ tptp.ord_less_int tptp.one_one_int) Z3))))
% 4.96/5.19 (assert (forall ((Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z3)) (@ _let_1 Z3)))))
% 4.96/5.19 (assert (forall ((X tptp.int) (B2 tptp.int) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real X)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B2)) W2)) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.power_power_int B2) W2)))))
% 4.96/5.19 (assert (forall ((X tptp.int) (B2 tptp.int) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int X)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B2)) W2)) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.power_power_int B2) W2)))))
% 4.96/5.19 (assert (forall ((B2 tptp.int) (W2 tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B2)) W2)) (@ tptp.ring_1_of_int_real X)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B2) W2)) X))))
% 4.96/5.19 (assert (forall ((B2 tptp.int) (W2 tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B2)) W2)) (@ tptp.ring_1_of_int_int X)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B2) W2)) X))))
% 4.96/5.19 (assert (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X)) N2) (@ tptp.ring_17405671764205052669omplex Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2) Y))))
% 4.96/5.19 (assert (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2))) (= (= _let_1 (@ tptp.ring_1_of_int_int Y)) (= _let_1 Y)))))
% 4.96/5.19 (assert (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N2) (@ tptp.ring_1_of_int_real Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2) Y))))
% 4.96/5.19 (assert (forall ((Y tptp.int) (X tptp.num) (N2 tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex Y) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X)) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))))
% 4.96/5.19 (assert (forall ((Y tptp.int) (X tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2))) (= (= (@ tptp.ring_1_of_int_int Y) _let_1) (= Y _let_1)))))
% 4.96/5.19 (assert (forall ((Y tptp.int) (X tptp.num) (N2 tptp.nat)) (= (= (@ tptp.ring_1_of_int_real Y) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))))
% 4.96/5.19 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M2))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.inc M2))))))
% 4.96/5.19 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc M2))))))
% 4.96/5.19 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.inc M2))))))
% 4.96/5.19 (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))))))
% 4.96/5.19 (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))))))
% 4.96/5.19 (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))))))
% 4.96/5.19 (assert (forall ((B2 tptp.int) (W2 tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B2)) W2)) (@ tptp.ring_1_of_int_real X)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B2) W2)) X))))
% 4.96/5.19 (assert (forall ((B2 tptp.int) (W2 tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B2)) W2)) (@ tptp.ring_1_of_int_int X)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B2) W2)) X))))
% 4.96/5.19 (assert (forall ((X tptp.int) (B2 tptp.int) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real X)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B2)) W2)) (@ (@ tptp.ord_less_int X) (@ (@ tptp.power_power_int B2) W2)))))
% 4.96/5.19 (assert (forall ((X tptp.int) (B2 tptp.int) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int X)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B2)) W2)) (@ (@ tptp.ord_less_int X) (@ (@ tptp.power_power_int B2) W2)))))
% 4.96/5.19 (assert (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N2)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))))
% 4.96/5.19 (assert (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_eq_int A) _let_1)))))
% 4.96/5.19 (assert (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N2)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)) A))))
% 4.96/5.19 (assert (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 4.96/5.19 (assert (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 4.96/5.19 (assert (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N2)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)) A))))
% 4.96/5.19 (assert (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_int A) _let_1)))))
% 4.96/5.19 (assert (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N2)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))))
% 4.96/5.19 (assert (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex X))) N2) (@ tptp.ring_17405671764205052669omplex Y)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2) Y))))
% 4.96/5.19 (assert (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2))) (= (= _let_1 (@ tptp.ring_1_of_int_int Y)) (= _let_1 Y)))))
% 4.96/5.19 (assert (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N2) (@ tptp.ring_1_of_int_real Y)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2) Y))))
% 4.96/5.19 (assert (forall ((Y tptp.int) (X tptp.num) (N2 tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex Y) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex X))) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)))))
% 4.96/5.19 (assert (forall ((Y tptp.int) (X tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2))) (= (= (@ tptp.ring_1_of_int_int Y) _let_1) (= Y _let_1)))))
% 4.96/5.19 (assert (forall ((Y tptp.int) (X tptp.num) (N2 tptp.nat)) (= (= (@ tptp.ring_1_of_int_real Y) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)))))
% 4.96/5.19 (assert (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N2)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)))))
% 4.96/5.19 (assert (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_eq_int A) _let_1)))))
% 4.96/5.19 (assert (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N2)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)) A))))
% 4.96/5.19 (assert (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 4.96/5.19 (assert (forall ((X tptp.real)) (exists ((Z tptp.int)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.ring_1_of_int_real Z)))))
% 4.96/5.19 (assert (forall ((X tptp.real)) (exists ((Z tptp.int)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z)) X))))
% 4.96/5.19 (assert (forall ((X tptp.real)) (exists ((Z tptp.int)) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real Z)))))
% 4.96/5.19 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_int X))) (= (@ (@ tptp.times_times_int _let_1) Y) (@ (@ tptp.times_times_int Y) _let_1)))))
% 4.96/5.19 (assert (forall ((X tptp.int) (Y tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real X))) (= (@ (@ tptp.times_times_real _let_1) Y) (@ (@ tptp.times_times_real Y) _let_1)))))
% 4.96/5.19 (assert (forall ((X tptp.int) (Y tptp.complex)) (let ((_let_1 (@ tptp.ring_17405671764205052669omplex X))) (= (@ (@ tptp.times_times_complex _let_1) Y) (@ (@ tptp.times_times_complex Y) _let_1)))))
% 4.96/5.19 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.ord_max_int X) Y)) (@ (@ tptp.ord_max_real (@ tptp.ring_1_of_int_real X)) (@ tptp.ring_1_of_int_real Y)))))
% 4.96/5.19 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.ord_max_int X) Y)) (@ (@ tptp.ord_max_int (@ tptp.ring_1_of_int_int X)) (@ tptp.ring_1_of_int_int Y)))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.bit_se2002935070580805687sk_nat N2))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat) (K tptp.int) (M2 tptp.nat) (L tptp.int) (R2 tptp.int)) (let ((_let_1 (@ (@ tptp.bit_concat_bit N2) K))) (= (@ _let_1 (@ (@ (@ tptp.bit_concat_bit M2) L) R2)) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.plus_plus_nat M2) N2)) (@ _let_1 L)) R2)))))
% 4.96/5.19 (assert (forall ((M2 tptp.int) (N2 tptp.int)) (let ((_let_1 (@ tptp.set_or1266510415728281911st_int M2))) (let ((_let_2 (@ (@ tptp.plus_plus_int tptp.one_one_int) N2))) (=> (@ (@ tptp.ord_less_eq_int M2) _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.insert_int _let_2) (@ _let_1 N2))))))))
% 4.96/5.19 (assert (= tptp.set_or1266510415728281911st_int (lambda ((I3 tptp.int) (J2 tptp.int)) (@ (@ (@ tptp.if_set_int (@ (@ tptp.ord_less_int J2) I3)) tptp.bot_bot_set_int) (@ (@ tptp.insert_int I3) (@ (@ tptp.set_or1266510415728281911st_int (@ (@ tptp.plus_plus_int I3) tptp.one_one_int)) J2))))))
% 4.96/5.19 (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)))))
% 4.96/5.19 (assert (forall ((Z3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z3) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ring_1_of_int_real Z3)))))
% 4.96/5.19 (assert (forall ((Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z3) (@ _let_1 (@ tptp.ring_1_of_int_int Z3))))))
% 4.96/5.19 (assert (forall ((Z3 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z3) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.ring_1_of_int_real Z3)))))
% 4.96/5.19 (assert (forall ((Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 Z3) (@ _let_1 (@ tptp.ring_1_of_int_int Z3))))))
% 4.96/5.19 (assert (forall ((X tptp.real)) (exists ((X5 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real X5)) X) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int X5) tptp.one_one_int))) (forall ((Y6 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Y6)) X) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Y6) tptp.one_one_int)))) (= Y6 X5)))))))
% 4.96/5.19 (assert (forall ((X tptp.real)) (exists ((Z tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z)) X) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Z) tptp.one_one_int)))))))
% 4.96/5.19 (assert (forall ((X tptp.num)) (= (@ tptp.numera6690914467698888265omplex (@ tptp.inc X)) (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex X)) tptp.one_one_complex))))
% 4.96/5.19 (assert (forall ((X tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.inc X)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat X)) tptp.one_one_nat))))
% 4.96/5.19 (assert (forall ((X tptp.num)) (= (@ tptp.numera1916890842035813515d_enat (@ tptp.inc X)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.numera1916890842035813515d_enat X)) tptp.one_on7984719198319812577d_enat))))
% 4.96/5.19 (assert (forall ((X tptp.num)) (= (@ tptp.numeral_numeral_int (@ tptp.inc X)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int X)) tptp.one_one_int))))
% 4.96/5.19 (assert (forall ((X tptp.num)) (= (@ tptp.numeral_numeral_real (@ tptp.inc X)) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real X)) tptp.one_one_real))))
% 4.96/5.19 (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))))
% 4.96/5.19 (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)))))
% 4.96/5.19 (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))))
% 4.96/5.19 (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))))
% 4.96/5.19 (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))))
% 4.96/5.19 (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))))
% 4.96/5.19 (assert (forall ((X tptp.real) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ring_1_of_int_real Y))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real X) _let_1)) _let_2) (=> (@ (@ tptp.ord_less_eq_real _let_2) (@ (@ tptp.plus_plus_real X) _let_1)) (= (@ tptp.archim8280529875227126926d_real X) Y)))))))
% 4.96/5.19 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X)))))
% 4.96/5.19 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X)))))
% 4.96/5.19 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X))) (@ (@ tptp.plus_plus_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 4.96/5.19 (assert (forall ((M2 tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int M2) N2) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X4 tptp.int)) X4)) (@ (@ tptp.set_or1266510415728281911st_int M2) 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 M2) (@ (@ tptp.minus_minus_int M2) tptp.one_one_int)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 4.96/5.19 (assert (forall ((X tptp.int) (Xa2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_3 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 X)) (not (@ _let_2 Xa2)))))) (let ((_let_4 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_5 (and (@ (@ tptp.member_int X) _let_4) (@ (@ tptp.member_int Xa2) _let_4)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X) Xa2) Y) (and (=> _let_5 (= Y (@ tptp.uminus_uminus_int _let_3))) (=> (not _let_5) (= Y (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int X) _let_1)) (@ (@ tptp.divide_divide_int Xa2) _let_1)))))))))))))))
% 4.96/5.19 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K2 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_3 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 K2)) (not (@ _let_2 L2)))))) (let ((_let_4 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (@ (@ (@ tptp.if_int (and (@ (@ tptp.member_int K2) _let_4) (@ (@ tptp.member_int L2) _let_4))) (@ tptp.uminus_uminus_int _let_3)) (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1))))))))))))
% 4.96/5.19 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 4.96/5.19 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 4.96/5.19 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 4.96/5.19 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 4.96/5.19 (assert (forall ((X tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.zero_zero_int) X) tptp.zero_zero_int)))
% 4.96/5.19 (assert (forall ((X tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int X) tptp.zero_zero_int) tptp.zero_zero_int)))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((Uu3 tptp.int)) tptp.zero_zero_int)) A2) tptp.zero_zero_int)))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Uu3 tptp.nat)) tptp.zero_zero_nat)) A2) tptp.zero_zero_nat)))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex)) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((Uu3 tptp.complex)) tptp.zero_zero_complex)) A2) tptp.zero_zero_complex)))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((Uu3 tptp.nat)) tptp.zero_zero_real)) A2) tptp.zero_zero_real)))
% 4.96/5.19 (assert (forall ((G (-> tptp.extended_enat tptp.nat))) (= (@ (@ tptp.groups2027974829824023292at_nat G) tptp.bot_bo7653980558646680370d_enat) tptp.zero_zero_nat)))
% 4.96/5.19 (assert (forall ((G (-> tptp.extended_enat tptp.real))) (= (@ (@ tptp.groups4148127829035722712t_real G) tptp.bot_bo7653980558646680370d_enat) tptp.zero_zero_real)))
% 4.96/5.19 (assert (forall ((G (-> tptp.extended_enat tptp.int))) (= (@ (@ tptp.groups2025484359314973016at_int G) tptp.bot_bo7653980558646680370d_enat) tptp.zero_zero_int)))
% 4.96/5.19 (assert (forall ((G (-> tptp.extended_enat tptp.complex))) (= (@ (@ tptp.groups6818542070133387226omplex G) tptp.bot_bo7653980558646680370d_enat) tptp.zero_zero_complex)))
% 4.96/5.19 (assert (forall ((G (-> tptp.extended_enat tptp.extended_enat))) (= (@ (@ tptp.groups2433450451889696826d_enat G) tptp.bot_bo7653980558646680370d_enat) tptp.zero_z5237406670263579293d_enat)))
% 4.96/5.19 (assert (forall ((G (-> tptp.real tptp.nat))) (= (@ (@ tptp.groups1935376822645274424al_nat G) tptp.bot_bot_set_real) tptp.zero_zero_nat)))
% 4.96/5.19 (assert (forall ((G (-> tptp.real tptp.real))) (= (@ (@ tptp.groups8097168146408367636l_real G) tptp.bot_bot_set_real) tptp.zero_zero_real)))
% 4.96/5.19 (assert (forall ((G (-> tptp.real tptp.int))) (= (@ (@ tptp.groups1932886352136224148al_int G) tptp.bot_bot_set_real) tptp.zero_zero_int)))
% 4.96/5.19 (assert (forall ((G (-> tptp.real tptp.complex))) (= (@ (@ tptp.groups5754745047067104278omplex G) tptp.bot_bot_set_real) tptp.zero_zero_complex)))
% 4.96/5.19 (assert (forall ((G (-> tptp.real tptp.extended_enat))) (= (@ (@ tptp.groups2800946370649118462d_enat G) tptp.bot_bot_set_real) tptp.zero_z5237406670263579293d_enat)))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (=> (not (@ tptp.finite3207457112153483333omplex A2)) (= (@ (@ tptp.groups5693394587270226106ex_nat G) A2) tptp.zero_zero_nat))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.nat))) (=> (not (@ tptp.finite_finite_int A2)) (= (@ (@ tptp.groups4541462559716669496nt_nat G) A2) tptp.zero_zero_nat))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.nat))) (=> (not (@ tptp.finite4001608067531595151d_enat A2)) (= (@ (@ tptp.groups2027974829824023292at_nat G) A2) tptp.zero_zero_nat))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.real))) (=> (not (@ tptp.finite3207457112153483333omplex A2)) (= (@ (@ tptp.groups5808333547571424918x_real G) A2) tptp.zero_zero_real))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.real))) (=> (not (@ tptp.finite_finite_int A2)) (= (@ (@ tptp.groups8778361861064173332t_real G) A2) tptp.zero_zero_real))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.real))) (=> (not (@ tptp.finite4001608067531595151d_enat A2)) (= (@ (@ tptp.groups4148127829035722712t_real G) A2) tptp.zero_zero_real))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.int))) (=> (not (@ tptp.finite_finite_nat A2)) (= (@ (@ tptp.groups3539618377306564664at_int G) A2) tptp.zero_zero_int))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.int))) (=> (not (@ tptp.finite3207457112153483333omplex A2)) (= (@ (@ tptp.groups5690904116761175830ex_int G) A2) tptp.zero_zero_int))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.int))) (=> (not (@ tptp.finite4001608067531595151d_enat A2)) (= (@ (@ tptp.groups2025484359314973016at_int G) A2) tptp.zero_zero_int))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.complex))) (=> (not (@ tptp.finite_finite_nat A2)) (= (@ (@ tptp.groups2073611262835488442omplex G) A2) tptp.zero_zero_complex))))
% 4.96/5.19 (assert (forall ((F3 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex F3) (= (= (@ (@ tptp.groups5693394587270226106ex_nat F) F3) tptp.zero_zero_nat) (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) F3) (= (@ F X4) tptp.zero_zero_nat)))))))
% 4.96/5.19 (assert (forall ((F3 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int F3) (= (= (@ (@ tptp.groups4541462559716669496nt_nat F) F3) tptp.zero_zero_nat) (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) F3) (= (@ F X4) tptp.zero_zero_nat)))))))
% 4.96/5.19 (assert (forall ((F3 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat F3) (= (= (@ (@ tptp.groups2027974829824023292at_nat F) F3) tptp.zero_zero_nat) (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) F3) (= (@ F X4) tptp.zero_zero_nat)))))))
% 4.96/5.19 (assert (forall ((F3 tptp.set_nat) (F (-> tptp.nat tptp.extended_enat))) (=> (@ tptp.finite_finite_nat F3) (= (= (@ (@ tptp.groups7108830773950497114d_enat F) F3) tptp.zero_z5237406670263579293d_enat) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) F3) (= (@ F X4) tptp.zero_z5237406670263579293d_enat)))))))
% 4.96/5.19 (assert (forall ((F3 tptp.set_complex) (F (-> tptp.complex tptp.extended_enat))) (=> (@ tptp.finite3207457112153483333omplex F3) (= (= (@ (@ tptp.groups1752964319039525884d_enat F) F3) tptp.zero_z5237406670263579293d_enat) (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) F3) (= (@ F X4) tptp.zero_z5237406670263579293d_enat)))))))
% 4.96/5.19 (assert (forall ((F3 tptp.set_int) (F (-> tptp.int tptp.extended_enat))) (=> (@ tptp.finite_finite_int F3) (= (= (@ (@ tptp.groups4225252721152677374d_enat F) F3) tptp.zero_z5237406670263579293d_enat) (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) F3) (= (@ F X4) tptp.zero_z5237406670263579293d_enat)))))))
% 4.96/5.19 (assert (forall ((F3 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.extended_enat))) (=> (@ tptp.finite4001608067531595151d_enat F3) (= (= (@ (@ tptp.groups2433450451889696826d_enat F) F3) tptp.zero_z5237406670263579293d_enat) (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) F3) (= (@ F X4) tptp.zero_z5237406670263579293d_enat)))))))
% 4.96/5.19 (assert (forall ((F3 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat F3) (= (= (@ (@ tptp.groups3542108847815614940at_nat F) F3) tptp.zero_zero_nat) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) F3) (= (@ F X4) tptp.zero_zero_nat)))))))
% 4.96/5.19 (assert (= (@ tptp.archim8280529875227126926d_real tptp.zero_zero_real) tptp.zero_zero_int))
% 4.96/5.19 (assert (forall ((S2 tptp.set_real) (A tptp.real) (B2 (-> tptp.real tptp.nat))) (let ((_let_1 (@ (@ tptp.member_real A) S2))) (=> (@ tptp.finite_finite_real S2) (and (=> _let_1 (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) tptp.zero_zero_nat))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) tptp.zero_zero_nat))) S2) tptp.zero_zero_nat)))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_complex) (A tptp.complex) (B2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_1 (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) tptp.zero_zero_nat))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) tptp.zero_zero_nat))) S2) tptp.zero_zero_nat)))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_int) (A tptp.int) (B2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ (@ tptp.member_int A) S2))) (=> (@ tptp.finite_finite_int S2) (and (=> _let_1 (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) tptp.zero_zero_nat))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) tptp.zero_zero_nat))) S2) tptp.zero_zero_nat)))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_Extended_enat) (A tptp.extended_enat) (B2 (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ (@ tptp.member_Extended_enat A) S2))) (=> (@ tptp.finite4001608067531595151d_enat S2) (and (=> _let_1 (= (@ (@ tptp.groups2027974829824023292at_nat (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) tptp.zero_zero_nat))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups2027974829824023292at_nat (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) tptp.zero_zero_nat))) S2) tptp.zero_zero_nat)))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_real) (A tptp.real) (B2 (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.member_real A) S2))) (=> (@ tptp.finite_finite_real S2) (and (=> _let_1 (= (@ (@ tptp.groups8097168146408367636l_real (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B2 K2)) tptp.zero_zero_real))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups8097168146408367636l_real (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B2 K2)) tptp.zero_zero_real))) S2) tptp.zero_zero_real)))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_complex) (A tptp.complex) (B2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_1 (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B2 K2)) tptp.zero_zero_real))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B2 K2)) tptp.zero_zero_real))) S2) tptp.zero_zero_real)))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_int) (A tptp.int) (B2 (-> tptp.int tptp.real))) (let ((_let_1 (@ (@ tptp.member_int A) S2))) (=> (@ tptp.finite_finite_int S2) (and (=> _let_1 (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B2 K2)) tptp.zero_zero_real))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B2 K2)) tptp.zero_zero_real))) S2) tptp.zero_zero_real)))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_Extended_enat) (A tptp.extended_enat) (B2 (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ (@ tptp.member_Extended_enat A) S2))) (=> (@ tptp.finite4001608067531595151d_enat S2) (and (=> _let_1 (= (@ (@ tptp.groups4148127829035722712t_real (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B2 K2)) tptp.zero_zero_real))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups4148127829035722712t_real (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B2 K2)) tptp.zero_zero_real))) S2) tptp.zero_zero_real)))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_real) (A tptp.real) (B2 (-> tptp.real tptp.int))) (let ((_let_1 (@ (@ tptp.member_real A) S2))) (=> (@ tptp.finite_finite_real S2) (and (=> _let_1 (= (@ (@ tptp.groups1932886352136224148al_int (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B2 K2)) tptp.zero_zero_int))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups1932886352136224148al_int (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B2 K2)) tptp.zero_zero_int))) S2) tptp.zero_zero_int)))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_nat) (A tptp.nat) (B2 (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.member_nat A) S2))) (=> (@ tptp.finite_finite_nat S2) (and (=> _let_1 (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B2 K2)) tptp.zero_zero_int))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B2 K2)) tptp.zero_zero_int))) S2) tptp.zero_zero_int)))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_real) (A tptp.real) (B2 (-> tptp.real tptp.nat))) (let ((_let_1 (@ (@ tptp.member_real A) S2))) (=> (@ tptp.finite_finite_real S2) (and (=> _let_1 (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_nat (= A K2)) (@ B2 K2)) tptp.zero_zero_nat))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_nat (= A K2)) (@ B2 K2)) tptp.zero_zero_nat))) S2) tptp.zero_zero_nat)))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_complex) (A tptp.complex) (B2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_1 (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_nat (= A K2)) (@ B2 K2)) tptp.zero_zero_nat))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_nat (= A K2)) (@ B2 K2)) tptp.zero_zero_nat))) S2) tptp.zero_zero_nat)))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_int) (A tptp.int) (B2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ (@ tptp.member_int A) S2))) (=> (@ tptp.finite_finite_int S2) (and (=> _let_1 (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_nat (= A K2)) (@ B2 K2)) tptp.zero_zero_nat))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_nat (= A K2)) (@ B2 K2)) tptp.zero_zero_nat))) S2) tptp.zero_zero_nat)))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_Extended_enat) (A tptp.extended_enat) (B2 (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ (@ tptp.member_Extended_enat A) S2))) (=> (@ tptp.finite4001608067531595151d_enat S2) (and (=> _let_1 (= (@ (@ tptp.groups2027974829824023292at_nat (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_nat (= A K2)) (@ B2 K2)) tptp.zero_zero_nat))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups2027974829824023292at_nat (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_nat (= A K2)) (@ B2 K2)) tptp.zero_zero_nat))) S2) tptp.zero_zero_nat)))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_real) (A tptp.real) (B2 (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.member_real A) S2))) (=> (@ tptp.finite_finite_real S2) (and (=> _let_1 (= (@ (@ tptp.groups8097168146408367636l_real (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_real (= A K2)) (@ B2 K2)) tptp.zero_zero_real))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups8097168146408367636l_real (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_real (= A K2)) (@ B2 K2)) tptp.zero_zero_real))) S2) tptp.zero_zero_real)))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_complex) (A tptp.complex) (B2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_1 (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_real (= A K2)) (@ B2 K2)) tptp.zero_zero_real))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_real (= A K2)) (@ B2 K2)) tptp.zero_zero_real))) S2) tptp.zero_zero_real)))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_int) (A tptp.int) (B2 (-> tptp.int tptp.real))) (let ((_let_1 (@ (@ tptp.member_int A) S2))) (=> (@ tptp.finite_finite_int S2) (and (=> _let_1 (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_real (= A K2)) (@ B2 K2)) tptp.zero_zero_real))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_real (= A K2)) (@ B2 K2)) tptp.zero_zero_real))) S2) tptp.zero_zero_real)))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_Extended_enat) (A tptp.extended_enat) (B2 (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ (@ tptp.member_Extended_enat A) S2))) (=> (@ tptp.finite4001608067531595151d_enat S2) (and (=> _let_1 (= (@ (@ tptp.groups4148127829035722712t_real (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_real (= A K2)) (@ B2 K2)) tptp.zero_zero_real))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups4148127829035722712t_real (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_real (= A K2)) (@ B2 K2)) tptp.zero_zero_real))) S2) tptp.zero_zero_real)))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_real) (A tptp.real) (B2 (-> tptp.real tptp.int))) (let ((_let_1 (@ (@ tptp.member_real A) S2))) (=> (@ tptp.finite_finite_real S2) (and (=> _let_1 (= (@ (@ tptp.groups1932886352136224148al_int (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_int (= A K2)) (@ B2 K2)) tptp.zero_zero_int))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups1932886352136224148al_int (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_int (= A K2)) (@ B2 K2)) tptp.zero_zero_int))) S2) tptp.zero_zero_int)))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_nat) (A tptp.nat) (B2 (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.member_nat A) S2))) (=> (@ tptp.finite_finite_nat S2) (and (=> _let_1 (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_int (= A K2)) (@ B2 K2)) tptp.zero_zero_int))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_int (= A K2)) (@ B2 K2)) tptp.zero_zero_int))) S2) tptp.zero_zero_int)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat G))) (=> (@ tptp.finite_finite_real A2) (=> (not (@ (@ tptp.member_real X) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X) A2)) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_1 A2))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (@ (@ tptp.member_complex X) A2)) (= (@ _let_1 (@ (@ tptp.insert_complex X) A2)) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_1 A2))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G))) (=> (@ tptp.finite_finite_int A2) (=> (not (@ (@ tptp.member_int X) A2)) (= (@ _let_1 (@ (@ tptp.insert_int X) A2)) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_1 A2))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (X tptp.extended_enat) (G (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2027974829824023292at_nat G))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (not (@ (@ tptp.member_Extended_enat X) A2)) (= (@ _let_1 (@ (@ tptp.insert_Extended_enat X) A2)) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_1 A2))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int G))) (=> (@ tptp.finite_finite_real A2) (=> (not (@ (@ tptp.member_real X) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X) A2)) (@ (@ tptp.plus_plus_int (@ G X)) (@ _let_1 A2))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (X tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ tptp.finite_finite_nat A2) (=> (not (@ (@ tptp.member_nat X) A2)) (= (@ _let_1 (@ (@ tptp.insert_nat X) A2)) (@ (@ tptp.plus_plus_int (@ G X)) (@ _let_1 A2))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (@ (@ tptp.member_complex X) A2)) (= (@ _let_1 (@ (@ tptp.insert_complex X) A2)) (@ (@ tptp.plus_plus_int (@ G X)) (@ _let_1 A2))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (X tptp.extended_enat) (G (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2025484359314973016at_int G))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (not (@ (@ tptp.member_Extended_enat X) A2)) (= (@ _let_1 (@ (@ tptp.insert_Extended_enat X) A2)) (@ (@ tptp.plus_plus_int (@ G X)) (@ _let_1 A2))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real G))) (=> (@ tptp.finite_finite_real A2) (=> (not (@ (@ tptp.member_real X) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X) A2)) (@ (@ tptp.plus_plus_real (@ G X)) (@ _let_1 A2))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (@ (@ tptp.member_complex X) A2)) (= (@ _let_1 (@ (@ tptp.insert_complex X) A2)) (@ (@ tptp.plus_plus_real (@ G X)) (@ _let_1 A2))))))))
% 4.96/5.19 (assert (forall ((F (-> tptp.complex tptp.int)) (A2 tptp.set_complex)) (= (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.groups5690904116761175830ex_int F) A2)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((X4 tptp.complex)) (@ tptp.ring_17405671764205052669omplex (@ F X4)))) A2))))
% 4.96/5.19 (assert (forall ((F (-> tptp.nat tptp.int)) (A2 tptp.set_nat)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.groups3539618377306564664at_int F) A2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((X4 tptp.nat)) (@ tptp.ring_1_of_int_real (@ F X4)))) A2))))
% 4.96/5.19 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.groups4538972089207619220nt_int F) A2)) (@ (@ tptp.groups8778361861064173332t_real (lambda ((X4 tptp.int)) (@ tptp.ring_1_of_int_real (@ F X4)))) A2))))
% 4.96/5.19 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X4 tptp.int)) (@ tptp.ring_1_of_int_int (@ F X4)))) A2))))
% 4.96/5.19 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X))) tptp.one_one_int) tptp.zero_zero_int)))
% 4.96/5.19 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) tptp.one_one_nat) tptp.zero_zero_nat)))
% 4.96/5.19 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) tptp.zero_zero_int)))
% 4.96/5.19 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) tptp.zero_zero_nat)))
% 4.96/5.19 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y)))))))
% 4.96/5.19 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.int))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (= (@ G X5) tptp.zero_zero_int))) (= (@ (@ tptp.groups4538972089207619220nt_int G) A2) tptp.zero_zero_int))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.nat))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (= (@ G X5) tptp.zero_zero_nat))) (= (@ (@ tptp.groups3542108847815614940at_nat G) A2) tptp.zero_zero_nat))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.complex))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (= (@ G X5) tptp.zero_zero_complex))) (= (@ (@ tptp.groups7754918857620584856omplex G) A2) tptp.zero_zero_complex))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.real))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (= (@ G X5) tptp.zero_zero_real))) (= (@ (@ tptp.groups6591440286371151544t_real G) A2) tptp.zero_zero_real))))
% 4.96/5.19 (assert (forall ((G (-> tptp.extended_enat tptp.nat)) (A2 tptp.set_Extended_enat)) (=> (not (= (@ (@ tptp.groups2027974829824023292at_nat G) A2) tptp.zero_zero_nat)) (not (forall ((A4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A4) A2) (= (@ G A4) tptp.zero_zero_nat)))))))
% 4.96/5.19 (assert (forall ((G (-> tptp.real tptp.nat)) (A2 tptp.set_real)) (=> (not (= (@ (@ tptp.groups1935376822645274424al_nat G) A2) tptp.zero_zero_nat)) (not (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) A2) (= (@ G A4) tptp.zero_zero_nat)))))))
% 4.96/5.19 (assert (forall ((G (-> tptp.int tptp.nat)) (A2 tptp.set_int)) (=> (not (= (@ (@ tptp.groups4541462559716669496nt_nat G) A2) tptp.zero_zero_nat)) (not (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) A2) (= (@ G A4) tptp.zero_zero_nat)))))))
% 4.96/5.19 (assert (forall ((G (-> tptp.extended_enat tptp.real)) (A2 tptp.set_Extended_enat)) (=> (not (= (@ (@ tptp.groups4148127829035722712t_real G) A2) tptp.zero_zero_real)) (not (forall ((A4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A4) A2) (= (@ G A4) tptp.zero_zero_real)))))))
% 4.96/5.19 (assert (forall ((G (-> tptp.real tptp.real)) (A2 tptp.set_real)) (=> (not (= (@ (@ tptp.groups8097168146408367636l_real G) A2) tptp.zero_zero_real)) (not (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) A2) (= (@ G A4) tptp.zero_zero_real)))))))
% 4.96/5.19 (assert (forall ((G (-> tptp.int tptp.real)) (A2 tptp.set_int)) (=> (not (= (@ (@ tptp.groups8778361861064173332t_real G) A2) tptp.zero_zero_real)) (not (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) A2) (= (@ G A4) tptp.zero_zero_real)))))))
% 4.96/5.19 (assert (forall ((G (-> tptp.extended_enat tptp.int)) (A2 tptp.set_Extended_enat)) (=> (not (= (@ (@ tptp.groups2025484359314973016at_int G) A2) tptp.zero_zero_int)) (not (forall ((A4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A4) A2) (= (@ G A4) tptp.zero_zero_int)))))))
% 4.96/5.19 (assert (forall ((G (-> tptp.real tptp.int)) (A2 tptp.set_real)) (=> (not (= (@ (@ tptp.groups1932886352136224148al_int G) A2) tptp.zero_zero_int)) (not (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) A2) (= (@ G A4) tptp.zero_zero_int)))))))
% 4.96/5.19 (assert (forall ((G (-> tptp.nat tptp.int)) (A2 tptp.set_nat)) (=> (not (= (@ (@ tptp.groups3539618377306564664at_int G) A2) tptp.zero_zero_int)) (not (forall ((A4 tptp.nat)) (=> (@ (@ tptp.member_nat A4) A2) (= (@ G A4) tptp.zero_zero_int)))))))
% 4.96/5.19 (assert (forall ((G (-> tptp.extended_enat tptp.complex)) (A2 tptp.set_Extended_enat)) (=> (not (= (@ (@ tptp.groups6818542070133387226omplex G) A2) tptp.zero_zero_complex)) (not (forall ((A4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A4) A2) (= (@ G A4) tptp.zero_zero_complex)))))))
% 4.96/5.19 (assert (forall ((K5 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real)) (G (-> tptp.extended_enat tptp.real))) (=> (forall ((I4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I4) K5) (@ (@ tptp.ord_less_eq_real (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups4148127829035722712t_real F) K5)) (@ (@ tptp.groups4148127829035722712t_real G) K5)))))
% 4.96/5.19 (assert (forall ((K5 tptp.set_real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) K5) (@ (@ tptp.ord_less_eq_real (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8097168146408367636l_real F) K5)) (@ (@ tptp.groups8097168146408367636l_real G) K5)))))
% 4.96/5.19 (assert (forall ((K5 tptp.set_int) (F (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) K5) (@ (@ tptp.ord_less_eq_real (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8778361861064173332t_real F) K5)) (@ (@ tptp.groups8778361861064173332t_real G) K5)))))
% 4.96/5.19 (assert (forall ((K5 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat)) (G (-> tptp.extended_enat tptp.nat))) (=> (forall ((I4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I4) K5) (@ (@ tptp.ord_less_eq_nat (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups2027974829824023292at_nat F) K5)) (@ (@ tptp.groups2027974829824023292at_nat G) K5)))))
% 4.96/5.19 (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)))))
% 4.96/5.19 (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)))))
% 4.96/5.19 (assert (forall ((K5 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.int)) (G (-> tptp.extended_enat tptp.int))) (=> (forall ((I4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I4) K5) (@ (@ tptp.ord_less_eq_int (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups2025484359314973016at_int F) K5)) (@ (@ tptp.groups2025484359314973016at_int G) K5)))))
% 4.96/5.19 (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)))))
% 4.96/5.19 (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)))))
% 4.96/5.19 (assert (forall ((K5 tptp.set_int) (F (-> tptp.int tptp.int)) (G (-> tptp.int tptp.int))) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) K5) (@ (@ tptp.ord_less_eq_int (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups4538972089207619220nt_int F) K5)) (@ (@ tptp.groups4538972089207619220nt_int G) K5)))))
% 4.96/5.19 (assert (forall ((G (-> tptp.int tptp.int)) (H2 (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X4 tptp.int)) (@ (@ tptp.plus_plus_int (@ G X4)) (@ H2 X4)))) A2) (@ (@ tptp.plus_plus_int (@ (@ tptp.groups4538972089207619220nt_int G) A2)) (@ (@ tptp.groups4538972089207619220nt_int H2) A2)))))
% 4.96/5.19 (assert (forall ((G (-> tptp.nat tptp.nat)) (H2 (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ G X4)) (@ H2 X4)))) A2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups3542108847815614940at_nat G) A2)) (@ (@ tptp.groups3542108847815614940at_nat H2) A2)))))
% 4.96/5.19 (assert (forall ((G (-> tptp.complex tptp.complex)) (H2 (-> tptp.complex tptp.complex)) (A2 tptp.set_complex)) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X4 tptp.complex)) (@ (@ tptp.plus_plus_complex (@ G X4)) (@ H2 X4)))) A2) (@ (@ tptp.plus_plus_complex (@ (@ tptp.groups7754918857620584856omplex G) A2)) (@ (@ tptp.groups7754918857620584856omplex H2) A2)))))
% 4.96/5.19 (assert (forall ((G (-> tptp.nat tptp.real)) (H2 (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((X4 tptp.nat)) (@ (@ tptp.plus_plus_real (@ G X4)) (@ H2 X4)))) A2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real G) A2)) (@ (@ tptp.groups6591440286371151544t_real H2) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (B tptp.set_int) (G (-> tptp.real tptp.int tptp.int)) (R (-> tptp.real tptp.int Bool))) (=> (@ tptp.finite_finite_real A2) (=> (@ tptp.finite_finite_int B) (= (@ (@ tptp.groups1932886352136224148al_int (lambda ((X4 tptp.real)) (@ (@ tptp.groups4538972089207619220nt_int (@ G X4)) (@ tptp.collect_int (lambda ((Y5 tptp.int)) (and (@ (@ tptp.member_int Y5) B) (@ (@ R X4) Y5))))))) A2) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((Y5 tptp.int)) (@ (@ tptp.groups1932886352136224148al_int (lambda ((X4 tptp.real)) (@ (@ G X4) Y5))) (@ tptp.collect_real (lambda ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) A2) (@ (@ R X4) Y5))))))) B))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (B tptp.set_int) (G (-> tptp.nat tptp.int tptp.int)) (R (-> tptp.nat tptp.int Bool))) (=> (@ tptp.finite_finite_nat A2) (=> (@ tptp.finite_finite_int B) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((X4 tptp.nat)) (@ (@ tptp.groups4538972089207619220nt_int (@ G X4)) (@ tptp.collect_int (lambda ((Y5 tptp.int)) (and (@ (@ tptp.member_int Y5) B) (@ (@ R X4) Y5))))))) A2) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((Y5 tptp.int)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((X4 tptp.nat)) (@ (@ G X4) Y5))) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A2) (@ (@ R X4) Y5))))))) B))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (B tptp.set_int) (G (-> tptp.complex tptp.int tptp.int)) (R (-> tptp.complex tptp.int Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ tptp.finite_finite_int B) (= (@ (@ tptp.groups5690904116761175830ex_int (lambda ((X4 tptp.complex)) (@ (@ tptp.groups4538972089207619220nt_int (@ G X4)) (@ tptp.collect_int (lambda ((Y5 tptp.int)) (and (@ (@ tptp.member_int Y5) B) (@ (@ R X4) Y5))))))) A2) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((Y5 tptp.int)) (@ (@ tptp.groups5690904116761175830ex_int (lambda ((X4 tptp.complex)) (@ (@ G X4) Y5))) (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A2) (@ (@ R X4) Y5))))))) B))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (B tptp.set_int) (G (-> tptp.extended_enat tptp.int tptp.int)) (R (-> tptp.extended_enat tptp.int Bool))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ tptp.finite_finite_int B) (= (@ (@ tptp.groups2025484359314973016at_int (lambda ((X4 tptp.extended_enat)) (@ (@ tptp.groups4538972089207619220nt_int (@ G X4)) (@ tptp.collect_int (lambda ((Y5 tptp.int)) (and (@ (@ tptp.member_int Y5) B) (@ (@ R X4) Y5))))))) A2) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((Y5 tptp.int)) (@ (@ tptp.groups2025484359314973016at_int (lambda ((X4 tptp.extended_enat)) (@ (@ G X4) Y5))) (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) A2) (@ (@ R X4) Y5))))))) B))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (B tptp.set_nat) (G (-> tptp.real tptp.nat tptp.nat)) (R (-> tptp.real tptp.nat Bool))) (=> (@ tptp.finite_finite_real A2) (=> (@ tptp.finite_finite_nat B) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((X4 tptp.real)) (@ (@ tptp.groups3542108847815614940at_nat (@ G X4)) (@ tptp.collect_nat (lambda ((Y5 tptp.nat)) (and (@ (@ tptp.member_nat Y5) B) (@ (@ R X4) Y5))))))) A2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Y5 tptp.nat)) (@ (@ tptp.groups1935376822645274424al_nat (lambda ((X4 tptp.real)) (@ (@ G X4) Y5))) (@ tptp.collect_real (lambda ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) A2) (@ (@ R X4) Y5))))))) B))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (B tptp.set_nat) (G (-> tptp.complex tptp.nat tptp.nat)) (R (-> tptp.complex tptp.nat Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ tptp.finite_finite_nat B) (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((X4 tptp.complex)) (@ (@ tptp.groups3542108847815614940at_nat (@ G X4)) (@ tptp.collect_nat (lambda ((Y5 tptp.nat)) (and (@ (@ tptp.member_nat Y5) B) (@ (@ R X4) Y5))))))) A2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Y5 tptp.nat)) (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((X4 tptp.complex)) (@ (@ G X4) Y5))) (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A2) (@ (@ R X4) Y5))))))) B))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (B tptp.set_nat) (G (-> tptp.int tptp.nat tptp.nat)) (R (-> tptp.int tptp.nat Bool))) (=> (@ tptp.finite_finite_int A2) (=> (@ tptp.finite_finite_nat B) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X4 tptp.int)) (@ (@ tptp.groups3542108847815614940at_nat (@ G X4)) (@ tptp.collect_nat (lambda ((Y5 tptp.nat)) (and (@ (@ tptp.member_nat Y5) B) (@ (@ R X4) Y5))))))) A2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Y5 tptp.nat)) (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X4 tptp.int)) (@ (@ G X4) Y5))) (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A2) (@ (@ R X4) Y5))))))) B))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (B tptp.set_nat) (G (-> tptp.extended_enat tptp.nat tptp.nat)) (R (-> tptp.extended_enat tptp.nat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ tptp.finite_finite_nat B) (= (@ (@ tptp.groups2027974829824023292at_nat (lambda ((X4 tptp.extended_enat)) (@ (@ tptp.groups3542108847815614940at_nat (@ G X4)) (@ tptp.collect_nat (lambda ((Y5 tptp.nat)) (and (@ (@ tptp.member_nat Y5) B) (@ (@ R X4) Y5))))))) A2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Y5 tptp.nat)) (@ (@ tptp.groups2027974829824023292at_nat (lambda ((X4 tptp.extended_enat)) (@ (@ G X4) Y5))) (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) A2) (@ (@ R X4) Y5))))))) B))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (B tptp.set_complex) (G (-> tptp.real tptp.complex tptp.complex)) (R (-> tptp.real tptp.complex Bool))) (=> (@ tptp.finite_finite_real A2) (=> (@ tptp.finite3207457112153483333omplex B) (= (@ (@ tptp.groups5754745047067104278omplex (lambda ((X4 tptp.real)) (@ (@ tptp.groups7754918857620584856omplex (@ G X4)) (@ tptp.collect_complex (lambda ((Y5 tptp.complex)) (and (@ (@ tptp.member_complex Y5) B) (@ (@ R X4) Y5))))))) A2) (@ (@ tptp.groups7754918857620584856omplex (lambda ((Y5 tptp.complex)) (@ (@ tptp.groups5754745047067104278omplex (lambda ((X4 tptp.real)) (@ (@ G X4) Y5))) (@ tptp.collect_real (lambda ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) A2) (@ (@ R X4) Y5))))))) B))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (B tptp.set_complex) (G (-> tptp.nat tptp.complex tptp.complex)) (R (-> tptp.nat tptp.complex Bool))) (=> (@ tptp.finite_finite_nat A2) (=> (@ tptp.finite3207457112153483333omplex B) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((X4 tptp.nat)) (@ (@ tptp.groups7754918857620584856omplex (@ G X4)) (@ tptp.collect_complex (lambda ((Y5 tptp.complex)) (and (@ (@ tptp.member_complex Y5) B) (@ (@ R X4) Y5))))))) A2) (@ (@ tptp.groups7754918857620584856omplex (lambda ((Y5 tptp.complex)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((X4 tptp.nat)) (@ (@ G X4) Y5))) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A2) (@ (@ R X4) Y5))))))) B))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.extended_enat))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) tptp.zero_z5237406670263579293d_enat))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups2433450451889696826d_enat F) A2)) tptp.zero_z5237406670263579293d_enat))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.extended_enat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) tptp.zero_z5237406670263579293d_enat))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups2800946370649118462d_enat F) A2)) tptp.zero_z5237406670263579293d_enat))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.extended_enat))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) tptp.zero_z5237406670263579293d_enat))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups7108830773950497114d_enat F) A2)) tptp.zero_z5237406670263579293d_enat))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.extended_enat))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) tptp.zero_z5237406670263579293d_enat))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups4225252721152677374d_enat F) A2)) tptp.zero_z5237406670263579293d_enat))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) A2) (@ (@ tptp.ord_less_eq_real (@ F X5)) tptp.zero_zero_real))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups4148127829035722712t_real F) A2)) tptp.zero_zero_real))))
% 4.96/5.19 (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))))
% 4.96/5.19 (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))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) A2) (@ (@ tptp.ord_less_eq_nat (@ F X5)) tptp.zero_zero_nat))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups2027974829824023292at_nat F) A2)) tptp.zero_zero_nat))))
% 4.96/5.19 (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))))
% 4.96/5.19 (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))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.extended_enat))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.groups2433450451889696826d_enat F) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.extended_enat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.groups2800946370649118462d_enat F) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.extended_enat))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.groups7108830773950497114d_enat F) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.extended_enat))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.groups4225252721152677374d_enat F) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups4148127829035722712t_real F) A2)))))
% 4.96/5.19 (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)))))
% 4.96/5.19 (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)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) A2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X5)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups2027974829824023292at_nat F) A2)))))
% 4.96/5.19 (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)))))
% 4.96/5.19 (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)))))
% 4.96/5.19 (assert (forall ((F (-> tptp.real tptp.real)) (I6 tptp.set_real) (G (-> tptp.real tptp.real)) (I tptp.real)) (=> (= (@ (@ tptp.groups8097168146408367636l_real F) I6) (@ (@ tptp.groups8097168146408367636l_real G) I6)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_real (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_real I) I6) (=> (@ tptp.finite_finite_real I6) (= (@ F I) (@ G I))))))))
% 4.96/5.19 (assert (forall ((F (-> tptp.complex tptp.real)) (I6 tptp.set_complex) (G (-> tptp.complex tptp.real)) (I tptp.complex)) (=> (= (@ (@ tptp.groups5808333547571424918x_real F) I6) (@ (@ tptp.groups5808333547571424918x_real G) I6)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_eq_real (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_complex I) I6) (=> (@ tptp.finite3207457112153483333omplex I6) (= (@ F I) (@ G I))))))))
% 4.96/5.19 (assert (forall ((F (-> tptp.int tptp.real)) (I6 tptp.set_int) (G (-> tptp.int tptp.real)) (I tptp.int)) (=> (= (@ (@ tptp.groups8778361861064173332t_real F) I6) (@ (@ tptp.groups8778361861064173332t_real G) I6)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_eq_real (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_int I) I6) (=> (@ tptp.finite_finite_int I6) (= (@ F I) (@ G I))))))))
% 4.96/5.19 (assert (forall ((F (-> tptp.extended_enat tptp.real)) (I6 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.real)) (I tptp.extended_enat)) (=> (= (@ (@ tptp.groups4148127829035722712t_real F) I6) (@ (@ tptp.groups4148127829035722712t_real G) I6)) (=> (forall ((I4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I4) I6) (@ (@ tptp.ord_less_eq_real (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_Extended_enat I) I6) (=> (@ tptp.finite4001608067531595151d_enat I6) (= (@ F I) (@ G I))))))))
% 4.96/5.19 (assert (forall ((F (-> tptp.real tptp.nat)) (I6 tptp.set_real) (G (-> tptp.real tptp.nat)) (I tptp.real)) (=> (= (@ (@ tptp.groups1935376822645274424al_nat F) I6) (@ (@ tptp.groups1935376822645274424al_nat G) I6)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_nat (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_real I) I6) (=> (@ tptp.finite_finite_real I6) (= (@ F I) (@ G I))))))))
% 4.96/5.19 (assert (forall ((F (-> tptp.complex tptp.nat)) (I6 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (I tptp.complex)) (=> (= (@ (@ tptp.groups5693394587270226106ex_nat F) I6) (@ (@ tptp.groups5693394587270226106ex_nat G) I6)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_eq_nat (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_complex I) I6) (=> (@ tptp.finite3207457112153483333omplex I6) (= (@ F I) (@ G I))))))))
% 4.96/5.19 (assert (forall ((F (-> tptp.int tptp.nat)) (I6 tptp.set_int) (G (-> tptp.int tptp.nat)) (I tptp.int)) (=> (= (@ (@ tptp.groups4541462559716669496nt_nat F) I6) (@ (@ tptp.groups4541462559716669496nt_nat G) I6)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_eq_nat (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_int I) I6) (=> (@ tptp.finite_finite_int I6) (= (@ F I) (@ G I))))))))
% 4.96/5.19 (assert (forall ((F (-> tptp.extended_enat tptp.nat)) (I6 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.nat)) (I tptp.extended_enat)) (=> (= (@ (@ tptp.groups2027974829824023292at_nat F) I6) (@ (@ tptp.groups2027974829824023292at_nat G) I6)) (=> (forall ((I4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I4) I6) (@ (@ tptp.ord_less_eq_nat (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_Extended_enat I) I6) (=> (@ tptp.finite4001608067531595151d_enat I6) (= (@ F I) (@ G I))))))))
% 4.96/5.19 (assert (forall ((F (-> tptp.real tptp.int)) (I6 tptp.set_real) (G (-> tptp.real tptp.int)) (I tptp.real)) (=> (= (@ (@ tptp.groups1932886352136224148al_int F) I6) (@ (@ tptp.groups1932886352136224148al_int G) I6)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_int (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_real I) I6) (=> (@ tptp.finite_finite_real I6) (= (@ F I) (@ G I))))))))
% 4.96/5.19 (assert (forall ((F (-> tptp.nat tptp.int)) (I6 tptp.set_nat) (G (-> tptp.nat tptp.int)) (I tptp.nat)) (=> (= (@ (@ tptp.groups3539618377306564664at_int F) I6) (@ (@ tptp.groups3539618377306564664at_int G) I6)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_eq_int (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_nat I) I6) (=> (@ tptp.finite_finite_nat I6) (= (@ F I) (@ G I))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.nat)) (P (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A2) (= (@ (@ tptp.groups1935376822645274424al_nat G) (@ tptp.collect_real (lambda ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) A2) (@ P X4))))) (@ (@ tptp.groups1935376822645274424al_nat (lambda ((X4 tptp.real)) (@ (@ (@ tptp.if_nat (@ P X4)) (@ G X4)) tptp.zero_zero_nat))) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (P (-> tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ (@ tptp.groups5693394587270226106ex_nat G) (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A2) (@ P X4))))) (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((X4 tptp.complex)) (@ (@ (@ tptp.if_nat (@ P X4)) (@ G X4)) tptp.zero_zero_nat))) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.nat)) (P (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A2) (= (@ (@ tptp.groups4541462559716669496nt_nat G) (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A2) (@ P X4))))) (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_nat (@ P X4)) (@ G X4)) tptp.zero_zero_nat))) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.nat)) (P (-> tptp.extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ (@ tptp.groups2027974829824023292at_nat G) (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) A2) (@ P X4))))) (@ (@ tptp.groups2027974829824023292at_nat (lambda ((X4 tptp.extended_enat)) (@ (@ (@ tptp.if_nat (@ P X4)) (@ G X4)) tptp.zero_zero_nat))) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.real)) (P (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A2) (= (@ (@ tptp.groups8097168146408367636l_real G) (@ tptp.collect_real (lambda ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) A2) (@ P X4))))) (@ (@ tptp.groups8097168146408367636l_real (lambda ((X4 tptp.real)) (@ (@ (@ tptp.if_real (@ P X4)) (@ G X4)) tptp.zero_zero_real))) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.real)) (P (-> tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ (@ tptp.groups5808333547571424918x_real G) (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A2) (@ P X4))))) (@ (@ tptp.groups5808333547571424918x_real (lambda ((X4 tptp.complex)) (@ (@ (@ tptp.if_real (@ P X4)) (@ G X4)) tptp.zero_zero_real))) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.real)) (P (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A2) (= (@ (@ tptp.groups8778361861064173332t_real G) (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A2) (@ P X4))))) (@ (@ tptp.groups8778361861064173332t_real (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_real (@ P X4)) (@ G X4)) tptp.zero_zero_real))) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.real)) (P (-> tptp.extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ (@ tptp.groups4148127829035722712t_real G) (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) A2) (@ P X4))))) (@ (@ tptp.groups4148127829035722712t_real (lambda ((X4 tptp.extended_enat)) (@ (@ (@ tptp.if_real (@ P X4)) (@ G X4)) tptp.zero_zero_real))) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.int)) (P (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A2) (= (@ (@ tptp.groups1932886352136224148al_int G) (@ tptp.collect_real (lambda ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) A2) (@ P X4))))) (@ (@ tptp.groups1932886352136224148al_int (lambda ((X4 tptp.real)) (@ (@ (@ tptp.if_int (@ P X4)) (@ G X4)) tptp.zero_zero_int))) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.int)) (P (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A2) (@ P X4))))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((X4 tptp.nat)) (@ (@ (@ tptp.if_int (@ P X4)) (@ G X4)) tptp.zero_zero_int))) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.extended_enat))) (=> (@ tptp.finite_finite_real A2) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (= (= (@ (@ tptp.groups2800946370649118462d_enat F) A2) tptp.zero_z5237406670263579293d_enat) (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A2) (= (@ F X4) tptp.zero_z5237406670263579293d_enat))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.extended_enat))) (=> (@ tptp.finite_finite_nat A2) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (= (= (@ (@ tptp.groups7108830773950497114d_enat F) A2) tptp.zero_z5237406670263579293d_enat) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A2) (= (@ F X4) tptp.zero_z5237406670263579293d_enat))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.extended_enat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (= (= (@ (@ tptp.groups1752964319039525884d_enat F) A2) tptp.zero_z5237406670263579293d_enat) (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A2) (= (@ F X4) tptp.zero_z5237406670263579293d_enat))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.extended_enat))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (= (= (@ (@ tptp.groups4225252721152677374d_enat F) A2) tptp.zero_z5237406670263579293d_enat) (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (= (@ F X4) tptp.zero_z5237406670263579293d_enat))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.extended_enat))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (= (= (@ (@ tptp.groups2433450451889696826d_enat F) A2) tptp.zero_z5237406670263579293d_enat) (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) A2) (= (@ F X4) tptp.zero_z5237406670263579293d_enat))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real A2) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (= (= (@ (@ tptp.groups8097168146408367636l_real F) A2) tptp.zero_zero_real) (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A2) (= (@ F X4) tptp.zero_zero_real))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (= (= (@ (@ tptp.groups5808333547571424918x_real F) A2) tptp.zero_zero_real) (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A2) (= (@ F X4) tptp.zero_zero_real))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (= (= (@ (@ tptp.groups8778361861064173332t_real F) A2) tptp.zero_zero_real) (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (= (@ F X4) tptp.zero_zero_real))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (= (= (@ (@ tptp.groups4148127829035722712t_real F) A2) tptp.zero_zero_real) (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) A2) (= (@ F X4) tptp.zero_zero_real))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real A2) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X5)))) (= (= (@ (@ tptp.groups1935376822645274424al_nat F) A2) tptp.zero_zero_nat) (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A2) (= (@ F X4) tptp.zero_zero_nat))))))))
% 4.96/5.19 (assert (forall ((S tptp.set_nat) (T tptp.set_nat) (G (-> tptp.nat tptp.extended_enat)) (I (-> tptp.nat tptp.nat)) (F (-> tptp.nat tptp.extended_enat))) (=> (@ tptp.finite_finite_nat S) (=> (@ tptp.finite_finite_nat T) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) T) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ G X5)))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) T) (= (@ I Xa) X5) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) (@ G Xa)))))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups7108830773950497114d_enat F) S)) (@ (@ tptp.groups7108830773950497114d_enat G) T))))))))
% 4.96/5.19 (assert (forall ((S tptp.set_nat) (T tptp.set_complex) (G (-> tptp.complex tptp.extended_enat)) (I (-> tptp.complex tptp.nat)) (F (-> tptp.nat tptp.extended_enat))) (=> (@ tptp.finite_finite_nat S) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) T) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ G X5)))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I Xa) X5) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) (@ G Xa)))))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups7108830773950497114d_enat F) S)) (@ (@ tptp.groups1752964319039525884d_enat G) T))))))))
% 4.96/5.19 (assert (forall ((S tptp.set_nat) (T tptp.set_int) (G (-> tptp.int tptp.extended_enat)) (I (-> tptp.int tptp.nat)) (F (-> tptp.nat tptp.extended_enat))) (=> (@ tptp.finite_finite_nat S) (=> (@ tptp.finite_finite_int T) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) T) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ G X5)))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) T) (= (@ I Xa) X5) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) (@ G Xa)))))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups7108830773950497114d_enat F) S)) (@ (@ tptp.groups4225252721152677374d_enat G) T))))))))
% 4.96/5.19 (assert (forall ((S tptp.set_nat) (T tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.extended_enat)) (I (-> tptp.extended_enat tptp.nat)) (F (-> tptp.nat tptp.extended_enat))) (=> (@ tptp.finite_finite_nat S) (=> (@ tptp.finite4001608067531595151d_enat T) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) T) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ G X5)))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S) (exists ((Xa tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat Xa) T) (= (@ I Xa) X5) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) (@ G Xa)))))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups7108830773950497114d_enat F) S)) (@ (@ tptp.groups2433450451889696826d_enat G) T))))))))
% 4.96/5.19 (assert (forall ((S tptp.set_complex) (T tptp.set_nat) (G (-> tptp.nat tptp.extended_enat)) (I (-> tptp.nat tptp.complex)) (F (-> tptp.complex tptp.extended_enat))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (@ tptp.finite_finite_nat T) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) T) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ G X5)))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) T) (= (@ I Xa) X5) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) (@ G Xa)))))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups1752964319039525884d_enat F) S)) (@ (@ tptp.groups7108830773950497114d_enat G) T))))))))
% 4.96/5.19 (assert (forall ((S tptp.set_complex) (T tptp.set_complex) (G (-> tptp.complex tptp.extended_enat)) (I (-> tptp.complex tptp.complex)) (F (-> tptp.complex tptp.extended_enat))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) T) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ G X5)))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I Xa) X5) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) (@ G Xa)))))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups1752964319039525884d_enat F) S)) (@ (@ tptp.groups1752964319039525884d_enat G) T))))))))
% 4.96/5.19 (assert (forall ((S tptp.set_complex) (T tptp.set_int) (G (-> tptp.int tptp.extended_enat)) (I (-> tptp.int tptp.complex)) (F (-> tptp.complex tptp.extended_enat))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (@ tptp.finite_finite_int T) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) T) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ G X5)))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) T) (= (@ I Xa) X5) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) (@ G Xa)))))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups1752964319039525884d_enat F) S)) (@ (@ tptp.groups4225252721152677374d_enat G) T))))))))
% 4.96/5.19 (assert (forall ((S tptp.set_complex) (T tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.extended_enat)) (I (-> tptp.extended_enat tptp.complex)) (F (-> tptp.complex tptp.extended_enat))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (@ tptp.finite4001608067531595151d_enat T) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) T) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ G X5)))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (exists ((Xa tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat Xa) T) (= (@ I Xa) X5) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) (@ G Xa)))))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups1752964319039525884d_enat F) S)) (@ (@ tptp.groups2433450451889696826d_enat G) T))))))))
% 4.96/5.19 (assert (forall ((S tptp.set_int) (T tptp.set_nat) (G (-> tptp.nat tptp.extended_enat)) (I (-> tptp.nat tptp.int)) (F (-> tptp.int tptp.extended_enat))) (=> (@ tptp.finite_finite_int S) (=> (@ tptp.finite_finite_nat T) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) T) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ G X5)))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) S) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) T) (= (@ I Xa) X5) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) (@ G Xa)))))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups4225252721152677374d_enat F) S)) (@ (@ tptp.groups7108830773950497114d_enat G) T))))))))
% 4.96/5.19 (assert (forall ((S tptp.set_int) (T tptp.set_complex) (G (-> tptp.complex tptp.extended_enat)) (I (-> tptp.complex tptp.int)) (F (-> tptp.int tptp.extended_enat))) (=> (@ tptp.finite_finite_int S) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) T) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ G X5)))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) S) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I Xa) X5) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) (@ G Xa)))))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups4225252721152677374d_enat F) S)) (@ (@ tptp.groups1752964319039525884d_enat G) T))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ G X5)))) (=> (exists ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (@ (@ tptp.ord_less_real (@ F X2)) (@ G X2)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups5808333547571424918x_real F) A2)) (@ (@ tptp.groups5808333547571424918x_real G) A2)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ G X5)))) (=> (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (@ (@ tptp.ord_less_real (@ F X2)) (@ G X2)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups8778361861064173332t_real F) A2)) (@ (@ tptp.groups8778361861064173332t_real G) A2)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real)) (G (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) A2) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ G X5)))) (=> (exists ((X2 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X2) A2) (@ (@ tptp.ord_less_real (@ F X2)) (@ G X2)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups4148127829035722712t_real F) A2)) (@ (@ tptp.groups4148127829035722712t_real G) A2)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ G X5)))) (=> (exists ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (@ (@ tptp.ord_less_nat (@ F X2)) (@ G X2)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups5693394587270226106ex_nat F) A2)) (@ (@ tptp.groups5693394587270226106ex_nat G) A2)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ G X5)))) (=> (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (@ (@ tptp.ord_less_nat (@ F X2)) (@ G X2)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) (@ (@ tptp.groups4541462559716669496nt_nat G) A2)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat)) (G (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) A2) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ G X5)))) (=> (exists ((X2 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X2) A2) (@ (@ tptp.ord_less_nat (@ F X2)) (@ G X2)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups2027974829824023292at_nat F) A2)) (@ (@ tptp.groups2027974829824023292at_nat G) A2)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat A2) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ G X5)))) (=> (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (@ (@ tptp.ord_less_int (@ F X2)) (@ G X2)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups3539618377306564664at_int F) A2)) (@ (@ tptp.groups3539618377306564664at_int G) A2)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.int)) (G (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ G X5)))) (=> (exists ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (@ (@ tptp.ord_less_int (@ F X2)) (@ G X2)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups5690904116761175830ex_int F) A2)) (@ (@ tptp.groups5690904116761175830ex_int G) A2)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.int)) (G (-> tptp.extended_enat tptp.int))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) A2) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ G X5)))) (=> (exists ((X2 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X2) A2) (@ (@ tptp.ord_less_int (@ F X2)) (@ G X2)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups2025484359314973016at_int F) A2)) (@ (@ tptp.groups2025484359314973016at_int G) A2)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.int)) (G (-> tptp.int tptp.int))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ G X5)))) (=> (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (@ (@ tptp.ord_less_int (@ F X2)) (@ G X2)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)) (@ (@ tptp.groups4538972089207619220nt_int G) A2)))))))
% 4.96/5.19 (assert (forall ((R (-> tptp.nat tptp.nat Bool)) (S2 tptp.set_complex) (H2 (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ (@ R tptp.zero_zero_nat) tptp.zero_zero_nat) (=> (forall ((X1 tptp.nat) (Y1 tptp.nat) (X23 tptp.nat) (Y22 tptp.nat)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.plus_plus_nat X1) Y1)) (@ (@ tptp.plus_plus_nat X23) Y22)))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S2) (@ (@ R (@ H2 X5)) (@ G X5)))) (@ (@ R (@ (@ tptp.groups5693394587270226106ex_nat H2) S2)) (@ (@ tptp.groups5693394587270226106ex_nat G) S2))))))))
% 4.96/5.19 (assert (forall ((R (-> tptp.nat tptp.nat Bool)) (S2 tptp.set_int) (H2 (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ (@ R tptp.zero_zero_nat) tptp.zero_zero_nat) (=> (forall ((X1 tptp.nat) (Y1 tptp.nat) (X23 tptp.nat) (Y22 tptp.nat)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.plus_plus_nat X1) Y1)) (@ (@ tptp.plus_plus_nat X23) Y22)))) (=> (@ tptp.finite_finite_int S2) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) S2) (@ (@ R (@ H2 X5)) (@ G X5)))) (@ (@ R (@ (@ tptp.groups4541462559716669496nt_nat H2) S2)) (@ (@ tptp.groups4541462559716669496nt_nat G) S2))))))))
% 4.96/5.19 (assert (forall ((R (-> tptp.nat tptp.nat Bool)) (S2 tptp.set_Extended_enat) (H2 (-> tptp.extended_enat tptp.nat)) (G (-> tptp.extended_enat tptp.nat))) (=> (@ (@ R tptp.zero_zero_nat) tptp.zero_zero_nat) (=> (forall ((X1 tptp.nat) (Y1 tptp.nat) (X23 tptp.nat) (Y22 tptp.nat)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.plus_plus_nat X1) Y1)) (@ (@ tptp.plus_plus_nat X23) Y22)))) (=> (@ tptp.finite4001608067531595151d_enat S2) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) S2) (@ (@ R (@ H2 X5)) (@ G X5)))) (@ (@ R (@ (@ tptp.groups2027974829824023292at_nat H2) S2)) (@ (@ tptp.groups2027974829824023292at_nat G) S2))))))))
% 4.96/5.19 (assert (forall ((R (-> tptp.real tptp.real Bool)) (S2 tptp.set_complex) (H2 (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ (@ R tptp.zero_zero_real) tptp.zero_zero_real) (=> (forall ((X1 tptp.real) (Y1 tptp.real) (X23 tptp.real) (Y22 tptp.real)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.plus_plus_real X1) Y1)) (@ (@ tptp.plus_plus_real X23) Y22)))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S2) (@ (@ R (@ H2 X5)) (@ G X5)))) (@ (@ R (@ (@ tptp.groups5808333547571424918x_real H2) S2)) (@ (@ tptp.groups5808333547571424918x_real G) S2))))))))
% 4.96/5.19 (assert (forall ((R (-> tptp.real tptp.real Bool)) (S2 tptp.set_int) (H2 (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (@ (@ R tptp.zero_zero_real) tptp.zero_zero_real) (=> (forall ((X1 tptp.real) (Y1 tptp.real) (X23 tptp.real) (Y22 tptp.real)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.plus_plus_real X1) Y1)) (@ (@ tptp.plus_plus_real X23) Y22)))) (=> (@ tptp.finite_finite_int S2) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) S2) (@ (@ R (@ H2 X5)) (@ G X5)))) (@ (@ R (@ (@ tptp.groups8778361861064173332t_real H2) S2)) (@ (@ tptp.groups8778361861064173332t_real G) S2))))))))
% 4.96/5.19 (assert (forall ((R (-> tptp.real tptp.real Bool)) (S2 tptp.set_Extended_enat) (H2 (-> tptp.extended_enat tptp.real)) (G (-> tptp.extended_enat tptp.real))) (=> (@ (@ R tptp.zero_zero_real) tptp.zero_zero_real) (=> (forall ((X1 tptp.real) (Y1 tptp.real) (X23 tptp.real) (Y22 tptp.real)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.plus_plus_real X1) Y1)) (@ (@ tptp.plus_plus_real X23) Y22)))) (=> (@ tptp.finite4001608067531595151d_enat S2) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) S2) (@ (@ R (@ H2 X5)) (@ G X5)))) (@ (@ R (@ (@ tptp.groups4148127829035722712t_real H2) S2)) (@ (@ tptp.groups4148127829035722712t_real G) S2))))))))
% 4.96/5.19 (assert (forall ((R (-> tptp.int tptp.int Bool)) (S2 tptp.set_nat) (H2 (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ (@ R tptp.zero_zero_int) tptp.zero_zero_int) (=> (forall ((X1 tptp.int) (Y1 tptp.int) (X23 tptp.int) (Y22 tptp.int)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.plus_plus_int X1) Y1)) (@ (@ tptp.plus_plus_int X23) Y22)))) (=> (@ tptp.finite_finite_nat S2) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S2) (@ (@ R (@ H2 X5)) (@ G X5)))) (@ (@ R (@ (@ tptp.groups3539618377306564664at_int H2) S2)) (@ (@ tptp.groups3539618377306564664at_int G) S2))))))))
% 4.96/5.19 (assert (forall ((R (-> tptp.int tptp.int Bool)) (S2 tptp.set_complex) (H2 (-> tptp.complex tptp.int)) (G (-> tptp.complex tptp.int))) (=> (@ (@ R tptp.zero_zero_int) tptp.zero_zero_int) (=> (forall ((X1 tptp.int) (Y1 tptp.int) (X23 tptp.int) (Y22 tptp.int)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.plus_plus_int X1) Y1)) (@ (@ tptp.plus_plus_int X23) Y22)))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S2) (@ (@ R (@ H2 X5)) (@ G X5)))) (@ (@ R (@ (@ tptp.groups5690904116761175830ex_int H2) S2)) (@ (@ tptp.groups5690904116761175830ex_int G) S2))))))))
% 4.96/5.19 (assert (forall ((R (-> tptp.int tptp.int Bool)) (S2 tptp.set_Extended_enat) (H2 (-> tptp.extended_enat tptp.int)) (G (-> tptp.extended_enat tptp.int))) (=> (@ (@ R tptp.zero_zero_int) tptp.zero_zero_int) (=> (forall ((X1 tptp.int) (Y1 tptp.int) (X23 tptp.int) (Y22 tptp.int)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.plus_plus_int X1) Y1)) (@ (@ tptp.plus_plus_int X23) Y22)))) (=> (@ tptp.finite4001608067531595151d_enat S2) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) S2) (@ (@ R (@ H2 X5)) (@ G X5)))) (@ (@ R (@ (@ tptp.groups2025484359314973016at_int H2) S2)) (@ (@ tptp.groups2025484359314973016at_int G) S2))))))))
% 4.96/5.19 (assert (forall ((R (-> tptp.complex tptp.complex Bool)) (S2 tptp.set_nat) (H2 (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.complex))) (=> (@ (@ R tptp.zero_zero_complex) tptp.zero_zero_complex) (=> (forall ((X1 tptp.complex) (Y1 tptp.complex) (X23 tptp.complex) (Y22 tptp.complex)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.plus_plus_complex X1) Y1)) (@ (@ tptp.plus_plus_complex X23) Y22)))) (=> (@ tptp.finite_finite_nat S2) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S2) (@ (@ R (@ H2 X5)) (@ G X5)))) (@ (@ R (@ (@ tptp.groups2073611262835488442omplex H2) S2)) (@ (@ tptp.groups2073611262835488442omplex G) S2))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (= A2 tptp.bot_bot_set_complex)) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_less_nat (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups5693394587270226106ex_nat F) A2)) (@ (@ tptp.groups5693394587270226106ex_nat G) A2)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat)) (G (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (not (= A2 tptp.bot_bo7653980558646680370d_enat)) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) A2) (@ (@ tptp.ord_less_nat (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups2027974829824023292at_nat F) A2)) (@ (@ tptp.groups2027974829824023292at_nat G) A2)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat)) (G (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real A2) (=> (not (= A2 tptp.bot_bot_set_real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_less_nat (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups1935376822645274424al_nat F) A2)) (@ (@ tptp.groups1935376822645274424al_nat G) A2)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (=> (not (= A2 tptp.bot_bot_set_int)) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_nat (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) (@ (@ tptp.groups4541462559716669496nt_nat G) A2)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.extended_enat)) (G (-> tptp.complex tptp.extended_enat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (= A2 tptp.bot_bot_set_complex)) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.groups1752964319039525884d_enat F) A2)) (@ (@ tptp.groups1752964319039525884d_enat G) A2)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.extended_enat)) (G (-> tptp.extended_enat tptp.extended_enat))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (not (= A2 tptp.bot_bo7653980558646680370d_enat)) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) A2) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.groups2433450451889696826d_enat F) A2)) (@ (@ tptp.groups2433450451889696826d_enat G) A2)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.extended_enat)) (G (-> tptp.real tptp.extended_enat))) (=> (@ tptp.finite_finite_real A2) (=> (not (= A2 tptp.bot_bot_set_real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.groups2800946370649118462d_enat F) A2)) (@ (@ tptp.groups2800946370649118462d_enat G) A2)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.extended_enat)) (G (-> tptp.nat tptp.extended_enat))) (=> (@ tptp.finite_finite_nat A2) (=> (not (= A2 tptp.bot_bot_set_nat)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.groups7108830773950497114d_enat F) A2)) (@ (@ tptp.groups7108830773950497114d_enat G) A2)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.extended_enat)) (G (-> tptp.int tptp.extended_enat))) (=> (@ tptp.finite_finite_int A2) (=> (not (= A2 tptp.bot_bot_set_int)) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.groups4225252721152677374d_enat F) A2)) (@ (@ tptp.groups4225252721152677374d_enat G) A2)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (= A2 tptp.bot_bot_set_complex)) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_less_real (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups5808333547571424918x_real F) A2)) (@ (@ tptp.groups5808333547571424918x_real G) A2)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_real X) A2)))) (let ((_let_4 (@ (@ tptp.member_real X) A2))) (=> (@ tptp.finite_finite_real A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_nat (@ G X)) _let_2)))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_complex X) A2)))) (let ((_let_4 (@ (@ tptp.member_complex X) A2))) (=> (@ tptp.finite3207457112153483333omplex A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_nat (@ G X)) _let_2)))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_int X) A2)))) (let ((_let_4 (@ (@ tptp.member_int X) A2))) (=> (@ tptp.finite_finite_int A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_nat (@ G X)) _let_2)))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (X tptp.extended_enat) (G (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2027974829824023292at_nat G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_Extended_enat X) A2)))) (let ((_let_4 (@ (@ tptp.member_Extended_enat X) A2))) (=> (@ tptp.finite4001608067531595151d_enat A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_nat (@ G X)) _let_2)))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_real X) A2)))) (let ((_let_4 (@ (@ tptp.member_real X) A2))) (=> (@ tptp.finite_finite_real A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_int (@ G X)) _let_2)))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (X tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_nat X) A2)))) (let ((_let_4 (@ (@ tptp.member_nat X) A2))) (=> (@ tptp.finite_finite_nat A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_int (@ G X)) _let_2)))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_complex X) A2)))) (let ((_let_4 (@ (@ tptp.member_complex X) A2))) (=> (@ tptp.finite3207457112153483333omplex A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_int (@ G X)) _let_2)))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (X tptp.extended_enat) (G (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2025484359314973016at_int G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_Extended_enat X) A2)))) (let ((_let_4 (@ (@ tptp.member_Extended_enat X) A2))) (=> (@ tptp.finite4001608067531595151d_enat A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_int (@ G X)) _let_2)))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_real X) A2)))) (let ((_let_4 (@ (@ tptp.member_real X) A2))) (=> (@ tptp.finite_finite_real A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_real (@ G X)) _let_2)))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_complex X) A2)))) (let ((_let_4 (@ (@ tptp.member_complex X) A2))) (=> (@ tptp.finite3207457112153483333omplex A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_real (@ G X)) _let_2)))))))))))
% 4.96/5.19 (assert (forall ((S5 tptp.set_real) (T5 tptp.set_real) (S2 tptp.set_real) (I (-> tptp.real tptp.real)) (J (-> tptp.real tptp.real)) (T3 tptp.set_real) (G (-> tptp.real tptp.nat)) (H2 (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real S5) (=> (@ tptp.finite_finite_real T5) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real S2) S5)) (= (@ I (@ J A4)) A4))) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real S2) S5)) (@ (@ tptp.member_real (@ J A4)) (@ (@ tptp.minus_minus_set_real T3) T5)))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real T3) T5)) (= (@ J (@ I B4)) B4))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real T3) T5)) (@ (@ tptp.member_real (@ I B4)) (@ (@ tptp.minus_minus_set_real S2) S5)))) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) S5) (= (@ G A4) tptp.zero_zero_nat))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) T5) (= (@ H2 B4) tptp.zero_zero_nat))) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) S2) (= (@ H2 (@ J A4)) (@ G A4)))) (= (@ (@ tptp.groups1935376822645274424al_nat G) S2) (@ (@ tptp.groups1935376822645274424al_nat H2) T3)))))))))))))
% 4.96/5.19 (assert (forall ((S5 tptp.set_real) (T5 tptp.set_complex) (S2 tptp.set_real) (I (-> tptp.complex tptp.real)) (J (-> tptp.real tptp.complex)) (T3 tptp.set_complex) (G (-> tptp.real tptp.nat)) (H2 (-> tptp.complex tptp.nat))) (=> (@ tptp.finite_finite_real S5) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real S2) S5)) (= (@ I (@ J A4)) A4))) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real S2) S5)) (@ (@ tptp.member_complex (@ J A4)) (@ (@ tptp.minus_811609699411566653omplex T3) T5)))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex T3) T5)) (= (@ J (@ I B4)) B4))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex T3) T5)) (@ (@ tptp.member_real (@ I B4)) (@ (@ tptp.minus_minus_set_real S2) S5)))) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) S5) (= (@ G A4) tptp.zero_zero_nat))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) T5) (= (@ H2 B4) tptp.zero_zero_nat))) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) S2) (= (@ H2 (@ J A4)) (@ G A4)))) (= (@ (@ tptp.groups1935376822645274424al_nat G) S2) (@ (@ tptp.groups5693394587270226106ex_nat H2) T3)))))))))))))
% 4.96/5.19 (assert (forall ((S5 tptp.set_real) (T5 tptp.set_int) (S2 tptp.set_real) (I (-> tptp.int tptp.real)) (J (-> tptp.real tptp.int)) (T3 tptp.set_int) (G (-> tptp.real tptp.nat)) (H2 (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_real S5) (=> (@ tptp.finite_finite_int T5) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real S2) S5)) (= (@ I (@ J A4)) A4))) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real S2) S5)) (@ (@ tptp.member_int (@ J A4)) (@ (@ tptp.minus_minus_set_int T3) T5)))) (=> (forall ((B4 tptp.int)) (=> (@ (@ tptp.member_int B4) (@ (@ tptp.minus_minus_set_int T3) T5)) (= (@ J (@ I B4)) B4))) (=> (forall ((B4 tptp.int)) (=> (@ (@ tptp.member_int B4) (@ (@ tptp.minus_minus_set_int T3) T5)) (@ (@ tptp.member_real (@ I B4)) (@ (@ tptp.minus_minus_set_real S2) S5)))) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) S5) (= (@ G A4) tptp.zero_zero_nat))) (=> (forall ((B4 tptp.int)) (=> (@ (@ tptp.member_int B4) T5) (= (@ H2 B4) tptp.zero_zero_nat))) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) S2) (= (@ H2 (@ J A4)) (@ G A4)))) (= (@ (@ tptp.groups1935376822645274424al_nat G) S2) (@ (@ tptp.groups4541462559716669496nt_nat H2) T3)))))))))))))
% 4.96/5.19 (assert (forall ((S5 tptp.set_real) (T5 tptp.set_Extended_enat) (S2 tptp.set_real) (I (-> tptp.extended_enat tptp.real)) (J (-> tptp.real tptp.extended_enat)) (T3 tptp.set_Extended_enat) (G (-> tptp.real tptp.nat)) (H2 (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite_finite_real S5) (=> (@ tptp.finite4001608067531595151d_enat T5) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real S2) S5)) (= (@ I (@ J A4)) A4))) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real S2) S5)) (@ (@ tptp.member_Extended_enat (@ J A4)) (@ (@ tptp.minus_925952699566721837d_enat T3) T5)))) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) (@ (@ tptp.minus_925952699566721837d_enat T3) T5)) (= (@ J (@ I B4)) B4))) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) (@ (@ tptp.minus_925952699566721837d_enat T3) T5)) (@ (@ tptp.member_real (@ I B4)) (@ (@ tptp.minus_minus_set_real S2) S5)))) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) S5) (= (@ G A4) tptp.zero_zero_nat))) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) T5) (= (@ H2 B4) tptp.zero_zero_nat))) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) S2) (= (@ H2 (@ J A4)) (@ G A4)))) (= (@ (@ tptp.groups1935376822645274424al_nat G) S2) (@ (@ tptp.groups2027974829824023292at_nat H2) T3)))))))))))))
% 4.96/5.19 (assert (forall ((S5 tptp.set_complex) (T5 tptp.set_real) (S2 tptp.set_complex) (I (-> tptp.real tptp.complex)) (J (-> tptp.complex tptp.real)) (T3 tptp.set_real) (G (-> tptp.complex tptp.nat)) (H2 (-> tptp.real tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex S5) (=> (@ tptp.finite_finite_real T5) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) (@ (@ tptp.minus_811609699411566653omplex S2) S5)) (= (@ I (@ J A4)) A4))) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) (@ (@ tptp.minus_811609699411566653omplex S2) S5)) (@ (@ tptp.member_real (@ J A4)) (@ (@ tptp.minus_minus_set_real T3) T5)))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real T3) T5)) (= (@ J (@ I B4)) B4))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real T3) T5)) (@ (@ tptp.member_complex (@ I B4)) (@ (@ tptp.minus_811609699411566653omplex S2) S5)))) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) S5) (= (@ G A4) tptp.zero_zero_nat))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) T5) (= (@ H2 B4) tptp.zero_zero_nat))) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) S2) (= (@ H2 (@ J A4)) (@ G A4)))) (= (@ (@ tptp.groups5693394587270226106ex_nat G) S2) (@ (@ tptp.groups1935376822645274424al_nat H2) T3)))))))))))))
% 4.96/5.19 (assert (forall ((S5 tptp.set_complex) (T5 tptp.set_complex) (S2 tptp.set_complex) (I (-> tptp.complex tptp.complex)) (J (-> tptp.complex tptp.complex)) (T3 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (H2 (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex S5) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) (@ (@ tptp.minus_811609699411566653omplex S2) S5)) (= (@ I (@ J A4)) A4))) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) (@ (@ tptp.minus_811609699411566653omplex S2) S5)) (@ (@ tptp.member_complex (@ J A4)) (@ (@ tptp.minus_811609699411566653omplex T3) T5)))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex T3) T5)) (= (@ J (@ I B4)) B4))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex T3) T5)) (@ (@ tptp.member_complex (@ I B4)) (@ (@ tptp.minus_811609699411566653omplex S2) S5)))) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) S5) (= (@ G A4) tptp.zero_zero_nat))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) T5) (= (@ H2 B4) tptp.zero_zero_nat))) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) S2) (= (@ H2 (@ J A4)) (@ G A4)))) (= (@ (@ tptp.groups5693394587270226106ex_nat G) S2) (@ (@ tptp.groups5693394587270226106ex_nat H2) T3)))))))))))))
% 4.96/5.19 (assert (forall ((S5 tptp.set_complex) (T5 tptp.set_int) (S2 tptp.set_complex) (I (-> tptp.int tptp.complex)) (J (-> tptp.complex tptp.int)) (T3 tptp.set_int) (G (-> tptp.complex tptp.nat)) (H2 (-> tptp.int tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex S5) (=> (@ tptp.finite_finite_int T5) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) (@ (@ tptp.minus_811609699411566653omplex S2) S5)) (= (@ I (@ J A4)) A4))) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) (@ (@ tptp.minus_811609699411566653omplex S2) S5)) (@ (@ tptp.member_int (@ J A4)) (@ (@ tptp.minus_minus_set_int T3) T5)))) (=> (forall ((B4 tptp.int)) (=> (@ (@ tptp.member_int B4) (@ (@ tptp.minus_minus_set_int T3) T5)) (= (@ J (@ I B4)) B4))) (=> (forall ((B4 tptp.int)) (=> (@ (@ tptp.member_int B4) (@ (@ tptp.minus_minus_set_int T3) T5)) (@ (@ tptp.member_complex (@ I B4)) (@ (@ tptp.minus_811609699411566653omplex S2) S5)))) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) S5) (= (@ G A4) tptp.zero_zero_nat))) (=> (forall ((B4 tptp.int)) (=> (@ (@ tptp.member_int B4) T5) (= (@ H2 B4) tptp.zero_zero_nat))) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) S2) (= (@ H2 (@ J A4)) (@ G A4)))) (= (@ (@ tptp.groups5693394587270226106ex_nat G) S2) (@ (@ tptp.groups4541462559716669496nt_nat H2) T3)))))))))))))
% 4.96/5.19 (assert (forall ((S5 tptp.set_complex) (T5 tptp.set_Extended_enat) (S2 tptp.set_complex) (I (-> tptp.extended_enat tptp.complex)) (J (-> tptp.complex tptp.extended_enat)) (T3 tptp.set_Extended_enat) (G (-> tptp.complex tptp.nat)) (H2 (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex S5) (=> (@ tptp.finite4001608067531595151d_enat T5) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) (@ (@ tptp.minus_811609699411566653omplex S2) S5)) (= (@ I (@ J A4)) A4))) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) (@ (@ tptp.minus_811609699411566653omplex S2) S5)) (@ (@ tptp.member_Extended_enat (@ J A4)) (@ (@ tptp.minus_925952699566721837d_enat T3) T5)))) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) (@ (@ tptp.minus_925952699566721837d_enat T3) T5)) (= (@ J (@ I B4)) B4))) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) (@ (@ tptp.minus_925952699566721837d_enat T3) T5)) (@ (@ tptp.member_complex (@ I B4)) (@ (@ tptp.minus_811609699411566653omplex S2) S5)))) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) S5) (= (@ G A4) tptp.zero_zero_nat))) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) T5) (= (@ H2 B4) tptp.zero_zero_nat))) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) S2) (= (@ H2 (@ J A4)) (@ G A4)))) (= (@ (@ tptp.groups5693394587270226106ex_nat G) S2) (@ (@ tptp.groups2027974829824023292at_nat H2) T3)))))))))))))
% 4.96/5.19 (assert (forall ((S5 tptp.set_int) (T5 tptp.set_real) (S2 tptp.set_int) (I (-> tptp.real tptp.int)) (J (-> tptp.int tptp.real)) (T3 tptp.set_real) (G (-> tptp.int tptp.nat)) (H2 (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_int S5) (=> (@ tptp.finite_finite_real T5) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) (@ (@ tptp.minus_minus_set_int S2) S5)) (= (@ I (@ J A4)) A4))) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) (@ (@ tptp.minus_minus_set_int S2) S5)) (@ (@ tptp.member_real (@ J A4)) (@ (@ tptp.minus_minus_set_real T3) T5)))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real T3) T5)) (= (@ J (@ I B4)) B4))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real T3) T5)) (@ (@ tptp.member_int (@ I B4)) (@ (@ tptp.minus_minus_set_int S2) S5)))) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) S5) (= (@ G A4) tptp.zero_zero_nat))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) T5) (= (@ H2 B4) tptp.zero_zero_nat))) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) S2) (= (@ H2 (@ J A4)) (@ G A4)))) (= (@ (@ tptp.groups4541462559716669496nt_nat G) S2) (@ (@ tptp.groups1935376822645274424al_nat H2) T3)))))))))))))
% 4.96/5.19 (assert (forall ((S5 tptp.set_int) (T5 tptp.set_complex) (S2 tptp.set_int) (I (-> tptp.complex tptp.int)) (J (-> tptp.int tptp.complex)) (T3 tptp.set_complex) (G (-> tptp.int tptp.nat)) (H2 (-> tptp.complex tptp.nat))) (=> (@ tptp.finite_finite_int S5) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) (@ (@ tptp.minus_minus_set_int S2) S5)) (= (@ I (@ J A4)) A4))) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) (@ (@ tptp.minus_minus_set_int S2) S5)) (@ (@ tptp.member_complex (@ J A4)) (@ (@ tptp.minus_811609699411566653omplex T3) T5)))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex T3) T5)) (= (@ J (@ I B4)) B4))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex T3) T5)) (@ (@ tptp.member_int (@ I B4)) (@ (@ tptp.minus_minus_set_int S2) S5)))) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) S5) (= (@ G A4) tptp.zero_zero_nat))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) T5) (= (@ H2 B4) tptp.zero_zero_nat))) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) S2) (= (@ H2 (@ J A4)) (@ G A4)))) (= (@ (@ tptp.groups4541462559716669496nt_nat G) S2) (@ (@ tptp.groups5693394587270226106ex_nat H2) T3)))))))))))))
% 4.96/5.19 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_int (@ tptp.archim8280529875227126926d_real X)) (@ tptp.archim8280529875227126926d_real Y)))))
% 4.96/5.19 (assert (forall ((S tptp.set_real) (F (-> tptp.real tptp.extended_enat)) (I tptp.real)) (=> (@ tptp.finite_finite_real S) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) S) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (=> (= (@ (@ tptp.groups2800946370649118462d_enat F) S) tptp.zero_z5237406670263579293d_enat) (=> (@ (@ tptp.member_real I) S) (= (@ F I) tptp.zero_z5237406670263579293d_enat)))))))
% 4.96/5.19 (assert (forall ((S tptp.set_nat) (F (-> tptp.nat tptp.extended_enat)) (I tptp.nat)) (=> (@ tptp.finite_finite_nat S) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) S) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (=> (= (@ (@ tptp.groups7108830773950497114d_enat F) S) tptp.zero_z5237406670263579293d_enat) (=> (@ (@ tptp.member_nat I) S) (= (@ F I) tptp.zero_z5237406670263579293d_enat)))))))
% 4.96/5.19 (assert (forall ((S tptp.set_complex) (F (-> tptp.complex tptp.extended_enat)) (I tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) S) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (=> (= (@ (@ tptp.groups1752964319039525884d_enat F) S) tptp.zero_z5237406670263579293d_enat) (=> (@ (@ tptp.member_complex I) S) (= (@ F I) tptp.zero_z5237406670263579293d_enat)))))))
% 4.96/5.19 (assert (forall ((S tptp.set_int) (F (-> tptp.int tptp.extended_enat)) (I tptp.int)) (=> (@ tptp.finite_finite_int S) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) S) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (=> (= (@ (@ tptp.groups4225252721152677374d_enat F) S) tptp.zero_z5237406670263579293d_enat) (=> (@ (@ tptp.member_int I) S) (= (@ F I) tptp.zero_z5237406670263579293d_enat)))))))
% 4.96/5.19 (assert (forall ((S tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.extended_enat)) (I tptp.extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat S) (=> (forall ((I4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I4) S) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (=> (= (@ (@ tptp.groups2433450451889696826d_enat F) S) tptp.zero_z5237406670263579293d_enat) (=> (@ (@ tptp.member_Extended_enat I) S) (= (@ F I) tptp.zero_z5237406670263579293d_enat)))))))
% 4.96/5.19 (assert (forall ((S tptp.set_real) (F (-> tptp.real tptp.real)) (I tptp.real)) (=> (@ tptp.finite_finite_real S) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) S) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4)))) (=> (= (@ (@ tptp.groups8097168146408367636l_real F) S) tptp.zero_zero_real) (=> (@ (@ tptp.member_real I) S) (= (@ F I) tptp.zero_zero_real)))))))
% 4.96/5.19 (assert (forall ((S tptp.set_complex) (F (-> tptp.complex tptp.real)) (I tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) S) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4)))) (=> (= (@ (@ tptp.groups5808333547571424918x_real F) S) tptp.zero_zero_real) (=> (@ (@ tptp.member_complex I) S) (= (@ F I) tptp.zero_zero_real)))))))
% 4.96/5.19 (assert (forall ((S tptp.set_int) (F (-> tptp.int tptp.real)) (I tptp.int)) (=> (@ tptp.finite_finite_int S) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) S) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4)))) (=> (= (@ (@ tptp.groups8778361861064173332t_real F) S) tptp.zero_zero_real) (=> (@ (@ tptp.member_int I) S) (= (@ F I) tptp.zero_zero_real)))))))
% 4.96/5.19 (assert (forall ((S tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real)) (I tptp.extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat S) (=> (forall ((I4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I4) S) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4)))) (=> (= (@ (@ tptp.groups4148127829035722712t_real F) S) tptp.zero_zero_real) (=> (@ (@ tptp.member_Extended_enat I) S) (= (@ F I) tptp.zero_zero_real)))))))
% 4.96/5.19 (assert (forall ((S tptp.set_real) (F (-> tptp.real tptp.nat)) (I tptp.real)) (=> (@ tptp.finite_finite_real S) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) S) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I4)))) (=> (= (@ (@ tptp.groups1935376822645274424al_nat F) S) tptp.zero_zero_nat) (=> (@ (@ tptp.member_real I) S) (= (@ F I) tptp.zero_zero_nat)))))))
% 4.96/5.19 (assert (forall ((S tptp.set_real) (F (-> tptp.real tptp.extended_enat)) (B tptp.extended_enat) (I tptp.real)) (=> (@ tptp.finite_finite_real S) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) S) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (=> (= (@ (@ tptp.groups2800946370649118462d_enat F) S) B) (=> (@ (@ tptp.member_real I) S) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F I)) B)))))))
% 4.96/5.19 (assert (forall ((S tptp.set_nat) (F (-> tptp.nat tptp.extended_enat)) (B tptp.extended_enat) (I tptp.nat)) (=> (@ tptp.finite_finite_nat S) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) S) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (=> (= (@ (@ tptp.groups7108830773950497114d_enat F) S) B) (=> (@ (@ tptp.member_nat I) S) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F I)) B)))))))
% 4.96/5.19 (assert (forall ((S tptp.set_complex) (F (-> tptp.complex tptp.extended_enat)) (B tptp.extended_enat) (I tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) S) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (=> (= (@ (@ tptp.groups1752964319039525884d_enat F) S) B) (=> (@ (@ tptp.member_complex I) S) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F I)) B)))))))
% 4.96/5.19 (assert (forall ((S tptp.set_int) (F (-> tptp.int tptp.extended_enat)) (B tptp.extended_enat) (I tptp.int)) (=> (@ tptp.finite_finite_int S) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) S) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (=> (= (@ (@ tptp.groups4225252721152677374d_enat F) S) B) (=> (@ (@ tptp.member_int I) S) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F I)) B)))))))
% 4.96/5.19 (assert (forall ((S tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.extended_enat)) (B tptp.extended_enat) (I tptp.extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat S) (=> (forall ((I4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I4) S) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (=> (= (@ (@ tptp.groups2433450451889696826d_enat F) S) B) (=> (@ (@ tptp.member_Extended_enat I) S) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F I)) B)))))))
% 4.96/5.19 (assert (forall ((S tptp.set_real) (F (-> tptp.real tptp.real)) (B tptp.real) (I tptp.real)) (=> (@ tptp.finite_finite_real S) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) S) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4)))) (=> (= (@ (@ tptp.groups8097168146408367636l_real F) S) B) (=> (@ (@ tptp.member_real I) S) (@ (@ tptp.ord_less_eq_real (@ F I)) B)))))))
% 4.96/5.19 (assert (forall ((S tptp.set_complex) (F (-> tptp.complex tptp.real)) (B tptp.real) (I tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) S) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4)))) (=> (= (@ (@ tptp.groups5808333547571424918x_real F) S) B) (=> (@ (@ tptp.member_complex I) S) (@ (@ tptp.ord_less_eq_real (@ F I)) B)))))))
% 4.96/5.19 (assert (forall ((S tptp.set_int) (F (-> tptp.int tptp.real)) (B tptp.real) (I tptp.int)) (=> (@ tptp.finite_finite_int S) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) S) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4)))) (=> (= (@ (@ tptp.groups8778361861064173332t_real F) S) B) (=> (@ (@ tptp.member_int I) S) (@ (@ tptp.ord_less_eq_real (@ F I)) B)))))))
% 4.96/5.19 (assert (forall ((S tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real)) (B tptp.real) (I tptp.extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat S) (=> (forall ((I4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I4) S) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4)))) (=> (= (@ (@ tptp.groups4148127829035722712t_real F) S) B) (=> (@ (@ tptp.member_Extended_enat I) S) (@ (@ tptp.ord_less_eq_real (@ F I)) B)))))))
% 4.96/5.19 (assert (forall ((S tptp.set_real) (F (-> tptp.real tptp.nat)) (B tptp.nat) (I tptp.real)) (=> (@ tptp.finite_finite_real S) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) S) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I4)))) (=> (= (@ (@ tptp.groups1935376822645274424al_nat F) S) B) (=> (@ (@ tptp.member_real I) S) (@ (@ tptp.ord_less_eq_nat (@ F I)) B)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat G))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ tptp.collect_real (lambda ((X4 tptp.real)) (= (@ G X4) tptp.zero_zero_nat))))) (@ _let_1 A2))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (= (@ G X4) tptp.zero_zero_nat))))) (@ _let_1 A2))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ tptp.collect_int (lambda ((X4 tptp.int)) (= (@ G X4) tptp.zero_zero_nat))))) (@ _let_1 A2))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2027974829824023292at_nat G))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (= (@ G X4) tptp.zero_zero_nat))))) (@ _let_1 A2))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real G))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ tptp.collect_real (lambda ((X4 tptp.real)) (= (@ G X4) tptp.zero_zero_real))))) (@ _let_1 A2))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (= (@ G X4) tptp.zero_zero_real))))) (@ _let_1 A2))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ tptp.collect_int (lambda ((X4 tptp.int)) (= (@ G X4) tptp.zero_zero_real))))) (@ _let_1 A2))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups4148127829035722712t_real G))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (= (@ G X4) tptp.zero_zero_real))))) (@ _let_1 A2))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int G))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ tptp.collect_real (lambda ((X4 tptp.real)) (= (@ G X4) tptp.zero_zero_int))))) (@ _let_1 A2))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (= (@ G X4) tptp.zero_zero_int))))) (@ _let_1 A2))))))
% 4.96/5.19 (assert (forall ((I6 tptp.set_real) (I tptp.real) (F (-> tptp.real tptp.extended_enat))) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat))) (=> (@ tptp.finite_finite_real I6) (=> (@ (@ tptp.member_real I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups2800946370649118462d_enat F) I6)))))))))
% 4.96/5.19 (assert (forall ((I6 tptp.set_nat) (I tptp.nat) (F (-> tptp.nat tptp.extended_enat))) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat))) (=> (@ tptp.finite_finite_nat I6) (=> (@ (@ tptp.member_nat I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups7108830773950497114d_enat F) I6)))))))))
% 4.96/5.19 (assert (forall ((I6 tptp.set_complex) (I tptp.complex) (F (-> tptp.complex tptp.extended_enat))) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (@ (@ tptp.member_complex I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups1752964319039525884d_enat F) I6)))))))))
% 4.96/5.19 (assert (forall ((I6 tptp.set_int) (I tptp.int) (F (-> tptp.int tptp.extended_enat))) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat))) (=> (@ tptp.finite_finite_int I6) (=> (@ (@ tptp.member_int I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups4225252721152677374d_enat F) I6)))))))))
% 4.96/5.19 (assert (forall ((I6 tptp.set_Extended_enat) (I tptp.extended_enat) (F (-> tptp.extended_enat tptp.extended_enat))) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat))) (=> (@ tptp.finite4001608067531595151d_enat I6) (=> (@ (@ tptp.member_Extended_enat I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I4) I6) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups2433450451889696826d_enat F) I6)))))))))
% 4.96/5.19 (assert (forall ((I6 tptp.set_real) (I tptp.real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.finite_finite_real I6) (=> (@ (@ tptp.member_real I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups8097168146408367636l_real F) I6)))))))))
% 4.96/5.19 (assert (forall ((I6 tptp.set_complex) (I tptp.complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (@ (@ tptp.member_complex I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups5808333547571424918x_real F) I6)))))))))
% 4.96/5.19 (assert (forall ((I6 tptp.set_int) (I tptp.int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.finite_finite_int I6) (=> (@ (@ tptp.member_int I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups8778361861064173332t_real F) I6)))))))))
% 4.96/5.19 (assert (forall ((I6 tptp.set_Extended_enat) (I tptp.extended_enat) (F (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.finite4001608067531595151d_enat I6) (=> (@ (@ tptp.member_Extended_enat I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I4) I6) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups4148127829035722712t_real F) I6)))))))))
% 4.96/5.19 (assert (forall ((I6 tptp.set_real) (I tptp.real) (F (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ tptp.finite_finite_real I6) (=> (@ (@ tptp.member_real I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups1935376822645274424al_nat F) I6)))))))))
% 4.96/5.19 (assert (forall ((I6 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (not (= I6 tptp.bot_bot_set_complex)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I4)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups5693394587270226106ex_nat F) I6)))))))
% 4.96/5.19 (assert (forall ((I6 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat I6) (=> (not (= I6 tptp.bot_bo7653980558646680370d_enat)) (=> (forall ((I4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I4) I6) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I4)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups2027974829824023292at_nat F) I6)))))))
% 4.96/5.19 (assert (forall ((I6 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real I6) (=> (not (= I6 tptp.bot_bot_set_real)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I4)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups1935376822645274424al_nat F) I6)))))))
% 4.96/5.19 (assert (forall ((I6 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int I6) (=> (not (= I6 tptp.bot_bot_set_int)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I4)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups4541462559716669496nt_nat F) I6)))))))
% 4.96/5.19 (assert (forall ((I6 tptp.set_complex) (F (-> tptp.complex tptp.extended_enat))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (not (= I6 tptp.bot_bot_set_complex)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.groups1752964319039525884d_enat F) I6)))))))
% 4.96/5.19 (assert (forall ((I6 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.extended_enat))) (=> (@ tptp.finite4001608067531595151d_enat I6) (=> (not (= I6 tptp.bot_bo7653980558646680370d_enat)) (=> (forall ((I4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I4) I6) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.groups2433450451889696826d_enat F) I6)))))))
% 4.96/5.19 (assert (forall ((I6 tptp.set_real) (F (-> tptp.real tptp.extended_enat))) (=> (@ tptp.finite_finite_real I6) (=> (not (= I6 tptp.bot_bot_set_real)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.groups2800946370649118462d_enat F) I6)))))))
% 4.96/5.19 (assert (forall ((I6 tptp.set_nat) (F (-> tptp.nat tptp.extended_enat))) (=> (@ tptp.finite_finite_nat I6) (=> (not (= I6 tptp.bot_bot_set_nat)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.groups7108830773950497114d_enat F) I6)))))))
% 4.96/5.19 (assert (forall ((I6 tptp.set_int) (F (-> tptp.int tptp.extended_enat))) (=> (@ tptp.finite_finite_int I6) (=> (not (= I6 tptp.bot_bot_set_int)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.groups4225252721152677374d_enat F) I6)))))))
% 4.96/5.19 (assert (forall ((I6 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (not (= I6 tptp.bot_bot_set_complex)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I4)))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.groups5808333547571424918x_real F) I6)))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_real) (S2 tptp.set_real) (G (-> tptp.real tptp.nat)) (H2 (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S2) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S2)) (= (@ G X5) tptp.zero_zero_nat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups1935376822645274424al_nat G) T3) (@ (@ tptp.groups1935376822645274424al_nat H2) S2))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (H2 (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X5) tptp.zero_zero_nat))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups5693394587270226106ex_nat G) T3) (@ (@ tptp.groups5693394587270226106ex_nat H2) S2))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.nat)) (H2 (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G X5) tptp.zero_zero_nat))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups2027974829824023292at_nat G) T3) (@ (@ tptp.groups2027974829824023292at_nat H2) S2))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_real) (S2 tptp.set_real) (G (-> tptp.real tptp.real)) (H2 (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S2) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S2)) (= (@ G X5) tptp.zero_zero_real))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups8097168146408367636l_real G) T3) (@ (@ tptp.groups8097168146408367636l_real H2) S2))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.real)) (H2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X5) tptp.zero_zero_real))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups5808333547571424918x_real G) T3) (@ (@ tptp.groups5808333547571424918x_real H2) S2))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.real)) (H2 (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G X5) tptp.zero_zero_real))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups4148127829035722712t_real G) T3) (@ (@ tptp.groups4148127829035722712t_real H2) S2))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_real) (S2 tptp.set_real) (G (-> tptp.real tptp.int)) (H2 (-> tptp.real tptp.int))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S2) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S2)) (= (@ G X5) tptp.zero_zero_int))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups1932886352136224148al_int G) T3) (@ (@ tptp.groups1932886352136224148al_int H2) S2))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.int)) (H2 (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X5) tptp.zero_zero_int))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups5690904116761175830ex_int G) T3) (@ (@ tptp.groups5690904116761175830ex_int H2) S2))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.int)) (H2 (-> tptp.extended_enat tptp.int))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G X5) tptp.zero_zero_int))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups2025484359314973016at_int G) T3) (@ (@ tptp.groups2025484359314973016at_int H2) S2))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_real) (S2 tptp.set_real) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S2) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S2)) (= (@ G X5) tptp.zero_zero_complex))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups5754745047067104278omplex G) T3) (@ (@ tptp.groups5754745047067104278omplex H2) S2))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_real) (S2 tptp.set_real) (H2 (-> tptp.real tptp.nat)) (G (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S2) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S2)) (= (@ H2 X5) tptp.zero_zero_nat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups1935376822645274424al_nat G) S2) (@ (@ tptp.groups1935376822645274424al_nat H2) T3))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (H2 (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ H2 X5) tptp.zero_zero_nat))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups5693394587270226106ex_nat G) S2) (@ (@ tptp.groups5693394587270226106ex_nat H2) T3))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (H2 (-> tptp.extended_enat tptp.nat)) (G (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ H2 X5) tptp.zero_zero_nat))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups2027974829824023292at_nat G) S2) (@ (@ tptp.groups2027974829824023292at_nat H2) T3))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_real) (S2 tptp.set_real) (H2 (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S2) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S2)) (= (@ H2 X5) tptp.zero_zero_real))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups8097168146408367636l_real G) S2) (@ (@ tptp.groups8097168146408367636l_real H2) T3))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (H2 (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ H2 X5) tptp.zero_zero_real))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups5808333547571424918x_real G) S2) (@ (@ tptp.groups5808333547571424918x_real H2) T3))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (H2 (-> tptp.extended_enat tptp.real)) (G (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ H2 X5) tptp.zero_zero_real))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups4148127829035722712t_real G) S2) (@ (@ tptp.groups4148127829035722712t_real H2) T3))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_real) (S2 tptp.set_real) (H2 (-> tptp.real tptp.int)) (G (-> tptp.real tptp.int))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S2) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S2)) (= (@ H2 X5) tptp.zero_zero_int))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups1932886352136224148al_int G) S2) (@ (@ tptp.groups1932886352136224148al_int H2) T3))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (H2 (-> tptp.complex tptp.int)) (G (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ H2 X5) tptp.zero_zero_int))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups5690904116761175830ex_int G) S2) (@ (@ tptp.groups5690904116761175830ex_int H2) T3))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (H2 (-> tptp.extended_enat tptp.int)) (G (-> tptp.extended_enat tptp.int))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ H2 X5) tptp.zero_zero_int))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups2025484359314973016at_int G) S2) (@ (@ tptp.groups2025484359314973016at_int H2) T3))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_real) (S2 tptp.set_real) (H2 (-> tptp.real tptp.complex)) (G (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S2) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S2)) (= (@ H2 X5) tptp.zero_zero_complex))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups5754745047067104278omplex G) S2) (@ (@ tptp.groups5754745047067104278omplex H2) T3))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X5) tptp.zero_zero_nat))) (= (@ _let_1 T3) (@ _let_1 S2))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2027974829824023292at_nat G))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G X5) tptp.zero_zero_nat))) (= (@ _let_1 T3) (@ _let_1 S2))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X5) tptp.zero_zero_real))) (= (@ _let_1 T3) (@ _let_1 S2))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups4148127829035722712t_real G))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G X5) tptp.zero_zero_real))) (= (@ _let_1 T3) (@ _let_1 S2))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X5) tptp.zero_zero_int))) (= (@ _let_1 T3) (@ _let_1 S2))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2025484359314973016at_int G))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G X5) tptp.zero_zero_int))) (= (@ _let_1 T3) (@ _let_1 S2))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.complex))) (let ((_let_1 (@ tptp.groups6818542070133387226omplex G))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G X5) tptp.zero_zero_complex))) (= (@ _let_1 T3) (@ _let_1 S2))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.extended_enat))) (let ((_let_1 (@ tptp.groups1752964319039525884d_enat G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X5) tptp.zero_z5237406670263579293d_enat))) (= (@ _let_1 T3) (@ _let_1 S2))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.extended_enat))) (let ((_let_1 (@ tptp.groups2433450451889696826d_enat G))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G X5) tptp.zero_z5237406670263579293d_enat))) (= (@ _let_1 T3) (@ _let_1 S2))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_nat) (S2 tptp.set_nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ tptp.finite_finite_nat T3) (=> (@ (@ tptp.ord_less_eq_set_nat S2) T3) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) (@ (@ tptp.minus_minus_set_nat T3) S2)) (= (@ G X5) tptp.zero_zero_int))) (= (@ _let_1 T3) (@ _let_1 S2))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X5) tptp.zero_zero_nat))) (= (@ _let_1 S2) (@ _let_1 T3))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2027974829824023292at_nat G))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G X5) tptp.zero_zero_nat))) (= (@ _let_1 S2) (@ _let_1 T3))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X5) tptp.zero_zero_real))) (= (@ _let_1 S2) (@ _let_1 T3))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups4148127829035722712t_real G))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G X5) tptp.zero_zero_real))) (= (@ _let_1 S2) (@ _let_1 T3))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X5) tptp.zero_zero_int))) (= (@ _let_1 S2) (@ _let_1 T3))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2025484359314973016at_int G))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G X5) tptp.zero_zero_int))) (= (@ _let_1 S2) (@ _let_1 T3))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.complex))) (let ((_let_1 (@ tptp.groups6818542070133387226omplex G))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G X5) tptp.zero_zero_complex))) (= (@ _let_1 S2) (@ _let_1 T3))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.extended_enat))) (let ((_let_1 (@ tptp.groups1752964319039525884d_enat G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X5) tptp.zero_z5237406670263579293d_enat))) (= (@ _let_1 S2) (@ _let_1 T3))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.extended_enat))) (let ((_let_1 (@ tptp.groups2433450451889696826d_enat G))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G X5) tptp.zero_z5237406670263579293d_enat))) (= (@ _let_1 S2) (@ _let_1 T3))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_nat) (S2 tptp.set_nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ tptp.finite_finite_nat T3) (=> (@ (@ tptp.ord_less_eq_set_nat S2) T3) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) (@ (@ tptp.minus_minus_set_nat T3) S2)) (= (@ G X5) tptp.zero_zero_int))) (= (@ _let_1 S2) (@ _let_1 T3))))))))
% 4.96/5.19 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B tptp.set_real) (G (-> tptp.real tptp.nat)) (H2 (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat H2))) (let ((_let_2 (@ tptp.groups1935376822645274424al_nat G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B) C4) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A4) tptp.zero_zero_nat))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real C4) B)) (= (@ H2 B4) tptp.zero_zero_nat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B))))))))))))
% 4.96/5.19 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B tptp.set_complex) (G (-> tptp.complex tptp.nat)) (H2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat H2))) (let ((_let_2 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B) C4) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A4) tptp.zero_zero_nat))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex C4) B)) (= (@ H2 B4) tptp.zero_zero_nat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B))))))))))))
% 4.96/5.19 (assert (forall ((C4 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.nat)) (H2 (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2027974829824023292at_nat H2))) (let ((_let_2 (@ tptp.groups2027974829824023292at_nat G))) (=> (@ tptp.finite4001608067531595151d_enat C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B) C4) (=> (forall ((A4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A4) (@ (@ tptp.minus_925952699566721837d_enat C4) A2)) (= (@ G A4) tptp.zero_zero_nat))) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) (@ (@ tptp.minus_925952699566721837d_enat C4) B)) (= (@ H2 B4) tptp.zero_zero_nat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B))))))))))))
% 4.96/5.19 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B tptp.set_real) (G (-> tptp.real tptp.real)) (H2 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real H2))) (let ((_let_2 (@ tptp.groups8097168146408367636l_real G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B) C4) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A4) tptp.zero_zero_real))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real C4) B)) (= (@ H2 B4) tptp.zero_zero_real))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B))))))))))))
% 4.96/5.19 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B tptp.set_complex) (G (-> tptp.complex tptp.real)) (H2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real H2))) (let ((_let_2 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B) C4) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A4) tptp.zero_zero_real))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex C4) B)) (= (@ H2 B4) tptp.zero_zero_real))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B))))))))))))
% 4.96/5.19 (assert (forall ((C4 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.real)) (H2 (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups4148127829035722712t_real H2))) (let ((_let_2 (@ tptp.groups4148127829035722712t_real G))) (=> (@ tptp.finite4001608067531595151d_enat C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B) C4) (=> (forall ((A4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A4) (@ (@ tptp.minus_925952699566721837d_enat C4) A2)) (= (@ G A4) tptp.zero_zero_real))) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) (@ (@ tptp.minus_925952699566721837d_enat C4) B)) (= (@ H2 B4) tptp.zero_zero_real))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B))))))))))))
% 4.96/5.19 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B tptp.set_real) (G (-> tptp.real tptp.int)) (H2 (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int H2))) (let ((_let_2 (@ tptp.groups1932886352136224148al_int G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B) C4) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A4) tptp.zero_zero_int))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real C4) B)) (= (@ H2 B4) tptp.zero_zero_int))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B))))))))))))
% 4.96/5.19 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B tptp.set_complex) (G (-> tptp.complex tptp.int)) (H2 (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int H2))) (let ((_let_2 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B) C4) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A4) tptp.zero_zero_int))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex C4) B)) (= (@ H2 B4) tptp.zero_zero_int))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B))))))))))))
% 4.96/5.19 (assert (forall ((C4 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.int)) (H2 (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2025484359314973016at_int H2))) (let ((_let_2 (@ tptp.groups2025484359314973016at_int G))) (=> (@ tptp.finite4001608067531595151d_enat C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B) C4) (=> (forall ((A4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A4) (@ (@ tptp.minus_925952699566721837d_enat C4) A2)) (= (@ G A4) tptp.zero_zero_int))) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) (@ (@ tptp.minus_925952699566721837d_enat C4) B)) (= (@ H2 B4) tptp.zero_zero_int))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B))))))))))))
% 4.96/5.19 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B tptp.set_real) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups5754745047067104278omplex H2))) (let ((_let_2 (@ tptp.groups5754745047067104278omplex G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B) C4) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A4) tptp.zero_zero_complex))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real C4) B)) (= (@ H2 B4) tptp.zero_zero_complex))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B))))))))))))
% 4.96/5.19 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B tptp.set_real) (G (-> tptp.real tptp.nat)) (H2 (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat H2))) (let ((_let_2 (@ tptp.groups1935376822645274424al_nat G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B) C4) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A4) tptp.zero_zero_nat))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real C4) B)) (= (@ H2 B4) tptp.zero_zero_nat))) (= (= (@ _let_2 A2) (@ _let_1 B)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 4.96/5.19 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B tptp.set_complex) (G (-> tptp.complex tptp.nat)) (H2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat H2))) (let ((_let_2 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B) C4) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A4) tptp.zero_zero_nat))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex C4) B)) (= (@ H2 B4) tptp.zero_zero_nat))) (= (= (@ _let_2 A2) (@ _let_1 B)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 4.96/5.19 (assert (forall ((C4 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.nat)) (H2 (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2027974829824023292at_nat H2))) (let ((_let_2 (@ tptp.groups2027974829824023292at_nat G))) (=> (@ tptp.finite4001608067531595151d_enat C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B) C4) (=> (forall ((A4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A4) (@ (@ tptp.minus_925952699566721837d_enat C4) A2)) (= (@ G A4) tptp.zero_zero_nat))) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) (@ (@ tptp.minus_925952699566721837d_enat C4) B)) (= (@ H2 B4) tptp.zero_zero_nat))) (= (= (@ _let_2 A2) (@ _let_1 B)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 4.96/5.19 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B tptp.set_real) (G (-> tptp.real tptp.real)) (H2 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real H2))) (let ((_let_2 (@ tptp.groups8097168146408367636l_real G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B) C4) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A4) tptp.zero_zero_real))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real C4) B)) (= (@ H2 B4) tptp.zero_zero_real))) (= (= (@ _let_2 A2) (@ _let_1 B)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 4.96/5.19 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B tptp.set_complex) (G (-> tptp.complex tptp.real)) (H2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real H2))) (let ((_let_2 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B) C4) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A4) tptp.zero_zero_real))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex C4) B)) (= (@ H2 B4) tptp.zero_zero_real))) (= (= (@ _let_2 A2) (@ _let_1 B)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 4.96/5.19 (assert (forall ((C4 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.real)) (H2 (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups4148127829035722712t_real H2))) (let ((_let_2 (@ tptp.groups4148127829035722712t_real G))) (=> (@ tptp.finite4001608067531595151d_enat C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B) C4) (=> (forall ((A4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A4) (@ (@ tptp.minus_925952699566721837d_enat C4) A2)) (= (@ G A4) tptp.zero_zero_real))) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) (@ (@ tptp.minus_925952699566721837d_enat C4) B)) (= (@ H2 B4) tptp.zero_zero_real))) (= (= (@ _let_2 A2) (@ _let_1 B)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 4.96/5.19 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B tptp.set_real) (G (-> tptp.real tptp.int)) (H2 (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int H2))) (let ((_let_2 (@ tptp.groups1932886352136224148al_int G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B) C4) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A4) tptp.zero_zero_int))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real C4) B)) (= (@ H2 B4) tptp.zero_zero_int))) (= (= (@ _let_2 A2) (@ _let_1 B)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 4.96/5.19 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B tptp.set_complex) (G (-> tptp.complex tptp.int)) (H2 (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int H2))) (let ((_let_2 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B) C4) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A4) tptp.zero_zero_int))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex C4) B)) (= (@ H2 B4) tptp.zero_zero_int))) (= (= (@ _let_2 A2) (@ _let_1 B)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 4.96/5.19 (assert (forall ((C4 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.int)) (H2 (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2025484359314973016at_int H2))) (let ((_let_2 (@ tptp.groups2025484359314973016at_int G))) (=> (@ tptp.finite4001608067531595151d_enat C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B) C4) (=> (forall ((A4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A4) (@ (@ tptp.minus_925952699566721837d_enat C4) A2)) (= (@ G A4) tptp.zero_zero_int))) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) (@ (@ tptp.minus_925952699566721837d_enat C4) B)) (= (@ H2 B4) tptp.zero_zero_int))) (= (= (@ _let_2 A2) (@ _let_1 B)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 4.96/5.19 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B tptp.set_real) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups5754745047067104278omplex H2))) (let ((_let_2 (@ tptp.groups5754745047067104278omplex G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B) C4) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A4) tptp.zero_zero_complex))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real C4) B)) (= (@ H2 B4) tptp.zero_zero_complex))) (= (= (@ _let_2 A2) (@ _let_1 B)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B))) (@ _let_1 B))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2027974829824023292at_nat G))) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B) A2) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) B))) (@ _let_1 B))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B))) (@ _let_1 B))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2025484359314973016at_int G))) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B) A2) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) B))) (@ _let_1 B))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B))) (@ _let_1 B))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups4148127829035722712t_real G))) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B) A2) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) B))) (@ _let_1 B))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.extended_enat))) (let ((_let_1 (@ tptp.groups1752964319039525884d_enat G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.plus_p3455044024723400733d_enat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B))) (@ _let_1 B))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.extended_enat))) (let ((_let_1 (@ tptp.groups2433450451889696826d_enat G))) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B) A2) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_1 A2) (@ (@ tptp.plus_p3455044024723400733d_enat (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) B))) (@ _let_1 B))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_nat) (A2 tptp.set_nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ (@ tptp.ord_less_eq_set_nat B) A2) (=> (@ tptp.finite_finite_nat A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B))) (@ _let_1 B))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_nat) (A2 tptp.set_nat) (G (-> tptp.nat tptp.extended_enat))) (let ((_let_1 (@ tptp.groups7108830773950497114d_enat G))) (=> (@ (@ tptp.ord_less_eq_set_nat B) A2) (=> (@ tptp.finite_finite_nat A2) (= (@ _let_1 A2) (@ (@ tptp.plus_p3455044024723400733d_enat (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B))) (@ _let_1 B))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (B tptp.set_complex) (F (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int F))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.ord_le211207098394363844omplex B) A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B)) (@ (@ tptp.minus_minus_int (@ _let_1 A2)) (@ _let_1 B))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2025484359314973016at_int F))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B) A2) (= (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) B)) (@ (@ tptp.minus_minus_int (@ _let_1 A2)) (@ _let_1 B))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (B tptp.set_complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real F))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.ord_le211207098394363844omplex B) A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B)) (@ (@ tptp.minus_minus_real (@ _let_1 A2)) (@ _let_1 B))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups4148127829035722712t_real F))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B) A2) (= (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) B)) (@ (@ tptp.minus_minus_real (@ _let_1 A2)) (@ _let_1 B))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int F))) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.ord_less_eq_set_nat B) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B)) (@ (@ tptp.minus_minus_int (@ _let_1 A2)) (@ _let_1 B))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (B tptp.set_int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real F))) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.ord_less_eq_set_int B) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B)) (@ (@ tptp.minus_minus_real (@ _let_1 A2)) (@ _let_1 B))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (B tptp.set_int) (F (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.groups4538972089207619220nt_int F))) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.ord_less_eq_set_int B) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B)) (@ (@ tptp.minus_minus_int (@ _let_1 A2)) (@ _let_1 B))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (B tptp.set_complex) (F (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups7754918857620584856omplex F))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.ord_le211207098394363844omplex B) A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B)) (@ (@ tptp.minus_minus_complex (@ _let_1 A2)) (@ _let_1 B))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups6591440286371151544t_real F))) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.ord_less_eq_set_nat B) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B)) (@ (@ tptp.minus_minus_real (@ _let_1 A2)) (@ _let_1 B))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.extended_enat))) (let ((_let_1 (@ tptp.groups2800946370649118462d_enat F))) (=> (@ tptp.finite_finite_real B) (=> (@ (@ tptp.ord_less_eq_set_real A2) B) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real B) A2)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F B4)))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ _let_1 A2)) (@ _let_1 B))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.extended_enat))) (let ((_let_1 (@ tptp.groups1752964319039525884d_enat F))) (=> (@ tptp.finite3207457112153483333omplex B) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex B) A2)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F B4)))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ _let_1 A2)) (@ _let_1 B))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.extended_enat))) (let ((_let_1 (@ tptp.groups2433450451889696826d_enat F))) (=> (@ tptp.finite4001608067531595151d_enat B) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) B) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) (@ (@ tptp.minus_925952699566721837d_enat B) A2)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F B4)))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ _let_1 A2)) (@ _let_1 B))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real F))) (=> (@ tptp.finite_finite_real B) (=> (@ (@ tptp.ord_less_eq_set_real A2) B) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real B) A2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F B4)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real F))) (=> (@ tptp.finite3207457112153483333omplex B) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex B) A2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F B4)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups4148127829035722712t_real F))) (=> (@ tptp.finite4001608067531595151d_enat B) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) B) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) (@ (@ tptp.minus_925952699566721837d_enat B) A2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F B4)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat F))) (=> (@ tptp.finite_finite_real B) (=> (@ (@ tptp.ord_less_eq_set_real A2) B) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real B) A2)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F B4)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat F))) (=> (@ tptp.finite3207457112153483333omplex B) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex B) A2)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F B4)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2027974829824023292at_nat F))) (=> (@ tptp.finite4001608067531595151d_enat B) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) B) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) (@ (@ tptp.minus_925952699566721837d_enat B) A2)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F B4)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int F))) (=> (@ tptp.finite_finite_real B) (=> (@ (@ tptp.ord_less_eq_set_real A2) B) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real B) A2)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F B4)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_int (@ G X)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_real (@ G X)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.extended_enat))) (let ((_let_1 (@ tptp.groups1752964319039525884d_enat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_p3455044024723400733d_enat (@ G X)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (X tptp.extended_enat) (G (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2027974829824023292at_nat G))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ (@ tptp.member_Extended_enat X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ (@ tptp.insert_Extended_enat X) tptp.bot_bo7653980558646680370d_enat))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (X tptp.extended_enat) (G (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2025484359314973016at_int G))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ (@ tptp.member_Extended_enat X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_int (@ G X)) (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ (@ tptp.insert_Extended_enat X) tptp.bot_bo7653980558646680370d_enat))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (X tptp.extended_enat) (G (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups4148127829035722712t_real G))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ (@ tptp.member_Extended_enat X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_real (@ G X)) (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ (@ tptp.insert_Extended_enat X) tptp.bot_bo7653980558646680370d_enat))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (X tptp.extended_enat) (G (-> tptp.extended_enat tptp.extended_enat))) (let ((_let_1 (@ tptp.groups2433450451889696826d_enat G))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ (@ tptp.member_Extended_enat X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_p3455044024723400733d_enat (@ G X)) (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ (@ tptp.insert_Extended_enat X) tptp.bot_bo7653980558646680370d_enat))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat G))) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int G))) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_int (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (X tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X))) (let ((_let_2 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_1 tptp.bot_bot_set_complex))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.int)) (X tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X))) (let ((_let_2 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_int (@ G X)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_1 tptp.bot_bot_set_complex))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.real)) (X tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X))) (let ((_let_2 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_real (@ G X)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_1 tptp.bot_bot_set_complex))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.extended_enat)) (X tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X))) (let ((_let_2 (@ tptp.groups1752964319039525884d_enat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ G X)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_1 tptp.bot_bot_set_complex))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.nat)) (X tptp.extended_enat)) (let ((_let_1 (@ tptp.insert_Extended_enat X))) (let ((_let_2 (@ tptp.groups2027974829824023292at_nat G))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_2 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ _let_1 tptp.bot_bo7653980558646680370d_enat))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.int)) (X tptp.extended_enat)) (let ((_let_1 (@ tptp.insert_Extended_enat X))) (let ((_let_2 (@ tptp.groups2025484359314973016at_int G))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_int (@ G X)) (@ _let_2 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ _let_1 tptp.bot_bo7653980558646680370d_enat))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.real)) (X tptp.extended_enat)) (let ((_let_1 (@ tptp.insert_Extended_enat X))) (let ((_let_2 (@ tptp.groups4148127829035722712t_real G))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_real (@ G X)) (@ _let_2 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ _let_1 tptp.bot_bo7653980558646680370d_enat))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.extended_enat)) (X tptp.extended_enat)) (let ((_let_1 (@ tptp.insert_Extended_enat X))) (let ((_let_2 (@ tptp.groups2433450451889696826d_enat G))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ G X)) (@ _let_2 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ _let_1 tptp.bot_bo7653980558646680370d_enat))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.nat)) (X tptp.real)) (let ((_let_1 (@ tptp.insert_real X))) (let ((_let_2 (@ tptp.groups1935376822645274424al_nat G))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_real A2) (@ _let_1 tptp.bot_bot_set_real))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.int)) (X tptp.real)) (let ((_let_1 (@ tptp.insert_real X))) (let ((_let_2 (@ tptp.groups1932886352136224148al_int G))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_int (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_real A2) (@ _let_1 tptp.bot_bot_set_real))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (A tptp.complex) (F (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_4 (@ (@ tptp.member_complex A) A2))) (=> (@ tptp.finite3207457112153483333omplex A2) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_int _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (A tptp.extended_enat) (F (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2025484359314973016at_int F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat))))) (let ((_let_4 (@ (@ tptp.member_Extended_enat A) A2))) (=> (@ tptp.finite4001608067531595151d_enat A2) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_int _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (A tptp.real) (F (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_4 (@ (@ tptp.member_real A) A2))) (=> (@ tptp.finite_finite_real A2) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_int _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (A tptp.complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_4 (@ (@ tptp.member_complex A) A2))) (=> (@ tptp.finite3207457112153483333omplex A2) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_real _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (A tptp.extended_enat) (F (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups4148127829035722712t_real F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat))))) (let ((_let_4 (@ (@ tptp.member_Extended_enat A) A2))) (=> (@ tptp.finite4001608067531595151d_enat A2) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_real _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (A tptp.real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_4 (@ (@ tptp.member_real A) A2))) (=> (@ tptp.finite_finite_real A2) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_real _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (A tptp.int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_4 (@ (@ tptp.member_int A) A2))) (=> (@ tptp.finite_finite_int A2) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_real _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (A tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))) (let ((_let_4 (@ (@ tptp.member_nat A) A2))) (=> (@ tptp.finite_finite_nat A2) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_int _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (A tptp.int) (F (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.groups4538972089207619220nt_int F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_4 (@ (@ tptp.member_int A) A2))) (=> (@ tptp.finite_finite_int A2) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_int _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (A tptp.complex) (F (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups7754918857620584856omplex F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_4 (@ (@ tptp.member_complex A) A2))) (=> (@ tptp.finite3207457112153483333omplex A2) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_complex _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_complex) (A tptp.complex) (B2 (-> tptp.complex tptp.nat)) (C (-> tptp.complex tptp.nat))) (let ((_let_1 (@ (@ tptp.groups5693394587270226106ex_nat C) (@ (@ tptp.minus_811609699411566653omplex S2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_2 (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) (@ (@ tptp.plus_plus_nat (@ B2 A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) _let_1))))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_complex) (A tptp.complex) (B2 (-> tptp.complex tptp.int)) (C (-> tptp.complex tptp.int))) (let ((_let_1 (@ (@ tptp.groups5690904116761175830ex_int C) (@ (@ tptp.minus_811609699411566653omplex S2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_2 (= (@ (@ tptp.groups5690904116761175830ex_int (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) (@ (@ tptp.plus_plus_int (@ B2 A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups5690904116761175830ex_int (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) _let_1))))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_complex) (A tptp.complex) (B2 (-> tptp.complex tptp.real)) (C (-> tptp.complex tptp.real))) (let ((_let_1 (@ (@ tptp.groups5808333547571424918x_real C) (@ (@ tptp.minus_811609699411566653omplex S2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_2 (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) (@ (@ tptp.plus_plus_real (@ B2 A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) _let_1))))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_complex) (A tptp.complex) (B2 (-> tptp.complex tptp.extended_enat)) (C (-> tptp.complex tptp.extended_enat))) (let ((_let_1 (@ (@ tptp.groups1752964319039525884d_enat C) (@ (@ tptp.minus_811609699411566653omplex S2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_2 (= (@ (@ tptp.groups1752964319039525884d_enat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_Extended_enat (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) (@ (@ tptp.plus_p3455044024723400733d_enat (@ B2 A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups1752964319039525884d_enat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_Extended_enat (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) _let_1))))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_Extended_enat) (A tptp.extended_enat) (B2 (-> tptp.extended_enat tptp.nat)) (C (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ (@ tptp.groups2027974829824023292at_nat C) (@ (@ tptp.minus_925952699566721837d_enat S2) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat))))) (let ((_let_2 (@ (@ tptp.member_Extended_enat A) S2))) (=> (@ tptp.finite4001608067531595151d_enat S2) (and (=> _let_2 (= (@ (@ tptp.groups2027974829824023292at_nat (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) (@ (@ tptp.plus_plus_nat (@ B2 A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups2027974829824023292at_nat (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) _let_1))))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_Extended_enat) (A tptp.extended_enat) (B2 (-> tptp.extended_enat tptp.int)) (C (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ (@ tptp.groups2025484359314973016at_int C) (@ (@ tptp.minus_925952699566721837d_enat S2) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat))))) (let ((_let_2 (@ (@ tptp.member_Extended_enat A) S2))) (=> (@ tptp.finite4001608067531595151d_enat S2) (and (=> _let_2 (= (@ (@ tptp.groups2025484359314973016at_int (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) (@ (@ tptp.plus_plus_int (@ B2 A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups2025484359314973016at_int (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) _let_1))))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_Extended_enat) (A tptp.extended_enat) (B2 (-> tptp.extended_enat tptp.real)) (C (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ (@ tptp.groups4148127829035722712t_real C) (@ (@ tptp.minus_925952699566721837d_enat S2) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat))))) (let ((_let_2 (@ (@ tptp.member_Extended_enat A) S2))) (=> (@ tptp.finite4001608067531595151d_enat S2) (and (=> _let_2 (= (@ (@ tptp.groups4148127829035722712t_real (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) (@ (@ tptp.plus_plus_real (@ B2 A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups4148127829035722712t_real (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) _let_1))))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_Extended_enat) (A tptp.extended_enat) (B2 (-> tptp.extended_enat tptp.extended_enat)) (C (-> tptp.extended_enat tptp.extended_enat))) (let ((_let_1 (@ (@ tptp.groups2433450451889696826d_enat C) (@ (@ tptp.minus_925952699566721837d_enat S2) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat))))) (let ((_let_2 (@ (@ tptp.member_Extended_enat A) S2))) (=> (@ tptp.finite4001608067531595151d_enat S2) (and (=> _let_2 (= (@ (@ tptp.groups2433450451889696826d_enat (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_Extended_enat (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) (@ (@ tptp.plus_p3455044024723400733d_enat (@ B2 A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups2433450451889696826d_enat (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_Extended_enat (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) _let_1))))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_real) (A tptp.real) (B2 (-> tptp.real tptp.nat)) (C (-> tptp.real tptp.nat))) (let ((_let_1 (@ (@ tptp.groups1935376822645274424al_nat C) (@ (@ tptp.minus_minus_set_real S2) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_2 (@ (@ tptp.member_real A) S2))) (=> (@ tptp.finite_finite_real S2) (and (=> _let_2 (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) (@ (@ tptp.plus_plus_nat (@ B2 A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) _let_1))))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_real) (A tptp.real) (B2 (-> tptp.real tptp.int)) (C (-> tptp.real tptp.int))) (let ((_let_1 (@ (@ tptp.groups1932886352136224148al_int C) (@ (@ tptp.minus_minus_set_real S2) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_2 (@ (@ tptp.member_real A) S2))) (=> (@ tptp.finite_finite_real S2) (and (=> _let_2 (= (@ (@ tptp.groups1932886352136224148al_int (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) (@ (@ tptp.plus_plus_int (@ B2 A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups1932886352136224148al_int (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) _let_1))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_real) (A2 tptp.set_real) (B2 tptp.real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real F))) (=> (@ tptp.finite_finite_real B) (=> (@ (@ tptp.ord_less_eq_set_real A2) B) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real B) A2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F B2)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) B) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B))))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_complex) (A2 tptp.set_complex) (B2 tptp.complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real F))) (=> (@ tptp.finite3207457112153483333omplex B) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex B) A2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F B2)) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) B) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B))))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (B2 tptp.extended_enat) (F (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups4148127829035722712t_real F))) (=> (@ tptp.finite4001608067531595151d_enat B) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) B) (=> (@ (@ tptp.member_Extended_enat B2) (@ (@ tptp.minus_925952699566721837d_enat B) A2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F B2)) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) B) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B))))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_real) (A2 tptp.set_real) (B2 tptp.real) (F (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat F))) (=> (@ tptp.finite_finite_real B) (=> (@ (@ tptp.ord_less_eq_set_real A2) B) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real B) A2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F B2)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) B) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X5)))) (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B))))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_complex) (A2 tptp.set_complex) (B2 tptp.complex) (F (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat F))) (=> (@ tptp.finite3207457112153483333omplex B) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex B) A2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F B2)) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) B) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X5)))) (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B))))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (B2 tptp.extended_enat) (F (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2027974829824023292at_nat F))) (=> (@ tptp.finite4001608067531595151d_enat B) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) B) (=> (@ (@ tptp.member_Extended_enat B2) (@ (@ tptp.minus_925952699566721837d_enat B) A2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F B2)) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) B) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X5)))) (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B))))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_real) (A2 tptp.set_real) (B2 tptp.real) (F (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int F))) (=> (@ tptp.finite_finite_real B) (=> (@ (@ tptp.ord_less_eq_set_real A2) B) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real B) A2)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F B2)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) B) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X5)))) (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B))))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_complex) (A2 tptp.set_complex) (B2 tptp.complex) (F (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int F))) (=> (@ tptp.finite3207457112153483333omplex B) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex B) A2)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F B2)) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) B) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X5)))) (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B))))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (B2 tptp.extended_enat) (F (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2025484359314973016at_int F))) (=> (@ tptp.finite4001608067531595151d_enat B) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) B) (=> (@ (@ tptp.member_Extended_enat B2) (@ (@ tptp.minus_925952699566721837d_enat B) A2)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F B2)) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) B) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X5)))) (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B))))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_nat) (A2 tptp.set_nat) (B2 tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int F))) (=> (@ tptp.finite_finite_nat B) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B) (=> (@ (@ tptp.member_nat B2) (@ (@ tptp.minus_minus_set_nat B) A2)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F B2)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) B) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X5)))) (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B))))))))))
% 4.96/5.19 (assert (forall ((I tptp.complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.extended_enat))) (=> (@ (@ tptp.member_complex I) A2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex I) tptp.bot_bot_set_complex))) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (=> (@ tptp.finite3207457112153483333omplex A2) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F I)) (@ (@ tptp.groups1752964319039525884d_enat F) A2)))))))
% 4.96/5.19 (assert (forall ((I tptp.extended_enat) (A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.extended_enat))) (=> (@ (@ tptp.member_Extended_enat I) A2) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat A2) (@ (@ tptp.insert_Extended_enat I) tptp.bot_bo7653980558646680370d_enat))) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (=> (@ tptp.finite4001608067531595151d_enat A2) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F I)) (@ (@ tptp.groups2433450451889696826d_enat F) A2)))))))
% 4.96/5.19 (assert (forall ((I tptp.real) (A2 tptp.set_real) (F (-> tptp.real tptp.extended_enat))) (=> (@ (@ tptp.member_real I) A2) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real I) tptp.bot_bot_set_real))) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (=> (@ tptp.finite_finite_real A2) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F I)) (@ (@ tptp.groups2800946370649118462d_enat F) A2)))))))
% 4.96/5.19 (assert (forall ((I tptp.int) (A2 tptp.set_int) (F (-> tptp.int tptp.extended_enat))) (=> (@ (@ tptp.member_int I) A2) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int I) tptp.bot_bot_set_int))) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (=> (@ tptp.finite_finite_int A2) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F I)) (@ (@ tptp.groups4225252721152677374d_enat F) A2)))))))
% 4.96/5.19 (assert (forall ((I tptp.nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.extended_enat))) (=> (@ (@ tptp.member_nat I) A2) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) (@ (@ tptp.minus_minus_set_nat A2) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (=> (@ tptp.finite_finite_nat A2) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F I)) (@ (@ tptp.groups7108830773950497114d_enat F) A2)))))))
% 4.96/5.19 (assert (forall ((I tptp.complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ (@ tptp.member_complex I) A2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex I) tptp.bot_bot_set_complex))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (=> (@ tptp.finite3207457112153483333omplex A2) (@ (@ tptp.ord_less_eq_real (@ F I)) (@ (@ tptp.groups5808333547571424918x_real F) A2)))))))
% 4.96/5.19 (assert (forall ((I tptp.extended_enat) (A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real))) (=> (@ (@ tptp.member_Extended_enat I) A2) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat A2) (@ (@ tptp.insert_Extended_enat I) tptp.bot_bo7653980558646680370d_enat))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (=> (@ tptp.finite4001608067531595151d_enat A2) (@ (@ tptp.ord_less_eq_real (@ F I)) (@ (@ tptp.groups4148127829035722712t_real F) A2)))))))
% 4.96/5.19 (assert (forall ((I tptp.real) (A2 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.member_real I) A2) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real I) tptp.bot_bot_set_real))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (=> (@ tptp.finite_finite_real A2) (@ (@ tptp.ord_less_eq_real (@ F I)) (@ (@ tptp.groups8097168146408367636l_real F) A2)))))))
% 4.96/5.19 (assert (forall ((I tptp.int) (A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ (@ tptp.member_int I) A2) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int I) tptp.bot_bot_set_int))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (=> (@ tptp.finite_finite_int A2) (@ (@ tptp.ord_less_eq_real (@ F I)) (@ (@ tptp.groups8778361861064173332t_real F) A2)))))))
% 4.96/5.19 (assert (forall ((I tptp.complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ (@ tptp.member_complex I) A2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex I) tptp.bot_bot_set_complex))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X5)))) (=> (@ tptp.finite3207457112153483333omplex A2) (@ (@ tptp.ord_less_eq_nat (@ F I)) (@ (@ tptp.groups5693394587270226106ex_nat F) A2)))))))
% 4.96/5.19 (assert (forall ((X tptp.int) (Xa2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int X) Xa2)))) (let ((_let_2 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ tptp.dvd_dvd_int _let_2))) (let ((_let_4 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_3 X)) (not (@ _let_3 Xa2)))))) (let ((_let_5 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_6 (and (@ (@ tptp.member_int X) _let_5) (@ (@ tptp.member_int Xa2) _let_5)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X) Xa2) Y) (=> _let_1 (not (=> (and (=> _let_6 (= Y (@ tptp.uminus_uminus_int _let_4))) (=> (not _let_6) (= Y (@ (@ tptp.plus_plus_int _let_4) (@ (@ tptp.times_times_int _let_2) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int X) _let_2)) (@ (@ tptp.divide_divide_int Xa2) _let_2))))))) (not _let_1)))))))))))))
% 4.96/5.19 (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))))))))))))))))
% 4.96/5.19 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N tptp.nat) (K2 tptp.int)) (let ((_let_1 (@ tptp.suc N))) (@ (@ tptp.minus_minus_int (@ (@ tptp.bit_se2923211474154528505it_int _let_1) K2)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K2) N))))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat M2) 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 M2) (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat)))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 4.96/5.19 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)) X))))
% 4.96/5.19 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)))))
% 4.96/5.19 (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)))))
% 4.96/5.19 (assert (= (@ tptp.bit_se1146084159140164899it_int tptp.zero_zero_int) tptp.bot_bot_nat_o))
% 4.96/5.19 (assert (= (@ tptp.bit_se1148574629649215175it_nat tptp.zero_zero_nat) tptp.bot_bot_nat_o))
% 4.96/5.19 (assert (= (@ tptp.archim7802044766580827645g_real tptp.zero_zero_real) tptp.zero_zero_int))
% 4.96/5.19 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)))
% 4.96/5.19 (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)))
% 4.96/5.19 (assert (forall ((M2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M2))) (@ tptp.suc N2)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int M2)) N2))))
% 4.96/5.19 (assert (forall ((M2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 M2))) (@ tptp.suc N2)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat M2)) N2))))
% 4.96/5.19 (assert (forall ((M2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M2))) (@ tptp.suc N2)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int M2)) N2))))
% 4.96/5.19 (assert (forall ((M2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 M2))) (@ tptp.suc N2)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat M2)) N2))))
% 4.96/5.19 (assert (forall ((X tptp.real) (Z3 tptp.int)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X) (@ tptp.ring_1_of_int_real Z3))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X)) Z3))))
% 4.96/5.19 (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)))
% 4.96/5.19 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat)))
% 4.96/5.19 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 4.96/5.19 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X))))
% 4.96/5.19 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.numeral_numeral_real V)))))
% 4.96/5.19 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 4.96/5.19 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X))))
% 4.96/5.19 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real V)) X))))
% 4.96/5.19 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real))))
% 4.96/5.19 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real tptp.one_one_real) X))))
% 4.96/5.19 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X) (@ tptp.numeral_numeral_real V))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.numeral_numeral_int V)))))
% 4.96/5.19 (assert (forall ((X tptp.real)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X)) tptp.one_one_int))))
% 4.96/5.19 (assert (forall ((W2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 W2)))) (@ tptp.suc N2)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W2))) N2))))
% 4.96/5.19 (assert (forall ((W2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 W2)))) (@ tptp.suc N2)) (not (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W2)) N2)))))
% 4.96/5.19 (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)))))
% 4.96/5.19 (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)))))
% 4.96/5.19 (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))))))
% 4.96/5.19 (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))))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat) (M2 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (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) M2))) (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))))))))))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat) (M2 tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_3 (@ tptp.groups2073611262835488442omplex G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M2))) (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))))))))))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat) (M2 tptp.nat) (G (-> tptp.nat tptp.extended_enat))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_3 (@ tptp.groups7108830773950497114d_enat G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M2))) (and (=> _let_5 (= _let_4 tptp.zero_z5237406670263579293d_enat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_p3455044024723400733d_enat (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat) (M2 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (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) M2))) (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))))))))))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat) (M2 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (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) M2))) (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))))))))))))
% 4.96/5.19 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real X) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 4.96/5.19 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.complex))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I3)))) A2) (@ C tptp.zero_zero_nat))) (=> (not _let_1) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I3)))) A2) tptp.zero_zero_complex))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.real))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I3)))) A2) (@ C tptp.zero_zero_nat))) (=> (not _let_1) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I3)))) A2) tptp.zero_zero_real))))))
% 4.96/5.19 (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)))))))
% 4.96/5.19 (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)))))))
% 4.96/5.19 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)))))
% 4.96/5.19 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)) X))))
% 4.96/5.19 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_real X) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))))))
% 4.96/5.19 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) X))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.complex)) (D (-> tptp.nat tptp.complex))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I3))) (@ D I3)))) A2) (@ (@ tptp.divide1717551699836669952omplex (@ C tptp.zero_zero_nat)) (@ D tptp.zero_zero_nat)))) (=> (not _let_1) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I3))) (@ D I3)))) A2) tptp.zero_zero_complex))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.real)) (D (-> tptp.nat tptp.real))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I3))) (@ D I3)))) A2) (@ (@ tptp.divide_divide_real (@ C tptp.zero_zero_nat)) (@ D tptp.zero_zero_nat)))) (=> (not _let_1) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I3))) (@ D I3)))) A2) tptp.zero_zero_real))))))
% 4.96/5.19 (assert (forall ((A tptp.int) (B2 tptp.int) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (or (not (@ (@ tptp.bit_se1146084159140164899it_int A) N3)) (not (@ (@ tptp.bit_se1146084159140164899it_int B2) N3)))) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.plus_plus_int A) B2)) N2) (or (@ (@ tptp.bit_se1146084159140164899it_int A) N2) (@ (@ tptp.bit_se1146084159140164899it_int B2) N2))))))
% 4.96/5.19 (assert (forall ((A tptp.nat) (B2 tptp.nat) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (or (not (@ (@ tptp.bit_se1148574629649215175it_nat A) N3)) (not (@ (@ tptp.bit_se1148574629649215175it_nat B2) N3)))) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.plus_plus_nat A) B2)) N2) (or (@ (@ tptp.bit_se1148574629649215175it_nat A) N2) (@ (@ tptp.bit_se1148574629649215175it_nat B2) N2))))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.bit_se1146084159140164899it_int tptp.one_one_int) (@ tptp.suc N2)))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat tptp.one_one_nat) (@ tptp.suc N2)))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int tptp.one_one_int) N2) (= N2 tptp.zero_zero_nat))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat tptp.one_one_nat) N2) (= N2 tptp.zero_zero_nat))))
% 4.96/5.19 (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))))))
% 4.96/5.19 (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))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (A tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se2925701944663578781it_nat M2) A)) N2) (and (@ (@ tptp.ord_less_nat N2) M2) (@ (@ tptp.bit_se1148574629649215175it_nat A) N2)))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se2923211474154528505it_int M2) A)) N2) (and (@ (@ tptp.ord_less_nat N2) M2) (@ (@ tptp.bit_se1146084159140164899it_int A) N2)))))
% 4.96/5.19 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y) X) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real Y)) (@ tptp.archim7802044766580827645g_real X)))))
% 4.96/5.19 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real X)))))
% 4.96/5.19 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.archim7802044766580827645g_real Y)) (@ (@ tptp.ord_less_real X) Y))))
% 4.96/5.19 (assert (forall ((B2 Bool) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.zero_n2684676970156552555ol_int B2)) N2) (and B2 (= N2 tptp.zero_zero_nat)))))
% 4.96/5.19 (assert (forall ((B2 Bool) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.zero_n2687167440665602831ol_nat B2)) N2) (and B2 (= N2 tptp.zero_zero_nat)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.nat)) (F (-> tptp.extended_enat tptp.nat))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) A2) (@ (@ tptp.ord_less_eq_nat (@ G X5)) (@ F X5)))) (= (@ (@ tptp.groups2027974829824023292at_nat (lambda ((X4 tptp.extended_enat)) (@ (@ tptp.minus_minus_nat (@ F X4)) (@ G X4)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups2027974829824023292at_nat F) A2)) (@ (@ tptp.groups2027974829824023292at_nat G) A2))))))
% 4.96/5.19 (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 ((X4 tptp.real)) (@ (@ tptp.minus_minus_nat (@ F X4)) (@ G X4)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups1935376822645274424al_nat F) A2)) (@ (@ tptp.groups1935376822645274424al_nat G) A2))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_set_nat) (G (-> tptp.set_nat tptp.nat)) (F (-> tptp.set_nat tptp.nat))) (=> (forall ((X5 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X5) A2) (@ (@ tptp.ord_less_eq_nat (@ G X5)) (@ F X5)))) (= (@ (@ tptp.groups8294997508430121362at_nat (lambda ((X4 tptp.set_nat)) (@ (@ tptp.minus_minus_nat (@ F X4)) (@ G X4)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups8294997508430121362at_nat F) A2)) (@ (@ tptp.groups8294997508430121362at_nat G) A2))))))
% 4.96/5.19 (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 ((X4 tptp.int)) (@ (@ tptp.minus_minus_nat (@ F X4)) (@ G X4)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) (@ (@ tptp.groups4541462559716669496nt_nat G) A2))))))
% 4.96/5.19 (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 ((X4 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ F X4)) (@ G X4)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups3542108847815614940at_nat G) A2))))))
% 4.96/5.19 (assert (forall ((G (-> tptp.nat tptp.nat)) (M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) (@ tptp.suc N2))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N2)))))
% 4.96/5.19 (assert (forall ((G (-> tptp.nat tptp.real)) (M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) (@ tptp.suc N2))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N2)))))
% 4.96/5.19 (assert (forall ((G (-> tptp.nat tptp.nat)) (M2 tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M2) 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 M2) N2)))))
% 4.96/5.19 (assert (forall ((G (-> tptp.nat tptp.real)) (M2 tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M2) 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 M2) N2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (= (@ (@ tptp.groups5693394587270226106ex_nat F) A2) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A2) (= (@ F X4) (@ tptp.suc tptp.zero_zero_nat)) (forall ((Y5 tptp.complex)) (=> (@ (@ tptp.member_complex Y5) A2) (=> (not (= X4 Y5)) (= (@ F Y5) tptp.zero_zero_nat))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (= (= (@ (@ tptp.groups4541462559716669496nt_nat F) A2) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A2) (= (@ F X4) (@ tptp.suc tptp.zero_zero_nat)) (forall ((Y5 tptp.int)) (=> (@ (@ tptp.member_int Y5) A2) (=> (not (= X4 Y5)) (= (@ F Y5) tptp.zero_zero_nat))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (= (@ (@ tptp.groups2027974829824023292at_nat F) A2) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) A2) (= (@ F X4) (@ tptp.suc tptp.zero_zero_nat)) (forall ((Y5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat Y5) A2) (=> (not (= X4 Y5)) (= (@ F Y5) tptp.zero_zero_nat))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (= (= (@ (@ tptp.groups3542108847815614940at_nat F) A2) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A2) (= (@ F X4) (@ tptp.suc tptp.zero_zero_nat)) (forall ((Y5 tptp.nat)) (=> (@ (@ tptp.member_nat Y5) A2) (=> (not (= X4 Y5)) (= (@ F Y5) tptp.zero_zero_nat))))))))))
% 4.96/5.19 (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)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (= (@ (@ tptp.groups5693394587270226106ex_nat F) A2) tptp.one_one_nat) (exists ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A2) (= (@ F X4) tptp.one_one_nat) (forall ((Y5 tptp.complex)) (=> (@ (@ tptp.member_complex Y5) A2) (=> (not (= X4 Y5)) (= (@ F Y5) tptp.zero_zero_nat))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (= (= (@ (@ tptp.groups4541462559716669496nt_nat F) A2) tptp.one_one_nat) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A2) (= (@ F X4) tptp.one_one_nat) (forall ((Y5 tptp.int)) (=> (@ (@ tptp.member_int Y5) A2) (=> (not (= X4 Y5)) (= (@ F Y5) tptp.zero_zero_nat))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (= (@ (@ tptp.groups2027974829824023292at_nat F) A2) tptp.one_one_nat) (exists ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) A2) (= (@ F X4) tptp.one_one_nat) (forall ((Y5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat Y5) A2) (=> (not (= X4 Y5)) (= (@ F Y5) tptp.zero_zero_nat))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (= (= (@ (@ tptp.groups3542108847815614940at_nat F) A2) tptp.one_one_nat) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A2) (= (@ F X4) tptp.one_one_nat) (forall ((Y5 tptp.nat)) (=> (@ (@ tptp.member_nat Y5) A2) (=> (not (= X4 Y5)) (= (@ F Y5) tptp.zero_zero_nat))))))))))
% 4.96/5.19 (assert (forall ((X tptp.real) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_real X) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) A))))
% 4.96/5.19 (assert (forall ((X tptp.real) (Z3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) Z3) (@ (@ tptp.ord_less_eq_real X) (@ tptp.ring_1_of_int_real Z3)))))
% 4.96/5.19 (assert (forall ((Z3 tptp.int) (X tptp.real)) (= (@ (@ tptp.ord_less_int Z3) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z3)) X))))
% 4.96/5.19 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X) Y))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.archim7802044766580827645g_real Y)))))
% 4.96/5.19 (assert (forall ((X tptp.int) (M2 tptp.nat) (I6 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_int X))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_int X) (@ (@ tptp.plus_plus_nat M2) I3)))) I6) (@ (@ tptp.times_times_int (@ _let_1 M2)) (@ (@ tptp.groups3539618377306564664at_int _let_1) I6))))))
% 4.96/5.19 (assert (forall ((X tptp.complex) (M2 tptp.nat) (I6 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_complex X))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_complex X) (@ (@ tptp.plus_plus_nat M2) I3)))) I6) (@ (@ tptp.times_times_complex (@ _let_1 M2)) (@ (@ tptp.groups2073611262835488442omplex _let_1) I6))))))
% 4.96/5.19 (assert (forall ((X tptp.real) (M2 tptp.nat) (I6 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_real X))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_real X) (@ (@ tptp.plus_plus_nat M2) I3)))) I6) (@ (@ tptp.times_times_real (@ _let_1 M2)) (@ (@ tptp.groups6591440286371151544t_real _let_1) I6))))))
% 4.96/5.19 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N2) M2))) (= (@ (@ tptp.groups3542108847815614940at_nat G) _let_1) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M2) N2)) I3)))) _let_1)))))
% 4.96/5.19 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N2) M2))) (= (@ (@ tptp.groups6591440286371151544t_real G) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M2) N2)) I3)))) _let_1)))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat) (C tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N2) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X4 tptp.complex)) X4)) (@ tptp.collect_complex (lambda ((Z6 tptp.complex)) (= (@ (@ tptp.power_power_complex Z6) N2) C)))) tptp.zero_zero_complex))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N2) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X4 tptp.complex)) X4)) (@ tptp.collect_complex (lambda ((Z6 tptp.complex)) (= (@ (@ tptp.power_power_complex Z6) N2) tptp.one_one_complex)))) tptp.zero_zero_complex))))
% 4.96/5.19 (assert (forall ((R2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real R2))) (@ (@ tptp.plus_plus_real R2) tptp.one_one_real))))
% 4.96/5.19 (assert (forall ((R2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real R2))) tptp.one_one_real)) R2)))
% 4.96/5.19 (assert (forall ((B tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat F))) (=> (@ tptp.finite3207457112153483333omplex B) (=> (@ (@ tptp.ord_le211207098394363844omplex B) A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B)) (@ (@ tptp.minus_minus_nat (@ _let_1 A2)) (@ _let_1 B))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2027974829824023292at_nat F))) (=> (@ tptp.finite4001608067531595151d_enat B) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B) A2) (= (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) B)) (@ (@ tptp.minus_minus_nat (@ _let_1 A2)) (@ _let_1 B))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat F))) (=> (@ tptp.finite_finite_int B) (=> (@ (@ tptp.ord_less_eq_set_int B) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B)) (@ (@ tptp.minus_minus_nat (@ _let_1 A2)) (@ _let_1 B))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat F))) (=> (@ tptp.finite_finite_nat B) (=> (@ (@ tptp.ord_less_eq_set_nat B) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B)) (@ (@ tptp.minus_minus_nat (@ _let_1 A2)) (@ _let_1 B))))))))
% 4.96/5.19 (assert (forall ((A tptp.set_nat) (A2 tptp.set_set_nat) (F (-> tptp.set_nat tptp.nat))) (let ((_let_1 (@ tptp.groups8294997508430121362at_nat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A2) (@ (@ tptp.insert_set_nat A) tptp.bot_bot_set_set_nat))))) (let ((_let_4 (@ (@ tptp.member_set_nat A) A2))) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2)))))))))
% 4.96/5.19 (assert (forall ((A tptp.extended_enat) (A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2027974829824023292at_nat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat))))) (let ((_let_4 (@ (@ tptp.member_Extended_enat A) A2))) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2)))))))))
% 4.96/5.19 (assert (forall ((A tptp.real) (A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_4 (@ (@ tptp.member_real A) A2))) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2)))))))))
% 4.96/5.19 (assert (forall ((A tptp.int) (A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_4 (@ (@ tptp.member_int A) A2))) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2)))))))))
% 4.96/5.19 (assert (forall ((A tptp.nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))) (let ((_let_4 (@ (@ tptp.member_nat A) A2))) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2)))))))))
% 4.96/5.19 (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)))))))
% 4.96/5.19 (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)))))))
% 4.96/5.19 (assert (forall ((F (-> tptp.nat tptp.extended_enat)) (K tptp.nat)) (let ((_let_1 (@ tptp.groups7108830773950497114d_enat F))) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_z5237406670263579293d_enat) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) K)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K)))))))
% 4.96/5.19 (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)))))))
% 4.96/5.19 (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)))))))
% 4.96/5.19 (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))))))))
% 4.96/5.19 (assert (forall ((G (-> tptp.nat tptp.extended_enat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups7108830773950497114d_enat G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))
% 4.96/5.19 (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))))))))
% 4.96/5.19 (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))))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int G))) (let ((_let_3 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_int (@ G _let_3)) (@ _let_2 (@ _let_1 N2))))))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.extended_enat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.groups7108830773950497114d_enat G))) (let ((_let_3 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ G _let_3)) (@ _let_2 (@ _let_1 N2))))))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.groups3542108847815614940at_nat G))) (let ((_let_3 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_nat (@ G _let_3)) (@ _let_2 (@ _let_1 N2))))))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real G))) (let ((_let_3 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_real (@ G _let_3)) (@ _let_2 (@ _let_1 N2))))))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N2)) (@ (@ tptp.plus_plus_int (@ G M2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N2))))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.extended_enat))) (let ((_let_1 (@ tptp.groups7108830773950497114d_enat G))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N2)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ G M2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N2))))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N2)) (@ (@ tptp.plus_plus_nat (@ G M2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N2))))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups6591440286371151544t_real G))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N2)) (@ (@ tptp.plus_plus_real (@ G M2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N2))))))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat) (M2 tptp.nat) (K tptp.int)) (=> (@ (@ tptp.ord_less_nat N2) M2) (=> (@ (@ tptp.bit_se1146084159140164899it_int K) N2) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int M2) K))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (K tptp.int) (L tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ (@ tptp.bit_concat_bit M2) K) L)) N2) (or (and (@ (@ tptp.ord_less_nat N2) M2) (@ (@ tptp.bit_se1146084159140164899it_int K) N2)) (and (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.bit_se1146084159140164899it_int L) (@ (@ tptp.minus_minus_nat N2) M2)))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.groups3539618377306564664at_int G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.plus_plus_int (@ G M2)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.extended_enat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.groups7108830773950497114d_enat G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.plus_p3455044024723400733d_enat (@ G M2)) (@ (@ tptp.groups7108830773950497114d_enat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups3542108847815614940at_nat G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.plus_plus_nat (@ G M2)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.plus_plus_real (@ G M2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_1) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I3))) (@ F I3)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N2)) (@ (@ tptp.minus_minus_int (@ F _let_1)) (@ F M2)))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_1) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F (@ tptp.suc I3))) (@ F I3)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N2)) (@ (@ tptp.minus_minus_real (@ F _let_1)) (@ F M2)))))))
% 4.96/5.19 (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)))))
% 4.96/5.19 (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)))))
% 4.96/5.19 (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))))
% 4.96/5.19 (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))))
% 4.96/5.19 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real X)))) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) X) (@ (@ tptp.ord_less_eq_real X) _let_1)))))
% 4.96/5.19 (assert (forall ((Z3 tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real Z3))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (= (@ tptp.archim7802044766580827645g_real X) Z3))))))
% 4.96/5.19 (assert (forall ((X tptp.real) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real A))) (= (= (@ tptp.archim7802044766580827645g_real X) A) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) X) (@ (@ tptp.ord_less_eq_real X) _let_1))))))
% 4.96/5.19 (assert (forall ((P (-> tptp.int Bool)) (T tptp.real)) (= (@ P (@ tptp.archim7802044766580827645g_real T)) (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)) T) (@ (@ tptp.ord_less_eq_real T) _let_1)) (@ P I3)))))))
% 4.96/5.19 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real (@ (@ tptp.times_times_real A) B2))) (@ (@ tptp.times_times_int (@ tptp.archim7802044766580827645g_real A)) (@ tptp.archim7802044766580827645g_real B2))))))))
% 4.96/5.19 (assert (forall ((X tptp.real) (Z3 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X)) Z3) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real Z3)) tptp.one_one_real)))))
% 4.96/5.19 (assert (forall ((Z3 tptp.int) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_int Z3) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real Z3)) tptp.one_one_real)) X))))
% 4.96/5.19 (assert (forall ((K tptp.int)) (not (forall ((N3 tptp.nat)) (let ((_let_1 (@ tptp.bit_se1146084159140164899it_int K))) (=> (forall ((M5 tptp.nat)) (let ((_let_1 (@ tptp.bit_se1146084159140164899it_int K))) (=> (@ (@ tptp.ord_less_eq_nat N3) M5) (= (@ _let_1 M5) (@ _let_1 N3))))) (not (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)) (not (@ _let_1 N3)))))))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int)) (P5 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (let ((_let_2 (@ _let_1 P5))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups3539618377306564664at_int G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _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))))))))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.extended_enat)) (P5 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (let ((_let_2 (@ _let_1 P5))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups7108830773950497114d_enat G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ _let_4 (@ _let_5 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat)) (P5 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (let ((_let_2 (@ _let_1 P5))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups3542108847815614940at_nat G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _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))))))))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.real)) (P5 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (let ((_let_2 (@ _let_1 P5))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups6591440286371151544t_real G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _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))))))))))))
% 4.96/5.19 (assert (forall ((Xs tptp.list_complex) (X8 tptp.set_complex)) (=> (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs)) X8) (=> (@ tptp.finite3207457112153483333omplex X8) (= (@ (@ tptp.groups5693394587270226106ex_nat (@ tptp.count_list_complex Xs)) X8) (@ tptp.size_s3451745648224563538omplex Xs))))))
% 4.96/5.19 (assert (forall ((Xs tptp.list_Extended_enat) (X8 tptp.set_Extended_enat)) (=> (@ (@ tptp.ord_le7203529160286727270d_enat (@ tptp.set_Extended_enat2 Xs)) X8) (=> (@ tptp.finite4001608067531595151d_enat X8) (= (@ (@ tptp.groups2027974829824023292at_nat (@ tptp.count_101369445342291426d_enat Xs)) X8) (@ tptp.size_s3941691890525107288d_enat Xs))))))
% 4.96/5.19 (assert (forall ((Xs tptp.list_VEBT_VEBT) (X8 tptp.set_VEBT_VEBT)) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) X8) (=> (@ tptp.finite5795047828879050333T_VEBT X8) (= (@ (@ tptp.groups771621172384141258BT_nat (@ tptp.count_list_VEBT_VEBT Xs)) X8) (@ tptp.size_s6755466524823107622T_VEBT Xs))))))
% 4.96/5.19 (assert (forall ((Xs tptp.list_int) (X8 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) X8) (=> (@ tptp.finite_finite_int X8) (= (@ (@ tptp.groups4541462559716669496nt_nat (@ tptp.count_list_int Xs)) X8) (@ tptp.size_size_list_int Xs))))))
% 4.96/5.19 (assert (forall ((Xs tptp.list_nat) (X8 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) X8) (=> (@ tptp.finite_finite_nat X8) (= (@ (@ tptp.groups3542108847815614940at_nat (@ tptp.count_list_nat Xs)) X8) (@ tptp.size_size_list_nat Xs))))))
% 4.96/5.19 (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)))))
% 4.96/5.19 (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)))))
% 4.96/5.19 (assert (forall ((Q3 tptp.real) (P5 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q3) (@ (@ tptp.ord_less_eq_real P5) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real (@ (@ tptp.divide_divide_real P5) Q3)))) Q3)))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N2))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M2) N2))) (and (=> _let_2 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_complex (@ F M2)) (@ F (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) tptp.zero_zero_complex)))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N2))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M2) N2))) (and (=> _let_2 (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_int (@ F M2)) (@ F (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) tptp.zero_zero_int)))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N2))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M2) N2))) (and (=> _let_2 (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_real (@ F M2)) (@ F (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) tptp.zero_zero_real)))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K2)) (@ F (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N2)) (@ (@ tptp.minus_minus_int (@ F N2)) (@ F M2))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K2)) (@ F (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N2)) (@ (@ tptp.minus_minus_real (@ F N2)) (@ F M2))))))
% 4.96/5.19 (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))))))
% 4.96/5.19 (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))))))
% 4.96/5.19 (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))))))
% 4.96/5.19 (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))))))
% 4.96/5.19 (assert (forall ((Q3 tptp.real) (P5 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 P5) Q3)))) tptp.one_one_real)) Q3)) P5))))
% 4.96/5.19 (assert (forall ((N2 tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N2))) (=> (@ (@ tptp.ord_less_real _let_1) X) (=> (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim7802044766580827645g_real X) (@ (@ tptp.plus_plus_int N2) tptp.one_one_int)))))))
% 4.96/5.19 (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))))))))
% 4.96/5.19 (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))))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (X tptp.int)) (let ((_let_1 (@ tptp.power_power_int X))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int tptp.one_one_int) X)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M2) N2))) (@ (@ tptp.minus_minus_int (@ _let_1 M2)) (@ _let_1 (@ tptp.suc N2))))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (X tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex tptp.one_one_complex) X)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M2) N2))) (@ (@ tptp.minus_minus_complex (@ _let_1 M2)) (@ _let_1 (@ tptp.suc N2))))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.power_power_real X))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M2) N2))) (@ (@ tptp.minus_minus_real (@ _let_1 M2)) (@ _let_1 (@ tptp.suc N2))))))))
% 4.96/5.19 (assert (forall ((G (-> tptp.nat tptp.int)) (M2 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 M2)) (@ 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 M2) N2))))))
% 4.96/5.19 (assert (forall ((G (-> tptp.nat tptp.extended_enat)) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups7108830773950497114d_enat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M2)) (@ tptp.suc (@ _let_1 N2)))) (@ (@ tptp.groups7108830773950497114d_enat (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.plus_p3455044024723400733d_enat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N2))))))
% 4.96/5.19 (assert (forall ((G (-> tptp.nat tptp.nat)) (M2 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 M2)) (@ 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 M2) N2))))))
% 4.96/5.19 (assert (forall ((G (-> tptp.nat tptp.real)) (M2 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 M2)) (@ 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 M2) N2))))))
% 4.96/5.19 (assert (forall ((A0 tptp.int) (A1 tptp.int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int A0) A1)) (=> (forall ((K3 tptp.int) (L4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int K3) L4)) (=> (=> (not (and (@ (@ tptp.member_int K3) _let_2) (@ (@ tptp.member_int L4) _let_2))) (@ (@ P (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L4) _let_1))) (@ (@ P K3) L4)))))) (@ (@ P A0) A1)))))
% 4.96/5.19 (assert (forall ((A tptp.int) (B2 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) B2))) (let ((_let_3 (= N2 tptp.zero_zero_nat))) (=> (forall ((J3 tptp.nat)) (not (@ (@ tptp.bit_se1146084159140164899it_int A) (@ tptp.suc J3)))) (= (@ (@ 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))))))))))
% 4.96/5.19 (assert (forall ((A tptp.nat) (B2 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) B2))) (let ((_let_3 (= N2 tptp.zero_zero_nat))) (=> (forall ((J3 tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat A) (@ tptp.suc J3)))) (= (@ (@ 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))))))))))
% 4.96/5.19 (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)))))))))
% 4.96/5.19 (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)))))))))
% 4.96/5.19 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (or (= M 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 M) _let_1)) (@ (@ tptp.modulo_modulo_nat N) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M) _let_1)) (@ (@ tptp.divide_divide_nat N) _let_1)))))))))
% 4.96/5.19 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M 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 M)) (not (@ _let_2 N))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M) _let_1)) (@ (@ tptp.divide_divide_nat N) _let_1)))))))))
% 4.96/5.19 (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))))))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ 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))))))
% 4.96/5.19 (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)))))
% 4.96/5.19 (assert (forall ((A0 tptp.int) (A1 tptp.int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int A0) A1)) (=> (forall ((I4 tptp.int) (J3 tptp.int)) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int I4) J3)) (=> (=> (@ (@ tptp.ord_less_eq_int I4) J3) (@ (@ P (@ (@ tptp.plus_plus_int I4) tptp.one_one_int)) J3)) (@ (@ P I4) J3)))) (@ (@ P A0) A1)))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat) (M2 tptp.nat) (X tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X))) (let ((_let_2 (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M2) N2)))) (let ((_let_3 (= X tptp.one_one_complex))) (let ((_let_4 (@ (@ tptp.ord_less_nat N2) M2))) (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)) M2)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ _let_1 M2)) (@ _let_1 (@ tptp.suc N2)))) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) X)))))))))))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat) (M2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.power_power_real X))) (let ((_let_2 (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M2) N2)))) (let ((_let_3 (= X tptp.one_one_real))) (let ((_let_4 (@ (@ tptp.ord_less_nat N2) M2))) (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)) M2)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ _let_1 M2)) (@ _let_1 (@ tptp.suc N2)))) (@ (@ tptp.minus_minus_real tptp.one_one_real) X)))))))))))))
% 4.96/5.19 (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)))))))
% 4.96/5.19 (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)))))))
% 4.96/5.19 (assert (forall ((X tptp.complex) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_2 (@ tptp.power_power_complex X))) (let ((_let_3 (@ (@ tptp.groups2073611262835488442omplex _let_2) (@ (@ tptp.set_or1269000886237332187st_nat M2) (@ (@ tptp.plus_plus_nat M2) N2))))) (let ((_let_4 (= X tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex N2)) tptp.one_one_complex))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ _let_2 M2)) (@ _let_1 (@ _let_2 (@ tptp.suc N2))))) (@ _let_1 X)))))))))))
% 4.96/5.19 (assert (forall ((X tptp.real) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (let ((_let_2 (@ tptp.power_power_real X))) (let ((_let_3 (@ (@ tptp.groups6591440286371151544t_real _let_2) (@ (@ tptp.set_or1269000886237332187st_nat M2) (@ (@ tptp.plus_plus_nat M2) N2))))) (let ((_let_4 (= X tptp.one_one_real))) (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N2)) tptp.one_one_real))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ _let_2 M2)) (@ _let_1 (@ _let_2 (@ tptp.suc N2))))) (@ _let_1 X)))))))))))
% 4.96/5.19 (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))))))
% 4.96/5.19 (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))))))
% 4.96/5.19 (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))))))
% 4.96/5.19 (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))))))
% 4.96/5.19 (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))))))
% 4.96/5.19 (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))))))
% 4.96/5.19 (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))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real M2) (@ tptp.semiri5074537144036343181t_real N2)) (= M2 N2))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M2) (@ tptp.semiri1314217659103216013at_int N2)) (= M2 N2))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M2) (@ tptp.semiri1316708129612266289at_nat N2)) (= M2 N2))))
% 4.96/5.19 (assert (forall ((N2 tptp.num) (M2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N2)) (@ tptp.semiri5074537144036343181t_real M2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N2)) M2))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (V tptp.num)) (= (= (@ tptp.semiri1314217659103216013at_int M2) (@ tptp.numeral_numeral_int V)) (= M2 (@ tptp.numeral_numeral_nat V)))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (= (= (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2)) (@ tptp.semiri1314217659103216013at_int M2)) (and (= N2 tptp.zero_zero_nat) (= M2 tptp.zero_zero_nat)))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat)) (= (@ tptp.ring_1_of_int_real (@ tptp.semiri1314217659103216013at_int N2)) (@ tptp.semiri5074537144036343181t_real N2))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) (@ tptp.semiri1314217659103216013at_int M2))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.dvd_dvd_nat M2) N2))))
% 4.96/5.19 (assert (= (@ tptp.semiri8010041392384452111omplex tptp.zero_zero_nat) tptp.zero_zero_complex))
% 4.96/5.19 (assert (= (@ tptp.semiri4216267220026989637d_enat tptp.zero_zero_nat) tptp.zero_z5237406670263579293d_enat))
% 4.96/5.19 (assert (= (@ tptp.semiri5074537144036343181t_real tptp.zero_zero_nat) tptp.zero_zero_real))
% 4.96/5.19 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 4.96/5.19 (assert (= (@ tptp.semiri1316708129612266289at_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 4.96/5.19 (assert (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_complex (@ tptp.semiri8010041392384452111omplex N2)) (= tptp.zero_zero_nat N2))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat)) (= (= tptp.zero_z5237406670263579293d_enat (@ tptp.semiri4216267220026989637d_enat N2)) (= tptp.zero_zero_nat N2))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_real (@ tptp.semiri5074537144036343181t_real N2)) (= tptp.zero_zero_nat N2))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_int (@ tptp.semiri1314217659103216013at_int N2)) (= tptp.zero_zero_nat N2))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_nat (@ tptp.semiri1316708129612266289at_nat N2)) (= tptp.zero_zero_nat N2))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex M2) tptp.zero_zero_complex) (= M2 tptp.zero_zero_nat))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat)) (= (= (@ tptp.semiri4216267220026989637d_enat M2) tptp.zero_z5237406670263579293d_enat) (= M2 tptp.zero_zero_nat))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real M2) tptp.zero_zero_real) (= M2 tptp.zero_zero_nat))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M2) tptp.zero_zero_int) (= M2 tptp.zero_zero_nat))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M2) tptp.zero_zero_nat) (= M2 tptp.zero_zero_nat))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.semiri4216267220026989637d_enat M2)) (@ tptp.semiri4216267220026989637d_enat N2)) (@ (@ tptp.ord_less_nat M2) N2))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.ord_less_nat M2) N2))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.ord_less_nat M2) N2))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M2)) (@ tptp.semiri1316708129612266289at_nat N2)) (@ (@ tptp.ord_less_nat M2) N2))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.ord_less_eq_nat M2) N2))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat M2)) (@ tptp.semiri1316708129612266289at_nat N2)) (@ (@ tptp.ord_less_eq_nat M2) N2))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.ord_less_eq_nat M2) N2))))
% 4.96/5.19 (assert (forall ((W2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real W2)) (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat W2)) N2))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat) (W2 tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.numeral_numeral_real W2)) (@ (@ tptp.ord_less_nat N2) (@ tptp.numeral_numeral_nat W2)))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri4216267220026989637d_enat (@ (@ tptp.plus_plus_nat M2) N2)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.semiri4216267220026989637d_enat M2)) (@ tptp.semiri4216267220026989637d_enat N2)))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat M2) N2)) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.semiri5074537144036343181t_real N2)))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat M2) N2)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N2)))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.plus_plus_nat M2) N2)) (@ (@ tptp.plus_plus_nat (@ tptp.semiri1316708129612266289at_nat M2)) (@ tptp.semiri1316708129612266289at_nat N2)))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.times_times_nat M2) N2)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex M2)) (@ tptp.semiri8010041392384452111omplex N2)))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri4216267220026989637d_enat (@ (@ tptp.times_times_nat M2) N2)) (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.semiri4216267220026989637d_enat M2)) (@ tptp.semiri4216267220026989637d_enat N2)))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.times_times_nat M2) N2)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.semiri5074537144036343181t_real N2)))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.times_times_nat M2) N2)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N2)))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.times_times_nat M2) N2)) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat M2)) (@ tptp.semiri1316708129612266289at_nat N2)))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex N2) tptp.one_one_complex) (= N2 tptp.one_one_nat))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real N2) tptp.one_one_real) (= N2 tptp.one_one_nat))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int N2) tptp.one_one_int) (= N2 tptp.one_one_nat))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat N2) tptp.one_one_nat) (= N2 tptp.one_one_nat))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat)) (= (= tptp.one_one_complex (@ tptp.semiri8010041392384452111omplex N2)) (= N2 tptp.one_one_nat))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat)) (= (= tptp.one_one_real (@ tptp.semiri5074537144036343181t_real N2)) (= N2 tptp.one_one_nat))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat)) (= (= tptp.one_one_int (@ tptp.semiri1314217659103216013at_int N2)) (= N2 tptp.one_one_nat))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat)) (= (= tptp.one_one_nat (@ tptp.semiri1316708129612266289at_nat N2)) (= N2 tptp.one_one_nat))))
% 4.96/5.19 (assert (= (@ tptp.semiri8010041392384452111omplex tptp.one_one_nat) tptp.one_one_complex))
% 4.96/5.19 (assert (= (@ tptp.semiri5074537144036343181t_real tptp.one_one_nat) tptp.one_one_real))
% 4.96/5.19 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))
% 4.96/5.19 (assert (= (@ tptp.semiri1316708129612266289at_nat tptp.one_one_nat) tptp.one_one_nat))
% 4.96/5.19 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2)))) (@ tptp.semiri1314217659103216013at_int M2))))
% 4.96/5.19 (assert (forall ((P Bool)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n3304061248610475627l_real P))))
% 4.96/5.19 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n2687167440665602831ol_nat P))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 4.96/5.19 (assert (forall ((P Bool)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2684676970156552555ol_int P))))
% 4.96/5.19 (assert (forall ((F (-> tptp.int tptp.nat)) (A2 tptp.set_int)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X4 tptp.int)) (@ tptp.semiri1314217659103216013at_int (@ F X4)))) A2))))
% 4.96/5.19 (assert (forall ((F (-> tptp.complex tptp.nat)) (A2 tptp.set_complex)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.groups5693394587270226106ex_nat F) A2)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((X4 tptp.complex)) (@ tptp.semiri8010041392384452111omplex (@ F X4)))) A2))))
% 4.96/5.19 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((X4 tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ F X4)))) A2))))
% 4.96/5.19 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) (@ tptp.semiri1316708129612266289at_nat (@ F X4)))) A2))))
% 4.96/5.19 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((X4 tptp.nat)) (@ tptp.semiri5074537144036343181t_real (@ F X4)))) A2))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.semiri4216267220026989637d_enat M2)) tptp.zero_z5237406670263579293d_enat) (= M2 tptp.zero_zero_nat))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real M2)) tptp.zero_zero_real) (= M2 tptp.zero_zero_nat))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat M2)) tptp.zero_zero_nat) (= M2 tptp.zero_zero_nat))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M2)) tptp.zero_zero_int) (= M2 tptp.zero_zero_nat))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.suc M2)) (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.semiri8010041392384452111omplex M2)))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat)) (= (@ tptp.semiri4216267220026989637d_enat (@ tptp.suc M2)) (@ (@ tptp.plus_p3455044024723400733d_enat tptp.one_on7984719198319812577d_enat) (@ tptp.semiri4216267220026989637d_enat M2)))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M2)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real M2)))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc M2)) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.semiri1314217659103216013at_int M2)))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc M2)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.semiri1316708129612266289at_nat M2)))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ tptp.semiri4216267220026989637d_enat N2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 4.96/5.19 (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))))
% 4.96/5.19 (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))))
% 4.96/5.19 (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)))))
% 4.96/5.19 (assert (forall ((B2 tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B2)) W2)) (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B2) W2)) X))))
% 4.96/5.19 (assert (forall ((B2 tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B2)) W2)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B2) W2)) X))))
% 4.96/5.19 (assert (forall ((B2 tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B2)) W2)) (@ tptp.semiri1316708129612266289at_nat X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B2) W2)) X))))
% 4.96/5.19 (assert (forall ((X tptp.nat) (B2 tptp.nat) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B2)) W2)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat B2) W2)))))
% 4.96/5.19 (assert (forall ((X tptp.nat) (B2 tptp.nat) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B2)) W2)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat B2) W2)))))
% 4.96/5.19 (assert (forall ((X tptp.nat) (B2 tptp.nat) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat X)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B2)) W2)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat B2) W2)))))
% 4.96/5.19 (assert (forall ((X tptp.nat) (B2 tptp.nat) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B2)) W2)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B2) W2)))))
% 4.96/5.19 (assert (forall ((X tptp.nat) (B2 tptp.nat) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat X)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B2)) W2)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B2) W2)))))
% 4.96/5.19 (assert (forall ((X tptp.nat) (B2 tptp.nat) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B2)) W2)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B2) W2)))))
% 4.96/5.19 (assert (forall ((B2 tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B2)) W2)) (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B2) W2)) X))))
% 4.96/5.19 (assert (forall ((B2 tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B2)) W2)) (@ tptp.semiri1316708129612266289at_nat X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B2) W2)) X))))
% 4.96/5.19 (assert (forall ((B2 tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B2)) W2)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B2) W2)) X))))
% 4.96/5.19 (assert (forall ((X tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real X)) N2)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X) (= N2 tptp.zero_zero_nat)))))
% 4.96/5.19 (assert (forall ((X tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int X)) N2)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X) (= N2 tptp.zero_zero_nat)))))
% 4.96/5.19 (assert (forall ((X tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat X)) N2)) (or (@ _let_1 X) (= N2 tptp.zero_zero_nat))))))
% 4.96/5.19 (assert (forall ((X tptp.nat) (I tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N2)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N2)))))
% 4.96/5.19 (assert (forall ((X tptp.nat) (I tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N2)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N2)))))
% 4.96/5.19 (assert (forall ((X tptp.nat) (I tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N2))) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat X)) _let_1) (@ (@ tptp.ord_less_nat X) _let_1)))))
% 4.96/5.19 (assert (forall ((I tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N2)) (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N2)) X))))
% 4.96/5.19 (assert (forall ((I tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N2)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N2)) X))))
% 4.96/5.19 (assert (forall ((I tptp.num) (N2 tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N2)))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat X)) (@ _let_1 X)))))
% 4.96/5.19 (assert (forall ((X tptp.nat) (I tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N2)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N2)))))
% 4.96/5.19 (assert (forall ((X tptp.nat) (I tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N2))) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat X)) _let_1) (@ (@ tptp.ord_less_eq_nat X) _let_1)))))
% 4.96/5.19 (assert (forall ((X tptp.nat) (I tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N2)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N2)))))
% 4.96/5.19 (assert (forall ((I tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N2)) (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N2)) X))))
% 4.96/5.19 (assert (forall ((I tptp.num) (N2 tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N2)))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat X)) (@ _let_1 X)))))
% 4.96/5.19 (assert (forall ((I tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N2)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N2)) X))))
% 4.96/5.19 (assert (forall ((X tptp.real)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.semiri5074537144036343181t_real N3)))))
% 4.96/5.19 (assert (forall ((X tptp.real)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real X) (@ tptp.semiri5074537144036343181t_real N3)))))
% 4.96/5.19 (assert (forall ((X tptp.nat) (Y tptp.complex)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex X))) (= (@ (@ tptp.times_times_complex _let_1) Y) (@ (@ tptp.times_times_complex Y) _let_1)))))
% 4.96/5.19 (assert (forall ((X tptp.nat) (Y tptp.extended_enat)) (let ((_let_1 (@ tptp.semiri4216267220026989637d_enat X))) (= (@ (@ tptp.times_7803423173614009249d_enat _let_1) Y) (@ (@ tptp.times_7803423173614009249d_enat Y) _let_1)))))
% 4.96/5.19 (assert (forall ((X tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real X))) (= (@ (@ tptp.times_times_real _let_1) Y) (@ (@ tptp.times_times_real Y) _let_1)))))
% 4.96/5.19 (assert (forall ((X tptp.nat) (Y tptp.int)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int X))) (= (@ (@ tptp.times_times_int _let_1) Y) (@ (@ tptp.times_times_int Y) _let_1)))))
% 4.96/5.19 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat X))) (= (@ (@ tptp.times_times_nat _let_1) Y) (@ (@ tptp.times_times_nat Y) _let_1)))))
% 4.96/5.19 (assert (= tptp.ord_less_nat (lambda ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N)) tptp.one_one_real)) (@ tptp.semiri5074537144036343181t_real M)))))
% 4.96/5.19 (assert (forall ((Z3 tptp.int)) (=> (forall ((N3 tptp.nat)) (not (= Z3 (@ tptp.semiri1314217659103216013at_int N3)))) (not (forall ((N3 tptp.nat)) (not (= Z3 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N3)))))))))
% 4.96/5.19 (assert (forall ((Z3 tptp.int)) (not (forall ((M3 tptp.nat) (N3 tptp.nat)) (not (= Z3 (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int M3)) (@ tptp.semiri1314217659103216013at_int N3))))))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.ring_1_of_int_real X)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N2)) X))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat) (X tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int X)) (@ _let_1 X)))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (= N2 tptp.zero_zero_nat))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.suc N2)))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ tptp.semiri4216267220026989637d_enat N2))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.semiri5074537144036343181t_real N2))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1316708129612266289at_nat N2))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1314217659103216013at_int N2))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat)) (not (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.semiri4216267220026989637d_enat M2)) tptp.zero_z5237406670263579293d_enat))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat)) (not (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M2)) tptp.zero_zero_real))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M2)) tptp.zero_zero_int))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M2)) tptp.zero_zero_nat))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri8010041392384452111omplex (@ tptp.suc N2)) tptp.zero_zero_complex))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri4216267220026989637d_enat (@ tptp.suc N2)) tptp.zero_z5237406670263579293d_enat))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2)) tptp.zero_zero_real))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2)) tptp.zero_zero_int))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc N2)) tptp.zero_zero_nat))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N2) (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.semiri4216267220026989637d_enat M2)) (@ tptp.semiri4216267220026989637d_enat N2)))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N2) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.semiri5074537144036343181t_real N2)))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N2) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N2)))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N2) (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M2)) (@ tptp.semiri1316708129612266289at_nat N2)))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.semiri4216267220026989637d_enat M2)) (@ tptp.semiri4216267220026989637d_enat N2)) (@ (@ tptp.ord_less_nat M2) N2))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.ord_less_nat M2) N2))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.ord_less_nat M2) N2))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M2)) (@ tptp.semiri1316708129612266289at_nat N2)) (@ (@ tptp.ord_less_nat M2) N2))))
% 4.96/5.19 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real I)) (@ tptp.semiri5074537144036343181t_real J)))))
% 4.96/5.19 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat I)) (@ tptp.semiri1316708129612266289at_nat J)))))
% 4.96/5.19 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int I)) (@ tptp.semiri1314217659103216013at_int J)))))
% 4.96/5.19 (assert (= tptp.ord_less_eq_nat (lambda ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M)) tptp.one_one_real)))))
% 4.96/5.19 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 4.96/5.19 (assert (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B3)))))
% 4.96/5.19 (assert (forall ((Z3 tptp.int)) (=> (forall ((N3 tptp.nat)) (not (= Z3 (@ tptp.semiri1314217659103216013at_int N3)))) (not (forall ((N3 tptp.nat)) (not (= Z3 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N3))))))))))
% 4.96/5.19 (assert (forall ((P (-> tptp.int Bool)) (Z3 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 Z3)))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.ord_less_eq_nat M2) N2))))
% 4.96/5.19 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B3)))))
% 4.96/5.19 (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))))))))
% 4.96/5.19 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (exists ((N3 tptp.nat)) (= K (@ tptp.semiri1314217659103216013at_int N3))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (Z3 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int M2)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N2)) Z3)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat M2) N2))) Z3))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat N2) M2)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N2)) (@ tptp.semiri1314217659103216013at_int M2)))))
% 4.96/5.19 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat A) B2)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B2)))))
% 4.96/5.19 (assert (= tptp.ord_less_eq_int (lambda ((W3 tptp.int) (Z6 tptp.int)) (exists ((N tptp.nat)) (= Z6 (@ (@ tptp.plus_plus_int W3) (@ tptp.semiri1314217659103216013at_int N)))))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N2)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int M2))))))
% 4.96/5.19 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.ord_max_nat X) Y)) (@ (@ tptp.ord_max_real (@ tptp.semiri5074537144036343181t_real X)) (@ tptp.semiri5074537144036343181t_real Y)))))
% 4.96/5.19 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.ord_max_nat X) Y)) (@ (@ tptp.ord_max_int (@ tptp.semiri1314217659103216013at_int X)) (@ tptp.semiri1314217659103216013at_int Y)))))
% 4.96/5.19 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.ord_max_nat X) Y)) (@ (@ tptp.ord_max_nat (@ tptp.semiri1316708129612266289at_nat X)) (@ tptp.semiri1316708129612266289at_nat Y)))))
% 4.96/5.19 (assert (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B3)))))
% 4.96/5.19 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B3)))))
% 4.96/5.19 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat N2)))))
% 4.96/5.19 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real Y) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) X))))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat M2) N2)) (@ (@ tptp.minus_minus_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.semiri5074537144036343181t_real N2))))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat M2) N2)) (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N2))))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat M2) N2)) (@ (@ tptp.minus_minus_nat (@ tptp.semiri1316708129612266289at_nat M2)) (@ tptp.semiri1316708129612266289at_nat N2))))))
% 4.96/5.19 (assert (forall ((X tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 C) (=> (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M3) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M3)) X)) C))) (= X tptp.zero_zero_real)))))))
% 4.96/5.19 (assert (forall ((M2 tptp.int)) (=> (forall ((N3 tptp.nat)) (not (= M2 (@ tptp.semiri1314217659103216013at_int N3)))) (not (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (not (= M2 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N3))))))))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int N2)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int M2))) (and (= N2 tptp.zero_zero_nat) (= M2 tptp.zero_zero_nat)))))
% 4.96/5.19 (assert (forall ((A tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc A)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A)) tptp.one_one_int))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N2)) tptp.one_one_int))))
% 4.96/5.19 (assert (= tptp.ord_less_int (lambda ((W3 tptp.int) (Z6 tptp.int)) (exists ((N tptp.nat)) (= Z6 (@ (@ tptp.plus_plus_int W3) (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N))))))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) tptp.zero_zero_int)))
% 4.96/5.19 (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)))))))))
% 4.96/5.19 (assert (forall ((F (-> tptp.int tptp.nat)) (A2 tptp.set_int)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X4 tptp.int)) (@ tptp.semiri1314217659103216013at_int (@ F X4)))) A2))))
% 4.96/5.19 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((X4 tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ F X4)))) A2))))
% 4.96/5.19 (assert (forall ((A tptp.int) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int M2))) (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)))))))))
% 4.96/5.19 (assert (forall ((A tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat M2))) (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)))))))))
% 4.96/5.19 (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)))))))
% 4.96/5.19 (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))))))))
% 4.96/5.19 (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)))))))))
% 4.96/5.19 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int K)))) (=> (@ (@ tptp.ord_less_int I) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_int (@ _let_1 I)) (@ _let_1 J)))))))
% 4.96/5.19 (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)))))))
% 4.96/5.19 (assert (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int X) tptp.zero_zero_int) (exists ((N3 tptp.nat)) (= X (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N3))))))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2)))) tptp.zero_zero_int)))
% 4.96/5.19 (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)))))))
% 4.96/5.19 (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))))
% 4.96/5.19 (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))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (=> (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ tptp.semiri5074537144036343181t_real M2))) (@ _let_1 (@ tptp.semiri5074537144036343181t_real N2))))))))
% 4.96/5.19 (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))))))))
% 4.96/5.19 (assert (forall ((P (-> tptp.int Bool)) (X tptp.nat) (Y tptp.nat)) (= (@ P (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat X) Y))) (and (=> (@ (@ tptp.ord_less_eq_nat Y) X) (@ P (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int X)) (@ tptp.semiri1314217659103216013at_int Y)))) (=> (@ (@ tptp.ord_less_nat X) Y) (@ P tptp.zero_zero_int))))))
% 4.96/5.19 (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))))))))
% 4.96/5.19 (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))))))))
% 4.96/5.19 (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))))))))
% 4.96/5.19 (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))))))))
% 4.96/5.19 (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))))))))
% 4.96/5.19 (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))))))
% 4.96/5.19 (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))))))
% 4.96/5.19 (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))))))
% 4.96/5.19 (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))))))
% 4.96/5.19 (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))))))
% 4.96/5.19 (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)))))))
% 4.96/5.19 (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)))))))
% 4.96/5.19 (assert (= tptp.semiri8010041392384452111omplex (lambda ((N tptp.nat)) (@ (@ (@ tptp.if_complex (= N tptp.zero_zero_nat)) tptp.zero_zero_complex) (@ (@ tptp.produc1917071388513777916omplex (lambda ((M tptp.nat) (Q5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ tptp.semiri8010041392384452111omplex M)))) (@ (@ (@ tptp.if_complex (= Q5 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex))))) (@ (@ tptp.divmod_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 4.96/5.19 (assert (= tptp.semiri4216267220026989637d_enat (lambda ((N tptp.nat)) (@ (@ (@ tptp.if_Extended_enat (= N tptp.zero_zero_nat)) tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.produc2676513652042109336d_enat (lambda ((M tptp.nat) (Q5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))) (@ tptp.semiri4216267220026989637d_enat M)))) (@ (@ (@ tptp.if_Extended_enat (= Q5 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) tptp.one_on7984719198319812577d_enat))))) (@ (@ tptp.divmod_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 4.96/5.19 (assert (= tptp.semiri5074537144036343181t_real (lambda ((N tptp.nat)) (@ (@ (@ tptp.if_real (= N tptp.zero_zero_nat)) tptp.zero_zero_real) (@ (@ tptp.produc1703576794950452218t_real (lambda ((M tptp.nat) (Q5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real M)))) (@ (@ (@ tptp.if_real (= Q5 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))))) (@ (@ tptp.divmod_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 4.96/5.19 (assert (= tptp.semiri1314217659103216013at_int (lambda ((N tptp.nat)) (@ (@ (@ tptp.if_int (= N tptp.zero_zero_nat)) tptp.zero_zero_int) (@ (@ tptp.produc6840382203811409530at_int (lambda ((M tptp.nat) (Q5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.semiri1314217659103216013at_int M)))) (@ (@ (@ tptp.if_int (= Q5 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))) (@ (@ tptp.divmod_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 4.96/5.19 (assert (= tptp.semiri1316708129612266289at_nat (lambda ((N tptp.nat)) (@ (@ (@ tptp.if_nat (= N tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.produc6842872674320459806at_nat (lambda ((M tptp.nat) (Q5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.semiri1316708129612266289at_nat M)))) (@ (@ (@ tptp.if_nat (= Q5 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))) (@ (@ tptp.divmod_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 4.96/5.19 (assert (forall ((H2 tptp.complex) (Z3 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 Z3))) (=> (not (= H2 tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z3) H2)) N2)) (@ _let_2 N2))) H2)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N2)) (@ _let_2 _let_1))) (@ (@ tptp.times_times_complex H2) (@ (@ tptp.groups2073611262835488442omplex (lambda ((P6 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((Q5 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z3) H2)) Q5)) (@ (@ tptp.power_power_complex Z3) (@ (@ 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))) P6))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))
% 4.96/5.19 (assert (forall ((H2 tptp.real) (Z3 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 Z3))) (=> (not (= H2 tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z3) H2)) N2)) (@ _let_2 N2))) H2)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ _let_2 _let_1))) (@ (@ tptp.times_times_real H2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((P6 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((Q5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z3) H2)) Q5)) (@ (@ tptp.power_power_real Z3) (@ (@ 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))) P6))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))
% 4.96/5.19 (assert (forall ((H2 tptp.real) (Z3 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 Z3))) (let ((_let_5 (@ (@ tptp.plus_plus_real Z3) H2))) (=> (not (= H2 tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real Z3)) K5) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real _let_5)) K5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real _let_5) N2)) (@ _let_4 N2))) H2)) (@ _let_3 (@ _let_4 _let_2))))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real _let_2))) (@ (@ tptp.power_power_real K5) (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ tptp.real_V7735802525324610683m_real H2)))))))))))))
% 4.96/5.19 (assert (forall ((H2 tptp.complex) (Z3 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 Z3))) (let ((_let_4 (@ (@ tptp.plus_plus_complex Z3) H2))) (=> (not (= H2 tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex Z3)) K5) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex _let_4)) K5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex _let_4) N2)) (@ _let_3 N2))) H2)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N2)) (@ _let_3 _let_2))))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.semiri5074537144036343181t_real _let_2))) (@ (@ tptp.power_power_real K5) (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ tptp.real_V1022390504157884413omplex H2))))))))))))
% 4.96/5.19 (assert (forall ((Z3 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) Z3)) _let_4) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.power_power_nat _let_3) _let_4))) (@ (@ tptp.comm_s2602460028002588243omplex Z3) N2))) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z3) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_2))) N2)))))))))
% 4.96/5.19 (assert (forall ((Z3 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) Z3)) _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 Z3) N2))) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z3) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2))) N2)))))))))
% 4.96/5.19 (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))))
% 4.96/5.19 (assert (= tptp.semiri4216267220026989637d_enat (lambda ((N tptp.nat)) (@ (@ (@ tptp.semiri8563196900006977889d_enat (lambda ((I3 tptp.extended_enat)) (@ (@ tptp.plus_p3455044024723400733d_enat I3) tptp.one_on7984719198319812577d_enat))) N) tptp.zero_z5237406670263579293d_enat))))
% 4.96/5.19 (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))))
% 4.96/5.19 (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))))
% 4.96/5.19 (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))))
% 4.96/5.19 (assert (forall ((B2 tptp.nat) (K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B2)) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int 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))))))))))
% 4.96/5.19 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (= (@ tptp.set_ord_lessThan_nat X) (@ tptp.set_ord_lessThan_nat Y)) (= X Y))))
% 4.96/5.19 (assert (forall ((X tptp.int) (Y tptp.int)) (= (= (@ tptp.set_ord_lessThan_int X) (@ tptp.set_ord_lessThan_int Y)) (= X Y))))
% 4.96/5.19 (assert (forall ((I tptp.set_nat) (K tptp.set_nat)) (= (@ (@ tptp.member_set_nat I) (@ tptp.set_or890127255671739683et_nat K)) (@ (@ tptp.ord_less_set_nat I) K))))
% 4.96/5.19 (assert (forall ((I tptp.extended_enat) (K tptp.extended_enat)) (= (@ (@ tptp.member_Extended_enat I) (@ tptp.set_or8419480210114673929d_enat K)) (@ (@ tptp.ord_le72135733267957522d_enat I) K))))
% 4.96/5.19 (assert (forall ((I tptp.real) (K tptp.real)) (= (@ (@ tptp.member_real I) (@ tptp.set_or5984915006950818249n_real K)) (@ (@ tptp.ord_less_real I) K))))
% 4.96/5.19 (assert (forall ((I tptp.nat) (K tptp.nat)) (= (@ (@ tptp.member_nat I) (@ tptp.set_ord_lessThan_nat K)) (@ (@ tptp.ord_less_nat I) K))))
% 4.96/5.19 (assert (forall ((I tptp.int) (K tptp.int)) (= (@ (@ tptp.member_int I) (@ tptp.set_ord_lessThan_int K)) (@ (@ tptp.ord_less_int I) K))))
% 4.96/5.19 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.set_ord_lessThan_nat K))))
% 4.96/5.19 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_or5984915006950818249n_real X)) (@ tptp.set_or5984915006950818249n_real Y)) (@ (@ tptp.ord_less_eq_real X) Y))))
% 4.96/5.19 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_ord_lessThan_nat X)) (@ tptp.set_ord_lessThan_nat Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))
% 4.96/5.19 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_lessThan_int X)) (@ tptp.set_ord_lessThan_int Y)) (@ (@ tptp.ord_less_eq_int X) Y))))
% 4.96/5.19 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 4.96/5.19 (assert (forall ((A tptp.int)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 4.96/5.19 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.comm_s2602460028002588243omplex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 4.96/5.19 (assert (forall ((A tptp.real)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 4.96/5.19 (assert (= (@ tptp.set_ord_lessThan_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat))
% 4.96/5.19 (assert (forall ((K tptp.extended_enat)) (let ((_let_1 (@ (@ tptp.insert_Extended_enat K) tptp.bot_bo7653980558646680370d_enat))) (= (@ (@ tptp.minus_925952699566721837d_enat _let_1) (@ tptp.set_or8419480210114673929d_enat K)) _let_1))))
% 4.96/5.19 (assert (forall ((K tptp.real)) (let ((_let_1 (@ (@ tptp.insert_real K) tptp.bot_bot_set_real))) (= (@ (@ tptp.minus_minus_set_real _let_1) (@ tptp.set_or5984915006950818249n_real K)) _let_1))))
% 4.96/5.19 (assert (forall ((K tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat K) tptp.bot_bot_set_nat))) (= (@ (@ tptp.minus_minus_set_nat _let_1) (@ tptp.set_ord_lessThan_nat K)) _let_1))))
% 4.96/5.19 (assert (forall ((K tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int K) tptp.bot_bot_set_int))) (= (@ (@ tptp.minus_minus_set_int _let_1) (@ tptp.set_ord_lessThan_int K)) _let_1))))
% 4.96/5.19 (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))))))
% 4.96/5.19 (assert (forall ((G (-> tptp.nat tptp.extended_enat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups7108830773950497114d_enat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_p3455044024723400733d_enat (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))))
% 4.96/5.19 (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))))))
% 4.96/5.19 (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))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M2) (@ tptp.semiri1314217659103216013at_int N2)) (= M2 N2))))
% 4.96/5.19 (assert (forall ((X tptp.real)) (not (= (@ tptp.set_or5984915006950818249n_real X) tptp.bot_bot_set_real))))
% 4.96/5.19 (assert (forall ((X tptp.int)) (not (= (@ tptp.set_ord_lessThan_int X) tptp.bot_bot_set_int))))
% 4.96/5.19 (assert (forall ((A tptp.int)) (not (@ tptp.finite_finite_int (@ tptp.set_ord_lessThan_int A)))))
% 4.96/5.19 (assert (= tptp.set_or890127255671739683et_nat (lambda ((U2 tptp.set_nat)) (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (@ (@ tptp.ord_less_set_nat X4) U2))))))
% 4.96/5.19 (assert (= tptp.set_or8419480210114673929d_enat (lambda ((U2 tptp.extended_enat)) (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (@ (@ tptp.ord_le72135733267957522d_enat X4) U2))))))
% 4.96/5.19 (assert (= tptp.set_or5984915006950818249n_real (lambda ((U2 tptp.real)) (@ tptp.collect_real (lambda ((X4 tptp.real)) (@ (@ tptp.ord_less_real X4) U2))))))
% 4.96/5.19 (assert (= tptp.set_ord_lessThan_nat (lambda ((U2 tptp.nat)) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.ord_less_nat X4) U2))))))
% 4.96/5.19 (assert (= tptp.set_ord_lessThan_int (lambda ((U2 tptp.int)) (@ tptp.collect_int (lambda ((X4 tptp.int)) (@ (@ tptp.ord_less_int X4) U2))))))
% 4.96/5.19 (assert (forall ((N2 tptp.extended_enat)) (= (= (@ tptp.set_or8419480210114673929d_enat N2) tptp.bot_bo7653980558646680370d_enat) (= N2 tptp.bot_bo4199563552545308370d_enat))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.set_ord_lessThan_nat N2) tptp.bot_bot_set_nat) (= N2 tptp.bot_bot_nat))))
% 4.96/5.19 (assert (forall ((M2 tptp.extended_enat) (N2 tptp.extended_enat)) (= (@ (@ tptp.ord_le2529575680413868914d_enat (@ tptp.set_or8419480210114673929d_enat M2)) (@ tptp.set_or8419480210114673929d_enat N2)) (@ (@ tptp.ord_le72135733267957522d_enat M2) N2))))
% 4.96/5.19 (assert (forall ((M2 tptp.real) (N2 tptp.real)) (= (@ (@ tptp.ord_less_set_real (@ tptp.set_or5984915006950818249n_real M2)) (@ tptp.set_or5984915006950818249n_real N2)) (@ (@ tptp.ord_less_real M2) N2))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_set_nat (@ tptp.set_ord_lessThan_nat M2)) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ tptp.ord_less_nat M2) N2))))
% 4.96/5.19 (assert (forall ((M2 tptp.int) (N2 tptp.int)) (= (@ (@ tptp.ord_less_set_int (@ tptp.set_ord_lessThan_int M2)) (@ tptp.set_ord_lessThan_int N2)) (@ (@ tptp.ord_less_int M2) N2))))
% 4.96/5.19 (assert (forall ((X tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.comm_s4663373288045622133er_nat X) N2))))))
% 4.96/5.19 (assert (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.comm_s7457072308508201937r_real X) N2))))))
% 4.96/5.19 (assert (forall ((X tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.comm_s4660882817536571857er_int X) N2))))))
% 4.96/5.19 (assert (forall ((A tptp.real) (N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A))) (=> (= (@ _let_1 N2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (= (@ _let_1 M2) tptp.zero_zero_real))))))
% 4.96/5.19 (assert (forall ((A tptp.complex) (N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex A))) (=> (= (@ _let_1 N2) tptp.zero_zero_complex) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (= (@ _let_1 M2) tptp.zero_zero_complex))))))
% 4.96/5.19 (assert (forall ((A tptp.real) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A))) (=> (not (= (@ _let_1 M2) tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (not (= (@ _let_1 N2) tptp.zero_zero_real)))))))
% 4.96/5.19 (assert (forall ((A tptp.complex) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex A))) (=> (not (= (@ _let_1 M2) tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (not (= (@ _let_1 N2) tptp.zero_zero_complex)))))))
% 4.96/5.19 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K)) (@ (@ tptp.insert_nat K) (@ tptp.set_ord_lessThan_nat K)))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.set_ord_lessThan_nat N2) tptp.bot_bot_set_nat) (= N2 tptp.zero_zero_nat))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S2) (exists ((K3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat S2) (@ tptp.set_ord_lessThan_nat K3))))))
% 4.96/5.19 (assert (= tptp.finite_finite_nat (lambda ((S6 tptp.set_nat)) (exists ((K2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat S6) (@ tptp.set_ord_lessThan_nat K2))))))
% 4.96/5.19 (assert (forall ((X tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.comm_s7457072308508201937r_real X) N2)))))
% 4.96/5.19 (assert (forall ((X tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.comm_s4663373288045622133er_nat X) N2)))))
% 4.96/5.19 (assert (forall ((X tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.comm_s4660882817536571857er_int X) N2)))))
% 4.96/5.19 (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)))))))
% 4.96/5.19 (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)))))))
% 4.96/5.19 (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)))))))
% 4.96/5.19 (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)))))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s3181272606743183617d_enat tptp.zero_z5237406670263579293d_enat) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_on7984719198319812577d_enat)) (=> (not _let_2) (= _let_1 tptp.zero_z5237406670263579293d_enat)))))))
% 4.96/5.19 (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))))))
% 4.96/5.19 (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)))))
% 4.96/5.19 (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)))))
% 4.96/5.19 (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 ((X4 tptp.int)) (@ (@ tptp.minus_minus_nat (@ P X4)) (@ Q X4)))) _let_1))))))
% 4.96/5.19 (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 ((X4 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ P X4)) (@ Q X4)))) _let_1))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (B2 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M2))) (=> (@ (@ tptp.ord_less_eq_real _let_1) (@ (@ tptp.power_power_real B2) N2)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B2) _let_1)) (@ tptp.semiri5074537144036343181t_real N2))))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (B2 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M2))) (=> (@ (@ tptp.ord_less_real _let_1) (@ (@ tptp.power_power_real B2) N2)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (@ (@ tptp.ord_less_real (@ (@ tptp.log B2) _let_1)) (@ tptp.semiri5074537144036343181t_real N2))))))))
% 4.96/5.19 (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)))))
% 4.96/5.19 (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)))))
% 4.96/5.19 (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)))))
% 4.96/5.19 (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)))))
% 4.96/5.19 (assert (forall ((A tptp.extended_enat) (N2 tptp.nat)) (= (@ (@ tptp.comm_s3181272606743183617d_enat A) (@ tptp.suc N2)) (@ (@ tptp.times_7803423173614009249d_enat A) (@ (@ tptp.comm_s3181272606743183617d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) tptp.one_on7984719198319812577d_enat)) N2)))))
% 4.96/5.19 (assert (forall ((Z3 tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex Z3))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex Z3) (@ tptp.semiri8010041392384452111omplex N2))) (@ _let_1 N2))))))
% 4.96/5.19 (assert (forall ((Z3 tptp.extended_enat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s3181272606743183617d_enat Z3))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_7803423173614009249d_enat (@ (@ tptp.plus_p3455044024723400733d_enat Z3) (@ tptp.semiri4216267220026989637d_enat N2))) (@ _let_1 N2))))))
% 4.96/5.19 (assert (forall ((Z3 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z3))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real Z3) (@ tptp.semiri5074537144036343181t_real N2))) (@ _let_1 N2))))))
% 4.96/5.19 (assert (forall ((Z3 tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z3))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int Z3) (@ tptp.semiri1314217659103216013at_int N2))) (@ _let_1 N2))))))
% 4.96/5.19 (assert (forall ((Z3 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z3))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat Z3) (@ tptp.semiri1316708129612266289at_nat N2))) (@ _let_1 N2))))))
% 4.96/5.19 (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)))))))
% 4.96/5.19 (assert (forall ((A tptp.extended_enat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s3181272606743183617d_enat A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_7803423173614009249d_enat (@ _let_1 N2)) (@ (@ tptp.plus_p3455044024723400733d_enat A) (@ tptp.semiri4216267220026989637d_enat N2)))))))
% 4.96/5.19 (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)))))))
% 4.96/5.19 (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)))))))
% 4.96/5.19 (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)))))))
% 4.96/5.19 (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))))
% 4.96/5.19 (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))))
% 4.96/5.19 (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))))
% 4.96/5.19 (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))))
% 4.96/5.19 (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))))
% 4.96/5.19 (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))))
% 4.96/5.19 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (= (= (@ (@ tptp.comm_s2602460028002588243omplex A) N2) tptp.zero_zero_complex) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_nat K2) N2) (= A (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex K2))))))))
% 4.96/5.19 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (= (@ (@ tptp.comm_s7457072308508201937r_real A) N2) tptp.zero_zero_real) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_nat K2) N2) (= A (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real K2))))))))
% 4.96/5.19 (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)))))
% 4.96/5.19 (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)))))
% 4.96/5.19 (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)))))
% 4.96/5.19 (assert (forall ((Z3 tptp.complex) (N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex Z3))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M2)) (@ (@ tptp.times_times_complex (@ _let_1 N2)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z3) (@ tptp.semiri8010041392384452111omplex N2))) M2))))))
% 4.96/5.19 (assert (forall ((Z3 tptp.extended_enat) (N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s3181272606743183617d_enat Z3))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M2)) (@ (@ tptp.times_7803423173614009249d_enat (@ _let_1 N2)) (@ (@ tptp.comm_s3181272606743183617d_enat (@ (@ tptp.plus_p3455044024723400733d_enat Z3) (@ tptp.semiri4216267220026989637d_enat N2))) M2))))))
% 4.96/5.19 (assert (forall ((Z3 tptp.real) (N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z3))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M2)) (@ (@ tptp.times_times_real (@ _let_1 N2)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z3) (@ tptp.semiri5074537144036343181t_real N2))) M2))))))
% 4.96/5.19 (assert (forall ((Z3 tptp.int) (N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z3))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M2)) (@ (@ tptp.times_times_int (@ _let_1 N2)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int Z3) (@ tptp.semiri1314217659103216013at_int N2))) M2))))))
% 4.96/5.19 (assert (forall ((Z3 tptp.nat) (N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z3))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M2)) (@ (@ tptp.times_times_nat (@ _let_1 N2)) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat Z3) (@ tptp.semiri1316708129612266289at_nat N2))) M2))))))
% 4.96/5.19 (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))))))
% 4.96/5.19 (assert (forall ((G (-> tptp.nat tptp.extended_enat)) (N2 tptp.nat)) (= (@ (@ tptp.groups7108830773950497114d_enat G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_p3455044024723400733d_enat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups7108830773950497114d_enat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 4.96/5.19 (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))))))
% 4.96/5.19 (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))))))
% 4.96/5.19 (assert (forall ((F (-> tptp.nat tptp.int)) (M2 tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc N))) (@ F N)))) (@ tptp.set_ord_lessThan_nat M2)) (@ (@ tptp.minus_minus_int (@ F M2)) (@ F tptp.zero_zero_nat)))))
% 4.96/5.19 (assert (forall ((F (-> tptp.nat tptp.real)) (M2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_real (@ F (@ tptp.suc N))) (@ F N)))) (@ tptp.set_ord_lessThan_nat M2)) (@ (@ tptp.minus_minus_real (@ F M2)) (@ F tptp.zero_zero_nat)))))
% 4.96/5.19 (assert (forall ((F (-> tptp.nat tptp.int)) (M2 tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_int (@ F N)) (@ F (@ tptp.suc N))))) (@ tptp.set_ord_lessThan_nat M2)) (@ (@ tptp.minus_minus_int (@ F tptp.zero_zero_nat)) (@ F M2)))))
% 4.96/5.19 (assert (forall ((F (-> tptp.nat tptp.real)) (M2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N)) (@ F (@ tptp.suc N))))) (@ tptp.set_ord_lessThan_nat M2)) (@ (@ tptp.minus_minus_real (@ F tptp.zero_zero_nat)) (@ F M2)))))
% 4.96/5.19 (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 ((K2 tptp.nat)) (@ G (@ tptp.suc K2)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 4.96/5.19 (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 ((K2 tptp.nat)) (@ G (@ tptp.suc K2)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat) (M2 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)) M2) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M2)))))))
% 4.96/5.19 (assert (forall ((X tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X))) (let ((_let_2 (@ tptp.minus_minus_int tptp.one_one_int))) (= (@ _let_2 (@ _let_1 N2)) (@ (@ tptp.times_times_int (@ _let_2 X)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.set_ord_lessThan_nat N2))))))))
% 4.96/5.19 (assert (forall ((X tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X))) (let ((_let_2 (@ tptp.minus_minus_complex tptp.one_one_complex))) (= (@ _let_2 (@ _let_1 N2)) (@ (@ tptp.times_times_complex (@ _let_2 X)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_lessThan_nat N2))))))))
% 4.96/5.19 (assert (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X))) (let ((_let_2 (@ tptp.minus_minus_real tptp.one_one_real))) (= (@ _let_2 (@ _let_1 N2)) (@ (@ tptp.times_times_real (@ _let_2 X)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_lessThan_nat N2))))))))
% 4.96/5.19 (assert (forall ((X tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X))) (= (@ (@ tptp.minus_minus_int (@ _let_1 N2)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) tptp.one_one_int)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.set_ord_lessThan_nat N2)))))))
% 4.96/5.19 (assert (forall ((X tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X))) (= (@ (@ tptp.minus_minus_complex (@ _let_1 N2)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X) tptp.one_one_complex)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_lessThan_nat N2)))))))
% 4.96/5.19 (assert (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X))) (= (@ (@ tptp.minus_minus_real (@ _let_1 N2)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X) tptp.one_one_real)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_lessThan_nat N2)))))))
% 4.96/5.19 (assert (forall ((X tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X))) (=> (not (= X tptp.one_one_complex)) (= (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ _let_1 N2)) tptp.one_one_complex)) (@ (@ tptp.minus_minus_complex X) tptp.one_one_complex)))))))
% 4.96/5.19 (assert (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X))) (=> (not (= X tptp.one_one_real)) (= (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ _let_1 N2)) tptp.one_one_real)) (@ (@ tptp.minus_minus_real X) tptp.one_one_real)))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (Z3 tptp.complex)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex Z3))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ _let_1 N2) (@ (@ tptp.times_times_complex (@ _let_1 M2)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z3) (@ tptp.semiri8010041392384452111omplex M2))) (@ (@ tptp.minus_minus_nat N2) M2))))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (Z3 tptp.extended_enat)) (let ((_let_1 (@ tptp.comm_s3181272606743183617d_enat Z3))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ _let_1 N2) (@ (@ tptp.times_7803423173614009249d_enat (@ _let_1 M2)) (@ (@ tptp.comm_s3181272606743183617d_enat (@ (@ tptp.plus_p3455044024723400733d_enat Z3) (@ tptp.semiri4216267220026989637d_enat M2))) (@ (@ tptp.minus_minus_nat N2) M2))))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (Z3 tptp.real)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z3))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ _let_1 N2) (@ (@ tptp.times_times_real (@ _let_1 M2)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z3) (@ tptp.semiri5074537144036343181t_real M2))) (@ (@ tptp.minus_minus_nat N2) M2))))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (Z3 tptp.int)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z3))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ _let_1 N2) (@ (@ tptp.times_times_int (@ _let_1 M2)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int Z3) (@ tptp.semiri1314217659103216013at_int M2))) (@ (@ tptp.minus_minus_nat N2) M2))))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z3))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ _let_1 N2) (@ (@ tptp.times_times_nat (@ _let_1 M2)) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat Z3) (@ tptp.semiri1316708129612266289at_nat M2))) (@ (@ tptp.minus_minus_nat N2) M2))))))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) M2) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M2)))))))
% 4.96/5.19 (assert (forall ((X tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_2 (@ tptp.power_power_complex X))) (let ((_let_3 (@ (@ tptp.groups2073611262835488442omplex _let_2) (@ tptp.set_ord_lessThan_nat N2)))) (let ((_let_4 (= X tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (@ tptp.semiri8010041392384452111omplex N2))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 (@ _let_2 N2))) (@ _let_1 X)))))))))))
% 4.96/5.19 (assert (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (let ((_let_2 (@ tptp.power_power_real X))) (let ((_let_3 (@ (@ tptp.groups6591440286371151544t_real _let_2) (@ tptp.set_ord_lessThan_nat N2)))) (let ((_let_4 (= X tptp.one_one_real))) (and (=> _let_4 (= _let_3 (@ tptp.semiri5074537144036343181t_real N2))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_real (@ _let_1 (@ _let_2 N2))) (@ _let_1 X)))))))))))
% 4.96/5.19 (assert (forall ((Z3 tptp.int) (H2 tptp.int) (M2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M2))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((P6 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int Z3))) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int Z3) H2)) (@ (@ tptp.minus_minus_nat M2) P6))) (@ _let_1 P6))) (@ _let_1 M2))))) _let_1) (@ (@ tptp.groups3539618377306564664at_int (lambda ((P6 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M2) P6))) (let ((_let_2 (@ tptp.power_power_int Z3))) (@ (@ tptp.times_times_int (@ _let_2 P6)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int Z3) H2)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 4.96/5.19 (assert (forall ((Z3 tptp.complex) (H2 tptp.complex) (M2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M2))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((P6 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex Z3))) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z3) H2)) (@ (@ tptp.minus_minus_nat M2) P6))) (@ _let_1 P6))) (@ _let_1 M2))))) _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((P6 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M2) P6))) (let ((_let_2 (@ tptp.power_power_complex Z3))) (@ (@ tptp.times_times_complex (@ _let_2 P6)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z3) H2)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 4.96/5.19 (assert (forall ((Z3 tptp.real) (H2 tptp.real) (M2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M2))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((P6 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real Z3))) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z3) H2)) (@ (@ tptp.minus_minus_nat M2) P6))) (@ _let_1 P6))) (@ _let_1 M2))))) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((P6 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M2) P6))) (let ((_let_2 (@ tptp.power_power_real Z3))) (@ (@ tptp.times_times_real (@ _let_2 P6)) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z3) H2)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 4.96/5.19 (assert (forall ((X tptp.int) (N2 tptp.nat) (Y tptp.int)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) Y)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((P6 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X) P6)) (@ (@ tptp.power_power_int Y) (@ (@ tptp.minus_minus_nat N2) P6))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 4.96/5.19 (assert (forall ((X tptp.complex) (N2 tptp.nat) (Y tptp.complex)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex X) _let_1)) (@ (@ tptp.power_power_complex Y) _let_1)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X) Y)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((P6 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex X) P6)) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat N2) P6))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 4.96/5.19 (assert (forall ((X tptp.real) (N2 tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X) Y)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((P6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real X) P6)) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat N2) P6))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 4.96/5.19 (assert (forall ((X tptp.int) (N2 tptp.nat) (Y tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int X) N2)) (@ (@ tptp.power_power_int Y) N2)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) Y)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int Y) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I3)))) (@ (@ tptp.power_power_int X) I3)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 4.96/5.19 (assert (forall ((X tptp.complex) (N2 tptp.nat) (Y tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex X) N2)) (@ (@ tptp.power_power_complex Y) N2)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X) Y)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I3)))) (@ (@ tptp.power_power_complex X) I3)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 4.96/5.19 (assert (forall ((X tptp.real) (N2 tptp.nat) (Y tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X) N2)) (@ (@ tptp.power_power_real Y) N2)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X) Y)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I3)))) (@ (@ tptp.power_power_real X) I3)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 4.96/5.19 (assert (forall ((R2 tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex R2))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex R2) (@ tptp.semiri8010041392384452111omplex K))) (@ (@ tptp.comm_s2602460028002588243omplex _let_1) K)) (@ (@ tptp.times_times_complex R2) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)) K))))))
% 4.96/5.19 (assert (forall ((R2 tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real R2))) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real R2) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.comm_s7457072308508201937r_real _let_1) K)) (@ (@ tptp.times_times_real R2) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) K))))))
% 4.96/5.19 (assert (forall ((R2 tptp.int) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int R2))) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int R2) (@ tptp.semiri1314217659103216013at_int K))) (@ (@ tptp.comm_s4660882817536571857er_int _let_1) K)) (@ (@ tptp.times_times_int R2) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) K))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (@ (@ tptp.ord_less_real (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M2))) (@ tptp.semiri5074537144036343181t_real N2)))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_nat M2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M2))) (@ tptp.semiri5074537144036343181t_real N2)))))))
% 4.96/5.19 (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))))))
% 4.96/5.19 (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))))))
% 4.96/5.19 (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))))))
% 4.96/5.19 (assert (forall ((X tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_int tptp.one_one_int))) (= (@ _let_1 (@ (@ tptp.power_power_int X) N2)) (@ (@ tptp.times_times_int (@ _let_1 X)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_int X) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I3))))) (@ tptp.set_ord_lessThan_nat N2)))))))
% 4.96/5.19 (assert (forall ((X tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (= (@ _let_1 (@ (@ tptp.power_power_complex X) N2)) (@ (@ tptp.times_times_complex (@ _let_1 X)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_complex X) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I3))))) (@ tptp.set_ord_lessThan_nat N2)))))))
% 4.96/5.19 (assert (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (= (@ _let_1 (@ (@ tptp.power_power_real X) N2)) (@ (@ tptp.times_times_real (@ _let_1 X)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_real X) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I3))))) (@ tptp.set_ord_lessThan_nat N2)))))))
% 4.96/5.19 (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))))))
% 4.96/5.19 (assert (forall ((B2 tptp.complex) (K tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex B2)) K) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex B2) (@ tptp.semiri8010041392384452111omplex K))) tptp.one_one_complex)) K)))))
% 4.96/5.19 (assert (forall ((B2 tptp.real) (K tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real B2)) K) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real B2) (@ tptp.semiri5074537144036343181t_real K))) tptp.one_one_real)) K)))))
% 4.96/5.19 (assert (forall ((B2 tptp.int) (K tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int B2)) K) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) K)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int B2) (@ tptp.semiri1314217659103216013at_int K))) tptp.one_one_int)) K)))))
% 4.96/5.19 (assert (forall ((B2 tptp.complex) (K tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex B2) (@ tptp.semiri8010041392384452111omplex K))) tptp.one_one_complex)) K) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K)) (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex B2)) K)))))
% 4.96/5.19 (assert (forall ((B2 tptp.real) (K tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real B2) (@ tptp.semiri5074537144036343181t_real K))) tptp.one_one_real)) K) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K)) (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real B2)) K)))))
% 4.96/5.19 (assert (forall ((B2 tptp.int) (K tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int B2) (@ tptp.semiri1314217659103216013at_int K))) tptp.one_one_int)) K) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) K)) (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int B2)) K)))))
% 4.96/5.19 (assert (forall ((B2 tptp.nat) (N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (=> (@ (@ 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))) B2) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B2)) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N2)) tptp.one_one_int))))))))
% 4.96/5.19 (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))))))))
% 4.96/5.19 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real X)) tptp.zero_zero_real) (= X tptp.zero_zero_real))))
% 4.96/5.19 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X)) tptp.zero_zero_real) (= X tptp.zero_zero_complex))))
% 4.96/5.19 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.real_V7735802525324610683m_real X)) (not (= X tptp.zero_zero_real)))))
% 4.96/5.19 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.real_V1022390504157884413omplex X)) (not (= X tptp.zero_zero_complex)))))
% 4.96/5.19 (assert (forall ((X tptp.real)) (= (= (@ tptp.real_V7735802525324610683m_real X) tptp.zero_zero_real) (= X tptp.zero_zero_real))))
% 4.96/5.19 (assert (forall ((X tptp.complex)) (= (= (@ tptp.real_V1022390504157884413omplex X) tptp.zero_zero_real) (= X tptp.zero_zero_complex))))
% 4.96/5.19 (assert (= (@ tptp.real_V7735802525324610683m_real tptp.zero_zero_real) tptp.zero_zero_real))
% 4.96/5.19 (assert (= (@ tptp.real_V1022390504157884413omplex tptp.zero_zero_complex) tptp.zero_zero_real))
% 4.96/5.19 (assert (forall ((B2 tptp.real) (A tptp.real)) (=> (not (= B2 tptp.zero_zero_real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.divide_divide_real A) B2)) (@ (@ tptp.divide_divide_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B2))))))
% 4.96/5.19 (assert (forall ((B2 tptp.complex) (A tptp.complex)) (=> (not (= B2 tptp.zero_zero_complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.divide1717551699836669952omplex A) B2)) (@ (@ tptp.divide_divide_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B2))))))
% 4.96/5.19 (assert (forall ((A tptp.real) (B2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B2))) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real A) B2)))))
% 4.96/5.19 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B2))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex A) B2)))))
% 4.96/5.19 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X)) Y)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X) Y)))))
% 4.96/5.19 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex X)) Y)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X) Y)))))
% 4.96/5.19 (assert (forall ((W2 tptp.real) (N2 tptp.nat) (Z3 tptp.real)) (=> (= (@ (@ tptp.power_power_real W2) N2) (@ (@ tptp.power_power_real Z3) N2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.real_V7735802525324610683m_real W2) (@ tptp.real_V7735802525324610683m_real Z3))))))
% 4.96/5.19 (assert (forall ((W2 tptp.complex) (N2 tptp.nat) (Z3 tptp.complex)) (=> (= (@ (@ tptp.power_power_complex W2) N2) (@ (@ tptp.power_power_complex Z3) N2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.real_V1022390504157884413omplex W2) (@ tptp.real_V1022390504157884413omplex Z3))))))
% 4.96/5.19 (assert (forall ((X tptp.real) (Y tptp.real) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y))) E2) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X) Y))) E2))))
% 4.96/5.19 (assert (forall ((X tptp.complex) (Y tptp.complex) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y))) E2) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X) Y))) E2))))
% 4.96/5.19 (assert (forall ((X tptp.real) (R2 tptp.real) (Y tptp.real) (S tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X)) R2) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Y)) S) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X) Y))) (@ (@ tptp.plus_plus_real R2) S))))))
% 4.96/5.19 (assert (forall ((X tptp.complex) (R2 tptp.real) (Y tptp.complex) (S tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X)) R2) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Y)) S) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X) Y))) (@ (@ tptp.plus_plus_real R2) S))))))
% 4.96/5.19 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real A) B2))) C) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real B2)) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real A)) C)))))
% 4.96/5.19 (assert (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex A) B2))) C) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex B2)) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex A)) C)))))
% 4.96/5.19 (assert (forall ((X tptp.real) (Y tptp.real) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y))) E2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X) Y))) E2))))
% 4.96/5.19 (assert (forall ((X tptp.complex) (Y tptp.complex) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y))) E2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X) Y))) E2))))
% 4.96/5.19 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X) Y))) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y)))))
% 4.96/5.19 (assert (forall ((X tptp.complex) (Y tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X) Y))) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y)))))
% 4.96/5.19 (assert (forall ((A tptp.real) (R2 tptp.real) (B2 tptp.real) (S tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real A)) R2) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real B2)) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real A) B2))) (@ (@ tptp.plus_plus_real R2) S))))))
% 4.96/5.19 (assert (forall ((A tptp.complex) (R2 tptp.real) (B2 tptp.complex) (S tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex A)) R2) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex B2)) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex A) B2))) (@ (@ tptp.plus_plus_real R2) S))))))
% 4.96/5.19 (assert (forall ((W2 tptp.real) (N2 tptp.nat)) (=> (= (@ (@ tptp.power_power_real W2) N2) tptp.one_one_real) (or (= (@ tptp.real_V7735802525324610683m_real W2) tptp.one_one_real) (= N2 tptp.zero_zero_nat)))))
% 4.96/5.19 (assert (forall ((W2 tptp.complex) (N2 tptp.nat)) (=> (= (@ (@ tptp.power_power_complex W2) N2) tptp.one_one_complex) (or (= (@ tptp.real_V1022390504157884413omplex W2) tptp.one_one_real) (= N2 tptp.zero_zero_nat)))))
% 4.96/5.19 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B2)) (@ (@ tptp.plus_plus_real C) D)))) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A) C))) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real B2) D))))))
% 4.96/5.19 (assert (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex) (D tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) B2)) (@ (@ tptp.plus_plus_complex C) D)))) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A) C))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex B2) D))))))
% 4.96/5.19 (assert (forall ((F (-> tptp.nat tptp.nat)) (Mm tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ F (@ tptp.suc K2)))) (@ tptp.set_ord_lessThan_nat Mm)) (@ (@ tptp.groups3542108847815614940at_nat F) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) Mm)))))
% 4.96/5.19 (assert (forall ((F (-> tptp.nat tptp.real)) (Mm tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ F (@ tptp.suc K2)))) (@ tptp.set_ord_lessThan_nat Mm)) (@ (@ tptp.groups6591440286371151544t_real F) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) Mm)))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M)) (@ (@ tptp.power_power_real tptp.zero_zero_real) M)))) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) tptp.one_one_real)))
% 4.96/5.19 (assert (forall ((Z3 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 Z3) _let_2)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z3) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex _let_1)))) _let_2)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((K2 tptp.nat)) (@ (@ tptp.plus_plus_complex Z3) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri8010041392384452111omplex K2)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) tptp.one_one_nat))))))))
% 4.96/5.19 (assert (forall ((Z3 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 Z3) _let_2)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z3) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1)))) _let_2)) (@ (@ tptp.groups129246275422532515t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.plus_plus_real Z3) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real K2)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) tptp.one_one_nat))))))))
% 4.96/5.19 (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)))))
% 4.96/5.19 (assert (= tptp.comm_s3181272606743183617d_enat (lambda ((A3 tptp.extended_enat) (N tptp.nat)) (@ (@ (@ tptp.if_Extended_enat (= N tptp.zero_zero_nat)) tptp.one_on7984719198319812577d_enat) (@ (@ (@ (@ tptp.set_fo2538466533108834004d_enat (lambda ((O tptp.nat) (__flatten_var_0 tptp.extended_enat)) (@ (@ tptp.times_7803423173614009249d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A3) (@ tptp.semiri4216267220026989637d_enat O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) tptp.one_on7984719198319812577d_enat)))))
% 4.96/5.19 (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)))))
% 4.96/5.19 (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)))))
% 4.96/5.19 (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)))))
% 4.96/5.19 (assert (forall ((X tptp.real) (B2 tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.powr_real B2))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B2) (= (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log B2) X)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int K)) tptp.one_one_int)) (and (@ (@ tptp.ord_less_real (@ _let_1 (@ tptp.semiri5074537144036343181t_real K))) X) (@ (@ tptp.ord_less_eq_real X) (@ _let_1 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))))))))
% 4.96/5.19 (assert (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Z3)) 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 Z3) N)))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real tptp.one_one_real) Z3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 4.96/5.19 (assert (forall ((Z3 tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Z3)) tptp.one_one_real) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ tptp.suc N))) (@ (@ tptp.power_power_complex Z3) N)))) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex tptp.one_one_complex) Z3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 4.96/5.19 (assert (forall ((W2 tptp.real) (Z3 tptp.real)) (= (= (@ (@ tptp.powr_real W2) Z3) tptp.zero_zero_real) (= W2 tptp.zero_zero_real))))
% 4.96/5.19 (assert (forall ((Z3 tptp.real)) (= (@ (@ tptp.powr_real tptp.zero_zero_real) Z3) tptp.zero_zero_real)))
% 4.96/5.19 (assert (forall ((F (-> tptp.int tptp.nat)) (A2 tptp.set_int)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups1707563613775114915nt_nat F) A2)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X4 tptp.int)) (@ tptp.semiri1314217659103216013at_int (@ F X4)))) A2))))
% 4.96/5.19 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.groups708209901874060359at_nat F) A2)) (@ (@ tptp.groups129246275422532515t_real (lambda ((X4 tptp.nat)) (@ tptp.semiri5074537144036343181t_real (@ F X4)))) A2))))
% 4.96/5.19 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups708209901874060359at_nat F) A2)) (@ (@ tptp.groups705719431365010083at_int (lambda ((X4 tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ F X4)))) A2))))
% 4.96/5.19 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.groups708209901874060359at_nat F) A2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) (@ tptp.semiri1316708129612266289at_nat (@ F X4)))) A2))))
% 4.96/5.19 (assert (forall ((F (-> tptp.nat tptp.int)) (A2 tptp.set_nat)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.groups705719431365010083at_int F) A2)) (@ (@ tptp.groups129246275422532515t_real (lambda ((X4 tptp.nat)) (@ tptp.ring_1_of_int_real (@ F X4)))) A2))))
% 4.96/5.19 (assert (forall ((F (-> tptp.nat tptp.int)) (A2 tptp.set_nat)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.groups705719431365010083at_int F) A2)) (@ (@ tptp.groups705719431365010083at_int (lambda ((X4 tptp.nat)) (@ tptp.ring_1_of_int_int (@ F X4)))) A2))))
% 4.96/5.19 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.groups1705073143266064639nt_int F) A2)) (@ (@ tptp.groups2316167850115554303t_real (lambda ((X4 tptp.int)) (@ tptp.ring_1_of_int_real (@ F X4)))) A2))))
% 4.96/5.19 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.groups1705073143266064639nt_int F) A2)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X4 tptp.int)) (@ tptp.ring_1_of_int_int (@ F X4)))) A2))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (= (@ (@ tptp.groups861055069439313189ex_nat F) A2) tptp.zero_zero_nat) (exists ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A2) (= (@ F X4) tptp.zero_zero_nat)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (= (= (@ (@ tptp.groups1707563613775114915nt_nat F) A2) tptp.zero_zero_nat) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A2) (= (@ F X4) tptp.zero_zero_nat)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (= (@ (@ tptp.groups2880970938130013265at_nat F) A2) tptp.zero_zero_nat) (exists ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) A2) (= (@ F X4) tptp.zero_zero_nat)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat A2) (= (= (@ (@ tptp.groups129246275422532515t_real F) A2) tptp.zero_zero_real) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A2) (= (@ F X4) tptp.zero_zero_real)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (= (@ (@ tptp.groups766887009212190081x_real F) A2) tptp.zero_zero_real) (exists ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A2) (= (@ F X4) tptp.zero_zero_real)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A2) (= (= (@ (@ tptp.groups2316167850115554303t_real F) A2) tptp.zero_zero_real) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A2) (= (@ F X4) tptp.zero_zero_real)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (= (@ (@ tptp.groups97031904164794029t_real F) A2) tptp.zero_zero_real) (exists ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) A2) (= (@ F X4) tptp.zero_zero_real)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (= (@ (@ tptp.groups858564598930262913ex_int F) A2) tptp.zero_zero_int) (exists ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A2) (= (@ F X4) tptp.zero_zero_int)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.int))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (= (@ (@ tptp.groups2878480467620962989at_int F) A2) tptp.zero_zero_int) (exists ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) A2) (= (@ F X4) tptp.zero_zero_int)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat A2) (= (= (@ (@ tptp.groups6464643781859351333omplex F) A2) tptp.zero_zero_complex) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A2) (= (@ F X4) tptp.zero_zero_complex)))))))
% 4.96/5.19 (assert (forall ((G (-> tptp.extended_enat tptp.nat))) (= (@ (@ tptp.groups2880970938130013265at_nat G) tptp.bot_bo7653980558646680370d_enat) tptp.one_one_nat)))
% 4.96/5.19 (assert (forall ((G (-> tptp.extended_enat tptp.int))) (= (@ (@ tptp.groups2878480467620962989at_int G) tptp.bot_bo7653980558646680370d_enat) tptp.one_one_int)))
% 4.96/5.19 (assert (forall ((G (-> tptp.extended_enat tptp.complex))) (= (@ (@ tptp.groups4622424608036095791omplex G) tptp.bot_bo7653980558646680370d_enat) tptp.one_one_complex)))
% 4.96/5.19 (assert (forall ((G (-> tptp.extended_enat tptp.real))) (= (@ (@ tptp.groups97031904164794029t_real G) tptp.bot_bo7653980558646680370d_enat) tptp.one_one_real)))
% 4.96/5.19 (assert (forall ((G (-> tptp.real tptp.nat))) (= (@ (@ tptp.groups4696554848551431203al_nat G) tptp.bot_bot_set_real) tptp.one_one_nat)))
% 4.96/5.19 (assert (forall ((G (-> tptp.real tptp.int))) (= (@ (@ tptp.groups4694064378042380927al_int G) tptp.bot_bot_set_real) tptp.one_one_int)))
% 4.96/5.19 (assert (forall ((G (-> tptp.real tptp.complex))) (= (@ (@ tptp.groups713298508707869441omplex G) tptp.bot_bot_set_real) tptp.one_one_complex)))
% 4.96/5.19 (assert (forall ((G (-> tptp.real tptp.real))) (= (@ (@ tptp.groups1681761925125756287l_real G) tptp.bot_bot_set_real) tptp.one_one_real)))
% 4.96/5.19 (assert (forall ((G (-> tptp.nat tptp.complex))) (= (@ (@ tptp.groups6464643781859351333omplex G) tptp.bot_bot_set_nat) tptp.one_one_complex)))
% 4.96/5.19 (assert (forall ((G (-> tptp.nat tptp.real))) (= (@ (@ tptp.groups129246275422532515t_real G) tptp.bot_bot_set_nat) tptp.one_one_real)))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (=> (not (@ tptp.finite3207457112153483333omplex A2)) (= (@ (@ tptp.groups861055069439313189ex_nat G) A2) tptp.one_one_nat))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.nat))) (=> (not (@ tptp.finite_finite_int A2)) (= (@ (@ tptp.groups1707563613775114915nt_nat G) A2) tptp.one_one_nat))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.nat))) (=> (not (@ tptp.finite4001608067531595151d_enat A2)) (= (@ (@ tptp.groups2880970938130013265at_nat G) A2) tptp.one_one_nat))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.int))) (=> (not (@ tptp.finite3207457112153483333omplex A2)) (= (@ (@ tptp.groups858564598930262913ex_int G) A2) tptp.one_one_int))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.int))) (=> (not (@ tptp.finite4001608067531595151d_enat A2)) (= (@ (@ tptp.groups2878480467620962989at_int G) A2) tptp.one_one_int))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.complex))) (=> (not (@ tptp.finite_finite_nat A2)) (= (@ (@ tptp.groups6464643781859351333omplex G) A2) tptp.one_one_complex))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.complex))) (=> (not (@ tptp.finite3207457112153483333omplex A2)) (= (@ (@ tptp.groups3708469109370488835omplex G) A2) tptp.one_one_complex))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.complex))) (=> (not (@ tptp.finite_finite_int A2)) (= (@ (@ tptp.groups7440179247065528705omplex G) A2) tptp.one_one_complex))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.complex))) (=> (not (@ tptp.finite4001608067531595151d_enat A2)) (= (@ (@ tptp.groups4622424608036095791omplex G) A2) tptp.one_one_complex))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.real))) (=> (not (@ tptp.finite_finite_nat A2)) (= (@ (@ tptp.groups129246275422532515t_real G) A2) tptp.one_one_real))))
% 4.96/5.19 (assert (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.powr_real X) tptp.zero_zero_real))) (let ((_let_2 (= X tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (A tptp.real) (F (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real A) A2) (@ (@ tptp.dvd_dvd_nat (@ F A)) (@ (@ tptp.groups4696554848551431203al_nat F) A2))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (A tptp.complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex A) A2) (@ (@ tptp.dvd_dvd_nat (@ F A)) (@ (@ tptp.groups861055069439313189ex_nat F) A2))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (A tptp.int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int A) A2) (@ (@ tptp.dvd_dvd_nat (@ F A)) (@ (@ tptp.groups1707563613775114915nt_nat F) A2))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (A tptp.extended_enat) (F (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ (@ tptp.member_Extended_enat A) A2) (@ (@ tptp.dvd_dvd_nat (@ F A)) (@ (@ tptp.groups2880970938130013265at_nat F) A2))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (A tptp.real) (F (-> tptp.real tptp.int))) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real A) A2) (@ (@ tptp.dvd_dvd_int (@ F A)) (@ (@ tptp.groups4694064378042380927al_int F) A2))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (A tptp.complex) (F (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex A) A2) (@ (@ tptp.dvd_dvd_int (@ F A)) (@ (@ tptp.groups858564598930262913ex_int F) A2))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (A tptp.extended_enat) (F (-> tptp.extended_enat tptp.int))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ (@ tptp.member_Extended_enat A) A2) (@ (@ tptp.dvd_dvd_int (@ F A)) (@ (@ tptp.groups2878480467620962989at_int F) A2))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (A tptp.nat) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.member_nat A) A2) (@ (@ tptp.dvd_dvd_int (@ F A)) (@ (@ tptp.groups705719431365010083at_int F) A2))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (A tptp.int) (F (-> tptp.int tptp.int))) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int A) A2) (@ (@ tptp.dvd_dvd_int (@ F A)) (@ (@ tptp.groups1705073143266064639nt_int F) A2))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (A tptp.nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.member_nat A) A2) (@ (@ tptp.dvd_dvd_nat (@ F A)) (@ (@ tptp.groups708209901874060359at_nat F) A2))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (A tptp.real) (B2 tptp.nat) (F (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real A) A2) (=> (= B2 (@ F A)) (@ (@ tptp.dvd_dvd_nat B2) (@ (@ tptp.groups4696554848551431203al_nat F) A2)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (A tptp.complex) (B2 tptp.nat) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex A) A2) (=> (= B2 (@ F A)) (@ (@ tptp.dvd_dvd_nat B2) (@ (@ tptp.groups861055069439313189ex_nat F) A2)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (A tptp.int) (B2 tptp.nat) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int A) A2) (=> (= B2 (@ F A)) (@ (@ tptp.dvd_dvd_nat B2) (@ (@ tptp.groups1707563613775114915nt_nat F) A2)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (A tptp.extended_enat) (B2 tptp.nat) (F (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ (@ tptp.member_Extended_enat A) A2) (=> (= B2 (@ F A)) (@ (@ tptp.dvd_dvd_nat B2) (@ (@ tptp.groups2880970938130013265at_nat F) A2)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (A tptp.real) (B2 tptp.int) (F (-> tptp.real tptp.int))) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real A) A2) (=> (= B2 (@ F A)) (@ (@ tptp.dvd_dvd_int B2) (@ (@ tptp.groups4694064378042380927al_int F) A2)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (A tptp.complex) (B2 tptp.int) (F (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex A) A2) (=> (= B2 (@ F A)) (@ (@ tptp.dvd_dvd_int B2) (@ (@ tptp.groups858564598930262913ex_int F) A2)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (A tptp.extended_enat) (B2 tptp.int) (F (-> tptp.extended_enat tptp.int))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ (@ tptp.member_Extended_enat A) A2) (=> (= B2 (@ F A)) (@ (@ tptp.dvd_dvd_int B2) (@ (@ tptp.groups2878480467620962989at_int F) A2)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (A tptp.nat) (B2 tptp.int) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.member_nat A) A2) (=> (= B2 (@ F A)) (@ (@ tptp.dvd_dvd_int B2) (@ (@ tptp.groups705719431365010083at_int F) A2)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (A tptp.int) (B2 tptp.int) (F (-> tptp.int tptp.int))) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int A) A2) (=> (= B2 (@ F A)) (@ (@ tptp.dvd_dvd_int B2) (@ (@ tptp.groups1705073143266064639nt_int F) A2)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (A tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.member_nat A) A2) (=> (= B2 (@ F A)) (@ (@ tptp.dvd_dvd_nat B2) (@ (@ tptp.groups708209901874060359at_nat F) A2)))))))
% 4.96/5.19 (assert (= (@ tptp.cos_coeff tptp.zero_zero_nat) tptp.one_one_real))
% 4.96/5.19 (assert (forall ((S2 tptp.set_real) (A tptp.real) (B2 (-> tptp.real tptp.nat))) (let ((_let_1 (@ (@ tptp.member_real A) S2))) (=> (@ tptp.finite_finite_real S2) (and (=> _let_1 (= (@ (@ tptp.groups4696554848551431203al_nat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) tptp.one_one_nat))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups4696554848551431203al_nat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) tptp.one_one_nat))) S2) tptp.one_one_nat)))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_complex) (A tptp.complex) (B2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_1 (= (@ (@ tptp.groups861055069439313189ex_nat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) tptp.one_one_nat))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups861055069439313189ex_nat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) tptp.one_one_nat))) S2) tptp.one_one_nat)))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_int) (A tptp.int) (B2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ (@ tptp.member_int A) S2))) (=> (@ tptp.finite_finite_int S2) (and (=> _let_1 (= (@ (@ tptp.groups1707563613775114915nt_nat (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) tptp.one_one_nat))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups1707563613775114915nt_nat (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) tptp.one_one_nat))) S2) tptp.one_one_nat)))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_Extended_enat) (A tptp.extended_enat) (B2 (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ (@ tptp.member_Extended_enat A) S2))) (=> (@ tptp.finite4001608067531595151d_enat S2) (and (=> _let_1 (= (@ (@ tptp.groups2880970938130013265at_nat (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) tptp.one_one_nat))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups2880970938130013265at_nat (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) tptp.one_one_nat))) S2) tptp.one_one_nat)))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_real) (A tptp.real) (B2 (-> tptp.real tptp.int))) (let ((_let_1 (@ (@ tptp.member_real A) S2))) (=> (@ tptp.finite_finite_real S2) (and (=> _let_1 (= (@ (@ tptp.groups4694064378042380927al_int (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B2 K2)) tptp.one_one_int))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups4694064378042380927al_int (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B2 K2)) tptp.one_one_int))) S2) tptp.one_one_int)))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_complex) (A tptp.complex) (B2 (-> tptp.complex tptp.int))) (let ((_let_1 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_1 (= (@ (@ tptp.groups858564598930262913ex_int (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B2 K2)) tptp.one_one_int))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups858564598930262913ex_int (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B2 K2)) tptp.one_one_int))) S2) tptp.one_one_int)))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_Extended_enat) (A tptp.extended_enat) (B2 (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ (@ tptp.member_Extended_enat A) S2))) (=> (@ tptp.finite4001608067531595151d_enat S2) (and (=> _let_1 (= (@ (@ tptp.groups2878480467620962989at_int (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B2 K2)) tptp.one_one_int))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups2878480467620962989at_int (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B2 K2)) tptp.one_one_int))) S2) tptp.one_one_int)))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_real) (A tptp.real) (B2 (-> tptp.real tptp.complex))) (let ((_let_1 (@ (@ tptp.member_real A) S2))) (=> (@ tptp.finite_finite_real S2) (and (=> _let_1 (= (@ (@ tptp.groups713298508707869441omplex (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B2 K2)) tptp.one_one_complex))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups713298508707869441omplex (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B2 K2)) tptp.one_one_complex))) S2) tptp.one_one_complex)))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_nat) (A tptp.nat) (B2 (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.member_nat A) S2))) (=> (@ tptp.finite_finite_nat S2) (and (=> _let_1 (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B2 K2)) tptp.one_one_complex))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B2 K2)) tptp.one_one_complex))) S2) tptp.one_one_complex)))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_complex) (A tptp.complex) (B2 (-> tptp.complex tptp.complex))) (let ((_let_1 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_1 (= (@ (@ tptp.groups3708469109370488835omplex (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B2 K2)) tptp.one_one_complex))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups3708469109370488835omplex (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B2 K2)) tptp.one_one_complex))) S2) tptp.one_one_complex)))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_real) (A tptp.real) (B2 (-> tptp.real tptp.nat))) (let ((_let_1 (@ (@ tptp.member_real A) S2))) (=> (@ tptp.finite_finite_real S2) (and (=> _let_1 (= (@ (@ tptp.groups4696554848551431203al_nat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_nat (= A K2)) (@ B2 K2)) tptp.one_one_nat))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups4696554848551431203al_nat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_nat (= A K2)) (@ B2 K2)) tptp.one_one_nat))) S2) tptp.one_one_nat)))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_complex) (A tptp.complex) (B2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_1 (= (@ (@ tptp.groups861055069439313189ex_nat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_nat (= A K2)) (@ B2 K2)) tptp.one_one_nat))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups861055069439313189ex_nat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_nat (= A K2)) (@ B2 K2)) tptp.one_one_nat))) S2) tptp.one_one_nat)))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_int) (A tptp.int) (B2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ (@ tptp.member_int A) S2))) (=> (@ tptp.finite_finite_int S2) (and (=> _let_1 (= (@ (@ tptp.groups1707563613775114915nt_nat (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_nat (= A K2)) (@ B2 K2)) tptp.one_one_nat))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups1707563613775114915nt_nat (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_nat (= A K2)) (@ B2 K2)) tptp.one_one_nat))) S2) tptp.one_one_nat)))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_Extended_enat) (A tptp.extended_enat) (B2 (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ (@ tptp.member_Extended_enat A) S2))) (=> (@ tptp.finite4001608067531595151d_enat S2) (and (=> _let_1 (= (@ (@ tptp.groups2880970938130013265at_nat (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_nat (= A K2)) (@ B2 K2)) tptp.one_one_nat))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups2880970938130013265at_nat (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_nat (= A K2)) (@ B2 K2)) tptp.one_one_nat))) S2) tptp.one_one_nat)))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_real) (A tptp.real) (B2 (-> tptp.real tptp.int))) (let ((_let_1 (@ (@ tptp.member_real A) S2))) (=> (@ tptp.finite_finite_real S2) (and (=> _let_1 (= (@ (@ tptp.groups4694064378042380927al_int (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_int (= A K2)) (@ B2 K2)) tptp.one_one_int))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups4694064378042380927al_int (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_int (= A K2)) (@ B2 K2)) tptp.one_one_int))) S2) tptp.one_one_int)))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_complex) (A tptp.complex) (B2 (-> tptp.complex tptp.int))) (let ((_let_1 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_1 (= (@ (@ tptp.groups858564598930262913ex_int (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_int (= A K2)) (@ B2 K2)) tptp.one_one_int))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups858564598930262913ex_int (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_int (= A K2)) (@ B2 K2)) tptp.one_one_int))) S2) tptp.one_one_int)))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_Extended_enat) (A tptp.extended_enat) (B2 (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ (@ tptp.member_Extended_enat A) S2))) (=> (@ tptp.finite4001608067531595151d_enat S2) (and (=> _let_1 (= (@ (@ tptp.groups2878480467620962989at_int (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_int (= A K2)) (@ B2 K2)) tptp.one_one_int))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups2878480467620962989at_int (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_int (= A K2)) (@ B2 K2)) tptp.one_one_int))) S2) tptp.one_one_int)))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_real) (A tptp.real) (B2 (-> tptp.real tptp.complex))) (let ((_let_1 (@ (@ tptp.member_real A) S2))) (=> (@ tptp.finite_finite_real S2) (and (=> _let_1 (= (@ (@ tptp.groups713298508707869441omplex (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B2 K2)) tptp.one_one_complex))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups713298508707869441omplex (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B2 K2)) tptp.one_one_complex))) S2) tptp.one_one_complex)))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_nat) (A tptp.nat) (B2 (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.member_nat A) S2))) (=> (@ tptp.finite_finite_nat S2) (and (=> _let_1 (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B2 K2)) tptp.one_one_complex))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B2 K2)) tptp.one_one_complex))) S2) tptp.one_one_complex)))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_complex) (A tptp.complex) (B2 (-> tptp.complex tptp.complex))) (let ((_let_1 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_1 (= (@ (@ tptp.groups3708469109370488835omplex (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B2 K2)) tptp.one_one_complex))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups3708469109370488835omplex (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B2 K2)) tptp.one_one_complex))) S2) tptp.one_one_complex)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups4696554848551431203al_nat G))) (=> (@ tptp.finite_finite_real A2) (=> (not (@ (@ tptp.member_real X) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X) A2)) (@ (@ tptp.times_times_nat (@ G X)) (@ _let_1 A2))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (@ (@ tptp.member_complex X) A2)) (= (@ _let_1 (@ (@ tptp.insert_complex X) A2)) (@ (@ tptp.times_times_nat (@ G X)) (@ _let_1 A2))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat G))) (=> (@ tptp.finite_finite_int A2) (=> (not (@ (@ tptp.member_int X) A2)) (= (@ _let_1 (@ (@ tptp.insert_int X) A2)) (@ (@ tptp.times_times_nat (@ G X)) (@ _let_1 A2))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (X tptp.extended_enat) (G (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2880970938130013265at_nat G))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (not (@ (@ tptp.member_Extended_enat X) A2)) (= (@ _let_1 (@ (@ tptp.insert_Extended_enat X) A2)) (@ (@ tptp.times_times_nat (@ G X)) (@ _let_1 A2))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups4694064378042380927al_int G))) (=> (@ tptp.finite_finite_real A2) (=> (not (@ (@ tptp.member_real X) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X) A2)) (@ (@ tptp.times_times_int (@ G X)) (@ _let_1 A2))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (@ (@ tptp.member_complex X) A2)) (= (@ _let_1 (@ (@ tptp.insert_complex X) A2)) (@ (@ tptp.times_times_int (@ G X)) (@ _let_1 A2))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (X tptp.extended_enat) (G (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2878480467620962989at_int G))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (not (@ (@ tptp.member_Extended_enat X) A2)) (= (@ _let_1 (@ (@ tptp.insert_Extended_enat X) A2)) (@ (@ tptp.times_times_int (@ G X)) (@ _let_1 A2))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real G))) (=> (@ tptp.finite_finite_real A2) (=> (not (@ (@ tptp.member_real X) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X) A2)) (@ (@ tptp.times_times_real (@ G X)) (@ _let_1 A2))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (X tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (=> (@ tptp.finite_finite_nat A2) (=> (not (@ (@ tptp.member_nat X) A2)) (= (@ _let_1 (@ (@ tptp.insert_nat X) A2)) (@ (@ tptp.times_times_real (@ G X)) (@ _let_1 A2))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (@ (@ tptp.member_complex X) A2)) (= (@ _let_1 (@ (@ tptp.insert_complex X) A2)) (@ (@ tptp.times_times_real (@ G X)) (@ _let_1 A2))))))))
% 4.96/5.19 (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))))))
% 4.96/5.19 (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))))))
% 4.96/5.19 (assert (forall ((G (-> tptp.nat tptp.extended_enat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups7961826882256487087d_enat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.times_7803423173614009249d_enat (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))))
% 4.96/5.19 (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))))))
% 4.96/5.19 (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))))))
% 4.96/5.19 (assert (forall ((A (-> tptp.nat tptp.real)) (X tptp.real)) (= (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ A N)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N)))) X) (= (@ A tptp.zero_zero_nat) X))))
% 4.96/5.19 (assert (forall ((A (-> tptp.nat tptp.complex)) (X tptp.complex)) (= (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ A N)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N)))) X) (= (@ A tptp.zero_zero_nat) X))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat) (M2 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (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) M2))) (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))))))))))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat) (M2 tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_3 (@ tptp.groups6464643781859351333omplex G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M2))) (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))))))))))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat) (M2 tptp.nat) (G (-> tptp.nat tptp.extended_enat))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_3 (@ tptp.groups7961826882256487087d_enat G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M2))) (and (=> _let_5 (= _let_4 tptp.one_on7984719198319812577d_enat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_7803423173614009249d_enat (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat) (M2 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (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) M2))) (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))))))))))))
% 4.96/5.19 (assert (forall ((N2 tptp.nat) (M2 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (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) M2))) (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))))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (B tptp.set_nat) (G (-> tptp.real tptp.nat tptp.int)) (R (-> tptp.real tptp.nat Bool))) (=> (@ tptp.finite_finite_real A2) (=> (@ tptp.finite_finite_nat B) (= (@ (@ tptp.groups4694064378042380927al_int (lambda ((X4 tptp.real)) (@ (@ tptp.groups705719431365010083at_int (@ G X4)) (@ tptp.collect_nat (lambda ((Y5 tptp.nat)) (and (@ (@ tptp.member_nat Y5) B) (@ (@ R X4) Y5))))))) A2) (@ (@ tptp.groups705719431365010083at_int (lambda ((Y5 tptp.nat)) (@ (@ tptp.groups4694064378042380927al_int (lambda ((X4 tptp.real)) (@ (@ G X4) Y5))) (@ tptp.collect_real (lambda ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) A2) (@ (@ R X4) Y5))))))) B))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (B tptp.set_nat) (G (-> tptp.complex tptp.nat tptp.int)) (R (-> tptp.complex tptp.nat Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ tptp.finite_finite_nat B) (= (@ (@ tptp.groups858564598930262913ex_int (lambda ((X4 tptp.complex)) (@ (@ tptp.groups705719431365010083at_int (@ G X4)) (@ tptp.collect_nat (lambda ((Y5 tptp.nat)) (and (@ (@ tptp.member_nat Y5) B) (@ (@ R X4) Y5))))))) A2) (@ (@ tptp.groups705719431365010083at_int (lambda ((Y5 tptp.nat)) (@ (@ tptp.groups858564598930262913ex_int (lambda ((X4 tptp.complex)) (@ (@ G X4) Y5))) (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A2) (@ (@ R X4) Y5))))))) B))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (B tptp.set_nat) (G (-> tptp.extended_enat tptp.nat tptp.int)) (R (-> tptp.extended_enat tptp.nat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ tptp.finite_finite_nat B) (= (@ (@ tptp.groups2878480467620962989at_int (lambda ((X4 tptp.extended_enat)) (@ (@ tptp.groups705719431365010083at_int (@ G X4)) (@ tptp.collect_nat (lambda ((Y5 tptp.nat)) (and (@ (@ tptp.member_nat Y5) B) (@ (@ R X4) Y5))))))) A2) (@ (@ tptp.groups705719431365010083at_int (lambda ((Y5 tptp.nat)) (@ (@ tptp.groups2878480467620962989at_int (lambda ((X4 tptp.extended_enat)) (@ (@ G X4) Y5))) (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) A2) (@ (@ R X4) Y5))))))) B))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (B tptp.set_int) (G (-> tptp.real tptp.int tptp.int)) (R (-> tptp.real tptp.int Bool))) (=> (@ tptp.finite_finite_real A2) (=> (@ tptp.finite_finite_int B) (= (@ (@ tptp.groups4694064378042380927al_int (lambda ((X4 tptp.real)) (@ (@ tptp.groups1705073143266064639nt_int (@ G X4)) (@ tptp.collect_int (lambda ((Y5 tptp.int)) (and (@ (@ tptp.member_int Y5) B) (@ (@ R X4) Y5))))))) A2) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((Y5 tptp.int)) (@ (@ tptp.groups4694064378042380927al_int (lambda ((X4 tptp.real)) (@ (@ G X4) Y5))) (@ tptp.collect_real (lambda ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) A2) (@ (@ R X4) Y5))))))) B))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (B tptp.set_int) (G (-> tptp.complex tptp.int tptp.int)) (R (-> tptp.complex tptp.int Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ tptp.finite_finite_int B) (= (@ (@ tptp.groups858564598930262913ex_int (lambda ((X4 tptp.complex)) (@ (@ tptp.groups1705073143266064639nt_int (@ G X4)) (@ tptp.collect_int (lambda ((Y5 tptp.int)) (and (@ (@ tptp.member_int Y5) B) (@ (@ R X4) Y5))))))) A2) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((Y5 tptp.int)) (@ (@ tptp.groups858564598930262913ex_int (lambda ((X4 tptp.complex)) (@ (@ G X4) Y5))) (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A2) (@ (@ R X4) Y5))))))) B))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (B tptp.set_int) (G (-> tptp.extended_enat tptp.int tptp.int)) (R (-> tptp.extended_enat tptp.int Bool))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ tptp.finite_finite_int B) (= (@ (@ tptp.groups2878480467620962989at_int (lambda ((X4 tptp.extended_enat)) (@ (@ tptp.groups1705073143266064639nt_int (@ G X4)) (@ tptp.collect_int (lambda ((Y5 tptp.int)) (and (@ (@ tptp.member_int Y5) B) (@ (@ R X4) Y5))))))) A2) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((Y5 tptp.int)) (@ (@ tptp.groups2878480467620962989at_int (lambda ((X4 tptp.extended_enat)) (@ (@ G X4) Y5))) (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) A2) (@ (@ R X4) Y5))))))) B))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (B tptp.set_nat) (G (-> tptp.real tptp.nat tptp.nat)) (R (-> tptp.real tptp.nat Bool))) (=> (@ tptp.finite_finite_real A2) (=> (@ tptp.finite_finite_nat B) (= (@ (@ tptp.groups4696554848551431203al_nat (lambda ((X4 tptp.real)) (@ (@ tptp.groups708209901874060359at_nat (@ G X4)) (@ tptp.collect_nat (lambda ((Y5 tptp.nat)) (and (@ (@ tptp.member_nat Y5) B) (@ (@ R X4) Y5))))))) A2) (@ (@ tptp.groups708209901874060359at_nat (lambda ((Y5 tptp.nat)) (@ (@ tptp.groups4696554848551431203al_nat (lambda ((X4 tptp.real)) (@ (@ G X4) Y5))) (@ tptp.collect_real (lambda ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) A2) (@ (@ R X4) Y5))))))) B))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (B tptp.set_nat) (G (-> tptp.complex tptp.nat tptp.nat)) (R (-> tptp.complex tptp.nat Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ tptp.finite_finite_nat B) (= (@ (@ tptp.groups861055069439313189ex_nat (lambda ((X4 tptp.complex)) (@ (@ tptp.groups708209901874060359at_nat (@ G X4)) (@ tptp.collect_nat (lambda ((Y5 tptp.nat)) (and (@ (@ tptp.member_nat Y5) B) (@ (@ R X4) Y5))))))) A2) (@ (@ tptp.groups708209901874060359at_nat (lambda ((Y5 tptp.nat)) (@ (@ tptp.groups861055069439313189ex_nat (lambda ((X4 tptp.complex)) (@ (@ G X4) Y5))) (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A2) (@ (@ R X4) Y5))))))) B))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (B tptp.set_nat) (G (-> tptp.int tptp.nat tptp.nat)) (R (-> tptp.int tptp.nat Bool))) (=> (@ tptp.finite_finite_int A2) (=> (@ tptp.finite_finite_nat B) (= (@ (@ tptp.groups1707563613775114915nt_nat (lambda ((X4 tptp.int)) (@ (@ tptp.groups708209901874060359at_nat (@ G X4)) (@ tptp.collect_nat (lambda ((Y5 tptp.nat)) (and (@ (@ tptp.member_nat Y5) B) (@ (@ R X4) Y5))))))) A2) (@ (@ tptp.groups708209901874060359at_nat (lambda ((Y5 tptp.nat)) (@ (@ tptp.groups1707563613775114915nt_nat (lambda ((X4 tptp.int)) (@ (@ G X4) Y5))) (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A2) (@ (@ R X4) Y5))))))) B))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (B tptp.set_nat) (G (-> tptp.extended_enat tptp.nat tptp.nat)) (R (-> tptp.extended_enat tptp.nat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ tptp.finite_finite_nat B) (= (@ (@ tptp.groups2880970938130013265at_nat (lambda ((X4 tptp.extended_enat)) (@ (@ tptp.groups708209901874060359at_nat (@ G X4)) (@ tptp.collect_nat (lambda ((Y5 tptp.nat)) (and (@ (@ tptp.member_nat Y5) B) (@ (@ R X4) Y5))))))) A2) (@ (@ tptp.groups708209901874060359at_nat (lambda ((Y5 tptp.nat)) (@ (@ tptp.groups2880970938130013265at_nat (lambda ((X4 tptp.extended_enat)) (@ (@ G X4) Y5))) (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) A2) (@ (@ R X4) Y5))))))) B))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real)) (G (-> tptp.extended_enat tptp.real))) (=> (forall ((I4 tptp.extended_enat)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_Extended_enat I4) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G I4)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups97031904164794029t_real F) A2)) (@ (@ tptp.groups97031904164794029t_real G) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (forall ((I4 tptp.real)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_real I4) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G I4)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups1681761925125756287l_real F) A2)) (@ (@ tptp.groups1681761925125756287l_real G) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (forall ((I4 tptp.nat)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_nat I4) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G I4)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups129246275422532515t_real F) A2)) (@ (@ tptp.groups129246275422532515t_real G) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (forall ((I4 tptp.int)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_int I4) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G I4)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups2316167850115554303t_real F) A2)) (@ (@ tptp.groups2316167850115554303t_real G) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat)) (G (-> tptp.extended_enat tptp.nat))) (=> (forall ((I4 tptp.extended_enat)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_Extended_enat I4) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) (@ G I4)))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups2880970938130013265at_nat F) A2)) (@ (@ tptp.groups2880970938130013265at_nat G) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat)) (G (-> tptp.real tptp.nat))) (=> (forall ((I4 tptp.real)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_real I4) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) (@ G I4)))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4696554848551431203al_nat F) A2)) (@ (@ tptp.groups4696554848551431203al_nat G) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (forall ((I4 tptp.int)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_int I4) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) (@ G I4)))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups1707563613775114915nt_nat F) A2)) (@ (@ tptp.groups1707563613775114915nt_nat G) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.int)) (G (-> tptp.extended_enat tptp.int))) (=> (forall ((I4 tptp.extended_enat)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_Extended_enat 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.groups2878480467620962989at_int F) A2)) (@ (@ tptp.groups2878480467620962989at_int G) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.int)) (G (-> tptp.real tptp.int))) (=> (forall ((I4 tptp.real)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_real I4) A2) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) _let_1) (@ (@ tptp.ord_less_eq_int _let_1) (@ G I4)))))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups4694064378042380927al_int F) A2)) (@ (@ tptp.groups4694064378042380927al_int G) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (forall ((I4 tptp.nat)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_nat 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.groups705719431365010083at_int F) A2)) (@ (@ tptp.groups705719431365010083at_int G) A2)))))
% 4.96/5.19 (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)))))
% 4.96/5.19 (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)))))
% 4.96/5.19 (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)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F X5)))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.groups705719431365010083at_int F) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.int))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F X5)))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.groups1705073143266064639nt_int F) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X5)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups708209901874060359at_nat F) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) A2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X5)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups97031904164794029t_real F) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X5)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups1681761925125756287l_real F) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X5)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups129246275422532515t_real F) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X5)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups2316167850115554303t_real F) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) A2) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ F X5)))) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ (@ tptp.groups2880970938130013265at_nat F) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ F X5)))) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ (@ tptp.groups4696554848551431203al_nat F) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ F X5)))) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ (@ tptp.groups1707563613775114915nt_nat F) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.int))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) A2) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F X5)))) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ (@ tptp.groups2878480467620962989at_int F) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.int))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F X5)))) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ (@ tptp.groups4694064378042380927al_int F) A2)))))
% 4.96/5.19 (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.one_one_int) (@ F X5)))) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ (@ tptp.groups705719431365010083at_int F) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (exists ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (= (@ F X2) tptp.zero_zero_nat))) (= (@ (@ tptp.groups861055069439313189ex_nat F) A2) tptp.zero_zero_nat)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (=> (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (= (@ F X2) tptp.zero_zero_nat))) (= (@ (@ tptp.groups1707563613775114915nt_nat F) A2) tptp.zero_zero_nat)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (exists ((X2 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X2) A2) (= (@ F X2) tptp.zero_zero_nat))) (= (@ (@ tptp.groups2880970938130013265at_nat F) A2) tptp.zero_zero_nat)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat A2) (=> (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (= (@ F X2) tptp.zero_zero_real))) (= (@ (@ tptp.groups129246275422532515t_real F) A2) tptp.zero_zero_real)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (exists ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (= (@ F X2) tptp.zero_zero_real))) (= (@ (@ tptp.groups766887009212190081x_real F) A2) tptp.zero_zero_real)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A2) (=> (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (= (@ F X2) tptp.zero_zero_real))) (= (@ (@ tptp.groups2316167850115554303t_real F) A2) tptp.zero_zero_real)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (exists ((X2 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X2) A2) (= (@ F X2) tptp.zero_zero_real))) (= (@ (@ tptp.groups97031904164794029t_real F) A2) tptp.zero_zero_real)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (exists ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (= (@ F X2) tptp.zero_zero_int))) (= (@ (@ tptp.groups858564598930262913ex_int F) A2) tptp.zero_zero_int)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.int))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (exists ((X2 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X2) A2) (= (@ F X2) tptp.zero_zero_int))) (= (@ (@ tptp.groups2878480467620962989at_int F) A2) tptp.zero_zero_int)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat A2) (=> (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (= (@ F X2) tptp.zero_zero_complex))) (= (@ (@ tptp.groups6464643781859351333omplex F) A2) tptp.zero_zero_complex)))))
% 4.96/5.19 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real F) (@ (@ tptp.set_or1269000886237332187st_nat A) B2)) (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ F A3)) __flatten_var_0))) A) B2) tptp.one_one_real))))
% 4.96/5.19 (assert (forall ((F (-> tptp.nat tptp.complex)) (A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.groups6464643781859351333omplex F) (@ (@ tptp.set_or1269000886237332187st_nat A) B2)) (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.times_times_complex (@ F A3)) __flatten_var_0))) A) B2) tptp.one_one_complex))))
% 4.96/5.19 (assert (forall ((F (-> tptp.nat tptp.extended_enat)) (A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.groups7961826882256487087d_enat F) (@ (@ tptp.set_or1269000886237332187st_nat A) B2)) (@ (@ (@ (@ tptp.set_fo2538466533108834004d_enat (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.extended_enat)) (@ (@ tptp.times_7803423173614009249d_enat (@ F A3)) __flatten_var_0))) A) B2) tptp.one_on7984719198319812577d_enat))))
% 4.96/5.19 (assert (forall ((F (-> tptp.nat tptp.int)) (A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int F) (@ (@ tptp.set_or1269000886237332187st_nat A) B2)) (@ (@ (@ (@ tptp.set_fo2581907887559384638at_int (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.times_times_int (@ F A3)) __flatten_var_0))) A) B2) tptp.one_one_int))))
% 4.96/5.19 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat F) (@ (@ tptp.set_or1269000886237332187st_nat A) B2)) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.times_times_nat (@ F A3)) __flatten_var_0))) A) B2) tptp.one_one_nat))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.nat)) (P (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A2) (= (@ (@ tptp.groups4696554848551431203al_nat G) (@ tptp.collect_real (lambda ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) A2) (@ P X4))))) (@ (@ tptp.groups4696554848551431203al_nat (lambda ((X4 tptp.real)) (@ (@ (@ tptp.if_nat (@ P X4)) (@ G X4)) tptp.one_one_nat))) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (P (-> tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ (@ tptp.groups861055069439313189ex_nat G) (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A2) (@ P X4))))) (@ (@ tptp.groups861055069439313189ex_nat (lambda ((X4 tptp.complex)) (@ (@ (@ tptp.if_nat (@ P X4)) (@ G X4)) tptp.one_one_nat))) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.nat)) (P (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A2) (= (@ (@ tptp.groups1707563613775114915nt_nat G) (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A2) (@ P X4))))) (@ (@ tptp.groups1707563613775114915nt_nat (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_nat (@ P X4)) (@ G X4)) tptp.one_one_nat))) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.nat)) (P (-> tptp.extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ (@ tptp.groups2880970938130013265at_nat G) (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) A2) (@ P X4))))) (@ (@ tptp.groups2880970938130013265at_nat (lambda ((X4 tptp.extended_enat)) (@ (@ (@ tptp.if_nat (@ P X4)) (@ G X4)) tptp.one_one_nat))) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.int)) (P (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A2) (= (@ (@ tptp.groups4694064378042380927al_int G) (@ tptp.collect_real (lambda ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) A2) (@ P X4))))) (@ (@ tptp.groups4694064378042380927al_int (lambda ((X4 tptp.real)) (@ (@ (@ tptp.if_int (@ P X4)) (@ G X4)) tptp.one_one_int))) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.int)) (P (-> tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ (@ tptp.groups858564598930262913ex_int G) (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A2) (@ P X4))))) (@ (@ tptp.groups858564598930262913ex_int (lambda ((X4 tptp.complex)) (@ (@ (@ tptp.if_int (@ P X4)) (@ G X4)) tptp.one_one_int))) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.int)) (P (-> tptp.extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ (@ tptp.groups2878480467620962989at_int G) (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) A2) (@ P X4))))) (@ (@ tptp.groups2878480467620962989at_int (lambda ((X4 tptp.extended_enat)) (@ (@ (@ tptp.if_int (@ P X4)) (@ G X4)) tptp.one_one_int))) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.complex)) (P (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A2) (= (@ (@ tptp.groups713298508707869441omplex G) (@ tptp.collect_real (lambda ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) A2) (@ P X4))))) (@ (@ tptp.groups713298508707869441omplex (lambda ((X4 tptp.real)) (@ (@ (@ tptp.if_complex (@ P X4)) (@ G X4)) tptp.one_one_complex))) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.complex)) (P (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.groups6464643781859351333omplex G) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A2) (@ P X4))))) (@ (@ tptp.groups6464643781859351333omplex (lambda ((X4 tptp.nat)) (@ (@ (@ tptp.if_complex (@ P X4)) (@ G X4)) tptp.one_one_complex))) A2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.complex)) (P (-> tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ (@ tptp.groups3708469109370488835omplex G) (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A2) (@ P X4))))) (@ (@ tptp.groups3708469109370488835omplex (lambda ((X4 tptp.complex)) (@ (@ (@ tptp.if_complex (@ P X4)) (@ G X4)) tptp.one_one_complex))) A2)))))
% 4.96/5.19 (assert (forall ((G (-> tptp.nat tptp.int)) (M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) (@ tptp.suc N2))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N2)))))
% 4.96/5.19 (assert (forall ((G (-> tptp.nat tptp.nat)) (M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) (@ tptp.suc N2))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N2)))))
% 4.96/5.19 (assert (forall ((G (-> tptp.nat tptp.int)) (M2 tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M2) K)) (@ (@ tptp.plus_plus_nat N2) K))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I3) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N2)))))
% 4.96/5.19 (assert (forall ((G (-> tptp.nat tptp.nat)) (M2 tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M2) K)) (@ (@ tptp.plus_plus_nat N2) K))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I3) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.extended_enat))) (=> (forall ((X5 tptp.extended_enat)) (let ((_let_1 (@ F X5))) (=> (@ (@ tptp.member_Extended_enat X5) A2) (and (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) _let_1) (@ (@ tptp.ord_le2932123472753598470d_enat _let_1) tptp.one_on7984719198319812577d_enat))))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups8932437906259616549d_enat F) A2)) tptp.one_on7984719198319812577d_enat))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.extended_enat))) (=> (forall ((X5 tptp.real)) (let ((_let_1 (@ F X5))) (=> (@ (@ tptp.member_real X5) A2) (and (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) _let_1) (@ (@ tptp.ord_le2932123472753598470d_enat _let_1) tptp.one_on7984719198319812577d_enat))))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups7973222482632965587d_enat F) A2)) tptp.one_on7984719198319812577d_enat))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.extended_enat))) (=> (forall ((X5 tptp.nat)) (let ((_let_1 (@ F X5))) (=> (@ (@ tptp.member_nat X5) A2) (and (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) _let_1) (@ (@ tptp.ord_le2932123472753598470d_enat _let_1) tptp.one_on7984719198319812577d_enat))))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups7961826882256487087d_enat F) A2)) tptp.one_on7984719198319812577d_enat))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.extended_enat))) (=> (forall ((X5 tptp.int)) (let ((_let_1 (@ F X5))) (=> (@ (@ tptp.member_int X5) A2) (and (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) _let_1) (@ (@ tptp.ord_le2932123472753598470d_enat _let_1) tptp.one_on7984719198319812577d_enat))))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups5078248829458667347d_enat F) A2)) tptp.one_on7984719198319812577d_enat))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real))) (=> (forall ((X5 tptp.extended_enat)) (let ((_let_1 (@ F X5))) (=> (@ (@ tptp.member_Extended_enat X5) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.one_one_real))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups97031904164794029t_real F) A2)) tptp.one_one_real))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (forall ((X5 tptp.real)) (let ((_let_1 (@ F X5))) (=> (@ (@ tptp.member_real X5) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.one_one_real))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups1681761925125756287l_real F) A2)) tptp.one_one_real))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (forall ((X5 tptp.nat)) (let ((_let_1 (@ F X5))) (=> (@ (@ tptp.member_nat X5) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.one_one_real))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups129246275422532515t_real F) A2)) tptp.one_one_real))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (forall ((X5 tptp.int)) (let ((_let_1 (@ F X5))) (=> (@ (@ tptp.member_int X5) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.one_one_real))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups2316167850115554303t_real F) A2)) tptp.one_one_real))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat))) (=> (forall ((X5 tptp.extended_enat)) (let ((_let_1 (@ F X5))) (=> (@ (@ tptp.member_Extended_enat X5) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) tptp.one_one_nat))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups2880970938130013265at_nat F) A2)) tptp.one_one_nat))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (forall ((X5 tptp.real)) (let ((_let_1 (@ F X5))) (=> (@ (@ tptp.member_real X5) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) tptp.one_one_nat))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4696554848551431203al_nat F) A2)) tptp.one_one_nat))))
% 4.96/5.19 (assert (forall ((R (-> tptp.nat tptp.nat Bool)) (S2 tptp.set_complex) (H2 (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ (@ R tptp.one_one_nat) tptp.one_one_nat) (=> (forall ((X1 tptp.nat) (Y1 tptp.nat) (X23 tptp.nat) (Y22 tptp.nat)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.times_times_nat X1) Y1)) (@ (@ tptp.times_times_nat X23) Y22)))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S2) (@ (@ R (@ H2 X5)) (@ G X5)))) (@ (@ R (@ (@ tptp.groups861055069439313189ex_nat H2) S2)) (@ (@ tptp.groups861055069439313189ex_nat G) S2))))))))
% 4.96/5.19 (assert (forall ((R (-> tptp.nat tptp.nat Bool)) (S2 tptp.set_int) (H2 (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ (@ R tptp.one_one_nat) tptp.one_one_nat) (=> (forall ((X1 tptp.nat) (Y1 tptp.nat) (X23 tptp.nat) (Y22 tptp.nat)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.times_times_nat X1) Y1)) (@ (@ tptp.times_times_nat X23) Y22)))) (=> (@ tptp.finite_finite_int S2) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) S2) (@ (@ R (@ H2 X5)) (@ G X5)))) (@ (@ R (@ (@ tptp.groups1707563613775114915nt_nat H2) S2)) (@ (@ tptp.groups1707563613775114915nt_nat G) S2))))))))
% 4.96/5.19 (assert (forall ((R (-> tptp.nat tptp.nat Bool)) (S2 tptp.set_Extended_enat) (H2 (-> tptp.extended_enat tptp.nat)) (G (-> tptp.extended_enat tptp.nat))) (=> (@ (@ R tptp.one_one_nat) tptp.one_one_nat) (=> (forall ((X1 tptp.nat) (Y1 tptp.nat) (X23 tptp.nat) (Y22 tptp.nat)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.times_times_nat X1) Y1)) (@ (@ tptp.times_times_nat X23) Y22)))) (=> (@ tptp.finite4001608067531595151d_enat S2) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) S2) (@ (@ R (@ H2 X5)) (@ G X5)))) (@ (@ R (@ (@ tptp.groups2880970938130013265at_nat H2) S2)) (@ (@ tptp.groups2880970938130013265at_nat G) S2))))))))
% 4.96/5.19 (assert (forall ((R (-> tptp.int tptp.int Bool)) (S2 tptp.set_complex) (H2 (-> tptp.complex tptp.int)) (G (-> tptp.complex tptp.int))) (=> (@ (@ R tptp.one_one_int) tptp.one_one_int) (=> (forall ((X1 tptp.int) (Y1 tptp.int) (X23 tptp.int) (Y22 tptp.int)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.times_times_int X1) Y1)) (@ (@ tptp.times_times_int X23) Y22)))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S2) (@ (@ R (@ H2 X5)) (@ G X5)))) (@ (@ R (@ (@ tptp.groups858564598930262913ex_int H2) S2)) (@ (@ tptp.groups858564598930262913ex_int G) S2))))))))
% 4.96/5.19 (assert (forall ((R (-> tptp.int tptp.int Bool)) (S2 tptp.set_Extended_enat) (H2 (-> tptp.extended_enat tptp.int)) (G (-> tptp.extended_enat tptp.int))) (=> (@ (@ R tptp.one_one_int) tptp.one_one_int) (=> (forall ((X1 tptp.int) (Y1 tptp.int) (X23 tptp.int) (Y22 tptp.int)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.times_times_int X1) Y1)) (@ (@ tptp.times_times_int X23) Y22)))) (=> (@ tptp.finite4001608067531595151d_enat S2) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) S2) (@ (@ R (@ H2 X5)) (@ G X5)))) (@ (@ R (@ (@ tptp.groups2878480467620962989at_int H2) S2)) (@ (@ tptp.groups2878480467620962989at_int G) S2))))))))
% 4.96/5.19 (assert (forall ((R (-> tptp.real tptp.real Bool)) (S2 tptp.set_nat) (H2 (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (@ (@ R tptp.one_one_real) tptp.one_one_real) (=> (forall ((X1 tptp.real) (Y1 tptp.real) (X23 tptp.real) (Y22 tptp.real)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.times_times_real X1) Y1)) (@ (@ tptp.times_times_real X23) Y22)))) (=> (@ tptp.finite_finite_nat S2) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S2) (@ (@ R (@ H2 X5)) (@ G X5)))) (@ (@ R (@ (@ tptp.groups129246275422532515t_real H2) S2)) (@ (@ tptp.groups129246275422532515t_real G) S2))))))))
% 4.96/5.19 (assert (forall ((R (-> tptp.real tptp.real Bool)) (S2 tptp.set_complex) (H2 (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ (@ R tptp.one_one_real) tptp.one_one_real) (=> (forall ((X1 tptp.real) (Y1 tptp.real) (X23 tptp.real) (Y22 tptp.real)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.times_times_real X1) Y1)) (@ (@ tptp.times_times_real X23) Y22)))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S2) (@ (@ R (@ H2 X5)) (@ G X5)))) (@ (@ R (@ (@ tptp.groups766887009212190081x_real H2) S2)) (@ (@ tptp.groups766887009212190081x_real G) S2))))))))
% 4.96/5.19 (assert (forall ((R (-> tptp.real tptp.real Bool)) (S2 tptp.set_int) (H2 (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (@ (@ R tptp.one_one_real) tptp.one_one_real) (=> (forall ((X1 tptp.real) (Y1 tptp.real) (X23 tptp.real) (Y22 tptp.real)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.times_times_real X1) Y1)) (@ (@ tptp.times_times_real X23) Y22)))) (=> (@ tptp.finite_finite_int S2) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) S2) (@ (@ R (@ H2 X5)) (@ G X5)))) (@ (@ R (@ (@ tptp.groups2316167850115554303t_real H2) S2)) (@ (@ tptp.groups2316167850115554303t_real G) S2))))))))
% 4.96/5.19 (assert (forall ((R (-> tptp.real tptp.real Bool)) (S2 tptp.set_Extended_enat) (H2 (-> tptp.extended_enat tptp.real)) (G (-> tptp.extended_enat tptp.real))) (=> (@ (@ R tptp.one_one_real) tptp.one_one_real) (=> (forall ((X1 tptp.real) (Y1 tptp.real) (X23 tptp.real) (Y22 tptp.real)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.times_times_real X1) Y1)) (@ (@ tptp.times_times_real X23) Y22)))) (=> (@ tptp.finite4001608067531595151d_enat S2) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) S2) (@ (@ R (@ H2 X5)) (@ G X5)))) (@ (@ R (@ (@ tptp.groups97031904164794029t_real H2) S2)) (@ (@ tptp.groups97031904164794029t_real G) S2))))))))
% 4.96/5.19 (assert (forall ((R (-> tptp.complex tptp.complex Bool)) (S2 tptp.set_nat) (H2 (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.complex))) (=> (@ (@ R tptp.one_one_complex) tptp.one_one_complex) (=> (forall ((X1 tptp.complex) (Y1 tptp.complex) (X23 tptp.complex) (Y22 tptp.complex)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.times_times_complex X1) Y1)) (@ (@ tptp.times_times_complex X23) Y22)))) (=> (@ tptp.finite_finite_nat S2) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S2) (@ (@ R (@ H2 X5)) (@ G X5)))) (@ (@ R (@ (@ tptp.groups6464643781859351333omplex H2) S2)) (@ (@ tptp.groups6464643781859351333omplex G) S2))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups4696554848551431203al_nat G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_real X) A2)))) (let ((_let_4 (@ (@ tptp.member_real X) A2))) (=> (@ tptp.finite_finite_real A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_nat (@ G X)) _let_2)))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_complex X) A2)))) (let ((_let_4 (@ (@ tptp.member_complex X) A2))) (=> (@ tptp.finite3207457112153483333omplex A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_nat (@ G X)) _let_2)))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_int X) A2)))) (let ((_let_4 (@ (@ tptp.member_int X) A2))) (=> (@ tptp.finite_finite_int A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_nat (@ G X)) _let_2)))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (X tptp.extended_enat) (G (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2880970938130013265at_nat G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_Extended_enat X) A2)))) (let ((_let_4 (@ (@ tptp.member_Extended_enat X) A2))) (=> (@ tptp.finite4001608067531595151d_enat A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_nat (@ G X)) _let_2)))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups4694064378042380927al_int G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_real X) A2)))) (let ((_let_4 (@ (@ tptp.member_real X) A2))) (=> (@ tptp.finite_finite_real A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_int (@ G X)) _let_2)))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_complex X) A2)))) (let ((_let_4 (@ (@ tptp.member_complex X) A2))) (=> (@ tptp.finite3207457112153483333omplex A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_int (@ G X)) _let_2)))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (X tptp.extended_enat) (G (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2878480467620962989at_int G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_Extended_enat X) A2)))) (let ((_let_4 (@ (@ tptp.member_Extended_enat X) A2))) (=> (@ tptp.finite4001608067531595151d_enat A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_int (@ G X)) _let_2)))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_real X) A2)))) (let ((_let_4 (@ (@ tptp.member_real X) A2))) (=> (@ tptp.finite_finite_real A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_real (@ G X)) _let_2)))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (X tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_nat X) A2)))) (let ((_let_4 (@ (@ tptp.member_nat X) A2))) (=> (@ tptp.finite_finite_nat A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_real (@ G X)) _let_2)))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_complex X) A2)))) (let ((_let_4 (@ (@ tptp.member_complex X) A2))) (=> (@ tptp.finite3207457112153483333omplex A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_real (@ G X)) _let_2)))))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat F))) (=> (@ tptp.finite3207457112153483333omplex B) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B) (@ (@ tptp.dvd_dvd_nat (@ _let_1 A2)) (@ _let_1 B)))))))
% 4.96/5.19 (assert (forall ((B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2880970938130013265at_nat F))) (=> (@ tptp.finite4001608067531595151d_enat B) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) B) (@ (@ tptp.dvd_dvd_nat (@ _let_1 A2)) (@ _let_1 B)))))))
% 4.96/5.19 (assert (forall ((B tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int F))) (=> (@ tptp.finite3207457112153483333omplex B) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B) (@ (@ tptp.dvd_dvd_int (@ _let_1 A2)) (@ _let_1 B)))))))
% 4.96/5.19 (assert (forall ((B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2878480467620962989at_int F))) (=> (@ tptp.finite4001608067531595151d_enat B) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) B) (@ (@ tptp.dvd_dvd_int (@ _let_1 A2)) (@ _let_1 B)))))))
% 4.96/5.19 (assert (forall ((B tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat F))) (=> (@ tptp.finite_finite_int B) (=> (@ (@ tptp.ord_less_eq_set_int A2) B) (@ (@ tptp.dvd_dvd_nat (@ _let_1 A2)) (@ _let_1 B)))))))
% 4.96/5.19 (assert (forall ((B tptp.set_nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups705719431365010083at_int F))) (=> (@ tptp.finite_finite_nat B) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B) (@ (@ tptp.dvd_dvd_int (@ _let_1 A2)) (@ _let_1 B)))))))
% 4.96/5.19 (assert (forall ((B tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.groups1705073143266064639nt_int F))) (=> (@ tptp.finite_finite_int B) (=> (@ (@ tptp.ord_less_eq_set_int A2) B) (@ (@ tptp.dvd_dvd_int (@ _let_1 A2)) (@ _let_1 B)))))))
% 4.96/5.19 (assert (forall ((B tptp.set_nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups708209901874060359at_nat F))) (=> (@ tptp.finite_finite_nat B) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B) (@ (@ tptp.dvd_dvd_nat (@ _let_1 A2)) (@ _let_1 B)))))))
% 4.96/5.19 (assert (forall ((B tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.nat)) (G (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real B) (=> (@ (@ tptp.ord_less_eq_set_real A2) B) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) A2) (@ (@ tptp.dvd_dvd_nat (@ F A4)) (@ G A4)))) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.groups4696554848551431203al_nat F) A2)) (@ (@ tptp.groups4696554848551431203al_nat G) B)))))))
% 4.96/5.19 (assert (forall ((B tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex B) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) A2) (@ (@ tptp.dvd_dvd_nat (@ F A4)) (@ G A4)))) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.groups861055069439313189ex_nat F) A2)) (@ (@ tptp.groups861055069439313189ex_nat G) B)))))))
% 4.96/5.19 (assert (forall ((B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat)) (G (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat B) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) B) (=> (forall ((A4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A4) A2) (@ (@ tptp.dvd_dvd_nat (@ F A4)) (@ G A4)))) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.groups2880970938130013265at_nat F) A2)) (@ (@ tptp.groups2880970938130013265at_nat G) B)))))))
% 4.96/5.19 (assert (forall ((B tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.int)) (G (-> tptp.real tptp.int))) (=> (@ tptp.finite_finite_real B) (=> (@ (@ tptp.ord_less_eq_set_real A2) B) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) A2) (@ (@ tptp.dvd_dvd_int (@ F A4)) (@ G A4)))) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.groups4694064378042380927al_int F) A2)) (@ (@ tptp.groups4694064378042380927al_int G) B)))))))
% 4.96/5.19 (assert (forall ((B tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.int)) (G (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex B) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) A2) (@ (@ tptp.dvd_dvd_int (@ F A4)) (@ G A4)))) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.groups858564598930262913ex_int F) A2)) (@ (@ tptp.groups858564598930262913ex_int G) B)))))))
% 4.96/5.19 (assert (forall ((B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.int)) (G (-> tptp.extended_enat tptp.int))) (=> (@ tptp.finite4001608067531595151d_enat B) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) B) (=> (forall ((A4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A4) A2) (@ (@ tptp.dvd_dvd_int (@ F A4)) (@ G A4)))) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.groups2878480467620962989at_int F) A2)) (@ (@ tptp.groups2878480467620962989at_int G) B)))))))
% 4.96/5.19 (assert (forall ((B tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int B) (=> (@ (@ tptp.ord_less_eq_set_int A2) B) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) A2) (@ (@ tptp.dvd_dvd_nat (@ F A4)) (@ G A4)))) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.groups1707563613775114915nt_nat F) A2)) (@ (@ tptp.groups1707563613775114915nt_nat G) B)))))))
% 4.96/5.19 (assert (forall ((B tptp.set_nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat B) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B) (=> (forall ((A4 tptp.nat)) (=> (@ (@ tptp.member_nat A4) A2) (@ (@ tptp.dvd_dvd_int (@ F A4)) (@ G A4)))) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.groups705719431365010083at_int F) A2)) (@ (@ tptp.groups705719431365010083at_int G) B)))))))
% 4.96/5.19 (assert (forall ((B tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.int)) (G (-> tptp.int tptp.int))) (=> (@ tptp.finite_finite_int B) (=> (@ (@ tptp.ord_less_eq_set_int A2) B) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) A2) (@ (@ tptp.dvd_dvd_int (@ F A4)) (@ G A4)))) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.groups1705073143266064639nt_int F) A2)) (@ (@ tptp.groups1705073143266064639nt_int G) B)))))))
% 4.96/5.19 (assert (forall ((B tptp.set_nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat B) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B) (=> (forall ((A4 tptp.nat)) (=> (@ (@ tptp.member_nat A4) A2) (@ (@ tptp.dvd_dvd_nat (@ F A4)) (@ G A4)))) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.groups708209901874060359at_nat F) A2)) (@ (@ tptp.groups708209901874060359at_nat G) B)))))))
% 4.96/5.19 (assert (forall ((S5 tptp.set_real) (T5 tptp.set_real) (S2 tptp.set_real) (I (-> tptp.real tptp.real)) (J (-> tptp.real tptp.real)) (T3 tptp.set_real) (G (-> tptp.real tptp.nat)) (H2 (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real S5) (=> (@ tptp.finite_finite_real T5) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real S2) S5)) (= (@ I (@ J A4)) A4))) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real S2) S5)) (@ (@ tptp.member_real (@ J A4)) (@ (@ tptp.minus_minus_set_real T3) T5)))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real T3) T5)) (= (@ J (@ I B4)) B4))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real T3) T5)) (@ (@ tptp.member_real (@ I B4)) (@ (@ tptp.minus_minus_set_real S2) S5)))) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) S5) (= (@ G A4) tptp.one_one_nat))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) T5) (= (@ H2 B4) tptp.one_one_nat))) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) S2) (= (@ H2 (@ J A4)) (@ G A4)))) (= (@ (@ tptp.groups4696554848551431203al_nat G) S2) (@ (@ tptp.groups4696554848551431203al_nat H2) T3)))))))))))))
% 4.96/5.19 (assert (forall ((S5 tptp.set_real) (T5 tptp.set_complex) (S2 tptp.set_real) (I (-> tptp.complex tptp.real)) (J (-> tptp.real tptp.complex)) (T3 tptp.set_complex) (G (-> tptp.real tptp.nat)) (H2 (-> tptp.complex tptp.nat))) (=> (@ tptp.finite_finite_real S5) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real S2) S5)) (= (@ I (@ J A4)) A4))) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real S2) S5)) (@ (@ tptp.member_complex (@ J A4)) (@ (@ tptp.minus_811609699411566653omplex T3) T5)))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex T3) T5)) (= (@ J (@ I B4)) B4))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex T3) T5)) (@ (@ tptp.member_real (@ I B4)) (@ (@ tptp.minus_minus_set_real S2) S5)))) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) S5) (= (@ G A4) tptp.one_one_nat))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) T5) (= (@ H2 B4) tptp.one_one_nat))) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) S2) (= (@ H2 (@ J A4)) (@ G A4)))) (= (@ (@ tptp.groups4696554848551431203al_nat G) S2) (@ (@ tptp.groups861055069439313189ex_nat H2) T3)))))))))))))
% 4.96/5.19 (assert (forall ((S5 tptp.set_real) (T5 tptp.set_int) (S2 tptp.set_real) (I (-> tptp.int tptp.real)) (J (-> tptp.real tptp.int)) (T3 tptp.set_int) (G (-> tptp.real tptp.nat)) (H2 (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_real S5) (=> (@ tptp.finite_finite_int T5) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real S2) S5)) (= (@ I (@ J A4)) A4))) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real S2) S5)) (@ (@ tptp.member_int (@ J A4)) (@ (@ tptp.minus_minus_set_int T3) T5)))) (=> (forall ((B4 tptp.int)) (=> (@ (@ tptp.member_int B4) (@ (@ tptp.minus_minus_set_int T3) T5)) (= (@ J (@ I B4)) B4))) (=> (forall ((B4 tptp.int)) (=> (@ (@ tptp.member_int B4) (@ (@ tptp.minus_minus_set_int T3) T5)) (@ (@ tptp.member_real (@ I B4)) (@ (@ tptp.minus_minus_set_real S2) S5)))) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) S5) (= (@ G A4) tptp.one_one_nat))) (=> (forall ((B4 tptp.int)) (=> (@ (@ tptp.member_int B4) T5) (= (@ H2 B4) tptp.one_one_nat))) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) S2) (= (@ H2 (@ J A4)) (@ G A4)))) (= (@ (@ tptp.groups4696554848551431203al_nat G) S2) (@ (@ tptp.groups1707563613775114915nt_nat H2) T3)))))))))))))
% 4.96/5.19 (assert (forall ((S5 tptp.set_real) (T5 tptp.set_Extended_enat) (S2 tptp.set_real) (I (-> tptp.extended_enat tptp.real)) (J (-> tptp.real tptp.extended_enat)) (T3 tptp.set_Extended_enat) (G (-> tptp.real tptp.nat)) (H2 (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite_finite_real S5) (=> (@ tptp.finite4001608067531595151d_enat T5) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real S2) S5)) (= (@ I (@ J A4)) A4))) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real S2) S5)) (@ (@ tptp.member_Extended_enat (@ J A4)) (@ (@ tptp.minus_925952699566721837d_enat T3) T5)))) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) (@ (@ tptp.minus_925952699566721837d_enat T3) T5)) (= (@ J (@ I B4)) B4))) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) (@ (@ tptp.minus_925952699566721837d_enat T3) T5)) (@ (@ tptp.member_real (@ I B4)) (@ (@ tptp.minus_minus_set_real S2) S5)))) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) S5) (= (@ G A4) tptp.one_one_nat))) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) T5) (= (@ H2 B4) tptp.one_one_nat))) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) S2) (= (@ H2 (@ J A4)) (@ G A4)))) (= (@ (@ tptp.groups4696554848551431203al_nat G) S2) (@ (@ tptp.groups2880970938130013265at_nat H2) T3)))))))))))))
% 4.96/5.19 (assert (forall ((S5 tptp.set_complex) (T5 tptp.set_real) (S2 tptp.set_complex) (I (-> tptp.real tptp.complex)) (J (-> tptp.complex tptp.real)) (T3 tptp.set_real) (G (-> tptp.complex tptp.nat)) (H2 (-> tptp.real tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex S5) (=> (@ tptp.finite_finite_real T5) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) (@ (@ tptp.minus_811609699411566653omplex S2) S5)) (= (@ I (@ J A4)) A4))) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) (@ (@ tptp.minus_811609699411566653omplex S2) S5)) (@ (@ tptp.member_real (@ J A4)) (@ (@ tptp.minus_minus_set_real T3) T5)))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real T3) T5)) (= (@ J (@ I B4)) B4))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real T3) T5)) (@ (@ tptp.member_complex (@ I B4)) (@ (@ tptp.minus_811609699411566653omplex S2) S5)))) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) S5) (= (@ G A4) tptp.one_one_nat))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) T5) (= (@ H2 B4) tptp.one_one_nat))) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) S2) (= (@ H2 (@ J A4)) (@ G A4)))) (= (@ (@ tptp.groups861055069439313189ex_nat G) S2) (@ (@ tptp.groups4696554848551431203al_nat H2) T3)))))))))))))
% 4.96/5.19 (assert (forall ((S5 tptp.set_complex) (T5 tptp.set_complex) (S2 tptp.set_complex) (I (-> tptp.complex tptp.complex)) (J (-> tptp.complex tptp.complex)) (T3 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (H2 (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex S5) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) (@ (@ tptp.minus_811609699411566653omplex S2) S5)) (= (@ I (@ J A4)) A4))) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) (@ (@ tptp.minus_811609699411566653omplex S2) S5)) (@ (@ tptp.member_complex (@ J A4)) (@ (@ tptp.minus_811609699411566653omplex T3) T5)))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex T3) T5)) (= (@ J (@ I B4)) B4))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex T3) T5)) (@ (@ tptp.member_complex (@ I B4)) (@ (@ tptp.minus_811609699411566653omplex S2) S5)))) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) S5) (= (@ G A4) tptp.one_one_nat))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) T5) (= (@ H2 B4) tptp.one_one_nat))) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) S2) (= (@ H2 (@ J A4)) (@ G A4)))) (= (@ (@ tptp.groups861055069439313189ex_nat G) S2) (@ (@ tptp.groups861055069439313189ex_nat H2) T3)))))))))))))
% 4.96/5.19 (assert (forall ((S5 tptp.set_complex) (T5 tptp.set_int) (S2 tptp.set_complex) (I (-> tptp.int tptp.complex)) (J (-> tptp.complex tptp.int)) (T3 tptp.set_int) (G (-> tptp.complex tptp.nat)) (H2 (-> tptp.int tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex S5) (=> (@ tptp.finite_finite_int T5) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) (@ (@ tptp.minus_811609699411566653omplex S2) S5)) (= (@ I (@ J A4)) A4))) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) (@ (@ tptp.minus_811609699411566653omplex S2) S5)) (@ (@ tptp.member_int (@ J A4)) (@ (@ tptp.minus_minus_set_int T3) T5)))) (=> (forall ((B4 tptp.int)) (=> (@ (@ tptp.member_int B4) (@ (@ tptp.minus_minus_set_int T3) T5)) (= (@ J (@ I B4)) B4))) (=> (forall ((B4 tptp.int)) (=> (@ (@ tptp.member_int B4) (@ (@ tptp.minus_minus_set_int T3) T5)) (@ (@ tptp.member_complex (@ I B4)) (@ (@ tptp.minus_811609699411566653omplex S2) S5)))) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) S5) (= (@ G A4) tptp.one_one_nat))) (=> (forall ((B4 tptp.int)) (=> (@ (@ tptp.member_int B4) T5) (= (@ H2 B4) tptp.one_one_nat))) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) S2) (= (@ H2 (@ J A4)) (@ G A4)))) (= (@ (@ tptp.groups861055069439313189ex_nat G) S2) (@ (@ tptp.groups1707563613775114915nt_nat H2) T3)))))))))))))
% 4.96/5.19 (assert (forall ((S5 tptp.set_complex) (T5 tptp.set_Extended_enat) (S2 tptp.set_complex) (I (-> tptp.extended_enat tptp.complex)) (J (-> tptp.complex tptp.extended_enat)) (T3 tptp.set_Extended_enat) (G (-> tptp.complex tptp.nat)) (H2 (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex S5) (=> (@ tptp.finite4001608067531595151d_enat T5) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) (@ (@ tptp.minus_811609699411566653omplex S2) S5)) (= (@ I (@ J A4)) A4))) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) (@ (@ tptp.minus_811609699411566653omplex S2) S5)) (@ (@ tptp.member_Extended_enat (@ J A4)) (@ (@ tptp.minus_925952699566721837d_enat T3) T5)))) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) (@ (@ tptp.minus_925952699566721837d_enat T3) T5)) (= (@ J (@ I B4)) B4))) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) (@ (@ tptp.minus_925952699566721837d_enat T3) T5)) (@ (@ tptp.member_complex (@ I B4)) (@ (@ tptp.minus_811609699411566653omplex S2) S5)))) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) S5) (= (@ G A4) tptp.one_one_nat))) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) T5) (= (@ H2 B4) tptp.one_one_nat))) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) S2) (= (@ H2 (@ J A4)) (@ G A4)))) (= (@ (@ tptp.groups861055069439313189ex_nat G) S2) (@ (@ tptp.groups2880970938130013265at_nat H2) T3)))))))))))))
% 4.96/5.19 (assert (forall ((S5 tptp.set_int) (T5 tptp.set_real) (S2 tptp.set_int) (I (-> tptp.real tptp.int)) (J (-> tptp.int tptp.real)) (T3 tptp.set_real) (G (-> tptp.int tptp.nat)) (H2 (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_int S5) (=> (@ tptp.finite_finite_real T5) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) (@ (@ tptp.minus_minus_set_int S2) S5)) (= (@ I (@ J A4)) A4))) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) (@ (@ tptp.minus_minus_set_int S2) S5)) (@ (@ tptp.member_real (@ J A4)) (@ (@ tptp.minus_minus_set_real T3) T5)))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real T3) T5)) (= (@ J (@ I B4)) B4))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real T3) T5)) (@ (@ tptp.member_int (@ I B4)) (@ (@ tptp.minus_minus_set_int S2) S5)))) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) S5) (= (@ G A4) tptp.one_one_nat))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) T5) (= (@ H2 B4) tptp.one_one_nat))) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) S2) (= (@ H2 (@ J A4)) (@ G A4)))) (= (@ (@ tptp.groups1707563613775114915nt_nat G) S2) (@ (@ tptp.groups4696554848551431203al_nat H2) T3)))))))))))))
% 4.96/5.19 (assert (forall ((S5 tptp.set_int) (T5 tptp.set_complex) (S2 tptp.set_int) (I (-> tptp.complex tptp.int)) (J (-> tptp.int tptp.complex)) (T3 tptp.set_complex) (G (-> tptp.int tptp.nat)) (H2 (-> tptp.complex tptp.nat))) (=> (@ tptp.finite_finite_int S5) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) (@ (@ tptp.minus_minus_set_int S2) S5)) (= (@ I (@ J A4)) A4))) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) (@ (@ tptp.minus_minus_set_int S2) S5)) (@ (@ tptp.member_complex (@ J A4)) (@ (@ tptp.minus_811609699411566653omplex T3) T5)))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex T3) T5)) (= (@ J (@ I B4)) B4))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex T3) T5)) (@ (@ tptp.member_int (@ I B4)) (@ (@ tptp.minus_minus_set_int S2) S5)))) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) S5) (= (@ G A4) tptp.one_one_nat))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) T5) (= (@ H2 B4) tptp.one_one_nat))) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) S2) (= (@ H2 (@ J A4)) (@ G A4)))) (= (@ (@ tptp.groups1707563613775114915nt_nat G) S2) (@ (@ tptp.groups861055069439313189ex_nat H2) T3)))))))))))))
% 4.96/5.19 (assert (forall ((X tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (= (@ _let_1 (@ (@ tptp.plus_plus_real A) B2)) (@ (@ tptp.times_times_real (@ _let_1 A)) (@ _let_1 B2))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups4696554848551431203al_nat G))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ tptp.collect_real (lambda ((X4 tptp.real)) (= (@ G X4) tptp.one_one_nat))))) (@ _let_1 A2))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (= (@ G X4) tptp.one_one_nat))))) (@ _let_1 A2))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat G))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ tptp.collect_int (lambda ((X4 tptp.int)) (= (@ G X4) tptp.one_one_nat))))) (@ _let_1 A2))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2880970938130013265at_nat G))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (= (@ G X4) tptp.one_one_nat))))) (@ _let_1 A2))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups4694064378042380927al_int G))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ tptp.collect_real (lambda ((X4 tptp.real)) (= (@ G X4) tptp.one_one_int))))) (@ _let_1 A2))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (= (@ G X4) tptp.one_one_int))))) (@ _let_1 A2))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2878480467620962989at_int G))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (= (@ G X4) tptp.one_one_int))))) (@ _let_1 A2))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups713298508707869441omplex G))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ tptp.collect_real (lambda ((X4 tptp.real)) (= (@ G X4) tptp.one_one_complex))))) (@ _let_1 A2))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups3708469109370488835omplex G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (= (@ G X4) tptp.one_one_complex))))) (@ _let_1 A2))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups7440179247065528705omplex G))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ tptp.collect_int (lambda ((X4 tptp.int)) (= (@ G X4) tptp.one_one_complex))))) (@ _let_1 A2))))))
% 4.96/5.19 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I3))))) _let_1) (@ (@ tptp.groups705719431365010083at_int G) _let_1)))))
% 4.96/5.19 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I3))))) _let_1) (@ (@ tptp.groups708209901874060359at_nat G) _let_1)))))
% 4.96/5.19 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N2) M2))) (= (@ (@ tptp.groups705719431365010083at_int G) _let_1) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M2) N2)) I3)))) _let_1)))))
% 4.96/5.19 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N2) M2))) (= (@ (@ tptp.groups708209901874060359at_nat G) _let_1) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M2) N2)) I3)))) _let_1)))))
% 4.96/5.19 (assert (forall ((I6 tptp.set_real) (I tptp.real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ tptp.finite_finite_real I6) (=> (@ (@ tptp.member_real I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups1681761925125756287l_real F) I6)))))))))
% 4.96/5.19 (assert (forall ((I6 tptp.set_nat) (I tptp.nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ tptp.finite_finite_nat I6) (=> (@ (@ tptp.member_nat I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups129246275422532515t_real F) I6)))))))))
% 4.96/5.19 (assert (forall ((I6 tptp.set_complex) (I tptp.complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (@ (@ tptp.member_complex I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups766887009212190081x_real F) I6)))))))))
% 4.96/5.19 (assert (forall ((I6 tptp.set_int) (I tptp.int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ tptp.finite_finite_int I6) (=> (@ (@ tptp.member_int I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups2316167850115554303t_real F) I6)))))))))
% 4.96/5.19 (assert (forall ((I6 tptp.set_Extended_enat) (I tptp.extended_enat) (F (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ tptp.finite4001608067531595151d_enat I6) (=> (@ (@ tptp.member_Extended_enat I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I4) I6) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups97031904164794029t_real F) I6)))))))))
% 4.96/5.19 (assert (forall ((I6 tptp.set_real) (I tptp.real) (F (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ tptp.finite_finite_real I6) (=> (@ (@ tptp.member_real I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups4694064378042380927al_int F) I6)))))))))
% 4.96/5.19 (assert (forall ((I6 tptp.set_complex) (I tptp.complex) (F (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (@ (@ tptp.member_complex I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups858564598930262913ex_int F) I6)))))))))
% 4.96/5.19 (assert (forall ((I6 tptp.set_Extended_enat) (I tptp.extended_enat) (F (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ tptp.finite4001608067531595151d_enat I6) (=> (@ (@ tptp.member_Extended_enat I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I4) I6) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups2878480467620962989at_int F) I6)))))))))
% 4.96/5.19 (assert (forall ((I6 tptp.set_nat) (I tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ tptp.finite_finite_nat I6) (=> (@ (@ tptp.member_nat I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups705719431365010083at_int F) I6)))))))))
% 4.96/5.19 (assert (forall ((I6 tptp.set_int) (I tptp.int) (F (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ tptp.finite_finite_int I6) (=> (@ (@ tptp.member_int I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups1705073143266064639nt_int F) I6)))))))))
% 4.96/5.19 (assert (forall ((I6 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (not (= I6 tptp.bot_bot_set_complex)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ F I4)))) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.groups766887009212190081x_real F) I6)))))))
% 4.96/5.19 (assert (forall ((I6 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat I6) (=> (not (= I6 tptp.bot_bo7653980558646680370d_enat)) (=> (forall ((I4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I4) I6) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ F I4)))) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.groups97031904164794029t_real F) I6)))))))
% 4.96/5.19 (assert (forall ((I6 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real I6) (=> (not (= I6 tptp.bot_bot_set_real)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ F I4)))) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.groups1681761925125756287l_real F) I6)))))))
% 4.96/5.19 (assert (forall ((I6 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat I6) (=> (not (= I6 tptp.bot_bot_set_nat)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ F I4)))) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.groups129246275422532515t_real F) I6)))))))
% 4.96/5.19 (assert (forall ((I6 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int I6) (=> (not (= I6 tptp.bot_bot_set_int)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ F I4)))) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.groups2316167850115554303t_real F) I6)))))))
% 4.96/5.19 (assert (forall ((I6 tptp.set_complex) (F (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (not (= I6 tptp.bot_bot_set_complex)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ F I4)))) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ (@ tptp.groups858564598930262913ex_int F) I6)))))))
% 4.96/5.19 (assert (forall ((I6 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.int))) (=> (@ tptp.finite4001608067531595151d_enat I6) (=> (not (= I6 tptp.bot_bo7653980558646680370d_enat)) (=> (forall ((I4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I4) I6) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ F I4)))) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ (@ tptp.groups2878480467620962989at_int F) I6)))))))
% 4.96/5.19 (assert (forall ((I6 tptp.set_real) (F (-> tptp.real tptp.int))) (=> (@ tptp.finite_finite_real I6) (=> (not (= I6 tptp.bot_bot_set_real)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ F I4)))) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ (@ tptp.groups4694064378042380927al_int F) I6)))))))
% 4.96/5.19 (assert (forall ((I6 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat I6) (=> (not (= I6 tptp.bot_bot_set_nat)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ F I4)))) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ (@ tptp.groups705719431365010083at_int F) I6)))))))
% 4.96/5.19 (assert (forall ((I6 tptp.set_int) (F (-> tptp.int tptp.int))) (=> (@ tptp.finite_finite_int I6) (=> (not (= I6 tptp.bot_bot_set_int)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ F I4)))) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ (@ tptp.groups1705073143266064639nt_int F) I6)))))))
% 4.96/5.19 (assert (forall ((B tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B))) (@ _let_1 B))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2880970938130013265at_nat G))) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B) A2) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) B))) (@ _let_1 B))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B))) (@ _let_1 B))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2878480467620962989at_int G))) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B) A2) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) B))) (@ _let_1 B))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B))) (@ _let_1 B))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups97031904164794029t_real G))) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B) A2) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) B))) (@ _let_1 B))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups3708469109370488835omplex G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_complex (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B))) (@ _let_1 B))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.complex))) (let ((_let_1 (@ tptp.groups4622424608036095791omplex G))) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B) A2) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_complex (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) B))) (@ _let_1 B))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.extended_enat))) (let ((_let_1 (@ tptp.groups8780218893797010257d_enat G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.times_7803423173614009249d_enat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B))) (@ _let_1 B))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.extended_enat))) (let ((_let_1 (@ tptp.groups8932437906259616549d_enat G))) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B) A2) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_1 A2) (@ (@ tptp.times_7803423173614009249d_enat (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) B))) (@ _let_1 B))))))))
% 4.96/5.19 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B tptp.set_real) (G (-> tptp.real tptp.nat)) (H2 (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups4696554848551431203al_nat H2))) (let ((_let_2 (@ tptp.groups4696554848551431203al_nat G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B) C4) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A4) tptp.one_one_nat))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real C4) B)) (= (@ H2 B4) tptp.one_one_nat))) (= (= (@ _let_2 A2) (@ _let_1 B)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 4.96/5.19 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B tptp.set_complex) (G (-> tptp.complex tptp.nat)) (H2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat H2))) (let ((_let_2 (@ tptp.groups861055069439313189ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B) C4) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A4) tptp.one_one_nat))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex C4) B)) (= (@ H2 B4) tptp.one_one_nat))) (= (= (@ _let_2 A2) (@ _let_1 B)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 4.96/5.19 (assert (forall ((C4 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.nat)) (H2 (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2880970938130013265at_nat H2))) (let ((_let_2 (@ tptp.groups2880970938130013265at_nat G))) (=> (@ tptp.finite4001608067531595151d_enat C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B) C4) (=> (forall ((A4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A4) (@ (@ tptp.minus_925952699566721837d_enat C4) A2)) (= (@ G A4) tptp.one_one_nat))) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) (@ (@ tptp.minus_925952699566721837d_enat C4) B)) (= (@ H2 B4) tptp.one_one_nat))) (= (= (@ _let_2 A2) (@ _let_1 B)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 4.96/5.19 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B tptp.set_real) (G (-> tptp.real tptp.int)) (H2 (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups4694064378042380927al_int H2))) (let ((_let_2 (@ tptp.groups4694064378042380927al_int G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B) C4) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A4) tptp.one_one_int))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real C4) B)) (= (@ H2 B4) tptp.one_one_int))) (= (= (@ _let_2 A2) (@ _let_1 B)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 4.96/5.19 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B tptp.set_complex) (G (-> tptp.complex tptp.int)) (H2 (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int H2))) (let ((_let_2 (@ tptp.groups858564598930262913ex_int G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B) C4) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A4) tptp.one_one_int))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex C4) B)) (= (@ H2 B4) tptp.one_one_int))) (= (= (@ _let_2 A2) (@ _let_1 B)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 4.96/5.19 (assert (forall ((C4 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.int)) (H2 (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2878480467620962989at_int H2))) (let ((_let_2 (@ tptp.groups2878480467620962989at_int G))) (=> (@ tptp.finite4001608067531595151d_enat C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B) C4) (=> (forall ((A4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A4) (@ (@ tptp.minus_925952699566721837d_enat C4) A2)) (= (@ G A4) tptp.one_one_int))) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) (@ (@ tptp.minus_925952699566721837d_enat C4) B)) (= (@ H2 B4) tptp.one_one_int))) (= (= (@ _let_2 A2) (@ _let_1 B)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 4.96/5.19 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B tptp.set_real) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups713298508707869441omplex H2))) (let ((_let_2 (@ tptp.groups713298508707869441omplex G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B) C4) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A4) tptp.one_one_complex))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real C4) B)) (= (@ H2 B4) tptp.one_one_complex))) (= (= (@ _let_2 A2) (@ _let_1 B)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 4.96/5.19 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B tptp.set_complex) (G (-> tptp.complex tptp.complex)) (H2 (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups3708469109370488835omplex H2))) (let ((_let_2 (@ tptp.groups3708469109370488835omplex G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B) C4) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A4) tptp.one_one_complex))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex C4) B)) (= (@ H2 B4) tptp.one_one_complex))) (= (= (@ _let_2 A2) (@ _let_1 B)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 4.96/5.19 (assert (forall ((C4 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.complex)) (H2 (-> tptp.extended_enat tptp.complex))) (let ((_let_1 (@ tptp.groups4622424608036095791omplex H2))) (let ((_let_2 (@ tptp.groups4622424608036095791omplex G))) (=> (@ tptp.finite4001608067531595151d_enat C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B) C4) (=> (forall ((A4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A4) (@ (@ tptp.minus_925952699566721837d_enat C4) A2)) (= (@ G A4) tptp.one_one_complex))) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) (@ (@ tptp.minus_925952699566721837d_enat C4) B)) (= (@ H2 B4) tptp.one_one_complex))) (= (= (@ _let_2 A2) (@ _let_1 B)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 4.96/5.19 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B tptp.set_real) (G (-> tptp.real tptp.real)) (H2 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real H2))) (let ((_let_2 (@ tptp.groups1681761925125756287l_real G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B) C4) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A4) tptp.one_one_real))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real C4) B)) (= (@ H2 B4) tptp.one_one_real))) (= (= (@ _let_2 A2) (@ _let_1 B)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 4.96/5.19 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B tptp.set_real) (G (-> tptp.real tptp.nat)) (H2 (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups4696554848551431203al_nat H2))) (let ((_let_2 (@ tptp.groups4696554848551431203al_nat G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B) C4) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A4) tptp.one_one_nat))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real C4) B)) (= (@ H2 B4) tptp.one_one_nat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B))))))))))))
% 4.96/5.19 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B tptp.set_complex) (G (-> tptp.complex tptp.nat)) (H2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat H2))) (let ((_let_2 (@ tptp.groups861055069439313189ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B) C4) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A4) tptp.one_one_nat))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex C4) B)) (= (@ H2 B4) tptp.one_one_nat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B))))))))))))
% 4.96/5.19 (assert (forall ((C4 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.nat)) (H2 (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2880970938130013265at_nat H2))) (let ((_let_2 (@ tptp.groups2880970938130013265at_nat G))) (=> (@ tptp.finite4001608067531595151d_enat C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B) C4) (=> (forall ((A4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A4) (@ (@ tptp.minus_925952699566721837d_enat C4) A2)) (= (@ G A4) tptp.one_one_nat))) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) (@ (@ tptp.minus_925952699566721837d_enat C4) B)) (= (@ H2 B4) tptp.one_one_nat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B))))))))))))
% 4.96/5.19 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B tptp.set_real) (G (-> tptp.real tptp.int)) (H2 (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups4694064378042380927al_int H2))) (let ((_let_2 (@ tptp.groups4694064378042380927al_int G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B) C4) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A4) tptp.one_one_int))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real C4) B)) (= (@ H2 B4) tptp.one_one_int))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B))))))))))))
% 4.96/5.19 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B tptp.set_complex) (G (-> tptp.complex tptp.int)) (H2 (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int H2))) (let ((_let_2 (@ tptp.groups858564598930262913ex_int G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B) C4) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A4) tptp.one_one_int))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex C4) B)) (= (@ H2 B4) tptp.one_one_int))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B))))))))))))
% 4.96/5.19 (assert (forall ((C4 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.int)) (H2 (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2878480467620962989at_int H2))) (let ((_let_2 (@ tptp.groups2878480467620962989at_int G))) (=> (@ tptp.finite4001608067531595151d_enat C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B) C4) (=> (forall ((A4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A4) (@ (@ tptp.minus_925952699566721837d_enat C4) A2)) (= (@ G A4) tptp.one_one_int))) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) (@ (@ tptp.minus_925952699566721837d_enat C4) B)) (= (@ H2 B4) tptp.one_one_int))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B))))))))))))
% 4.96/5.19 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B tptp.set_real) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups713298508707869441omplex H2))) (let ((_let_2 (@ tptp.groups713298508707869441omplex G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B) C4) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A4) tptp.one_one_complex))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real C4) B)) (= (@ H2 B4) tptp.one_one_complex))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B))))))))))))
% 4.96/5.19 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B tptp.set_complex) (G (-> tptp.complex tptp.complex)) (H2 (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups3708469109370488835omplex H2))) (let ((_let_2 (@ tptp.groups3708469109370488835omplex G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B) C4) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A4) tptp.one_one_complex))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex C4) B)) (= (@ H2 B4) tptp.one_one_complex))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B))))))))))))
% 4.96/5.19 (assert (forall ((C4 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.complex)) (H2 (-> tptp.extended_enat tptp.complex))) (let ((_let_1 (@ tptp.groups4622424608036095791omplex H2))) (let ((_let_2 (@ tptp.groups4622424608036095791omplex G))) (=> (@ tptp.finite4001608067531595151d_enat C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B) C4) (=> (forall ((A4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A4) (@ (@ tptp.minus_925952699566721837d_enat C4) A2)) (= (@ G A4) tptp.one_one_complex))) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) (@ (@ tptp.minus_925952699566721837d_enat C4) B)) (= (@ H2 B4) tptp.one_one_complex))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B))))))))))))
% 4.96/5.19 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B tptp.set_real) (G (-> tptp.real tptp.real)) (H2 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real H2))) (let ((_let_2 (@ tptp.groups1681761925125756287l_real G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B) C4) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A4) tptp.one_one_real))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real C4) B)) (= (@ H2 B4) tptp.one_one_real))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B))))))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X5) tptp.one_one_nat))) (= (@ _let_1 S2) (@ _let_1 T3))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2880970938130013265at_nat G))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G X5) tptp.one_one_nat))) (= (@ _let_1 S2) (@ _let_1 T3))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X5) tptp.one_one_int))) (= (@ _let_1 S2) (@ _let_1 T3))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2878480467620962989at_int G))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G X5) tptp.one_one_int))) (= (@ _let_1 S2) (@ _let_1 T3))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups3708469109370488835omplex G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X5) tptp.one_one_complex))) (= (@ _let_1 S2) (@ _let_1 T3))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.complex))) (let ((_let_1 (@ tptp.groups4622424608036095791omplex G))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G X5) tptp.one_one_complex))) (= (@ _let_1 S2) (@ _let_1 T3))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X5) tptp.one_one_real))) (= (@ _let_1 S2) (@ _let_1 T3))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups97031904164794029t_real G))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G X5) tptp.one_one_real))) (= (@ _let_1 S2) (@ _let_1 T3))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_nat) (S2 tptp.set_nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups6464643781859351333omplex G))) (=> (@ tptp.finite_finite_nat T3) (=> (@ (@ tptp.ord_less_eq_set_nat S2) T3) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) (@ (@ tptp.minus_minus_set_nat T3) S2)) (= (@ G X5) tptp.one_one_complex))) (= (@ _let_1 S2) (@ _let_1 T3))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_nat) (S2 tptp.set_nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (=> (@ tptp.finite_finite_nat T3) (=> (@ (@ tptp.ord_less_eq_set_nat S2) T3) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) (@ (@ tptp.minus_minus_set_nat T3) S2)) (= (@ G X5) tptp.one_one_real))) (= (@ _let_1 S2) (@ _let_1 T3))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X5) tptp.one_one_nat))) (= (@ _let_1 T3) (@ _let_1 S2))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2880970938130013265at_nat G))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G X5) tptp.one_one_nat))) (= (@ _let_1 T3) (@ _let_1 S2))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X5) tptp.one_one_int))) (= (@ _let_1 T3) (@ _let_1 S2))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2878480467620962989at_int G))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G X5) tptp.one_one_int))) (= (@ _let_1 T3) (@ _let_1 S2))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups3708469109370488835omplex G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X5) tptp.one_one_complex))) (= (@ _let_1 T3) (@ _let_1 S2))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.complex))) (let ((_let_1 (@ tptp.groups4622424608036095791omplex G))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G X5) tptp.one_one_complex))) (= (@ _let_1 T3) (@ _let_1 S2))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X5) tptp.one_one_real))) (= (@ _let_1 T3) (@ _let_1 S2))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups97031904164794029t_real G))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G X5) tptp.one_one_real))) (= (@ _let_1 T3) (@ _let_1 S2))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_nat) (S2 tptp.set_nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups6464643781859351333omplex G))) (=> (@ tptp.finite_finite_nat T3) (=> (@ (@ tptp.ord_less_eq_set_nat S2) T3) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) (@ (@ tptp.minus_minus_set_nat T3) S2)) (= (@ G X5) tptp.one_one_complex))) (= (@ _let_1 T3) (@ _let_1 S2))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_nat) (S2 tptp.set_nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (=> (@ tptp.finite_finite_nat T3) (=> (@ (@ tptp.ord_less_eq_set_nat S2) T3) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) (@ (@ tptp.minus_minus_set_nat T3) S2)) (= (@ G X5) tptp.one_one_real))) (= (@ _let_1 T3) (@ _let_1 S2))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_real) (S2 tptp.set_real) (H2 (-> tptp.real tptp.nat)) (G (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S2) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S2)) (= (@ H2 X5) tptp.one_one_nat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups4696554848551431203al_nat G) S2) (@ (@ tptp.groups4696554848551431203al_nat H2) T3))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (H2 (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ H2 X5) tptp.one_one_nat))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups861055069439313189ex_nat G) S2) (@ (@ tptp.groups861055069439313189ex_nat H2) T3))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (H2 (-> tptp.extended_enat tptp.nat)) (G (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ H2 X5) tptp.one_one_nat))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups2880970938130013265at_nat G) S2) (@ (@ tptp.groups2880970938130013265at_nat H2) T3))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_real) (S2 tptp.set_real) (H2 (-> tptp.real tptp.int)) (G (-> tptp.real tptp.int))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S2) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S2)) (= (@ H2 X5) tptp.one_one_int))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups4694064378042380927al_int G) S2) (@ (@ tptp.groups4694064378042380927al_int H2) T3))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (H2 (-> tptp.complex tptp.int)) (G (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ H2 X5) tptp.one_one_int))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups858564598930262913ex_int G) S2) (@ (@ tptp.groups858564598930262913ex_int H2) T3))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (H2 (-> tptp.extended_enat tptp.int)) (G (-> tptp.extended_enat tptp.int))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ H2 X5) tptp.one_one_int))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups2878480467620962989at_int G) S2) (@ (@ tptp.groups2878480467620962989at_int H2) T3))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_real) (S2 tptp.set_real) (H2 (-> tptp.real tptp.complex)) (G (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S2) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S2)) (= (@ H2 X5) tptp.one_one_complex))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups713298508707869441omplex G) S2) (@ (@ tptp.groups713298508707869441omplex H2) T3))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (H2 (-> tptp.complex tptp.complex)) (G (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ H2 X5) tptp.one_one_complex))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups3708469109370488835omplex G) S2) (@ (@ tptp.groups3708469109370488835omplex H2) T3))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (H2 (-> tptp.extended_enat tptp.complex)) (G (-> tptp.extended_enat tptp.complex))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ H2 X5) tptp.one_one_complex))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups4622424608036095791omplex G) S2) (@ (@ tptp.groups4622424608036095791omplex H2) T3))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_real) (S2 tptp.set_real) (H2 (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S2) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S2)) (= (@ H2 X5) tptp.one_one_real))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups1681761925125756287l_real G) S2) (@ (@ tptp.groups1681761925125756287l_real H2) T3))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_real) (S2 tptp.set_real) (G (-> tptp.real tptp.nat)) (H2 (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S2) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S2)) (= (@ G X5) tptp.one_one_nat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups4696554848551431203al_nat G) T3) (@ (@ tptp.groups4696554848551431203al_nat H2) S2))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (H2 (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X5) tptp.one_one_nat))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups861055069439313189ex_nat G) T3) (@ (@ tptp.groups861055069439313189ex_nat H2) S2))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.nat)) (H2 (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G X5) tptp.one_one_nat))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups2880970938130013265at_nat G) T3) (@ (@ tptp.groups2880970938130013265at_nat H2) S2))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_real) (S2 tptp.set_real) (G (-> tptp.real tptp.int)) (H2 (-> tptp.real tptp.int))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S2) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S2)) (= (@ G X5) tptp.one_one_int))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups4694064378042380927al_int G) T3) (@ (@ tptp.groups4694064378042380927al_int H2) S2))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.int)) (H2 (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X5) tptp.one_one_int))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups858564598930262913ex_int G) T3) (@ (@ tptp.groups858564598930262913ex_int H2) S2))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.int)) (H2 (-> tptp.extended_enat tptp.int))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G X5) tptp.one_one_int))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups2878480467620962989at_int G) T3) (@ (@ tptp.groups2878480467620962989at_int H2) S2))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_real) (S2 tptp.set_real) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S2) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S2)) (= (@ G X5) tptp.one_one_complex))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups713298508707869441omplex G) T3) (@ (@ tptp.groups713298508707869441omplex H2) S2))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.complex)) (H2 (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X5) tptp.one_one_complex))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups3708469109370488835omplex G) T3) (@ (@ tptp.groups3708469109370488835omplex H2) S2))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.complex)) (H2 (-> tptp.extended_enat tptp.complex))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G X5) tptp.one_one_complex))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups4622424608036095791omplex G) T3) (@ (@ tptp.groups4622424608036095791omplex H2) S2))))))))
% 4.96/5.19 (assert (forall ((T3 tptp.set_real) (S2 tptp.set_real) (G (-> tptp.real tptp.real)) (H2 (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S2) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S2)) (= (@ G X5) tptp.one_one_real))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups1681761925125756287l_real G) T3) (@ (@ tptp.groups1681761925125756287l_real H2) S2))))))))
% 4.96/5.19 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups129246275422532515t_real G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_real (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))
% 4.96/5.19 (assert (forall ((G (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups6464643781859351333omplex G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_complex (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))
% 4.96/5.19 (assert (forall ((G (-> tptp.nat tptp.extended_enat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups7961826882256487087d_enat G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_7803423173614009249d_enat (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))
% 4.96/5.19 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups705719431365010083at_int G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_int (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))
% 4.96/5.19 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups708209901874060359at_nat G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_nat (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))
% 4.96/5.19 (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))))
% 4.96/5.19 (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))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N2)) (@ (@ tptp.times_times_real (@ G M2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N2))))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups6464643781859351333omplex G))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N2)) (@ (@ tptp.times_times_complex (@ G M2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N2))))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.extended_enat))) (let ((_let_1 (@ tptp.groups7961826882256487087d_enat G))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N2)) (@ (@ tptp.times_7803423173614009249d_enat (@ G M2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N2))))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups705719431365010083at_int G))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N2)) (@ (@ tptp.times_times_int (@ G M2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N2))))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups708209901874060359at_nat G))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N2)) (@ (@ tptp.times_times_nat (@ G M2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N2))))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.groups129246275422532515t_real G))) (let ((_let_3 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_real (@ G _let_3)) (@ _let_2 (@ _let_1 N2))))))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.groups6464643781859351333omplex G))) (let ((_let_3 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_complex (@ G _let_3)) (@ _let_2 (@ _let_1 N2))))))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.extended_enat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.groups7961826882256487087d_enat G))) (let ((_let_3 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_7803423173614009249d_enat (@ G _let_3)) (@ _let_2 (@ _let_1 N2))))))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.groups705719431365010083at_int G))) (let ((_let_3 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_int (@ G _let_3)) (@ _let_2 (@ _let_1 N2))))))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.groups708209901874060359at_nat G))) (let ((_let_3 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_nat (@ G _let_3)) (@ _let_2 (@ _let_1 N2))))))))))
% 4.96/5.19 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 4.96/5.19 (assert (forall ((G (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (= (@ (@ tptp.groups6464643781859351333omplex G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_complex (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 4.96/5.19 (assert (forall ((G (-> tptp.nat tptp.extended_enat)) (N2 tptp.nat)) (= (@ (@ tptp.groups7961826882256487087d_enat G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.times_7803423173614009249d_enat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups7961826882256487087d_enat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 4.96/5.19 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 4.96/5.19 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups129246275422532515t_real G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.times_times_real (@ G M2)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ (@ tptp.times_times_complex (@ (@ tptp.groups6464643781859351333omplex G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.times_times_complex (@ G M2)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.extended_enat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ (@ tptp.times_7803423173614009249d_enat (@ (@ tptp.groups7961826882256487087d_enat G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.times_7803423173614009249d_enat (@ G M2)) (@ (@ tptp.groups7961826882256487087d_enat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups705719431365010083at_int G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.times_times_int (@ G M2)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups708209901874060359at_nat G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.times_times_nat (@ G M2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))))
% 4.96/5.19 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2)) (@ (@ tptp.groups705719431365010083at_int (lambda ((K2 tptp.nat)) (@ G (@ tptp.suc K2)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 4.96/5.19 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((K2 tptp.nat)) (@ G (@ tptp.suc K2)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((I4 tptp.complex)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_complex I4) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G I4)))))) (=> (not (= A2 tptp.bot_bot_set_complex)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups766887009212190081x_real F) A2)) (@ (@ tptp.groups766887009212190081x_real G) A2)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real)) (G (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (forall ((I4 tptp.extended_enat)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_Extended_enat I4) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G I4)))))) (=> (not (= A2 tptp.bot_bo7653980558646680370d_enat)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups97031904164794029t_real F) A2)) (@ (@ tptp.groups97031904164794029t_real G) A2)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real A2) (=> (forall ((I4 tptp.real)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_real I4) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G I4)))))) (=> (not (= A2 tptp.bot_bot_set_real)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups1681761925125756287l_real F) A2)) (@ (@ tptp.groups1681761925125756287l_real G) A2)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat A2) (=> (forall ((I4 tptp.nat)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_nat I4) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G I4)))))) (=> (not (= A2 tptp.bot_bot_set_nat)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups129246275422532515t_real F) A2)) (@ (@ tptp.groups129246275422532515t_real G) A2)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((I4 tptp.int)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_int I4) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G I4)))))) (=> (not (= A2 tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups2316167850115554303t_real F) A2)) (@ (@ tptp.groups2316167850115554303t_real G) A2)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((I4 tptp.complex)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_complex I4) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_nat _let_1) (@ G I4)))))) (=> (not (= A2 tptp.bot_bot_set_complex)) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups861055069439313189ex_nat F) A2)) (@ (@ tptp.groups861055069439313189ex_nat G) A2)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat)) (G (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (forall ((I4 tptp.extended_enat)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_Extended_enat I4) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_nat _let_1) (@ G I4)))))) (=> (not (= A2 tptp.bot_bo7653980558646680370d_enat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups2880970938130013265at_nat F) A2)) (@ (@ tptp.groups2880970938130013265at_nat G) A2)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat)) (G (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real A2) (=> (forall ((I4 tptp.real)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_real I4) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_nat _let_1) (@ G I4)))))) (=> (not (= A2 tptp.bot_bot_set_real)) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups4696554848551431203al_nat F) A2)) (@ (@ tptp.groups4696554848551431203al_nat G) A2)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((I4 tptp.int)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_int I4) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_nat _let_1) (@ G I4)))))) (=> (not (= A2 tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups1707563613775114915nt_nat F) A2)) (@ (@ tptp.groups1707563613775114915nt_nat G) A2)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.int)) (G (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((I4 tptp.complex)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_complex I4) A2) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) _let_1) (@ (@ tptp.ord_less_int _let_1) (@ G I4)))))) (=> (not (= A2 tptp.bot_bot_set_complex)) (@ (@ tptp.ord_less_int (@ (@ tptp.groups858564598930262913ex_int F) A2)) (@ (@ tptp.groups858564598930262913ex_int G) A2)))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups861055069439313189ex_nat F) A2)) (exists ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A2) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ F X4))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups1707563613775114915nt_nat F) A2)) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A2) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ F X4))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2880970938130013265at_nat F) A2)) (exists ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) A2) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ F X4))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups858564598930262913ex_int F) A2)) (exists ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A2) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ F X4))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.int))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2878480467620962989at_int F) A2)) (exists ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) A2) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ F X4))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups705719431365010083at_int F) A2)) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A2) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ F X4))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.int))) (=> (@ tptp.finite_finite_int A2) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups1705073143266064639nt_int F) A2)) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A2) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ F X4))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups708209901874060359at_nat F) A2)) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A2) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ F X4))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (X tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X))) (let ((_let_2 (@ tptp.groups861055069439313189ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_nat (@ G X)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_1 tptp.bot_bot_set_complex))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.nat)) (X tptp.extended_enat)) (let ((_let_1 (@ tptp.insert_Extended_enat X))) (let ((_let_2 (@ tptp.groups2880970938130013265at_nat G))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_nat (@ G X)) (@ _let_2 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ _let_1 tptp.bot_bo7653980558646680370d_enat))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.nat)) (X tptp.real)) (let ((_let_1 (@ tptp.insert_real X))) (let ((_let_2 (@ tptp.groups4696554848551431203al_nat G))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_nat (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_real A2) (@ _let_1 tptp.bot_bot_set_real))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.nat)) (X tptp.int)) (let ((_let_1 (@ tptp.insert_int X))) (let ((_let_2 (@ tptp.groups1707563613775114915nt_nat G))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_nat (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_int A2) (@ _let_1 tptp.bot_bot_set_int))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.int)) (X tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X))) (let ((_let_2 (@ tptp.groups858564598930262913ex_int G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_int (@ G X)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_1 tptp.bot_bot_set_complex))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.int)) (X tptp.extended_enat)) (let ((_let_1 (@ tptp.insert_Extended_enat X))) (let ((_let_2 (@ tptp.groups2878480467620962989at_int G))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_int (@ G X)) (@ _let_2 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ _let_1 tptp.bot_bo7653980558646680370d_enat))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.int)) (X tptp.real)) (let ((_let_1 (@ tptp.insert_real X))) (let ((_let_2 (@ tptp.groups4694064378042380927al_int G))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_int (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_real A2) (@ _let_1 tptp.bot_bot_set_real))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.real)) (X tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X))) (let ((_let_2 (@ tptp.groups766887009212190081x_real G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_real (@ G X)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_1 tptp.bot_bot_set_complex))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.real)) (X tptp.extended_enat)) (let ((_let_1 (@ tptp.insert_Extended_enat X))) (let ((_let_2 (@ tptp.groups97031904164794029t_real G))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_real (@ G X)) (@ _let_2 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ _let_1 tptp.bot_bo7653980558646680370d_enat))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.real)) (X tptp.real)) (let ((_let_1 (@ tptp.insert_real X))) (let ((_let_2 (@ tptp.groups1681761925125756287l_real G))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_real (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_real A2) (@ _let_1 tptp.bot_bot_set_real))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex X) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_nat (@ G X)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (X tptp.extended_enat) (G (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2880970938130013265at_nat G))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ (@ tptp.member_Extended_enat X) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_nat (@ G X)) (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ (@ tptp.insert_Extended_enat X) tptp.bot_bo7653980558646680370d_enat))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups4696554848551431203al_nat G))) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real X) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_nat (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat G))) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int X) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_nat (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex X) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_int (@ G X)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (X tptp.extended_enat) (G (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2878480467620962989at_int G))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ (@ tptp.member_Extended_enat X) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_int (@ G X)) (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ (@ tptp.insert_Extended_enat X) tptp.bot_bo7653980558646680370d_enat))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups4694064378042380927al_int G))) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real X) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_int (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex X) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_real (@ G X)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (X tptp.extended_enat) (G (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups97031904164794029t_real G))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ (@ tptp.member_Extended_enat X) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_real (@ G X)) (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ (@ tptp.insert_Extended_enat X) tptp.bot_bo7653980558646680370d_enat))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real G))) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real X) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_real (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))))))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.real)) (P5 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (let ((_let_2 (@ _let_1 P5))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups129246275422532515t_real G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_real (@ _let_4 (@ _let_5 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.complex)) (P5 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (let ((_let_2 (@ _let_1 P5))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups6464643781859351333omplex G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_complex (@ _let_4 (@ _let_5 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.extended_enat)) (P5 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (let ((_let_2 (@ _let_1 P5))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups7961826882256487087d_enat G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_7803423173614009249d_enat (@ _let_4 (@ _let_5 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int)) (P5 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (let ((_let_2 (@ _let_1 P5))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups705719431365010083at_int G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_int (@ _let_4 (@ _let_5 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 4.96/5.19 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat)) (P5 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (let ((_let_2 (@ _let_1 P5))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups708209901874060359at_nat G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_nat (@ _let_4 (@ _let_5 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_complex) (A tptp.complex) (B2 (-> tptp.complex tptp.nat)) (C (-> tptp.complex tptp.nat))) (let ((_let_1 (@ (@ tptp.groups861055069439313189ex_nat C) (@ (@ tptp.minus_811609699411566653omplex S2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_2 (= (@ (@ tptp.groups861055069439313189ex_nat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) (@ (@ tptp.times_times_nat (@ B2 A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups861055069439313189ex_nat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) _let_1))))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_Extended_enat) (A tptp.extended_enat) (B2 (-> tptp.extended_enat tptp.nat)) (C (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ (@ tptp.groups2880970938130013265at_nat C) (@ (@ tptp.minus_925952699566721837d_enat S2) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat))))) (let ((_let_2 (@ (@ tptp.member_Extended_enat A) S2))) (=> (@ tptp.finite4001608067531595151d_enat S2) (and (=> _let_2 (= (@ (@ tptp.groups2880970938130013265at_nat (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) (@ (@ tptp.times_times_nat (@ B2 A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups2880970938130013265at_nat (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) _let_1))))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_real) (A tptp.real) (B2 (-> tptp.real tptp.nat)) (C (-> tptp.real tptp.nat))) (let ((_let_1 (@ (@ tptp.groups4696554848551431203al_nat C) (@ (@ tptp.minus_minus_set_real S2) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_2 (@ (@ tptp.member_real A) S2))) (=> (@ tptp.finite_finite_real S2) (and (=> _let_2 (= (@ (@ tptp.groups4696554848551431203al_nat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) (@ (@ tptp.times_times_nat (@ B2 A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups4696554848551431203al_nat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) _let_1))))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_int) (A tptp.int) (B2 (-> tptp.int tptp.nat)) (C (-> tptp.int tptp.nat))) (let ((_let_1 (@ (@ tptp.groups1707563613775114915nt_nat C) (@ (@ tptp.minus_minus_set_int S2) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_2 (@ (@ tptp.member_int A) S2))) (=> (@ tptp.finite_finite_int S2) (and (=> _let_2 (= (@ (@ tptp.groups1707563613775114915nt_nat (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) (@ (@ tptp.times_times_nat (@ B2 A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups1707563613775114915nt_nat (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) _let_1))))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_complex) (A tptp.complex) (B2 (-> tptp.complex tptp.int)) (C (-> tptp.complex tptp.int))) (let ((_let_1 (@ (@ tptp.groups858564598930262913ex_int C) (@ (@ tptp.minus_811609699411566653omplex S2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_2 (= (@ (@ tptp.groups858564598930262913ex_int (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) (@ (@ tptp.times_times_int (@ B2 A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups858564598930262913ex_int (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) _let_1))))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_Extended_enat) (A tptp.extended_enat) (B2 (-> tptp.extended_enat tptp.int)) (C (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ (@ tptp.groups2878480467620962989at_int C) (@ (@ tptp.minus_925952699566721837d_enat S2) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat))))) (let ((_let_2 (@ (@ tptp.member_Extended_enat A) S2))) (=> (@ tptp.finite4001608067531595151d_enat S2) (and (=> _let_2 (= (@ (@ tptp.groups2878480467620962989at_int (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) (@ (@ tptp.times_times_int (@ B2 A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups2878480467620962989at_int (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) _let_1))))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_real) (A tptp.real) (B2 (-> tptp.real tptp.int)) (C (-> tptp.real tptp.int))) (let ((_let_1 (@ (@ tptp.groups4694064378042380927al_int C) (@ (@ tptp.minus_minus_set_real S2) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_2 (@ (@ tptp.member_real A) S2))) (=> (@ tptp.finite_finite_real S2) (and (=> _let_2 (= (@ (@ tptp.groups4694064378042380927al_int (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) (@ (@ tptp.times_times_int (@ B2 A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups4694064378042380927al_int (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) _let_1))))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_complex) (A tptp.complex) (B2 (-> tptp.complex tptp.real)) (C (-> tptp.complex tptp.real))) (let ((_let_1 (@ (@ tptp.groups766887009212190081x_real C) (@ (@ tptp.minus_811609699411566653omplex S2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_2 (= (@ (@ tptp.groups766887009212190081x_real (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) (@ (@ tptp.times_times_real (@ B2 A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups766887009212190081x_real (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) _let_1))))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_Extended_enat) (A tptp.extended_enat) (B2 (-> tptp.extended_enat tptp.real)) (C (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ (@ tptp.groups97031904164794029t_real C) (@ (@ tptp.minus_925952699566721837d_enat S2) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat))))) (let ((_let_2 (@ (@ tptp.member_Extended_enat A) S2))) (=> (@ tptp.finite4001608067531595151d_enat S2) (and (=> _let_2 (= (@ (@ tptp.groups97031904164794029t_real (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) (@ (@ tptp.times_times_real (@ B2 A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups97031904164794029t_real (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) _let_1))))))))
% 4.96/5.19 (assert (forall ((S2 tptp.set_real) (A tptp.real) (B2 (-> tptp.real tptp.real)) (C (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.groups1681761925125756287l_real C) (@ (@ tptp.minus_minus_set_real S2) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_2 (@ (@ tptp.member_real A) S2))) (=> (@ tptp.finite_finite_real S2) (and (=> _let_2 (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) (@ (@ tptp.times_times_real (@ B2 A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) _let_1))))))))
% 4.96/5.19 (assert (forall ((X (-> tptp.nat tptp.nat tptp.nat)) (Xa2 tptp.nat) (Xb tptp.nat) (Xc tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.set_fo2584398358068434914at_nat X))) (let ((_let_2 (@ (@ tptp.ord_less_nat Xb) Xa2))) (=> (= (@ (@ (@ _let_1 Xa2) Xb) Xc) Y) (and (=> _let_2 (= Y Xc)) (=> (not _let_2) (= Y (@ (@ (@ _let_1 (@ (@ tptp.plus_plus_nat Xa2) tptp.one_one_nat)) Xb) (@ (@ X Xa2) Xc))))))))))
% 4.96/5.19 (assert (= tptp.set_fo2584398358068434914at_nat (lambda ((F5 (-> tptp.nat tptp.nat tptp.nat)) (A3 tptp.nat) (B3 tptp.nat) (Acc2 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat B3) A3)) Acc2) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat F5) (@ (@ tptp.plus_plus_nat A3) tptp.one_one_nat)) B3) (@ (@ F5 A3) Acc2))))))
% 4.96/5.19 (assert (forall ((B tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real F))) (=> (@ tptp.finite_finite_real B) (=> (@ (@ tptp.ord_less_eq_set_real A2) B) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real B) A2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F B4)))) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F A4)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B)))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real F))) (=> (@ tptp.finite3207457112153483333omplex B) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex B) A2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F B4)))) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F A4)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B)))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups97031904164794029t_real F))) (=> (@ tptp.finite4001608067531595151d_enat B) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) B) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) (@ (@ tptp.minus_925952699566721837d_enat B) A2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F B4)))) (=> (forall ((A4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A4) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F A4)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B)))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups4694064378042380927al_int F))) (=> (@ tptp.finite_finite_real B) (=> (@ (@ tptp.ord_less_eq_set_real A2) B) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real B) A2)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F B4)))) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) A2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F A4)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B)))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int F))) (=> (@ tptp.finite3207457112153483333omplex B) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex B) A2)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F B4)))) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) A2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F A4)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B)))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2878480467620962989at_int F))) (=> (@ tptp.finite4001608067531595151d_enat B) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) B) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) (@ (@ tptp.minus_925952699566721837d_enat B) A2)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F B4)))) (=> (forall ((A4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A4) A2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F A4)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B)))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real F))) (=> (@ tptp.finite_finite_nat B) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B) (=> (forall ((B4 tptp.nat)) (=> (@ (@ tptp.member_nat B4) (@ (@ tptp.minus_minus_set_nat B) A2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F B4)))) (=> (forall ((A4 tptp.nat)) (=> (@ (@ tptp.member_nat A4) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F A4)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B)))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real F))) (=> (@ tptp.finite_finite_int B) (=> (@ (@ tptp.ord_less_eq_set_int A2) B) (=> (forall ((B4 tptp.int)) (=> (@ (@ tptp.member_int B4) (@ (@ tptp.minus_minus_set_int B) A2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F B4)))) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F A4)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B)))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups705719431365010083at_int F))) (=> (@ tptp.finite_finite_nat B) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B) (=> (forall ((B4 tptp.nat)) (=> (@ (@ tptp.member_nat B4) (@ (@ tptp.minus_minus_set_nat B) A2)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F B4)))) (=> (forall ((A4 tptp.nat)) (=> (@ (@ tptp.member_nat A4) A2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F A4)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B)))))))))
% 4.96/5.19 (assert (forall ((B tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.groups1705073143266064639nt_int F))) (=> (@ tptp.finite_finite_int B) (=> (@ (@ tptp.ord_less_eq_set_int A2) B) (=> (forall ((B4 tptp.int)) (=> (@ (@ tptp.member_int B4) (@ (@ tptp.minus_minus_set_int B) A2)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F B4)))) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) A2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F A4)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B)))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.complex)) (A tptp.complex)) (let ((_let_1 (@ tptp.groups3708469109370488835omplex F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_4 (@ (@ tptp.member_complex A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (= _let_5 tptp.zero_zero_complex)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide1717551699836669952omplex _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.complex)) (A tptp.extended_enat)) (let ((_let_1 (@ tptp.groups4622424608036095791omplex F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat))))) (let ((_let_4 (@ (@ tptp.member_Extended_enat A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (not (= _let_5 tptp.zero_zero_complex)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide1717551699836669952omplex _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.complex)) (A tptp.real)) (let ((_let_1 (@ tptp.groups713298508707869441omplex F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_4 (@ (@ tptp.member_real A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite_finite_real A2) (=> (not (= _let_5 tptp.zero_zero_complex)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide1717551699836669952omplex _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.complex)) (A tptp.int)) (let ((_let_1 (@ tptp.groups7440179247065528705omplex F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_4 (@ (@ tptp.member_int A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite_finite_int A2) (=> (not (= _let_5 tptp.zero_zero_complex)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide1717551699836669952omplex _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.complex)) (A tptp.nat)) (let ((_let_1 (@ tptp.groups6464643781859351333omplex F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))) (let ((_let_4 (@ (@ tptp.member_nat A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite_finite_nat A2) (=> (not (= _let_5 tptp.zero_zero_complex)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide1717551699836669952omplex _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (A tptp.complex)) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_4 (@ (@ tptp.member_complex A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (= _let_5 tptp.zero_zero_nat)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat)) (A tptp.extended_enat)) (let ((_let_1 (@ tptp.groups2880970938130013265at_nat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat))))) (let ((_let_4 (@ (@ tptp.member_Extended_enat A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (not (= _let_5 tptp.zero_zero_nat)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat)) (A tptp.real)) (let ((_let_1 (@ tptp.groups4696554848551431203al_nat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_4 (@ (@ tptp.member_real A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite_finite_real A2) (=> (not (= _let_5 tptp.zero_zero_nat)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat)) (A tptp.int)) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_4 (@ (@ tptp.member_int A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite_finite_int A2) (=> (not (= _let_5 tptp.zero_zero_nat)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 4.96/5.19 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.int)) (A tptp.complex)) (let ((_let_1 (@ tptp.groups858564598930262913ex_int F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_4 (@ (@ tptp.member_complex A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (= _let_5 tptp.zero_zero_int)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide_divide_int _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 4.96/5.19 (assert (forall ((A tptp.extended_enat) (N2 tptp.nat)) (= (@ (@ tptp.comm_s3181272606743183617d_enat A) (@ tptp.suc N2)) (@ (@ tptp.groups7961826882256487087d_enat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_p3455044024723400733d_enat A) (@ tptp.semiri4216267220026989637d_enat I3)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))))
% 4.96/5.19 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) (@ tptp.suc N2)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real I3)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))))
% 4.96/5.19 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) (@ tptp.suc N2)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ tptp.semiri1314217659103216013at_int I3)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))))
% 4.96/5.19 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) (@ tptp.suc N2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ tptp.semiri1316708129612266289at_nat I3)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))))
% 4.96/5.19 (assert (= tptp.comm_s3181272606743183617d_enat (lambda ((A3 tptp.extended_enat) (N tptp.nat)) (@ (@ tptp.groups7961826882256487087d_enat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_p3455044024723400733d_enat A3) (@ tptp.semiri4216267220026989637d_enat (@ (@ tptp.minus_minus_nat N) I3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N)))))
% 4.96/5.19 (assert (= tptp.comm_s7457072308508201937r_real (lambda ((A3 tptp.real) (N tptp.nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_real A3) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat N) I3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N)))))
% 4.96/5.19 (assert (= tptp.comm_s4660882817536571857er_int (lambda ((A3 tptp.int) (N tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_int A3) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat N) I3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N)))))
% 4.96/5.19 (assert (= tptp.comm_s4663373288045622133er_nat (lambda ((A3 tptp.nat) (N tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_nat A3) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat N) I3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N)))))
% 4.96/5.19 (assert (forall ((G (-> tptp.nat tptp.real)) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups129246275422532515t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M2)) (@ tptp.suc (@ _let_1 N2)))) (@ (@ tptp.groups129246275422532515t_real (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.times_times_real (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N2))))))
% 4.96/5.19 (assert (forall ((G (-> tptp.nat tptp.complex)) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups6464643781859351333omplex G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M2)) (@ tptp.suc (@ _let_1 N2)))) (@ (@ tptp.groups6464643781859351333omplex (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.times_times_complex (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N2))))))
% 4.96/5.20 (assert (forall ((G (-> tptp.nat tptp.extended_enat)) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups7961826882256487087d_enat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M2)) (@ tptp.suc (@ _let_1 N2)))) (@ (@ tptp.groups7961826882256487087d_enat (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.times_7803423173614009249d_enat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N2))))))
% 4.96/5.20 (assert (forall ((G (-> tptp.nat tptp.int)) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M2)) (@ tptp.suc (@ _let_1 N2)))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.times_times_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N2))))))
% 4.96/5.20 (assert (forall ((G (-> tptp.nat tptp.nat)) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M2)) (@ tptp.suc (@ _let_1 N2)))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.times_times_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N2))))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.int)) (A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int F) (@ (@ tptp.set_or1269000886237332187st_nat A) B2)) (@ (@ (@ (@ tptp.set_fo2581907887559384638at_int (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.plus_plus_int (@ F A3)) __flatten_var_0))) A) B2) tptp.zero_zero_int))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.complex)) (A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex F) (@ (@ tptp.set_or1269000886237332187st_nat A) B2)) (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.plus_plus_complex (@ F A3)) __flatten_var_0))) A) B2) tptp.zero_zero_complex))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.extended_enat)) (A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.groups7108830773950497114d_enat F) (@ (@ tptp.set_or1269000886237332187st_nat A) B2)) (@ (@ (@ (@ tptp.set_fo2538466533108834004d_enat (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.extended_enat)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ F A3)) __flatten_var_0))) A) B2) tptp.zero_z5237406670263579293d_enat))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat F) (@ (@ tptp.set_or1269000886237332187st_nat A) B2)) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F A3)) __flatten_var_0))) A) B2) tptp.zero_zero_nat))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real F) (@ (@ tptp.set_or1269000886237332187st_nat A) B2)) (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.plus_plus_real (@ F A3)) __flatten_var_0))) A) B2) tptp.zero_zero_real))))
% 4.96/5.20 (assert (forall ((A tptp.extended_enat) (N2 tptp.nat)) (= (@ (@ tptp.comm_s3181272606743183617d_enat A) (@ tptp.suc N2)) (@ (@ tptp.groups7961826882256487087d_enat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_p3455044024723400733d_enat A) (@ tptp.semiri4216267220026989637d_enat (@ (@ tptp.minus_minus_nat N2) I3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))))
% 4.96/5.20 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) (@ tptp.suc N2)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat N2) I3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))))
% 4.96/5.20 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) (@ tptp.suc N2)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat N2) I3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))))
% 4.96/5.20 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) (@ tptp.suc N2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat N2) I3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))))
% 4.96/5.20 (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))
% 4.96/5.20 (assert (@ (@ tptp.sums_nat (lambda ((N tptp.nat)) tptp.zero_zero_nat)) tptp.zero_zero_nat))
% 4.96/5.20 (assert (@ (@ tptp.sums_real (lambda ((N tptp.nat)) tptp.zero_zero_real)) tptp.zero_zero_real))
% 4.96/5.20 (assert (@ (@ tptp.sums_int (lambda ((N tptp.nat)) tptp.zero_zero_int)) tptp.zero_zero_int))
% 4.96/5.20 (assert (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) tptp.zero_zero_complex)) tptp.zero_zero_complex))
% 4.96/5.20 (assert (forall ((G (-> tptp.nat tptp.real)) (S2 tptp.real) (A2 tptp.set_nat) (S5 tptp.real) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.sums_real G) S2) (=> (@ tptp.finite_finite_nat A2) (=> (= S5 (@ (@ tptp.plus_plus_real S2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N)) (@ G N)))) A2))) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.member_nat N) A2)) (@ F N)) (@ G N)))) S5))))))
% 4.96/5.20 (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))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (= (@ (@ tptp.groups861055069439313189ex_nat F) A2) tptp.one_one_nat) (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A2) (= (@ F X4) tptp.one_one_nat)))))))
% 4.96/5.20 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (= (= (@ (@ tptp.groups1707563613775114915nt_nat F) A2) tptp.one_one_nat) (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (= (@ F X4) tptp.one_one_nat)))))))
% 4.96/5.20 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (= (@ (@ tptp.groups2880970938130013265at_nat F) A2) tptp.one_one_nat) (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) A2) (= (@ F X4) tptp.one_one_nat)))))))
% 4.96/5.20 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (= (= (@ (@ tptp.groups708209901874060359at_nat F) A2) tptp.one_one_nat) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A2) (= (@ F X4) tptp.one_one_nat)))))))
% 4.96/5.20 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups861055069439313189ex_nat F) A2)) (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X4))))))))
% 4.96/5.20 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups1707563613775114915nt_nat F) A2)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X4))))))))
% 4.96/5.20 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups2880970938130013265at_nat F) A2)) (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) A2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X4))))))))
% 4.96/5.20 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups708209901874060359at_nat F) A2)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X4))))))))
% 4.96/5.20 (assert (forall ((F (-> tptp.int tptp.nat)) (A2 tptp.set_int)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups1707563613775114915nt_nat F) A2)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X4 tptp.int)) (@ tptp.semiri1314217659103216013at_int (@ F X4)))) A2))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups708209901874060359at_nat F) A2)) (@ (@ tptp.groups705719431365010083at_int (lambda ((X4 tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ F X4)))) A2))))
% 4.96/5.20 (assert (forall ((I tptp.nat) (J tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat I) J)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X4 tptp.int)) X4)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int I)) (@ tptp.semiri1314217659103216013at_int J))))))
% 4.96/5.20 (assert (forall ((I6 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real I6) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I4)))) (= (@ tptp.ln_ln_real (@ (@ tptp.groups1681761925125756287l_real F) I6)) (@ (@ tptp.groups8097168146408367636l_real (lambda ((X4 tptp.real)) (@ tptp.ln_ln_real (@ F X4)))) I6))))))
% 4.96/5.20 (assert (forall ((I6 tptp.set_set_nat) (F (-> tptp.set_nat tptp.real))) (=> (@ tptp.finite1152437895449049373et_nat I6) (=> (forall ((I4 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat I4) I6) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I4)))) (= (@ tptp.ln_ln_real (@ (@ tptp.groups3619160379726066777t_real F) I6)) (@ (@ tptp.groups5107569545109728110t_real (lambda ((X4 tptp.set_nat)) (@ tptp.ln_ln_real (@ F X4)))) I6))))))
% 4.96/5.20 (assert (forall ((I6 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I4)))) (= (@ tptp.ln_ln_real (@ (@ tptp.groups766887009212190081x_real F) I6)) (@ (@ tptp.groups5808333547571424918x_real (lambda ((X4 tptp.complex)) (@ tptp.ln_ln_real (@ F X4)))) I6))))))
% 4.96/5.20 (assert (forall ((I6 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int I6) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I4)))) (= (@ tptp.ln_ln_real (@ (@ tptp.groups2316167850115554303t_real F) I6)) (@ (@ tptp.groups8778361861064173332t_real (lambda ((X4 tptp.int)) (@ tptp.ln_ln_real (@ F X4)))) I6))))))
% 4.96/5.20 (assert (forall ((I6 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat I6) (=> (forall ((I4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I4) I6) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I4)))) (= (@ tptp.ln_ln_real (@ (@ tptp.groups97031904164794029t_real F) I6)) (@ (@ tptp.groups4148127829035722712t_real (lambda ((X4 tptp.extended_enat)) (@ tptp.ln_ln_real (@ F X4)))) I6))))))
% 4.96/5.20 (assert (forall ((I6 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat I6) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I4)))) (= (@ tptp.ln_ln_real (@ (@ tptp.groups129246275422532515t_real F) I6)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((X4 tptp.nat)) (@ tptp.ln_ln_real (@ F X4)))) I6))))))
% 4.96/5.20 (assert (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I) J))) (= (@ (@ tptp.groups705719431365010083at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat I) _let_1)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X4 tptp.int)) X4)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int I)) (@ tptp.semiri1314217659103216013at_int _let_1)))))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real)) (S tptp.real) (T tptp.real)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ G N3))) (=> (@ (@ tptp.sums_real F) S) (=> (@ (@ tptp.sums_real G) T) (@ (@ tptp.ord_less_eq_real S) T))))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat)) (S tptp.nat) (T tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N3)) (@ G N3))) (=> (@ (@ tptp.sums_nat F) S) (=> (@ (@ tptp.sums_nat G) T) (@ (@ tptp.ord_less_eq_nat S) T))))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int)) (S tptp.int) (T tptp.int)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N3)) (@ G N3))) (=> (@ (@ tptp.sums_int F) S) (=> (@ (@ tptp.sums_int G) T) (@ (@ tptp.ord_less_eq_int S) T))))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.nat))) (=> (forall ((N3 tptp.nat)) (= (@ F N3) tptp.zero_zero_nat)) (@ (@ tptp.sums_nat F) tptp.zero_zero_nat))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (forall ((N3 tptp.nat)) (= (@ F N3) tptp.zero_zero_real)) (@ (@ tptp.sums_real F) tptp.zero_zero_real))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.int))) (=> (forall ((N3 tptp.nat)) (= (@ F N3) tptp.zero_zero_int)) (@ (@ tptp.sums_int F) tptp.zero_zero_int))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.complex))) (=> (forall ((N3 tptp.nat)) (= (@ F N3) tptp.zero_zero_complex)) (@ (@ tptp.sums_complex F) tptp.zero_zero_complex))))
% 4.96/5.20 (assert (forall ((I tptp.nat) (F (-> tptp.nat tptp.nat))) (@ (@ tptp.sums_nat (lambda ((R4 tptp.nat)) (@ (@ (@ tptp.if_nat (= R4 I)) (@ F R4)) tptp.zero_zero_nat))) (@ F I))))
% 4.96/5.20 (assert (forall ((I tptp.nat) (F (-> tptp.nat tptp.real))) (@ (@ tptp.sums_real (lambda ((R4 tptp.nat)) (@ (@ (@ tptp.if_real (= R4 I)) (@ F R4)) tptp.zero_zero_real))) (@ F I))))
% 4.96/5.20 (assert (forall ((I tptp.nat) (F (-> tptp.nat tptp.int))) (@ (@ tptp.sums_int (lambda ((R4 tptp.nat)) (@ (@ (@ tptp.if_int (= R4 I)) (@ F R4)) tptp.zero_zero_int))) (@ F I))))
% 4.96/5.20 (assert (forall ((I tptp.nat) (F (-> tptp.nat tptp.complex))) (@ (@ tptp.sums_complex (lambda ((R4 tptp.nat)) (@ (@ (@ tptp.if_complex (= R4 I)) (@ F R4)) tptp.zero_zero_complex))) (@ F I))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (G (-> tptp.nat tptp.nat)) (B2 tptp.nat)) (=> (@ (@ tptp.sums_nat F) A) (=> (@ (@ tptp.sums_nat G) B2) (@ (@ tptp.sums_nat (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F N)) (@ G N)))) (@ (@ tptp.plus_plus_nat A) B2))))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.int)) (A tptp.int) (G (-> tptp.nat tptp.int)) (B2 tptp.int)) (=> (@ (@ tptp.sums_int F) A) (=> (@ (@ tptp.sums_int G) B2) (@ (@ tptp.sums_int (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_int (@ F N)) (@ G N)))) (@ (@ tptp.plus_plus_int A) B2))))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.real) (G (-> tptp.nat tptp.real)) (B2 tptp.real)) (=> (@ (@ tptp.sums_real F) A) (=> (@ (@ tptp.sums_real G) B2) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_real (@ F N)) (@ G N)))) (@ (@ tptp.plus_plus_real A) B2))))))
% 4.96/5.20 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real)) (D tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N)))) (@ (@ tptp.times_times_real C) D)) (@ (@ tptp.sums_real F) D)))))
% 4.96/5.20 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex)) (D tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N)))) (@ (@ tptp.times_times_complex C) D)) (@ (@ tptp.sums_complex F) D)))))
% 4.96/5.20 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real)) (D tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) C))) (@ (@ tptp.times_times_real D) C)) (@ (@ tptp.sums_real F) D)))))
% 4.96/5.20 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex)) (D tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) C))) (@ (@ tptp.times_times_complex D) C)) (@ (@ tptp.sums_complex F) D)))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (assert (forall ((N6 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat N6) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N6)) (= (@ F N3) tptp.zero_zero_int))) (@ (@ tptp.sums_int F) (@ (@ tptp.groups3539618377306564664at_int F) N6))))))
% 4.96/5.20 (assert (forall ((N6 tptp.set_nat) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat N6) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N6)) (= (@ F N3) tptp.zero_zero_complex))) (@ (@ tptp.sums_complex F) (@ (@ tptp.groups2073611262835488442omplex F) N6))))))
% 4.96/5.20 (assert (forall ((N6 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat N6) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N6)) (= (@ F N3) tptp.zero_zero_nat))) (@ (@ tptp.sums_nat F) (@ (@ tptp.groups3542108847815614940at_nat F) N6))))))
% 4.96/5.20 (assert (forall ((N6 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat N6) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N6)) (= (@ F N3) tptp.zero_zero_real))) (@ (@ tptp.sums_real F) (@ (@ tptp.groups6591440286371151544t_real F) N6))))))
% 4.96/5.20 (assert (forall ((P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.collect_nat P))) (=> (@ tptp.finite_finite_nat _let_1) (@ (@ tptp.sums_int (lambda ((R4 tptp.nat)) (@ (@ (@ tptp.if_int (@ P R4)) (@ F R4)) tptp.zero_zero_int))) (@ (@ tptp.groups3539618377306564664at_int F) _let_1))))))
% 4.96/5.20 (assert (forall ((P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.collect_nat P))) (=> (@ tptp.finite_finite_nat _let_1) (@ (@ tptp.sums_complex (lambda ((R4 tptp.nat)) (@ (@ (@ tptp.if_complex (@ P R4)) (@ F R4)) tptp.zero_zero_complex))) (@ (@ tptp.groups2073611262835488442omplex F) _let_1))))))
% 4.96/5.20 (assert (forall ((P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.collect_nat P))) (=> (@ tptp.finite_finite_nat _let_1) (@ (@ tptp.sums_nat (lambda ((R4 tptp.nat)) (@ (@ (@ tptp.if_nat (@ P R4)) (@ F R4)) tptp.zero_zero_nat))) (@ (@ tptp.groups3542108847815614940at_nat F) _let_1))))))
% 4.96/5.20 (assert (forall ((P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.collect_nat P))) (=> (@ tptp.finite_finite_nat _let_1) (@ (@ tptp.sums_real (lambda ((R4 tptp.nat)) (@ (@ (@ tptp.if_real (@ P R4)) (@ F R4)) tptp.zero_zero_real))) (@ (@ tptp.groups6591440286371151544t_real F) _let_1))))))
% 4.96/5.20 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat A2) (@ (@ tptp.sums_int (lambda ((R4 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.member_nat R4) A2)) (@ F R4)) tptp.zero_zero_int))) (@ (@ tptp.groups3539618377306564664at_int F) A2)))))
% 4.96/5.20 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat A2) (@ (@ tptp.sums_complex (lambda ((R4 tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.member_nat R4) A2)) (@ F R4)) tptp.zero_zero_complex))) (@ (@ tptp.groups2073611262835488442omplex F) A2)))))
% 4.96/5.20 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (@ (@ tptp.sums_nat (lambda ((R4 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.member_nat R4) A2)) (@ F R4)) tptp.zero_zero_nat))) (@ (@ tptp.groups3542108847815614940at_nat F) A2)))))
% 4.96/5.20 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat A2) (@ (@ tptp.sums_real (lambda ((R4 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.member_nat R4) A2)) (@ F R4)) tptp.zero_zero_real))) (@ (@ tptp.groups6591440286371151544t_real F) A2)))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (Z3 tptp.int)) (@ (@ tptp.sums_int (lambda ((N tptp.nat)) (@ (@ tptp.times_times_int (@ (@ (@ tptp.if_int (= N M2)) tptp.one_one_int) tptp.zero_zero_int)) (@ (@ tptp.power_power_int Z3) N)))) (@ (@ tptp.power_power_int Z3) M2))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (Z3 tptp.real)) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ (@ tptp.if_real (= N M2)) tptp.one_one_real) tptp.zero_zero_real)) (@ (@ tptp.power_power_real Z3) N)))) (@ (@ tptp.power_power_real Z3) M2))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (Z3 tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ (@ tptp.if_complex (= N M2)) tptp.one_one_complex) tptp.zero_zero_complex)) (@ (@ tptp.power_power_complex Z3) N)))) (@ (@ tptp.power_power_complex Z3) M2))))
% 4.96/5.20 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.ln_ln_real X) (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) tptp.one_one_real)) (@ tptp.suc N))))))))))
% 4.96/5.20 (assert (= tptp.arcosh_real (lambda ((X4 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X4) (@ (@ tptp.powr_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X4) (@ 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))))))))))
% 4.96/5.20 (assert (= tptp.arsinh_real (lambda ((X4 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X4) (@ (@ tptp.powr_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) (@ 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))))))))))
% 4.96/5.20 (assert (forall ((B2 tptp.nat) (K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B2)) (@ tptp.semiri5074537144036343181t_real K))) (@ tptp.semiri1314217659103216013at_int 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))))))))))
% 4.96/5.20 (assert (forall ((R2 tptp.complex) (M2 tptp.nat)) (let ((_let_1 (@ tptp.suc M2))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex R2) K2)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex R2) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ tptp.semiri8010041392384452111omplex K2))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) M2)) (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_complex R2) _let_1))))))
% 4.96/5.20 (assert (forall ((R2 tptp.real) (M2 tptp.nat)) (let ((_let_1 (@ tptp.suc M2))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real R2) K2)) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real R2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real K2))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) M2)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_real R2) _let_1))))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.binomial _let_1) N2) _let_1))))
% 4.96/5.20 (assert (= (@ tptp.suminf_nat (lambda ((N tptp.nat)) tptp.zero_zero_nat)) tptp.zero_zero_nat))
% 4.96/5.20 (assert (= (@ tptp.suminf_real (lambda ((N tptp.nat)) tptp.zero_zero_real)) tptp.zero_zero_real))
% 4.96/5.20 (assert (= (@ tptp.suminf_int (lambda ((N tptp.nat)) tptp.zero_zero_int)) tptp.zero_zero_int))
% 4.96/5.20 (assert (= (@ tptp.suminf_complex (lambda ((N tptp.nat)) tptp.zero_zero_complex)) tptp.zero_zero_complex))
% 4.96/5.20 (assert (forall ((X tptp.real)) (= (= (@ tptp.real_V1803761363581548252l_real X) tptp.zero_zero_real) (= X tptp.zero_zero_real))))
% 4.96/5.20 (assert (forall ((X tptp.real)) (= (= (@ tptp.real_V4546457046886955230omplex X) tptp.zero_zero_complex) (= X tptp.zero_zero_real))))
% 4.96/5.20 (assert (= (@ tptp.real_V1803761363581548252l_real tptp.zero_zero_real) tptp.zero_zero_real))
% 4.96/5.20 (assert (= (@ tptp.real_V4546457046886955230omplex tptp.zero_zero_real) tptp.zero_zero_complex))
% 4.96/5.20 (assert (= (@ tptp.archim6058952711729229775r_real tptp.zero_zero_real) tptp.zero_zero_int))
% 4.96/5.20 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_nat tptp.zero_zero_nat) (@ tptp.suc K)) tptp.zero_zero_nat)))
% 4.96/5.20 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_real tptp.zero_zero_real) (@ tptp.suc K)) tptp.zero_zero_real)))
% 4.96/5.20 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_int tptp.zero_zero_int) (@ tptp.suc K)) tptp.zero_zero_int)))
% 4.96/5.20 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_complex tptp.zero_zero_complex) (@ tptp.suc K)) tptp.zero_zero_complex)))
% 4.96/5.20 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.binomial tptp.zero_zero_nat) (@ tptp.suc K)) tptp.zero_zero_nat)))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.binomial N2) (@ tptp.suc tptp.zero_zero_nat)) N2)))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.binomial N2) K) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat N2) K))))
% 4.96/5.20 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.gbinomial_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 4.96/5.20 (assert (forall ((A tptp.int)) (= (@ (@ tptp.gbinomial_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 4.96/5.20 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.gbinomial_complex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 4.96/5.20 (assert (forall ((A tptp.real)) (= (@ (@ tptp.gbinomial_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 4.96/5.20 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real X)) (@ tptp.real_V1803761363581548252l_real Y)))))
% 4.96/5.20 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex X)) (@ tptp.real_V4546457046886955230omplex Y)))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.binomial N2) tptp.zero_zero_nat) tptp.one_one_nat)))
% 4.96/5.20 (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))))
% 4.96/5.20 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X))))
% 4.96/5.20 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_real X) tptp.zero_zero_real))))
% 4.96/5.20 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real V)) X))))
% 4.96/5.20 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X))))
% 4.96/5.20 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_real X) tptp.one_one_real))))
% 4.96/5.20 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_real X) (@ tptp.numeral_numeral_real V)))))
% 4.96/5.20 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X))))
% 4.96/5.20 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X)) tptp.one_one_int) (@ (@ tptp.ord_less_real X) tptp.one_one_real))))
% 4.96/5.20 (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))))
% 4.96/5.20 (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))))
% 4.96/5.20 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)) X))))
% 4.96/5.20 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)))))
% 4.96/5.20 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) X))))
% 4.96/5.20 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) tptp.one_one_int) (@ (@ tptp.ord_less_real X) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 4.96/5.20 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) X))))
% 4.96/5.20 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_real X) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))))))
% 4.96/5.20 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)) X))))
% 4.96/5.20 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)))))
% 4.96/5.20 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.archim6058952711729229775r_real Y)))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K) (= (@ (@ tptp.binomial N2) K) tptp.zero_zero_nat))))
% 4.96/5.20 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real X))) X)))
% 4.96/5.20 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.archim6058952711729229775r_real Y)) (@ (@ tptp.ord_less_real X) Y))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (R2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M2))) (let ((_let_2 (@ _let_1 R2))) (let ((_let_3 (@ tptp.binomial (@ (@ tptp.plus_plus_nat _let_2) K)))) (let ((_let_4 (@ _let_1 K))) (= (@ (@ tptp.times_times_nat (@ _let_3 _let_4)) (@ (@ tptp.binomial _let_4) K)) (@ (@ tptp.times_times_nat (@ _let_3 K)) (@ (@ tptp.binomial _let_2) M2)))))))))
% 4.96/5.20 (assert (forall ((R2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat R2) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.binomial N2) R2)) (@ (@ tptp.power_power_nat N2) R2)))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (assert (forall ((Z3 tptp.int) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_int Z3) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z3)) X))))
% 4.96/5.20 (assert (forall ((X tptp.real) (Z3 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X)) Z3) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real Z3)))))
% 4.96/5.20 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ tptp.suc (@ (@ tptp.plus_plus_nat A) B2))))) (let ((_let_2 (@ tptp.suc A))) (= (@ (@ tptp.times_times_nat _let_2) (@ _let_1 _let_2)) (@ (@ tptp.times_times_nat (@ tptp.suc B2)) (@ _let_1 A)))))))
% 4.96/5.20 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.archim6058952711729229775r_real Y))) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X) Y)))))
% 4.96/5.20 (assert (forall ((Z3 tptp.int) (X tptp.real)) (= (@ (@ tptp.plus_plus_int Z3) (@ tptp.archim6058952711729229775r_real X)) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real Z3)) X)))))
% 4.96/5.20 (assert (forall ((X tptp.real) (Z3 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X)) Z3) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X) (@ tptp.ring_1_of_int_real Z3))))))
% 4.96/5.20 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.binomial N2))) (=> (@ (@ tptp.ord_less_eq_nat K) M2) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ (@ tptp.times_times_nat (@ _let_1 M2)) (@ (@ tptp.binomial M2) K)) (@ (@ tptp.times_times_nat (@ _let_1 K)) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N2) K)) (@ (@ tptp.minus_minus_nat M2) K)))))))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (assert (forall ((N6 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat N6) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N6)) (= (@ F N3) tptp.zero_zero_int))) (= (@ tptp.suminf_int F) (@ (@ tptp.groups3539618377306564664at_int F) N6))))))
% 4.96/5.20 (assert (forall ((N6 tptp.set_nat) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat N6) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N6)) (= (@ F N3) tptp.zero_zero_complex))) (= (@ tptp.suminf_complex F) (@ (@ tptp.groups2073611262835488442omplex F) N6))))))
% 4.96/5.20 (assert (forall ((N6 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat N6) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N6)) (= (@ F N3) tptp.zero_zero_nat))) (= (@ tptp.suminf_nat F) (@ (@ tptp.groups3542108847815614940at_nat F) N6))))))
% 4.96/5.20 (assert (forall ((N6 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat N6) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N6)) (= (@ F N3) tptp.zero_zero_real))) (= (@ tptp.suminf_real F) (@ (@ tptp.groups6591440286371151544t_real F) N6))))))
% 4.96/5.20 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.real_V7735802525324610683m_real X))) (@ (@ tptp.ord_less_real _let_1) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real _let_1)) tptp.one_one_real))))))
% 4.96/5.20 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex X))) (@ (@ tptp.ord_less_real _let_1) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex _let_1)) tptp.one_one_complex))))))
% 4.96/5.20 (assert (forall ((X tptp.real)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X)) tptp.one_one_int) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (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)))))))))
% 4.96/5.20 (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)))))))))
% 4.96/5.20 (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)))))))))
% 4.96/5.20 (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)))))))))
% 4.96/5.20 (assert (forall ((P (-> tptp.int Bool)) (T tptp.real)) (= (@ P (@ tptp.archim6058952711729229775r_real T)) (forall ((I3 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real I3))) (=> (and (@ (@ tptp.ord_less_eq_real _let_1) T) (@ (@ tptp.ord_less_real T) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))) (@ P I3)))))))
% 4.96/5.20 (assert (forall ((X tptp.real) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real A))) (= (= (@ tptp.archim6058952711729229775r_real X) A) (and (@ (@ tptp.ord_less_eq_real _let_1) X) (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))))))
% 4.96/5.20 (assert (forall ((Z3 tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real Z3))) (=> (@ (@ tptp.ord_less_eq_real _let_1) X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X) Z3))))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int (@ tptp.archim6058952711729229775r_real A)) (@ tptp.archim6058952711729229775r_real B2))) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.times_times_real A) B2))))))))
% 4.96/5.20 (assert (forall ((Z3 tptp.int) (X tptp.real)) (= (@ (@ tptp.ord_less_int Z3) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real Z3)) tptp.one_one_real)) X))))
% 4.96/5.20 (assert (forall ((X tptp.real) (Z3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) Z3) (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real Z3)) tptp.one_one_real)))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (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))))))))
% 4.96/5.20 (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))))))))
% 4.96/5.20 (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))))
% 4.96/5.20 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.archim6058952711729229775r_real X))) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real _let_1)) X) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))))
% 4.96/5.20 (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)))))))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (assert (forall ((K tptp.nat) (M2 tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.gbinomial_complex A))) (=> (@ (@ tptp.ord_less_eq_nat K) M2) (= (@ (@ tptp.times_times_complex (@ _let_1 M2)) (@ (@ tptp.gbinomial_complex (@ tptp.semiri8010041392384452111omplex M2)) K)) (@ (@ tptp.times_times_complex (@ _let_1 K)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex A) (@ tptp.semiri8010041392384452111omplex K))) (@ (@ tptp.minus_minus_nat M2) K))))))))
% 4.96/5.20 (assert (forall ((K tptp.nat) (M2 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.gbinomial_real A))) (=> (@ (@ tptp.ord_less_eq_nat K) M2) (= (@ (@ tptp.times_times_real (@ _let_1 M2)) (@ (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real M2)) K)) (@ (@ tptp.times_times_real (@ _let_1 K)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.minus_minus_nat M2) K))))))))
% 4.96/5.20 (assert (forall ((Q3 tptp.real) (P5 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 P5) Q3)))) Q3)) P5))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (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))))))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (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))))))))
% 4.96/5.20 (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))))))))
% 4.96/5.20 (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))))))))
% 4.96/5.20 (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))))))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (assert (forall ((Q3 tptp.real) (P5 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q3) (@ (@ tptp.ord_less_real P5) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real P5) Q3)))) tptp.one_one_real)) Q3)))))
% 4.96/5.20 (assert (= tptp.archim8280529875227126926d_real (lambda ((X4 tptp.real)) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X4) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((J2 tptp.nat)) (@ (@ tptp.gbinomial_complex (@ tptp.semiri8010041392384452111omplex J2)) 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)))))
% 4.96/5.20 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((J2 tptp.nat)) (@ (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real J2)) 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)))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (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))))))))
% 4.96/5.20 (assert (forall ((B2 tptp.nat) (N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (=> (@ (@ 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))) B2) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B2)) (@ tptp.semiri5074537144036343181t_real K))) (@ tptp.semiri1314217659103216013at_int N2))))))))
% 4.96/5.20 (assert (= (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ tptp.suminf_real (lambda ((K2 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K2)) tptp.one_one_real)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat)))))))
% 4.96/5.20 (assert (forall ((A tptp.complex) (M2 tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex A) K2)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex A) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ tptp.semiri8010041392384452111omplex K2))))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex M2)) tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_complex A) (@ (@ tptp.plus_plus_nat M2) tptp.one_one_nat))))))
% 4.96/5.20 (assert (forall ((A tptp.real) (M2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real A) K2)) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real A) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real K2))))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M2)) tptp.one_one_real)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_real A) (@ (@ tptp.plus_plus_nat M2) tptp.one_one_nat))))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (assert (= tptp.archim8280529875227126926d_real (lambda ((X4 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 X4))) (@ tptp.archim7802044766580827645g_real X4)) (@ tptp.archim6058952711729229775r_real X4)))))
% 4.96/5.20 (assert (forall ((M2 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 M2))) tptp.one_one_complex))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.power_power_complex _let_2) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) M2)))))))
% 4.96/5.20 (assert (forall ((M2 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 M2))) tptp.one_one_real))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.power_power_real _let_2) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) M2)))))))
% 4.96/5.20 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (= (@ tptp.set_ord_atMost_nat X) (@ tptp.set_ord_atMost_nat Y)) (= X Y))))
% 4.96/5.20 (assert (forall ((X tptp.int) (Y tptp.int)) (= (= (@ tptp.set_ord_atMost_int X) (@ tptp.set_ord_atMost_int Y)) (= X Y))))
% 4.96/5.20 (assert (forall ((I tptp.extended_enat) (K tptp.extended_enat)) (= (@ (@ tptp.member_Extended_enat I) (@ tptp.set_or8332593352340944941d_enat K)) (@ (@ tptp.ord_le2932123472753598470d_enat I) K))))
% 4.96/5.20 (assert (forall ((I tptp.real) (K tptp.real)) (= (@ (@ tptp.member_real I) (@ tptp.set_ord_atMost_real K)) (@ (@ tptp.ord_less_eq_real I) K))))
% 4.96/5.20 (assert (forall ((I tptp.set_nat) (K tptp.set_nat)) (= (@ (@ tptp.member_set_nat I) (@ tptp.set_or4236626031148496127et_nat K)) (@ (@ tptp.ord_less_eq_set_nat I) K))))
% 4.96/5.20 (assert (forall ((I tptp.set_int) (K tptp.set_int)) (= (@ (@ tptp.member_set_int I) (@ tptp.set_or58775011639299419et_int K)) (@ (@ tptp.ord_less_eq_set_int I) K))))
% 4.96/5.20 (assert (forall ((I tptp.nat) (K tptp.nat)) (= (@ (@ tptp.member_nat I) (@ tptp.set_ord_atMost_nat K)) (@ (@ tptp.ord_less_eq_nat I) K))))
% 4.96/5.20 (assert (forall ((I tptp.int) (K tptp.int)) (= (@ (@ tptp.member_int I) (@ tptp.set_ord_atMost_int K)) (@ (@ tptp.ord_less_eq_int I) K))))
% 4.96/5.20 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.set_ord_atMost_nat K))))
% 4.96/5.20 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_ord_atMost_real X)) (@ tptp.set_ord_atMost_real Y)) (@ (@ tptp.ord_less_eq_real X) Y))))
% 4.96/5.20 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.set_or4236626031148496127et_nat X)) (@ tptp.set_or4236626031148496127et_nat Y)) (@ (@ tptp.ord_less_eq_set_nat X) Y))))
% 4.96/5.20 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (@ (@ tptp.ord_le4403425263959731960et_int (@ tptp.set_or58775011639299419et_int X)) (@ tptp.set_or58775011639299419et_int Y)) (@ (@ tptp.ord_less_eq_set_int X) Y))))
% 4.96/5.20 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_ord_atMost_nat X)) (@ tptp.set_ord_atMost_nat Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))
% 4.96/5.20 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_atMost_int X)) (@ tptp.set_ord_atMost_int Y)) (@ (@ tptp.ord_less_eq_int X) Y))))
% 4.96/5.20 (assert (forall ((Z3 tptp.int)) (= (@ tptp.archim2898591450579166408c_real (@ tptp.ring_1_of_int_real Z3)) tptp.zero_zero_real)))
% 4.96/5.20 (assert (forall ((L tptp.set_nat) (H2 tptp.set_nat) (H3 tptp.set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.set_or4548717258645045905et_nat L) H2)) (@ tptp.set_or4236626031148496127et_nat H3)) (or (not (@ (@ tptp.ord_less_eq_set_nat L) H2)) (@ (@ tptp.ord_less_eq_set_nat H2) H3)))))
% 4.96/5.20 (assert (forall ((L tptp.set_int) (H2 tptp.set_int) (H3 tptp.set_int)) (= (@ (@ tptp.ord_le4403425263959731960et_int (@ (@ tptp.set_or370866239135849197et_int L) H2)) (@ tptp.set_or58775011639299419et_int H3)) (or (not (@ (@ tptp.ord_less_eq_set_int L) H2)) (@ (@ tptp.ord_less_eq_set_int H2) H3)))))
% 4.96/5.20 (assert (forall ((L tptp.nat) (H2 tptp.nat) (H3 tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.set_or1269000886237332187st_nat L) H2)) (@ tptp.set_ord_atMost_nat H3)) (or (not (@ (@ tptp.ord_less_eq_nat L) H2)) (@ (@ tptp.ord_less_eq_nat H2) H3)))))
% 4.96/5.20 (assert (forall ((L tptp.int) (H2 tptp.int) (H3 tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.set_or1266510415728281911st_int L) H2)) (@ tptp.set_ord_atMost_int H3)) (or (not (@ (@ tptp.ord_less_eq_int L) H2)) (@ (@ tptp.ord_less_eq_int H2) H3)))))
% 4.96/5.20 (assert (forall ((L tptp.real) (H2 tptp.real) (H3 tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.set_or1222579329274155063t_real L) H2)) (@ tptp.set_ord_atMost_real H3)) (or (not (@ (@ tptp.ord_less_eq_real L) H2)) (@ (@ tptp.ord_less_eq_real H2) H3)))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (assert (forall ((G (-> tptp.nat tptp.extended_enat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.groups7108830773950497114d_enat G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ _let_2 (@ tptp.set_ord_atMost_nat N2))) (@ G _let_1)))))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (assert (forall ((G (-> tptp.nat tptp.extended_enat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.groups7961826882256487087d_enat G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_7803423173614009249d_enat (@ _let_2 (@ tptp.set_ord_atMost_nat N2))) (@ G _let_1)))))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (assert (= (@ tptp.set_ord_atMost_nat tptp.zero_zero_nat) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))
% 4.96/5.20 (assert (forall ((H2 tptp.extended_enat)) (not (= tptp.bot_bo7653980558646680370d_enat (@ tptp.set_or8332593352340944941d_enat H2)))))
% 4.96/5.20 (assert (forall ((H2 tptp.real)) (not (= tptp.bot_bot_set_real (@ tptp.set_ord_atMost_real H2)))))
% 4.96/5.20 (assert (forall ((H2 tptp.nat)) (not (= tptp.bot_bot_set_nat (@ tptp.set_ord_atMost_nat H2)))))
% 4.96/5.20 (assert (forall ((H2 tptp.int)) (not (= tptp.bot_bot_set_int (@ tptp.set_ord_atMost_int H2)))))
% 4.96/5.20 (assert (forall ((A tptp.int)) (not (@ tptp.finite_finite_int (@ tptp.set_ord_atMost_int A)))))
% 4.96/5.20 (assert (forall ((H3 tptp.int) (L tptp.int) (H2 tptp.int)) (not (= (@ tptp.set_ord_atMost_int H3) (@ (@ tptp.set_or1266510415728281911st_int L) H2)))))
% 4.96/5.20 (assert (forall ((H3 tptp.real) (L tptp.real) (H2 tptp.real)) (not (= (@ tptp.set_ord_atMost_real H3) (@ (@ tptp.set_or1222579329274155063t_real L) H2)))))
% 4.96/5.20 (assert (= tptp.set_ord_atMost_real (lambda ((U2 tptp.real)) (@ tptp.collect_real (lambda ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real X4) U2))))))
% 4.96/5.20 (assert (= tptp.set_or4236626031148496127et_nat (lambda ((U2 tptp.set_nat)) (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat X4) U2))))))
% 4.96/5.20 (assert (= tptp.set_or58775011639299419et_int (lambda ((U2 tptp.set_int)) (@ tptp.collect_set_int (lambda ((X4 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int X4) U2))))))
% 4.96/5.20 (assert (= tptp.set_ord_atMost_nat (lambda ((U2 tptp.nat)) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X4) U2))))))
% 4.96/5.20 (assert (= tptp.set_ord_atMost_int (lambda ((U2 tptp.int)) (@ tptp.collect_int (lambda ((X4 tptp.int)) (@ (@ tptp.ord_less_eq_int X4) U2))))))
% 4.96/5.20 (assert (= tptp.set_ord_atMost_nat (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat)))
% 4.96/5.20 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K)) (@ tptp.set_ord_atMost_nat K))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (assert (forall ((H2 tptp.int) (L3 tptp.int) (H3 tptp.int)) (not (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_atMost_int H2)) (@ (@ tptp.set_or1266510415728281911st_int L3) H3)))))
% 4.96/5.20 (assert (forall ((H2 tptp.real) (L3 tptp.real) (H3 tptp.real)) (not (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_ord_atMost_real H2)) (@ (@ tptp.set_or1222579329274155063t_real L3) H3)))))
% 4.96/5.20 (assert (= tptp.finite_finite_nat (lambda ((S6 tptp.set_nat)) (exists ((K2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat S6) (@ tptp.set_ord_atMost_nat K2))))))
% 4.96/5.20 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.archim2898591450579166408c_real X))))
% 4.96/5.20 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.archim2898591450579166408c_real X)) tptp.one_one_real)))
% 4.96/5.20 (assert (forall ((X tptp.real)) (= (@ tptp.archim2898591450579166408c_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)) (@ tptp.archim2898591450579166408c_real X))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (= (@ (@ tptp.ord_le7203529160286727270d_enat (@ tptp.set_or8332593352340944941d_enat A)) (@ tptp.set_or8419480210114673929d_enat B2)) (@ (@ tptp.ord_le72135733267957522d_enat A) B2))))
% 4.96/5.20 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_ord_atMost_real A)) (@ tptp.set_or5984915006950818249n_real B2)) (@ (@ tptp.ord_less_real A) B2))))
% 4.96/5.20 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_ord_atMost_nat A)) (@ tptp.set_ord_lessThan_nat B2)) (@ (@ tptp.ord_less_nat A) B2))))
% 4.96/5.20 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_atMost_int A)) (@ tptp.set_ord_lessThan_int B2)) (@ (@ tptp.ord_less_int A) B2))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.binomial K2) M2))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.binomial (@ tptp.suc N2)) (@ tptp.suc M2)))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (assert (forall ((G (-> tptp.nat tptp.extended_enat)) (N2 tptp.nat)) (= (@ (@ tptp.groups7108830773950497114d_enat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N2))) (@ (@ tptp.plus_p3455044024723400733d_enat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups7108830773950497114d_enat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_atMost_nat N2))))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.int)) (I tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F I3)) (@ F (@ tptp.suc I3))))) (@ tptp.set_ord_atMost_nat I)) (@ (@ tptp.minus_minus_int (@ F tptp.zero_zero_nat)) (@ F (@ tptp.suc I))))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.real)) (I tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F I3)) (@ F (@ tptp.suc I3))))) (@ tptp.set_ord_atMost_nat I)) (@ (@ tptp.minus_minus_real (@ F tptp.zero_zero_nat)) (@ F (@ tptp.suc I))))))
% 4.96/5.20 (assert (forall ((C (-> tptp.nat tptp.complex)) (N2 tptp.nat) (D (-> tptp.nat tptp.complex))) (= (forall ((X4 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 X4) I3)))) _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ D I3)) (@ (@ tptp.power_power_complex X4) I3)))) _let_1)))) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) N2) (= (@ C I3) (@ D I3)))))))
% 4.96/5.20 (assert (forall ((C (-> tptp.nat tptp.real)) (N2 tptp.nat) (D (-> tptp.nat tptp.real))) (= (forall ((X4 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 X4) I3)))) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ D I3)) (@ (@ tptp.power_power_real X4) I3)))) _let_1)))) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) N2) (= (@ C I3) (@ D I3)))))))
% 4.96/5.20 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_atMost_nat N2))))))
% 4.96/5.20 (assert (forall ((G (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (= (@ (@ tptp.groups6464643781859351333omplex G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_complex (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_atMost_nat N2))))))
% 4.96/5.20 (assert (forall ((G (-> tptp.nat tptp.extended_enat)) (N2 tptp.nat)) (= (@ (@ tptp.groups7961826882256487087d_enat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N2))) (@ (@ tptp.times_7803423173614009249d_enat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups7961826882256487087d_enat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_atMost_nat N2))))))
% 4.96/5.20 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_atMost_nat N2))))))
% 4.96/5.20 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_atMost_nat N2))))))
% 4.96/5.20 (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 ((J2 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ A I3) J2))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J2)) N2)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 4.96/5.20 (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 ((J2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ A I3) J2))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J2)) N2)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 4.96/5.20 (assert (forall ((A (-> tptp.nat tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (@ A I3)) (@ tptp.set_ord_lessThan_nat I3)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.groups705719431365010083at_int (lambda ((J2 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ (@ A I3) J2))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J2)) N2)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 4.96/5.20 (assert (forall ((A (-> tptp.nat tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (@ A I3)) (@ tptp.set_ord_lessThan_nat I3)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ (@ A I3) J2))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J2)) N2)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 4.96/5.20 (assert (forall ((R2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat R2) K2)) K2))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.binomial (@ tptp.suc (@ (@ tptp.plus_plus_nat R2) N2))) N2))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat N2) J2)) N2))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat N2) M2)) tptp.one_one_nat)) M2))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat N2) J2)) N2))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat (@ _let_1 M2)) tptp.one_one_nat)) (@ _let_1 tptp.one_one_nat))))))
% 4.96/5.20 (assert (forall ((X tptp.real)) (= (= (@ tptp.archim2898591450579166408c_real X) X) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_real X) tptp.one_one_real)))))
% 4.96/5.20 (assert (forall ((C (-> tptp.nat tptp.complex)) (N2 tptp.nat) (K tptp.nat)) (=> (forall ((W tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex W) I3)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ C K) tptp.zero_zero_complex)))))
% 4.96/5.20 (assert (forall ((C (-> tptp.nat tptp.real)) (N2 tptp.nat) (K tptp.nat)) (=> (forall ((W tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real W) I3)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ C K) tptp.zero_zero_real)))))
% 4.96/5.20 (assert (forall ((C (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (= (forall ((X4 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex X4) 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))))))
% 4.96/5.20 (assert (forall ((C (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (forall ((X4 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real X4) 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))))))
% 4.96/5.20 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ tptp.archim2898591450579166408c_real X)) (@ tptp.archim2898591450579166408c_real Y)))) (let ((_let_2 (@ tptp.archim2898591450579166408c_real (@ (@ tptp.plus_plus_real X) Y)))) (let ((_let_3 (@ (@ tptp.ord_less_real _let_1) tptp.one_one_real))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)))))))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (assert (forall ((G (-> tptp.nat tptp.extended_enat)) (N2 tptp.nat)) (= (@ (@ tptp.groups7108830773950497114d_enat G) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups7108830773950497114d_enat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.int)) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M2) 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 M2))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) _let_1))))))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.extended_enat)) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M2) N2))) (let ((_let_2 (@ tptp.groups7108830773950497114d_enat F))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ _let_2 (@ tptp.set_ord_atMost_nat M2))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) _let_1))))))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.nat)) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M2) 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 M2))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) _let_1))))))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.real)) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M2) 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 M2))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) _let_1))))))))
% 4.96/5.20 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real G) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 4.96/5.20 (assert (forall ((G (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (= (@ (@ tptp.groups6464643781859351333omplex G) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_complex (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 4.96/5.20 (assert (forall ((G (-> tptp.nat tptp.extended_enat)) (N2 tptp.nat)) (= (@ (@ tptp.groups7961826882256487087d_enat G) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_7803423173614009249d_enat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups7961826882256487087d_enat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 4.96/5.20 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 4.96/5.20 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex A) (@ tptp.semiri8010041392384452111omplex K2))) K2))) (@ 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))))
% 4.96/5.20 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real K2))) K2))) (@ 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))))
% 4.96/5.20 (assert (forall ((G (-> tptp.nat tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups977919841031483927at_nat (@ tptp.produc6842872674320459806at_nat G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I3 tptp.nat) (J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I3) J2)) N2))))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ G I3) (@ (@ tptp.minus_minus_nat K2) I3)))) (@ tptp.set_ord_atMost_nat K2)))) (@ tptp.set_ord_atMost_nat N2)))))
% 4.96/5.20 (assert (forall ((G (-> tptp.nat tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups4567486121110086003t_real (@ tptp.produc1703576794950452218t_real G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I3 tptp.nat) (J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I3) J2)) N2))))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ G I3) (@ (@ tptp.minus_minus_nat K2) I3)))) (@ tptp.set_ord_atMost_nat K2)))) (@ tptp.set_ord_atMost_nat N2)))))
% 4.96/5.20 (assert (forall ((G (-> tptp.nat tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups4075276357253098568at_int (@ tptp.produc6840382203811409530at_int G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I3 tptp.nat) (J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I3) J2)) N2))))) (@ (@ tptp.groups705719431365010083at_int (lambda ((K2 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ (@ G I3) (@ (@ tptp.minus_minus_nat K2) I3)))) (@ tptp.set_ord_atMost_nat K2)))) (@ tptp.set_ord_atMost_nat N2)))))
% 4.96/5.20 (assert (forall ((G (-> tptp.nat tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups4077766827762148844at_nat (@ tptp.produc6842872674320459806at_nat G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I3 tptp.nat) (J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I3) J2)) N2))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ (@ G I3) (@ (@ tptp.minus_minus_nat K2) I3)))) (@ tptp.set_ord_atMost_nat K2)))) (@ tptp.set_ord_atMost_nat N2)))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N2) K2)) (@ (@ tptp.minus_minus_nat M2) K2)))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.binomial (@ tptp.suc N2)) M2)))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (R2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.binomial M2) K2)) (@ (@ tptp.binomial N2) (@ (@ tptp.minus_minus_nat R2) K2))))) (@ tptp.set_ord_atMost_nat R2)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat M2) N2)) R2))))
% 4.96/5.20 (assert (forall ((X tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X))) (let ((_let_2 (@ tptp.minus_minus_int tptp.one_one_int))) (= (@ (@ tptp.times_times_int (@ _let_2 X)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.set_ord_atMost_nat N2))) (@ _let_2 (@ _let_1 (@ tptp.suc N2))))))))
% 4.96/5.20 (assert (forall ((X tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X))) (let ((_let_2 (@ tptp.minus_minus_complex tptp.one_one_complex))) (= (@ (@ tptp.times_times_complex (@ _let_2 X)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_atMost_nat N2))) (@ _let_2 (@ _let_1 (@ tptp.suc N2))))))))
% 4.96/5.20 (assert (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X))) (let ((_let_2 (@ tptp.minus_minus_real tptp.one_one_real))) (= (@ (@ tptp.times_times_real (@ _let_2 X)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_atMost_nat N2))) (@ _let_2 (@ _let_1 (@ tptp.suc N2))))))))
% 4.96/5.20 (assert (forall ((C (-> tptp.nat tptp.complex)) (K tptp.nat) (N2 tptp.nat)) (=> (not (= (@ C K) tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z6 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex Z6) I3)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_complex))))))))
% 4.96/5.20 (assert (forall ((C (-> tptp.nat tptp.real)) (K tptp.nat) (N2 tptp.nat)) (=> (not (= (@ C K) tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((Z6 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real Z6) I3)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_real))))))))
% 4.96/5.20 (assert (forall ((C (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (= (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex X4) I3)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_complex)))) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I3) N2) (not (= (@ C I3) tptp.zero_zero_complex)))))))
% 4.96/5.20 (assert (forall ((C (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((X4 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real X4) I3)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_real)))) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I3) N2) (not (= (@ C I3) tptp.zero_zero_real)))))))
% 4.96/5.20 (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 ((B4 (-> tptp.nat tptp.int))) (not (forall ((Z4 tptp.int)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ C I3)) (@ (@ tptp.power_power_int Z4) I3)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int Z4) A)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ B4 I3)) (@ (@ tptp.power_power_int Z4) I3)))) (@ tptp.set_ord_lessThan_nat N2)))))))))))
% 4.96/5.20 (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 ((B4 (-> tptp.nat tptp.complex))) (not (forall ((Z4 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex Z4) I3)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex Z4) A)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ B4 I3)) (@ (@ tptp.power_power_complex Z4) I3)))) (@ tptp.set_ord_lessThan_nat N2)))))))))))
% 4.96/5.20 (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 ((B4 (-> tptp.nat tptp.real))) (not (forall ((Z4 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real Z4) I3)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real Z4) A)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ B4 I3)) (@ (@ tptp.power_power_real Z4) I3)))) (@ tptp.set_ord_lessThan_nat N2)))))))))))
% 4.96/5.20 (assert (forall ((C (-> tptp.nat tptp.int)) (N2 tptp.nat) (A tptp.int)) (exists ((B4 (-> tptp.nat tptp.int))) (forall ((Z4 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 Z4) I3)))) _let_1) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int Z4) A)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ B4 I3)) (@ (@ tptp.power_power_int Z4) 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))))))))
% 4.96/5.20 (assert (forall ((C (-> tptp.nat tptp.complex)) (N2 tptp.nat) (A tptp.complex)) (exists ((B4 (-> tptp.nat tptp.complex))) (forall ((Z4 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 Z4) I3)))) _let_1) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex Z4) A)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ B4 I3)) (@ (@ tptp.power_power_complex Z4) 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))))))))
% 4.96/5.20 (assert (forall ((C (-> tptp.nat tptp.real)) (N2 tptp.nat) (A tptp.real)) (exists ((B4 (-> tptp.nat tptp.real))) (forall ((Z4 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 Z4) I3)))) _let_1) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real Z4) A)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ B4 I3)) (@ (@ tptp.power_power_real Z4) 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))))))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (X tptp.int)) (let ((_let_1 (@ tptp.power_power_int X))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M2) N2)) (@ (@ tptp.times_times_int (@ _let_1 M2)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N2) M2))))))))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (X tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X))) (let ((_let_2 (@ tptp.groups2073611262835488442omplex _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M2) N2)) (@ (@ tptp.times_times_complex (@ _let_1 M2)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N2) M2))))))))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.power_power_real X))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M2) N2)) (@ (@ tptp.times_times_real (@ _let_1 M2)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N2) M2))))))))))
% 4.96/5.20 (assert (forall ((G (-> tptp.nat tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups977919841031483927at_nat (@ tptp.produc6842872674320459806at_nat G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I3 tptp.nat) (J2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I3) J2)) N2))))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ G I3) (@ (@ tptp.minus_minus_nat K2) I3)))) (@ tptp.set_ord_atMost_nat K2)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 4.96/5.20 (assert (forall ((G (-> tptp.nat tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups4567486121110086003t_real (@ tptp.produc1703576794950452218t_real G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I3 tptp.nat) (J2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I3) J2)) N2))))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ G I3) (@ (@ tptp.minus_minus_nat K2) I3)))) (@ tptp.set_ord_atMost_nat K2)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 4.96/5.20 (assert (forall ((G (-> tptp.nat tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups4075276357253098568at_int (@ tptp.produc6840382203811409530at_int G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I3 tptp.nat) (J2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I3) J2)) N2))))) (@ (@ tptp.groups705719431365010083at_int (lambda ((K2 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ (@ G I3) (@ (@ tptp.minus_minus_nat K2) I3)))) (@ tptp.set_ord_atMost_nat K2)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 4.96/5.20 (assert (forall ((G (-> tptp.nat tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups4077766827762148844at_nat (@ tptp.produc6842872674320459806at_nat G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I3 tptp.nat) (J2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I3) J2)) N2))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ (@ G I3) (@ (@ tptp.minus_minus_nat K2) I3)))) (@ tptp.set_ord_atMost_nat K2)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 4.96/5.20 (assert (forall ((A tptp.nat) (B2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat A) B2)) N2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.binomial N2) K2))) (@ (@ tptp.power_power_nat A) K2))) (@ (@ tptp.power_power_nat B2) (@ (@ tptp.minus_minus_nat N2) K2))))) (@ tptp.set_ord_atMost_nat N2)))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (assert (forall ((G (-> tptp.nat tptp.extended_enat)) (N2 tptp.nat)) (= (@ (@ tptp.groups7108830773950497114d_enat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ (@ tptp.groups7108830773950497114d_enat (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.plus_p3455044024723400733d_enat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N2)))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (A (-> tptp.nat tptp.int)) (N2 tptp.nat) (B2 (-> tptp.nat tptp.int)) (X tptp.int)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) I4) (= (@ A I4) tptp.zero_zero_int))) (=> (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) J3) (= (@ B2 J3) 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 X) I3)))) (@ tptp.set_ord_atMost_nat M2))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((J2 tptp.nat)) (@ (@ tptp.times_times_int (@ B2 J2)) (@ (@ tptp.power_power_int X) J2)))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((R4 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_int (@ A K2)) (@ B2 (@ (@ tptp.minus_minus_nat R4) K2))))) (@ tptp.set_ord_atMost_nat R4))) (@ (@ tptp.power_power_int X) R4)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M2) N2))))))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (A (-> tptp.nat tptp.complex)) (N2 tptp.nat) (B2 (-> tptp.nat tptp.complex)) (X tptp.complex)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) I4) (= (@ A I4) tptp.zero_zero_complex))) (=> (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) J3) (= (@ B2 J3) tptp.zero_zero_complex))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I3)) (@ (@ tptp.power_power_complex X) I3)))) (@ tptp.set_ord_atMost_nat M2))) (@ (@ tptp.groups2073611262835488442omplex (lambda ((J2 tptp.nat)) (@ (@ tptp.times_times_complex (@ B2 J2)) (@ (@ tptp.power_power_complex X) J2)))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.groups2073611262835488442omplex (lambda ((R4 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_complex (@ A K2)) (@ B2 (@ (@ tptp.minus_minus_nat R4) K2))))) (@ tptp.set_ord_atMost_nat R4))) (@ (@ tptp.power_power_complex X) R4)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M2) N2))))))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (A (-> tptp.nat tptp.real)) (N2 tptp.nat) (B2 (-> tptp.nat tptp.real)) (X tptp.real)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) I4) (= (@ A I4) tptp.zero_zero_real))) (=> (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) J3) (= (@ B2 J3) 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 X) I3)))) (@ tptp.set_ord_atMost_nat M2))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J2 tptp.nat)) (@ (@ tptp.times_times_real (@ B2 J2)) (@ (@ tptp.power_power_real X) J2)))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((R4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_real (@ A K2)) (@ B2 (@ (@ tptp.minus_minus_nat R4) K2))))) (@ tptp.set_ord_atMost_nat R4))) (@ (@ tptp.power_power_real X) R4)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M2) N2))))))))
% 4.96/5.20 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ (@ tptp.groups129246275422532515t_real (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.times_times_real (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N2)))))
% 4.96/5.20 (assert (forall ((G (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (= (@ (@ tptp.groups6464643781859351333omplex G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ (@ tptp.groups6464643781859351333omplex (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.times_times_complex (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N2)))))
% 4.96/5.20 (assert (forall ((G (-> tptp.nat tptp.extended_enat)) (N2 tptp.nat)) (= (@ (@ tptp.groups7961826882256487087d_enat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ (@ tptp.groups7961826882256487087d_enat (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.times_7803423173614009249d_enat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N2)))))
% 4.96/5.20 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.times_times_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N2)))))
% 4.96/5.20 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.times_times_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N2)))))
% 4.96/5.20 (assert (forall ((C (-> tptp.nat tptp.complex)) (N2 tptp.nat) (K tptp.complex)) (= (forall ((X4 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex X4) I3)))) (@ tptp.set_ord_atMost_nat N2)) K)) (and (= (@ C tptp.zero_zero_nat) K) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2)) (= (@ C X4) tptp.zero_zero_complex)))))))
% 4.96/5.20 (assert (forall ((C (-> tptp.nat tptp.real)) (N2 tptp.nat) (K tptp.real)) (= (forall ((X4 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real X4) I3)))) (@ tptp.set_ord_atMost_nat N2)) K)) (and (= (@ C tptp.zero_zero_nat) K) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2)) (= (@ C X4) tptp.zero_zero_real)))))))
% 4.96/5.20 (assert (forall ((A tptp.complex) (B2 tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex A) B2)) N2) (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N2) K2))) (@ (@ tptp.power_power_complex A) K2))) (@ (@ tptp.power_power_complex B2) (@ (@ tptp.minus_minus_nat N2) K2))))) (@ tptp.set_ord_atMost_nat N2)))))
% 4.96/5.20 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (N2 tptp.nat)) (= (@ (@ tptp.power_8040749407984259932d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) B2)) N2) (@ (@ tptp.groups7108830773950497114d_enat (lambda ((K2 tptp.nat)) (@ (@ tptp.times_7803423173614009249d_enat (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.semiri4216267220026989637d_enat (@ (@ tptp.binomial N2) K2))) (@ (@ tptp.power_8040749407984259932d_enat A) K2))) (@ (@ tptp.power_8040749407984259932d_enat B2) (@ (@ tptp.minus_minus_nat N2) K2))))) (@ tptp.set_ord_atMost_nat N2)))))
% 4.96/5.20 (assert (forall ((A tptp.int) (B2 tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int A) B2)) N2) (@ (@ tptp.groups3539618377306564664at_int (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N2) K2))) (@ (@ tptp.power_power_int A) K2))) (@ (@ tptp.power_power_int B2) (@ (@ tptp.minus_minus_nat N2) K2))))) (@ tptp.set_ord_atMost_nat N2)))))
% 4.96/5.20 (assert (forall ((A tptp.nat) (B2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat A) B2)) N2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.binomial N2) K2))) (@ (@ tptp.power_power_nat A) K2))) (@ (@ tptp.power_power_nat B2) (@ (@ tptp.minus_minus_nat N2) K2))))) (@ tptp.set_ord_atMost_nat N2)))))
% 4.96/5.20 (assert (forall ((A tptp.real) (B2 tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real A) B2)) N2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N2) K2))) (@ (@ tptp.power_power_real A) K2))) (@ (@ tptp.power_power_real B2) (@ (@ tptp.minus_minus_nat N2) K2))))) (@ tptp.set_ord_atMost_nat N2)))))
% 4.96/5.20 (assert (forall ((A tptp.complex) (B2 tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex A) B2)) N2) (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N2) K2))) (@ (@ tptp.comm_s2602460028002588243omplex A) K2))) (@ (@ tptp.comm_s2602460028002588243omplex B2) (@ (@ tptp.minus_minus_nat N2) K2))))) (@ tptp.set_ord_atMost_nat N2)))))
% 4.96/5.20 (assert (forall ((A tptp.int) (B2 tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int A) B2)) N2) (@ (@ tptp.groups3539618377306564664at_int (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N2) K2))) (@ (@ tptp.comm_s4660882817536571857er_int A) K2))) (@ (@ tptp.comm_s4660882817536571857er_int B2) (@ (@ tptp.minus_minus_nat N2) K2))))) (@ tptp.set_ord_atMost_nat N2)))))
% 4.96/5.20 (assert (forall ((A tptp.real) (B2 tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real A) B2)) N2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N2) K2))) (@ (@ tptp.comm_s7457072308508201937r_real A) K2))) (@ (@ tptp.comm_s7457072308508201937r_real B2) (@ (@ tptp.minus_minus_nat N2) K2))))) (@ tptp.set_ord_atMost_nat N2)))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (A (-> tptp.nat tptp.nat)) (N2 tptp.nat) (B2 (-> tptp.nat tptp.nat)) (X tptp.nat)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) I4) (= (@ A I4) tptp.zero_zero_nat))) (=> (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) J3) (= (@ B2 J3) 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 X) I3)))) (@ tptp.set_ord_atMost_nat M2))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.times_times_nat (@ B2 J2)) (@ (@ tptp.power_power_nat X) J2)))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((R4 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_nat (@ A K2)) (@ B2 (@ (@ tptp.minus_minus_nat R4) K2))))) (@ tptp.set_ord_atMost_nat R4))) (@ (@ tptp.power_power_nat X) R4)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M2) N2))))))))
% 4.96/5.20 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.archim6058952711729229775r_real Y)))) (let ((_let_2 (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X) Y)))) (let ((_let_3 (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.archim2898591450579166408c_real X)) (@ tptp.archim2898591450579166408c_real Y))) tptp.one_one_real))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))))))
% 4.96/5.20 (assert (forall ((P5 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.int)) (H2 (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P5) (=> (@ (@ tptp.ord_less_eq_nat K) P5) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((J2 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_nat J2) K)) (@ G J2)) (@ (@ (@ tptp.if_int (= J2 K)) tptp.zero_zero_int) (@ H2 (@ (@ tptp.minus_minus_nat J2) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P5)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((J2 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_nat J2) K)) (@ G J2)) (@ H2 J2)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P5) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 4.96/5.20 (assert (forall ((P5 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.complex)) (H2 (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P5) (=> (@ (@ tptp.ord_less_eq_nat K) P5) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((J2 tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_nat J2) K)) (@ G J2)) (@ (@ (@ tptp.if_complex (= J2 K)) tptp.zero_zero_complex) (@ H2 (@ (@ tptp.minus_minus_nat J2) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P5)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((J2 tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_nat J2) K)) (@ G J2)) (@ H2 J2)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P5) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 4.96/5.20 (assert (forall ((P5 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.extended_enat)) (H2 (-> tptp.nat tptp.extended_enat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P5) (=> (@ (@ tptp.ord_less_eq_nat K) P5) (= (@ (@ tptp.groups7108830773950497114d_enat (lambda ((J2 tptp.nat)) (@ (@ (@ tptp.if_Extended_enat (@ (@ tptp.ord_less_nat J2) K)) (@ G J2)) (@ (@ (@ tptp.if_Extended_enat (= J2 K)) tptp.zero_z5237406670263579293d_enat) (@ H2 (@ (@ tptp.minus_minus_nat J2) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P5)) (@ (@ tptp.groups7108830773950497114d_enat (lambda ((J2 tptp.nat)) (@ (@ (@ tptp.if_Extended_enat (@ (@ tptp.ord_less_nat J2) K)) (@ G J2)) (@ H2 J2)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P5) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 4.96/5.20 (assert (forall ((P5 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.nat)) (H2 (-> tptp.nat tptp.nat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P5) (=> (@ (@ tptp.ord_less_eq_nat K) P5) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J2 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat J2) K)) (@ G J2)) (@ (@ (@ tptp.if_nat (= J2 K)) tptp.zero_zero_nat) (@ H2 (@ (@ tptp.minus_minus_nat J2) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P5)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J2 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat J2) K)) (@ G J2)) (@ H2 J2)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P5) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 4.96/5.20 (assert (forall ((P5 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.real)) (H2 (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P5) (=> (@ (@ tptp.ord_less_eq_nat K) P5) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((J2 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_nat J2) K)) (@ G J2)) (@ (@ (@ tptp.if_real (= J2 K)) tptp.zero_zero_real) (@ H2 (@ (@ tptp.minus_minus_nat J2) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P5)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J2 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_nat J2) K)) (@ G J2)) (@ H2 J2)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P5) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 4.96/5.20 (assert (forall ((P5 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.complex)) (H2 (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P5) (=> (@ (@ tptp.ord_less_eq_nat K) P5) (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((J2 tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_nat J2) K)) (@ G J2)) (@ (@ (@ tptp.if_complex (= J2 K)) tptp.one_one_complex) (@ H2 (@ (@ tptp.minus_minus_nat J2) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P5)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((J2 tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_nat J2) K)) (@ G J2)) (@ H2 J2)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P5) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 4.96/5.20 (assert (forall ((P5 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.real)) (H2 (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P5) (=> (@ (@ tptp.ord_less_eq_nat K) P5) (= (@ (@ tptp.groups129246275422532515t_real (lambda ((J2 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_nat J2) K)) (@ G J2)) (@ (@ (@ tptp.if_real (= J2 K)) tptp.one_one_real) (@ H2 (@ (@ tptp.minus_minus_nat J2) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P5)) (@ (@ tptp.groups129246275422532515t_real (lambda ((J2 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_nat J2) K)) (@ G J2)) (@ H2 J2)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P5) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 4.96/5.20 (assert (forall ((P5 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.int)) (H2 (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P5) (=> (@ (@ tptp.ord_less_eq_nat K) P5) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((J2 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_nat J2) K)) (@ G J2)) (@ (@ (@ tptp.if_int (= J2 K)) tptp.one_one_int) (@ H2 (@ (@ tptp.minus_minus_nat J2) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P5)) (@ (@ tptp.groups705719431365010083at_int (lambda ((J2 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_nat J2) K)) (@ G J2)) (@ H2 J2)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P5) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 4.96/5.20 (assert (forall ((P5 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.nat)) (H2 (-> tptp.nat tptp.nat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P5) (=> (@ (@ tptp.ord_less_eq_nat K) P5) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((J2 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat J2) K)) (@ G J2)) (@ (@ (@ tptp.if_nat (= J2 K)) tptp.one_one_nat) (@ H2 (@ (@ tptp.minus_minus_nat J2) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P5)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((J2 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat J2) K)) (@ G J2)) (@ H2 J2)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P5) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (A tptp.complex) (X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat M2))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex M2)) A)) K2)) (@ (@ tptp.power_power_complex X) K2))) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat M2) K2))))) _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex (@ tptp.uminus1482373934393186551omplex A)) K2)) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X)) K2))) (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex X) Y)) (@ (@ tptp.minus_minus_nat M2) K2))))) _let_1)))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat M2))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M2)) A)) K2)) (@ (@ tptp.power_power_real X) K2))) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat M2) K2))))) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real (@ tptp.uminus_uminus_real A)) K2)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X)) K2))) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.minus_minus_nat M2) K2))))) _let_1)))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (Z3 tptp.complex) (A tptp.complex)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (= (@ (@ tptp.power_power_complex Z3) 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 Z3) I3)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_complex)))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (Z3 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (= (@ (@ tptp.power_power_int Z3) 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 Z3) I3)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_int)))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (Z3 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (= (@ (@ tptp.power_power_real Z3) 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 Z3) I3)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_real)))))
% 4.96/5.20 (assert (forall ((X tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_2 (@ tptp.power_power_complex X))) (let ((_let_3 (@ (@ tptp.groups2073611262835488442omplex _let_2) (@ tptp.set_ord_atMost_nat N2)))) (let ((_let_4 (= X tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat)))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 (@ _let_2 (@ tptp.suc N2)))) (@ _let_1 X)))))))))))
% 4.96/5.20 (assert (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (let ((_let_2 (@ tptp.power_power_real X))) (let ((_let_3 (@ (@ tptp.groups6591440286371151544t_real _let_2) (@ tptp.set_ord_atMost_nat N2)))) (let ((_let_4 (= X tptp.one_one_real))) (and (=> _let_4 (= _let_3 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat)))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_real (@ _let_1 (@ _let_2 (@ tptp.suc N2)))) (@ _let_1 X)))))))))))
% 4.96/5.20 (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))))
% 4.96/5.20 (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))))
% 4.96/5.20 (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))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.gbinomial_complex (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.plus_plus_nat M2) K2))) K2)) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) K2)))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) M2))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat M2) K2))) K2)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) K2)))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) M2))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (A tptp.complex) (X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat M2))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex M2)) A)) K2)) (@ (@ tptp.power_power_complex X) K2))) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat M2) K2))))) _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex K2)) A)) tptp.one_one_complex)) K2)) (@ (@ tptp.power_power_complex X) K2))) (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex X) Y)) (@ (@ tptp.minus_minus_nat M2) K2))))) _let_1)))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat M2))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M2)) A)) K2)) (@ (@ tptp.power_power_real X) K2))) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat M2) K2))))) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real K2)) A)) tptp.one_one_real)) K2)) (@ (@ tptp.power_power_real X) K2))) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.minus_minus_nat M2) K2))))) _let_1)))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (A (-> tptp.nat tptp.int)) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ A I3)) (@ (@ tptp.power_power_int X) 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 X) Y)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((J2 tptp.nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ A (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat J2) K2)) tptp.one_one_nat))) (@ (@ tptp.power_power_int Y) K2))) (@ (@ tptp.power_power_int X) J2)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N2) J2))))) (@ tptp.set_ord_lessThan_nat N2))))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (A (-> tptp.nat tptp.complex)) (X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I3)) (@ (@ tptp.power_power_complex X) 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 X) Y)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((J2 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ A (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat J2) K2)) tptp.one_one_nat))) (@ (@ tptp.power_power_complex Y) K2))) (@ (@ tptp.power_power_complex X) J2)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N2) J2))))) (@ tptp.set_ord_lessThan_nat N2))))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (A (-> tptp.nat tptp.real)) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ A I3)) (@ (@ tptp.power_power_real X) 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 X) Y)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ A (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat J2) K2)) tptp.one_one_nat))) (@ (@ tptp.power_power_real Y) K2))) (@ (@ tptp.power_power_real X) J2)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N2) J2))))) (@ tptp.set_ord_lessThan_nat N2))))))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_nat _let_1) M2))) (= (@ (@ tptp.groups3542108847815614940at_nat (@ tptp.binomial (@ (@ tptp.plus_plus_nat _let_2) tptp.one_one_nat))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.power_power_nat _let_1) _let_2))))))
% 4.96/5.20 (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))))
% 4.96/5.20 (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))))
% 4.96/5.20 (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))))
% 4.96/5.20 (assert (forall ((E2 tptp.real) (C (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (exists ((M8 tptp.real)) (forall ((Z4 tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex Z4))) (=> (@ (@ tptp.ord_less_eq_real M8) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex Z4) I3)))) (@ tptp.set_ord_atMost_nat N2)))) (@ (@ tptp.times_times_real E2) (@ (@ tptp.power_power_real _let_1) (@ tptp.suc N2)))))))))))
% 4.96/5.20 (assert (forall ((E2 tptp.real) (C (-> tptp.nat tptp.real)) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (exists ((M8 tptp.real)) (forall ((Z4 tptp.real)) (let ((_let_1 (@ tptp.real_V7735802525324610683m_real Z4))) (=> (@ (@ tptp.ord_less_eq_real M8) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real Z4) I3)))) (@ tptp.set_ord_atMost_nat N2)))) (@ (@ tptp.times_times_real E2) (@ (@ tptp.power_power_real _let_1) (@ tptp.suc N2)))))))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (A (-> tptp.nat tptp.int)) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ A I3)) (@ (@ tptp.power_power_int X) 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 X) Y)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((J2 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) J2)) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J2)) N2))) (@ (@ tptp.power_power_int X) J2)))) (@ tptp.set_ord_lessThan_nat N2))))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (A (-> tptp.nat tptp.complex)) (X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I3)) (@ (@ tptp.power_power_complex X) 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 X) Y)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((J2 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) J2)) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J2)) N2))) (@ (@ tptp.power_power_complex X) J2)))) (@ tptp.set_ord_lessThan_nat N2))))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (A (-> tptp.nat tptp.real)) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ A I3)) (@ (@ tptp.power_power_real X) 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 X) Y)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J2 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) J2)) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J2)) N2))) (@ (@ tptp.power_power_real X) J2)))) (@ tptp.set_ord_lessThan_nat N2))))))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (assert (forall ((M2 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)) M2))))) (@ tptp.numeral_numeral_real _let_1))) tptp.zero_zero_real))))
% 4.96/5.20 (assert (= tptp.gbinomial_complex (lambda ((A3 tptp.complex) (K2 tptp.nat)) (@ (@ (@ tptp.if_complex (= K2 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.divide1717551699836669952omplex (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((L2 tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex A3) (@ tptp.semiri8010041392384452111omplex L2))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat)) tptp.one_one_complex)) (@ tptp.semiri5044797733671781792omplex K2))))))
% 4.96/5.20 (assert (= tptp.gbinomial_real (lambda ((A3 tptp.real) (K2 tptp.nat)) (@ (@ (@ tptp.if_real (= K2 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.divide_divide_real (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((L2 tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A3) (@ tptp.semiri5074537144036343181t_real L2))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat)) tptp.one_one_real)) (@ tptp.semiri2265585572941072030t_real K2))))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (=> (@ tptp.summable_real F) (=> (forall ((D5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))) D5))) (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))))))
% 4.96/5.20 (assert (= tptp.binomial (lambda ((N tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N) K2))) (let ((_let_2 (@ tptp.ord_less_nat N))) (@ (@ (@ tptp.if_nat (@ _let_2 K2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ _let_2 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K2))) (@ (@ tptp.binomial 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 K2)))))))))
% 4.96/5.20 (assert (forall ((L tptp.int) (K tptp.int) (N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat M2) 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 M2)))) (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) M2)))))) _let_1)))))))))))))))))
% 4.96/5.20 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.sgn_sgn_int A))) (= (@ tptp.sgn_sgn_int _let_1) _let_1))))
% 4.96/5.20 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.sgn_sgn_real A))) (= (@ tptp.sgn_sgn_real _let_1) _let_1))))
% 4.96/5.20 (assert (= tptp.semiri1316708129612266289at_nat (lambda ((N tptp.nat)) N)))
% 4.96/5.20 (assert (= (@ tptp.sin_real tptp.zero_zero_real) tptp.zero_zero_real))
% 4.96/5.20 (assert (= (@ tptp.sin_complex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 4.96/5.20 (assert (= (@ tptp.sgn_sgn_real tptp.zero_zero_real) tptp.zero_zero_real))
% 4.96/5.20 (assert (= (@ tptp.sgn_sgn_int tptp.zero_zero_int) tptp.zero_zero_int))
% 4.96/5.20 (assert (= (@ tptp.sgn_sgn_complex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 4.96/5.20 (assert (= (@ tptp.sgn_sgn_real tptp.zero_zero_real) tptp.zero_zero_real))
% 4.96/5.20 (assert (= (@ tptp.sgn_sgn_complex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 4.96/5.20 (assert (= (@ tptp.sgn_sgn_complex tptp.one_one_complex) tptp.one_one_complex))
% 4.96/5.20 (assert (= (@ tptp.sgn_sgn_int tptp.one_one_int) tptp.one_one_int))
% 4.96/5.20 (assert (= (@ tptp.sgn_sgn_real tptp.one_one_real) tptp.one_one_real))
% 4.96/5.20 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ tptp.sgn_sgn_real (@ (@ tptp.divide_divide_real A) B2)) (@ (@ tptp.divide_divide_real (@ tptp.sgn_sgn_real A)) (@ tptp.sgn_sgn_real B2)))))
% 4.96/5.20 (assert (forall ((A tptp.int)) (= (@ tptp.sgn_sgn_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int (@ tptp.sgn_sgn_int A)))))
% 4.96/5.20 (assert (forall ((A tptp.real)) (= (@ tptp.sgn_sgn_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real (@ tptp.sgn_sgn_real A)))))
% 4.96/5.20 (assert (@ tptp.summable_nat (lambda ((N tptp.nat)) tptp.zero_zero_nat)))
% 4.96/5.20 (assert (@ tptp.summable_real (lambda ((N tptp.nat)) tptp.zero_zero_real)))
% 4.96/5.20 (assert (@ tptp.summable_int (lambda ((N tptp.nat)) tptp.zero_zero_int)))
% 4.96/5.20 (assert (@ tptp.summable_complex (lambda ((N tptp.nat)) tptp.zero_zero_complex)))
% 4.96/5.20 (assert (forall ((I tptp.nat) (F (-> tptp.nat tptp.nat))) (@ tptp.summable_nat (lambda ((R4 tptp.nat)) (@ (@ (@ tptp.if_nat (= R4 I)) (@ F R4)) tptp.zero_zero_nat)))))
% 4.96/5.20 (assert (forall ((I tptp.nat) (F (-> tptp.nat tptp.real))) (@ tptp.summable_real (lambda ((R4 tptp.nat)) (@ (@ (@ tptp.if_real (= R4 I)) (@ F R4)) tptp.zero_zero_real)))))
% 4.96/5.20 (assert (forall ((I tptp.nat) (F (-> tptp.nat tptp.int))) (@ tptp.summable_int (lambda ((R4 tptp.nat)) (@ (@ (@ tptp.if_int (= R4 I)) (@ F R4)) tptp.zero_zero_int)))))
% 4.96/5.20 (assert (forall ((I tptp.nat) (F (-> tptp.nat tptp.complex))) (@ tptp.summable_complex (lambda ((R4 tptp.nat)) (@ (@ (@ tptp.if_complex (= R4 I)) (@ F R4)) tptp.zero_zero_complex)))))
% 4.96/5.20 (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))))
% 4.96/5.20 (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))))
% 4.96/5.20 (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))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (assert (= (@ tptp.cos_real tptp.zero_zero_real) tptp.one_one_real))
% 4.96/5.20 (assert (= (@ tptp.cos_complex tptp.zero_zero_complex) tptp.one_one_complex))
% 4.96/5.20 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.sgn_sgn_real B2))) (= (@ (@ tptp.divide_divide_real A) _let_1) (@ (@ tptp.times_times_real A) _let_1)))))
% 4.96/5.20 (assert (= (@ tptp.semiri1406184849735516958ct_int tptp.zero_zero_nat) tptp.one_one_int))
% 4.96/5.20 (assert (= (@ tptp.semiri5044797733671781792omplex tptp.zero_zero_nat) tptp.one_one_complex))
% 4.96/5.20 (assert (= (@ tptp.semiri1408675320244567234ct_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 4.96/5.20 (assert (= (@ tptp.semiri2265585572941072030t_real tptp.zero_zero_nat) tptp.one_one_real))
% 4.96/5.20 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real))) (= (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N)))) (or (= C tptp.zero_zero_real) (@ tptp.summable_real F)))))
% 4.96/5.20 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex))) (= (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N)))) (or (= C tptp.zero_zero_complex) (@ tptp.summable_complex F)))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (@ tptp.summable_nat (lambda ((R4 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.member_nat R4) A2)) (@ F R4)) tptp.zero_zero_nat))))))
% 4.96/5.20 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat A2) (@ tptp.summable_real (lambda ((R4 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.member_nat R4) A2)) (@ F R4)) tptp.zero_zero_real))))))
% 4.96/5.20 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat A2) (@ tptp.summable_int (lambda ((R4 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.member_nat R4) A2)) (@ F R4)) tptp.zero_zero_int))))))
% 4.96/5.20 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat A2) (@ tptp.summable_complex (lambda ((R4 tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.member_nat R4) A2)) (@ F R4)) tptp.zero_zero_complex))))))
% 4.96/5.20 (assert (forall ((P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat P)) (@ tptp.summable_nat (lambda ((R4 tptp.nat)) (@ (@ (@ tptp.if_nat (@ P R4)) (@ F R4)) tptp.zero_zero_nat))))))
% 4.96/5.20 (assert (forall ((P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat P)) (@ tptp.summable_real (lambda ((R4 tptp.nat)) (@ (@ (@ tptp.if_real (@ P R4)) (@ F R4)) tptp.zero_zero_real))))))
% 4.96/5.20 (assert (forall ((P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat P)) (@ tptp.summable_int (lambda ((R4 tptp.nat)) (@ (@ (@ tptp.if_int (@ P R4)) (@ F R4)) tptp.zero_zero_int))))))
% 4.96/5.20 (assert (forall ((P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat P)) (@ tptp.summable_complex (lambda ((R4 tptp.nat)) (@ (@ (@ tptp.if_complex (@ P R4)) (@ F R4)) tptp.zero_zero_complex))))))
% 4.96/5.20 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ tptp.sgn_sgn_real A) tptp.one_one_real))))
% 4.96/5.20 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (= (@ tptp.sgn_sgn_int A) tptp.one_one_int))))
% 4.96/5.20 (assert (= (@ tptp.semiri1406184849735516958ct_int (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_int))
% 4.96/5.20 (assert (= (@ tptp.semiri5044797733671781792omplex (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_complex))
% 4.96/5.20 (assert (= (@ tptp.semiri1408675320244567234ct_nat (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat))
% 4.96/5.20 (assert (= (@ tptp.semiri2265585572941072030t_real (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_real))
% 4.96/5.20 (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))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.semiri4449623510593786356d_enat _let_1) (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.semiri4216267220026989637d_enat _let_1)) (@ tptp.semiri4449623510593786356d_enat N2))))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (assert (= (@ tptp.sin_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) tptp.zero_zero_real))
% 4.96/5.20 (assert (= (@ tptp.sin_complex (@ tptp.real_V4546457046886955230omplex tptp.pi)) tptp.zero_zero_complex))
% 4.96/5.20 (assert (forall ((L tptp.int) (K tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int L))) (= (@ _let_1 (@ (@ tptp.times_times_int K) (@ tptp.sgn_sgn_int R2))) (or (@ _let_1 K) (= R2 tptp.zero_zero_int))))))
% 4.96/5.20 (assert (forall ((L tptp.int) (R2 tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int L))) (= (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int R2)) K)) (or (@ _let_1 K) (= R2 tptp.zero_zero_int))))))
% 4.96/5.20 (assert (forall ((L tptp.int) (R2 tptp.int) (K tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int L) (@ tptp.sgn_sgn_int R2))) K) (and (@ (@ tptp.dvd_dvd_int L) K) (=> (= R2 tptp.zero_zero_int) (= K tptp.zero_zero_int))))))
% 4.96/5.20 (assert (forall ((R2 tptp.int) (L tptp.int) (K tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int R2)) L)) K) (and (@ (@ tptp.dvd_dvd_int L) K) (=> (= R2 tptp.zero_zero_int) (= K tptp.zero_zero_int))))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.sin_real X))) (let ((_let_2 (@ tptp.cos_real X))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real _let_2) _let_2)) (@ (@ tptp.times_times_real _let_1) _let_1)) tptp.one_one_real)))))
% 4.96/5.20 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.sin_complex X))) (let ((_let_2 (@ tptp.cos_complex X))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex _let_2) _let_2)) (@ (@ tptp.times_times_complex _let_1) _let_1)) tptp.one_one_complex)))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.cos_real X)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.sin_real X)) _let_1)) tptp.one_one_real))))
% 4.96/5.20 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.cos_complex X)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.sin_complex X)) _let_1)) tptp.one_one_complex))))
% 4.96/5.20 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.sin_real X)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.cos_real X)) _let_1)) tptp.one_one_real))))
% 4.96/5.20 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.sin_complex X)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.cos_complex X)) _let_1)) tptp.one_one_complex))))
% 4.96/5.20 (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))
% 4.96/5.20 (assert (= (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) tptp.zero_zero_complex))
% 4.96/5.20 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.sin_real Y))))))
% 4.96/5.20 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.sin_complex (@ (@ tptp.plus_plus_complex X) Y)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.sin_complex X)) (@ tptp.cos_complex Y))) (@ (@ tptp.times_times_complex (@ tptp.cos_complex X)) (@ tptp.sin_complex Y))))))
% 4.96/5.20 (assert (forall ((X tptp.real)) (=> (= (@ tptp.cos_real X) tptp.one_one_real) (= (@ tptp.sin_real X) tptp.zero_zero_real))))
% 4.96/5.20 (assert (forall ((X tptp.complex)) (=> (= (@ tptp.cos_complex X) tptp.one_one_complex) (= (@ tptp.sin_complex X) tptp.zero_zero_complex))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.semiri1408675320244567234ct_nat N2))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat M2)) (@ tptp.semiri1408675320244567234ct_nat N2)))))
% 4.96/5.20 (assert (forall ((A tptp.real)) (= (= (@ tptp.sgn_sgn_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 4.96/5.20 (assert (forall ((A tptp.int)) (= (= (@ tptp.sgn_sgn_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 4.96/5.20 (assert (forall ((A tptp.complex)) (= (= (@ tptp.sgn_sgn_complex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 4.96/5.20 (assert (forall ((A tptp.real)) (= (= (@ tptp.sgn_sgn_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 4.96/5.20 (assert (forall ((A tptp.int)) (= (= (@ tptp.sgn_sgn_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 4.96/5.20 (assert (forall ((X tptp.real)) (= (= (@ tptp.sgn_sgn_real X) tptp.zero_zero_real) (= X tptp.zero_zero_real))))
% 4.96/5.20 (assert (forall ((X tptp.complex)) (= (= (@ tptp.sgn_sgn_complex X) tptp.zero_zero_complex) (= X tptp.zero_zero_complex))))
% 4.96/5.20 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ tptp.sgn_sgn_int (@ (@ tptp.times_times_int A) B2)) (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int A)) (@ tptp.sgn_sgn_int B2)))))
% 4.96/5.20 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ tptp.sgn_sgn_real (@ (@ tptp.times_times_real A) B2)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real A)) (@ tptp.sgn_sgn_real B2)))))
% 4.96/5.20 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (@ tptp.sgn_sgn_complex (@ (@ tptp.times_times_complex A) B2)) (@ (@ tptp.times_times_complex (@ tptp.sgn_sgn_complex A)) (@ tptp.sgn_sgn_complex B2)))))
% 4.96/5.20 (assert (forall ((B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.sgn_sgn_int A))) (=> (= (@ tptp.sgn_sgn_int B2) _let_1) (= (@ tptp.sgn_sgn_int (@ (@ tptp.plus_plus_int A) B2)) _let_1)))))
% 4.96/5.20 (assert (forall ((B2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.sgn_sgn_real A))) (=> (= (@ tptp.sgn_sgn_real B2) _let_1) (= (@ tptp.sgn_sgn_real (@ (@ tptp.plus_plus_real A) B2)) _let_1)))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri1406184849735516958ct_int N2) tptp.zero_zero_int))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri5044797733671781792omplex N2) tptp.zero_zero_complex))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri4449623510593786356d_enat N2) tptp.zero_z5237406670263579293d_enat))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri1408675320244567234ct_nat N2) tptp.zero_zero_nat))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri2265585572941072030t_real N2) tptp.zero_zero_real))))
% 4.96/5.20 (assert (forall ((C tptp.real)) (= (@ tptp.summable_real (lambda ((Uu3 tptp.nat)) C)) (= C tptp.zero_zero_real))))
% 4.96/5.20 (assert (forall ((C tptp.complex)) (= (@ tptp.summable_complex (lambda ((Uu3 tptp.nat)) C)) (= C tptp.zero_zero_complex))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (exists ((N8 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F N3))) (@ G N3))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real F)))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.real))) (=> (exists ((N8 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N3))) (@ G N3))))) (=> (@ tptp.summable_real G) (@ tptp.summable_complex F)))))
% 4.96/5.20 (assert (forall ((G (-> tptp.nat tptp.real)) (N6 tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real G) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N6) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F N3))) (@ G N3)))) (@ tptp.summable_real F)))))
% 4.96/5.20 (assert (forall ((G (-> tptp.nat tptp.real)) (N6 tptp.nat) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_real G) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N6) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N3))) (@ G N3)))) (@ tptp.summable_complex F)))))
% 4.96/5.20 (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))))))))
% 4.96/5.20 (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))))))))
% 4.96/5.20 (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))))))))
% 4.96/5.20 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real X) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.sin_real Y))))))
% 4.96/5.20 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.cos_complex (@ (@ tptp.minus_minus_complex X) Y)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.cos_complex X)) (@ tptp.cos_complex Y))) (@ (@ tptp.times_times_complex (@ tptp.sin_complex X)) (@ tptp.sin_complex Y))))))
% 4.96/5.20 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.sin_real Y))))))
% 4.96/5.20 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex X) Y)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex (@ tptp.cos_complex X)) (@ tptp.cos_complex Y))) (@ (@ tptp.times_times_complex (@ tptp.sin_complex X)) (@ tptp.sin_complex Y))))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.real))) (= (@ tptp.summable_real (lambda ((N tptp.nat)) (@ F (@ tptp.suc N)))) (@ tptp.summable_real F))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (assert (forall ((X tptp.real)) (=> (= (@ tptp.sin_real X) tptp.zero_zero_real) (= (@ tptp.real_V7735802525324610683m_real (@ tptp.cos_real X)) tptp.one_one_real))))
% 4.96/5.20 (assert (forall ((X tptp.complex)) (=> (= (@ tptp.sin_complex X) tptp.zero_zero_complex) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.cos_complex X)) tptp.one_one_real))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (assert (forall ((N6 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat N6) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N6)) (= (@ F N3) tptp.zero_zero_nat))) (@ tptp.summable_nat F)))))
% 4.96/5.20 (assert (forall ((N6 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat N6) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N6)) (= (@ F N3) tptp.zero_zero_real))) (@ tptp.summable_real F)))))
% 4.96/5.20 (assert (forall ((N6 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat N6) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N6)) (= (@ F N3) tptp.zero_zero_int))) (@ tptp.summable_int F)))))
% 4.96/5.20 (assert (forall ((N6 tptp.set_nat) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat N6) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N6)) (= (@ F N3) tptp.zero_zero_complex))) (@ tptp.summable_complex F)))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_nat M2) N2) (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat M2)) (@ tptp.semiri1408675320244567234ct_nat N2))))))
% 4.96/5.20 (assert (forall ((B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.sgn_sgn_int B2))) (let ((_let_2 (@ tptp.sgn_sgn_int A))) (=> (not (= _let_1 _let_2)) (=> (not (= _let_2 tptp.zero_zero_int)) (=> (not (= _let_1 tptp.zero_zero_int)) (= _let_2 (@ tptp.uminus_uminus_int _let_1)))))))))
% 4.96/5.20 (assert (forall ((B2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.sgn_sgn_real B2))) (let ((_let_2 (@ tptp.sgn_sgn_real A))) (=> (not (= _let_1 _let_2)) (=> (not (= _let_2 tptp.zero_zero_real)) (=> (not (= _let_1 tptp.zero_zero_real)) (= _let_2 (@ tptp.uminus_uminus_real _let_1)))))))))
% 4.96/5.20 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ tptp.sgn_sgn_complex _let_1) _let_1)))
% 4.96/5.20 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ tptp.sgn_sgn_int _let_1) _let_1)))
% 4.96/5.20 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ tptp.sgn_sgn_real _let_1) _let_1)))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1406184849735516958ct_int N2))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1408675320244567234ct_nat N2))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.semiri2265585572941072030t_real N2))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.semiri1406184849735516958ct_int N2))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.semiri1408675320244567234ct_nat N2))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.semiri2265585572941072030t_real N2))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1406184849735516958ct_int N2)) tptp.zero_zero_int))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat N2)) tptp.zero_zero_nat))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_real (@ tptp.semiri2265585572941072030t_real N2)) tptp.zero_zero_real))))
% 4.96/5.20 (assert (forall ((K tptp.int)) (not (forall ((N3 tptp.nat) (L4 tptp.int)) (not (= K (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int L4)) (@ tptp.semiri1314217659103216013at_int N3))))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.semiri1406184849735516958ct_int N2))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.semiri1408675320244567234ct_nat N2))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.semiri2265585572941072030t_real N2))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1406184849735516958ct_int M2)) (@ tptp.semiri1406184849735516958ct_int N2)))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat M2)) (@ tptp.semiri1408675320244567234ct_nat N2)))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri2265585572941072030t_real M2)) (@ tptp.semiri2265585572941072030t_real N2)))))
% 4.96/5.20 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N)))) (=> (not (= C tptp.zero_zero_real)) (@ tptp.summable_real F)))))
% 4.96/5.20 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N)))) (=> (not (= C tptp.zero_zero_complex)) (@ tptp.summable_complex F)))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (@ (@ tptp.dvd_dvd_int (@ tptp.semiri1406184849735516958ct_int N2)) (@ tptp.semiri1406184849735516958ct_int M2)))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (@ (@ tptp.dvd_dvd_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ tptp.semiri1408675320244567234ct_nat M2)))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (@ (@ tptp.dvd_dvd_real (@ tptp.semiri2265585572941072030t_real N2)) (@ tptp.semiri2265585572941072030t_real M2)))))
% 4.96/5.20 (assert (@ tptp.summable_real (@ tptp.power_power_real tptp.zero_zero_real)))
% 4.96/5.20 (assert (@ tptp.summable_complex (@ tptp.power_power_complex tptp.zero_zero_complex)))
% 4.96/5.20 (assert (@ tptp.summable_int (@ tptp.power_power_int tptp.zero_zero_int)))
% 4.96/5.20 (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)))))))))
% 4.96/5.20 (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)))))))))
% 4.96/5.20 (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)))))))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.semiri1408675320244567234ct_nat N2))))
% 4.96/5.20 (assert (forall ((A tptp.real)) (= (= (@ tptp.sgn_sgn_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) A))))
% 4.96/5.20 (assert (forall ((A tptp.int)) (= (= (@ tptp.sgn_sgn_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) M2) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.dvd_dvd_nat M2) (@ tptp.semiri1408675320244567234ct_nat N2))))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.real)) (Z3 tptp.real)) (= (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_real Z3) N)))) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z3) N)))))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z3 tptp.complex)) (= (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_complex Z3) N)))) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z3) N)))))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.real)) (Z3 tptp.real)) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z3) N)))) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_real Z3) N)))))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z3 tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z3) N)))) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_complex Z3) N)))))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.real)) (M2 tptp.nat) (Z3 tptp.real)) (= (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ (@ tptp.plus_plus_nat N) M2))) (@ (@ tptp.power_power_real Z3) N)))) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z3) N)))))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.complex)) (M2 tptp.nat) (Z3 tptp.complex)) (= (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ (@ tptp.plus_plus_nat N) M2))) (@ (@ tptp.power_power_complex Z3) N)))) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z3) N)))))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_nat M2) N2) (@ (@ tptp.ord_less_int (@ tptp.semiri1406184849735516958ct_int M2)) (@ tptp.semiri1406184849735516958ct_int N2))))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_nat M2) N2) (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat M2)) (@ tptp.semiri1408675320244567234ct_nat N2))))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_nat M2) N2) (@ (@ tptp.ord_less_real (@ tptp.semiri2265585572941072030t_real M2)) (@ tptp.semiri2265585572941072030t_real N2))))))
% 4.96/5.20 (assert (forall ((W2 tptp.complex) (Z3 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.sin_complex W2)) (@ tptp.sin_complex Z3)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.cos_complex (@ (@ tptp.minus_minus_complex W2) Z3))) (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex W2) Z3)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 4.96/5.20 (assert (forall ((W2 tptp.real) (Z3 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.sin_real W2)) (@ tptp.sin_real Z3)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.cos_real (@ (@ tptp.minus_minus_real W2) Z3))) (@ tptp.cos_real (@ (@ tptp.plus_plus_real W2) Z3)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 4.96/5.20 (assert (forall ((W2 tptp.complex) (Z3 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.sin_complex W2)) (@ tptp.cos_complex Z3)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.sin_complex (@ (@ tptp.plus_plus_complex W2) Z3))) (@ tptp.sin_complex (@ (@ tptp.minus_minus_complex W2) Z3)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 4.96/5.20 (assert (forall ((W2 tptp.real) (Z3 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.sin_real W2)) (@ tptp.cos_real Z3)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real W2) Z3))) (@ tptp.sin_real (@ (@ tptp.minus_minus_real W2) Z3)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 4.96/5.20 (assert (forall ((W2 tptp.complex) (Z3 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.cos_complex W2)) (@ tptp.sin_complex Z3)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.sin_complex (@ (@ tptp.plus_plus_complex W2) Z3))) (@ tptp.sin_complex (@ (@ tptp.minus_minus_complex W2) Z3)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 4.96/5.20 (assert (forall ((W2 tptp.real) (Z3 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.cos_real W2)) (@ tptp.sin_real Z3)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real W2) Z3))) (@ tptp.sin_real (@ (@ tptp.minus_minus_real W2) Z3)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 4.96/5.20 (assert (forall ((W2 tptp.complex) (Z3 tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ tptp.sin_complex W2)) (@ tptp.sin_complex Z3)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_1) (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex W2) Z3)) _let_1)))) (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex W2) Z3)) _let_1)))))))
% 4.96/5.20 (assert (forall ((W2 tptp.real) (Z3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ tptp.sin_real W2)) (@ tptp.sin_real Z3)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_1) (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real W2) Z3)) _let_1)))) (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real W2) Z3)) _let_1)))))))
% 4.96/5.20 (assert (forall ((W2 tptp.complex) (Z3 tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_complex (@ tptp.sin_complex W2)) (@ tptp.sin_complex Z3)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_1) (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex W2) Z3)) _let_1)))) (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex W2) Z3)) _let_1)))))))
% 4.96/5.20 (assert (forall ((W2 tptp.real) (Z3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_real (@ tptp.sin_real W2)) (@ tptp.sin_real Z3)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_1) (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real W2) Z3)) _let_1)))) (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real W2) Z3)) _let_1)))))))
% 4.96/5.20 (assert (forall ((W2 tptp.complex) (Z3 tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_complex (@ tptp.cos_complex W2)) (@ tptp.cos_complex Z3)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_1) (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex W2) Z3)) _let_1)))) (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex Z3) W2)) _let_1)))))))
% 4.96/5.20 (assert (forall ((W2 tptp.real) (Z3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_real (@ tptp.cos_real W2)) (@ tptp.cos_real Z3)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_1) (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real W2) Z3)) _let_1)))) (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real Z3) W2)) _let_1)))))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1406184849735516958ct_int N2)) (@ tptp.semiri1406184849735516958ct_int M2)) tptp.zero_zero_int))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ tptp.semiri1408675320244567234ct_nat M2)) tptp.zero_zero_nat))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1406184849735516958ct_int N2)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.power_power_nat N2) N2)))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.power_power_nat N2) N2)))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri2265585572941072030t_real N2)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.power_power_nat N2) N2)))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.real))) (=> (exists ((N8 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N3))) (@ G N3))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F N))))))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.real)) (I tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.summable_real F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N3))) (=> (@ _let_1 (@ F I)) (@ _let_1 (@ tptp.suminf_real F))))))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.nat)) (I tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N3))) (=> (@ _let_1 (@ F I)) (@ _let_1 (@ tptp.suminf_nat F))))))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.int)) (I tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ tptp.summable_int F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N3))) (=> (@ _let_1 (@ F I)) (@ _let_1 (@ tptp.suminf_int F))))))))
% 4.96/5.20 (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))))))))
% 4.96/5.20 (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))))))))
% 4.96/5.20 (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))))))))
% 4.96/5.20 (assert (forall ((X tptp.real)) (= (@ tptp.uminus_uminus_real (@ tptp.sin_real X)) (@ tptp.cos_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 4.96/5.20 (assert (forall ((X tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ tptp.sin_complex X)) (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.int)) (X 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))) X)) (@ (@ tptp.ord_less_eq_int (@ tptp.suminf_int F)) X)))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.nat)) (X 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))) X)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suminf_nat F)) X)))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.real)) (X 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))) X)) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real F)) X)))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.suc M2))) (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 M2) N2)))))))))
% 4.96/5.20 (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))))
% 4.96/5.20 (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))))
% 4.96/5.20 (assert (= tptp.sgn_sgn_int (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_int (= X4 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) X4)) tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 4.96/5.20 (assert (= tptp.sgn_sgn_real (lambda ((X4 tptp.real)) (@ (@ (@ tptp.if_real (= X4 tptp.zero_zero_real)) tptp.zero_zero_real) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4)) tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (assert (forall ((R2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat R2) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N2) R2)))) (@ (@ tptp.power_power_nat N2) R2)))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.int)) (X 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))) X)) (@ tptp.summable_int F)))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.nat)) (X 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))) X)) (@ tptp.summable_nat F)))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.real)) (X 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))) X)) (@ tptp.summable_real F)))))
% 4.96/5.20 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.real_V7735802525324610683m_real (@ tptp.sgn_sgn_real X)))) (let ((_let_2 (= X tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))))
% 4.96/5.20 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex (@ tptp.sgn_sgn_complex X)))) (let ((_let_2 (= X tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))))
% 4.96/5.20 (assert (forall ((A (-> tptp.nat tptp.int)) (B 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))) B)) (@ tptp.summable_int A)))))
% 4.96/5.20 (assert (forall ((A (-> tptp.nat tptp.nat)) (B 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))) B)) (@ tptp.summable_nat A)))))
% 4.96/5.20 (assert (forall ((A (-> tptp.nat tptp.real)) (B 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))) B)) (@ tptp.summable_real A)))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (= (@ tptp.semiri1408675320244567234ct_nat M2) (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc N2)) M2)))))))
% 4.96/5.20 (assert (forall ((X tptp.real) (M2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.plus_plus_real X))) (= (@ tptp.sin_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M2))) tptp.pi)) _let_1))) (@ tptp.cos_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M2)) tptp.pi)) _let_1))))))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.int)) (I6 tptp.set_nat)) (=> (@ tptp.summable_int F) (=> (@ tptp.finite_finite_nat I6) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.member_nat N3) (@ tptp.uminus5710092332889474511et_nat I6)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N3)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) I6)) (@ tptp.suminf_int F)))))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.nat)) (I6 tptp.set_nat)) (=> (@ tptp.summable_nat F) (=> (@ tptp.finite_finite_nat I6) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.member_nat N3) (@ tptp.uminus5710092332889474511et_nat I6)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F) I6)) (@ tptp.suminf_nat F)))))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.real)) (I6 tptp.set_nat)) (=> (@ tptp.summable_real F) (=> (@ tptp.finite_finite_nat I6) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.member_nat N3) (@ tptp.uminus5710092332889474511et_nat I6)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N3)))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real F) I6)) (@ tptp.suminf_real F)))))))
% 4.96/5.20 (assert (forall ((X tptp.real) (M2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.plus_plus_real X))) (= (@ tptp.cos_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M2))) tptp.pi)) _let_1))) (@ tptp.uminus_uminus_real (@ tptp.sin_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M2)) tptp.pi)) _let_1)))))))))
% 4.96/5.20 (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))))))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (= (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat M2)) (@ tptp.semiri1408675320244567234ct_nat N2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat)) M2))))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat)) (=> (@ tptp.summable_int F) (=> (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M3) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F M3)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat N2))) (@ tptp.suminf_int F))))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (=> (@ tptp.summable_nat F) (=> (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M3) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F M3)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat N2))) (@ tptp.suminf_nat F))))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat)) (=> (@ tptp.summable_real F) (=> (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M3) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F M3)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N2))) (@ tptp.suminf_real F))))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.real)) (Z3 tptp.real)) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z3) N)))) (= (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z3) 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 Z3) N))))) Z3))))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z3 tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z3) N)))) (= (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z3) 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 Z3) N))))) Z3))))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.real)) (Z3 tptp.real)) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z3) N)))) (= (@ (@ tptp.times_times_real (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_real Z3) N))))) Z3) (@ (@ tptp.minus_minus_real (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z3) N))))) (@ F tptp.zero_zero_nat))))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z3 tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z3) N)))) (= (@ (@ tptp.times_times_complex (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_complex Z3) N))))) Z3) (@ (@ tptp.minus_minus_complex (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z3) N))))) (@ F tptp.zero_zero_nat))))))
% 4.96/5.20 (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 ((N9 tptp.nat)) (not (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N9) M5) (forall ((N7 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex F) (@ (@ tptp.set_or1269000886237332187st_nat M5) N7)))) E2)))))))))))
% 4.96/5.20 (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 ((N9 tptp.nat)) (not (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N9) M5) (forall ((N7 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.groups6591440286371151544t_real F) (@ (@ tptp.set_or1269000886237332187st_nat M5) N7)))) E2)))))))))))
% 4.96/5.20 (assert (forall ((R2 tptp.real) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (=> (@ tptp.summable_real F) (exists ((N9 tptp.nat)) (forall ((N7 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N9) N7) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ tptp.suminf_real (lambda ((I3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I3) N7)))))) R2))))))))
% 4.96/5.20 (assert (forall ((R2 tptp.real) (F (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (=> (@ tptp.summable_complex F) (exists ((N9 tptp.nat)) (forall ((N7 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N9) N7) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ tptp.suminf_complex (lambda ((I3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I3) N7)))))) R2))))))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (assert (forall ((X tptp.real)) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)) (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1))))) (@ tptp.sin_real X))))
% 4.96/5.20 (assert (= tptp.semiri5044797733671781792omplex (lambda ((M tptp.nat)) (@ (@ (@ tptp.if_complex (= M tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex M)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)))))))
% 4.96/5.20 (assert (= tptp.semiri4449623510593786356d_enat (lambda ((M tptp.nat)) (@ (@ (@ tptp.if_Extended_enat (= M tptp.zero_zero_nat)) tptp.one_on7984719198319812577d_enat) (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.semiri4216267220026989637d_enat M)) (@ tptp.semiri4449623510593786356d_enat (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)))))))
% 4.96/5.20 (assert (= tptp.semiri1406184849735516958ct_int (lambda ((M tptp.nat)) (@ (@ (@ tptp.if_int (= M tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)))))))
% 4.96/5.20 (assert (= tptp.semiri1408675320244567234ct_nat (lambda ((M tptp.nat)) (@ (@ (@ tptp.if_nat (= M tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)))))))
% 4.96/5.20 (assert (= tptp.semiri2265585572941072030t_real (lambda ((M tptp.nat)) (@ (@ (@ tptp.if_real (= M tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)))))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.semiri4449623510593786356d_enat N2) (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.semiri4216267220026989637d_enat N2)) (@ tptp.semiri4449623510593786356d_enat (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (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))))))))
% 4.96/5.20 (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))))))))
% 4.96/5.20 (assert (forall ((W2 tptp.complex) (Z3 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.cos_complex W2)) (@ tptp.cos_complex Z3)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.cos_complex (@ (@ tptp.minus_minus_complex W2) Z3))) (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex W2) Z3)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 4.96/5.20 (assert (forall ((W2 tptp.real) (Z3 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.cos_real W2)) (@ tptp.cos_real Z3)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.cos_real (@ (@ tptp.minus_minus_real W2) Z3))) (@ tptp.cos_real (@ (@ tptp.plus_plus_real W2) Z3)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 4.96/5.20 (assert (forall ((W2 tptp.complex) (Z3 tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ tptp.cos_complex W2)) (@ tptp.cos_complex Z3)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_1) (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex W2) Z3)) _let_1)))) (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex W2) Z3)) _let_1)))))))
% 4.96/5.20 (assert (forall ((W2 tptp.real) (Z3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ tptp.cos_real W2)) (@ tptp.cos_real Z3)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_1) (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real W2) Z3)) _let_1)))) (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real W2) Z3)) _let_1)))))))
% 4.96/5.20 (assert (forall ((C tptp.real) (N6 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 N6) 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)))))
% 4.96/5.20 (assert (forall ((C tptp.real) (N6 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 N6) 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)))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat) (I tptp.nat)) (=> (@ tptp.summable_int F) (=> (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M3) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F M3)))) (=> (@ (@ tptp.ord_less_eq_nat N2) I) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F I)) (@ (@ tptp.ord_less_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat N2))) (@ tptp.suminf_int F))))))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat) (I tptp.nat)) (=> (@ tptp.summable_nat F) (=> (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M3) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F M3)))) (=> (@ (@ tptp.ord_less_eq_nat N2) I) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I)) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat N2))) (@ tptp.suminf_nat F))))))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat) (I tptp.nat)) (=> (@ tptp.summable_real F) (=> (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M3) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F M3)))) (=> (@ (@ tptp.ord_less_eq_nat N2) I) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N2))) (@ tptp.suminf_real F))))))))
% 4.96/5.20 (assert (= tptp.gbinomial_complex (lambda ((A3 tptp.complex) (K2 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex A3) (@ tptp.semiri8010041392384452111omplex K2))) tptp.one_one_complex)) K2)) (@ tptp.semiri5044797733671781792omplex K2)))))
% 4.96/5.20 (assert (= tptp.gbinomial_real (lambda ((A3 tptp.real) (K2 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A3) (@ tptp.semiri5074537144036343181t_real K2))) tptp.one_one_real)) K2)) (@ tptp.semiri2265585572941072030t_real K2)))))
% 4.96/5.20 (assert (forall ((X tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.nat tptp.real))) (=> (= X tptp.zero_zero_real) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M) tptp.zero_zero_nat)) (@ tptp.semiri2265585572941072030t_real M))) (@ (@ tptp.power_power_real X) M)))) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_nat))))))
% 4.96/5.20 (assert (forall ((X tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real))) (=> (= X tptp.zero_zero_real) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M))) (@ (@ tptp.power_power_real X) M)))) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_real))))))
% 4.96/5.20 (assert (forall ((X tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.int tptp.real))) (=> (= X tptp.zero_zero_real) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M) tptp.zero_zero_int)) (@ tptp.semiri2265585572941072030t_real M))) (@ (@ tptp.power_power_real X) M)))) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_int))))))
% 4.96/5.20 (assert (forall ((X tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.complex tptp.real))) (=> (= X tptp.zero_zero_real) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M) tptp.zero_zero_complex)) (@ tptp.semiri2265585572941072030t_real M))) (@ (@ tptp.power_power_real X) M)))) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_complex))))))
% 4.96/5.20 (assert (forall ((X tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.extended_enat tptp.real))) (=> (= X tptp.zero_zero_real) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M) tptp.zero_z5237406670263579293d_enat)) (@ tptp.semiri2265585572941072030t_real M))) (@ (@ tptp.power_power_real X) M)))) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_z5237406670263579293d_enat))))))
% 4.96/5.20 (assert (forall ((X tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_real T6) X) (= (@ tptp.cos_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M)) (@ (@ tptp.power_power_real X) M)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real T6) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N2))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2))))))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_real X) T6) (@ (@ tptp.ord_less_real T6) tptp.zero_zero_real) (= (@ tptp.cos_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M)) (@ (@ tptp.power_power_real X) M)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real T6) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N2))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2))))))))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (assert (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_real A) _let_1) (@ (@ tptp.divide_divide_real (@ (@ tptp.groups129246275422532515t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_real A) (@ tptp.semiri5074537144036343181t_real I3)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri2265585572941072030t_real _let_1))))))
% 4.96/5.20 (assert (forall ((A tptp.int) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_int A) _let_1) (@ (@ tptp.divide_divide_int (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_int A) (@ tptp.semiri1314217659103216013at_int I3)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri1406184849735516958ct_int _let_1))))))
% 4.96/5.20 (assert (forall ((A tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_nat A) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_nat A) (@ tptp.semiri1316708129612266289at_nat I3)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri1408675320244567234ct_nat _let_1))))))
% 4.96/5.20 (assert (forall ((L tptp.int) (K tptp.int) (N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.divide_divide_nat M2) 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 M2))) (@ (@ 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) M2)))))))))))))))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_real T6) X) (= (@ tptp.sin_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M)) (@ (@ tptp.power_power_real X) M)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T6) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N2))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2))))))))))
% 4.96/5.20 (assert (= tptp.listrel1p_nat (lambda ((R4 (-> tptp.nat tptp.nat Bool)) (Xs3 tptp.list_nat) (Ys3 tptp.list_nat)) (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat Xs3) Ys3)) (@ tptp.listrel1_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o R4)))))))
% 4.96/5.20 (assert (= tptp.listrel1p_int (lambda ((R4 (-> tptp.int tptp.int Bool)) (Xs3 tptp.list_int) (Ys3 tptp.list_int)) (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int Xs3) Ys3)) (@ tptp.listrel1_int (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o R4)))))))
% 4.96/5.20 (assert (forall ((X tptp.complex) (Y tptp.complex)) (@ (@ tptp.sums_complex (lambda ((P6 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 P6) (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 P6) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P6) N))))) (@ tptp.semiri2265585572941072030t_real P6)))) (@ (@ tptp.power_power_complex X) N))) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat P6) N)))) tptp.zero_zero_complex))))) (@ tptp.set_ord_atMost_nat P6)))) (@ (@ tptp.times_times_complex (@ tptp.sin_complex X)) (@ tptp.sin_complex Y)))))
% 4.96/5.20 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.sums_real (lambda ((P6 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 P6) (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 P6) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P6) N))))) (@ tptp.semiri2265585572941072030t_real P6)))) (@ (@ tptp.power_power_real X) N))) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat P6) N)))) tptp.zero_zero_real))))) (@ tptp.set_ord_atMost_nat P6)))) (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.sin_real Y)))))
% 4.96/5.20 (assert (forall ((X tptp.complex) (Y tptp.complex)) (@ (@ tptp.sums_complex (lambda ((P6 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) P6)) (@ (@ 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 P6) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P6) N))))) (@ tptp.semiri2265585572941072030t_real P6))) (@ (@ tptp.power_power_complex X) N))) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat P6) N)))) tptp.zero_zero_complex)))) (@ tptp.set_ord_atMost_nat P6)))) (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex X) Y)))))
% 4.96/5.20 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.sums_real (lambda ((P6 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) P6)) (@ (@ 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 P6) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P6) N))))) (@ tptp.semiri2265585572941072030t_real P6))) (@ (@ tptp.power_power_real X) N))) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat P6) N)))) tptp.zero_zero_real)))) (@ tptp.set_ord_atMost_nat P6)))) (@ tptp.cos_real (@ (@ tptp.plus_plus_real X) Y)))))
% 4.96/5.20 (assert (forall ((X tptp.complex) (Y tptp.complex)) (@ (@ tptp.sums_complex (lambda ((P6 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 P6) (@ _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 P6) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P6) N))))) (@ tptp.semiri2265585572941072030t_real P6))) (@ (@ tptp.power_power_complex X) N))) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat P6) N)))) tptp.zero_zero_complex))))) (@ tptp.set_ord_atMost_nat P6)))) (@ (@ tptp.times_times_complex (@ tptp.cos_complex X)) (@ tptp.cos_complex Y)))))
% 4.96/5.20 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.sums_real (lambda ((P6 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 P6) (@ _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 P6) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P6) N))))) (@ tptp.semiri2265585572941072030t_real P6))) (@ (@ tptp.power_power_real X) N))) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat P6) N)))) tptp.zero_zero_real))))) (@ tptp.set_ord_atMost_nat P6)))) (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.cos_real Y)))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (assert (forall ((A tptp.real) (X tptp.real) (B2 tptp.real)) (= (= (@ (@ tptp.real_V1485227260804924795R_real A) X) (@ (@ tptp.real_V1485227260804924795R_real B2) X)) (or (= A B2) (= X tptp.zero_zero_real)))))
% 4.96/5.20 (assert (forall ((A tptp.real) (X tptp.complex) (B2 tptp.real)) (= (= (@ (@ tptp.real_V2046097035970521341omplex A) X) (@ (@ tptp.real_V2046097035970521341omplex B2) X)) (or (= A B2) (= X tptp.zero_zero_complex)))))
% 4.96/5.20 (assert (forall ((A tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 4.96/5.20 (assert (forall ((A tptp.real)) (= (@ (@ tptp.real_V2046097035970521341omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 4.96/5.20 (assert (forall ((A tptp.real) (X tptp.real)) (= (= (@ (@ tptp.real_V1485227260804924795R_real A) X) tptp.zero_zero_real) (or (= A tptp.zero_zero_real) (= X tptp.zero_zero_real)))))
% 4.96/5.20 (assert (forall ((A tptp.real) (X tptp.complex)) (= (= (@ (@ tptp.real_V2046097035970521341omplex A) X) tptp.zero_zero_complex) (or (= A tptp.zero_zero_real) (= X tptp.zero_zero_complex)))))
% 4.96/5.20 (assert (forall ((X tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real tptp.zero_zero_real) X) tptp.zero_zero_real)))
% 4.96/5.20 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.real_V2046097035970521341omplex tptp.zero_zero_real) X) tptp.zero_zero_complex)))
% 4.96/5.20 (assert (forall ((B2 tptp.real) (U tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real U))) (= (= (@ (@ tptp.plus_plus_real B2) (@ _let_1 A)) (@ (@ tptp.plus_plus_real A) (@ _let_1 B2))) (or (= A B2) (= U tptp.one_one_real))))))
% 4.96/5.20 (assert (= (@ tptp.sin_coeff tptp.zero_zero_nat) tptp.zero_zero_real))
% 4.96/5.20 (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)))
% 4.96/5.20 (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)))
% 4.96/5.20 (assert (forall ((X tptp.real) (A tptp.real) (B2 tptp.real)) (=> (not (= X tptp.zero_zero_real)) (=> (= (@ (@ tptp.real_V1485227260804924795R_real A) X) (@ (@ tptp.real_V1485227260804924795R_real B2) X)) (= A B2)))))
% 4.96/5.20 (assert (forall ((X tptp.complex) (A tptp.real) (B2 tptp.real)) (=> (not (= X tptp.zero_zero_complex)) (=> (= (@ (@ tptp.real_V2046097035970521341omplex A) X) (@ (@ tptp.real_V2046097035970521341omplex B2) X)) (= A B2)))))
% 4.96/5.20 (assert (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.plus_plus_real (@ _let_1 X)) (@ _let_1 Y))))))
% 4.96/5.20 (assert (forall ((X tptp.real) (Y tptp.real) (Xa2 tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.plus_plus_real X) Y)) Xa2) (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real X) Xa2)) (@ (@ tptp.real_V1485227260804924795R_real Y) Xa2)))))
% 4.96/5.20 (assert (forall ((A tptp.real) (B2 tptp.real) (X tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.plus_plus_real A) B2)) X) (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real A) X)) (@ (@ tptp.real_V1485227260804924795R_real B2) X)))))
% 4.96/5.20 (assert (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B2) A) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) C)) (@ (@ tptp.real_V1485227260804924795R_real B2) C))))))
% 4.96/5.20 (assert (forall ((A tptp.real) (B2 tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) X)) (@ (@ tptp.real_V1485227260804924795R_real B2) X))))))
% 4.96/5.20 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real C))) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B2)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B2)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B2) A)))))))
% 4.96/5.20 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real C))) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_real B2) A))))))
% 4.96/5.20 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real C))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_real A) B2))))))
% 4.96/5.20 (assert (forall ((X tptp.real) (Y tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real A))) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y)))))))
% 4.96/5.20 (assert (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real C))) (=> (@ (@ tptp.ord_less_eq_real B2) A) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B2)))))))
% 4.96/5.20 (assert (forall ((X tptp.real) (U tptp.real) (V tptp.real) (A tptp.real)) (let ((_let_1 (= V tptp.zero_zero_real))) (= (= X (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.divide_divide_real U) V)) A)) (and (=> _let_1 (= X tptp.zero_zero_real)) (=> (not _let_1) (= (@ (@ tptp.real_V1485227260804924795R_real V) X) (@ (@ tptp.real_V1485227260804924795R_real U) A))))))))
% 4.96/5.20 (assert (forall ((X tptp.complex) (U tptp.real) (V tptp.real) (A tptp.complex)) (let ((_let_1 (= V tptp.zero_zero_real))) (= (= X (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.divide_divide_real U) V)) A)) (and (=> _let_1 (= X tptp.zero_zero_complex)) (=> (not _let_1) (= (@ (@ tptp.real_V2046097035970521341omplex V) X) (@ (@ tptp.real_V2046097035970521341omplex U) A))))))))
% 4.96/5.20 (assert (forall ((U tptp.real) (V tptp.real) (A tptp.real) (X tptp.real)) (let ((_let_1 (= V tptp.zero_zero_real))) (= (= (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.divide_divide_real U) V)) A) X) (and (=> _let_1 (= X tptp.zero_zero_real)) (=> (not _let_1) (= (@ (@ tptp.real_V1485227260804924795R_real U) A) (@ (@ tptp.real_V1485227260804924795R_real V) X))))))))
% 4.96/5.20 (assert (forall ((U tptp.real) (V tptp.real) (A tptp.complex) (X tptp.complex)) (let ((_let_1 (= V tptp.zero_zero_real))) (= (= (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.divide_divide_real U) V)) A) X) (and (=> _let_1 (= X tptp.zero_zero_complex)) (=> (not _let_1) (= (@ (@ tptp.real_V2046097035970521341omplex U) A) (@ (@ tptp.real_V2046097035970521341omplex V) X))))))))
% 4.96/5.20 (assert (forall ((A tptp.real) (E2 tptp.real) (C tptp.real) (B2 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 B2) E2)) D)) (@ (@ tptp.ord_less_eq_real C) (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.minus_minus_real B2) A)) E2)) D)))))
% 4.96/5.20 (assert (forall ((A tptp.real) (E2 tptp.real) (C tptp.real) (B2 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 B2) E2)) D)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.minus_minus_real A) B2)) E2)) C)) D))))
% 4.96/5.20 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.real_V1485227260804924795R_real A) B2)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real)) (= A tptp.zero_zero_real))))))
% 4.96/5.20 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) B2)) tptp.zero_zero_real) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B2)) (= A tptp.zero_zero_real)))))
% 4.96/5.20 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.real_V1485227260804924795R_real A) B2))))))
% 4.96/5.20 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) X)) tptp.zero_zero_real)))))
% 4.96/5.20 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) X)) tptp.zero_zero_real)))))
% 4.96/5.20 (assert (forall ((A tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.real_V1485227260804924795R_real A) X)))))))
% 4.96/5.20 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (@ _let_1 A) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real))) (@ _let_1 (@ (@ tptp.real_V1485227260804924795R_real A) B2))))))
% 4.96/5.20 (assert (forall ((A tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ _let_1 X))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) X)) tptp.zero_zero_real)))))
% 4.96/5.20 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_eq_real C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) C)) (@ (@ tptp.real_V1485227260804924795R_real B2) D)))))))))
% 4.96/5.20 (assert (forall ((A tptp.real) (B2 tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ _let_1 B2) (=> (@ _let_1 X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) X)) (@ (@ tptp.real_V1485227260804924795R_real B2) Y)))))))))
% 4.96/5.20 (assert (forall ((X tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) X)) X)))))
% 4.96/5.20 (assert (forall ((X tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) X) (@ (@ tptp.plus_plus_real X) X))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ tptp.summable_real (lambda ((K2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K2)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1)))))))))
% 4.96/5.20 (assert (forall ((C (-> tptp.nat tptp.complex)) (X tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N)) (@ (@ tptp.power_power_complex X) N)))) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N)) (@ C N))) (@ (@ tptp.power_power_complex X) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N)) (@ (@ tptp.power_power_complex X) N))))))))
% 4.96/5.20 (assert (forall ((C (-> tptp.nat tptp.real)) (X tptp.real)) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N)) (@ (@ tptp.power_power_real X) N)))) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ C N))) (@ (@ tptp.power_power_real X) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N)) (@ (@ tptp.power_power_real X) N))))))))
% 4.96/5.20 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_complex X))) (let ((_let_3 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)))) (let ((_let_4 (@ _let_3 X))) (=> (not (= (@ tptp.cos_complex X) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex _let_4) tptp.zero_zero_complex)) (= (@ tptp.tan_complex _let_4) (@ (@ tptp.divide1717551699836669952omplex (@ _let_3 _let_2)) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex _let_2) (@ tptp.numeral_numeral_nat _let_1)))))))))))))
% 4.96/5.20 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_real X))) (let ((_let_3 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)))) (let ((_let_4 (@ _let_3 X))) (=> (not (= (@ tptp.cos_real X) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real _let_4) tptp.zero_zero_real)) (= (@ tptp.tan_real _let_4) (@ (@ tptp.divide_divide_real (@ _let_3 _let_2)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real _let_2) (@ tptp.numeral_numeral_nat _let_1)))))))))))))
% 4.96/5.20 (assert (= tptp.tan_complex (lambda ((X4 tptp.complex)) (let ((_let_1 (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) X4))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex _let_1)) (@ (@ tptp.plus_plus_complex (@ tptp.cos_complex _let_1)) tptp.one_one_complex))))))
% 4.96/5.20 (assert (= tptp.tan_real (lambda ((X4 tptp.real)) (let ((_let_1 (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) X4))) (@ (@ tptp.divide_divide_real (@ tptp.sin_real _let_1)) (@ (@ tptp.plus_plus_real (@ tptp.cos_real _let_1)) tptp.one_one_real))))))
% 4.96/5.20 (assert (= tptp.int_ge_less_than2 (lambda ((D4 tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z7 tptp.int) (Z6 tptp.int)) (and (@ (@ tptp.ord_less_eq_int D4) Z6) (@ (@ tptp.ord_less_int Z7) Z6))))))))
% 4.96/5.20 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real A))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 4.96/5.20 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int A))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 4.96/5.20 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real A))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 4.96/5.20 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int A))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 4.96/5.20 (assert (= (@ tptp.abs_abs_real tptp.zero_zero_real) tptp.zero_zero_real))
% 4.96/5.20 (assert (= (@ tptp.abs_abs_int tptp.zero_zero_int) tptp.zero_zero_int))
% 4.96/5.20 (assert (= (@ tptp.abs_abs_complex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 4.96/5.20 (assert (= (@ tptp.abs_abs_real tptp.zero_zero_real) tptp.zero_zero_real))
% 4.96/5.20 (assert (= (@ tptp.abs_abs_int tptp.zero_zero_int) tptp.zero_zero_int))
% 4.96/5.20 (assert (forall ((A tptp.real)) (= (= (@ tptp.abs_abs_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 4.96/5.20 (assert (forall ((A tptp.int)) (= (= (@ tptp.abs_abs_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 4.96/5.20 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ tptp.abs_abs_real A)) (= A tptp.zero_zero_real))))
% 4.96/5.20 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ tptp.abs_abs_int A)) (= A tptp.zero_zero_int))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (assert (= (@ tptp.abs_abs_int tptp.one_one_int) tptp.one_one_int))
% 4.96/5.20 (assert (= (@ tptp.abs_abs_complex tptp.one_one_complex) tptp.one_one_complex))
% 4.96/5.20 (assert (= (@ tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real))
% 4.96/5.20 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B2)))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 4.96/5.20 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B2)))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 4.96/5.20 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real A) B2)) (@ (@ tptp.divide_divide_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B2)))))
% 4.96/5.20 (assert (forall ((A tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 4.96/5.20 (assert (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 4.96/5.20 (assert (forall ((A tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 4.96/5.20 (assert (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 4.96/5.20 (assert (forall ((M2 tptp.real) (K tptp.real)) (= (@ (@ tptp.dvd_dvd_real (@ tptp.abs_abs_real M2)) K) (@ (@ tptp.dvd_dvd_real M2) K))))
% 4.96/5.20 (assert (forall ((M2 tptp.int) (K tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.abs_abs_int M2)) K) (@ (@ tptp.dvd_dvd_int M2) K))))
% 4.96/5.20 (assert (forall ((M2 tptp.real) (K tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real M2))) (= (@ _let_1 (@ tptp.abs_abs_real K)) (@ _let_1 K)))))
% 4.96/5.20 (assert (forall ((M2 tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int M2))) (= (@ _let_1 (@ tptp.abs_abs_int K)) (@ _let_1 K)))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N2))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 4.96/5.20 (assert (forall ((X tptp.int)) (= (@ tptp.ring_1_of_int_int (@ tptp.abs_abs_int X)) (@ tptp.abs_abs_int (@ tptp.ring_1_of_int_int X)))))
% 4.96/5.20 (assert (forall ((X tptp.int)) (= (@ tptp.ring_1_of_int_real (@ tptp.abs_abs_int X)) (@ tptp.abs_abs_real (@ tptp.ring_1_of_int_real X)))))
% 4.96/5.20 (assert (= (@ tptp.tan_real tptp.zero_zero_real) tptp.zero_zero_real))
% 4.96/5.20 (assert (= (@ tptp.tan_complex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 4.96/5.20 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n3304061248610475627l_real P))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 4.96/5.20 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n2684676970156552555ol_int P))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 4.96/5.20 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A))))
% 4.96/5.20 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))))
% 4.96/5.20 (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))))
% 4.96/5.20 (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))))
% 4.96/5.20 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 4.96/5.20 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 4.96/5.20 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.abs_abs_real A)) (not (= A tptp.zero_zero_real)))))
% 4.96/5.20 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.abs_abs_int A)) (not (= A tptp.zero_zero_int)))))
% 4.96/5.20 (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))))
% 4.96/5.20 (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))))
% 4.96/5.20 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A) (@ tptp.abs_abs_real B2))) tptp.zero_zero_real) (or (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (= B2 tptp.zero_zero_real)))))
% 4.96/5.20 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real A) (@ tptp.abs_abs_real B2))) (or (@ _let_1 A) (= B2 tptp.zero_zero_real))))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ tptp.abs_abs_real (@ tptp.sgn_sgn_real A)) tptp.one_one_real))))
% 4.96/5.20 (assert (forall ((A tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ tptp.abs_abs_int (@ tptp.sgn_sgn_int A)) tptp.one_one_int))))
% 4.96/5.20 (assert (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.sgn_sgn_real A)) (@ tptp.zero_n3304061248610475627l_real (not (= A tptp.zero_zero_real))))))
% 4.96/5.20 (assert (forall ((A tptp.complex)) (= (@ tptp.abs_abs_complex (@ tptp.sgn_sgn_complex A)) (@ tptp.zero_n1201886186963655149omplex (not (= A tptp.zero_zero_complex))))))
% 4.96/5.20 (assert (forall ((A tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.sgn_sgn_int A)) (@ tptp.zero_n2684676970156552555ol_int (not (= A tptp.zero_zero_int))))))
% 4.96/5.20 (assert (forall ((A tptp.real)) (= (@ tptp.sgn_sgn_real (@ tptp.abs_abs_real A)) (@ tptp.zero_n3304061248610475627l_real (not (= A tptp.zero_zero_real))))))
% 4.96/5.20 (assert (forall ((A tptp.complex)) (= (@ tptp.sgn_sgn_complex (@ tptp.abs_abs_complex A)) (@ tptp.zero_n1201886186963655149omplex (not (= A tptp.zero_zero_complex))))))
% 4.96/5.20 (assert (forall ((A tptp.int)) (= (@ tptp.sgn_sgn_int (@ tptp.abs_abs_int A)) (@ tptp.zero_n2684676970156552555ol_int (not (= A tptp.zero_zero_int))))))
% 4.96/5.20 (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))))
% 4.96/5.20 (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))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (assert (forall ((X tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real X)) tptp.one_one_real)) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)))))
% 4.96/5.20 (assert (forall ((X tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex X)) tptp.one_one_complex)) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)))))
% 4.96/5.20 (assert (forall ((X tptp.real) (B2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real B2))) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real X)) _let_1)) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X) _let_1))))))
% 4.96/5.20 (assert (forall ((X tptp.real) (B2 tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex X)) (@ tptp.numera6690914467698888265omplex B2))) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X) (@ tptp.numeral_numeral_real B2))))))
% 4.96/5.20 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) B2)) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int B2) A)))))
% 4.96/5.20 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) B2)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B2) A)))))
% 4.96/5.20 (assert (forall ((X tptp.int) (Y tptp.int)) (= (= (@ tptp.abs_abs_int X) (@ tptp.abs_abs_int Y)) (or (= X Y) (= X (@ tptp.uminus_uminus_int Y))))))
% 4.96/5.20 (assert (forall ((X tptp.real) (Y tptp.real)) (= (= (@ tptp.abs_abs_real X) (@ tptp.abs_abs_real Y)) (or (= X Y) (= X (@ tptp.uminus_uminus_real Y))))))
% 4.96/5.20 (assert (forall ((L tptp.real) (K tptp.real)) (=> (= (@ tptp.abs_abs_real L) (@ tptp.abs_abs_real K)) (@ (@ tptp.dvd_dvd_real L) K))))
% 4.96/5.20 (assert (forall ((L tptp.int) (K tptp.int)) (=> (= (@ tptp.abs_abs_int L) (@ tptp.abs_abs_int K)) (@ (@ tptp.dvd_dvd_int L) K))))
% 4.96/5.20 (assert (= (@ tptp.abs_abs_int tptp.one_one_int) tptp.one_one_int))
% 4.96/5.20 (assert (= (@ tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real))
% 4.96/5.20 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ tptp.abs_abs_int (@ (@ tptp.times_times_int A) B2)) (@ (@ tptp.times_times_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B2)))))
% 4.96/5.20 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ tptp.abs_abs_real (@ (@ tptp.times_times_real A) B2)) (@ (@ tptp.times_times_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B2)))))
% 4.96/5.20 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (@ tptp.abs_abs_complex (@ (@ tptp.times_times_complex A) B2)) (@ (@ tptp.times_times_complex (@ tptp.abs_abs_complex A)) (@ tptp.abs_abs_complex B2)))))
% 4.96/5.20 (assert (forall ((A tptp.real)) (= (= (@ tptp.abs_abs_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 4.96/5.20 (assert (forall ((A tptp.int)) (= (= (@ tptp.abs_abs_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 4.96/5.20 (assert (forall ((A tptp.complex)) (= (= (@ tptp.abs_abs_complex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 4.96/5.20 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) B2) (@ (@ tptp.ord_less_eq_real A) B2))))
% 4.96/5.20 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) B2) (@ (@ tptp.ord_less_eq_int A) B2))))
% 4.96/5.20 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real A) (@ tptp.abs_abs_real A))))
% 4.96/5.20 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) (@ tptp.abs_abs_int A))))
% 4.96/5.20 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.abs_abs_real A))))
% 4.96/5.20 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.abs_abs_int A))))
% 4.96/5.20 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A))))
% 4.96/5.20 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))))
% 4.96/5.20 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real A)) tptp.zero_zero_real))))
% 4.96/5.20 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int))))
% 4.96/5.20 (assert (forall ((A tptp.real) (B2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real A) B2))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B2)))))
% 4.96/5.20 (assert (forall ((A tptp.int) (B2 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.plus_plus_int A) B2))) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B2)))))
% 4.96/5.20 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real B2))) (let ((_let_2 (@ tptp.abs_abs_real A))) (=> (@ (@ tptp.ord_less_real _let_2) C) (=> (@ (@ tptp.ord_less_real _let_1) D) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real _let_2) _let_1)) (@ (@ tptp.times_times_real C) D))))))))
% 4.96/5.20 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int B2))) (let ((_let_2 (@ tptp.abs_abs_int A))) (=> (@ (@ tptp.ord_less_int _let_2) C) (=> (@ (@ tptp.ord_less_int _let_1) D) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int _let_2) _let_1)) (@ (@ tptp.times_times_int C) D))))))))
% 4.96/5.20 (assert (forall ((A tptp.real) (B2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B2))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B2) A)))))
% 4.96/5.20 (assert (forall ((A tptp.int) (B2 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B2))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int B2) A)))))
% 4.96/5.20 (assert (forall ((A tptp.real) (B2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B2)))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) B2)))))
% 4.96/5.20 (assert (forall ((A tptp.int) (B2 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B2)))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) B2)))))
% 4.96/5.20 (assert (forall ((A tptp.real) (B2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B2))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) B2)))))
% 4.96/5.20 (assert (forall ((A tptp.int) (B2 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B2))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) B2)))))
% 4.96/5.20 (assert (forall ((B2 tptp.real) (A tptp.real)) (=> (not (= B2 tptp.zero_zero_real)) (= (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real A) B2)) (@ (@ tptp.divide_divide_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B2))))))
% 4.96/5.20 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 4.96/5.20 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 4.96/5.20 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) B2) (and (@ (@ tptp.ord_less_eq_real A) B2) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) B2)))))
% 4.96/5.20 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) B2) (and (@ (@ tptp.ord_less_eq_int A) B2) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) B2)))))
% 4.96/5.20 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) B2) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) B2))))
% 4.96/5.20 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) B2) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) B2))))
% 4.96/5.20 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) B2) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) B2)))))
% 4.96/5.20 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) B2) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) B2)))))
% 4.96/5.20 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int A)) B2) (and (@ (@ tptp.ord_less_int A) B2) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) B2)))))
% 4.96/5.20 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real A)) B2) (and (@ (@ tptp.ord_less_real A) B2) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) B2)))))
% 4.96/5.20 (assert (= tptp.abs_abs_int (lambda ((K2 tptp.int)) (@ (@ tptp.times_times_int K2) (@ tptp.sgn_sgn_int K2)))))
% 4.96/5.20 (assert (= tptp.abs_abs_real (lambda ((K2 tptp.real)) (@ (@ tptp.times_times_real K2) (@ tptp.sgn_sgn_real K2)))))
% 4.96/5.20 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.abs_abs_int A)) (@ tptp.sgn_sgn_int A)) A)))
% 4.96/5.20 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.abs_abs_real A)) (@ tptp.sgn_sgn_real A)) A)))
% 4.96/5.20 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.abs_abs_complex A)) (@ tptp.sgn_sgn_complex A)) A)))
% 4.96/5.20 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int A)) (@ tptp.abs_abs_int A)) A)))
% 4.96/5.20 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real A)) (@ tptp.abs_abs_real A)) A)))
% 4.96/5.20 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.sgn_sgn_complex A)) (@ tptp.abs_abs_complex A)) A)))
% 4.96/5.20 (assert (forall ((X tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int X)) (@ tptp.abs_abs_int X)) X)))
% 4.96/5.20 (assert (forall ((X tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real X)) (@ tptp.abs_abs_real X)) X)))
% 4.96/5.20 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (= (@ tptp.sgn_sgn_int B2) (@ tptp.sgn_sgn_int A)) (= (@ tptp.abs_abs_int (@ (@ tptp.plus_plus_int A) B2)) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B2))))))
% 4.96/5.20 (assert (forall ((B2 tptp.real) (A tptp.real)) (=> (= (@ tptp.sgn_sgn_real B2) (@ tptp.sgn_sgn_real A)) (= (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real A) B2)) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B2))))))
% 4.96/5.20 (assert (forall ((X tptp.real)) (=> (forall ((E tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) E))) (= X tptp.zero_zero_real))))
% 4.96/5.20 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.times_times_real (@ tptp.abs_abs_real Y)) X) (@ tptp.abs_abs_real (@ (@ tptp.times_times_real Y) X))))))
% 4.96/5.20 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (= (@ (@ tptp.times_times_int (@ tptp.abs_abs_int Y)) X) (@ tptp.abs_abs_int (@ (@ tptp.times_times_int Y) X))))))
% 4.96/5.20 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (and (or (@ _let_1 A) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real)) (or (@ _let_1 B2) (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real))) (= (@ tptp.abs_abs_real (@ (@ tptp.times_times_real A) B2)) (@ (@ tptp.times_times_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B2)))))))
% 4.96/5.20 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (and (or (@ _let_1 A) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)) (or (@ _let_1 B2) (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int))) (= (@ tptp.abs_abs_int (@ (@ tptp.times_times_int A) B2)) (@ (@ tptp.times_times_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B2)))))))
% 4.96/5.20 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (= (@ tptp.abs_abs_real A) B2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B2) (or (= A B2) (= A (@ tptp.uminus_uminus_real B2)))))))
% 4.96/5.20 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (= (@ tptp.abs_abs_int A) B2) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B2) (or (= A B2) (= A (@ tptp.uminus_uminus_int B2)))))))
% 4.96/5.20 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (= A (@ tptp.abs_abs_real B2)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (or (= B2 A) (= B2 (@ tptp.uminus_uminus_real A)))))))
% 4.96/5.20 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (= A (@ tptp.abs_abs_int B2)) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (or (= B2 A) (= B2 (@ tptp.uminus_uminus_int A)))))))
% 4.96/5.20 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.abs_abs_real A))) tptp.zero_zero_real)))
% 4.96/5.20 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.abs_abs_int A))) tptp.zero_zero_int)))
% 4.96/5.20 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (= (@ (@ tptp.divide_divide_real (@ tptp.abs_abs_real X)) Y) (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real X) Y))))))
% 4.96/5.20 (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))))
% 4.96/5.20 (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))))
% 4.96/5.20 (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))))
% 4.96/5.20 (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))))
% 4.96/5.20 (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))))
% 4.96/5.20 (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))))
% 4.96/5.20 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (= (@ tptp.abs_abs_int A) (@ tptp.uminus_uminus_int A)))))
% 4.96/5.20 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ tptp.abs_abs_real A) (@ tptp.uminus_uminus_real A)))))
% 4.96/5.20 (assert (forall ((X tptp.real) (A tptp.real) (R2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) A))) R2) (and (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) R2)) X) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.plus_plus_real A) R2))))))
% 4.96/5.20 (assert (forall ((X tptp.int) (A tptp.int) (R2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X) A))) R2) (and (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) R2)) X) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.plus_plus_int A) R2))))))
% 4.96/5.20 (assert (forall ((A tptp.real) (B2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) B2))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B2)))))
% 4.96/5.20 (assert (forall ((A tptp.int) (B2 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) B2))) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B2)))))
% 4.96/5.20 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B2)) (@ (@ tptp.plus_plus_real C) D)))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) C))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B2) D))))))
% 4.96/5.20 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B2)) (@ (@ tptp.plus_plus_int C) D)))) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) C))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int B2) D))))))
% 4.96/5.20 (assert (forall ((X tptp.real) (A tptp.real) (R2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) A))) R2) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) R2)) X) (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real A) R2))))))
% 4.96/5.20 (assert (forall ((X tptp.int) (A tptp.int) (R2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X) A))) R2) (and (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) R2)) X) (@ (@ tptp.ord_less_int X) (@ (@ tptp.plus_plus_int A) R2))))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (exists ((N8 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ F N3))) (@ G N3))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.abs_abs_real (@ F N))))))))
% 4.96/5.20 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.abs_abs_real X)))))
% 4.96/5.20 (assert (forall ((X tptp.int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.abs_abs_int X)))))
% 4.96/5.20 (assert (forall ((N2 tptp.int) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.ring_1_of_int_real N2))) X) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X)))))
% 4.96/5.20 (assert (forall ((N2 tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ tptp.ring_1_of_int_int N2))) X) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) X)))))
% 4.96/5.20 (assert (forall ((N2 tptp.int) (X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ tptp.ring_1_of_int_real N2))) X) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_less_real tptp.one_one_real) X)))))
% 4.96/5.20 (assert (forall ((N2 tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ tptp.ring_1_of_int_int N2))) X) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) X)))))
% 4.96/5.20 (assert (forall ((A tptp.real) (N2 tptp.nat) (X tptp.real) (B2 tptp.real)) (=> (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real A)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N2)) X) (=> (= X (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real B2)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real B2)) N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= A B2))))))
% 4.96/5.20 (assert (forall ((Z3 tptp.real) (M2 tptp.int)) (let ((_let_1 (@ tptp.minus_minus_real Z3))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ _let_1 (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real Z3))))) (@ tptp.abs_abs_real (@ _let_1 (@ tptp.ring_1_of_int_real M2)))))))
% 4.96/5.20 (assert (= tptp.diffs_complex (lambda ((C3 (-> tptp.nat tptp.complex)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ C3 _let_1))))))
% 4.96/5.20 (assert (= tptp.diffs_real (lambda ((C3 (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ C3 _let_1))))))
% 4.96/5.20 (assert (= tptp.diffs_int (lambda ((C3 (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int _let_1)) (@ C3 _let_1))))))
% 4.96/5.20 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) (@ tptp.abs_abs_real Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))))))
% 4.96/5.20 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X)) (@ tptp.abs_abs_int Y)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))))))
% 4.96/5.20 (assert (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) Y))))))
% 4.96/5.20 (assert (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X)) Y))))))
% 4.96/5.20 (assert (forall ((P (-> tptp.real tptp.real Bool)) (X tptp.real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X5) (@ (@ P X5) (@ (@ tptp.power_power_real X5) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P (@ tptp.abs_abs_real X)) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 4.96/5.20 (assert (forall ((P (-> tptp.int tptp.int Bool)) (X tptp.int)) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X5) (@ (@ P X5) (@ (@ tptp.power_power_int X5) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P (@ tptp.abs_abs_int X)) (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 4.96/5.20 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real))))
% 4.96/5.20 (assert (forall ((X tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X)) tptp.one_one_int))))
% 4.96/5.20 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real))))
% 4.96/5.20 (assert (forall ((X tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int X)) tptp.one_one_int))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (A tptp.real) (B2 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 B2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B2) N2))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (A tptp.int) (B2 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 B2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B2) N2))))))
% 4.96/5.20 (assert (forall ((I6 tptp.set_Extended_enat) (X (-> tptp.extended_enat tptp.real)) (A (-> tptp.extended_enat tptp.real)) (B2 tptp.real) (Delta tptp.real)) (=> (forall ((I4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I4) I6) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X I4)))) (=> (= (@ (@ tptp.groups4148127829035722712t_real X) I6) tptp.one_one_real) (=> (forall ((I4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I4) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A I4)) B2))) Delta))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups4148127829035722712t_real (lambda ((I3 tptp.extended_enat)) (@ (@ tptp.times_times_real (@ A I3)) (@ X I3)))) I6)) B2))) Delta))))))
% 4.96/5.20 (assert (forall ((I6 tptp.set_real) (X (-> tptp.real tptp.real)) (A (-> tptp.real tptp.real)) (B2 tptp.real) (Delta tptp.real)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X I4)))) (=> (= (@ (@ tptp.groups8097168146408367636l_real X) I6) tptp.one_one_real) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A I4)) B2))) 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)) (@ X I3)))) I6)) B2))) Delta))))))
% 4.96/5.20 (assert (forall ((I6 tptp.set_set_nat) (X (-> tptp.set_nat tptp.real)) (A (-> tptp.set_nat tptp.real)) (B2 tptp.real) (Delta tptp.real)) (=> (forall ((I4 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat I4) I6) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X I4)))) (=> (= (@ (@ tptp.groups5107569545109728110t_real X) I6) tptp.one_one_real) (=> (forall ((I4 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat I4) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A I4)) B2))) Delta))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups5107569545109728110t_real (lambda ((I3 tptp.set_nat)) (@ (@ tptp.times_times_real (@ A I3)) (@ X I3)))) I6)) B2))) Delta))))))
% 4.96/5.20 (assert (forall ((I6 tptp.set_int) (X (-> tptp.int tptp.real)) (A (-> tptp.int tptp.real)) (B2 tptp.real) (Delta tptp.real)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X I4)))) (=> (= (@ (@ tptp.groups8778361861064173332t_real X) I6) tptp.one_one_real) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A I4)) B2))) 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)) (@ X I3)))) I6)) B2))) Delta))))))
% 4.96/5.20 (assert (forall ((I6 tptp.set_Extended_enat) (X (-> tptp.extended_enat tptp.int)) (A (-> tptp.extended_enat tptp.int)) (B2 tptp.int) (Delta tptp.int)) (=> (forall ((I4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I4) I6) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ X I4)))) (=> (= (@ (@ tptp.groups2025484359314973016at_int X) I6) tptp.one_one_int) (=> (forall ((I4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I4) I6) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ A I4)) B2))) Delta))) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.groups2025484359314973016at_int (lambda ((I3 tptp.extended_enat)) (@ (@ tptp.times_times_int (@ A I3)) (@ X I3)))) I6)) B2))) Delta))))))
% 4.96/5.20 (assert (forall ((I6 tptp.set_real) (X (-> tptp.real tptp.int)) (A (-> tptp.real tptp.int)) (B2 tptp.int) (Delta tptp.int)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ X I4)))) (=> (= (@ (@ tptp.groups1932886352136224148al_int X) I6) tptp.one_one_int) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ A I4)) B2))) Delta))) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.groups1932886352136224148al_int (lambda ((I3 tptp.real)) (@ (@ tptp.times_times_int (@ A I3)) (@ X I3)))) I6)) B2))) Delta))))))
% 4.96/5.20 (assert (forall ((I6 tptp.set_set_nat) (X (-> tptp.set_nat tptp.int)) (A (-> tptp.set_nat tptp.int)) (B2 tptp.int) (Delta tptp.int)) (=> (forall ((I4 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat I4) I6) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ X I4)))) (=> (= (@ (@ tptp.groups8292507037921071086at_int X) I6) tptp.one_one_int) (=> (forall ((I4 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat I4) I6) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ A I4)) B2))) Delta))) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.groups8292507037921071086at_int (lambda ((I3 tptp.set_nat)) (@ (@ tptp.times_times_int (@ A I3)) (@ X I3)))) I6)) B2))) Delta))))))
% 4.96/5.20 (assert (forall ((I6 tptp.set_nat) (X (-> tptp.nat tptp.int)) (A (-> tptp.nat tptp.int)) (B2 tptp.int) (Delta tptp.int)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ X I4)))) (=> (= (@ (@ tptp.groups3539618377306564664at_int X) I6) tptp.one_one_int) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ A I4)) B2))) Delta))) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ A I3)) (@ X I3)))) I6)) B2))) Delta))))))
% 4.96/5.20 (assert (forall ((I6 tptp.set_int) (X (-> tptp.int tptp.int)) (A (-> tptp.int tptp.int)) (B2 tptp.int) (Delta tptp.int)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ X I4)))) (=> (= (@ (@ tptp.groups4538972089207619220nt_int X) I6) tptp.one_one_int) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ A I4)) B2))) Delta))) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I3 tptp.int)) (@ (@ tptp.times_times_int (@ A I3)) (@ X I3)))) I6)) B2))) Delta))))))
% 4.96/5.20 (assert (forall ((I6 tptp.set_nat) (X (-> tptp.nat tptp.real)) (A (-> tptp.nat tptp.real)) (B2 tptp.real) (Delta tptp.real)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X I4)))) (=> (= (@ (@ tptp.groups6591440286371151544t_real X) I6) tptp.one_one_real) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A I4)) B2))) Delta))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ A I3)) (@ X I3)))) I6)) B2))) Delta))))))
% 4.96/5.20 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ tptp.topolo6980174941875973593q_real (lambda ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1))))))))
% 4.96/5.20 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (= (@ tptp.arctan X) (@ tptp.suminf_real (lambda ((K2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K2)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1))))))))))
% 4.96/5.20 (assert (= tptp.int_ge_less_than (lambda ((D4 tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z7 tptp.int) (Z6 tptp.int)) (and (@ (@ tptp.ord_less_eq_int D4) Z7) (@ (@ tptp.ord_less_int Z7) Z6))))))))
% 4.96/5.20 (assert (forall ((X tptp.real) (N2 tptp.nat)) (=> (not (= X tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (exists ((T6 tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real T6))) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ tptp.abs_abs_real X)) (= (@ tptp.exp_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X) M)) (@ tptp.semiri2265585572941072030t_real M)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.exp_real T6)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2)))))))))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (assert (forall ((X tptp.int)) (= (@ (@ tptp.dvd_dvd_int X) tptp.one_one_int) (= (@ tptp.abs_abs_int X) tptp.one_one_int))))
% 4.96/5.20 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int Z3)) tptp.one_one_int) (= Z3 tptp.zero_zero_int))))
% 4.96/5.20 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 X)))))
% 4.96/5.20 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X)))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B2) (=> (@ (@ tptp.dvd_dvd_int B2) A) (= (@ tptp.abs_abs_int A) (@ tptp.abs_abs_int B2))))))
% 4.96/5.20 (assert (forall ((M2 tptp.int) (N2 tptp.int)) (=> (= (@ tptp.abs_abs_int (@ (@ tptp.times_times_int M2) N2)) tptp.one_one_int) (= (@ tptp.abs_abs_int M2) tptp.one_one_int))))
% 4.96/5.20 (assert (forall ((S2 tptp.set_int)) (= (not (@ tptp.finite_finite_int S2)) (forall ((M tptp.int)) (exists ((N tptp.int)) (and (@ (@ tptp.ord_less_eq_int M) (@ tptp.abs_abs_int N)) (@ (@ tptp.member_int N) S2)))))))
% 4.96/5.20 (assert (forall ((S2 tptp.set_int)) (= (not (@ tptp.finite_finite_int S2)) (forall ((M tptp.int)) (exists ((N tptp.int)) (and (@ (@ tptp.ord_less_int M) (@ tptp.abs_abs_int N)) (@ (@ tptp.member_int N) S2)))))))
% 4.96/5.20 (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))))
% 4.96/5.20 (assert (forall ((I tptp.int) (D tptp.int)) (=> (not (= I tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int D) I) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int D)) (@ tptp.abs_abs_int I))))))
% 4.96/5.20 (assert (forall ((M2 tptp.int) (N2 tptp.int)) (=> (not (= M2 tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int M2) N2)) M2) (= (@ tptp.abs_abs_int N2) tptp.one_one_int)))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I4 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat M2) 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 M2) N2) (=> (@ (@ tptp.ord_less_eq_int (@ F M2)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N2)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M2) I4) (@ (@ tptp.ord_less_eq_nat I4) N2) (= (@ F I4) K)))))))))
% 4.96/5.20 (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))))))))
% 4.96/5.20 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M tptp.zero_zero_nat)) N) (@ (@ (@ tptp.if_nat (= N tptp.zero_zero_nat)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat M) _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 M) _let_1)) (@ (@ tptp.divide_divide_nat N) _let_1))))))))))
% 4.96/5.20 (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))))))))
% 4.96/5.20 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M 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 M)) (not (@ _let_2 N)))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se6528837805403552850or_nat (@ (@ tptp.divide_divide_nat M) _let_1)) (@ (@ tptp.divide_divide_nat N) _let_1)))))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N2))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X) _let_1))) N2)) (@ tptp.exp_real X)))))))
% 4.96/5.20 (assert (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N2))) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X) _let_1))) N2)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X))))))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (assert (= tptp.divide_divide_int (lambda ((K2 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.nat2 (@ tptp.abs_abs_int K2))) (@ tptp.nat2 (@ tptp.abs_abs_int L2))))) (@ (@ (@ tptp.if_int (= L2 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (= (@ tptp.sgn_sgn_int K2) (@ tptp.sgn_sgn_int L2))) (@ tptp.semiri1314217659103216013at_int _let_1)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat _let_1) (@ tptp.zero_n2687167440665602831ol_nat (not (@ (@ tptp.dvd_dvd_int L2) K2))))))))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (= (@ tptp.nat2 (@ tptp.semiri1314217659103216013at_int N2)) N2)))
% 4.96/5.20 (assert (forall ((K tptp.num)) (= (@ tptp.nat2 (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_nat K))))
% 4.96/5.20 (assert (forall ((P Bool)) (= (@ tptp.nat2 (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2687167440665602831ol_nat P))))
% 4.96/5.20 (assert (= (@ tptp.nat2 tptp.one_one_int) (@ tptp.suc tptp.zero_zero_nat)))
% 4.96/5.20 (assert (forall ((Z3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z3) tptp.zero_zero_int) (= (@ tptp.nat2 Z3) tptp.zero_zero_nat))))
% 4.96/5.20 (assert (forall ((I tptp.int)) (= (= (@ tptp.nat2 I) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_int I) tptp.zero_zero_int))))
% 4.96/5.20 (assert (forall ((W2 tptp.int) (Z3 tptp.int)) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W2)) (@ tptp.nat2 Z3)) (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z3) (@ (@ tptp.ord_less_int W2) Z3)))))
% 4.96/5.20 (assert (forall ((K tptp.num)) (= (@ tptp.nat2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.zero_zero_nat)))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (= (@ tptp.nat2 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) tptp.zero_zero_nat)))
% 4.96/5.20 (assert (forall ((Z3 tptp.int)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 Z3)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z3))) (and (=> _let_2 (= _let_1 Z3)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))))
% 4.96/5.20 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.nat2 Z3)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z3))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (assert (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2) (@ tptp.nat2 Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2) Y))))
% 4.96/5.20 (assert (forall ((Y tptp.int) (X tptp.num) (N2 tptp.nat)) (= (= (@ tptp.nat2 Y) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.dvd_dvd_nat N2) (@ tptp.nat2 (@ tptp.abs_abs_int K))) (@ (@ tptp.dvd_dvd_int (@ tptp.semiri1314217659103216013at_int N2)) K))))
% 4.96/5.20 (assert (forall ((K tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.nat2 (@ tptp.abs_abs_int K))) N2) (@ (@ tptp.dvd_dvd_int K) (@ tptp.semiri1314217659103216013at_int N2)))))
% 4.96/5.20 (assert (forall ((X tptp.real) (A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real X))) A) (@ (@ tptp.ord_less_eq_real X) (@ tptp.semiri5074537144036343181t_real A)))))
% 4.96/5.20 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.nat2 Z3)) (@ (@ tptp.ord_less_int tptp.one_one_int) Z3))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (assert (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2)) (@ tptp.nat2 A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)) A))))
% 4.96/5.20 (assert (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 A)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))))
% 4.96/5.20 (assert (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 A)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))))
% 4.96/5.20 (assert (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2)) (@ tptp.nat2 A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)) A))))
% 4.96/5.20 (assert (= tptp.zero_zero_nat (@ tptp.nat2 tptp.zero_zero_int)))
% 4.96/5.20 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y)))))
% 4.96/5.20 (assert (= (lambda ((P2 (-> tptp.nat Bool))) (exists ((X7 tptp.nat)) (@ P2 X7))) (lambda ((P3 (-> tptp.nat Bool))) (exists ((X4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X4) (@ P3 (@ tptp.nat2 X4)))))))
% 4.96/5.20 (assert (= (lambda ((P2 (-> tptp.nat Bool))) (forall ((X7 tptp.nat)) (@ P2 X7))) (lambda ((P3 (-> tptp.nat Bool))) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X4) (@ P3 (@ tptp.nat2 X4)))))))
% 4.96/5.20 (assert (forall ((Z3 tptp.int) (Z8 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z3) (=> (@ _let_1 Z8) (= (= (@ tptp.nat2 Z3) (@ tptp.nat2 Z8)) (= Z3 Z8)))))))
% 4.96/5.20 (assert (forall ((Z3 tptp.int) (W2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z3) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W2)) (@ tptp.nat2 Z3)) (@ (@ tptp.ord_less_int W2) Z3)))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (Z3 tptp.int)) (= (@ (@ tptp.ord_less_nat M2) (@ tptp.nat2 Z3)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M2)) Z3))))
% 4.96/5.20 (assert (forall ((X tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 X)) N2) (@ (@ tptp.ord_less_eq_int X) (@ tptp.semiri1314217659103216013at_int N2)))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (Z3 tptp.int)) (= (= (@ tptp.semiri1314217659103216013at_int M2) Z3) (and (= M2 (@ tptp.nat2 Z3)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z3)))))
% 4.96/5.20 (assert (forall ((Z3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z3) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 Z3)) Z3))))
% 4.96/5.20 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B2))) (@ (@ tptp.plus_plus_nat A) B2))))
% 4.96/5.20 (assert (forall ((W2 tptp.int) (Z3 tptp.int)) (= (@ tptp.nat2 (@ tptp.abs_abs_int (@ (@ tptp.times_times_int W2) Z3))) (@ (@ tptp.times_times_nat (@ tptp.nat2 (@ tptp.abs_abs_int W2))) (@ tptp.nat2 (@ tptp.abs_abs_int Z3))))))
% 4.96/5.20 (assert (= tptp.plus_plus_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B3))))))
% 4.96/5.20 (assert (forall ((W2 tptp.int) (Z3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W2) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W2)) (@ tptp.nat2 Z3)) (@ (@ tptp.ord_less_int W2) Z3)))))
% 4.96/5.20 (assert (forall ((W2 tptp.int) (Z3 tptp.int)) (=> (or (@ (@ tptp.ord_less_int tptp.zero_zero_int) W2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z3)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 W2)) (@ tptp.nat2 Z3)) (@ (@ tptp.ord_less_eq_int W2) Z3)))))
% 4.96/5.20 (assert (forall ((W2 tptp.int) (M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W2))) (= (= (@ tptp.nat2 W2) M2) (and (=> _let_1 (= W2 (@ tptp.semiri1314217659103216013at_int M2))) (=> (not _let_1) (= M2 tptp.zero_zero_nat)))))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (W2 tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W2))) (= (= M2 (@ tptp.nat2 W2)) (and (=> _let_1 (= W2 (@ tptp.semiri1314217659103216013at_int M2))) (=> (not _let_1) (= M2 tptp.zero_zero_nat)))))))
% 4.96/5.20 (assert (forall ((P (-> tptp.nat Bool)) (I tptp.int)) (= (@ P (@ tptp.nat2 I)) (and (forall ((N tptp.nat)) (=> (= I (@ tptp.semiri1314217659103216013at_int N)) (@ P N))) (=> (@ (@ tptp.ord_less_int I) tptp.zero_zero_int) (@ P tptp.zero_zero_nat))))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (assert (forall ((Z3 tptp.int) (Z8 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z3) (=> (@ _let_1 Z8) (= (@ tptp.nat2 (@ (@ tptp.plus_plus_int Z3) Z8)) (@ (@ tptp.plus_plus_nat (@ tptp.nat2 Z3)) (@ tptp.nat2 Z8))))))))
% 4.96/5.20 (assert (forall ((Z3 tptp.int) (Z8 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z3) (= (@ tptp.nat2 (@ (@ tptp.times_times_int Z3) Z8)) (@ (@ tptp.times_times_nat (@ tptp.nat2 Z3)) (@ tptp.nat2 Z8))))))
% 4.96/5.20 (assert (= tptp.suc (lambda ((A3 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A3)) tptp.one_one_int)))))
% 4.96/5.20 (assert (forall ((P (-> tptp.real Bool)) (E2 tptp.real)) (=> (forall ((D5 tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_real D5) E) (=> (@ P D5) (@ 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))))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (assert (forall ((P (-> tptp.real Bool)) (E2 tptp.real)) (=> (forall ((D5 tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_real D5) E) (=> (@ P D5) (@ 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))))))
% 4.96/5.20 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ tptp.nat2 (@ (@ tptp.minus_minus_int X) Y)) (@ (@ tptp.minus_minus_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y))))))))
% 4.96/5.20 (assert (forall ((Z8 tptp.int) (Z3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z8) (=> (@ (@ tptp.ord_less_eq_int Z8) Z3) (= (@ tptp.nat2 (@ (@ tptp.minus_minus_int Z3) Z8)) (@ (@ tptp.minus_minus_nat (@ tptp.nat2 Z3)) (@ tptp.nat2 Z8)))))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X)) tptp.zero_zero_nat))))
% 4.96/5.20 (assert (forall ((Z3 tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z3) (= (@ tptp.nat2 (@ (@ tptp.power_power_int Z3) N2)) (@ (@ tptp.power_power_nat (@ tptp.nat2 Z3)) N2)))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) X) (=> (@ (@ tptp.ord_less_real X) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2))) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X)) N2)))))
% 4.96/5.20 (assert (forall ((X tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X)) A) (@ (@ tptp.ord_less_eq_nat X) (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real A))))))
% 4.96/5.20 (assert (= (@ tptp.nat2 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))))
% 4.96/5.20 (assert (forall ((Z3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z3) (= (@ tptp.suc (@ tptp.nat2 Z3)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int tptp.one_one_int) Z3))))))
% 4.96/5.20 (assert (forall ((W2 tptp.int) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W2) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W2)) M2) (@ (@ tptp.ord_less_int W2) (@ tptp.semiri1314217659103216013at_int M2))))))
% 4.96/5.20 (assert (forall ((Z3 tptp.int) (Z8 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z3) tptp.zero_zero_int) (= (@ tptp.nat2 (@ (@ tptp.times_times_int Z3) Z8)) (@ (@ tptp.times_times_nat (@ tptp.nat2 (@ tptp.uminus_uminus_int Z3))) (@ tptp.nat2 (@ tptp.uminus_uminus_int Z8)))))))
% 4.96/5.20 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.nat2 (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B2)))))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat A) B2))) (and (=> _let_2 (= _let_1 (@ (@ tptp.minus_minus_nat B2) A))) (=> (not _let_2) (= _let_1 (@ (@ tptp.minus_minus_nat A) B2))))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N2)) X) (=> (@ (@ tptp.ord_less_real X) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2))) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X)) N2)))))
% 4.96/5.20 (assert (forall ((Z8 tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int Z3) Z8))) (let ((_let_2 (@ tptp.nat2 Z3))) (let ((_let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ tptp.nat2 Z8)))) (let ((_let_4 (@ (@ tptp.ord_less_int Z8) 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)))))))))))
% 4.96/5.20 (assert (forall ((Z3 tptp.int) (M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z3))) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.nat2 Z3)) M2) (and (=> _let_1 (@ (@ tptp.dvd_dvd_int Z3) (@ tptp.semiri1314217659103216013at_int M2))) (=> (not _let_1) (= M2 tptp.zero_zero_nat)))))))
% 4.96/5.20 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M tptp.zero_zero_nat)) N) (@ (@ (@ tptp.if_nat (= N tptp.zero_zero_nat)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat (@ (@ tptp.modulo_modulo_nat M) _let_1)) (@ (@ tptp.modulo_modulo_nat N) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M) _let_1)) (@ (@ tptp.divide_divide_nat N) _let_1))))))))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or4665077453230672383an_nat M2) 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 M2) (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat)))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (assert (= tptp.topolo4055970368930404560y_real (lambda ((X6 (-> tptp.nat tptp.real))) (forall ((J2 tptp.nat)) (exists ((M9 tptp.nat)) (forall ((M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M9) M) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M9) N) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ X6 M)) (@ X6 N)))) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc J2)))))))))))))
% 4.96/5.20 (assert (forall ((L tptp.nat) (U tptp.nat)) (@ tptp.finite_finite_nat (@ (@ tptp.set_or4665077453230672383an_nat L) U))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat M2) (@ tptp.suc M2)) (@ (@ tptp.insert_nat M2) tptp.bot_bot_set_nat))))
% 4.96/5.20 (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))))
% 4.96/5.20 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 X)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat _let_1) (@ tptp.suc tptp.zero_zero_nat)) _let_1))))
% 4.96/5.20 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X)))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M tptp.nat)) (and (@ (@ tptp.ord_less_nat M) N2) (@ P M))) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)) (@ P X4))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ P M))) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)) (@ P X4))))))
% 4.96/5.20 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat L) (@ tptp.suc U)) (@ (@ tptp.set_or1269000886237332187st_nat L) U))))
% 4.96/5.20 (assert (= tptp.set_ord_lessThan_nat (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat)))
% 4.96/5.20 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat M2) tptp.zero_zero_nat) tptp.bot_bot_set_nat)))
% 4.96/5.20 (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))))))
% 4.96/5.20 (assert (forall ((N6 tptp.set_nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N6) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)) (@ tptp.finite_finite_nat N6))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M2))) (let ((_let_2 (@ _let_1 (@ tptp.suc N2)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat M2) N2))) (and (=> _let_3 (= _let_2 (@ (@ tptp.insert_nat N2) (@ _let_1 N2)))) (=> (not _let_3) (= _let_2 tptp.bot_bot_set_nat))))))))
% 4.96/5.20 (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))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)) (@ tptp.semiri1408675320244567234ct_nat N2))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (K tptp.num)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M2))) (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 M2) _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)))))))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M 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 M)) (not (@ _let_2 N))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M) _let_1)) (@ (@ tptp.divide_divide_nat N) _let_1)))))))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (A (-> tptp.nat tptp.nat)) (B2 (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2))) (=> (forall ((I4 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I4) J3) (=> (@ (@ tptp.ord_less_nat J3) N2) (@ (@ tptp.ord_less_eq_nat (@ A I4)) (@ A J3))))) (=> (forall ((I4 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I4) J3) (=> (@ (@ tptp.ord_less_nat J3) N2) (@ (@ tptp.ord_less_eq_nat (@ B2 J3)) (@ B2 I4))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat N2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_nat (@ A I3)) (@ B2 I3)))) _let_1))) (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat A) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat B2) _let_1))))))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (assert (forall ((L tptp.int) (U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or4662586982721622107an_int L) U))))
% 4.96/5.20 (assert (forall ((U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) U))))
% 4.96/5.20 (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))))
% 4.96/5.20 (assert (forall ((X21 Bool) (X222 Bool)) (= (@ tptp.vEBT_size_VEBT (@ (@ tptp.vEBT_Leaf X21) X222)) tptp.zero_zero_nat)))
% 4.96/5.20 (assert (forall ((U tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.set_ord_lessThan_nat U)) U)))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.ord_less_nat I3) N2)))) N2)))
% 4.96/5.20 (assert (forall ((U tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.set_ord_atMost_nat U)) (@ tptp.suc U))))
% 4.96/5.20 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or4665077453230672383an_nat L) U)) (@ (@ tptp.minus_minus_nat U) L))))
% 4.96/5.20 (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))))
% 4.96/5.20 (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))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (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))))
% 4.96/5.20 (assert (forall ((U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) U)) (@ tptp.nat2 U))))
% 4.96/5.20 (assert (forall ((Nat tptp.nat)) (= (= Nat tptp.zero_zero_nat) (@ (@ (@ tptp.case_nat_o true) (lambda ((Uu3 tptp.nat)) false)) Nat))))
% 4.96/5.20 (assert (forall ((Nat tptp.nat)) (= (not (= Nat tptp.zero_zero_nat)) (@ (@ (@ tptp.case_nat_o false) (lambda ((Uu3 tptp.nat)) true)) Nat))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (K tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se545348938243370406it_int M2) K)) N2) (and (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.bit_se1146084159140164899it_int K) (@ (@ tptp.minus_minus_nat N2) M2))))))
% 4.96/5.20 (assert (forall ((M7 tptp.set_nat) (I tptp.nat)) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) M7)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K2)) M7) (@ (@ tptp.ord_less_nat K2) I))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (and (@ (@ tptp.member_nat K2) M7) (@ (@ tptp.ord_less_nat K2) (@ tptp.suc I))))))))))
% 4.96/5.20 (assert (forall ((M7 tptp.set_nat) (I tptp.nat)) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) M7) (= (@ tptp.suc (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K2)) M7) (@ (@ tptp.ord_less_nat K2) I)))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (and (@ (@ tptp.member_nat K2) M7) (@ (@ tptp.ord_less_nat K2) (@ tptp.suc I))))))))))
% 4.96/5.20 (assert (forall ((M7 tptp.set_nat) (I tptp.nat)) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) M7) (not (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (and (@ (@ tptp.member_nat K2) M7) (@ (@ tptp.ord_less_nat K2) (@ tptp.suc I)))))) tptp.zero_zero_nat)))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (Q3 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se547839408752420682it_nat M2) Q3)) N2) (and (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.bit_se1148574629649215175it_nat Q3) (@ (@ tptp.minus_minus_nat N2) M2))))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N2) (@ (@ (@ tptp.case_nat_o false) (@ tptp.ord_less_eq_nat M2)) N2))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.ord_max_nat M2) _let_1) (@ (@ (@ tptp.case_nat_nat _let_1) (lambda ((M4 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat M4) N2)))) M2)))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.ord_max_nat _let_1) M2) (@ (@ (@ tptp.case_nat_nat _let_1) (lambda ((M4 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat N2) M4)))) M2)))))
% 4.96/5.20 (assert (forall ((N6 tptp.set_nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N6) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat N6)) N2))))
% 4.96/5.20 (assert (forall ((S2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.finite_card_nat S2)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) X4)) S2))))
% 4.96/5.20 (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 ((Z6 tptp.complex)) (= (@ (@ tptp.power_power_complex Z6) N2) C)))) N2)))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((Z6 tptp.complex)) (= (@ (@ tptp.power_power_complex Z6) N2) tptp.one_one_complex)))) N2))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M2))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((K2 tptp.nat)) K2)) (@ _let_1 N2))))))
% 4.96/5.20 (assert (= tptp.binomial (lambda ((N tptp.nat) (K2 tptp.nat)) (@ tptp.finite_card_set_nat (@ tptp.collect_set_nat (lambda ((K7 tptp.set_nat)) (and (@ (@ tptp.member_set_nat K7) (@ tptp.pow_nat (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N))) (= (@ tptp.finite_card_nat K7) K2))))))))
% 4.96/5.20 (assert (= tptp.pred (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((X24 tptp.nat)) X24))))
% 4.96/5.20 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.bezw X) tptp.zero_zero_nat) (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))))
% 4.96/5.20 (assert (= tptp.nat_prod_decode_aux (lambda ((K2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat M) K2)) (@ (@ tptp.product_Pair_nat_nat M) (@ (@ tptp.minus_minus_nat K2) M))) (@ (@ tptp.nat_prod_decode_aux _let_1) (@ (@ tptp.minus_minus_nat M) _let_1)))))))
% 4.96/5.20 (assert (forall ((X tptp.nat) (Xa2 tptp.nat) (Y tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.suc X))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat Xa2) X))) (=> (= (@ (@ tptp.nat_prod_decode_aux X) Xa2) Y) (and (=> _let_2 (= Y (@ (@ tptp.product_Pair_nat_nat Xa2) (@ (@ tptp.minus_minus_nat X) Xa2)))) (=> (not _let_2) (= Y (@ (@ tptp.nat_prod_decode_aux _let_1) (@ (@ tptp.minus_minus_nat Xa2) _let_1))))))))))
% 4.96/5.20 (assert (forall ((S2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S2) (exists ((R3 (-> tptp.nat tptp.nat))) (and (@ (@ tptp.strict1292158309912662752at_nat R3) (@ tptp.set_ord_lessThan_nat (@ tptp.finite_card_nat S2))) (forall ((N7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N7) (@ tptp.finite_card_nat S2)) (@ (@ tptp.member_nat (@ R3 N7)) S2))))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.root N2) X) (@ (@ tptp.powr_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real N2))))))))
% 4.96/5.20 (assert (forall ((X tptp.real)) (= (@ (@ tptp.root (@ tptp.suc tptp.zero_zero_nat)) X) X)))
% 4.96/5.20 (assert (forall ((X tptp.real)) (= (@ (@ tptp.root tptp.zero_zero_nat) X) tptp.zero_zero_real)))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (= (@ _let_1 X) (@ _let_1 Y)) (= X Y))))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (= (@ (@ tptp.root N2) X) tptp.zero_zero_real) (= X tptp.zero_zero_real)))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_real X) Y))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_real X) Y))))))
% 4.96/5.20 (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))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (= (@ (@ tptp.root N2) X) tptp.one_one_real) (= X tptp.one_one_real)))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_real (@ (@ tptp.root N2) X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) tptp.zero_zero_real)))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N2) X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real)))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_real (@ (@ tptp.root N2) X)) tptp.one_one_real) (@ (@ tptp.ord_less_real X) tptp.one_one_real)))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N2) X)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real)))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N2) X)) N2) X)))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_real (@ _let_1 X)) (@ _let_1 Y)))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y)))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (X tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ _let_1 (@ (@ tptp.power_power_real X) K)) (@ (@ tptp.power_power_real (@ _let_1 X)) K))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ _let_1 (@ tptp.abs_abs_real X)) (@ tptp.abs_abs_real (@ _let_1 X)))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.sgn_sgn_real (@ (@ tptp.root N2) X)) (@ tptp.sgn_sgn_real X)))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.root N2) X)))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (N6 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_nat N2) N6) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ tptp.ord_less_real (@ (@ tptp.root N6) X)) (@ (@ tptp.root N2) X)))))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.root N2) X))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (N6 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_nat N2) N6) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.root N2) X)) (@ (@ tptp.root N6) X))))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (N6 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_nat N2) N6) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N6) X)) (@ (@ tptp.root N2) X)))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N2) X)) N2) X)))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (= (@ (@ tptp.power_power_real Y) N2) X) (= (@ (@ tptp.root N2) X) Y))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.root N2) (@ (@ tptp.power_power_real X) N2)) X)))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (N6 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_nat N2) N6) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N2) X)) (@ (@ tptp.root N6) X))))))))
% 4.96/5.20 (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))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ (@ tptp.root N2) X))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real _let_1)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real _let_1)) N2)) X)))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B2) (= (@ tptp.ln_ln_real (@ (@ tptp.root N2) B2)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real B2)) (@ tptp.semiri5074537144036343181t_real N2)))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.log B2))) (=> (@ (@ 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))))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (B2 tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B2) (= (@ (@ tptp.log (@ (@ tptp.root N2) B2)) X) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.log B2) X)))))))
% 4.96/5.20 (assert (forall ((P (-> tptp.real Bool)) (N2 tptp.nat) (X tptp.real)) (= (@ P (@ (@ tptp.root N2) X)) (and (=> (= N2 tptp.zero_zero_nat) (@ P tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (forall ((Y5 tptp.real)) (=> (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y5)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y5)) N2)) X) (@ P Y5))))))))
% 4.96/5.20 (assert (= (@ tptp.complete_Sup_Sup_nat tptp.bot_bot_set_nat) tptp.zero_zero_nat))
% 4.96/5.20 (assert (forall ((K5 tptp.set_nat)) (=> (not (= K5 tptp.bot_bot_set_nat)) (@ (@ tptp.member_nat (@ tptp.complete_Inf_Inf_nat K5)) K5))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.compow_nat_nat N2) tptp.suc) (@ tptp.plus_plus_nat N2))))
% 4.96/5.20 (assert (forall ((L tptp.int) (U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or5832277885323065728an_int L) U))))
% 4.96/5.20 (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))))
% 4.96/5.20 (assert (forall ((L tptp.nat) (U tptp.nat)) (@ tptp.finite_finite_nat (@ (@ tptp.set_or5834768355832116004an_nat L) U))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc L)) U) (@ (@ tptp.set_or5834768355832116004an_nat L) U))))
% 4.96/5.20 (assert (@ (@ (@ (@ tptp.semila1623282765462674594er_nat tptp.ord_max_nat) tptp.zero_zero_nat) (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y5) X4))) (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.ord_less_nat Y5) X4))))
% 4.96/5.20 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.times_times_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X4 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 X4))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U2)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U2))))))) __flatten_var_0))) Xa2) X)))))
% 4.96/5.20 (assert (forall ((M7 tptp.set_nat)) (=> (@ tptp.finite_finite_nat M7) (= (@ tptp.gcd_Gcd_nat M7) (@ tptp.gcd_Gcd_nat (@ (@ tptp.minus_minus_set_nat M7) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))))))
% 4.96/5.20 (assert (forall ((P (-> tptp.int Bool)) (X tptp.int)) (=> (forall ((Y3 tptp.product_prod_nat_nat)) (@ P (@ tptp.abs_Integ Y3))) (@ P X))))
% 4.96/5.20 (assert (forall ((Z3 tptp.int)) (not (forall ((X5 tptp.nat) (Y3 tptp.nat)) (not (= Z3 (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat X5) Y3))))))))
% 4.96/5.20 (assert (forall ((X tptp.product_prod_nat_nat)) (= (@ tptp.nat2 (@ tptp.abs_Integ X)) (@ (@ tptp.produc6842872674320459806at_nat tptp.minus_minus_nat) X))))
% 4.96/5.20 (assert (= tptp.zero_zero_int (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat))))
% 4.96/5.20 (assert (= tptp.semiri1314217659103216013at_int (lambda ((N tptp.nat)) (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat N) tptp.zero_zero_nat)))))
% 4.96/5.20 (assert (forall ((X tptp.product_prod_nat_nat)) (= (@ tptp.uminus_uminus_int (@ tptp.abs_Integ X)) (@ tptp.abs_Integ (@ (@ tptp.produc2626176000494625587at_nat (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y5) X4))) X)))))
% 4.96/5.20 (assert (= tptp.one_one_int (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat))))
% 4.96/5.20 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((X4 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 X4) V4)) (@ (@ tptp.plus_plus_nat U2) Y5)))) __flatten_var_0))) Xa2) X))))
% 4.96/5.20 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((X4 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 X4) V4)) (@ (@ tptp.plus_plus_nat U2) Y5)))) __flatten_var_0))) Xa2) X))))
% 4.96/5.20 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.plus_plus_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X4 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 X4) U2)) (@ (@ tptp.plus_plus_nat Y5) V4)))) __flatten_var_0))) Xa2) X)))))
% 4.96/5.20 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.minus_minus_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X4 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 X4) V4)) (@ (@ tptp.plus_plus_nat Y5) U2)))) __flatten_var_0))) Xa2) X)))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (assert (= (@ tptp.num_of_nat tptp.zero_zero_nat) tptp.one))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.numeral_numeral_nat (@ tptp.num_of_nat N2)) N2))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) tptp.one_one_nat) (= (@ tptp.num_of_nat N2) tptp.one))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 M2) (=> (@ _let_1 N2) (= (@ tptp.num_of_nat (@ (@ tptp.plus_plus_nat M2) N2)) (@ (@ tptp.plus_plus_num (@ tptp.num_of_nat M2)) (@ tptp.num_of_nat N2))))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.minus_minus_nat J) (@ tptp.suc I))) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat I) J))) N2) (@ tptp.suc (@ (@ tptp.plus_plus_nat I) N2))))))
% 4.96/5.20 (assert (= tptp.ord_less_eq_int (lambda ((X4 tptp.int) (Xa3 tptp.int)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((Y5 tptp.nat) (Z6 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) Z6)))) __flatten_var_0))) (@ tptp.rep_Integ X4)) (@ tptp.rep_Integ Xa3)))))
% 4.96/5.20 (assert (= tptp.ord_less_int (lambda ((X4 tptp.int) (Xa3 tptp.int)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((Y5 tptp.nat) (Z6 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) Z6)))) __flatten_var_0))) (@ tptp.rep_Integ X4)) (@ tptp.rep_Integ Xa3)))))
% 4.96/5.20 (assert (= tptp.nat2 (lambda ((X4 tptp.int)) (@ (@ tptp.produc6842872674320459806at_nat tptp.minus_minus_nat) (@ tptp.rep_Integ X4)))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.minus_minus_nat J) I)) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat I) J))) N2) (@ tptp.suc (@ (@ tptp.plus_plus_nat I) N2))))))
% 4.96/5.20 (assert (= tptp.uminus_uminus_int (@ (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ) (@ tptp.produc2626176000494625587at_nat (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y5) X4))))))
% 4.96/5.20 (assert (= tptp.nat_prod_encode (@ tptp.produc6842872674320459806at_nat (lambda ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle (@ (@ tptp.plus_plus_nat M) N))) M)))))
% 4.96/5.20 (assert (forall ((L tptp.nat) (U tptp.nat)) (@ tptp.finite_finite_nat (@ (@ tptp.set_or6659071591806873216st_nat L) U))))
% 4.96/5.20 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or6659071591806873216st_nat L) U)) (@ (@ tptp.minus_minus_nat U) L))))
% 4.96/5.20 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc L)) U) (@ (@ tptp.set_or6659071591806873216st_nat L) U))))
% 4.96/5.20 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat A) B2)))))
% 4.96/5.20 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (@ (@ tptp.ord_less_eq_nat B2) (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat A) B2)))))
% 4.96/5.20 (assert (forall ((K tptp.nat) (M2 tptp.nat)) (= (@ tptp.nat_prod_encode (@ (@ tptp.nat_prod_decode_aux K) M2)) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle K)) M2))))
% 4.96/5.20 (assert (= tptp.times_times_int (@ (@ (@ tptp.map_fu4960017516451851995nt_int tptp.rep_Integ) (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ)) (@ tptp.produc27273713700761075at_nat (lambda ((X4 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 X4))) (@ (@ 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))))))
% 4.96/5.20 (assert (= tptp.minus_minus_int (@ (@ (@ tptp.map_fu4960017516451851995nt_int tptp.rep_Integ) (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ)) (@ tptp.produc27273713700761075at_nat (lambda ((X4 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 X4) V4)) (@ (@ tptp.plus_plus_nat Y5) U2)))) __flatten_var_0))))))
% 4.96/5.20 (assert (= tptp.plus_plus_int (@ (@ (@ tptp.map_fu4960017516451851995nt_int tptp.rep_Integ) (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ)) (@ tptp.produc27273713700761075at_nat (lambda ((X4 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 X4) U2)) (@ (@ tptp.plus_plus_nat Y5) V4)))) __flatten_var_0))))))
% 4.96/5.20 (assert (forall ((C tptp.nat) (Y tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat X) Y))) (let ((_let_2 (@ (@ tptp.ord_less_nat X) Y))) (let ((_let_3 (@ (@ tptp.ord_less_nat C) Y))) (and (=> _let_3 (= (@ (@ tptp.image_nat_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_nat I3) C))) _let_1) (@ (@ tptp.set_or4665077453230672383an_nat (@ (@ tptp.minus_minus_nat X) C)) (@ (@ tptp.minus_minus_nat Y) C)))) (=> (not _let_3) (and (=> _let_2 (= (@ (@ tptp.image_nat_nat (lambda ((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))))))))))
% 4.96/5.20 (assert (forall ((L tptp.int) (U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or6656581121297822940st_int L) U))))
% 4.96/5.20 (assert (forall ((I tptp.nat) (J tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ (@ tptp.set_or1269000886237332187st_nat I) J)) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc I)) (@ tptp.suc J)))))
% 4.96/5.20 (assert (forall ((I tptp.nat) (J tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat I) J)) (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc I)) (@ tptp.suc J)))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (assert (forall ((A2 tptp.set_nat)) (not (@ (@ tptp.member_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) A2)))))
% 4.96/5.20 (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))))
% 4.96/5.20 (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))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (assert (= tptp.semiri1316708129612266289at_nat tptp.id_nat))
% 4.96/5.20 (assert (= tptp.ord_less_int (@ (@ (@ tptp.map_fu434086159418415080_int_o tptp.rep_Integ) (@ (@ tptp.map_fu4826362097070443709at_o_o tptp.rep_Integ) tptp.id_o)) (@ tptp.produc8739625826339149834_nat_o (lambda ((X4 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 X4) V4)) (@ (@ tptp.plus_plus_nat U2) Y5)))) __flatten_var_0))))))
% 4.96/5.20 (assert (= tptp.ord_less_eq_int (@ (@ (@ tptp.map_fu434086159418415080_int_o tptp.rep_Integ) (@ (@ tptp.map_fu4826362097070443709at_o_o tptp.rep_Integ) tptp.id_o)) (@ tptp.produc8739625826339149834_nat_o (lambda ((X4 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 X4) V4)) (@ (@ tptp.plus_plus_nat U2) Y5)))) __flatten_var_0))))))
% 4.96/5.20 (assert (= tptp.finite_finite_int (lambda ((S6 tptp.set_int)) (exists ((K2 tptp.int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_int_int tptp.abs_abs_int) S6)) (@ tptp.set_ord_atMost_int K2))))))
% 4.96/5.20 (assert (= tptp.finite_finite_int (lambda ((S6 tptp.set_int)) (exists ((K2 tptp.int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_int_int tptp.abs_abs_int) S6)) (@ tptp.set_ord_lessThan_int K2))))))
% 4.96/5.20 (assert (= tptp.nat2 (@ (@ (@ tptp.map_fu2345160673673942751at_nat tptp.rep_Integ) tptp.id_nat) (@ tptp.produc6842872674320459806at_nat tptp.minus_minus_nat))))
% 4.96/5.20 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.image_nat_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat A) B2)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B2)))))
% 4.96/5.20 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.image_nat_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or4665077453230672383an_nat A) B2)) (@ (@ tptp.set_or4662586982721622107an_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B2)))))
% 4.96/5.20 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ (@ tptp.image_int_int (lambda ((X4 tptp.int)) (@ (@ tptp.plus_plus_int X4) L))) (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int U) L))) (@ (@ tptp.set_or4662586982721622107an_int L) U))))
% 4.96/5.20 (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)))))))
% 4.96/5.20 (assert (= (@ tptp.finite410649719033368117t_unit tptp.top_to1996260823553986621t_unit) tptp.one_one_nat))
% 4.96/5.20 (assert (forall ((A tptp.real)) (let ((_let_1 (@ (@ tptp.image_real_real (@ tptp.times_times_real A)) tptp.top_top_set_real))) (let ((_let_2 (= A tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 (@ (@ tptp.insert_real tptp.zero_zero_real) tptp.bot_bot_set_real))) (=> (not _let_2) (= _let_1 tptp.top_top_set_real)))))))
% 4.96/5.20 (assert (not (@ tptp.finite_finite_nat tptp.top_top_set_nat)))
% 4.96/5.20 (assert (not (@ tptp.finite_finite_nat tptp.top_top_set_nat)))
% 4.96/5.20 (assert (not (@ tptp.finite_finite_int tptp.top_top_set_int)))
% 4.96/5.20 (assert (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat tptp.set_ord_lessThan_nat) tptp.top_top_set_nat)) tptp.top_top_set_nat))
% 4.96/5.20 (assert (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat tptp.set_ord_atMost_nat) tptp.top_top_set_nat)) tptp.top_top_set_nat))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.member_int (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.image_int_int tptp.abs_abs_int) tptp.top_top_set_int))))
% 4.96/5.20 (assert (= tptp.top_top_set_nat (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.image_nat_nat (lambda ((M tptp.nat)) (@ (@ tptp.modulo_modulo_nat M) N2))) tptp.top_top_set_nat) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)))))
% 4.96/5.20 (assert (= tptp.root (lambda ((N tptp.nat) (X4 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)))) X4)))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (X tptp.real) (D6 tptp.real)) (let ((_let_1 (@ tptp.root N2))) (let ((_let_2 (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.power_power_real (@ _let_1 X)) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))))))) (let ((_let_3 (= D6 _let_2))) (let ((_let_4 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (not (= X tptp.zero_zero_real)) (=> (=> _let_4 (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) _let_3)) (=> (=> _let_4 (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (= D6 (@ tptp.uminus_uminus_real _let_2)))) (=> (=> (not _let_4) _let_3) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) D6) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))))))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N2))) (@ (@ tptp.power_power_real (@ _let_1 X)) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))))))))
% 4.96/5.20 (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 ((X4 tptp.real)) (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real X4) (@ 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)))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.power_power_real (@ _let_1 X)) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))))
% 4.96/5.20 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (X tptp.real) (N2 tptp.nat)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M3 tptp.nat) (X5 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M3)) (@ (@ Diff (@ tptp.suc M3)) X5)) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real))) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T6)) (@ tptp.abs_abs_real X)) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M))) (@ (@ tptp.power_power_real X) M)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T6)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2))))))))))
% 4.96/5.20 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (X tptp.real) (N2 tptp.nat)) (=> (and (= (@ Diff tptp.zero_zero_nat) F) (forall ((M3 tptp.nat) (X5 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M3)) (@ (@ Diff (@ tptp.suc M3)) X5)) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)))) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T6)) (@ tptp.abs_abs_real X)) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M))) (@ (@ tptp.power_power_real X) M)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T6)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2)))))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (=> (not (= X tptp.zero_zero_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.power_power_real (@ _let_1 X)) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))))
% 4.96/5.20 (assert (forall ((H2 tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real H2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M3 tptp.nat) (T6 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M3) N2) (@ (@ tptp.ord_less_eq_real H2) T6) (@ (@ tptp.ord_less_eq_real T6) tptp.zero_zero_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M3)) (@ (@ Diff (@ tptp.suc M3)) T6)) (@ (@ tptp.topolo2177554685111907308n_real T6) tptp.top_top_set_real)))) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_real H2) T6) (@ (@ tptp.ord_less_real T6) tptp.zero_zero_real) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M))) (@ (@ tptp.power_power_real H2) M)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T6)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real H2) N2))))))))))))
% 4.96/5.20 (assert (forall ((H2 tptp.real) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H2) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M3 tptp.nat) (T6 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M3) N2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_eq_real T6) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M3)) (@ (@ Diff (@ tptp.suc M3)) T6)) (@ (@ tptp.topolo2177554685111907308n_real T6) tptp.top_top_set_real)))) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_eq_real T6) H2) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M))) (@ (@ tptp.power_power_real H2) M)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T6)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real H2) N2)))))))))))
% 4.96/5.20 (assert (forall ((H2 tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M3 tptp.nat) (T6 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M3) N2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_eq_real T6) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M3)) (@ (@ Diff (@ tptp.suc M3)) T6)) (@ (@ tptp.topolo2177554685111907308n_real T6) tptp.top_top_set_real)))) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_real T6) H2) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M))) (@ (@ tptp.power_power_real H2) M)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T6)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real H2) N2))))))))))))
% 4.96/5.20 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N2 tptp.nat) (X tptp.real)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (not (= X tptp.zero_zero_real)) (=> (forall ((M3 tptp.nat) (X5 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M3)) (@ (@ Diff (@ tptp.suc M3)) X5)) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real))) (exists ((T6 tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real T6))) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ tptp.abs_abs_real X)) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M))) (@ (@ tptp.power_power_real X) M)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T6)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2)))))))))))))
% 4.96/5.20 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N2 tptp.nat) (X tptp.real)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M3 tptp.nat) (T6 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M3) N2) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T6)) (@ tptp.abs_abs_real X))) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M3)) (@ (@ Diff (@ tptp.suc M3)) T6)) (@ (@ tptp.topolo2177554685111907308n_real T6) tptp.top_top_set_real)))) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T6)) (@ tptp.abs_abs_real X)) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M))) (@ (@ tptp.power_power_real X) M)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T6)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2))))))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B2 tptp.real) (C tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M3 tptp.nat) (T6 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M3) N2) (@ (@ tptp.ord_less_eq_real A) T6) (@ (@ tptp.ord_less_eq_real T6) B2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M3)) (@ (@ Diff (@ tptp.suc M3)) T6)) (@ (@ tptp.topolo2177554685111907308n_real T6) tptp.top_top_set_real)))) (=> (@ _let_1 C) (=> (@ (@ tptp.ord_less_eq_real C) B2) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) B2) (=> (not (= X C)) (exists ((T6 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real T6))) (let ((_let_2 (@ tptp.ord_less_real X))) (let ((_let_3 (@ _let_2 C))) (and (=> _let_3 (and (@ _let_2 T6) (@ _let_1 C))) (=> (not _let_3) (and (@ (@ tptp.ord_less_real C) T6) (@ _let_1 X))) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M) C)) (@ tptp.semiri2265585572941072030t_real M))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) C)) M)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T6)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) C)) N2))))))))))))))))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M3 tptp.nat) (T6 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M3) N2) (@ (@ tptp.ord_less_eq_real A) T6) (@ (@ tptp.ord_less_eq_real T6) B2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M3)) (@ (@ Diff (@ tptp.suc M3)) T6)) (@ (@ tptp.topolo2177554685111907308n_real T6) tptp.top_top_set_real)))) (=> (@ (@ tptp.ord_less_eq_real A) C) (=> (@ (@ tptp.ord_less_real C) B2) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_real C) T6) (@ (@ tptp.ord_less_real T6) B2) (= (@ F B2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M) C)) (@ tptp.semiri2265585572941072030t_real M))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real B2) C)) M)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T6)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real B2) C)) N2)))))))))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M3 tptp.nat) (T6 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M3) N2) (@ (@ tptp.ord_less_eq_real A) T6) (@ (@ tptp.ord_less_eq_real T6) B2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M3)) (@ (@ Diff (@ tptp.suc M3)) T6)) (@ (@ tptp.topolo2177554685111907308n_real T6) tptp.top_top_set_real)))) (=> (@ (@ tptp.ord_less_real A) C) (=> (@ (@ tptp.ord_less_eq_real C) B2) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_real A) T6) (@ (@ tptp.ord_less_real T6) C) (= (@ F A) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M) C)) (@ tptp.semiri2265585572941072030t_real M))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real A) C)) M)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T6)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real A) C)) N2)))))))))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (H2 tptp.real) (Diff (-> tptp.nat tptp.real tptp.real)) (K tptp.nat) (B tptp.real)) (=> (forall ((M3 tptp.nat) (T6 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M3) N2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_eq_real T6) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M3)) (@ (@ Diff (@ tptp.suc M3)) T6)) (@ (@ tptp.topolo2177554685111907308n_real T6) tptp.top_top_set_real)))) (=> (= N2 (@ tptp.suc K)) (forall ((M5 tptp.nat) (T7 tptp.real)) (let ((_let_1 (@ tptp.suc M5))) (let ((_let_2 (@ (@ tptp.minus_minus_nat N2) _let_1))) (=> (and (@ (@ tptp.ord_less_nat M5) N2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T7) (@ (@ tptp.ord_less_eq_real T7) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((U2 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N2) M5))) (@ (@ tptp.minus_minus_real (@ (@ Diff M5) U2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((P6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff (@ (@ tptp.plus_plus_nat M5) P6)) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real P6))) (@ (@ tptp.power_power_real U2) P6)))) (@ tptp.set_ord_lessThan_nat _let_1))) (@ (@ tptp.times_times_real B) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real U2) _let_1)) (@ tptp.semiri2265585572941072030t_real _let_1)))))))) (@ (@ tptp.minus_minus_real (@ (@ Diff _let_1) T7)) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((P6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff (@ (@ tptp.plus_plus_nat (@ tptp.suc M5)) P6)) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real P6))) (@ (@ tptp.power_power_real T7) P6)))) (@ tptp.set_ord_lessThan_nat _let_2))) (@ (@ tptp.times_times_real B) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real T7) _let_2)) (@ tptp.semiri2265585572941072030t_real _let_2)))))) (@ (@ tptp.topolo2177554685111907308n_real T7) tptp.top_top_set_real))))))))))
% 4.96/5.20 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X9 tptp.real)) (@ tptp.suminf_real (lambda ((K2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K2)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X9) _let_1)))))))) (@ tptp.suminf_real (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K2)) (@ (@ tptp.power_power_real X) (@ (@ tptp.times_times_nat K2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (X tptp.real) (S tptp.set_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X4 tptp.real)) (@ (@ tptp.power_power_real X4) N2))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.power_power_real X) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))))) (@ (@ tptp.topolo2177554685111907308n_real X) S))))
% 4.96/5.20 (assert (forall ((M7 tptp.set_nat)) (=> (@ tptp.finite_finite_nat M7) (=> (not (= M7 tptp.bot_bot_set_nat)) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) M7)) (= (@ tptp.gcd_Gcd_nat M7) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.image_nat_set_nat (lambda ((M tptp.nat)) (@ tptp.collect_nat (lambda ((D4 tptp.nat)) (@ (@ tptp.dvd_dvd_nat D4) M))))) M7)))))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((D4 tptp.nat)) (@ (@ tptp.dvd_dvd_nat D4) N2)))) N2))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (assert (= tptp.complete_Sup_Sup_nat (lambda ((X6 tptp.set_nat)) (@ (@ (@ tptp.if_nat (= X6 tptp.bot_bot_set_nat)) tptp.zero_zero_nat) (@ tptp.lattic8265883725875713057ax_nat X6)))))
% 4.96/5.20 (assert (= tptp.divide_divide_nat (lambda ((M tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_nat (= N tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat K2) N)) M))))))))
% 4.96/5.20 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (=> (@ (@ tptp.ord_less_real (@ A tptp.zero_zero_nat)) tptp.zero_zero_real) (forall ((N7 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N7))) (@ (@ tptp.member_real (@ tptp.suminf_real (lambda ((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)))))))))))
% 4.96/5.20 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ A tptp.zero_zero_nat)) (forall ((N7 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N7))) (@ (@ tptp.member_real (@ tptp.suminf_real (lambda ((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))))))))))))
% 4.96/5.20 (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)))))))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (assert (not (= tptp.at_top_nat tptp.bot_bot_filter_nat)))
% 4.96/5.20 (assert (@ (@ (@ tptp.filterlim_nat_nat tptp.suc) tptp.at_top_nat) tptp.at_top_nat))
% 4.96/5.20 (assert (forall ((C tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ (@ tptp.filterlim_nat_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.times_times_nat X4) C))) tptp.at_top_nat) tptp.at_top_nat))))
% 4.96/5.20 (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))))
% 4.96/5.20 (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 ((N7 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N7)) L4)) (@ (@ (@ tptp.filterlim_nat_real F) _let_1) tptp.at_top_nat) (forall ((N7 tptp.nat)) (@ (@ tptp.ord_less_eq_real L4) (@ G N7))) (@ (@ (@ tptp.filterlim_nat_real G) _let_1) tptp.at_top_nat))))))))))
% 4.96/5.20 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((R3 tptp.real)) (exists ((N8 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N3) (@ (@ tptp.ord_less_real R3) (@ X8 N3)))))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ tptp.inverse_inverse_real (@ X8 N)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 4.96/5.20 (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))
% 4.96/5.20 (assert (forall ((R2 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_real R2) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N)))))) (@ tptp.topolo2815343760600316023s_real R2)) tptp.at_top_nat)))
% 4.96/5.20 (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 ((N7 tptp.nat)) (@ (@ tptp.ord_less_eq_real L) (@ (@ tptp.plus_plus_real (@ F N7)) E))))) (@ (@ (@ tptp.filterlim_nat_real F) (@ tptp.topolo2815343760600316023s_real L)) tptp.at_top_nat))))))
% 4.96/5.20 (assert (forall ((R2 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_real R2) (@ tptp.uminus_uminus_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N))))))) (@ tptp.topolo2815343760600316023s_real R2)) tptp.at_top_nat)))
% 4.96/5.20 (assert (forall ((R2 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real R2) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N)))))))) (@ tptp.topolo2815343760600316023s_real R2)) tptp.at_top_nat)))
% 4.96/5.20 (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)))))))))
% 4.96/5.20 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1))))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 4.96/5.20 (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))))))))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N3))) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (exists ((L4 tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real L4))) (and (forall ((N7 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((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))) N7)))) 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 ((N7 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))) N7)) 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)))))))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (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))))
% 4.96/5.20 (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))))
% 4.96/5.20 (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))))
% 4.96/5.20 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat P) tptp.at_top_nat) (exists ((N5 tptp.nat)) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N5) N) (@ P N)))))))
% 4.96/5.20 (assert (forall ((F3 tptp.filter_nat)) (= (@ (@ tptp.ord_le2510731241096832064er_nat F3) tptp.at_top_nat) (forall ((N5 tptp.nat)) (@ (@ tptp.eventually_nat (@ tptp.ord_less_eq_nat N5)) F3)))))
% 4.96/5.20 (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))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (F (-> tptp.real tptp.real)) (F3 tptp.filter_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_bot_real) F3) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (@ (@ (@ tptp.filterlim_real_real (lambda ((X4 tptp.real)) (@ (@ tptp.power_power_real (@ F X4)) N2))) tptp.at_top_real) F3))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (F (-> tptp.real tptp.real)) (F3 tptp.filter_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_bot_real) F3) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ (@ (@ tptp.filterlim_real_real (lambda ((X4 tptp.real)) (@ (@ tptp.power_power_real (@ F X4)) N2))) tptp.at_bot_real) F3))))))
% 4.96/5.20 (assert (let ((_let_1 (@ (@ tptp.comp_nat_nat_nat tptp.suc) tptp.suc))) (= _let_1 _let_1)))
% 4.96/5.20 (assert (forall ((S2 tptp.set_int)) (= (not (@ tptp.finite_finite_int S2)) (not (@ tptp.finite_finite_nat (@ (@ tptp.image_int_nat (@ (@ tptp.comp_int_nat_int tptp.nat2) tptp.abs_abs_int)) S2))))))
% 4.96/5.20 (assert (@ tptp.order_mono_nat_nat tptp.suc))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ tptp.order_mono_nat_nat (@ tptp.times_times_nat N2)))))
% 4.96/5.20 (assert (= (@ tptp.set_or1210151606488870762an_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat)))
% 4.96/5.20 (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))))))
% 4.96/5.20 (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 ((M tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat K) M)) M))))))
% 4.96/5.20 (assert (= (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.image_nat_set_nat tptp.set_or1210151606488870762an_nat) tptp.top_top_set_nat)) tptp.bot_bot_set_nat))
% 4.96/5.20 (assert (= (@ tptp.set_ord_atLeast_nat tptp.zero_zero_nat) tptp.top_top_set_nat))
% 4.96/5.20 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_atLeast_nat (@ tptp.suc K)) (@ tptp.set_or1210151606488870762an_nat K))))
% 4.96/5.20 (assert (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat tptp.set_ord_atLeast_nat) tptp.top_top_set_nat)) tptp.top_top_set_nat))
% 4.96/5.20 (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)))))
% 4.96/5.20 (assert (= (@ (@ tptp.image_int_int tptp.abs_abs_int) tptp.top_top_set_int) tptp.semiring_1_Nats_int))
% 4.96/5.20 (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))))
% 4.96/5.20 (assert (@ tptp.fun_is_measure_int (@ (@ tptp.comp_int_nat_int tptp.nat2) tptp.abs_abs_int)))
% 4.96/5.20 (assert (forall ((N6 tptp.set_nat)) (@ (@ tptp.inj_on_nat_nat tptp.suc) N6)))
% 4.96/5.20 (assert (forall ((N6 tptp.set_nat) (K tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.member_nat N3) N6) (@ (@ tptp.ord_less_eq_nat K) N3))) (@ (@ tptp.inj_on_nat_nat (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_nat N) K))) N6))))
% 4.96/5.20 (assert (@ (@ tptp.inj_on_set_nat_nat tptp.nat_set_encode) (@ tptp.collect_set_nat tptp.finite_finite_nat)))
% 4.96/5.20 (assert (= tptp.pred_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((M tptp.nat) (N tptp.nat)) (= N (@ tptp.suc M)))))))
% 4.96/5.20 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_valid X) Xa2)) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (= Xa2 tptp.one_one_nat)) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) Summary2)) (and (= Deg2 Xa2) (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_VEBT_valid X5) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X6))) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X6))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((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 ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I3)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I3))))) (=> _let_2 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X6)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X4) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X4) (and (@ (@ tptp.ord_less_nat Mi3) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma3)))))))))))))) Mima)))))))))))
% 4.96/5.20 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid X) Xa2) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (not (= Xa2 tptp.one_one_nat))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) Summary2)) (not (and (= Deg2 Xa2) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_VEBT_valid X2) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X6))) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X6))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((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 ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I3)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I3))))) (=> _let_2 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X6)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X4) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X4) (and (@ (@ tptp.ord_less_nat Mi3) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma3)))))))))))))) Mima))))))))))))
% 4.96/5.20 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_valid X) Xa2) Y) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (= Y (not (= Xa2 tptp.one_one_nat)))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) Summary2)) (= Y (not (and (= Deg2 Xa2) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_VEBT_valid X4) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X6))) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X6))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((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 ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I3)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I3))))) (=> _let_2 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X6)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X4) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X4) (and (@ (@ tptp.ord_less_nat Mi3) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma3)))))))))))))) Mima)))))))))))))
% 4.96/5.20 (assert (forall ((Mima2 tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (Deg3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg) (@ (@ tptp.divide_divide_nat Deg) _let_1)))) (= (@ (@ tptp.vEBT_VEBT_valid (@ (@ (@ (@ tptp.vEBT_Node Mima2) Deg) TreeList2) Summary)) Deg3) (and (= Deg Deg3) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_VEBT_valid X4) (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X6))) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X6))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg)) (forall ((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 ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I3))))) (=> _let_2 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X6)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg) _let_1)) TreeList2) Ma3) (forall ((X4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X4) (@ (@ tptp.power_power_nat _let_1) Deg)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg) _let_1)) TreeList2) X4) (and (@ (@ tptp.ord_less_nat Mi3) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma3)))))))))))))) Mima2)))))))
% 4.96/5.20 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_valid X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (=> (= Y (= Xa2 tptp.one_one_nat)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) Summary2))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_2)))) (=> (= X _let_1) (=> (= Y (and (= Deg2 Xa2) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_VEBT_valid X4) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_3) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat _let_2) _let_3)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X6))) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X6))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((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 ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I3)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I3))))) (=> _let_2 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X6)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X4) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X4) (and (@ (@ tptp.ord_less_nat Mi3) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma3)))))))))))))) Mima))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))))))))))))
% 4.96/5.20 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid X) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)) (not (= Xa2 tptp.one_one_nat)))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (let ((_let_3 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) Summary2))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (= Deg2 Xa2) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_VEBT_valid X2) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X6))) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X6))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((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 ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I3)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I3))))) (=> _let_2 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X6)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X4) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X4) (and (@ (@ tptp.ord_less_nat Mi3) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma3)))))))))))))) Mima)))))))))))))))
% 4.96/5.20 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_valid X) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)) (= Xa2 tptp.one_one_nat))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (let ((_let_3 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) Summary2))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (and (= Deg2 Xa2) (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_VEBT_valid X5) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X6))) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X6))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((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 ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I3)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I3))))) (=> _let_2 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X6)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X4) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X4) (and (@ (@ tptp.ord_less_nat Mi3) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma3)))))))))))))) Mima))))))))))))))
% 4.96/5.20 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat J) K))) (let ((_let_2 (@ tptp.set_or4665077453230672383an_nat I))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ _let_2 _let_1) (@ (@ tptp.sup_sup_set_nat (@ _let_2 J)) (@ (@ tptp.set_or4665077453230672383an_nat J) _let_1))))))))
% 4.96/5.20 (assert (= tptp.sup_sup_int tptp.ord_max_int))
% 4.96/5.20 (assert (= tptp.sup_sup_nat tptp.ord_max_nat))
% 4.96/5.20 (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))))))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat M2) N2)) (@ tptp.transi6264000038957366511cl_nat tptp.pred_nat)) (@ (@ tptp.ord_less_nat M2) N2))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat M2) N2)) (@ tptp.transi2905341329935302413cl_nat tptp.pred_nat)) (@ (@ tptp.ord_less_eq_nat M2) N2))))
% 4.96/5.20 (assert (= tptp.condit2214826472909112428ve_nat tptp.finite_finite_nat))
% 4.96/5.20 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.bit_take_bit_num tptp.zero_zero_nat) M2) tptp.none_num)))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N2)) tptp.one) (@ tptp.some_num tptp.one))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (M2 tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N2)) (@ tptp.bit0 M2)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q5 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q5)))) (@ (@ tptp.bit_take_bit_num N2) M2)))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (M2 tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N2)) (@ tptp.bit1 M2)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num N2) M2))))))
% 4.96/5.20 (assert (= tptp.bit_take_bit_num (lambda ((N tptp.nat) (M tptp.num)) (let ((_let_1 (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.numeral_numeral_nat M)))) (@ (@ (@ tptp.if_option_num (= _let_1 tptp.zero_zero_nat)) tptp.none_num) (@ tptp.some_num (@ tptp.num_of_nat _let_1)))))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ tptp.suc M2)) (@ tptp.suc N2)) (@ tptp.suc (@ (@ tptp.ord_min_nat M2) N2)))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_min_nat tptp.zero_zero_nat) N2) tptp.zero_zero_nat)))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_min_nat N2) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 4.96/5.20 (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)))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (I tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ (@ tptp.minus_minus_nat M2) I)) (@ (@ tptp.minus_minus_nat N2) I)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.ord_min_nat M2) N2)) I))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (Q3 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.ord_min_nat M2) N2)) Q3) (@ (@ tptp.ord_min_nat (@ (@ tptp.times_times_nat M2) Q3)) (@ (@ tptp.times_times_nat N2) Q3)))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (Q3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M2))) (= (@ _let_1 (@ (@ tptp.ord_min_nat N2) Q3)) (@ (@ tptp.ord_min_nat (@ _let_1 N2)) (@ _let_1 Q3))))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_min_nat M2) (@ tptp.suc N2)) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((M4 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_min_nat M4) N2)))) M2))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ tptp.suc N2)) M2) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((M4 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_min_nat N2) M4)))) M2))))
% 4.96/5.20 (assert (= tptp.inf_inf_nat tptp.ord_min_nat))
% 4.96/5.20 (assert (= tptp.inf_inf_int tptp.ord_min_int))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ (@ tptp.bij_betw_nat_complex (lambda ((K2 tptp.nat)) (@ tptp.cis (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ tptp.semiri5074537144036343181t_real K2))) (@ tptp.semiri5074537144036343181t_real N2))))) (@ tptp.set_ord_lessThan_nat N2)) (@ tptp.collect_complex (lambda ((Z6 tptp.complex)) (= (@ (@ tptp.power_power_complex Z6) N2) tptp.one_one_complex)))))))
% 4.96/5.20 (assert (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.suc I))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) J) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat I) J)) (@ (@ tptp.cons_nat _let_1) (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat _let_1) J))))))))
% 4.96/5.20 (assert (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.suc I))) (=> (@ (@ tptp.ord_less_nat _let_1) J) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat I) J)) (@ (@ tptp.cons_nat _let_1) (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat _let_1) J))))))))
% 4.96/5.20 (assert (forall ((M7 tptp.set_nat) (N6 tptp.set_nat)) (= (@ (@ (@ tptp.bij_betw_nat_nat tptp.suc) M7) N6) (= (@ (@ tptp.image_nat_nat tptp.suc) M7) N6))))
% 4.96/5.20 (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 ((Z6 tptp.complex)) (= (@ (@ tptp.power_power_complex Z6) N2) tptp.one_one_complex)))) (@ tptp.collect_complex (lambda ((Z6 tptp.complex)) (= (@ (@ tptp.power_power_complex Z6) N2) C))))))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (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))))))
% 4.96/5.20 (assert (forall ((X tptp.list_nat) (Y tptp.nat)) (=> (= (@ tptp.nat_list_encode X) Y) (=> (=> (= X tptp.nil_nat) (not (= Y tptp.zero_zero_nat))) (not (forall ((X5 tptp.nat) (Xs2 tptp.list_nat)) (=> (= X (@ (@ tptp.cons_nat X5) Xs2)) (not (= Y (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X5) (@ tptp.nat_list_encode Xs2)))))))))))))
% 4.96/5.20 (assert (= (@ tptp.nat_list_encode tptp.nil_nat) tptp.zero_zero_nat))
% 4.96/5.20 (assert (forall ((X tptp.nat) (Xs tptp.list_nat)) (= (@ tptp.nat_list_encode (@ (@ tptp.cons_nat X) Xs)) (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X) (@ tptp.nat_list_encode Xs)))))))
% 4.96/5.20 (assert (= tptp.upto_aux (lambda ((I3 tptp.int) (J2 tptp.int) (Js tptp.list_int)) (@ (@ (@ tptp.if_list_int (@ (@ tptp.ord_less_int J2) I3)) Js) (@ (@ (@ tptp.upto_aux I3) (@ (@ tptp.minus_minus_int J2) tptp.one_one_int)) (@ (@ tptp.cons_int J2) Js))))))
% 4.96/5.20 (assert (forall ((I tptp.int) (J tptp.int)) (let ((_let_1 (@ (@ tptp.upto I) J))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int I) J))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int I) J)) (and (=> _let_2 (= _let_1 (@ (@ tptp.cons_int I) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I) tptp.one_one_int)) J)))) (=> (not _let_2) (= _let_1 tptp.nil_int))))))))
% 4.96/5.20 (assert (forall ((X tptp.int) (Xa2 tptp.int) (Y tptp.list_int)) (let ((_let_1 (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int X) Xa2)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int X) Xa2))) (=> (= (@ (@ tptp.upto X) Xa2) Y) (=> _let_1 (not (=> (and (=> _let_2 (= Y (@ (@ tptp.cons_int X) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int X) tptp.one_one_int)) Xa2)))) (=> (not _let_2) (= Y tptp.nil_int))) (not _let_1)))))))))
% 4.96/5.20 (assert (forall ((I tptp.int) (J tptp.int)) (= (= (@ (@ tptp.upto I) J) tptp.nil_int) (@ (@ tptp.ord_less_int J) I))))
% 4.96/5.20 (assert (forall ((I tptp.int) (J tptp.int)) (= (= tptp.nil_int (@ (@ tptp.upto I) J)) (@ (@ tptp.ord_less_int J) I))))
% 4.96/5.20 (assert (forall ((J tptp.int) (I tptp.int)) (=> (@ (@ tptp.ord_less_int J) I) (= (@ (@ tptp.upto I) J) tptp.nil_int))))
% 4.96/5.20 (assert (forall ((I tptp.int)) (= (@ (@ tptp.upto I) I) (@ (@ tptp.cons_int I) tptp.nil_int))))
% 4.96/5.20 (assert (forall ((I tptp.int) (K tptp.nat) (J tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int I) (@ tptp.semiri1314217659103216013at_int K)))) (=> (@ (@ tptp.ord_less_eq_int _let_1) J) (= (@ (@ tptp.nth_int (@ (@ tptp.upto I) J)) K) _let_1)))))
% 4.96/5.20 (assert (forall ((I tptp.int) (J tptp.int)) (= (@ tptp.size_size_list_int (@ (@ tptp.upto I) J)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int J) I)) tptp.one_one_int)))))
% 4.96/5.20 (assert (forall ((M2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.numeral_numeral_int M2))) (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)))))))))
% 4.96/5.20 (assert (forall ((M2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2)))) (let ((_let_2 (@ tptp.numeral_numeral_int M2))) (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)))))))))
% 4.96/5.20 (assert (forall ((M2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2)))) (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)))))))))
% 4.96/5.20 (assert (forall ((M2 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 M2)))) (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)))))))))
% 4.96/5.20 (assert (= tptp.upto (lambda ((I3 tptp.int) (J2 tptp.int)) (@ (@ (@ tptp.upto_aux I3) J2) tptp.nil_int))))
% 4.96/5.20 (assert (= tptp.upto_aux (lambda ((I3 tptp.int) (J2 tptp.int) (__flatten_var_0 tptp.list_int)) (@ (@ tptp.append_int (@ (@ tptp.upto I3) J2)) __flatten_var_0))))
% 4.96/5.20 (assert (forall ((I tptp.int) (J tptp.int)) (@ tptp.distinct_int (@ (@ tptp.upto I) J))))
% 4.96/5.20 (assert (= tptp.set_or1266510415728281911st_int (lambda ((I3 tptp.int) (J2 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto I3) J2)))))
% 4.96/5.20 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I))) (=> (@ (@ tptp.ord_less_eq_int I) J) (=> (@ (@ tptp.ord_less_eq_int J) K) (= (@ _let_1 K) (@ (@ tptp.append_int (@ _let_1 J)) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int J) tptp.one_one_int)) K))))))))
% 4.96/5.20 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I))) (=> (@ (@ tptp.ord_less_eq_int I) J) (=> (@ (@ tptp.ord_less_eq_int J) K) (= (@ _let_1 K) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J) tptp.one_one_int))) (@ (@ tptp.upto J) K))))))))
% 4.96/5.20 (assert (= tptp.set_or4662586982721622107an_int (lambda ((I3 tptp.int) (J2 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto I3) (@ (@ tptp.minus_minus_int J2) tptp.one_one_int))))))
% 4.96/5.20 (assert (= tptp.set_or6656581121297822940st_int (lambda ((I3 tptp.int) (J2 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I3) tptp.one_one_int)) J2)))))
% 4.96/5.20 (assert (= tptp.upto (lambda ((I3 tptp.int) (J2 tptp.int)) (@ (@ (@ tptp.if_list_int (@ (@ tptp.ord_less_eq_int I3) J2)) (@ (@ tptp.cons_int I3) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I3) tptp.one_one_int)) J2))) tptp.nil_int))))
% 4.96/5.20 (assert (forall ((X tptp.int) (Xa2 tptp.int) (Y tptp.list_int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int X) Xa2))) (=> (= (@ (@ tptp.upto X) Xa2) Y) (and (=> _let_1 (= Y (@ (@ tptp.cons_int X) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int X) tptp.one_one_int)) Xa2)))) (=> (not _let_1) (= Y tptp.nil_int)))))))
% 4.96/5.20 (assert (forall ((I tptp.int) (J tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I) J) (= (@ (@ tptp.upto I) J) (@ (@ tptp.cons_int I) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I) tptp.one_one_int)) J))))))
% 4.96/5.20 (assert (forall ((I tptp.int) (J tptp.int)) (let ((_let_1 (@ tptp.upto I))) (=> (@ (@ tptp.ord_less_eq_int I) J) (= (@ _let_1 J) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J) tptp.one_one_int))) (@ (@ tptp.cons_int J) tptp.nil_int)))))))
% 4.96/5.20 (assert (= tptp.set_or5832277885323065728an_int (lambda ((I3 tptp.int) (J2 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I3) tptp.one_one_int)) (@ (@ tptp.minus_minus_int J2) tptp.one_one_int))))))
% 4.96/5.20 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I))) (=> (@ (@ tptp.ord_less_eq_int I) J) (=> (@ (@ tptp.ord_less_eq_int J) K) (= (@ _let_1 K) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J) tptp.one_one_int))) (@ (@ tptp.cons_int J) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int J) tptp.one_one_int)) K)))))))))
% 4.96/5.20 (assert (forall ((X tptp.list_nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.accp_list_nat tptp.nat_list_encode_rel))) (=> (= (@ tptp.nat_list_encode X) Y) (=> (@ _let_1 X) (=> (=> (= X tptp.nil_nat) (=> (= Y tptp.zero_zero_nat) (not (@ _let_1 tptp.nil_nat)))) (not (forall ((X5 tptp.nat) (Xs2 tptp.list_nat)) (let ((_let_1 (@ (@ tptp.cons_nat X5) Xs2))) (=> (= X _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)))))))))))))
% 4.96/5.20 (assert (forall ((M2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (let ((_let_2 (@ tptp.numeral_numeral_nat M2))) (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)))))))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.upt M2) N2))) (= (@ tptp.remdups_nat _let_1) _let_1))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ tptp.tl_nat (@ (@ tptp.upt M2) N2)) (@ (@ tptp.upt (@ tptp.suc M2)) N2))))
% 4.96/5.20 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (= (@ tptp.hd_nat (@ (@ tptp.upt I) J)) I))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (I tptp.nat) (J tptp.nat)) (= (@ (@ tptp.drop_nat M2) (@ (@ tptp.upt I) J)) (@ (@ tptp.upt (@ (@ tptp.plus_plus_nat I) M2)) J))))
% 4.96/5.20 (assert (forall ((I tptp.nat) (J tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.upt I) J)) (@ (@ tptp.minus_minus_nat J) I))))
% 4.96/5.20 (assert (forall ((I tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I) M2))) (let ((_let_2 (@ tptp.upt I))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) N2) (= (@ (@ tptp.take_nat M2) (@ _let_2 N2)) (@ _let_2 _let_1)))))))
% 4.96/5.20 (assert (forall ((J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (@ (@ tptp.upt I) J) tptp.nil_nat))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or4665077453230672383an_nat M2) N2)) (@ (@ tptp.upt M2) N2))))
% 4.96/5.20 (assert (forall ((I tptp.nat) (J tptp.nat)) (= (= (@ (@ tptp.upt I) J) tptp.nil_nat) (or (= J tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat J) I)))))
% 4.96/5.20 (assert (forall ((I tptp.nat) (K tptp.nat) (J tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I) K))) (=> (@ (@ tptp.ord_less_nat _let_1) J) (= (@ (@ tptp.nth_nat (@ (@ tptp.upt I) J)) K) _let_1)))))
% 4.96/5.20 (assert (forall ((I tptp.nat)) (= (@ (@ tptp.upt I) tptp.zero_zero_nat) tptp.nil_nat)))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (N2 tptp.nat) (Ns tptp.list_nat) (Q3 tptp.nat)) (let ((_let_1 (@ (@ tptp.cons_nat N2) Ns))) (= (= (@ (@ tptp.cons_nat M2) _let_1) (@ (@ tptp.upt M2) Q3)) (= _let_1 (@ (@ tptp.upt (@ tptp.suc M2)) Q3))))))
% 4.96/5.20 (assert (= tptp.set_or6659071591806873216st_nat (lambda ((N tptp.nat) (M tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N)) (@ tptp.suc M))))))
% 4.96/5.20 (assert (forall ((I tptp.nat) (J tptp.nat)) (@ tptp.distinct_nat (@ (@ tptp.upt I) J))))
% 4.96/5.20 (assert (= tptp.set_or1269000886237332187st_nat (lambda ((N tptp.nat) (M tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt N) (@ tptp.suc M))))))
% 4.96/5.20 (assert (= tptp.set_or4665077453230672383an_nat (lambda ((I3 tptp.nat) (J2 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt I3) J2)))))
% 4.96/5.20 (assert (= tptp.set_ord_lessThan_nat (lambda ((N tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt tptp.zero_zero_nat) N)))))
% 4.96/5.20 (assert (= tptp.set_or5834768355832116004an_nat (lambda ((N tptp.nat) (M tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N)) M)))))
% 4.96/5.20 (assert (= tptp.set_ord_atMost_nat (lambda ((N tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt tptp.zero_zero_nat) (@ tptp.suc N))))))
% 4.96/5.20 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (= (@ (@ tptp.upt I) J) (@ (@ tptp.cons_nat I) (@ (@ tptp.upt (@ tptp.suc I)) J))))))
% 4.96/5.20 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat J) K))) (let ((_let_2 (@ tptp.upt I))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ _let_2 _let_1) (@ (@ tptp.append_nat (@ _let_2 J)) (@ (@ tptp.upt J) _let_1))))))))
% 4.96/5.20 (assert (forall ((I tptp.nat) (J tptp.nat) (X tptp.nat) (Xs tptp.list_nat)) (= (= (@ (@ tptp.upt I) J) (@ (@ tptp.cons_nat X) Xs)) (and (@ (@ tptp.ord_less_nat I) J) (= I X) (= (@ (@ tptp.upt (@ (@ tptp.plus_plus_nat I) tptp.one_one_nat)) J) Xs)))))
% 4.96/5.20 (assert (= tptp.upt (lambda ((I3 tptp.nat) (J2 tptp.nat)) (@ (@ (@ tptp.if_list_nat (@ (@ tptp.ord_less_nat I3) J2)) (@ (@ tptp.cons_nat I3) (@ (@ tptp.upt (@ tptp.suc I3)) J2))) tptp.nil_nat))))
% 4.96/5.20 (assert (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.upt I))) (let ((_let_2 (@ _let_1 (@ tptp.suc J)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat I) J))) (and (=> _let_3 (= _let_2 (@ (@ tptp.append_nat (@ _let_1 J)) (@ (@ tptp.cons_nat J) tptp.nil_nat)))) (=> (not _let_3) (= _let_2 tptp.nil_nat))))))))
% 4.96/5.20 (assert (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.upt I))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ _let_1 (@ tptp.suc J)) (@ (@ tptp.append_nat (@ _let_1 J)) (@ (@ tptp.cons_nat J) tptp.nil_nat)))))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.map_nat_nat tptp.suc) (@ (@ tptp.upt M2) N2)) (@ (@ tptp.upt (@ tptp.suc M2)) (@ tptp.suc N2)))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_nat I3) N2))) (@ (@ tptp.upt tptp.zero_zero_nat) M2)) (@ (@ tptp.upt N2) (@ (@ tptp.plus_plus_nat M2) N2)))))
% 4.96/5.20 (assert (forall ((M2 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 M2)) (@ tptp.suc N2))) (@ (@ tptp.upt M2) N2))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ tptp.groups4561878855575611511st_nat (@ (@ tptp.upt M2) N2)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or4665077453230672383an_nat M2) N2))))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (N6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) M2) (= (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L2) M2) (= (@ tptp.groups4561878855575611511st_nat L2) N6))))) (@ (@ 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 M2) tptp.one_one_nat)) (= (@ tptp.groups4561878855575611511st_nat L2) N6)))))) (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L2) M2) (= (@ (@ tptp.plus_plus_nat (@ tptp.groups4561878855575611511st_nat L2)) tptp.one_one_nat) N6))))))))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (N6 tptp.nat)) (= (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L2) M2) (= (@ tptp.groups4561878855575611511st_nat L2) N6))))) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N6) M2)) tptp.one_one_nat)) N6))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_nat) (@ (@ tptp.upt M2) N2))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) (@ (@ tptp.upt M2) N2))))
% 4.96/5.20 (assert (forall ((Ns tptp.list_nat) (I tptp.nat)) (=> (@ (@ tptp.sorted_wrt_nat tptp.ord_less_nat) Ns) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Ns)) (@ (@ tptp.ord_less_eq_nat I) (@ (@ tptp.nth_nat Ns) I))))))
% 4.96/5.20 (assert (forall ((I tptp.int) (J tptp.int)) (@ (@ tptp.sorted_wrt_int tptp.ord_less_int) (@ (@ tptp.upto I) J))))
% 4.96/5.20 (assert (forall ((M2 tptp.int) (N2 tptp.int)) (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) (@ (@ tptp.upto M2) N2))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat)) (= (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I3 tptp.nat) (J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I3) J2)) M2)))) (@ (@ tptp.produc457027306803732586at_nat (@ tptp.set_ord_atMost_nat M2)) (lambda ((R4 tptp.nat)) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat M2) R4)))))))
% 4.96/5.20 (assert (= tptp.bNF_Ca8459412986667044542atLess (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o tptp.ord_less_nat))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat tptp.bNF_Ca8665028551170535155natLeq) (@ (@ tptp.produc457027306803732586at_nat (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.ord_less_nat X4) N2)))) (lambda ((Uu3 tptp.nat)) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.ord_less_nat X4) N2)))))) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_nat X4) N2) (@ (@ tptp.ord_less_nat Y5) N2) (@ (@ tptp.ord_less_eq_nat X4) Y5))))))))
% 4.96/5.20 (assert (= tptp.bNF_Ca8665028551170535155natLeq (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o tptp.ord_less_eq_nat))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat tptp.bNF_Ca8665028551170535155natLeq) (@ (@ tptp.produc457027306803732586at_nat (@ (@ tptp.order_underS_nat tptp.bNF_Ca8665028551170535155natLeq) N2)) (lambda ((Uu3 tptp.nat)) (@ (@ tptp.order_underS_nat tptp.bNF_Ca8665028551170535155natLeq) N2)))) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_nat X4) N2) (@ (@ tptp.ord_less_nat Y5) N2) (@ (@ tptp.ord_less_eq_nat X4) Y5))))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.order_underS_nat tptp.bNF_Ca8665028551170535155natLeq) N2) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.ord_less_nat X4) N2))))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.upt M2) N2))) (= (@ (@ tptp.linord738340561235409698at_nat (lambda ((X4 tptp.nat)) X4)) _let_1) _let_1))))
% 4.96/5.20 (assert (forall ((I tptp.int) (J tptp.int)) (let ((_let_1 (@ (@ tptp.upto I) J))) (= (@ (@ tptp.linord1735203802627413978nt_int (lambda ((X4 tptp.int)) X4)) _let_1) _let_1))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (= (@ tptp.field_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_nat X4) N2) (@ (@ tptp.ord_less_nat Y5) N2) (@ (@ tptp.ord_less_eq_nat X4) Y5)))))) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.ord_less_nat X4) N2))))))
% 4.96/5.20 (assert (@ tptp.wf_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o tptp.ord_less_nat))))
% 4.96/5.20 (assert (forall ((D tptp.int)) (@ tptp.wf_int (@ tptp.int_ge_less_than2 D))))
% 4.96/5.20 (assert (forall ((D tptp.int)) (@ tptp.wf_int (@ tptp.int_ge_less_than D))))
% 4.96/5.20 (assert (forall ((S2 tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat S2)) (exists ((R3 (-> tptp.nat tptp.nat))) (and (@ tptp.order_5726023648592871131at_nat R3) (forall ((N7 tptp.nat)) (@ (@ tptp.member_nat (@ R3 N7)) S2)))))))
% 4.96/5.20 (assert (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (=> (@ tptp.order_5726023648592871131at_nat F) (@ (@ tptp.ord_less_eq_nat N2) (@ F N2)))))
% 4.96/5.20 (assert (forall ((S2 tptp.set_nat) (S tptp.nat)) (=> (not (@ tptp.finite_finite_nat S2)) (=> (@ (@ tptp.member_nat S) S2) (exists ((N3 tptp.nat)) (= (@ (@ tptp.infini8530281810654367211te_nat S2) N3) S))))))
% 4.96/5.20 (assert (forall ((S2 tptp.set_nat) (N2 tptp.nat)) (=> (not (@ tptp.finite_finite_nat S2)) (@ (@ tptp.ord_less_eq_nat N2) (@ (@ tptp.infini8530281810654367211te_nat S2) N2)))))
% 4.96/5.20 (assert (forall ((S2 tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat S2)) (@ tptp.order_5726023648592871131at_nat (@ tptp.infini8530281810654367211te_nat S2)))))
% 4.96/5.20 (assert (forall ((S2 tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat S2)) (= (@ (@ tptp.image_nat_nat (@ tptp.infini8530281810654367211te_nat S2)) tptp.top_top_set_nat) S2))))
% 4.96/5.20 (assert (forall ((S2 tptp.set_nat) (N2 tptp.nat)) (=> (@ tptp.finite_finite_nat S2) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.finite_card_nat S2)) (@ (@ tptp.ord_less_eq_nat N2) (@ (@ tptp.infini8530281810654367211te_nat S2) N2))))))
% 4.96/5.20 (assert (forall ((S2 tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat S2)) (@ (@ (@ tptp.bij_betw_nat_nat (@ tptp.infini8530281810654367211te_nat S2)) tptp.top_top_set_nat) S2))))
% 4.96/5.20 (assert (forall ((P (-> tptp.nat Bool))) (=> (@ P tptp.zero_zero_nat) (= (@ tptp.ord_Least_nat P) tptp.zero_zero_nat))))
% 4.96/5.20 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat) (Q (-> tptp.nat Bool)) (M2 tptp.nat)) (=> (@ P N2) (=> (@ Q M2) (=> (not (@ P tptp.zero_zero_nat)) (=> (forall ((K3 tptp.nat)) (= (@ P (@ tptp.suc K3)) (@ Q K3))) (= (@ tptp.ord_Least_nat P) (@ tptp.suc (@ tptp.ord_Least_nat Q)))))))))
% 4.96/5.20 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P N2) (=> (not (@ P tptp.zero_zero_nat)) (= (@ tptp.ord_Least_nat P) (@ tptp.suc (@ tptp.ord_Least_nat (lambda ((M tptp.nat)) (@ P (@ tptp.suc M))))))))))
% 4.96/5.20 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (= (@ tptp.last_nat (@ (@ tptp.upt I) J)) (@ (@ tptp.minus_minus_nat J) tptp.one_one_nat)))))
% 4.96/5.20 (assert (forall ((A2 tptp.set_nat)) (let ((_let_1 (@ tptp.vimage_nat_nat tptp.suc))) (= (@ _let_1 (@ (@ tptp.insert_nat tptp.zero_zero_nat) A2)) (@ _let_1 A2)))))
% 4.96/5.20 (assert (forall ((F3 tptp.set_nat)) (= (@ tptp.finite_finite_nat (@ (@ tptp.vimage_nat_nat tptp.suc) F3)) (@ tptp.finite_finite_nat F3))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.vimage_nat_nat tptp.suc))) (= (@ _let_1 (@ (@ tptp.insert_nat (@ tptp.suc N2)) A2)) (@ (@ tptp.insert_nat N2) (@ _let_1 A2))))))
% 4.96/5.20 (assert (forall ((X tptp.nat)) (= (@ tptp.nat_set_decode (@ (@ tptp.divide_divide_nat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.vimage_nat_nat tptp.suc) (@ tptp.nat_set_decode X)))))
% 4.96/5.20 (assert (forall ((A2 tptp.set_nat)) (= (@ tptp.nat_set_encode (@ (@ tptp.vimage_nat_nat tptp.suc) A2)) (@ (@ tptp.divide_divide_nat (@ tptp.nat_set_encode A2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 4.96/5.20 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B2 tptp.nat)) (=> (@ P K) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B2))) (@ P (@ tptp.order_Greatest_nat P))))))
% 4.96/5.20 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B2 tptp.nat)) (=> (@ P K) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B2))) (@ (@ tptp.ord_less_eq_nat K) (@ tptp.order_Greatest_nat P))))))
% 4.96/5.20 (assert (forall ((P (-> tptp.nat Bool)) (B2 tptp.nat)) (=> (exists ((X_1 tptp.nat)) (@ P X_1)) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B2))) (@ P (@ tptp.order_Greatest_nat P))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (@ tptp.bNF_We3818239936649020644el_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_nat X4) N2) (@ (@ tptp.ord_less_nat Y5) N2) (@ (@ tptp.ord_less_eq_nat X4) Y5))))))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (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)))))
% 4.96/5.20 (assert (forall ((Y tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw Y) (@ (@ tptp.modulo_modulo_nat X) Y)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Y) (= (@ (@ tptp.bezw X) Y) (@ (@ tptp.product_Pair_int_int _let_2) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_1)) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X) Y)))))))))))
% 4.96/5.20 (assert (forall ((X tptp.nat) (Xa2 tptp.nat) (Y tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.bezw Xa2) (@ (@ tptp.modulo_modulo_nat X) Xa2)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X) Xa2) Y) (and (=> _let_3 (= Y (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_3) (= Y (@ (@ tptp.product_Pair_int_int _let_2) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_1)) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X) Xa2))))))))))))))
% 4.96/5.20 (assert (= tptp.bezw (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw Y5) (@ (@ tptp.modulo_modulo_nat X4) 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 X4) Y5)))))))))))
% 4.96/5.20 (assert (forall ((X tptp.nat) (Xa2 tptp.nat) (Y tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.bezw_rel) (@ (@ tptp.product_Pair_nat_nat X) Xa2)))) (let ((_let_2 (@ (@ tptp.bezw Xa2) (@ (@ tptp.modulo_modulo_nat X) Xa2)))) (let ((_let_3 (@ tptp.product_snd_int_int _let_2))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X) Xa2) Y) (=> _let_1 (not (=> (and (=> _let_4 (= Y (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_4) (= Y (@ (@ tptp.product_Pair_int_int _let_3) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_2)) (@ (@ tptp.times_times_int _let_3) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X) Xa2)))))))) (not _let_1)))))))))))
% 4.96/5.20 (assert (forall ((A tptp.nat) (B2 tptp.nat) (S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ tptp.ord_less_nat S) T) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.product_Pair_nat_nat A) S)) (@ (@ tptp.product_Pair_nat_nat B2) T))) tptp.fun_pair_less)))))
% 4.96/5.20 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.product_Pair_nat_nat X))) (= (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ _let_1 Y)) (@ _let_1 Z3))) tptp.fun_pair_less) (@ (@ tptp.ord_less_nat Y) Z3)))))
% 4.96/5.20 (assert (forall ((A tptp.nat) (B2 tptp.nat) (S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.product_Pair_nat_nat A) S)) (@ (@ tptp.product_Pair_nat_nat B2) T))) tptp.fun_pair_less))))
% 4.96/5.20 (assert (forall ((X tptp.nat) (Xa2 tptp.nat) (Y tptp.product_prod_nat_nat)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.nat_pr5047031295181774490ux_rel) (@ (@ tptp.product_Pair_nat_nat X) Xa2)))) (let ((_let_2 (@ tptp.suc X))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat Xa2) X))) (=> (= (@ (@ tptp.nat_prod_decode_aux X) Xa2) Y) (=> _let_1 (not (=> (and (=> _let_3 (= Y (@ (@ tptp.product_Pair_nat_nat Xa2) (@ (@ tptp.minus_minus_nat X) Xa2)))) (=> (not _let_3) (= Y (@ (@ tptp.nat_prod_decode_aux _let_2) (@ (@ tptp.minus_minus_nat Xa2) _let_2))))) (not _let_1))))))))))
% 4.96/5.20 (assert (forall ((A tptp.nat) (B2 tptp.nat) (S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ tptp.ord_less_eq_nat S) T) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.product_Pair_nat_nat A) S)) (@ (@ tptp.product_Pair_nat_nat B2) T))) tptp.fun_pair_leq)))))
% 4.96/5.20 (assert (forall ((A tptp.nat) (B2 tptp.nat) (S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.product_Pair_nat_nat A) S)) (@ (@ tptp.product_Pair_nat_nat B2) T))) tptp.fun_pair_leq))))
% 4.96/5.20 (assert (@ (@ (@ tptp.ordering_top_nat tptp.dvd_dvd_nat) (lambda ((M tptp.nat) (N tptp.nat)) (and (@ (@ tptp.dvd_dvd_nat M) N) (not (= M N))))) tptp.zero_zero_nat))
% 4.96/5.20 (assert (@ (@ (@ tptp.ordering_top_nat (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y5) X4))) (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.ord_less_nat Y5) X4))) tptp.zero_zero_nat))
% 4.96/5.20 (assert (= tptp.ord_le2932123472753598470d_enat (lambda ((M tptp.extended_enat) (__flatten_var_0 tptp.extended_enat)) (@ (@ (@ tptp.extended_case_enat_o (lambda ((N1 tptp.nat)) (@ (@ (@ tptp.extended_case_enat_o (lambda ((M1 tptp.nat)) (@ (@ tptp.ord_less_eq_nat M1) N1))) false) M))) true) __flatten_var_0))))
% 4.96/5.20 (assert (= tptp.ord_le72135733267957522d_enat (lambda ((M tptp.extended_enat) (N tptp.extended_enat)) (@ (@ (@ tptp.extended_case_enat_o (lambda ((M1 tptp.nat)) (@ (@ (@ tptp.extended_case_enat_o (@ tptp.ord_less_nat M1)) true) N))) false) M))))
% 4.96/5.20 (assert (forall ((K tptp.nat) (M2 tptp.nat)) (= (@ tptp.nat_prod_decode (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle K)) M2)) (@ (@ tptp.nat_prod_decode_aux K) M2))))
% 4.96/5.20 (assert (= tptp.nat_prod_decode (@ tptp.nat_prod_decode_aux tptp.zero_zero_nat)))
% 4.96/5.20 (assert (forall ((A0 tptp.nat) (P (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.accp_nat tptp.nat_list_decode_rel))) (=> (@ _let_1 A0) (=> (=> (@ _let_1 tptp.zero_zero_nat) (@ P tptp.zero_zero_nat)) (=> (forall ((N3 tptp.nat)) (let ((_let_1 (@ tptp.suc N3))) (=> (@ (@ tptp.accp_nat tptp.nat_list_decode_rel) _let_1) (=> (forall ((X2 tptp.nat) (Y6 tptp.nat)) (=> (= (@ (@ tptp.product_Pair_nat_nat X2) Y6) (@ tptp.nat_prod_decode N3)) (@ P Y6))) (@ P _let_1))))) (@ P A0)))))))
% 4.96/5.20 (assert (forall ((X tptp.nat) (Y tptp.list_nat)) (=> (= (@ tptp.nat_list_decode X) Y) (=> (=> (= X tptp.zero_zero_nat) (not (= Y tptp.nil_nat))) (not (forall ((N3 tptp.nat)) (=> (= X (@ tptp.suc N3)) (not (= Y (@ (@ tptp.produc2761476792215241774st_nat (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.cons_nat X4) (@ tptp.nat_list_decode Y5)))) (@ tptp.nat_prod_decode N3)))))))))))
% 4.96/5.20 (assert (=> (@ (@ tptp.accp_nat tptp.nat_list_decode_rel) tptp.zero_zero_nat) (= (@ tptp.nat_list_decode tptp.zero_zero_nat) tptp.nil_nat)))
% 4.96/5.20 (assert (= (@ tptp.nat_list_decode tptp.zero_zero_nat) tptp.nil_nat))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ tptp.accp_nat tptp.nat_list_decode_rel) _let_1) (= (@ tptp.nat_list_decode _let_1) (@ (@ tptp.produc2761476792215241774st_nat (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.cons_nat X4) (@ tptp.nat_list_decode Y5)))) (@ tptp.nat_prod_decode N2)))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (= (@ tptp.nat_list_decode (@ tptp.suc N2)) (@ (@ tptp.produc2761476792215241774st_nat (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.cons_nat X4) (@ tptp.nat_list_decode Y5)))) (@ tptp.nat_prod_decode N2)))))
% 4.96/5.20 (assert (forall ((X tptp.nat) (Y tptp.list_nat)) (let ((_let_1 (@ tptp.accp_nat tptp.nat_list_decode_rel))) (=> (= (@ tptp.nat_list_decode X) Y) (=> (@ _let_1 X) (=> (=> (= X tptp.zero_zero_nat) (=> (= Y tptp.nil_nat) (not (@ _let_1 tptp.zero_zero_nat)))) (not (forall ((N3 tptp.nat)) (let ((_let_1 (@ tptp.suc N3))) (=> (= X _let_1) (=> (= Y (@ (@ tptp.produc2761476792215241774st_nat (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.cons_nat X4) (@ tptp.nat_list_decode Y5)))) (@ tptp.nat_prod_decode N3))) (not (@ (@ tptp.accp_nat tptp.nat_list_decode_rel) _let_1)))))))))))))
% 4.96/5.20 (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)))))))))))))
% 4.96/5.20 (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))))))))))))
% 4.96/5.20 (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))))))))))))
% 4.96/5.20 (assert (@ (@ tptp.pcr_int (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat)) tptp.one_one_int))
% 4.96/5.20 (assert (@ (@ tptp.pcr_int (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat)) tptp.zero_zero_int))
% 4.96/5.20 (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))))))))))))
% 4.96/5.20 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.member_real X) tptp.field_5140801741446780682s_real) (not (forall ((M3 tptp.nat) (N3 tptp.nat)) (=> (not (= N3 tptp.zero_zero_nat)) (=> (= (@ tptp.abs_abs_real X) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real M3)) (@ tptp.semiri5074537144036343181t_real N3))) (not (@ (@ tptp.algebr934650988132801477me_nat M3) N3)))))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.algebr934650988132801477me_nat (@ tptp.suc N2)) N2)))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.algebr934650988132801477me_nat N2) (@ tptp.suc N2))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.algebr934650988132801477me_nat (@ tptp.suc tptp.zero_zero_nat)) N2)))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.algebr934650988132801477me_nat N2) (@ tptp.suc tptp.zero_zero_nat))))
% 4.96/5.20 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool))) (= (@ (@ tptp.eventu1038000079068216329at_nat P) (@ (@ tptp.prod_filter_nat_nat tptp.at_top_nat) tptp.at_top_nat)) (exists ((N5 tptp.nat)) (forall ((M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N5) M) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N5) N) (@ P (@ (@ tptp.product_Pair_nat_nat N) M))))))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.algebr934650988132801477me_nat (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) N2))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.algebr934650988132801477me_nat N2) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))))
% 4.96/5.20 (assert (@ (@ (@ (@ tptp.bNF_re7408651293131936558nt_int tptp.pcr_int) (@ (@ tptp.bNF_re7400052026677387805at_int tptp.pcr_int) tptp.pcr_int)) (@ tptp.produc27273713700761075at_nat (lambda ((X4 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 X4) V4)) (@ (@ tptp.plus_plus_nat Y5) U2)))) __flatten_var_0)))) tptp.minus_minus_int))
% 4.96/5.20 (assert (@ (@ (@ (@ tptp.bNF_re7408651293131936558nt_int tptp.pcr_int) (@ (@ tptp.bNF_re7400052026677387805at_int tptp.pcr_int) tptp.pcr_int)) (@ tptp.produc27273713700761075at_nat (lambda ((X4 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 X4) U2)) (@ (@ tptp.plus_plus_nat Y5) V4)))) __flatten_var_0)))) tptp.plus_plus_int))
% 4.96/5.20 (assert (@ (@ (@ (@ tptp.bNF_re717283939379294677_int_o tptp.pcr_int) (@ (@ tptp.bNF_re6644619430987730960nt_o_o tptp.pcr_int) (lambda ((Y4 Bool) (Z2 Bool)) (= Y4 Z2)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X4 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 X4) V4)) (@ (@ tptp.plus_plus_nat U2) Y5)))) __flatten_var_0)))) tptp.ord_less_int))
% 4.96/5.20 (assert (@ (@ (@ (@ tptp.bNF_re717283939379294677_int_o tptp.pcr_int) (@ (@ tptp.bNF_re6644619430987730960nt_o_o tptp.pcr_int) (lambda ((Y4 Bool) (Z2 Bool)) (= Y4 Z2)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X4 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 X4) V4)) (@ (@ tptp.plus_plus_nat U2) Y5)))) __flatten_var_0)))) tptp.ord_less_eq_int))
% 4.96/5.20 (assert (@ (@ (@ (@ tptp.bNF_re7408651293131936558nt_int tptp.pcr_int) (@ (@ tptp.bNF_re7400052026677387805at_int tptp.pcr_int) tptp.pcr_int)) (@ tptp.produc27273713700761075at_nat (lambda ((X4 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 X4))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U2)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U2))))))) __flatten_var_0)))) tptp.times_times_int))
% 4.96/5.20 (assert (@ (@ (@ (@ tptp.bNF_re7400052026677387805at_int tptp.pcr_int) tptp.pcr_int) (@ tptp.produc2626176000494625587at_nat (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y5) X4)))) tptp.uminus_uminus_int))
% 4.96/5.20 (assert (@ (@ (@ (@ tptp.bNF_re4555766996558763186at_nat tptp.pcr_int) (lambda ((Y4 tptp.nat) (Z2 tptp.nat)) (= Y4 Z2))) (@ tptp.produc6842872674320459806at_nat tptp.minus_minus_nat)) tptp.nat2))
% 4.96/5.20 (assert (@ (@ (@ (@ tptp.bNF_re6830278522597306478at_int (lambda ((Y4 tptp.nat) (Z2 tptp.nat)) (= Y4 Z2))) tptp.pcr_int) (lambda ((N tptp.nat)) (@ (@ tptp.product_Pair_nat_nat N) tptp.zero_zero_nat))) tptp.semiri1314217659103216013at_int))
% 4.96/5.20 (assert (@ (@ (@ (@ tptp.bNF_re3099431351363272937at_nat tptp.intrel) (@ (@ tptp.bNF_re2241393799969408733at_nat tptp.intrel) tptp.intrel)) (@ tptp.produc27273713700761075at_nat (lambda ((X4 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 X4))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U2)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U2))))))) __flatten_var_0)))) (@ tptp.produc27273713700761075at_nat (lambda ((X4 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 X4))) (@ (@ 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)))))
% 4.96/5.20 (assert (forall ((X tptp.nat) (Y tptp.nat) (U tptp.nat) (V tptp.nat)) (= (@ (@ tptp.intrel (@ (@ tptp.product_Pair_nat_nat X) Y)) (@ (@ tptp.product_Pair_nat_nat U) V)) (= (@ (@ tptp.plus_plus_nat X) V) (@ (@ tptp.plus_plus_nat U) Y)))))
% 4.96/5.20 (assert (let ((_let_1 (@ tptp.produc6842872674320459806at_nat tptp.minus_minus_nat))) (@ (@ (@ (@ tptp.bNF_re8246922863344978751at_nat tptp.intrel) (lambda ((Y4 tptp.nat) (Z2 tptp.nat)) (= Y4 Z2))) _let_1) _let_1)))
% 4.96/5.20 (assert (@ (@ (@ (@ tptp.bNF_re2241393799969408733at_nat tptp.intrel) tptp.intrel) (@ tptp.produc2626176000494625587at_nat (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y5) X4)))) (@ tptp.produc2626176000494625587at_nat (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y5) X4)))))
% 4.96/5.20 (assert (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (= (@ tptp.abs_Integ X) (@ tptp.abs_Integ Y)) (@ (@ tptp.intrel X) Y))))
% 4.96/5.20 (assert (let ((_let_1 (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat))) (@ (@ tptp.intrel _let_1) _let_1)))
% 4.96/5.20 (assert (let ((_let_1 (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat))) (@ (@ tptp.intrel _let_1) _let_1)))
% 4.96/5.20 (assert (= tptp.intrel (@ tptp.produc8739625826339149834_nat_o (lambda ((X4 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.plus_plus_nat X4) V4) (@ (@ tptp.plus_plus_nat U2) Y5)))) __flatten_var_0)))))
% 4.96/5.20 (assert (@ (@ (@ (@ tptp.bNF_re4202695980764964119_nat_o tptp.intrel) (@ (@ tptp.bNF_re3666534408544137501at_o_o tptp.intrel) (lambda ((Y4 Bool) (Z2 Bool)) (= Y4 Z2)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X4 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 X4) V4)) (@ (@ tptp.plus_plus_nat U2) Y5)))) __flatten_var_0)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X4 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 X4) V4)) (@ (@ tptp.plus_plus_nat U2) Y5)))) __flatten_var_0)))))
% 4.96/5.20 (assert (@ (@ (@ (@ tptp.bNF_re4202695980764964119_nat_o tptp.intrel) (@ (@ tptp.bNF_re3666534408544137501at_o_o tptp.intrel) (lambda ((Y4 Bool) (Z2 Bool)) (= Y4 Z2)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X4 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 X4) V4)) (@ (@ tptp.plus_plus_nat U2) Y5)))) __flatten_var_0)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X4 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 X4) V4)) (@ (@ tptp.plus_plus_nat U2) Y5)))) __flatten_var_0)))))
% 4.96/5.20 (assert (@ (@ (@ (@ tptp.bNF_re717283939379294677_int_o tptp.pcr_int) (@ (@ tptp.bNF_re6644619430987730960nt_o_o tptp.pcr_int) (lambda ((Y4 Bool) (Z2 Bool)) (= Y4 Z2)))) tptp.intrel) (lambda ((Y4 tptp.int) (Z2 tptp.int)) (= Y4 Z2))))
% 4.96/5.20 (assert (@ (@ (@ (@ tptp.bNF_re3099431351363272937at_nat tptp.intrel) (@ (@ tptp.bNF_re2241393799969408733at_nat tptp.intrel) tptp.intrel)) (@ tptp.produc27273713700761075at_nat (lambda ((X4 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 X4) V4)) (@ (@ tptp.plus_plus_nat Y5) U2)))) __flatten_var_0)))) (@ tptp.produc27273713700761075at_nat (lambda ((X4 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 X4) V4)) (@ (@ tptp.plus_plus_nat Y5) U2)))) __flatten_var_0)))))
% 4.96/5.20 (assert (@ (@ (@ (@ tptp.bNF_re3099431351363272937at_nat tptp.intrel) (@ (@ tptp.bNF_re2241393799969408733at_nat tptp.intrel) tptp.intrel)) (@ tptp.produc27273713700761075at_nat (lambda ((X4 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 X4) U2)) (@ (@ tptp.plus_plus_nat Y5) V4)))) __flatten_var_0)))) (@ tptp.produc27273713700761075at_nat (lambda ((X4 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 X4) U2)) (@ (@ tptp.plus_plus_nat Y5) V4)))) __flatten_var_0)))))
% 4.96/5.20 (assert (@ tptp.bi_tot896582865486249351at_int tptp.pcr_int))
% 4.96/5.20 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) tptp.less_than) (@ (@ tptp.ord_less_nat X) Y))))
% 4.96/5.20 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N2 tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList2) Summary))) (=> (@ (@ tptp.vEBT_invar_vebt _let_1) N2) (= (@ (@ tptp.vEBT_VEBT_elim_dead _let_1) (@ tptp.extended_enat2 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) _let_1)))))
% 4.96/5.20 (assert (forall ((N2 tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat N2) (@ tptp.extended_enat2 tptp.zero_zero_nat)) N2)))
% 4.96/5.20 (assert (forall ((N2 tptp.extended_enat)) (let ((_let_1 (@ tptp.extended_enat2 tptp.zero_zero_nat))) (= (@ (@ tptp.minus_3235023915231533773d_enat _let_1) N2) _let_1))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.extended_enat2 M2)) (@ tptp.extended_enat2 N2)) (@ tptp.extended_enat2 (@ (@ tptp.plus_plus_nat M2) N2)))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.extended_enat2 M2)) (@ tptp.extended_enat2 N2)) (@ (@ tptp.ord_less_nat M2) N2))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.extended_enat2 M2)) (@ tptp.extended_enat2 N2)) (@ (@ tptp.ord_less_eq_nat M2) N2))))
% 4.96/5.20 (assert (forall ((M2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat M2)) (@ tptp.extended_enat2 N2)) (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat M2)) N2))))
% 4.96/5.20 (assert (forall ((M2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat M2)) (@ tptp.extended_enat2 N2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat M2)) N2))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat) (N2 tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.extended_enat2 (@ tptp.suc M2))) N2) (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.extended_enat2 M2)) N2))))
% 4.96/5.20 (assert (forall ((A2 tptp.set_Extended_enat) (N2 tptp.nat)) (=> (forall ((Y3 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat Y3) A2) (@ (@ tptp.ord_le2932123472753598470d_enat Y3) (@ tptp.extended_enat2 N2)))) (@ tptp.finite4001608067531595151d_enat A2))))
% 4.96/5.20 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat) (N2 tptp.nat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.plus_p3455044024723400733d_enat X) Y)) (@ tptp.extended_enat2 N2)) (exists ((Y7 tptp.nat) (X9 tptp.nat)) (and (= X (@ tptp.extended_enat2 X9)) (= Y (@ tptp.extended_enat2 Y7)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X9) Y7)) N2))))))
% 4.96/5.20 (assert (forall ((X tptp.nat)) (= (= tptp.zero_z5237406670263579293d_enat (@ tptp.extended_enat2 X)) (= X tptp.zero_zero_nat))))
% 4.96/5.20 (assert (forall ((X tptp.nat)) (= (= (@ tptp.extended_enat2 X) tptp.zero_z5237406670263579293d_enat) (= X tptp.zero_zero_nat))))
% 4.96/5.20 (assert (= tptp.zero_z5237406670263579293d_enat (@ tptp.extended_enat2 tptp.zero_zero_nat)))
% 4.96/5.20 (assert (forall ((N2 tptp.extended_enat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat N2) (@ tptp.extended_enat2 M2)) (not (forall ((K3 tptp.nat)) (=> (= N2 (@ tptp.extended_enat2 K3)) (not (@ (@ tptp.ord_less_nat K3) M2))))))))
% 4.96/5.20 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N2 tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList2) Summary))) (=> (@ (@ tptp.vEBT_invar_vebt _let_1) N2) (= (@ (@ tptp.vEBT_VEBT_elim_dead _let_1) tptp.extend5688581933313929465d_enat) _let_1)))))
% 4.96/5.20 (assert (forall ((M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.extended_enat2 M2)) tptp.extend5688581933313929465d_enat))) (let ((_let_2 (= M2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.zero_z5237406670263579293d_enat)) (=> (not _let_2) (= _let_1 tptp.extend5688581933313929465d_enat)))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_7803423173614009249d_enat tptp.extend5688581933313929465d_enat) (@ tptp.extended_enat2 N2)))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.zero_z5237406670263579293d_enat)) (=> (not _let_2) (= _let_1 tptp.extend5688581933313929465d_enat)))))))
% 4.96/5.20 (assert (= tptp.comple2295165028678016749d_enat (lambda ((A5 tptp.set_Extended_enat)) (@ (@ (@ tptp.if_Extended_enat (= A5 tptp.bot_bo7653980558646680370d_enat)) tptp.extend5688581933313929465d_enat) (@ tptp.ord_Le1955565732374568822d_enat (lambda ((X4 tptp.extended_enat)) (@ (@ tptp.member_Extended_enat X4) A5)))))))
% 4.96/5.20 (assert (= tptp.bot_bo4199563552545308370d_enat tptp.zero_z5237406670263579293d_enat))
% 4.96/5.20 (assert (= tptp.comple4398354569131411667d_enat (lambda ((A5 tptp.set_Extended_enat)) (@ (@ (@ tptp.if_Extended_enat (= A5 tptp.bot_bo7653980558646680370d_enat)) tptp.zero_z5237406670263579293d_enat) (@ (@ (@ tptp.if_Extended_enat (@ tptp.finite4001608067531595151d_enat A5)) (@ tptp.lattic921264341876707157d_enat A5)) tptp.extend5688581933313929465d_enat)))))
% 4.96/5.20 (assert (= tptp.times_7803423173614009249d_enat (lambda ((M tptp.extended_enat) (N tptp.extended_enat)) (@ (@ (@ tptp.extend3600170679010898289d_enat (lambda ((O tptp.nat)) (@ (@ (@ tptp.extend3600170679010898289d_enat (lambda ((P6 tptp.nat)) (@ tptp.extended_enat2 (@ (@ tptp.times_times_nat O) P6)))) (@ (@ (@ tptp.if_Extended_enat (= O tptp.zero_zero_nat)) tptp.zero_z5237406670263579293d_enat) tptp.extend5688581933313929465d_enat)) N))) (@ (@ (@ tptp.if_Extended_enat (= N tptp.zero_z5237406670263579293d_enat)) tptp.zero_z5237406670263579293d_enat) tptp.extend5688581933313929465d_enat)) M))))
% 4.96/5.20 (assert (= tptp.plus_p3455044024723400733d_enat (lambda ((M tptp.extended_enat) (N tptp.extended_enat)) (@ (@ (@ tptp.extend3600170679010898289d_enat (lambda ((O tptp.nat)) (@ (@ (@ tptp.extend3600170679010898289d_enat (lambda ((P6 tptp.nat)) (@ tptp.extended_enat2 (@ (@ tptp.plus_plus_nat O) P6)))) tptp.extend5688581933313929465d_enat) N))) tptp.extend5688581933313929465d_enat) M))))
% 4.96/5.20 (assert (forall ((A2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (not (= A2 tptp.bot_bo7653980558646680370d_enat)) (= (@ tptp.extended_eSuc (@ tptp.lattic921264341876707157d_enat A2)) (@ tptp.lattic921264341876707157d_enat (@ (@ tptp.image_80655429650038917d_enat tptp.extended_eSuc) A2)))))))
% 4.96/5.20 (assert (= tptp.extended_eSuc (@ (@ tptp.extend3600170679010898289d_enat (lambda ((N tptp.nat)) (@ tptp.extended_enat2 (@ tptp.suc N)))) tptp.extend5688581933313929465d_enat)))
% 4.96/5.20 (assert (forall ((Y tptp.nat) (X tptp.extended_enat)) (= (= (@ tptp.extended_enat2 Y) (@ tptp.extended_eSuc X)) (exists ((N tptp.nat)) (and (= Y (@ tptp.suc N)) (= (@ tptp.extended_enat2 N) X))))))
% 4.96/5.20 (assert (forall ((X tptp.extended_enat) (Y tptp.nat)) (= (= (@ tptp.extended_eSuc X) (@ tptp.extended_enat2 Y)) (exists ((N tptp.nat)) (and (= Y (@ tptp.suc N)) (= X (@ tptp.extended_enat2 N)))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (= (@ tptp.extended_eSuc (@ tptp.extended_enat2 N2)) (@ tptp.extended_enat2 (@ tptp.suc N2)))))
% 4.96/5.20 (assert (forall ((A2 tptp.set_Extended_enat)) (=> (not (= A2 tptp.bot_bo7653980558646680370d_enat)) (= (@ tptp.extended_eSuc (@ tptp.comple4398354569131411667d_enat A2)) (@ tptp.comple4398354569131411667d_enat (@ (@ tptp.image_80655429650038917d_enat tptp.extended_eSuc) A2))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.order_2888998067076097458on_nat (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.ord_less_nat X4) N2)))) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_nat X4) N2) (@ (@ tptp.ord_less_nat Y5) N2) (@ (@ tptp.ord_less_eq_nat X4) Y5))))))))
% 4.96/5.20 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.order_2888998067076097458on_nat (@ tptp.field_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_nat X4) N2) (@ (@ tptp.ord_less_nat Y5) N2) (@ (@ tptp.ord_less_eq_nat X4) Y5))))))) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_nat X4) N2) (@ (@ tptp.ord_less_nat Y5) N2) (@ (@ tptp.ord_less_eq_nat X4) Y5))))))))
% 4.96/5.20 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ (@ tptp.if_int false) X) Y) Y)))
% 4.96/5.20 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ (@ tptp.if_int true) X) Y) X)))
% 4.96/5.20 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat false) X) Y) Y)))
% 4.96/5.20 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat true) X) Y) X)))
% 4.96/5.20 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ (@ tptp.if_real false) X) Y) Y)))
% 4.96/5.20 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ (@ tptp.if_real true) X) Y) X)))
% 4.96/5.20 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ (@ (@ tptp.if_complex false) X) Y) Y)))
% 4.96/5.20 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ (@ (@ tptp.if_complex true) X) Y) X)))
% 4.96/5.20 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (= (@ (@ (@ tptp.if_Extended_enat false) X) Y) Y)))
% 4.96/5.20 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (= (@ (@ (@ tptp.if_Extended_enat true) X) Y) X)))
% 4.96/5.20 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (@ (@ (@ tptp.if_set_int false) X) Y) Y)))
% 4.96/5.20 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (@ (@ (@ tptp.if_set_int true) X) Y) X)))
% 4.96/5.20 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ (@ tptp.if_set_nat false) X) Y) Y)))
% 4.96/5.20 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ (@ tptp.if_set_nat true) X) Y) X)))
% 4.96/5.20 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.vEBT_VEBT)) (= (@ (@ (@ tptp.if_VEBT_VEBT false) X) Y) Y)))
% 4.96/5.20 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.vEBT_VEBT)) (= (@ (@ (@ tptp.if_VEBT_VEBT true) X) Y) X)))
% 4.96/5.20 (assert (forall ((X tptp.list_int) (Y tptp.list_int)) (= (@ (@ (@ tptp.if_list_int false) X) Y) Y)))
% 4.96/5.20 (assert (forall ((X tptp.list_int) (Y tptp.list_int)) (= (@ (@ (@ tptp.if_list_int true) X) Y) X)))
% 99.06/99.38 (assert (forall ((X tptp.list_nat) (Y tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat false) X) Y) Y)))
% 99.06/99.38 (assert (forall ((X tptp.list_nat) (Y tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat true) X) Y) X)))
% 99.06/99.38 (assert (forall ((X (-> tptp.int tptp.int)) (Y (-> tptp.int tptp.int))) (= (@ (@ (@ tptp.if_int_int false) X) Y) Y)))
% 99.06/99.38 (assert (forall ((X (-> tptp.int tptp.int)) (Y (-> tptp.int tptp.int))) (= (@ (@ (@ tptp.if_int_int true) X) Y) X)))
% 99.06/99.38 (assert (forall ((X tptp.option_num) (Y tptp.option_num)) (= (@ (@ (@ tptp.if_option_num false) X) Y) Y)))
% 99.06/99.38 (assert (forall ((X tptp.option_num) (Y tptp.option_num)) (= (@ (@ (@ tptp.if_option_num true) X) Y) X)))
% 99.06/99.38 (assert (forall ((X tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int false) X) Y) Y)))
% 99.06/99.38 (assert (forall ((X tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int true) X) Y) X)))
% 99.06/99.38 (assert (forall ((P Bool)) (or (= P true) (= P false))))
% 99.06/99.38 (assert (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat false) X) Y) Y)))
% 99.06/99.38 (assert (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat true) X) Y) X)))
% 99.06/99.38 (assert (let ((_let_1 (@ (@ tptp.vEBT_VEBT_high tptp.mi) tptp.na))) (let ((_let_2 (@ (@ tptp.vEBT_vebt_insert (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_1)) (@ (@ tptp.vEBT_VEBT_low tptp.mi) tptp.na)))) (not (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT tptp.treeList) _let_1) _let_2)) tptp.i) _let_2)))))
% 99.06/99.38 (set-info :filename cvc5---1.0.5_31553)
% 99.06/99.38 (check-sat-assuming ( true ))
% 99.06/99.38 ------- get file name : TPTP file name is ITP234^1
% 99.06/99.38 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_31553.smt2...
% 99.06/99.38 --- Run --ho-elim --full-saturate-quant at 10...
% 99.06/99.38 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10...
% 99.06/99.38 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10...
% 99.06/99.38 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5...
% 99.06/99.38 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5...
% 99.06/99.38 --- Run --no-ho-matching --full-saturate-quant --enum-inst-interleave --ho-elim-store-ax at 10...
% 99.06/99.38 --- Run --no-ho-matching --full-saturate-quant --macros-quant-mode=all at 10...
% 99.06/99.38 --- Run --ho-elim --full-saturate-quant --enum-inst-interleave at 10...
% 99.06/99.38 --- Run --no-ho-matching --full-saturate-quant --ho-elim-store-ax at 10...
% 99.06/99.38 --- Run --ho-elim --no-ho-elim-store-ax --full-saturate-quant...
% 99.06/99.38 % SZS status Theorem for ITP234^1
% 99.06/99.38 % SZS output start Proof for ITP234^1
% 99.06/99.38 (
% 99.06/99.38 (let ((_let_1 (@ (@ tptp.vEBT_VEBT_low tptp.mi) tptp.na))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high tptp.mi) tptp.na))) (let ((_let_3 (@ tptp.nth_VEBT_VEBT tptp.treeList))) (let ((_let_4 (@ _let_3 _let_2))) (let ((_let_5 (@ (@ tptp.vEBT_vebt_insert _let_4) _let_1))) (let ((_let_6 (@ tptp.list_u1324408373059187874T_VEBT tptp.treeList))) (let ((_let_7 (@ (@ _let_6 _let_2) _let_5))) (let ((_let_8 (@ tptp.nth_VEBT_VEBT _let_7))) (let ((_let_9 (@ _let_8 tptp.i))) (let ((_let_10 (not (= _let_9 _let_5)))) (let ((_let_11 (= tptp.extended_eSuc (@ (@ tptp.extend3600170679010898289d_enat (lambda ((N tptp.nat)) (@ tptp.extended_enat2 (@ tptp.suc N)))) tptp.extend5688581933313929465d_enat)))) (let ((_let_12 (= tptp.plus_p3455044024723400733d_enat (lambda ((M tptp.extended_enat) (N tptp.extended_enat)) (@ (@ (@ tptp.extend3600170679010898289d_enat (lambda ((O tptp.nat)) (@ (@ (@ tptp.extend3600170679010898289d_enat (lambda ((P6 tptp.nat)) (@ tptp.extended_enat2 (@ (@ tptp.plus_plus_nat O) P6)))) tptp.extend5688581933313929465d_enat) N))) tptp.extend5688581933313929465d_enat) M))))) (let ((_let_13 (= tptp.times_7803423173614009249d_enat (lambda ((M tptp.extended_enat) (N tptp.extended_enat)) (@ (@ (@ tptp.extend3600170679010898289d_enat (lambda ((O tptp.nat)) (@ (@ (@ tptp.extend3600170679010898289d_enat (lambda ((P6 tptp.nat)) (@ tptp.extended_enat2 (@ (@ tptp.times_times_nat O) P6)))) (@ (@ (@ tptp.if_Extended_enat (= O tptp.zero_zero_nat)) tptp.zero_z5237406670263579293d_enat) tptp.extend5688581933313929465d_enat)) N))) (@ (@ (@ tptp.if_Extended_enat (= N tptp.zero_z5237406670263579293d_enat)) tptp.zero_z5237406670263579293d_enat) tptp.extend5688581933313929465d_enat)) M))))) (let ((_let_14 (= tptp.comple4398354569131411667d_enat (lambda ((A5 tptp.set_Extended_enat)) (@ (@ (@ tptp.if_Extended_enat (= A5 tptp.bot_bo7653980558646680370d_enat)) tptp.zero_z5237406670263579293d_enat) (@ (@ (@ tptp.if_Extended_enat (@ tptp.finite4001608067531595151d_enat A5)) (@ tptp.lattic921264341876707157d_enat A5)) tptp.extend5688581933313929465d_enat)))))) (let ((_let_15 (= tptp.bot_bo4199563552545308370d_enat tptp.zero_z5237406670263579293d_enat))) (let ((_let_16 (= tptp.comple2295165028678016749d_enat (lambda ((A5 tptp.set_Extended_enat)) (@ (@ (@ tptp.if_Extended_enat (= A5 tptp.bot_bo7653980558646680370d_enat)) tptp.extend5688581933313929465d_enat) (@ tptp.ord_Le1955565732374568822d_enat (lambda ((X4 tptp.extended_enat)) (@ (@ tptp.member_Extended_enat X4) A5)))))))) (let ((_let_17 (@ (@ tptp.bNF_re2241393799969408733at_nat tptp.intrel) tptp.intrel))) (let ((_let_18 (@ (@ tptp.bNF_re3099431351363272937at_nat tptp.intrel) _let_17))) (let ((_let_19 (@ tptp.bNF_re6644619430987730960nt_o_o tptp.pcr_int))) (let ((_let_20 (@ tptp.bNF_re717283939379294677_int_o tptp.pcr_int))) (let ((_let_21 (@ tptp.bNF_re3666534408544137501at_o_o tptp.intrel))) (let ((_let_22 (@ tptp.bNF_re4202695980764964119_nat_o tptp.intrel))) (let ((_let_23 (= tptp.intrel (@ tptp.produc8739625826339149834_nat_o (lambda ((X4 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.plus_plus_nat X4) V4) (@ (@ tptp.plus_plus_nat U2) Y5)))) __flatten_var_0)))))) (let ((_let_24 (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat))) (let ((_let_25 (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat))) (let ((_let_26 (@ tptp.produc6842872674320459806at_nat tptp.minus_minus_nat))) (let ((_let_27 (@ (@ tptp.bNF_re7400052026677387805at_int tptp.pcr_int) tptp.pcr_int))) (let ((_let_28 (@ (@ tptp.bNF_re7408651293131936558nt_int tptp.pcr_int) _let_27))) (let ((_let_29 (@ tptp.bit0 tptp.one))) (let ((_let_30 (@ tptp.bit0 _let_29))) (let ((_let_31 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (let ((_let_32 (@ _let_31 (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 _let_30)))))))))) (let ((_let_33 (= tptp.top_top_set_char (@ (@ tptp.image_nat_char tptp.unique3096191561947761185of_nat) _let_32)))) (let ((_let_34 (@ tptp.nat_list_decode tptp.zero_zero_nat))) (let ((_let_35 (= _let_34 tptp.nil_nat))) (let ((_let_36 (= tptp.nat_prod_decode (@ tptp.nat_prod_decode_aux tptp.zero_zero_nat)))) (let ((_let_37 (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o tptp.ord_less_nat)))) (let ((_let_38 (= tptp.bNF_Ca8665028551170535155natLeq (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o tptp.ord_less_eq_nat))))) (let ((_let_39 (= tptp.bNF_Ca8459412986667044542atLess _let_37))) (let ((_let_40 (= tptp.set_or5834768355832116004an_nat (lambda ((N tptp.nat) (M tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N)) M)))))) (let ((_let_41 (= tptp.set_or4665077453230672383an_nat (lambda ((I3 tptp.nat) (J2 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt I3) J2)))))) (let ((_let_42 (= tptp.set_or1269000886237332187st_nat (lambda ((N tptp.nat) (M tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt N) (@ tptp.suc M))))))) (let ((_let_43 (= tptp.set_or6659071591806873216st_nat (lambda ((N tptp.nat) (M tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N)) (@ tptp.suc M))))))) (let ((_let_44 (= tptp.set_or5832277885323065728an_int (lambda ((I3 tptp.int) (J2 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I3) tptp.one_one_int)) (@ (@ tptp.minus_minus_int J2) tptp.one_one_int))))))) (let ((_let_45 (= tptp.set_or6656581121297822940st_int (lambda ((I3 tptp.int) (J2 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I3) tptp.one_one_int)) J2)))))) (let ((_let_46 (= tptp.set_or4662586982721622107an_int (lambda ((I3 tptp.int) (J2 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto I3) (@ (@ tptp.minus_minus_int J2) tptp.one_one_int))))))) (let ((_let_47 (= tptp.set_or1266510415728281911st_int (lambda ((I3 tptp.int) (J2 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto I3) J2)))))) (let ((_let_48 (= tptp.upto (lambda ((I3 tptp.int) (J2 tptp.int)) (@ (@ (@ tptp.upto_aux I3) J2) tptp.nil_int))))) (let ((_let_49 (= tptp.inf_inf_int tptp.ord_min_int))) (let ((_let_50 (= tptp.inf_inf_nat tptp.ord_min_nat))) (let ((_let_51 (= tptp.bit_take_bit_num (lambda ((N tptp.nat) (M tptp.num)) (let ((_let_1 (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.numeral_numeral_nat M)))) (@ (@ (@ tptp.if_option_num (= _let_1 tptp.zero_zero_nat)) tptp.none_num) (@ tptp.some_num (@ tptp.num_of_nat _let_1)))))))) (let ((_let_52 (= tptp.condit2214826472909112428ve_nat tptp.finite_finite_nat))) (let ((_let_53 (= 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_54 (= tptp.sup_sup_nat tptp.ord_max_nat))) (let ((_let_55 (= tptp.sup_sup_int tptp.ord_max_int))) (let ((_let_56 (= tptp.pred_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((M tptp.nat) (N tptp.nat)) (= N (@ tptp.suc M)))))))) (let ((_let_57 (@ (@ tptp.image_int_int tptp.abs_abs_int) tptp.top_top_set_int))) (let ((_let_58 (= _let_57 tptp.semiring_1_Nats_int))) (let ((_let_59 (@ tptp.set_ord_atLeast_nat tptp.zero_zero_nat))) (let ((_let_60 (= _let_59 tptp.top_top_set_nat))) (let ((_let_61 (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat))) (let ((_let_62 (@ (@ tptp.comp_nat_nat_nat tptp.suc) tptp.suc))) (let ((_let_63 (= tptp.divide_divide_nat (lambda ((M tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_nat (= N tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat K2) N)) M))))))))) (let ((_let_64 (= tptp.complete_Sup_Sup_nat (lambda ((X6 tptp.set_nat)) (@ (@ (@ tptp.if_nat (= X6 tptp.bot_bot_set_nat)) tptp.zero_zero_nat) (@ tptp.lattic8265883725875713057ax_nat X6)))))) (let ((_let_65 (= tptp.root (lambda ((N tptp.nat) (X4 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)))) X4)))))) (let ((_let_66 (@ tptp.insert_nat tptp.zero_zero_nat))) (let ((_let_67 (not (@ tptp.finite_finite_nat tptp.top_top_set_nat)))) (let ((_let_68 (= tptp.finite_finite_int (lambda ((S6 tptp.set_int)) (exists ((K2 tptp.int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_int_int tptp.abs_abs_int) S6)) (@ tptp.set_ord_atMost_int K2))))))) (let ((_let_69 (@ (@ tptp.map_fu434086159418415080_int_o tptp.rep_Integ) (@ (@ tptp.map_fu4826362097070443709at_o_o tptp.rep_Integ) tptp.id_o)))) (let ((_let_70 (= tptp.semiri1316708129612266289at_nat tptp.id_nat))) (let ((_let_71 (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ))) (let ((_let_72 (@ (@ tptp.map_fu4960017516451851995nt_int tptp.rep_Integ) _let_71))) (let ((_let_73 (= tptp.times_times_int (@ _let_72 (@ tptp.produc27273713700761075at_nat (lambda ((X4 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 X4))) (@ (@ 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))))))) (let ((_let_74 (= tptp.nat_prod_encode (@ tptp.produc6842872674320459806at_nat (lambda ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle (@ (@ tptp.plus_plus_nat M) N))) M)))))) (let ((_let_75 (= tptp.uminus_uminus_int (@ _let_71 (@ tptp.produc2626176000494625587at_nat (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y5) X4))))))) (let ((_let_76 (= tptp.nat2 (lambda ((X4 tptp.int)) (@ (@ tptp.produc6842872674320459806at_nat tptp.minus_minus_nat) (@ tptp.rep_Integ X4)))))) (let ((_let_77 (= tptp.pred (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((X24 tptp.nat)) X24))))) (let ((_let_78 (= tptp.binomial (lambda ((N tptp.nat) (K2 tptp.nat)) (@ tptp.finite_card_set_nat (@ tptp.collect_set_nat (lambda ((K7 tptp.set_nat)) (and (@ (@ tptp.member_set_nat K7) (@ tptp.pow_nat (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N))) (= (@ tptp.finite_card_nat K7) K2))))))))) (let ((_let_79 (= tptp.topolo4055970368930404560y_real (lambda ((X6 (-> tptp.nat tptp.real))) (forall ((J2 tptp.nat)) (exists ((M9 tptp.nat)) (forall ((M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M9) M) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M9) N) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ X6 M)) (@ X6 N)))) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc J2)))))))))))))) (let ((_let_80 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_81 (@ tptp.suc _let_80))) (let ((_let_82 (@ tptp.numeral_numeral_int _let_29))) (let ((_let_83 (= tptp.suc (lambda ((A3 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A3)) tptp.one_one_int)))))) (let ((_let_84 (= tptp.plus_plus_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B3))))))) (let ((_let_85 (= tptp.int_ge_less_than (lambda ((D4 tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z7 tptp.int) (Z6 tptp.int)) (and (@ (@ tptp.ord_less_eq_int D4) Z7) (@ (@ tptp.ord_less_int Z7) Z6))))))))) (let ((_let_86 (= tptp.diffs_int (lambda ((C3 (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int _let_1)) (@ C3 _let_1))))))) (let ((_let_87 (= tptp.diffs_real (lambda ((C3 (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ C3 _let_1))))))) (let ((_let_88 (= tptp.diffs_complex (lambda ((C3 (-> tptp.nat tptp.complex)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ C3 _let_1))))))) (let ((_let_89 (= tptp.abs_abs_real (lambda ((K2 tptp.real)) (@ (@ tptp.times_times_real K2) (@ tptp.sgn_sgn_real K2)))))) (let ((_let_90 (= tptp.abs_abs_int (lambda ((K2 tptp.int)) (@ (@ tptp.times_times_int K2) (@ tptp.sgn_sgn_int K2)))))) (let ((_let_91 (= (@ tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real))) (let ((_let_92 (= (@ tptp.abs_abs_int tptp.one_one_int) tptp.one_one_int))) (let ((_let_93 (= (@ tptp.abs_abs_int tptp.zero_zero_int) tptp.zero_zero_int))) (let ((_let_94 (= (@ tptp.abs_abs_real tptp.zero_zero_real) tptp.zero_zero_real))) (let ((_let_95 (= tptp.int_ge_less_than2 (lambda ((D4 tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z7 tptp.int) (Z6 tptp.int)) (and (@ (@ tptp.ord_less_eq_int D4) Z6) (@ (@ tptp.ord_less_int Z7) Z6))))))))) (let ((_let_96 (= tptp.tan_real (lambda ((X4 tptp.real)) (let ((_let_1 (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) X4))) (@ (@ tptp.divide_divide_real (@ tptp.sin_real _let_1)) (@ (@ tptp.plus_plus_real (@ tptp.cos_real _let_1)) tptp.one_one_real))))))) (let ((_let_97 (= tptp.tan_complex (lambda ((X4 tptp.complex)) (let ((_let_1 (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) X4))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex _let_1)) (@ (@ tptp.plus_plus_complex (@ tptp.cos_complex _let_1)) tptp.one_one_complex))))))) (let ((_let_98 (= 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_99 (= tptp.listrel1p_int (lambda ((R4 (-> tptp.int tptp.int Bool)) (Xs3 tptp.list_int) (Ys3 tptp.list_int)) (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int Xs3) Ys3)) (@ tptp.listrel1_int (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o R4)))))))) (let ((_let_100 (= tptp.listrel1p_nat (lambda ((R4 (-> tptp.nat tptp.nat Bool)) (Xs3 tptp.list_nat) (Ys3 tptp.list_nat)) (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat Xs3) Ys3)) (@ tptp.listrel1_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o R4)))))))) (let ((_let_101 (= tptp.sgn_sgn_real (lambda ((X4 tptp.real)) (@ (@ (@ tptp.if_real (= X4 tptp.zero_zero_real)) tptp.zero_zero_real) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4)) tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))))) (let ((_let_102 (= tptp.sgn_sgn_int (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_int (= X4 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) X4)) tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))))) (let ((_let_103 (@ tptp.power_power_int tptp.zero_zero_int))) (let ((_let_104 (@ tptp.power_power_complex tptp.zero_zero_complex))) (let ((_let_105 (@ tptp.power_power_real tptp.zero_zero_real))) (let ((_let_106 (@ tptp.uminus_uminus_real tptp.one_one_real))) (let ((_let_107 (@ tptp.uminus_uminus_int tptp.one_one_int))) (let ((_let_108 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (let ((_let_109 (@ tptp.numera6690914467698888265omplex _let_29))) (let ((_let_110 (@ tptp.real_V4546457046886955230omplex tptp.pi))) (let ((_let_111 (@ tptp.numeral_numeral_real _let_29))) (let ((_let_112 (@ tptp.real_V1803761363581548252l_real tptp.pi))) (let ((_let_113 (= (@ tptp.sgn_sgn_complex tptp.zero_zero_complex) tptp.zero_zero_complex))) (let ((_let_114 (= (@ tptp.sgn_sgn_real tptp.zero_zero_real) tptp.zero_zero_real))) (let ((_let_115 (= tptp.gbinomial_real (lambda ((A3 tptp.real) (K2 tptp.nat)) (@ (@ (@ tptp.if_real (= K2 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.divide_divide_real (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((L2 tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A3) (@ tptp.semiri5074537144036343181t_real L2))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat)) tptp.one_one_real)) (@ tptp.semiri2265585572941072030t_real K2))))))) (let ((_let_116 (= tptp.gbinomial_complex (lambda ((A3 tptp.complex) (K2 tptp.nat)) (@ (@ (@ tptp.if_complex (= K2 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.divide1717551699836669952omplex (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((L2 tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex A3) (@ tptp.semiri8010041392384452111omplex L2))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat)) tptp.one_one_complex)) (@ tptp.semiri5044797733671781792omplex K2))))))) (let ((_let_117 (= tptp.set_ord_atMost_int (lambda ((U2 tptp.int)) (@ tptp.collect_int (lambda ((X4 tptp.int)) (@ (@ tptp.ord_less_eq_int X4) U2))))))) (let ((_let_118 (= tptp.set_ord_atMost_nat (lambda ((U2 tptp.nat)) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X4) U2))))))) (let ((_let_119 (= tptp.set_or58775011639299419et_int (lambda ((U2 tptp.set_int)) (@ tptp.collect_set_int (lambda ((X4 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int X4) U2))))))) (let ((_let_120 (= tptp.set_or4236626031148496127et_nat (lambda ((U2 tptp.set_nat)) (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat X4) U2))))))) (let ((_let_121 (= tptp.set_ord_atMost_real (lambda ((U2 tptp.real)) (@ tptp.collect_real (lambda ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real X4) U2))))))) (let ((_let_122 (= tptp.archim8280529875227126926d_real (lambda ((X4 tptp.real)) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X4) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))) (let ((_let_123 (= tptp.arsinh_real (lambda ((X4 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X4) (@ (@ tptp.powr_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) (@ 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_124 (= tptp.arcosh_real (lambda ((X4 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X4) (@ (@ tptp.powr_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X4) (@ 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_125 (= 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_126 (= 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_127 (= 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_128 (= tptp.comm_s3181272606743183617d_enat (lambda ((A3 tptp.extended_enat) (N tptp.nat)) (@ (@ (@ tptp.if_Extended_enat (= N tptp.zero_zero_nat)) tptp.one_on7984719198319812577d_enat) (@ (@ (@ (@ tptp.set_fo2538466533108834004d_enat (lambda ((O tptp.nat) (__flatten_var_0 tptp.extended_enat)) (@ (@ tptp.times_7803423173614009249d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A3) (@ tptp.semiri4216267220026989637d_enat O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) tptp.one_on7984719198319812577d_enat)))))) (let ((_let_129 (= 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_130 (= tptp.set_ord_lessThan_int (lambda ((U2 tptp.int)) (@ tptp.collect_int (lambda ((X4 tptp.int)) (@ (@ tptp.ord_less_int X4) U2))))))) (let ((_let_131 (= tptp.set_ord_lessThan_nat (lambda ((U2 tptp.nat)) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.ord_less_nat X4) U2))))))) (let ((_let_132 (= tptp.set_or5984915006950818249n_real (lambda ((U2 tptp.real)) (@ tptp.collect_real (lambda ((X4 tptp.real)) (@ (@ tptp.ord_less_real X4) U2))))))) (let ((_let_133 (= tptp.set_or8419480210114673929d_enat (lambda ((U2 tptp.extended_enat)) (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (@ (@ tptp.ord_le72135733267957522d_enat X4) U2))))))) (let ((_let_134 (= tptp.set_or890127255671739683et_nat (lambda ((U2 tptp.set_nat)) (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (@ (@ tptp.ord_less_set_nat X4) U2))))))) (let ((_let_135 (= 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_136 (= 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_137 (= 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_138 (= tptp.semiri4216267220026989637d_enat (lambda ((N tptp.nat)) (@ (@ (@ tptp.semiri8563196900006977889d_enat (lambda ((I3 tptp.extended_enat)) (@ (@ tptp.plus_p3455044024723400733d_enat I3) tptp.one_on7984719198319812577d_enat))) N) tptp.zero_z5237406670263579293d_enat))))) (let ((_let_139 (= 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_140 (= tptp.ord_less_eq_int (lambda ((W3 tptp.int) (Z6 tptp.int)) (exists ((N tptp.nat)) (= Z6 (@ (@ tptp.plus_plus_int W3) (@ tptp.semiri1314217659103216013at_int N)))))))) (let ((_let_141 (= (@ tptp.semiri1314217659103216013at_int tptp.zero_zero_nat) tptp.zero_zero_int))) (let ((_let_142 (@ tptp.bit_se1146084159140164899it_int tptp.zero_zero_int))) (let ((_let_143 (= _let_142 tptp.bot_bot_nat_o))) (let ((_let_144 (= tptp.numeral_numeral_nat (lambda ((K2 tptp.num)) (@ tptp.suc (@ tptp.pred_numeral K2)))))) (let ((_let_145 (= tptp.insert_int (lambda ((A3 tptp.int) (B5 tptp.set_int)) (@ tptp.collect_int (lambda ((X4 tptp.int)) (or (= X4 A3) (@ (@ tptp.member_int X4) B5)))))))) (let ((_let_146 (= tptp.insert_nat (lambda ((A3 tptp.nat) (B5 tptp.set_nat)) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (or (= X4 A3) (@ (@ tptp.member_nat X4) B5)))))))) (let ((_let_147 (= tptp.insert_set_nat (lambda ((A3 tptp.set_nat) (B5 tptp.set_set_nat)) (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (or (= X4 A3) (@ (@ tptp.member_set_nat X4) B5)))))))) (let ((_let_148 (= tptp.insert_list_nat (lambda ((A3 tptp.list_nat) (B5 tptp.set_list_nat)) (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (or (= X4 A3) (@ (@ tptp.member_list_nat X4) B5)))))))) (let ((_let_149 (= tptp.insert_real (lambda ((A3 tptp.real) (B5 tptp.set_real)) (@ tptp.collect_real (lambda ((X4 tptp.real)) (or (= X4 A3) (@ (@ tptp.member_real X4) B5)))))))) (let ((_let_150 (= tptp.insert_Extended_enat (lambda ((A3 tptp.extended_enat) (B5 tptp.set_Extended_enat)) (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (or (= X4 A3) (@ (@ tptp.member_Extended_enat X4) B5)))))))) (let ((_let_151 (= tptp.uminus1532241313380277803et_int (lambda ((A5 tptp.set_int)) (@ tptp.collect_int (@ tptp.uminus_uminus_int_o (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) A5)))))))) (let ((_let_152 (= tptp.uminus5710092332889474511et_nat (lambda ((A5 tptp.set_nat)) (@ tptp.collect_nat (@ tptp.uminus_uminus_nat_o (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) A5)))))))) (let ((_let_153 (= tptp.uminus613421341184616069et_nat (lambda ((A5 tptp.set_set_nat)) (@ tptp.collect_set_nat (@ tptp.uminus6401447641752708672_nat_o (lambda ((X4 tptp.set_nat)) (@ (@ tptp.member_set_nat X4) A5)))))))) (let ((_let_154 (= tptp.uminus3195874150345416415st_nat (lambda ((A5 tptp.set_list_nat)) (@ tptp.collect_list_nat (@ tptp.uminus5770388063884162150_nat_o (lambda ((X4 tptp.list_nat)) (@ (@ tptp.member_list_nat X4) A5)))))))) (let ((_let_155 (= tptp.uminus612125837232591019t_real (lambda ((A5 tptp.set_real)) (@ tptp.collect_real (@ tptp.uminus_uminus_real_o (lambda ((X4 tptp.real)) (@ (@ tptp.member_real X4) A5)))))))) (let ((_let_156 (= tptp.uminus417252749190364093d_enat (lambda ((A5 tptp.set_Extended_enat)) (@ tptp.collec4429806609662206161d_enat (@ tptp.uminus6636779312473996640enat_o (lambda ((X4 tptp.extended_enat)) (@ (@ tptp.member_Extended_enat X4) A5)))))))) (let ((_let_157 (= tptp.minus_minus_set_nat (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X4))) (and (@ _let_1 A5) (not (@ _let_1 B5)))))))))) (let ((_let_158 (= tptp.minus_minus_set_int (lambda ((A5 tptp.set_int) (B5 tptp.set_int)) (@ tptp.collect_int (lambda ((X4 tptp.int)) (let ((_let_1 (@ tptp.member_int X4))) (and (@ _let_1 A5) (not (@ _let_1 B5)))))))))) (let ((_let_159 (= tptp.minus_2163939370556025621et_nat (lambda ((A5 tptp.set_set_nat) (B5 tptp.set_set_nat)) (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X4))) (and (@ _let_1 A5) (not (@ _let_1 B5)))))))))) (let ((_let_160 (= tptp.minus_7954133019191499631st_nat (lambda ((A5 tptp.set_list_nat) (B5 tptp.set_list_nat)) (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (let ((_let_1 (@ tptp.member_list_nat X4))) (and (@ _let_1 A5) (not (@ _let_1 B5)))))))))) (let ((_let_161 (= tptp.minus_minus_set_real (lambda ((A5 tptp.set_real) (B5 tptp.set_real)) (@ tptp.collect_real (lambda ((X4 tptp.real)) (let ((_let_1 (@ tptp.member_real X4))) (and (@ _let_1 A5) (not (@ _let_1 B5)))))))))) (let ((_let_162 (= tptp.minus_925952699566721837d_enat (lambda ((A5 tptp.set_Extended_enat) (B5 tptp.set_Extended_enat)) (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat X4))) (and (@ _let_1 A5) (not (@ _let_1 B5)))))))))) (let ((_let_163 (= tptp.unique5026877609467782581ep_nat (lambda ((L2 tptp.num) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q5 tptp.nat) (R4 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) R4)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R4) _let_2))) (@ (@ tptp.product_Pair_nat_nat _let_1) R4)))))) __flatten_var_0))))) (let ((_let_164 (= tptp.unique5024387138958732305ep_int (lambda ((L2 tptp.num) (__flatten_var_0 tptp.product_prod_int_int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q5 tptp.int) (R4 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) R4)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R4) _let_2))) (@ (@ tptp.product_Pair_int_int _let_1) R4)))))) __flatten_var_0))))) (let ((_let_165 (@ tptp.ord_less_real _let_106))) (let ((_let_166 (@ tptp.ord_less_int _let_107))) (let ((_let_167 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_168 (@ tptp.ord_less_int tptp.zero_zero_int))) (let ((_let_169 (@ tptp.ord_less_eq_int _let_107))) (let ((_let_170 (@ tptp.ord_less_eq_real _let_106))) (let ((_let_171 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_172 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_173 (= tptp.minus_minus_real (lambda ((A3 tptp.real) (B3 tptp.real)) (@ (@ tptp.plus_plus_real A3) (@ tptp.uminus_uminus_real B3)))))) (let ((_let_174 (= tptp.minus_minus_int (lambda ((A3 tptp.int) (B3 tptp.int)) (@ (@ tptp.plus_plus_int A3) (@ tptp.uminus_uminus_int B3)))))) (let ((_let_175 (@ tptp.ord_less_real tptp.one_one_real))) (let ((_let_176 (@ tptp.ord_less_int tptp.one_one_int))) (let ((_let_177 (@ tptp.ord_less_eq_int tptp.one_one_int))) (let ((_let_178 (@ tptp.ord_less_eq_real tptp.one_one_real))) (let ((_let_179 (= tptp.bit_ri631733984087533419it_int (lambda ((N tptp.nat) (K2 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 K2) _let_1))) _let_1)))))) (let ((_let_180 (= (@ tptp.uminus_uminus_int tptp.zero_zero_int) tptp.zero_zero_int))) (let ((_let_181 (@ tptp.plus_plus_real _let_106))) (let ((_let_182 (@ tptp.plus_plus_int _let_107))) (let ((_let_183 (@ tptp.plus_plus_complex _let_108))) (let ((_let_184 (@ tptp.plus_plus_real tptp.one_one_real))) (let ((_let_185 (@ tptp.plus_plus_int tptp.one_one_int))) (let ((_let_186 (@ tptp.plus_plus_complex tptp.one_one_complex))) (let ((_let_187 (= tptp.artanh_real (lambda ((X4 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X4)) (@ (@ tptp.minus_minus_real tptp.one_one_real) X4)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))) (let ((_let_188 (= tptp.zero_n2687167440665602831ol_nat (lambda ((P6 Bool)) (@ (@ (@ tptp.if_nat P6) tptp.one_one_nat) tptp.zero_zero_nat))))) (let ((_let_189 (@ tptp.zero_n2684676970156552555ol_int true))) (let ((_let_190 (= _let_189 tptp.one_one_int))) (let ((_let_191 (= (@ tptp.zero_n1046097342994218471d_enat false) tptp.zero_z5237406670263579293d_enat))) (let ((_let_192 (= (@ tptp.zero_n1201886186963655149omplex false) tptp.zero_zero_complex))) (let ((_let_193 (= (@ tptp.zero_n3304061248610475627l_real false) tptp.zero_zero_real))) (let ((_let_194 (@ tptp.numeral_numeral_nat _let_29))) (let ((_let_195 (= tptp.vEBT_set_vebt (lambda ((T2 tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_V8194947554948674370ptions T2)))))) (let ((_let_196 (= tptp.dvd_dv3785147216227455552d_enat (lambda ((B3 tptp.extended_enat) (A3 tptp.extended_enat)) (exists ((K2 tptp.extended_enat)) (= A3 (@ (@ tptp.times_7803423173614009249d_enat B3) K2))))))) (let ((_let_197 (= tptp.dvd_dvd_complex (lambda ((A3 tptp.complex) (B3 tptp.complex)) (=> (= A3 tptp.zero_zero_complex) (= B3 tptp.zero_zero_complex)))))) (let ((_let_198 (= tptp.dvd_dvd_real (lambda ((A3 tptp.real) (B3 tptp.real)) (=> (= A3 tptp.zero_zero_real) (= B3 tptp.zero_zero_real)))))) (let ((_let_199 (= tptp.bot_bo4898103413517107610_nat_o (lambda ((X4 tptp.product_prod_nat_nat) (Y5 tptp.product_prod_nat_nat)) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X4) Y5)) tptp.bot_bo5327735625951526323at_nat))))) (let ((_let_200 (= tptp.bot_bot_int_int_o (lambda ((X4 tptp.int) (Y5 tptp.int)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X4) Y5)) tptp.bot_bo1796632182523588997nt_int))))) (let ((_let_201 (= tptp.bot_bo1565574316222977092_nat_o (lambda ((X4 tptp.vEBT_VEBT) (Y5 tptp.nat)) (@ (@ tptp.member373505688050248522BT_nat (@ (@ tptp.produc738532404422230701BT_nat X4) Y5)) tptp.bot_bo1642239108664514429BT_nat))))) (let ((_let_202 (= tptp.bot_bot_nat_nat_o (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X4) Y5)) tptp.bot_bo2099793752762293965at_nat))))) (let ((_let_203 (= tptp.dvd_dvd_int (lambda ((A3 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.modulo_modulo_int B3) A3) tptp.zero_zero_int))))) (let ((_let_204 (= tptp.dvd_dvd_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat B3) A3) tptp.zero_zero_nat))))) (let ((_let_205 (= tptp.ord_less_set_set_nat (lambda ((A5 tptp.set_set_nat) (B5 tptp.set_set_nat)) (@ (@ tptp.ord_less_set_nat_o (lambda ((X4 tptp.set_nat)) (@ (@ tptp.member_set_nat X4) A5))) (lambda ((X4 tptp.set_nat)) (@ (@ tptp.member_set_nat X4) B5))))))) (let ((_let_206 (= tptp.ord_less_set_real (lambda ((A5 tptp.set_real) (B5 tptp.set_real)) (@ (@ tptp.ord_less_real_o (lambda ((X4 tptp.real)) (@ (@ tptp.member_real X4) A5))) (lambda ((X4 tptp.real)) (@ (@ tptp.member_real X4) B5))))))) (let ((_let_207 (= tptp.ord_le2529575680413868914d_enat (lambda ((A5 tptp.set_Extended_enat) (B5 tptp.set_Extended_enat)) (@ (@ tptp.ord_le8499522857272258027enat_o (lambda ((X4 tptp.extended_enat)) (@ (@ tptp.member_Extended_enat X4) A5))) (lambda ((X4 tptp.extended_enat)) (@ (@ tptp.member_Extended_enat X4) B5))))))) (let ((_let_208 (= tptp.vEBT_VEBT_set_vebt (lambda ((T2 tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_vebt_member T2)))))) (let ((_let_209 (= tptp.vEBT_VEBT_low (lambda ((X4 tptp.nat) (N tptp.nat)) (@ (@ tptp.modulo_modulo_nat X4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))) (let ((_let_210 (= 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_211 (@ (@ tptp.vEBT_Leaf false) false))) (let ((_let_212 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (let ((_let_213 (= tptp.vEBT_VEBT_bit_concat (lambda ((H tptp.nat) (L2 tptp.nat) (D4 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) D4))) L2))))) (let ((_let_214 (@ tptp.plus_plus_nat tptp.one_one_nat))) (let ((_let_215 (@ _let_214 tptp.one_one_nat))) (let ((_let_216 (= _let_215 _let_194))) (let ((_let_217 (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)))))))) (let ((_let_218 (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)))))))) (let ((_let_219 (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8040749407984259932d_enat tptp.zero_z5237406670263579293d_enat) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_on7984719198319812577d_enat)) (=> (not _let_2) (= _let_1 tptp.zero_z5237406670263579293d_enat)))))))) (let ((_let_220 (@ _let_185 tptp.one_one_int))) (let ((_let_221 (@ _let_184 tptp.one_one_real))) (let ((_let_222 (@ (@ tptp.plus_p3455044024723400733d_enat tptp.one_on7984719198319812577d_enat) tptp.one_on7984719198319812577d_enat))) (let ((_let_223 (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat))) (let ((_let_224 (= tptp.one_one_nat _let_80))) (let ((_let_225 (@ _let_168 tptp.one_one_int))) (let ((_let_226 (@ _let_167 tptp.one_one_real))) (let ((_let_227 (@ _let_223 tptp.one_on7984719198319812577d_enat))) (let ((_let_228 (@ _let_212 tptp.one_one_nat))) (let ((_let_229 (@ tptp.ord_le72135733267957522d_enat tptp.one_on7984719198319812577d_enat))) (let ((_let_230 (@ tptp.ord_less_nat tptp.one_one_nat))) (let ((_let_231 (@ _let_171 tptp.one_one_int))) (let ((_let_232 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_233 (@ _let_232 tptp.one_one_nat))) (let ((_let_234 (@ _let_172 tptp.one_one_real))) (let ((_let_235 (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat))) (let ((_let_236 (@ _let_235 tptp.one_on7984719198319812577d_enat))) (let ((_let_237 (@ tptp.ord_less_eq_nat tptp.one_one_nat))) (let ((_let_238 (= (@ (@ tptp.divide_divide_int tptp.one_one_int) _let_82) tptp.zero_zero_int))) (let ((_let_239 (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) _let_194) tptp.zero_zero_nat))) (let ((_let_240 (@ tptp.power_8040749407984259932d_enat tptp.zero_z5237406670263579293d_enat))) (let ((_let_241 (= tptp.vEBT_VEBT_high (lambda ((X4 tptp.nat) (N tptp.nat)) (@ (@ tptp.divide_divide_nat X4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))) (let ((_let_242 (@ tptp.size_size_num tptp.one))) (let ((_let_243 (= _let_242 tptp.zero_zero_nat))) (let ((_let_244 (@ tptp.power_power_nat _let_194))) (let ((_let_245 (@ _let_244 tptp.m))) (let ((_let_246 (@ _let_244 tptp.deg))) (let ((_let_247 (@ (@ tptp.ord_less_nat tptp.ma) _let_246))) (let ((_let_248 (@ (@ tptp.ord_less_eq_nat tptp.mi) tptp.ma))) (let ((_let_249 (@ tptp.ord_less_nat tptp.xa))) (let ((_let_250 (= tptp.gen_length_nat (lambda ((N tptp.nat) (Xs3 tptp.list_nat)) (@ (@ tptp.plus_plus_nat N) (@ tptp.size_size_list_nat Xs3)))))) (let ((_let_251 (= tptp.gen_length_int (lambda ((N tptp.nat) (Xs3 tptp.list_int)) (@ (@ tptp.plus_plus_nat N) (@ tptp.size_size_list_int Xs3)))))) (let ((_let_252 (= tptp.gen_length_VEBT_VEBT (lambda ((N tptp.nat) (Xs3 tptp.list_VEBT_VEBT)) (@ (@ tptp.plus_plus_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs3)))))) (let ((_let_253 (= tptp.mi tptp.ma))) (let ((_let_254 (= tptp.ord_max_int (lambda ((A3 tptp.int) (B3 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int A3) B3)) B3) A3))))) (let ((_let_255 (= tptp.ord_max_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_eq_nat A3) B3)) B3) A3))))) (let ((_let_256 (= tptp.ord_max_set_int (lambda ((A3 tptp.set_int) (B3 tptp.set_int)) (@ (@ (@ tptp.if_set_int (@ (@ tptp.ord_less_eq_set_int A3) B3)) B3) A3))))) (let ((_let_257 (= tptp.ord_max_set_nat (lambda ((A3 tptp.set_nat) (B3 tptp.set_nat)) (@ (@ (@ tptp.if_set_nat (@ (@ tptp.ord_less_eq_set_nat A3) B3)) B3) A3))))) (let ((_let_258 (= tptp.ord_max_real (lambda ((A3 tptp.real) (B3 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_eq_real A3) B3)) B3) A3))))) (let ((_let_259 (@ (@ tptp.vEBT_vebt_insert tptp.summary) _let_2))) (let ((_let_260 (@ tptp.vEBT_VEBT_minNull _let_4))) (let ((_let_261 (@ (@ (@ tptp.if_VEBT_VEBT _let_260) _let_259) tptp.summary))) (let ((_let_262 (= tptp.bot_bot_nat tptp.zero_zero_nat))) (let ((_let_263 (= tptp.bot_bot_set_int (@ tptp.collect_int tptp.bot_bot_int_o)))) (let ((_let_264 (= tptp.bot_bot_set_nat (@ tptp.collect_nat tptp.bot_bot_nat_o)))) (let ((_let_265 (= tptp.bot_bot_set_real (@ tptp.collect_real tptp.bot_bot_real_o)))) (let ((_let_266 (= tptp.bot_bo7653980558646680370d_enat (@ tptp.collec4429806609662206161d_enat tptp.bot_bo1954855461789132331enat_o)))) (let ((_let_267 (= tptp.bot_bot_set_set_nat (@ tptp.collect_set_nat tptp.bot_bot_set_nat_o)))) (let ((_let_268 (= tptp.bot_bot_set_list_nat (@ tptp.collect_list_nat tptp.bot_bot_list_nat_o)))) (let ((_let_269 (= tptp.finite_finite_nat (lambda ((N5 tptp.set_nat)) (exists ((M tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) N5) (@ (@ tptp.ord_less_eq_nat X4) M)))))))) (let ((_let_270 (= tptp.ord_less_eq_set_int (lambda ((A5 tptp.set_int) (B5 tptp.set_int)) (forall ((T2 tptp.int)) (let ((_let_1 (@ tptp.member_int T2))) (=> (@ _let_1 A5) (@ _let_1 B5)))))))) (let ((_let_271 (= tptp.ord_less_eq_set_nat (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (forall ((T2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat T2))) (=> (@ _let_1 A5) (@ _let_1 B5)))))))) (let ((_let_272 (= tptp.ord_le6893508408891458716et_nat (lambda ((A5 tptp.set_set_nat) (B5 tptp.set_set_nat)) (forall ((T2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat T2))) (=> (@ _let_1 A5) (@ _let_1 B5)))))))) (let ((_let_273 (= tptp.ord_less_eq_set_real (lambda ((A5 tptp.set_real) (B5 tptp.set_real)) (forall ((T2 tptp.real)) (let ((_let_1 (@ tptp.member_real T2))) (=> (@ _let_1 A5) (@ _let_1 B5)))))))) (let ((_let_274 (= tptp.ord_le7203529160286727270d_enat (lambda ((A5 tptp.set_Extended_enat) (B5 tptp.set_Extended_enat)) (forall ((T2 tptp.extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat T2))) (=> (@ _let_1 A5) (@ _let_1 B5)))))))) (let ((_let_275 (= tptp.vEBT_V8194947554948674370ptions (lambda ((T2 tptp.vEBT_VEBT) (X4 tptp.nat)) (or (@ (@ tptp.vEBT_V5719532721284313246member T2) X4) (@ (@ tptp.vEBT_VEBT_membermima T2) X4)))))) (let ((_let_276 (= tptp.ord_le2932123472753598470d_enat (lambda ((A3 tptp.extended_enat) (B3 tptp.extended_enat)) (exists ((C3 tptp.extended_enat)) (= B3 (@ (@ tptp.plus_p3455044024723400733d_enat A3) C3))))))) (let ((_let_277 (= tptp.ord_less_int (lambda ((X4 tptp.int) (Y5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X4) Y5) (not (= X4 Y5))))))) (let ((_let_278 (= tptp.ord_less_set_int (lambda ((X4 tptp.set_int) (Y5 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int X4) Y5) (not (= X4 Y5))))))) (let ((_let_279 (= tptp.ord_less_set_nat (lambda ((X4 tptp.set_nat) (Y5 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat X4) Y5) (not (= X4 Y5))))))) (let ((_let_280 (= tptp.ord_less_real (lambda ((X4 tptp.real) (Y5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real X4) Y5) (not (= X4 Y5))))))) (let ((_let_281 (= tptp.ord_le72135733267957522d_enat (lambda ((X4 tptp.extended_enat) (Y5 tptp.extended_enat)) (and (@ (@ tptp.ord_le2932123472753598470d_enat X4) Y5) (not (= X4 Y5))))))) (let ((_let_282 (= tptp.ord_less_eq_nat (lambda ((M tptp.nat) (N tptp.nat)) (exists ((K2 tptp.nat)) (= N (@ (@ tptp.plus_plus_nat M) K2))))))) (let ((_let_283 (= tptp.ord_less_nat (lambda ((M tptp.nat) (N tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M) N) (not (= M N))))))) (let ((_let_284 (= tptp.deg (@ (@ tptp.plus_plus_nat tptp.na) tptp.m)))) (let ((_let_285 (= tptp.vEBT_VEBT_valid tptp.vEBT_invar_vebt))) (let ((_let_286 (= (@ tptp.suc tptp.na) tptp.m))) (let ((_let_287 (= tptp.vEBT_V5917875025757280293ildren (lambda ((N tptp.nat) (TreeList tptp.list_VEBT_VEBT) (X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) (@ (@ tptp.vEBT_VEBT_high X4) N))) (@ (@ tptp.vEBT_VEBT_low X4) N)))))) (let ((_let_288 (@ _let_8 _let_2))) (let ((_let_289 (= _let_288 _let_5))) (let ((_let_290 (= tptp.i _let_2))) (let ((_let_291 (ho_5857 k_6099 (ho_5981 k_5980 k_12624)))) (let ((_let_292 (ho_5778 k_5777 tptp.one))) (let ((_let_293 (ho_5794 (ho_5768 (ho_6101 k_6100 BOOLEAN_TERM_VARIABLE_1455748) _let_292) _let_291))) (let ((_let_294 (ho_5756 k_5755 BOOLEAN_TERM_VARIABLE_1455755))) (let ((_let_295 (ho_5752 k_5751 tptp.one))) (let ((_let_296 (ho_5754 k_5753 _let_295))) (let ((_let_297 (ho_5763 (ho_5762 k_5761 k_5760) (ho_5778 k_5832 _let_295)))) (let ((_let_298 (ho_5770 k_5769 k_5767))) (let ((_let_299 (ho_5768 k_6153 tptp.mi))) (let ((_let_300 (ho_7807 k_7806 tptp.treeList))) (let ((_let_301 (ho_7808 (ho_12626 k_12625 (ho_7808 _let_300 _let_293)) (ho_5794 _let_299 (ho_5794 (ho_5768 k_6102 (ho_5771 _let_298 (ho_5766 k_5765 (ho_5759 (ho_5758 k_5764 (ho_5759 _let_297 (ho_5759 (ho_5758 k_5757 _let_294) _let_296))) _let_294)))) tptp.na))))) (let ((_let_302 (ho_12628 k_12627 tptp.treeList))) (let ((_let_303 (APPLY_UF ho_7808))) (let ((_let_304 (APPLY_UF ho_5794))) (let ((_let_305 (APPLY_UF ho_5768))) (let ((_let_306 (ho_5756 k_5755 true))) (let ((_let_307 (ho_5794 (ho_5768 k_6102 (ho_5771 _let_298 (ho_5766 k_5765 (ho_5759 (ho_5758 k_5764 (ho_5759 _let_297 (ho_5759 (ho_5758 k_5757 _let_306) _let_296))) _let_306)))) tptp.na))) (let ((_let_308 (= _let_292 _let_307))) (let ((_let_309 (CONG (CONG (CONG (REFL :args (k_6100)) (MACRO_SR_PRED_INTRO :args ((= _let_308 BOOLEAN_TERM_VARIABLE_1455748))) :args (APPLY_UF ho_6101)) (REFL :args (_let_292)) :args _let_305) (REFL :args (_let_291)) :args _let_304))) (let ((_let_310 (APPLY_UF ho_5759))) (let ((_let_311 (CONG (REFL :args (k_5755)) (MACRO_SR_PRED_INTRO :args ((= true BOOLEAN_TERM_VARIABLE_1455755))) :args (APPLY_UF ho_5756)))) (let ((_let_312 (APPLY_UF ho_5758))) (let ((_let_313 (CONG (CONG (REFL :args (k_12625)) (CONG (REFL :args (_let_300)) _let_309 :args _let_303) :args (APPLY_UF ho_12626)) (CONG (REFL :args (_let_299)) (CONG (CONG (REFL :args (k_6102)) (CONG (REFL :args (_let_298)) (CONG (REFL :args (k_5765)) (CONG (CONG (REFL :args (k_5764)) (CONG (REFL :args (_let_297)) (CONG (CONG (REFL :args (k_5757)) _let_311 :args _let_312) (REFL :args (_let_296)) :args _let_310) :args _let_310) :args _let_312) _let_311 :args _let_310) :args (APPLY_UF ho_5766)) :args (APPLY_UF ho_5771)) :args _let_305) (REFL :args (tptp.na)) :args _let_304) :args _let_304) :args _let_303))) (let ((_let_314 (CONG _let_313 (CONG (CONG (REFL :args (k_7806)) (CONG (CONG (REFL :args (_let_302)) _let_309 :args (APPLY_UF ho_12629)) _let_313 :args (APPLY_UF ho_12630)) :args (APPLY_UF ho_7807)) _let_309 :args _let_303) :args (=)))) (let ((_let_315 (ho_5794 (ho_5768 (ho_6101 k_6100 _let_308) _let_292) _let_291))) (let ((_let_316 (ho_7808 (ho_12626 k_12625 (ho_7808 _let_300 _let_315)) (ho_5794 _let_299 _let_307)))) (let ((_let_317 (= _let_316 (ho_7808 (ho_7807 k_7806 (ho_12630 (ho_12629 _let_302 _let_315) _let_316)) _let_315)))) (let ((_let_318 (@ (@ tptp.divide_divide_int _let_189) _let_82))) (let ((_let_319 (@ tptp.pred_numeral _let_29))) (let ((_let_320 (@ (@ tptp.power_power_nat (@ _let_26 (@ tptp.rep_Integ (@ (@ tptp.plus_plus_int (@ (@ (@ tptp.semiri8420488043553186161ux_int ll_3) _let_319) _let_318)) _let_189)))) tptp.na))) (let ((_let_321 (@ (@ (@ tptp.if_nat (= _let_242 _let_320)) _let_242) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat ll_2))))) (let ((_let_322 (@ tptp.modulo_modulo_nat tptp.mi))) (let ((_let_323 (@ (@ tptp.vEBT_vebt_insert (@ _let_3 _let_321)) (@ _let_322 _let_320)))) (let ((_let_324 (= _let_323 (@ (@ tptp.nth_VEBT_VEBT (@ (@ _let_6 _let_321) _let_323)) _let_321)))) (let ((_let_325 (@ (@ tptp.power_power_nat (@ _let_26 (@ tptp.rep_Integ (@ (@ tptp.plus_plus_int (@ (@ (@ tptp.semiri8420488043553186161ux_int (lambda ((I3 tptp.int)) (@ (@ tptp.plus_plus_int I3) (@ tptp.zero_n2684676970156552555ol_int true)))) _let_319) _let_318)) _let_189)))) tptp.na))) (let ((_let_326 (@ (@ (@ tptp.if_nat (= _let_242 _let_325)) _let_242) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (not (forall ((K2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.zero_n2684676970156552555ol_int true))) (let ((_let_3 (@ (@ tptp.divide_divide_int _let_2) (@ tptp.numeral_numeral_int _let_1)))) (let ((_let_4 (@ tptp.semiri8420488043553186161ux_int (lambda ((I3 tptp.int)) (@ (@ tptp.plus_plus_int I3) (@ tptp.zero_n2684676970156552555ol_int true)))))) (let 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(EQ_RESOLVE (ASSUME :args (_let_282)) (MACRO_SR_EQ_INTRO :args (_let_282 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_336 (ASSUME :args (_let_281)))) (let ((_let_337 (ASSUME :args (_let_280)))) (let ((_let_338 (ASSUME :args (_let_279)))) (let ((_let_339 (ASSUME :args (_let_278)))) (let ((_let_340 (ASSUME :args (_let_277)))) (let ((_let_341 (EQ_RESOLVE (ASSUME :args (_let_276)) (MACRO_SR_EQ_INTRO :args (_let_276 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_342 (ASSUME :args (_let_275)))) (let ((_let_343 (EQ_RESOLVE (ASSUME :args (_let_274)) (MACRO_SR_EQ_INTRO :args (_let_274 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_344 (EQ_RESOLVE (ASSUME :args (_let_273)) (MACRO_SR_EQ_INTRO :args (_let_273 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_345 (EQ_RESOLVE (ASSUME :args (_let_272)) (MACRO_SR_EQ_INTRO :args (_let_272 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_346 (EQ_RESOLVE (ASSUME :args (_let_271)) (MACRO_SR_EQ_INTRO :args (_let_271 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_347 (EQ_RESOLVE (ASSUME :args (_let_270)) (MACRO_SR_EQ_INTRO :args (_let_270 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_348 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_269)) (MACRO_SR_EQ_INTRO :args (_let_269 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args ((= tptp.finite_finite_nat (lambda ((N5 tptp.set_nat)) (not (forall ((M tptp.nat)) (not (forall ((X4 tptp.nat)) (or (not (@ (@ tptp.member_nat X4) N5)) (@ (@ tptp.ord_less_eq_nat X4) M)))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_349 (ASSUME :args (_let_268)))) (let ((_let_350 (ASSUME :args (_let_267)))) (let ((_let_351 (ASSUME :args (_let_266)))) (let ((_let_352 (ASSUME :args (_let_265)))) (let ((_let_353 (ASSUME :args (_let_264)))) (let ((_let_354 (ASSUME :args (_let_263)))) (let ((_let_355 (SYMM (ASSUME :args (_let_262))))) (let ((_let_356 (ASSUME :args (_let_258)))) (let ((_let_357 (EQ_RESOLVE (ASSUME :args (_let_257)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_257 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_358 (EQ_RESOLVE (ASSUME :args (_let_256)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_256 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_359 (EQ_RESOLVE (ASSUME :args (_let_255)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_255 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_360 (ASSUME :args (_let_254)))) (let ((_let_361 (ASSUME :args (_let_252)))) (let ((_let_362 (ASSUME :args (_let_251)))) (let ((_let_363 (ASSUME :args (_let_250)))) (let ((_let_364 (EQ_RESOLVE (SYMM (ASSUME :args (_let_243))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args ((= tptp.zero_zero_nat _let_242) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_365 (ASSUME :args (_let_241)))) (let ((_let_366 (SYMM (ASSUME :args (_let_238))))) (let ((_let_367 (EQ_RESOLVE (ASSUME :args (_let_224)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_224 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_368 (0))) (let ((_let_369 (EQ_RESOLVE (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_219)) (MACRO_SR_EQ_INTRO :args (_let_219 SB_DEFAULT SBA_FIXPOINT))) :args _let_368) (MACRO_SR_EQ_INTRO (AND_INTRO _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args ((= tptp.one_on7984719198319812577d_enat (@ _let_240 tptp.zero_zero_nat)) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_370 (EQ_RESOLVE (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_218)) (MACRO_SR_EQ_INTRO :args (_let_218 SB_DEFAULT SBA_FIXPOINT))) :args _let_368) (MACRO_SR_EQ_INTRO (AND_INTRO _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args ((= tptp.one_one_real (@ _let_105 tptp.zero_zero_nat)) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_371 (EQ_RESOLVE (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_217)) (MACRO_SR_EQ_INTRO :args (_let_217 SB_DEFAULT SBA_FIXPOINT))) :args _let_368) (MACRO_SR_EQ_INTRO (AND_INTRO _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args ((= tptp.one_one_complex (@ _let_104 tptp.zero_zero_nat)) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_372 (ASSUME :args (_let_213)))) (let ((_let_373 (ASSUME :args (_let_210)))) (let ((_let_374 (ASSUME :args (_let_209)))) (let ((_let_375 (ASSUME :args (_let_208)))) (let ((_let_376 (ASSUME :args (_let_207)))) (let ((_let_377 (ASSUME :args (_let_206)))) (let ((_let_378 (ASSUME :args (_let_205)))) (let ((_let_379 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_204)) (MACRO_SR_EQ_INTRO :args (_let_204 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args ((= tptp.dvd_dvd_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (= tptp.zero_zero_nat (@ (@ tptp.modulo_modulo_nat B3) A3)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_380 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_203)) (MACRO_SR_EQ_INTRO :args (_let_203 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args ((= tptp.dvd_dvd_int (lambda ((A3 tptp.int) (B3 tptp.int)) (= tptp.zero_zero_int (@ (@ tptp.modulo_modulo_int B3) A3)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_381 (ASSUME :args (_let_202)))) (let ((_let_382 (ASSUME :args (_let_201)))) (let ((_let_383 (ASSUME :args (_let_200)))) (let ((_let_384 (ASSUME :args (_let_199)))) (let ((_let_385 (EQ_RESOLVE (ASSUME :args (_let_198)) (MACRO_SR_EQ_INTRO :args (_let_198 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_386 (EQ_RESOLVE (ASSUME :args (_let_197)) (MACRO_SR_EQ_INTRO :args (_let_197 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_387 (EQ_RESOLVE (ASSUME :args (_let_196)) (MACRO_SR_EQ_INTRO :args (_let_196 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_388 (EQ_RESOLVE (ASSUME :args (_let_195)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_195 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_389 (SYMM (ASSUME :args (_let_193))))) (let ((_let_390 (SYMM (ASSUME :args (_let_192))))) (let ((_let_391 (SYMM (ASSUME :args (_let_191))))) (let ((_let_392 (SYMM (ASSUME :args (_let_190))))) (let ((_let_393 (EQ_RESOLVE (ASSUME :args (_let_188)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_188 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_394 (EQ_RESOLVE (ASSUME :args (_let_187)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_187 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_395 (ASSUME :args (_let_179)))) (let ((_let_396 (ASSUME :args (_let_174)))) (let ((_let_397 (ASSUME :args (_let_173)))) (let ((_let_398 (EQ_RESOLVE (ASSUME :args (_let_164)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_164 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_399 (EQ_RESOLVE (ASSUME :args (_let_163)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_398 _let_397 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(let ((_let_408 (ASSUME :args (_let_154)))) (let ((_let_409 (ASSUME :args (_let_153)))) (let ((_let_410 (ASSUME :args (_let_152)))) (let ((_let_411 (ASSUME :args (_let_151)))) (let ((_let_412 (EQ_RESOLVE (ASSUME :args (_let_150)) (MACRO_SR_EQ_INTRO :args (_let_150 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_413 (EQ_RESOLVE (ASSUME :args (_let_149)) (MACRO_SR_EQ_INTRO :args (_let_149 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_414 (EQ_RESOLVE (ASSUME :args (_let_148)) (MACRO_SR_EQ_INTRO :args (_let_148 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_415 (EQ_RESOLVE (ASSUME :args (_let_147)) (MACRO_SR_EQ_INTRO :args (_let_147 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_416 (EQ_RESOLVE (ASSUME :args (_let_146)) (MACRO_SR_EQ_INTRO :args (_let_146 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_417 (EQ_RESOLVE (ASSUME :args (_let_145)) (MACRO_SR_EQ_INTRO :args (_let_145 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_418 (ASSUME :args (_let_144)))) (let ((_let_419 (EQ_RESOLVE (SYMM (ASSUME :args (_let_143))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args ((= tptp.bot_bot_nat_o _let_142) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_420 (EQ_RESOLVE (ASSUME :args (_let_140)) (MACRO_SR_EQ_INTRO :args (_let_140 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_421 (EQ_RESOLVE (ASSUME :args (_let_139)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_139 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_422 (EQ_RESOLVE (ASSUME :args (_let_138)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_138 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_423 (EQ_RESOLVE (ASSUME :args (_let_137)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_137 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_424 (EQ_RESOLVE (ASSUME :args (_let_136)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_136 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_425 (EQ_RESOLVE (ASSUME :args (_let_135)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_135 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_426 (EQ_RESOLVE (ASSUME :args (_let_134)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_134 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_427 (EQ_RESOLVE (ASSUME :args (_let_133)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_133 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_428 (EQ_RESOLVE (ASSUME :args (_let_132)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_132 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_429 (EQ_RESOLVE (ASSUME :args (_let_131)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_131 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_430 (EQ_RESOLVE (ASSUME :args (_let_130)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_130 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_431 (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_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :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_432 (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_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args ((= tptp.comm_s3181272606743183617d_enat (lambda ((A3 tptp.extended_enat) (N tptp.nat)) (@ (@ (@ tptp.if_Extended_enat (= tptp.zero_zero_nat N)) tptp.one_on7984719198319812577d_enat) (@ (@ (@ (@ tptp.set_fo2538466533108834004d_enat (lambda ((O tptp.nat) (__flatten_var_0 tptp.extended_enat)) (@ (@ tptp.times_7803423173614009249d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A3) (@ tptp.semiri4216267220026989637d_enat O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) tptp.one_on7984719198319812577d_enat)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_433 (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_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :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_434 (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_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :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_435 (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_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :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_436 (EQ_RESOLVE (ASSUME :args (_let_124)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_124 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_437 (EQ_RESOLVE (ASSUME :args (_let_123)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_123 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_438 (EQ_RESOLVE (ASSUME :args (_let_122)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_122 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_439 (ASSUME :args (_let_121)))) (let ((_let_440 (EQ_RESOLVE (ASSUME :args (_let_120)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_120 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_441 (EQ_RESOLVE (ASSUME :args (_let_119)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_119 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_442 (EQ_RESOLVE (ASSUME :args (_let_118)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_118 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_443 (EQ_RESOLVE (ASSUME :args (_let_117)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_117 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_444 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_116)) (MACRO_SR_EQ_INTRO :args (_let_116 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args ((= tptp.gbinomial_complex (lambda ((A3 tptp.complex) (K2 tptp.nat)) (@ (@ (@ tptp.if_complex (= tptp.zero_zero_nat K2)) tptp.one_one_complex) (@ (@ tptp.divide1717551699836669952omplex (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((L2 tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex A3) (@ tptp.semiri8010041392384452111omplex L2))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat)) tptp.one_one_complex)) (@ tptp.semiri5044797733671781792omplex K2))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_445 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_115)) (MACRO_SR_EQ_INTRO :args (_let_115 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args ((= tptp.gbinomial_real (lambda ((A3 tptp.real) (K2 tptp.nat)) (@ (@ (@ tptp.if_real (= tptp.zero_zero_nat K2)) tptp.one_one_real) (@ (@ tptp.divide_divide_real (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((L2 tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A3) (@ tptp.semiri5074537144036343181t_real L2))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat)) tptp.one_one_real)) (@ tptp.semiri2265585572941072030t_real K2))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_446 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_102)) (MACRO_SR_EQ_INTRO :args (_let_102 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args ((= tptp.sgn_sgn_int (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_int (= tptp.zero_zero_int X4)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) X4)) tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_447 (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_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args ((= tptp.sgn_sgn_real (lambda ((X4 tptp.real)) (@ (@ (@ tptp.if_real (= tptp.zero_zero_real X4)) tptp.zero_zero_real) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4)) tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_448 (ASSUME :args (_let_100)))) (let ((_let_449 (ASSUME :args (_let_99)))) (let ((_let_450 (EQ_RESOLVE (ASSUME :args (_let_98)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_98 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_451 (EQ_RESOLVE (ASSUME :args (_let_97)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_97 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_452 (EQ_RESOLVE (ASSUME :args (_let_96)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_96 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_453 (EQ_RESOLVE (ASSUME :args (_let_95)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_95 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_454 (EQ_RESOLVE (ASSUME :args (_let_90)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_90 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_455 (EQ_RESOLVE (ASSUME :args (_let_89)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_89 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_456 (EQ_RESOLVE (ASSUME :args (_let_88)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_88 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_457 (EQ_RESOLVE (ASSUME :args (_let_87)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_87 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_458 (EQ_RESOLVE (ASSUME :args (_let_86)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_86 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_459 (EQ_RESOLVE (ASSUME :args (_let_85)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_85 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_460 (EQ_RESOLVE (ASSUME :args (_let_84)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_84 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_461 (EQ_RESOLVE (ASSUME :args (_let_83)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_83 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_462 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_79)) (MACRO_SR_EQ_INTRO :args (_let_79 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args ((= tptp.topolo4055970368930404560y_real (lambda ((X6 (-> tptp.nat tptp.real))) (forall ((J2 tptp.nat)) (not (forall ((M9 tptp.nat)) (not (forall ((M tptp.nat) (BOUND_VARIABLE_195603 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat M9))) (or (not (@ _let_1 M)) (not (@ _let_1 BOUND_VARIABLE_195603)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ X6 M)) (@ X6 BOUND_VARIABLE_195603)))) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc J2))))))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_463 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_78)) (MACRO_SR_EQ_INTRO :args (_let_78 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args ((= tptp.binomial (lambda ((N tptp.nat) (K2 tptp.nat)) (@ tptp.finite_card_set_nat (@ tptp.collect_set_nat (lambda ((K7 tptp.set_nat)) (and (@ (@ tptp.member_set_nat K7) (@ tptp.pow_nat (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N))) (= K2 (@ tptp.finite_card_nat K7)))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_464 (EQ_RESOLVE (ASSUME :args (_let_77)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_77 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_465 (ASSUME :args (_let_76)))) (let ((_let_466 (ASSUME :args (_let_75)))) (let ((_let_467 (EQ_RESOLVE (ASSUME :args (_let_74)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_74 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_468 (EQ_RESOLVE (ASSUME :args (_let_73)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_73 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_469 (EQ_RESOLVE (SYMM (ASSUME :args (_let_70))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args ((= tptp.id_nat tptp.semiri1316708129612266289at_nat) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_470 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_68)) (MACRO_SR_EQ_INTRO :args (_let_68 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args ((= tptp.finite_finite_int (lambda ((S6 tptp.set_int)) (not (forall ((K2 tptp.int)) (not (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_int_int tptp.abs_abs_int) S6)) (@ tptp.set_ord_atMost_int K2))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_471 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_65)) (MACRO_SR_EQ_INTRO :args (_let_65 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args ((= tptp.root (lambda ((N tptp.nat) (X4 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)))) X4)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_472 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_64)) (MACRO_SR_EQ_INTRO :args (_let_64 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args ((= tptp.complete_Sup_Sup_nat (lambda ((X6 tptp.set_nat)) (@ (@ (@ tptp.if_nat (= tptp.bot_bot_set_nat X6)) tptp.zero_zero_nat) (@ tptp.lattic8265883725875713057ax_nat X6)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_473 (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_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args ((= tptp.divide_divide_nat (lambda ((M tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_nat (= tptp.zero_zero_nat N)) tptp.zero_zero_nat) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat K2) N)) M))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_474 (EQ_RESOLVE (SYMM (ASSUME :args (_let_60))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args ((= tptp.top_top_set_nat _let_59) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_475 (EQ_RESOLVE (SYMM (ASSUME :args (_let_58))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args ((= tptp.semiring_1_Nats_int _let_57) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_476 (EQ_RESOLVE (ASSUME :args (_let_56)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_56 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_477 (EQ_RESOLVE (ASSUME :args (_let_55)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_55 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_478 (EQ_RESOLVE (ASSUME :args (_let_54)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_54 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_479 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_53)) (MACRO_SR_EQ_INTRO :args (_let_53 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :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_480 (EQ_RESOLVE (ASSUME :args (_let_52)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_52 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_481 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_51)) (MACRO_SR_EQ_INTRO :args (_let_51 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args ((= tptp.bit_take_bit_num (lambda ((N tptp.nat) (M tptp.num)) (let ((_let_1 (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.numeral_numeral_nat M)))) (@ (@ (@ 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_482 (ASSUME :args (_let_50)))) (let ((_let_483 (ASSUME :args (_let_49)))) (let ((_let_484 (ASSUME :args (_let_48)))) (let ((_let_485 (EQ_RESOLVE (ASSUME :args (_let_47)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_47 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_486 (EQ_RESOLVE (ASSUME :args (_let_46)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_46 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_487 (EQ_RESOLVE (ASSUME :args (_let_45)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_45 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_488 (EQ_RESOLVE (ASSUME :args (_let_44)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_44 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_489 (EQ_RESOLVE (ASSUME :args (_let_43)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_43 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_490 (EQ_RESOLVE (ASSUME :args (_let_42)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_42 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_491 (ASSUME :args (_let_41)))) (let ((_let_492 (EQ_RESOLVE (ASSUME :args (_let_40)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_40 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_493 (EQ_RESOLVE (ASSUME :args (_let_39)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_39 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_494 (EQ_RESOLVE (ASSUME :args (_let_38)) (MACRO_SR_EQ_INTRO (AND_INTRO _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_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_38 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_495 (EQ_RESOLVE (ASSUME :args (_let_36)) (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 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_36 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_496 (EQ_RESOLVE (SYMM (ASSUME :args (_let_35))) (MACRO_SR_EQ_INTRO (AND_INTRO _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_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args ((= tptp.nil_nat _let_34) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_497 (EQ_RESOLVE (ASSUME :args (_let_33)) (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 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_33 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_498 (EQ_RESOLVE (ASSUME :args (_let_23)) (MACRO_SR_EQ_INTRO (AND_INTRO _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_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_23 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_499 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _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_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args ((= tptp.comple2295165028678016749d_enat (lambda ((A5 tptp.set_Extended_enat)) (@ (@ (@ tptp.if_Extended_enat (= tptp.bot_bo7653980558646680370d_enat A5)) tptp.extend5688581933313929465d_enat) (@ tptp.ord_Le1955565732374568822d_enat (lambda ((X4 tptp.extended_enat)) (@ (@ tptp.member_Extended_enat X4) A5)))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_500 (EQ_RESOLVE (SYMM (ASSUME :args (_let_15))) (MACRO_SR_EQ_INTRO (AND_INTRO _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_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args ((= tptp.zero_z5237406670263579293d_enat tptp.bot_bo4199563552545308370d_enat) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_501 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _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_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args ((= tptp.comple4398354569131411667d_enat (lambda ((A5 tptp.set_Extended_enat)) (@ (@ (@ tptp.if_Extended_enat (= tptp.bot_bo7653980558646680370d_enat A5)) tptp.zero_z5237406670263579293d_enat) (@ (@ (@ tptp.if_Extended_enat (@ tptp.finite4001608067531595151d_enat A5)) (@ tptp.lattic921264341876707157d_enat A5)) tptp.extend5688581933313929465d_enat)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_502 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_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_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args ((= tptp.times_7803423173614009249d_enat (lambda ((M tptp.extended_enat) (N tptp.extended_enat)) (@ (@ (@ tptp.extend3600170679010898289d_enat (lambda ((O tptp.nat)) (@ (@ (@ tptp.extend3600170679010898289d_enat (lambda ((P6 tptp.nat)) (@ tptp.extended_enat2 (@ (@ tptp.times_times_nat O) P6)))) (@ (@ (@ tptp.if_Extended_enat (= tptp.zero_zero_nat O)) tptp.zero_z5237406670263579293d_enat) tptp.extend5688581933313929465d_enat)) N))) (@ (@ (@ tptp.if_Extended_enat (= tptp.zero_z5237406670263579293d_enat N)) tptp.zero_z5237406670263579293d_enat) tptp.extend5688581933313929465d_enat)) M))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_503 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO (AND_INTRO _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_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_504 (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_11)) (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 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329) :args (_let_11 SB_DEFAULT SBA_FIXPOINT))) _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_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329))) (let ((_let_505 (not _let_324))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (ASSUME :args (_let_10)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_504 :args ((not (= _let_5 _let_9)) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not _let_328) _let_505))) (PREPROCESS :args ((= _let_505 (not _let_317)))) (CONG _let_314 :args (not)))) (EQ_RESOLVE (ASSUME :args (_let_289)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_289 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_504 :args ((= _let_5 _let_288) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= _let_328 _let_324))) (PREPROCESS :args ((= _let_324 _let_317))) _let_314)) :args (false false (= _let_301 (ho_7808 (ho_7807 k_7806 (ho_12630 (ho_12629 _let_302 _let_293) _let_301)) _let_293)))) :args (_let_290 _let_289 (forall ((X tptp.nat) (D tptp.nat)) (= (@ (@ (@ tptp.vEBT_VEBT_bit_concat (@ (@ tptp.vEBT_VEBT_high X) D)) (@ (@ tptp.vEBT_VEBT_low X) D)) D) X)) _let_260 (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ (@ tptp.vEBT_VEBT_high tptp.mi) tptp.na))) X_1))) (forall ((Xs tptp.list_nat) (I tptp.nat)) (= (@ (@ (@ tptp.list_update_nat Xs) I) (@ (@ tptp.nth_nat Xs) I)) Xs)) (forall ((Xs tptp.list_int) (I tptp.nat)) (= (@ (@ (@ tptp.list_update_int Xs) I) (@ (@ tptp.nth_int Xs) I)) Xs)) (forall ((Xs tptp.list_VEBT_VEBT) (I tptp.nat)) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) (@ (@ tptp.nth_VEBT_VEBT Xs) I)) Xs)) (forall ((I tptp.nat) (J tptp.nat) (Xs tptp.list_nat) (X tptp.nat)) (=> (not (= I J)) (= (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs) I) X)) J) (@ (@ tptp.nth_nat Xs) J)))) (forall ((I tptp.nat) (J tptp.nat) (Xs tptp.list_int) (X tptp.int)) (=> (not (= I J)) (= (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int Xs) I) X)) J) (@ (@ tptp.nth_int Xs) J)))) (forall ((I tptp.nat) (J tptp.nat) (Xs tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (not (= I J)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) X)) J) (@ (@ tptp.nth_VEBT_VEBT Xs) J)))) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ (@ tptp.vEBT_VEBT_high tptp.mi) tptp.na))) X_1))) (forall ((Xs tptp.list_int) (I tptp.nat) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.list_update_int Xs) I))) (= (@ (@ (@ tptp.list_update_int (@ _let_1 X)) I) Y) (@ _let_1 Y)))) (forall ((Xs tptp.list_nat) (I tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.list_update_nat Xs) I))) (= (@ (@ (@ tptp.list_update_nat (@ _let_1 X)) I) Y) (@ _let_1 Y)))) (forall ((Xs tptp.list_VEBT_VEBT) (I tptp.nat) (X tptp.vEBT_VEBT) (Y tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I))) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ _let_1 X)) I) Y) (@ _let_1 Y)))) (=> (not _let_260) (= tptp.summary _let_259)) (forall ((X2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.vEBT_VEBT_high tptp.mi) tptp.na))) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT tptp.treeList) _let_1) (@ (@ tptp.vEBT_vebt_insert (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_1)) (@ (@ tptp.vEBT_VEBT_low tptp.mi) tptp.na))))) (@ (@ tptp.vEBT_invar_vebt X2) tptp.na)))) (not (@ (@ tptp.ord_less_nat tptp.mi) tptp.xa)) (forall ((I tptp.nat) (I2 tptp.nat) (Xs tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT) (X3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.list_u1324408373059187874T_VEBT Xs))) (=> (not (= I I2)) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ (@ _let_1 I) X)) I2) X3) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ (@ _let_1 I2) X3)) I) X))))) (forall ((I tptp.nat) (I2 tptp.nat) (Xs tptp.list_int) (X tptp.int) (X3 tptp.int)) (let ((_let_1 (@ tptp.list_update_int Xs))) (=> (not (= I I2)) (= (@ (@ (@ tptp.list_update_int (@ (@ _let_1 I) X)) I2) X3) (@ (@ (@ tptp.list_update_int (@ (@ _let_1 I2) X3)) I) X))))) (forall ((I tptp.nat) (I2 tptp.nat) (Xs tptp.list_nat) (X tptp.nat) (X3 tptp.nat)) (let ((_let_1 (@ tptp.list_update_nat Xs))) (=> (not (= I I2)) (= (@ (@ (@ tptp.list_update_nat (@ (@ _let_1 I) X)) I2) X3) (@ (@ (@ tptp.list_update_nat (@ (@ _let_1 I2) X3)) I) X))))) _let_287 _let_248 (@ (@ tptp.vEBT_invar_vebt _let_261) tptp.m) (forall ((T tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull T)) (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) X_12)))) (forall ((T tptp.vEBT_VEBT) (X tptp.nat)) (=> (@ tptp.vEBT_VEBT_minNull T) (not (@ (@ tptp.vEBT_vebt_member T) X)))) (@ (@ tptp.vEBT_invar_vebt tptp.summary) tptp.m) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (= (@ (@ tptp.vEBT_V8194947554948674370ptions T) X) (@ (@ tptp.vEBT_vebt_member T) X)))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions T) X) (@ (@ tptp.vEBT_vebt_member T) X)))) (=> _let_253 (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_249 tptp.mi) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (= (@ (@ tptp.vEBT_vebt_member T) X) (@ (@ tptp.member_nat X) (@ tptp.vEBT_set_vebt T))))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 tptp.treeList)) (@ (@ tptp.vEBT_invar_vebt X2) tptp.na))) (not (@ (@ tptp.vEBT_V8194947554948674370ptions tptp.summary) tptp.i)) (and (not (= tptp.xa tptp.mi)) (not (= tptp.xa tptp.ma))) _let_286 (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (= (@ tptp.vEBT_set_vebt T) (@ tptp.vEBT_VEBT_set_vebt T)))) _let_285 (forall ((T tptp.vEBT_VEBT) (D tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) D) (@ (@ tptp.vEBT_VEBT_valid T) D))) (forall ((T tptp.vEBT_VEBT) (D tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid T) D) (@ (@ tptp.vEBT_invar_vebt T) D))) (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real X) X)) (forall ((X tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat X) X)) (forall ((X tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int X) X)) (forall ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat X) X)) (forall ((X tptp.int)) (@ (@ tptp.ord_less_eq_int X) X)) (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real A) A)) (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A) A)) (forall ((A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int 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 ((Xs tptp.list_Extended_enat) (P (-> tptp.extended_enat Bool)) (N2 tptp.nat)) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ tptp.set_Extended_enat2 Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s3941691890525107288d_enat Xs)) (@ P (@ (@ tptp.nth_Extended_enat Xs) N2))))) (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_set_nat) (P (-> tptp.set_nat Bool)) (N2 tptp.nat)) (=> (forall ((X5 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X5) (@ tptp.set_set_nat2 Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s3254054031482475050et_nat Xs)) (@ P (@ (@ tptp.nth_set_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_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 ((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 ((T tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))) _let_284 _let_283 (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N2) (@ (@ tptp.ord_less_eq_nat M2) N2))) (forall ((X tptp.nat)) (=> (forall ((N3 tptp.nat)) (not (= X (@ (@ tptp.plus_plus_nat N3) N3)))) (not (forall ((N3 tptp.nat)) (not (= X (@ (@ tptp.plus_plus_nat N3) (@ tptp.suc N3)))))))) (forall ((T tptp.vEBT_VEBT)) (not (@ (@ tptp.vEBT_invar_vebt T) tptp.zero_zero_nat))) (forall ((T tptp.vEBT_VEBT)) (not (@ (@ tptp.vEBT_invar_vebt T) tptp.zero_zero_nat))) (forall ((Nat tptp.nat) (Nat2 tptp.nat)) (= (= (@ tptp.suc Nat) (@ tptp.suc Nat2)) (= Nat Nat2))) (forall ((X22 tptp.nat) (Y2 tptp.nat)) (= (= (@ tptp.suc X22) (@ tptp.suc Y2)) (= X22 Y2))) (forall ((A tptp.extended_enat) (P (-> tptp.extended_enat Bool))) (= (@ (@ tptp.member_Extended_enat A) (@ tptp.collec4429806609662206161d_enat 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.set_nat) (P (-> tptp.set_nat Bool))) (= (@ (@ tptp.member_set_nat A) (@ tptp.collect_set_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_Extended_enat)) (= (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (@ (@ tptp.member_Extended_enat X4) A2))) A2)) (forall ((A2 tptp.set_real)) (= (@ tptp.collect_real (lambda ((X4 tptp.real)) (@ (@ tptp.member_real X4) A2))) A2)) (forall ((A2 tptp.set_list_nat)) (= (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (@ (@ tptp.member_list_nat X4) A2))) A2)) (forall ((A2 tptp.set_set_nat)) (= (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (@ (@ tptp.member_set_nat X4) A2))) A2)) (forall ((A2 tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) A2))) A2)) (forall ((A2 tptp.set_int)) (= (@ tptp.collect_int (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) A2))) A2)) (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.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (=> (forall ((X5 tptp.set_nat)) (= (@ P X5) (@ Q X5))) (= (@ tptp.collect_set_nat P) (@ tptp.collect_set_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 ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc M2)) (@ tptp.suc N2)) (@ (@ tptp.ord_less_nat M2) N2))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N2) (@ (@ tptp.ord_less_nat (@ tptp.suc M2)) (@ tptp.suc N2)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat N2) (@ tptp.suc N2))) (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) (M2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) (@ tptp.suc M2)) (@ (@ tptp.ord_less_eq_nat N2) M2))) (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 ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M2))) (= (@ _let_1 (@ tptp.suc N2)) (@ tptp.suc (@ _let_1 N2))))) (forall ((M2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat M2) tptp.zero_zero_nat) M2)) (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat M2) N2) tptp.zero_zero_nat) (and (= M2 tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat)))) (forall ((K tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M2)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M2) N2)))) (forall ((K tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M2)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M2) N2)))) (forall ((Xs tptp.list_VEBT_VEBT) (I tptp.nat) (X tptp.vEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) X)) (@ tptp.size_s6755466524823107622T_VEBT Xs))) (forall ((Xs tptp.list_int) (I tptp.nat) (X tptp.int)) (= (@ tptp.size_size_list_int (@ (@ (@ tptp.list_update_int Xs) I) X)) (@ tptp.size_size_list_int Xs))) (forall ((Xs tptp.list_nat) (I tptp.nat) (X tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ (@ tptp.list_update_nat Xs) I) X)) (@ tptp.size_size_list_nat Xs))) (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 ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N2)) (or (@ _let_1 M2) (@ _let_1 N2))))) (forall ((Xs tptp.list_VEBT_VEBT) (I tptp.nat) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) I) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) X) Xs))) (forall ((Xs tptp.list_int) (I tptp.nat) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs)) I) (= (@ (@ (@ tptp.list_update_int Xs) I) X) Xs))) (forall ((Xs tptp.list_nat) (I tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs)) I) (= (@ (@ (@ tptp.list_update_nat Xs) I) X) Xs))) (forall ((I tptp.nat) (Xs tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) X)) I) X))) (forall ((I tptp.nat) (Xs tptp.list_int) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int Xs) I) X)) I) X))) (forall ((I tptp.nat) (Xs tptp.list_nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs) I) X)) I) X))) (forall ((I tptp.nat) (Xs tptp.list_VEBT_VEBT) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_VEBT_VEBT Xs))) (let ((_let_2 (@ tptp.size_s6755466524823107622T_VEBT Xs))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ tptp.set_VEBT_VEBT2 Xs))))))) (forall ((I tptp.nat) (Xs tptp.list_int) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs))) (let ((_let_2 (@ tptp.size_size_list_int Xs))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int (@ (@ (@ tptp.list_update_int Xs) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ tptp.set_int2 Xs))))))) (forall ((I tptp.nat) (Xs tptp.list_nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (let ((_let_2 (@ tptp.size_size_list_nat Xs))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat (@ (@ (@ tptp.list_update_nat Xs) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ tptp.set_nat2 Xs))))))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N2) (not (forall ((Q2 tptp.nat)) (not (= N2 (@ tptp.suc (@ (@ tptp.plus_plus_nat M2) Q2)))))))) (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 ((M tptp.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 tptp.zero_zero_nat) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N2) (@ P (@ tptp.suc I3))))))) (forall ((I tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_nat I) (@ tptp.suc (@ (@ tptp.plus_plus_nat I) M2)))) (forall ((I tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_nat I) (@ tptp.suc (@ (@ tptp.plus_plus_nat M2) I)))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (exists ((M3 tptp.nat)) (= N2 (@ tptp.suc M3))))) (= tptp.ord_less_nat (lambda ((M tptp.nat) (N tptp.nat)) (exists ((K2 tptp.nat)) (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M) K2)))))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N2) (exists ((K3 tptp.nat)) (= N2 (@ tptp.suc (@ (@ tptp.plus_plus_nat M2) K3)))))) (forall ((N2 tptp.nat)) (exists ((Xs2 tptp.list_VEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) N2))) (forall ((N2 tptp.nat)) (exists ((Xs2 tptp.list_int)) (= (@ tptp.size_size_list_int Xs2) N2))) (forall ((N2 tptp.nat)) (exists ((Xs2 tptp.list_nat)) (= (@ tptp.size_size_list_nat Xs2) N2))) (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_int) (Ys tptp.list_int)) (=> (not (= (@ tptp.size_size_list_int Xs) (@ tptp.size_size_list_int 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 ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat M2) (@ tptp.suc N2)) (or (= M2 tptp.zero_zero_nat) (exists ((J2 tptp.nat)) (and (= M2 (@ tptp.suc J2)) (@ (@ tptp.ord_less_nat J2) N2)))))) (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (= (@ (@ tptp.plus_plus_nat I) K3) J))))) (forall ((X tptp.list_VEBT_VEBT) (Y tptp.list_VEBT_VEBT)) (=> (not (= (@ tptp.size_s6755466524823107622T_VEBT X) (@ tptp.size_s6755466524823107622T_VEBT Y))) (not (= X Y)))) (forall ((X tptp.num) (Y tptp.num)) (=> (not (= (@ tptp.size_size_num X) (@ tptp.size_size_num Y))) (not (= X Y)))) (forall ((X tptp.vEBT_VEBT) (Y tptp.vEBT_VEBT)) (=> (not (= (@ tptp.size_size_VEBT_VEBT X) (@ tptp.size_size_VEBT_VEBT Y))) (not (= X Y)))) (forall ((X tptp.list_int) (Y tptp.list_int)) (=> (not (= (@ tptp.size_size_list_int X) (@ tptp.size_size_list_int Y))) (not (= X Y)))) (forall ((X tptp.list_nat) (Y tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat X) (@ tptp.size_size_list_nat Y))) (not (= X Y)))) (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (exists ((M3 tptp.nat)) (= N2 (@ tptp.suc M3))))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat M2) N2) M2) (= N2 tptp.zero_zero_nat))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M2)) N2) (@ (@ tptp.plus_plus_nat M2) (@ tptp.suc N2)))) (forall ((M2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M2)))) (forall ((M2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M2)))) (forall ((M2 tptp.nat)) (not (= (@ tptp.suc M2) 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 ((N2 tptp.nat)) (not (= N2 (@ tptp.suc N2)))) (forall ((P (-> tptp.nat tptp.nat Bool)) (M2 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 M2) N2))))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.plus_plus_nat M2) N2)) (or (and (= M2 _let_1) (= N2 tptp.zero_zero_nat)) (and (= M2 tptp.zero_zero_nat) (= N2 _let_1)))))) (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 ((X tptp.nat) (Y tptp.nat)) (=> (= (@ tptp.suc X) (@ tptp.suc Y)) (= X Y))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.plus_plus_nat M2) N2) _let_1) (or (and (= M2 _let_1) (= N2 tptp.zero_zero_nat)) (and (= M2 tptp.zero_zero_nat) (= N2 _let_1)))))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M2)) N2) (@ tptp.suc (@ (@ tptp.plus_plus_nat M2) N2)))) (forall ((Y tptp.nat)) (=> (not (= Y tptp.zero_zero_nat)) (not (forall ((Nat3 tptp.nat)) (not (= Y (@ tptp.suc Nat3))))))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) N2) 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 ((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 ((N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N2))) (=> (not (@ _let_1 M2)) (= (@ _let_1 (@ tptp.suc M2)) (= N2 M2))))) (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I) 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 I))))) (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I) J) (=> (forall ((I4 tptp.nat)) (@ (@ P I4) (@ tptp.suc I4))) (=> (forall ((I4 tptp.nat) (J3 tptp.nat) (K3 tptp.nat)) (let ((_let_1 (@ P I4))) (=> (@ (@ tptp.ord_less_nat I4) J3) (=> (@ (@ tptp.ord_less_nat J3) K3) (=> (@ _let_1 J3) (=> (@ (@ P J3) K3) (@ _let_1 K3))))))) (@ (@ P I) J))))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat J) K) (@ (@ tptp.ord_less_nat (@ tptp.suc I)) K)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M2)) (@ tptp.suc N2)) (@ (@ tptp.ord_less_nat M2) N2))) (forall ((N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N2))) (=> (not (@ _let_1 M2)) (=> (@ _let_1 (@ tptp.suc M2)) (= M2 N2))))) (forall ((N2 tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N2)) M2) (exists ((M4 tptp.nat)) (and (= M2 (@ tptp.suc M4)) (@ (@ tptp.ord_less_nat N2) M4))))) (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 ((M2 tptp.nat) (N2 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat M2) N2)) (@ (@ tptp.ord_less_nat N2) (@ tptp.suc M2)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M2))) (= (@ _let_1 (@ tptp.suc N2)) (or (@ _let_1 N2) (= M2 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 ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M2))) (=> (@ _let_1 N2) (@ _let_1 (@ tptp.suc N2))))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M2))) (=> (@ _let_1 (@ tptp.suc N2)) (=> (not (@ _let_1 N2)) (= M2 N2))))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc M2))) (=> (@ (@ tptp.ord_less_nat M2) N2) (=> (not (= _let_1 N2)) (@ (@ tptp.ord_less_nat _let_1) N2))))) (forall ((I tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc I)) K) (not (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J3) (not (= K (@ tptp.suc J3)))))))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M2)) N2) (@ (@ tptp.ord_less_nat M2) N2))) (forall ((I tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K) (=> (not (= K (@ tptp.suc I))) (not (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J3) (not (= K (@ tptp.suc J3))))))))) (forall ((K tptp.nat) (L tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) L) (=> (= (@ (@ tptp.plus_plus_nat M2) L) (@ (@ tptp.plus_plus_nat K) N2)) (@ (@ tptp.ord_less_nat M2) N2)))) (forall ((I tptp.nat) (J tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M2) J))))) (forall ((I tptp.nat) (J tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M2))))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) K)))) (forall ((J tptp.nat) (I tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat J) I)) I))) (forall ((I tptp.nat) (J tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) J)) I))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat K) L) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L))))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) J)) K) (@ (@ tptp.ord_less_nat I) K))) (forall ((M2 tptp.nat) (N2 tptp.nat) (R (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (=> (forall ((X5 tptp.nat)) (@ (@ R X5) X5)) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ R X5))) (=> (@ _let_1 Y3) (=> (@ (@ R Y3) Z) (@ _let_1 Z))))) (=> (forall ((N3 tptp.nat)) (@ (@ R N3) (@ tptp.suc N3))) (@ (@ R M2) N2)))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (=> (@ P M2) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N3) (=> (@ P N3) (@ P (@ tptp.suc N3))))) (@ P N2))))) (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M5)) N3) (@ P M5))) (@ P N3))) (@ P N2))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat M2) N2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) M2))) (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) N2))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.ord_less_eq_nat M2))) (= (@ _let_2 _let_1) (or (@ _let_2 N2) (= M2 _let_1)))))) (forall ((N2 tptp.nat) (M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) M6) (exists ((M3 tptp.nat)) (= M6 (@ tptp.suc M3))))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat M2))) (=> (@ _let_1 N2) (@ _let_1 (@ tptp.suc N2))))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.ord_less_eq_nat M2))) (=> (@ _let_2 _let_1) (=> (not (@ _let_2 N2)) (= M2 _let_1)))))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N2) (@ (@ tptp.ord_less_eq_nat M2) N2))) _let_282 (forall ((I tptp.nat) (J tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M2) J))))) (forall ((I tptp.nat) (J tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M2))))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) K)))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ (@ tptp.ord_less_eq_nat K) L) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L))))) (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 ((M2 tptp.nat) (K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M2) K)) N2) (@ (@ tptp.ord_less_eq_nat K) N2))) (forall ((M2 tptp.nat) (K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M2) K)) N2) (@ (@ tptp.ord_less_eq_nat M2) N2))) (forall ((N2 tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) (@ (@ tptp.plus_plus_nat M2) N2))) (forall ((N2 tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) (@ (@ tptp.plus_plus_nat N2) M2))) (forall ((M2 tptp.nat) (K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M2) K)) N2) (not (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (not (@ (@ tptp.ord_less_eq_nat K) N2)))))) (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 ((M5 tptp.nat)) (and (@ (@ tptp.ord_less_nat M5) N3) (not (@ P M5))))))) (@ P N2)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) 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 ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P N2) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat K3) N2) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I5) K3) (not (@ P I5)))) (@ P (@ tptp.suc K3))))))) (forall ((X tptp.extended_enat) (Xs tptp.list_Extended_enat)) (=> (@ (@ tptp.member_Extended_enat X) (@ tptp.set_Extended_enat2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s3941691890525107288d_enat Xs)))) (forall ((X tptp.real) (Xs tptp.list_real)) (=> (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_real Xs)))) (forall ((X tptp.set_nat) (Xs tptp.list_set_nat)) (=> (@ (@ tptp.member_set_nat X) (@ tptp.set_set_nat2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s3254054031482475050et_nat Xs)))) (forall ((X tptp.vEBT_VEBT) (Xs tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s6755466524823107622T_VEBT Xs)))) (forall ((X tptp.int) (Xs tptp.list_int)) (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_int Xs)))) (forall ((X tptp.nat) (Xs tptp.list_nat)) (=> (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_nat Xs)))) (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_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 ((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 ((Xs tptp.list_Extended_enat) (B tptp.set_Extended_enat)) (= (@ (@ tptp.ord_le7203529160286727270d_enat (@ tptp.set_Extended_enat2 Xs)) B) (forall ((X4 tptp.extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat X4))) (=> (@ _let_1 (@ tptp.set_Extended_enat2 Xs)) (@ _let_1 B)))))) (forall ((Xs tptp.list_real) (B tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 Xs)) B) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.member_real X4))) (=> (@ _let_1 (@ tptp.set_real2 Xs)) (@ _let_1 B)))))) (forall ((Xs tptp.list_set_nat) (B tptp.set_set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.set_set_nat2 Xs)) B) (forall ((X4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X4))) (=> (@ _let_1 (@ tptp.set_set_nat2 Xs)) (@ _let_1 B)))))) (forall ((Xs tptp.list_VEBT_VEBT) (B tptp.set_VEBT_VEBT)) (= (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) B) (forall ((X4 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.member_VEBT_VEBT X4))) (=> (@ _let_1 (@ tptp.set_VEBT_VEBT2 Xs)) (@ _let_1 B)))))) (forall ((Xs tptp.list_nat) (B tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) B) (forall ((X4 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X4))) (=> (@ _let_1 (@ tptp.set_nat2 Xs)) (@ _let_1 B)))))) (forall ((Xs tptp.list_int) (B tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) B) (forall ((X4 tptp.int)) (let ((_let_1 (@ tptp.member_int X4))) (=> (@ _let_1 (@ tptp.set_int2 Xs)) (@ _let_1 B)))))) (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat) (M2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_nat (@ F N2)) (@ F M2)) (@ (@ tptp.ord_less_nat N2) M2)))) (forall ((F (-> tptp.nat tptp.extended_enat)) (N2 tptp.nat) (M2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_le72135733267957522d_enat (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ F N2)) (@ F M2)) (@ (@ tptp.ord_less_nat N2) M2)))) (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat) (M2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_real (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_real (@ F N2)) (@ F M2)) (@ (@ tptp.ord_less_nat N2) M2)))) (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat) (M2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_int (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_int (@ F N2)) (@ F M2)) (@ (@ tptp.ord_less_nat N2) M2)))) (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N2) N4) (@ (@ tptp.ord_less_nat (@ F N2)) (@ F N4))))) (forall ((F (-> tptp.nat tptp.extended_enat)) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_le72135733267957522d_enat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N2) N4) (@ (@ tptp.ord_le72135733267957522d_enat (@ F N2)) (@ F N4))))) (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_real (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N2) N4) (@ (@ tptp.ord_less_real (@ F N2)) (@ F N4))))) (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_int (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N2) N4) (@ (@ tptp.ord_less_int (@ F N2)) (@ F N4))))) (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (@ (@ tptp.ord_less_eq_real (@ F N4)) (@ F N2))))) (forall ((F (-> tptp.nat tptp.set_nat)) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (@ (@ tptp.ord_less_eq_set_nat (@ F N4)) (@ F N2))))) (forall ((F (-> tptp.nat tptp.set_int)) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (@ (@ tptp.ord_less_eq_set_int (@ F N4)) (@ F N2))))) (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (@ (@ tptp.ord_less_eq_nat (@ F N4)) (@ F N2))))) (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (@ (@ tptp.ord_less_eq_int (@ F N4)) (@ F N2))))) (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (@ (@ tptp.ord_less_eq_real (@ F N2)) (@ F N4))))) (forall ((F (-> tptp.nat tptp.set_nat)) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (@ (@ tptp.ord_less_eq_set_nat (@ F N2)) (@ F N4))))) (forall ((F (-> tptp.nat tptp.set_int)) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (@ (@ tptp.ord_less_eq_set_int (@ F N2)) (@ F N4))))) (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (@ (@ tptp.ord_less_eq_nat (@ F N2)) (@ F N4))))) (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (@ (@ tptp.ord_less_eq_int (@ F N2)) (@ F N4))))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_nat M2) (@ 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 ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat M2) (@ tptp.suc N2)) (@ (@ tptp.ord_less_eq_nat M2) N2))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ (@ tptp.ord_less_nat N2) (@ tptp.suc M2)) (= N2 M2)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N2) (@ (@ tptp.ord_less_nat M2) N2))) (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ P J) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) N3) (=> (@ (@ tptp.ord_less_nat N3) J) (=> (@ P (@ tptp.suc N3)) (@ P N3))))) (@ P I))))) (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ P I) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) N3) (=> (@ (@ tptp.ord_less_nat N3) J) (=> (@ P N3) (@ P (@ tptp.suc N3)))))) (@ P J))))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N2) (@ (@ tptp.ord_less_nat M2) N2))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N2) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N2))) (forall ((F (-> tptp.nat tptp.nat)) (M2 tptp.nat) (K tptp.nat)) (=> (forall ((M3 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M3) N3) (@ (@ tptp.ord_less_nat (@ F M3)) (@ F N3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ F M2)) K)) (@ F (@ (@ tptp.plus_plus_nat M2) K))))) (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P N2) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat K3) N2) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) K3) (not (@ P I5)))) (@ P K3)))))) (= (lambda ((Y4 tptp.list_VEBT_VEBT) (Z2 tptp.list_VEBT_VEBT)) (= Y4 Z2)) (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 ((Y4 tptp.list_int) (Z2 tptp.list_int)) (= Y4 Z2)) (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))))))) (= (lambda ((Y4 tptp.list_nat) (Z2 tptp.list_nat)) (= Y4 Z2)) (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))))))) (forall ((K tptp.nat) (P (-> tptp.nat tptp.vEBT_VEBT Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (exists ((X6 tptp.vEBT_VEBT)) (@ (@ P I3) X6)))) (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 tptp.int Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (exists ((X6 tptp.int)) (@ (@ P I3) X6)))) (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 ((K tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (exists ((X6 tptp.nat)) (@ (@ P I3) X6)))) (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 ((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_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)))) (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_Extended_enat) (A2 tptp.set_Extended_enat) (X tptp.extended_enat) (I tptp.nat)) (=> (@ (@ tptp.ord_le7203529160286727270d_enat (@ tptp.set_Extended_enat2 Xs)) A2) (=> (@ (@ tptp.member_Extended_enat X) A2) (@ (@ tptp.ord_le7203529160286727270d_enat (@ tptp.set_Extended_enat2 (@ (@ (@ tptp.list_u3071683517702156500d_enat Xs) I) X))) A2)))) (forall ((Xs tptp.list_real) (A2 tptp.set_real) (X tptp.real) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 Xs)) A2) (=> (@ (@ tptp.member_real X) A2) (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real Xs) I) X))) A2)))) (forall ((Xs tptp.list_set_nat) (A2 tptp.set_set_nat) (X tptp.set_nat) (I tptp.nat)) (=> (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.set_set_nat2 Xs)) A2) (=> (@ (@ tptp.member_set_nat X) A2) (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.set_set_nat2 (@ (@ (@ tptp.list_update_set_nat Xs) I) X))) A2)))) (forall ((Xs tptp.list_VEBT_VEBT) (A2 tptp.set_VEBT_VEBT) (X tptp.vEBT_VEBT) (I tptp.nat)) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) A2) (=> (@ (@ tptp.member_VEBT_VEBT X) A2) (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) X))) A2)))) (forall ((Xs tptp.list_nat) (A2 tptp.set_nat) (X tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) A2) (=> (@ (@ tptp.member_nat X) A2) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs) I) X))) A2)))) (forall ((Xs tptp.list_int) (A2 tptp.set_int) (X tptp.int) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) A2) (=> (@ (@ tptp.member_int X) A2) (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs) I) X))) A2)))) (forall ((Xs tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Xs)) (@ P X4))) (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_int) (P (-> tptp.int Bool))) (= (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) (@ tptp.set_int2 Xs)) (@ P X4))) (forall ((I3 tptp.nat)) (=> 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(=> (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs)) (@ P X)))) (forall ((X tptp.extended_enat) (Xs tptp.list_Extended_enat)) (= (@ (@ tptp.member_Extended_enat X) (@ tptp.set_Extended_enat2 Xs)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s3941691890525107288d_enat Xs)) (= (@ (@ tptp.nth_Extended_enat Xs) I3) X))))) (forall ((X tptp.real) (Xs tptp.list_real)) (= (@ (@ tptp.member_real X) (@ 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) X))))) (forall ((X tptp.set_nat) (Xs tptp.list_set_nat)) (= (@ (@ tptp.member_set_nat X) (@ tptp.set_set_nat2 Xs)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s3254054031482475050et_nat Xs)) (= (@ (@ tptp.nth_set_nat Xs) I3) X))))) (forall ((X tptp.vEBT_VEBT) (Xs tptp.list_VEBT_VEBT)) (= (@ (@ tptp.member_VEBT_VEBT X) (@ 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) X))))) (forall ((X tptp.int) (Xs tptp.list_int)) (= (@ (@ tptp.member_int X) (@ 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) X))))) (forall ((X tptp.nat) (Xs tptp.list_nat)) (= (@ (@ tptp.member_nat X) (@ 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) X))))) (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_int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_int Xs)) (=> (forall ((X5 tptp.int)) (=> (@ (@ 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Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))) (forall ((A tptp.int) (B2 tptp.int) (F (-> tptp.int tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (= (@ F B2) C) (=> (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))) (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.set_nat)) (C tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (= (@ F B2) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X5) Y3) (@ (@ tptp.ord_less_eq_set_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_set_nat (@ F A)) C))))) (forall ((A tptp.real) (F (-> tptp.real tptp.real)) (B2 tptp.real) (C tptp.real)) (=> (= A (@ F B2)) (=> (@ (@ tptp.ord_less_eq_real B2) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_real A) (@ F C)))))) (forall ((A tptp.nat) (F (-> tptp.real tptp.nat)) (B2 tptp.real) (C tptp.real)) (=> (= A (@ F B2)) (=> (@ (@ tptp.ord_less_eq_real B2) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real 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.real tptp.int)) (B2 tptp.real) (C tptp.real)) (=> (= A (@ F B2)) (=> (@ (@ tptp.ord_less_eq_real B2) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int A) (@ F C)))))) (forall ((A tptp.real) (F (-> tptp.nat tptp.real)) (B2 tptp.nat) (C tptp.nat)) (=> (= A (@ F B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_real A) (@ F C)))))) (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B2 tptp.nat) (C tptp.nat)) (=> (= A (@ F B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat 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.nat tptp.int)) (B2 tptp.nat) (C tptp.nat)) (=> (= A (@ F B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int A) (@ F C)))))) (forall ((A tptp.real) (F (-> tptp.int tptp.real)) (B2 tptp.int) (C tptp.int)) (=> (= A (@ F B2)) (=> (@ (@ tptp.ord_less_eq_int B2) C) (=> (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_real A) (@ F C)))))) (forall ((A tptp.nat) (F (-> tptp.int tptp.nat)) (B2 tptp.int) (C tptp.int)) (=> (= A (@ F B2)) (=> (@ (@ tptp.ord_less_eq_int B2) C) (=> (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int 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.int tptp.int)) (B2 tptp.int) (C tptp.int)) (=> (= A (@ F B2)) (=> (@ (@ tptp.ord_less_eq_int B2) C) (=> (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int A) (@ F C)))))) (forall ((A tptp.set_nat) (F (-> tptp.real tptp.set_nat)) (B2 tptp.real) (C tptp.real)) (=> (= A (@ F B2)) (=> (@ (@ tptp.ord_less_eq_real B2) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X5) Y3) (@ (@ tptp.ord_less_eq_set_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_set_nat A) (@ F C)))))) (forall ((X tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real Y) X))) (forall ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X) Y) (@ (@ tptp.ord_less_eq_nat Y) X))) (forall ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_eq_int X) Y) (@ (@ tptp.ord_less_eq_int Y) X))) (forall ((X tptp.real) (Y tptp.real)) (=> (= X Y) (@ (@ tptp.ord_less_eq_real X) Y))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (= X Y) (@ (@ tptp.ord_less_eq_set_nat X) Y))) (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (= X Y) (@ (@ tptp.ord_less_eq_set_int X) Y))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (= X Y) (@ (@ tptp.ord_less_eq_nat X) Y))) (forall ((X tptp.int) (Y tptp.int)) (=> (= X Y) (@ (@ tptp.ord_less_eq_int X) Y))) (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_eq_real (@ F B2)) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_real (@ F A)) C))))) (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_eq_nat (@ F B2)) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))) (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_eq_int (@ F B2)) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))) (forall ((A tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ tptp.ord_less_eq_real (@ F B2)) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_real (@ F A)) C))))) (forall ((A tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ tptp.ord_less_eq_nat (@ F B2)) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))) (forall ((A tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ tptp.ord_less_eq_int (@ F B2)) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))) (forall ((A tptp.int) (B2 tptp.int) (F (-> tptp.int tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (@ (@ tptp.ord_less_eq_real (@ F B2)) C) (=> (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_real (@ F A)) C))))) (forall ((A tptp.int) (B2 tptp.int) (F (-> tptp.int tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (@ (@ tptp.ord_less_eq_nat (@ F B2)) C) (=> (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))) (forall ((A tptp.int) (B2 tptp.int) (F (-> tptp.int tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (@ (@ tptp.ord_less_eq_int (@ F B2)) C) (=> (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))) (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.set_nat)) (C tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_eq_set_nat (@ F B2)) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X5) Y3) (@ (@ tptp.ord_less_eq_set_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_set_nat (@ F A)) C))))) (forall ((A tptp.real) (F (-> tptp.real tptp.real)) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_real B2) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.real) (F (-> tptp.nat tptp.real)) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.real) (F (-> tptp.int tptp.real)) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_int B2) C) (=> (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.nat) (F (-> tptp.real tptp.nat)) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_real B2) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.nat) (F (-> tptp.int tptp.nat)) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_int B2) C) (=> (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.int) (F (-> tptp.real tptp.int)) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_real B2) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.int) (F (-> tptp.nat tptp.int)) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.int) (F (-> tptp.int tptp.int)) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_int B2) C) (=> (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.real) (F (-> tptp.set_nat tptp.real)) (B2 tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_set_nat B2) C) (=> (forall ((X5 tptp.set_nat) (Y3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))) (= (lambda ((Y4 tptp.real) (Z2 tptp.real)) (= Y4 Z2)) (lambda ((A3 tptp.real) (B3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A3) B3) (@ (@ tptp.ord_less_eq_real B3) A3)))) (= (lambda ((Y4 tptp.set_nat) (Z2 tptp.set_nat)) (= Y4 Z2)) (lambda ((A3 tptp.set_nat) (B3 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A3) B3) (@ (@ tptp.ord_less_eq_set_nat B3) A3)))) (= (lambda ((Y4 tptp.set_int) (Z2 tptp.set_int)) (= Y4 Z2)) (lambda ((A3 tptp.set_int) (B3 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A3) B3) (@ (@ tptp.ord_less_eq_set_int B3) A3)))) (= (lambda ((Y4 tptp.nat) (Z2 tptp.nat)) (= Y4 Z2)) (lambda ((A3 tptp.nat) (B3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A3) B3) (@ (@ tptp.ord_less_eq_nat B3) A3)))) (= (lambda ((Y4 tptp.int) (Z2 tptp.int)) (= Y4 Z2)) (lambda ((A3 tptp.int) (B3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A3) B3) (@ (@ tptp.ord_less_eq_int B3) A3)))) (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_eq_real B2) A) (= A B2)))) (forall ((A tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B2) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A) (= A B2)))) (forall ((A tptp.set_int) (B2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) B2) (=> (@ (@ tptp.ord_less_eq_set_int B2) A) (= A B2)))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ tptp.ord_less_eq_nat B2) A) (= A B2)))) (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (@ (@ tptp.ord_less_eq_int B2) A) (= A B2)))) (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real C))) (=> (@ (@ tptp.ord_less_eq_real B2) A) (=> (@ _let_1 B2) (@ _let_1 A))))) (forall ((B2 tptp.set_nat) (A tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat C))) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A) (=> (@ _let_1 B2) (@ _let_1 A))))) (forall ((B2 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 B2) A) (=> (@ _let_1 B2) (@ _let_1 A))))) (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B2) A) (=> (@ _let_1 B2) (@ _let_1 A))))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (=> (@ (@ tptp.ord_less_eq_int B2) A) (=> (@ _let_1 B2) (@ _let_1 A))))) (forall ((B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B2) A) (=> (@ (@ tptp.ord_less_eq_real A) B2) (= A B2)))) (forall ((B2 tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A) (=> (@ (@ tptp.ord_less_eq_set_nat A) B2) (= A B2)))) (forall ((B2 tptp.set_int) (A tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int B2) A) (=> (@ (@ tptp.ord_less_eq_set_int A) B2) (= A B2)))) (forall ((B2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B2) A) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (= A B2)))) (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B2) A) (=> (@ (@ tptp.ord_less_eq_int A) B2) (= A B2)))) (= (lambda ((Y4 tptp.real) (Z2 tptp.real)) (= Y4 Z2)) (lambda ((A3 tptp.real) (B3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real B3) A3) (@ (@ tptp.ord_less_eq_real A3) B3)))) (= (lambda ((Y4 tptp.set_nat) (Z2 tptp.set_nat)) (= Y4 Z2)) (lambda ((A3 tptp.set_nat) (B3 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat B3) A3) (@ (@ tptp.ord_less_eq_set_nat A3) B3)))) (= (lambda ((Y4 tptp.set_int) (Z2 tptp.set_int)) (= Y4 Z2)) (lambda ((A3 tptp.set_int) (B3 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int B3) A3) (@ (@ tptp.ord_less_eq_set_int A3) B3)))) (= (lambda ((Y4 tptp.nat) (Z2 tptp.nat)) (= Y4 Z2)) (lambda ((A3 tptp.nat) (B3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B3) A3) (@ (@ tptp.ord_less_eq_nat A3) B3)))) (= (lambda ((Y4 tptp.int) (Z2 tptp.int)) (= Y4 Z2)) (lambda ((A3 tptp.int) (B3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B3) A3) (@ (@ tptp.ord_less_eq_int A3) B3)))) (forall ((P (-> tptp.real tptp.real Bool)) (A tptp.real) (B2 tptp.real)) (=> (forall ((A4 tptp.real) (B4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A4) B4) (@ (@ P A4) B4))) (=> (forall ((A4 tptp.real) (B4 tptp.real)) (=> (@ (@ P B4) A4) (@ (@ P A4) B4))) (@ (@ P A) B2)))) (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B2 tptp.nat)) (=> (forall ((A4 tptp.nat) (B4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A4) B4) (@ (@ P A4) B4))) (=> (forall ((A4 tptp.nat) (B4 tptp.nat)) (=> (@ (@ P B4) A4) (@ (@ P A4) B4))) (@ (@ P A) B2)))) (forall ((P (-> tptp.int tptp.int Bool)) (A 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tptp.nat) (F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat A) B2) (=> (@ (@ tptp.ord_less_real (@ F B2)) 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.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_nat A) B2) (=> (@ (@ tptp.ord_less_int (@ F B2)) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y3) (@ (@ tptp.ord_less_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (F (-> tptp.extended_enat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B2) (=> (@ (@ tptp.ord_less_nat (@ F B2)) C) (=> (forall ((X5 tptp.extended_enat) (Y3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y3) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ 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(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.extended_enat) (B2 tptp.extended_enat) (F (-> tptp.extended_enat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B2) (=> (@ (@ tptp.ord_less_eq_real (@ F B2)) C) (=> (forall ((X5 tptp.extended_enat) (Y3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))) (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.ord_less_eq_real (@ F B2)) C) (=> (forall ((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.int) (B2 tptp.int) (F (-> tptp.int tptp.real)) (C tptp.real)) (=> (@ (@ 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X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.int) (F (-> tptp.real tptp.int)) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_real B2) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.extended_enat) (F (-> tptp.nat tptp.extended_enat)) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.real) (F (-> tptp.nat tptp.real)) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.int) (F (-> tptp.nat tptp.int)) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.extended_enat) (F (-> tptp.int tptp.extended_enat)) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_int B2) C) (=> (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y3) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.real) (F (-> tptp.int tptp.real)) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_int B2) C) (=> (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.extended_enat)) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_le72135733267957522d_enat (@ F B2)) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X5) Y3) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_le72135733267957522d_enat (@ F A)) C))))) (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.real)) (C tptp.real)) (=> (@ (@ 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tptp.extended_enat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ tptp.ord_le72135733267957522d_enat (@ F B2)) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_le72135733267957522d_enat (@ F A)) C))))) (forall ((A tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ tptp.ord_less_real (@ F B2)) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))) (forall ((A tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ tptp.ord_less_nat (@ F B2)) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))) (forall ((A tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ tptp.ord_less_int (@ F B2)) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))) (forall ((A tptp.int) (B2 tptp.int) (F (-> tptp.int tptp.extended_enat)) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (@ (@ tptp.ord_le72135733267957522d_enat (@ F B2)) C) (=> (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y3) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_le72135733267957522d_enat (@ F A)) C))))) (forall ((A tptp.int) (B2 tptp.int) (F (-> tptp.int tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (@ (@ tptp.ord_less_real (@ F B2)) C) (=> (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))) (forall ((A tptp.extended_enat) (F (-> tptp.nat tptp.extended_enat)) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) (@ F B2)) (=> (@ (@ tptp.ord_less_nat B2) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y3) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_le72135733267957522d_enat A) (@ F C)))))) (forall ((A tptp.extended_enat) (F (-> tptp.extended_enat tptp.extended_enat)) (B2 tptp.extended_enat) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) (@ F B2)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B2) C) (=> (forall ((X5 tptp.extended_enat) (Y3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y3) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_le72135733267957522d_enat A) (@ F C)))))) (forall ((A tptp.extended_enat) (F (-> tptp.real tptp.extended_enat)) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) (@ F B2)) (=> (@ (@ tptp.ord_less_real B2) C) (=> (forall ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_le72135733267957522d_enat A) (@ F C)))))) (forall ((A tptp.extended_enat) (F (-> tptp.int tptp.extended_enat)) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) (@ F B2)) (=> (@ (@ tptp.ord_less_int B2) C) (=> (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Y3) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_le72135733267957522d_enat A) (@ F C)))))) (forall ((A tptp.real) (F (-> tptp.nat tptp.real)) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B2)) (=> (@ (@ tptp.ord_less_nat B2) C) (=> (forall ((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.extended_enat tptp.real)) (B2 tptp.extended_enat) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B2)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B2) C) (=> (forall ((X5 tptp.extended_enat) (Y3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real A) (@ F C)))))) (forall ((A tptp.real) (F (-> tptp.real tptp.real)) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B2)) (=> (@ (@ tptp.ord_less_real B2) C) (=> (forall ((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.int tptp.real)) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B2)) (=> (@ (@ tptp.ord_less_int B2) 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.nat) (F (-> tptp.nat tptp.nat)) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) (@ F B2)) (=> (@ (@ tptp.ord_less_nat B2) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y3) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_nat A) (@ F C)))))) (forall ((A tptp.nat) (F (-> tptp.extended_enat tptp.nat)) (B2 tptp.extended_enat) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_less_eq_nat A) (@ F B2)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B2) C) (=> (forall ((X5 tptp.extended_enat) (Y3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y3) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_nat A) (@ F C)))))) (forall ((X tptp.extended_enat) (Y tptp.extended_enat) (Z3 tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Y) Z3) (@ _let_1 Z3))))) (forall ((X tptp.real) (Y tptp.real) (Z3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) Z3) (@ _let_1 Z3))))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z3 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_set_nat Y) Z3) (@ _let_1 Z3))))) (forall ((X tptp.set_int) (Y tptp.set_int) (Z3 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_set_int Y) Z3) (@ _let_1 Z3))))) (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_nat Y) Z3) (@ _let_1 Z3))))) (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z3) (@ _let_1 Z3))))) (forall ((X tptp.extended_enat) (Y tptp.extended_enat) (Z3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat X) Y) (=> (@ (@ tptp.ord_le72135733267957522d_enat Y) Z3) (@ (@ tptp.ord_le72135733267957522d_enat X) Z3)))) (forall ((X tptp.real) (Y tptp.real) (Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ (@ tptp.ord_less_real Y) Z3) (@ (@ tptp.ord_less_real X) Z3)))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (=> (@ (@ tptp.ord_less_set_nat Y) Z3) (@ (@ tptp.ord_less_set_nat X) Z3)))) (forall ((X tptp.set_int) (Y tptp.set_int) (Z3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X) Y) (=> (@ (@ tptp.ord_less_set_int Y) Z3) (@ (@ tptp.ord_less_set_int X) Z3)))) (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (=> (@ (@ tptp.ord_less_nat Y) Z3) (@ (@ tptp.ord_less_nat X) Z3)))) (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (=> (@ (@ tptp.ord_less_int Y) Z3) (@ (@ tptp.ord_less_int X) Z3)))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (=> (not (= A B2)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B2) (@ (@ tptp.ord_le72135733267957522d_enat A) B2)))) (forall ((A tptp.real) (B2 tptp.real)) (=> (not (= A B2)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (@ (@ tptp.ord_less_real A) B2)))) (forall ((A tptp.set_nat) (B2 tptp.set_nat)) (=> (not (= A B2)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B2) (@ (@ tptp.ord_less_set_nat A) B2)))) (forall ((A tptp.set_int) (B2 tptp.set_int)) (=> (not (= A B2)) (=> (@ (@ tptp.ord_less_eq_set_int A) B2) (@ (@ tptp.ord_less_set_int A) B2)))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (not (= A B2)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (@ (@ tptp.ord_less_nat A) B2)))) (forall ((A tptp.int) (B2 tptp.int)) (=> (not (= A B2)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (@ (@ tptp.ord_less_int A) B2)))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B2) (=> (not (= A B2)) (@ (@ tptp.ord_le72135733267957522d_enat A) B2)))) (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (not (= A B2)) (@ (@ tptp.ord_less_real A) B2)))) (forall ((A tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B2) (=> (not (= A B2)) (@ (@ tptp.ord_less_set_nat A) B2)))) (forall ((A tptp.set_int) (B2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) B2) (=> (not (= A B2)) (@ (@ tptp.ord_less_set_int A) B2)))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (not (= A B2)) (@ (@ tptp.ord_less_nat A) B2)))) (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (not (= A B2)) (@ (@ tptp.ord_less_int A) B2)))) (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X) Y) (@ (@ tptp.ord_le2932123472753598470d_enat X) Y))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_eq_real X) Y))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat X) Y) (@ (@ tptp.ord_less_eq_set_nat X) Y))) (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int X) Y) (@ (@ tptp.ord_less_eq_set_int X) Y))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (@ (@ tptp.ord_less_eq_nat X) Y))) (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (@ (@ tptp.ord_less_eq_int X) Y))) (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (= (not (@ (@ tptp.ord_le72135733267957522d_enat X) Y)) (@ (@ tptp.ord_le2932123472753598470d_enat Y) X))) (forall ((X tptp.real) (Y tptp.real)) (= (not (@ (@ tptp.ord_less_real X) Y)) (@ (@ tptp.ord_less_eq_real Y) X))) (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))) (forall ((X tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_eq_int Y) X))) (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (= (not (@ (@ tptp.ord_le2932123472753598470d_enat X) Y)) (@ (@ tptp.ord_le72135733267957522d_enat Y) X))) (forall ((X tptp.real) (Y tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real X) Y)) (@ (@ tptp.ord_less_real Y) X))) (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X))) (forall ((X tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int X) Y)) (@ (@ tptp.ord_less_int Y) X))) _let_281 _let_280 _let_279 _let_278 (= tptp.ord_less_nat (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X4) Y5) (not (= X4 Y5))))) _let_277 (= tptp.ord_le2932123472753598470d_enat (lambda ((X4 tptp.extended_enat) (Y5 tptp.extended_enat)) (or (@ (@ tptp.ord_le72135733267957522d_enat X4) Y5) (= X4 Y5)))) (= tptp.ord_less_eq_real (lambda ((X4 tptp.real) (Y5 tptp.real)) (or (@ (@ tptp.ord_less_real X4) Y5) (= X4 Y5)))) (= tptp.ord_less_eq_set_nat (lambda ((X4 tptp.set_nat) (Y5 tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat X4) Y5) (= X4 Y5)))) (= tptp.ord_less_eq_set_int (lambda ((X4 tptp.set_int) (Y5 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int X4) Y5) (= X4 Y5)))) (= tptp.ord_less_eq_nat (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (or (@ (@ tptp.ord_less_nat X4) Y5) (= X4 Y5)))) (= tptp.ord_less_eq_int (lambda ((X4 tptp.int) (Y5 tptp.int)) (or (@ (@ tptp.ord_less_int X4) Y5) (= X4 Y5)))) (forall ((B2 tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B2) A) (@ (@ tptp.ord_le2932123472753598470d_enat B2) A))) (forall ((B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B2) A) (@ (@ tptp.ord_less_eq_real B2) A))) (forall ((B2 tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B2) A) (@ (@ tptp.ord_less_eq_set_nat B2) A))) (forall ((B2 tptp.set_int) (A tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int B2) A) (@ (@ tptp.ord_less_eq_set_int B2) A))) (forall ((B2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B2) A) (@ (@ tptp.ord_less_eq_nat B2) A))) (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B2) A) (@ (@ tptp.ord_less_eq_int B2) A))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B2) (@ (@ tptp.ord_le2932123472753598470d_enat A) B2))) (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (@ (@ tptp.ord_less_eq_real A) B2))) (forall ((A tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A) B2) (@ (@ tptp.ord_less_eq_set_nat A) B2))) (forall ((A tptp.set_int) (B2 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A) B2) (@ (@ tptp.ord_less_eq_set_int A) B2))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (@ (@ tptp.ord_less_eq_nat A) B2))) (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B2) (@ (@ tptp.ord_less_eq_int A) B2))) (= tptp.ord_le72135733267957522d_enat (lambda ((B3 tptp.extended_enat) (A3 tptp.extended_enat)) (and (@ (@ tptp.ord_le2932123472753598470d_enat B3) A3) (not (@ (@ tptp.ord_le2932123472753598470d_enat A3) B3))))) (= tptp.ord_less_real (lambda ((B3 tptp.real) (A3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real B3) A3) (not (@ (@ tptp.ord_less_eq_real A3) B3))))) (= tptp.ord_less_set_nat (lambda ((B3 tptp.set_nat) (A3 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat B3) A3) (not (@ (@ tptp.ord_less_eq_set_nat A3) B3))))) (= tptp.ord_less_set_int (lambda ((B3 tptp.set_int) (A3 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int B3) A3) (not (@ (@ tptp.ord_less_eq_set_int A3) B3))))) (= tptp.ord_less_nat (lambda ((B3 tptp.nat) (A3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B3) A3) (not (@ (@ tptp.ord_less_eq_nat A3) B3))))) (= tptp.ord_less_int (lambda ((B3 tptp.int) (A3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B3) A3) (not (@ (@ tptp.ord_less_eq_int A3) B3))))) (forall ((B2 tptp.extended_enat) (A tptp.extended_enat) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B2) A) (=> (@ (@ tptp.ord_le2932123472753598470d_enat C) B2) (@ (@ tptp.ord_le72135733267957522d_enat C) A)))) (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real B2) A) (=> (@ (@ tptp.ord_less_eq_real C) B2) (@ (@ tptp.ord_less_real C) A)))) (forall ((B2 tptp.set_nat) (A tptp.set_nat) (C tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B2) A) (=> (@ (@ tptp.ord_less_eq_set_nat C) B2) (@ (@ tptp.ord_less_set_nat C) A)))) (forall ((B2 tptp.set_int) (A tptp.set_int) (C tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int B2) A) (=> (@ (@ tptp.ord_less_eq_set_int C) B2) (@ (@ tptp.ord_less_set_int C) A)))) (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat B2) A) (=> (@ (@ tptp.ord_less_eq_nat C) B2) (@ (@ tptp.ord_less_nat C) A)))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int B2) A) (=> (@ (@ tptp.ord_less_eq_int C) B2) (@ (@ tptp.ord_less_int C) A)))) (forall ((B2 tptp.extended_enat) (A tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat C))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B2) A) (=> (@ _let_1 B2) (@ _let_1 A))))) (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C))) (=> (@ (@ tptp.ord_less_eq_real B2) A) (=> (@ _let_1 B2) (@ _let_1 A))))) (forall ((B2 tptp.set_nat) (A tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat C))) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A) (=> (@ _let_1 B2) (@ _let_1 A))))) (forall ((B2 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 B2) A) (=> (@ _let_1 B2) (@ _let_1 A))))) (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B2) A) (=> (@ _let_1 B2) (@ _let_1 A))))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ (@ tptp.ord_less_eq_int B2) A) (=> (@ _let_1 B2) (@ _let_1 A))))) (= tptp.ord_le72135733267957522d_enat (lambda ((B3 tptp.extended_enat) (A3 tptp.extended_enat)) (and (@ (@ tptp.ord_le2932123472753598470d_enat B3) A3) (not (= A3 B3))))) (= tptp.ord_less_real (lambda ((B3 tptp.real) (A3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real B3) A3) (not (= A3 B3))))) (= tptp.ord_less_set_nat (lambda ((B3 tptp.set_nat) (A3 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat B3) A3) (not (= A3 B3))))) (= tptp.ord_less_set_int (lambda ((B3 tptp.set_int) (A3 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int B3) A3) (not (= A3 B3))))) (= tptp.ord_less_nat (lambda ((B3 tptp.nat) (A3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B3) A3) (not (= A3 B3))))) (= tptp.ord_less_int (lambda ((B3 tptp.int) (A3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B3) A3) (not (= A3 B3))))) (= tptp.ord_le2932123472753598470d_enat (lambda ((B3 tptp.extended_enat) (A3 tptp.extended_enat)) (or (@ (@ tptp.ord_le72135733267957522d_enat B3) A3) (= A3 B3)))) (= tptp.ord_less_eq_real (lambda ((B3 tptp.real) (A3 tptp.real)) (or (@ (@ tptp.ord_less_real B3) A3) (= A3 B3)))) (= tptp.ord_less_eq_set_nat (lambda ((B3 tptp.set_nat) (A3 tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat B3) A3) (= A3 B3)))) (= tptp.ord_less_eq_set_int (lambda ((B3 tptp.set_int) (A3 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int B3) A3) (= A3 B3)))) (= tptp.ord_less_eq_nat (lambda ((B3 tptp.nat) (A3 tptp.nat)) (or (@ (@ tptp.ord_less_nat B3) A3) (= A3 B3)))) (= tptp.ord_less_eq_int (lambda ((B3 tptp.int) (A3 tptp.int)) (or (@ (@ tptp.ord_less_int B3) A3) (= A3 B3)))) (forall ((X tptp.real) (Y tptp.real) (Z3 tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (=> (forall ((W tptp.real)) (=> (@ (@ tptp.ord_less_real X) W) (=> (@ (@ tptp.ord_less_real W) Y) (@ (@ tptp.ord_less_eq_real W) Z3)))) (@ (@ tptp.ord_less_eq_real Y) Z3)))) (forall ((Z3 tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X) (=> (forall ((W tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) W) (=> (@ (@ tptp.ord_less_real W) X) (@ (@ tptp.ord_less_eq_real Y) W)))) (@ (@ tptp.ord_less_eq_real Y) Z3)))) (= tptp.ord_le72135733267957522d_enat (lambda ((A3 tptp.extended_enat) (B3 tptp.extended_enat)) (and (@ (@ tptp.ord_le2932123472753598470d_enat A3) B3) (not (@ (@ tptp.ord_le2932123472753598470d_enat B3) A3))))) (= tptp.ord_less_real (lambda ((A3 tptp.real) (B3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A3) B3) (not (@ (@ tptp.ord_less_eq_real B3) A3))))) (= tptp.ord_less_set_nat (lambda ((A3 tptp.set_nat) (B3 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A3) B3) (not (@ (@ tptp.ord_less_eq_set_nat B3) A3))))) (= tptp.ord_less_set_int (lambda ((A3 tptp.set_int) (B3 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A3) B3) (not (@ (@ tptp.ord_less_eq_set_int B3) A3))))) (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A3) B3) (not (@ (@ tptp.ord_less_eq_nat B3) A3))))) (= tptp.ord_less_int (lambda ((A3 tptp.int) (B3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A3) B3) (not (@ (@ tptp.ord_less_eq_int B3) A3))))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat A))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B2) C) (@ _let_1 C))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_real B2) C) (@ _let_1 C))))) (forall ((A tptp.set_nat) (B2 tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat A))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_set_nat B2) C) (@ _let_1 C))))) (forall ((A tptp.set_int) (B2 tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int A))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_set_int B2) C) (@ _let_1 C))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (@ _let_1 C))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_int B2) C) (@ _let_1 C))))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B2) (=> (@ (@ tptp.ord_le72135733267957522d_enat B2) C) (@ (@ tptp.ord_le72135733267957522d_enat A) C)))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_real B2) C) (@ (@ tptp.ord_less_real A) C)))) (forall ((A tptp.set_nat) (B2 tptp.set_nat) (C tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B2) (=> (@ (@ tptp.ord_less_set_nat B2) C) (@ (@ tptp.ord_less_set_nat A) C)))) (forall ((A tptp.set_int) (B2 tptp.set_int) (C tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) B2) (=> (@ (@ tptp.ord_less_set_int B2) C) (@ (@ tptp.ord_less_set_int A) C)))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ tptp.ord_less_nat B2) C) (@ (@ tptp.ord_less_nat A) C)))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (@ (@ tptp.ord_less_int B2) C) (@ (@ tptp.ord_less_int A) C)))) (= tptp.ord_le72135733267957522d_enat (lambda ((A3 tptp.extended_enat) (B3 tptp.extended_enat)) (and (@ (@ tptp.ord_le2932123472753598470d_enat A3) B3) (not (= A3 B3))))) (= tptp.ord_less_real (lambda ((A3 tptp.real) (B3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A3) B3) (not (= A3 B3))))) (= tptp.ord_less_set_nat (lambda ((A3 tptp.set_nat) (B3 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A3) B3) (not (= A3 B3))))) (= tptp.ord_less_set_int (lambda ((A3 tptp.set_int) (B3 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A3) B3) (not (= A3 B3))))) (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A3) B3) (not (= A3 B3))))) (= tptp.ord_less_int (lambda ((A3 tptp.int) (B3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A3) B3) (not (= A3 B3))))) (= tptp.ord_le2932123472753598470d_enat (lambda ((A3 tptp.extended_enat) (B3 tptp.extended_enat)) (or (@ (@ tptp.ord_le72135733267957522d_enat A3) B3) (= A3 B3)))) (= tptp.ord_less_eq_real (lambda ((A3 tptp.real) (B3 tptp.real)) (or (@ (@ tptp.ord_less_real A3) B3) (= A3 B3)))) (= tptp.ord_less_eq_set_nat (lambda ((A3 tptp.set_nat) (B3 tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat A3) B3) (= A3 B3)))) (= tptp.ord_less_eq_set_int (lambda ((A3 tptp.set_int) (B3 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int A3) B3) (= A3 B3)))) (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (or (@ (@ tptp.ord_less_nat A3) B3) (= A3 B3)))) (= tptp.ord_less_eq_int (lambda ((A3 tptp.int) (B3 tptp.int)) (or (@ (@ tptp.ord_less_int A3) B3) (= A3 B3)))) (forall ((Y tptp.extended_enat) (X tptp.extended_enat)) (=> (not (@ (@ tptp.ord_le2932123472753598470d_enat Y) X)) (@ (@ tptp.ord_le72135733267957522d_enat X) Y))) (forall ((Y tptp.real) (X tptp.real)) (=> (not (@ (@ tptp.ord_less_eq_real Y) X)) (@ (@ tptp.ord_less_real X) Y))) (forall ((Y tptp.nat) (X tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat Y) X)) (@ (@ tptp.ord_less_nat X) Y))) (forall ((Y tptp.int) (X tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int Y) X)) (@ (@ tptp.ord_less_int X) Y))) (= tptp.ord_le72135733267957522d_enat (lambda ((X4 tptp.extended_enat) (Y5 tptp.extended_enat)) (and (@ (@ tptp.ord_le2932123472753598470d_enat X4) Y5) (not (@ (@ tptp.ord_le2932123472753598470d_enat Y5) X4))))) (= tptp.ord_less_real (lambda ((X4 tptp.real) (Y5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real X4) Y5) (not (@ (@ tptp.ord_less_eq_real Y5) X4))))) (= tptp.ord_less_set_nat (lambda ((X4 tptp.set_nat) (Y5 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat X4) Y5) (not (@ (@ tptp.ord_less_eq_set_nat Y5) X4))))) (= tptp.ord_less_set_int (lambda ((X4 tptp.set_int) (Y5 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int X4) Y5) (not (@ (@ tptp.ord_less_eq_set_int Y5) X4))))) (= tptp.ord_less_nat (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X4) Y5) (not (@ (@ tptp.ord_less_eq_nat Y5) X4))))) (= tptp.ord_less_int (lambda ((X4 tptp.int) (Y5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X4) Y5) (not (@ (@ tptp.ord_less_eq_int Y5) X4))))) (forall ((Y tptp.real) (Z3 tptp.real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y) (@ (@ tptp.ord_less_eq_real X5) Z3))) (@ (@ tptp.ord_less_eq_real Y) Z3))) (forall ((Z3 tptp.real) (Y tptp.real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X5) (@ (@ tptp.ord_less_eq_real Y) X5))) (@ (@ tptp.ord_less_eq_real Y) Z3))) (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat X) Y) (= (not (@ (@ tptp.ord_le72135733267957522d_enat X) Y)) (= X Y)))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (= (not (@ (@ tptp.ord_less_real X) Y)) (= X Y)))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (= (not (@ (@ tptp.ord_less_set_nat X) Y)) (= X Y)))) (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X) Y) (= (not (@ (@ tptp.ord_less_set_int X) Y)) (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (= (not (@ (@ tptp.ord_less_nat X) Y)) (= X Y)))) (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (= (not (@ (@ tptp.ord_less_int X) Y)) (= X Y)))) (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (not (@ (@ tptp.ord_le72135733267957522d_enat X) Y)) (= (@ (@ tptp.ord_le2932123472753598470d_enat X) Y) (= X Y)))) (forall ((X tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_real X) Y)) (= (@ (@ tptp.ord_less_eq_real X) Y) (= X Y)))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (not (@ (@ tptp.ord_less_set_nat X) Y)) (= (@ (@ tptp.ord_less_eq_set_nat X) Y) (= X Y)))) (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (not (@ (@ tptp.ord_less_set_int X) Y)) (= (@ (@ tptp.ord_less_eq_set_int X) Y) (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (= (@ (@ tptp.ord_less_eq_nat X) Y) (= X Y)))) (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (= (@ (@ tptp.ord_less_eq_int X) Y) (= X Y)))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (= (not (@ (@ tptp.ord_le72135733267957522d_enat A) B2)) (or (not (@ (@ tptp.ord_le2932123472753598470d_enat A) B2)) (= A B2)))) (forall ((A tptp.real) (B2 tptp.real)) (= (not (@ (@ tptp.ord_less_real A) B2)) (or (not (@ (@ tptp.ord_less_eq_real A) B2)) (= A B2)))) (forall ((A tptp.set_nat) (B2 tptp.set_nat)) (= (not (@ (@ tptp.ord_less_set_nat A) B2)) (or (not (@ (@ tptp.ord_less_eq_set_nat A) B2)) (= A B2)))) (forall ((A tptp.set_int) (B2 tptp.set_int)) (= (not (@ (@ tptp.ord_less_set_int A) B2)) (or (not (@ (@ tptp.ord_less_eq_set_int A) B2)) (= A B2)))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat A) B2)) (or (not (@ (@ tptp.ord_less_eq_nat A) B2)) (= A B2)))) (forall ((A tptp.int) (B2 tptp.int)) (= (not (@ (@ tptp.ord_less_int A) B2)) (or (not (@ (@ tptp.ord_less_eq_int A) B2)) (= A B2)))) (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (not (@ (@ tptp.ord_le72135733267957522d_enat X) Y)) (@ (@ tptp.ord_le2932123472753598470d_enat Y) X))) (forall ((X tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_real X) Y)) (@ (@ tptp.ord_less_eq_real Y) X))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))) (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_eq_int Y) X))) (forall ((Y tptp.extended_enat) (X tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Y) X) (not (@ (@ tptp.ord_le72135733267957522d_enat X) Y)))) (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y) X) (not (@ (@ tptp.ord_less_real X) Y)))) (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X) (not (@ (@ tptp.ord_less_set_nat X) Y)))) (forall ((Y tptp.set_int) (X tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y) X) (not (@ (@ tptp.ord_less_set_int X) Y)))) (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (not (@ (@ tptp.ord_less_nat X) Y)))) (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (not (@ (@ tptp.ord_less_int X) Y)))) (forall ((F (-> tptp.nat tptp.nat)) (I tptp.nat) (J tptp.nat)) (=> (forall ((I4 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) J3) (@ (@ tptp.ord_less_nat (@ F I4)) (@ F J3)))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ F I)) (@ F J))))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (=> (not (= M2 N2)) (@ (@ tptp.ord_less_nat M2) N2)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat M2) N2) (= M2 N2)) (@ (@ tptp.ord_less_eq_nat M2) N2))) (= tptp.ord_less_eq_nat (lambda ((M tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_nat M) N) (= M N)))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.vEBT_invar_vebt (@ tptp.vEBT_vebt_buildup N2)) N2))) (forall ((B2 tptp.nat) (A tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat B2) A)) B2) (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))) (forall ((B2 tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real B2) A)) B2) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))) (forall ((B2 tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int B2) A)) B2) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) B2)) B2) (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))) (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B2)) B2) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))) (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B2)) B2) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat A) B2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2))) (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real A) B2)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) B2))) (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int A) B2)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat B2) A)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2))) (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real B2) A)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) B2))) (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int B2) A)) (@ (@ 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(@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int B2) A)) B2) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int))) (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) B2)) B2) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) B2)) B2) (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat))) (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) B2)) B2) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int))) (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.plus_plus_real A) B2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B2))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.plus_plus_nat A) B2)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B2))) (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.plus_plus_int A) B2)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B2))) (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.plus_plus_real B2) A)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B2))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.plus_plus_nat B2) A)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B2))) (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.plus_plus_int B2) A)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B2))) (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))) (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))) (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B2) A) (@ (@ tptp.plus_plus_nat C) A)) (= B2 C))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (= (= (@ (@ tptp.plus_plus_int B2) A) (@ (@ tptp.plus_plus_int C) A)) (= B2 C))) (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (= (= (@ (@ tptp.plus_plus_real B2) A) (@ (@ tptp.plus_plus_real C) A)) (= B2 C))) (forall ((N2 tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat N2) tptp.zero_z5237406670263579293d_enat) (= N2 tptp.zero_z5237406670263579293d_enat))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N2) tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat 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tptp.nat) (C tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B2) C)) (@ (@ tptp.ord_less_eq_nat A) B2))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B2) C)) (@ (@ tptp.ord_less_eq_int A) B2))) (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)) (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)) (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)) (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)) (forall ((A tptp.extended_enat)) (= (@ (@ tptp.plus_p3455044024723400733d_enat A) tptp.zero_z5237406670263579293d_enat) A)) (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.plus_plus_real A) A)) (= A tptp.zero_zero_real))) (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ (@ tptp.plus_plus_int A) A)) (= A 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tptp.zero_zero_nat))) (forall ((A tptp.real) (B2 tptp.real)) (= (= A (@ (@ tptp.plus_plus_real B2) A)) (= B2 tptp.zero_zero_real))) (forall ((A tptp.int) (B2 tptp.int)) (= (= A (@ (@ tptp.plus_plus_int B2) A)) (= B2 tptp.zero_zero_int))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (= A (@ (@ tptp.plus_plus_complex B2) A)) (= B2 tptp.zero_zero_complex))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat A) B2)) (= B2 tptp.zero_zero_nat))) (forall ((A tptp.real) (B2 tptp.real)) (= (= A (@ (@ tptp.plus_plus_real A) B2)) (= B2 tptp.zero_zero_real))) (forall ((A tptp.int) (B2 tptp.int)) (= (= A (@ (@ tptp.plus_plus_int A) B2)) (= B2 tptp.zero_zero_int))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (= A (@ (@ tptp.plus_plus_complex A) B2)) (= B2 tptp.zero_zero_complex))) (forall ((X tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))) (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (= (= (@ (@ tptp.plus_p3455044024723400733d_enat X) Y) tptp.zero_z5237406670263579293d_enat) (and (= X tptp.zero_z5237406670263579293d_enat) (= Y tptp.zero_z5237406670263579293d_enat)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.plus_plus_nat X) Y)) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))) (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (= (= tptp.zero_z5237406670263579293d_enat (@ (@ tptp.plus_p3455044024723400733d_enat X) Y)) (and (= X tptp.zero_z5237406670263579293d_enat) (= Y tptp.zero_z5237406670263579293d_enat)))) (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)) (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)) (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)) (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)) (forall ((A tptp.extended_enat)) (= (@ (@ tptp.plus_p3455044024723400733d_enat tptp.zero_z5237406670263579293d_enat) A) A)) (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (= (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_nat A) B2)))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_real A) B2)))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_int A) B2)))) (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B2) C)) (@ (@ tptp.ord_less_nat A) B2))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B2) C)) (@ (@ tptp.ord_less_real A) B2))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B2) C)) (@ (@ tptp.ord_less_int A) B2))) (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.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 ((X tptp.nat)) (= (= tptp.zero_zero_nat X) (= X tptp.zero_zero_nat))) (forall ((X tptp.real)) (= (= tptp.zero_zero_real X) (= X tptp.zero_zero_real))) (forall ((X tptp.int)) (= (= tptp.zero_zero_int X) (= X tptp.zero_zero_int))) (forall ((X tptp.complex)) (= (= tptp.zero_zero_complex X) (= X tptp.zero_zero_complex))) (forall ((X tptp.extended_enat)) (= (= tptp.zero_z5237406670263579293d_enat X) (= X tptp.zero_z5237406670263579293d_enat))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B2) C))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B2) C))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_real B2) C))))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat A))) (= (@ (@ tptp.plus_p3455044024723400733d_enat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_p3455044024723400733d_enat B2) C))))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I J) (= K L)) (= (@ (@ tptp.plus_plus_nat I) K) (@ (@ tptp.plus_plus_nat J) L)))) (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (= I J) (= K L)) (= (@ (@ tptp.plus_plus_int I) K) (@ (@ tptp.plus_plus_int J) L)))) (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (= I J) (= K L)) (= (@ (@ tptp.plus_plus_real I) K) (@ (@ tptp.plus_plus_real J) L)))) (forall ((I tptp.extended_enat) (J tptp.extended_enat) (K tptp.extended_enat) (L tptp.extended_enat)) (=> (and (= I J) (= K L)) (= (@ (@ tptp.plus_p3455044024723400733d_enat I) K) (@ (@ tptp.plus_p3455044024723400733d_enat J) L)))) (forall ((A2 tptp.nat) (K tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_nat A2) B2) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B2)))))) (forall ((A2 tptp.int) (K tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_int A2) B2) (@ _let_1 (@ (@ tptp.plus_plus_int A) B2)))))) (forall ((A2 tptp.real) (K tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_real A2) B2) (@ _let_1 (@ (@ tptp.plus_plus_real A) B2)))))) (forall ((A2 tptp.extended_enat) (K tptp.extended_enat) (A tptp.extended_enat) (B2 tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.plus_p3455044024723400733d_enat A2) B2) (@ _let_1 (@ (@ tptp.plus_p3455044024723400733d_enat A) B2)))))) (forall ((B tptp.nat) (K tptp.nat) (B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (let ((_let_2 (@ tptp.plus_plus_nat K))) (=> (= B (@ _let_2 B2)) (= (@ _let_1 B) (@ _let_2 (@ _let_1 B2))))))) (forall ((B tptp.int) (K tptp.int) (B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (let ((_let_2 (@ tptp.plus_plus_int K))) (=> (= B (@ _let_2 B2)) (= (@ _let_1 B) (@ _let_2 (@ _let_1 B2))))))) (forall ((B tptp.real) (K tptp.real) (B2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (let ((_let_2 (@ tptp.plus_plus_real K))) (=> (= B (@ _let_2 B2)) (= (@ _let_1 B) (@ _let_2 (@ _let_1 B2))))))) (forall ((B tptp.extended_enat) (K tptp.extended_enat) (B2 tptp.extended_enat) (A tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat A))) (let ((_let_2 (@ tptp.plus_p3455044024723400733d_enat K))) (=> (= B (@ _let_2 B2)) (= (@ _let_1 B) (@ _let_2 (@ _let_1 B2))))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B2) C))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B2) C))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_real B2) C))))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat A))) (= (@ (@ tptp.plus_p3455044024723400733d_enat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_p3455044024723400733d_enat B2) C))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (= (= (@ (@ tptp.plus_plus_int B2) A) (@ (@ tptp.plus_plus_int C) A)) (= B2 C))) (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (= (= (@ (@ tptp.plus_plus_real B2) A) (@ (@ tptp.plus_plus_real C) A)) (= B2 C))) (= tptp.plus_plus_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.plus_plus_nat B3) A3))) (= tptp.plus_plus_int (lambda ((A3 tptp.int) (B3 tptp.int)) (@ (@ tptp.plus_plus_int B3) A3))) (= tptp.plus_plus_real (lambda ((A3 tptp.real) (B3 tptp.real)) (@ (@ tptp.plus_plus_real B3) A3))) (= tptp.plus_p3455044024723400733d_enat (lambda ((A3 tptp.extended_enat) (B3 tptp.extended_enat)) (@ (@ tptp.plus_p3455044024723400733d_enat B3) A3))) (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat B2))) (let ((_let_2 (@ tptp.plus_plus_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int B2))) (let ((_let_2 (@ tptp.plus_plus_int A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real B2))) (let ((_let_2 (@ tptp.plus_plus_real A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((B2 tptp.extended_enat) (A tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat B2))) (let ((_let_2 (@ tptp.plus_p3455044024723400733d_enat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (=> (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (=> (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (=> (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))) (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat B2) A) (@ (@ tptp.plus_plus_nat C) A)) (= B2 C))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (= (@ (@ tptp.plus_plus_int B2) A) (@ (@ tptp.plus_plus_int C) A)) (= B2 C))) (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (=> (= (@ (@ tptp.plus_plus_real B2) A) (@ (@ tptp.plus_plus_real C) A)) (= B2 C))) (forall ((X tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) X)) (forall ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X)) (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))) (forall ((N2 tptp.extended_enat)) (=> (not (= N2 tptp.zero_z5237406670263579293d_enat)) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) N2))) (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) tptp.zero_zero_nat))) (forall ((N2 tptp.extended_enat)) (not (@ (@ tptp.ord_le72135733267957522d_enat N2) tptp.zero_z5237406670263579293d_enat))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N2) (not (= N2 tptp.zero_zero_nat)))) (forall ((M2 tptp.extended_enat) (N2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat M2) N2) (not (= N2 tptp.zero_z5237406670263579293d_enat)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (not (= N2 tptp.zero_zero_nat)))) (forall ((N2 tptp.extended_enat)) (= (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) N2) (not (= N2 tptp.zero_z5237406670263579293d_enat)))) (forall ((I tptp.extended_enat) (J tptp.extended_enat) (K tptp.extended_enat) (L tptp.extended_enat)) (=> (and (@ (@ tptp.ord_le2932123472753598470d_enat I) J) (= K L)) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.plus_p3455044024723400733d_enat I) K)) (@ (@ tptp.plus_p3455044024723400733d_enat J) L)))) (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I) J) (= K L)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L)))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I) J) (= K L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))) (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I) J) (= K L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L)))) (forall ((I tptp.extended_enat) (J tptp.extended_enat) (K tptp.extended_enat) (L tptp.extended_enat)) (=> (and (= I J) (@ (@ tptp.ord_le2932123472753598470d_enat K) L)) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.plus_p3455044024723400733d_enat I) K)) (@ (@ tptp.plus_p3455044024723400733d_enat J) L)))) (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (= I J) (@ (@ tptp.ord_less_eq_real K) L)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L)))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I J) (@ (@ tptp.ord_less_eq_nat K) L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))) (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (= I J) (@ (@ tptp.ord_less_eq_int K) L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L)))) (forall ((I tptp.extended_enat) (J tptp.extended_enat) (K tptp.extended_enat) (L tptp.extended_enat)) (=> (and (@ (@ tptp.ord_le2932123472753598470d_enat I) J) (@ (@ tptp.ord_le2932123472753598470d_enat K) L)) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.plus_p3455044024723400733d_enat I) K)) (@ (@ tptp.plus_p3455044024723400733d_enat J) L)))) (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I) J) (@ (@ tptp.ord_less_eq_real K) L)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L)))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat K) L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))) (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I) J) (@ (@ tptp.ord_less_eq_int K) L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L)))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat) (D tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B2) (=> (@ (@ tptp.ord_le2932123472753598470d_enat C) D) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) C)) (@ (@ tptp.plus_p3455044024723400733d_enat B2) D))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_eq_real C) D) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B2) D))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ tptp.ord_less_eq_nat C) D) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B2) D))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (@ (@ tptp.ord_less_eq_int C) D) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B2) D))))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat C))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B2) (@ (@ tptp.ord_le2932123472753598470d_enat (@ _let_1 A)) (@ _let_1 B2))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (=> (@ (@ tptp.ord_less_eq_real A) B2) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B2))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B2))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_eq_int A) B2) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B2))))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B2) (not (forall ((C2 tptp.extended_enat)) (not (= B2 (@ (@ tptp.plus_p3455044024723400733d_enat A) C2))))))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (not (forall ((C2 tptp.nat)) (not (= B2 (@ (@ tptp.plus_plus_nat A) C2))))))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B2) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) C)) (@ (@ tptp.plus_p3455044024723400733d_enat B2) C)))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B2) C)))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B2) C)))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B2) C)))) _let_276 (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (exists ((C3 tptp.nat)) (= B3 (@ (@ tptp.plus_plus_nat A3) C3))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (=> (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_real A) B2)))) (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_nat A) B2)))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_int A) B2)))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B2) C)) (@ (@ tptp.ord_less_eq_real A) B2))) (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B2) C)) (@ (@ tptp.ord_less_eq_nat A) B2))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B2) C)) (@ (@ tptp.ord_less_eq_int A) B2))) (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)) (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)) (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)) (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)) (forall ((A tptp.extended_enat)) (= (@ (@ tptp.plus_p3455044024723400733d_enat tptp.zero_z5237406670263579293d_enat) A) A)) (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)) (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)) (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)) (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)) (forall ((A tptp.extended_enat)) (= (@ (@ tptp.plus_p3455044024723400733d_enat A) tptp.zero_z5237406670263579293d_enat) A)) (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)) (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)) (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I) J) (@ (@ tptp.ord_less_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))) (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_real I) J) (@ (@ tptp.ord_less_real K) L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ 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(@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B2))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B2) C)))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B2) C)))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B2) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B2) C)))) (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_nat A) B2)))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_real A) B2)))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_int A) B2)))) (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B2) C)) (@ (@ tptp.ord_less_nat A) B2))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B2) C)) (@ (@ tptp.ord_less_real A) B2))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B2) C)) (@ (@ tptp.ord_less_int A) B2))) (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat X) tptp.zero_z5237406670263579293d_enat) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Y) tptp.zero_z5237406670263579293d_enat) (= (= (@ (@ tptp.plus_p3455044024723400733d_enat X) Y) tptp.zero_z5237406670263579293d_enat) (and (= X tptp.zero_z5237406670263579293d_enat) (= Y tptp.zero_z5237406670263579293d_enat)))))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (= (= (@ (@ tptp.plus_plus_real X) Y) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real)))))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat Y) tptp.zero_zero_nat) (= (= (@ (@ tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))) (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.zero_zero_int) (= (= (@ (@ tptp.plus_plus_int X) Y) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))))) (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_p3455044024723400733d_enat X) Y) tptp.zero_z5237406670263579293d_enat) (and (= X tptp.zero_z5237406670263579293d_enat) (= Y tptp.zero_z5237406670263579293d_enat))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_real X) Y) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real))))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat))))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_int X) Y) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int))))))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) tptp.zero_z5237406670263579293d_enat) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B2) tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) B2)) tptp.zero_z5237406670263579293d_enat)))) (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) B2)) tptp.zero_zero_real)))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat B2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) B2)) tptp.zero_zero_nat)))) (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) B2)) tptp.zero_zero_int)))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_p3455044024723400733d_enat A) B2)))))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_real A) B2)))))) (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B2)))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_int A) B2)))))) (forall ((C tptp.extended_enat) (B2 tptp.extended_enat) (A tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat B2))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_p3455044024723400733d_enat A) C)))))) (forall ((C tptp.real) (B2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real B2))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_real A) C)))))) (forall ((C tptp.nat) (B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C)))))) (forall ((C tptp.int) (B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int B2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_int A) C)))))) (forall ((C tptp.extended_enat) (A tptp.extended_enat) (B2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat C) tptp.zero_z5237406670263579293d_enat) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B2) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) C)) B2)))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real A) B2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) B2)))) (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) B2)))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int A) B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) B2)))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat B2))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_p3455044024723400733d_enat A) C)))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real B2))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_real A) C)))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C)))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int B2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int A) C)))))) (forall ((A tptp.extended_enat) (C tptp.extended_enat) (B2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) tptp.zero_z5237406670263579293d_enat) (=> (@ (@ tptp.ord_le2932123472753598470d_enat C) B2) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) C)) B2)))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real C) B2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) B2)))) (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat C) B2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) B2)))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int C) B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) B2)))) (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I) J) (@ (@ tptp.ord_less_real K) L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L)))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))) (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I) J) (@ (@ tptp.ord_less_int K) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L)))) (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_real I) J) (@ (@ tptp.ord_less_eq_real K) L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L)))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I) J) (@ (@ tptp.ord_less_eq_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))) (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I) J) (@ (@ tptp.ord_less_eq_int K) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L)))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_real C) D) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B2) D))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ tptp.ord_less_nat C) D) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B2) D))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (@ (@ tptp.ord_less_int C) D) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B2) D))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.ord_less_eq_real C) D) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B2) D))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (=> (@ (@ tptp.ord_less_eq_nat C) D) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B2) D))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A) B2) (=> (@ (@ tptp.ord_less_eq_int C) D) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B2) D))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat B2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C)))))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat B2))) (=> (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_p3455044024723400733d_enat A) C)))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real B2))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_real A) C)))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int A) C)))))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (not (forall ((C2 tptp.nat)) (=> (= B2 (@ (@ tptp.plus_plus_nat A) C2)) (= C2 tptp.zero_zero_nat)))))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B2) (not (forall ((C2 tptp.extended_enat)) (=> (= B2 (@ (@ tptp.plus_p3455044024723400733d_enat A) C2)) (= C2 tptp.zero_z5237406670263579293d_enat)))))) (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B2)))))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_p3455044024723400733d_enat A) B2)))))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_real A) B2)))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_int A) B2)))))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat B2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) B2)) tptp.zero_zero_nat)))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) tptp.zero_z5237406670263579293d_enat) (=> (@ (@ tptp.ord_le72135733267957522d_enat B2) tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) B2)) tptp.zero_z5237406670263579293d_enat)))) (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real B2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B2)) tptp.zero_zero_real)))) (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B2)) tptp.zero_zero_int)))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) tptp.zero_z5237406670263579293d_enat) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B2) tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) B2)) tptp.zero_z5237406670263579293d_enat)))) (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B2)) tptp.zero_zero_real)))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat B2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) B2)) tptp.zero_zero_nat)))) (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B2)) tptp.zero_zero_int)))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_p3455044024723400733d_enat A) B2)))))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_real A) B2)))))) (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B2)))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_int A) B2)))))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) tptp.zero_z5237406670263579293d_enat) (=> (@ (@ tptp.ord_le72135733267957522d_enat B2) tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) B2)) tptp.zero_z5237406670263579293d_enat)))) (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real B2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B2)) tptp.zero_zero_real)))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat B2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) B2)) tptp.zero_zero_nat)))) (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B2)) tptp.zero_zero_int)))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) B2) (@ _let_1 (@ (@ tptp.plus_p3455044024723400733d_enat A) B2)))))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B2) (@ _let_1 (@ (@ tptp.plus_plus_real A) B2)))))) (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B2) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B2)))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B2) (@ _let_1 (@ (@ tptp.plus_plus_int A) B2)))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real B2) C) (@ (@ tptp.ord_less_real B2) (@ (@ tptp.plus_plus_real A) C))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (@ (@ tptp.ord_less_nat B2) (@ (@ tptp.plus_plus_nat A) C))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int B2) C) (@ (@ tptp.ord_less_int B2) (@ (@ tptp.plus_plus_int A) C))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real B2))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_real A) C)))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat B2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C)))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int A) C)))))) (forall ((A tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((A tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) A) tptp.zero_zero_int) (= A tptp.zero_zero_int))) (forall ((N2 tptp.nat) (X tptp.nat)) (not (@ (@ tptp.vEBT_V5719532721284313246member (@ tptp.vEBT_vebt_buildup N2)) X))) (forall ((X tptp.real) (Y tptp.real)) (=> (forall ((E tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.plus_plus_real Y) E)))) (@ (@ tptp.ord_less_eq_real X) Y))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real X) Y)) tptp.zero_zero_real) (or (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real)))) (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int X) Y)) tptp.zero_zero_int) (or (@ (@ tptp.ord_less_int X) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Y) tptp.zero_zero_int)))) (forall ((N2 tptp.nat)) (= (@ tptp.vEBT_VEBT_set_vebt (@ tptp.vEBT_vebt_buildup N2)) tptp.bot_bot_set_nat)) (forall ((A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat)) (=> (forall ((X5 tptp.extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat X5))) (=> (@ _let_1 A2) (@ _let_1 B)))) (@ (@ tptp.ord_le7203529160286727270d_enat A2) B))) (forall ((A2 tptp.set_real) (B tptp.set_real)) (=> (forall ((X5 tptp.real)) (let ((_let_1 (@ tptp.member_real X5))) (=> (@ _let_1 A2) (@ _let_1 B)))) (@ (@ tptp.ord_less_eq_set_real A2) B))) (forall ((A2 tptp.set_set_nat) (B tptp.set_set_nat)) (=> (forall ((X5 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X5))) (=> (@ _let_1 A2) (@ _let_1 B)))) (@ (@ tptp.ord_le6893508408891458716et_nat A2) B))) (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (=> (forall ((X5 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X5))) (=> (@ _let_1 A2) (@ _let_1 B)))) (@ (@ tptp.ord_less_eq_set_nat A2) B))) (forall ((A2 tptp.set_int) (B tptp.set_int)) (=> (forall ((X5 tptp.int)) (let ((_let_1 (@ tptp.member_int X5))) (=> (@ _let_1 A2) (@ _let_1 B)))) (@ (@ tptp.ord_less_eq_set_int A2) B))) (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B) (=> (not (= A2 B)) (@ (@ tptp.ord_less_set_nat A2) B)))) (forall ((A2 tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B) (=> (not (= A2 B)) (@ (@ tptp.ord_less_set_int A2) B)))) (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B) (=> (@ (@ tptp.ord_less_eq_set_nat B) A2) (= A2 B)))) (forall ((A2 tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B) (=> (@ (@ tptp.ord_less_eq_set_int B) A2) (= A2 B)))) (forall ((N2 tptp.nat) (X tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ tptp.vEBT_vebt_buildup N2)) X))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (@ tptp.finite_finite_nat (@ tptp.vEBT_VEBT_set_vebt T)))) _let_275 (forall ((P (-> tptp.list_nat Bool))) (= (= tptp.bot_bot_set_list_nat (@ tptp.collect_list_nat P)) (forall ((X4 tptp.list_nat)) (not (@ P X4))))) (forall ((P (-> tptp.set_nat Bool))) (= (= tptp.bot_bot_set_set_nat (@ tptp.collect_set_nat P)) (forall ((X4 tptp.set_nat)) (not (@ P X4))))) (forall ((P (-> tptp.extended_enat Bool))) (= (= tptp.bot_bo7653980558646680370d_enat (@ tptp.collec4429806609662206161d_enat P)) (forall ((X4 tptp.extended_enat)) (not (@ P X4))))) (forall ((P (-> tptp.real Bool))) (= (= tptp.bot_bot_set_real (@ tptp.collect_real P)) (forall ((X4 tptp.real)) (not (@ P X4))))) (forall ((P (-> tptp.nat Bool))) (= (= tptp.bot_bot_set_nat (@ tptp.collect_nat P)) (forall ((X4 tptp.nat)) (not (@ P X4))))) (forall ((P (-> tptp.int Bool))) (= (= tptp.bot_bot_set_int (@ tptp.collect_int P)) (forall ((X4 tptp.int)) (not (@ P X4))))) (forall ((P (-> tptp.list_nat Bool))) (= (= (@ tptp.collect_list_nat P) tptp.bot_bot_set_list_nat) (forall ((X4 tptp.list_nat)) (not (@ P X4))))) (forall ((P (-> tptp.set_nat Bool))) (= (= (@ tptp.collect_set_nat P) tptp.bot_bot_set_set_nat) (forall ((X4 tptp.set_nat)) (not (@ P X4))))) (forall ((P (-> tptp.extended_enat Bool))) (= (= (@ tptp.collec4429806609662206161d_enat P) tptp.bot_bo7653980558646680370d_enat) (forall ((X4 tptp.extended_enat)) (not (@ P X4))))) (forall ((P (-> tptp.real Bool))) (= (= (@ tptp.collect_real P) tptp.bot_bot_set_real) (forall ((X4 tptp.real)) (not (@ P X4))))) (forall ((P (-> tptp.nat Bool))) (= (= (@ tptp.collect_nat P) tptp.bot_bot_set_nat) (forall ((X4 tptp.nat)) (not (@ P X4))))) (forall ((P (-> tptp.int Bool))) (= (= (@ tptp.collect_int P) tptp.bot_bot_set_int) (forall ((X4 tptp.int)) (not (@ P X4))))) (forall ((A2 tptp.set_set_nat)) (= (forall ((X4 tptp.set_nat)) (not (@ (@ tptp.member_set_nat X4) A2))) (= A2 tptp.bot_bot_set_set_nat))) (forall ((A2 tptp.set_Extended_enat)) (= (forall ((X4 tptp.extended_enat)) (not (@ (@ tptp.member_Extended_enat X4) A2))) (= A2 tptp.bot_bo7653980558646680370d_enat))) (forall ((A2 tptp.set_real)) (= (forall ((X4 tptp.real)) (not (@ (@ tptp.member_real X4) A2))) (= A2 tptp.bot_bot_set_real))) (forall ((A2 tptp.set_nat)) (= (forall ((X4 tptp.nat)) (not (@ (@ tptp.member_nat X4) A2))) (= A2 tptp.bot_bot_set_nat))) (forall ((A2 tptp.set_int)) (= (forall ((X4 tptp.int)) (not (@ (@ tptp.member_int X4) A2))) (= A2 tptp.bot_bot_set_int))) (forall ((C tptp.set_nat)) (not (@ (@ tptp.member_set_nat C) tptp.bot_bot_set_set_nat))) (forall ((C tptp.extended_enat)) (not (@ (@ tptp.member_Extended_enat C) tptp.bot_bo7653980558646680370d_enat))) (forall ((C tptp.real)) (not (@ (@ tptp.member_real C) tptp.bot_bot_set_real))) (forall ((C tptp.nat)) (not (@ (@ tptp.member_nat C) tptp.bot_bot_set_nat))) (forall ((C tptp.int)) (not (@ (@ tptp.member_int C) tptp.bot_bot_set_int))) (forall ((Tree tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt Tree) N2) (=> (@ (@ tptp.vEBT_vebt_member Tree) X) (or (@ (@ tptp.vEBT_V5719532721284313246member Tree) X) (@ (@ tptp.vEBT_VEBT_membermima Tree) X))))) (forall ((A2 tptp.set_Extended_enat)) (@ (@ tptp.ord_le7203529160286727270d_enat tptp.bot_bo7653980558646680370d_enat) A2)) (forall ((A2 tptp.set_real)) (@ (@ tptp.ord_less_eq_set_real tptp.bot_bot_set_real) A2)) (forall ((A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat tptp.bot_bot_set_nat) A2)) (forall ((A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int tptp.bot_bot_set_int) A2)) (forall ((A2 tptp.set_Extended_enat)) (= (@ (@ tptp.ord_le7203529160286727270d_enat A2) tptp.bot_bo7653980558646680370d_enat) (= A2 tptp.bot_bo7653980558646680370d_enat))) (forall ((A2 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real A2) tptp.bot_bot_set_real) (= A2 tptp.bot_bot_set_real))) (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A2) tptp.bot_bot_set_nat) (= A2 tptp.bot_bot_set_nat))) (forall ((A2 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A2) tptp.bot_bot_set_int) (= A2 tptp.bot_bot_set_int))) (forall ((Xs tptp.list_VEBT_VEBT)) (@ tptp.finite5795047828879050333T_VEBT (@ tptp.set_VEBT_VEBT2 Xs))) (forall ((Xs tptp.list_nat)) (@ tptp.finite_finite_nat (@ tptp.set_nat2 Xs))) (forall ((Xs tptp.list_complex)) (@ tptp.finite3207457112153483333omplex (@ tptp.set_complex2 Xs))) (forall ((Xs tptp.list_int)) (@ tptp.finite_finite_int (@ tptp.set_int2 Xs))) (forall ((Xs tptp.list_Extended_enat)) (@ tptp.finite4001608067531595151d_enat (@ tptp.set_Extended_enat2 Xs))) (forall ((S2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S2) (=> (not (= S2 tptp.bot_bot_set_nat)) (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) S2) (not (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) S2) (@ (@ tptp.ord_less_nat Xa) X5))))))))) (forall ((S2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat S2) (=> (not (= S2 tptp.bot_bo7653980558646680370d_enat)) (exists ((X5 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X5) S2) (not (exists ((Xa tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat Xa) S2) (@ (@ tptp.ord_le72135733267957522d_enat Xa) X5))))))))) (forall ((S2 tptp.set_real)) (=> (@ tptp.finite_finite_real S2) (=> (not (= S2 tptp.bot_bot_set_real)) (exists ((X5 tptp.real)) (and (@ (@ tptp.member_real X5) S2) (not (exists ((Xa tptp.real)) (and (@ (@ tptp.member_real Xa) S2) (@ (@ tptp.ord_less_real Xa) X5))))))))) (forall ((S2 tptp.set_int)) (=> (@ tptp.finite_finite_int S2) (=> (not (= S2 tptp.bot_bot_set_int)) (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) S2) (not (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) S2) (@ (@ tptp.ord_less_int Xa) X5))))))))) (forall ((A2 tptp.set_Extended_enat)) (not (@ (@ tptp.ord_le2529575680413868914d_enat A2) tptp.bot_bo7653980558646680370d_enat))) (forall ((A2 tptp.set_real)) (not (@ (@ tptp.ord_less_set_real A2) tptp.bot_bot_set_real))) (forall ((A2 tptp.set_nat)) (not (@ (@ tptp.ord_less_set_nat A2) tptp.bot_bot_set_nat))) (forall ((A2 tptp.set_int)) (not (@ (@ tptp.ord_less_set_int A2) tptp.bot_bot_set_int))) (forall ((A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat C))) (=> (@ (@ tptp.ord_le2529575680413868914d_enat A2) B) (=> (@ _let_1 A2) (@ _let_1 B))))) (forall ((A2 tptp.set_real) (B tptp.set_real) (C tptp.real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ (@ tptp.ord_less_set_real A2) B) (=> (@ _let_1 A2) (@ _let_1 B))))) (forall ((A2 tptp.set_set_nat) (B tptp.set_set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ (@ tptp.ord_less_set_set_nat A2) B) (=> (@ _let_1 A2) (@ _let_1 B))))) (forall ((A2 tptp.set_nat) (B tptp.set_nat) (C tptp.nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ (@ tptp.ord_less_set_nat A2) B) (=> (@ _let_1 A2) (@ _let_1 B))))) (forall ((A2 tptp.set_int) (B tptp.set_int) (C tptp.int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ (@ tptp.ord_less_set_int A2) B) (=> (@ _let_1 A2) (@ _let_1 B))))) (forall ((X8 tptp.set_nat)) (=> (not (= X8 tptp.bot_bot_set_nat)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) X8) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) X8) (@ (@ tptp.ord_less_nat X5) Xa))))) (not (@ tptp.finite_finite_nat X8))))) (forall ((X8 tptp.set_Extended_enat)) (=> (not (= X8 tptp.bot_bo7653980558646680370d_enat)) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) X8) (exists ((Xa tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat Xa) X8) (@ (@ tptp.ord_le72135733267957522d_enat X5) Xa))))) (not (@ tptp.finite4001608067531595151d_enat X8))))) (forall ((X8 tptp.set_real)) (=> (not (= X8 tptp.bot_bot_set_real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) X8) (exists ((Xa tptp.real)) (and (@ (@ tptp.member_real Xa) X8) (@ (@ tptp.ord_less_real X5) Xa))))) (not (@ tptp.finite_finite_real X8))))) (forall ((X8 tptp.set_int)) (=> (not (= X8 tptp.bot_bot_set_int)) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) X8) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) X8) (@ (@ tptp.ord_less_int X5) Xa))))) (not (@ tptp.finite_finite_int X8))))) (forall ((A2 tptp.set_set_nat)) (= (exists ((X4 tptp.set_nat)) (@ (@ tptp.member_set_nat X4) A2)) (not (= A2 tptp.bot_bot_set_set_nat)))) (forall ((A2 tptp.set_Extended_enat)) (= (exists ((X4 tptp.extended_enat)) (@ (@ tptp.member_Extended_enat X4) A2)) (not (= A2 tptp.bot_bo7653980558646680370d_enat)))) (forall ((A2 tptp.set_real)) (= (exists ((X4 tptp.real)) (@ (@ tptp.member_real X4) A2)) (not (= A2 tptp.bot_bot_set_real)))) (forall ((A2 tptp.set_nat)) (= (exists ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) A2)) (not (= A2 tptp.bot_bot_set_nat)))) (forall ((A2 tptp.set_int)) (= (exists ((X4 tptp.int)) (@ (@ tptp.member_int X4) A2)) (not (= A2 tptp.bot_bot_set_int)))) (forall ((A2 tptp.set_set_nat)) (=> (forall ((Y3 tptp.set_nat)) (not (@ (@ tptp.member_set_nat Y3) A2))) (= A2 tptp.bot_bot_set_set_nat))) (forall ((A2 tptp.set_Extended_enat)) (=> (forall ((Y3 tptp.extended_enat)) (not (@ (@ tptp.member_Extended_enat Y3) A2))) (= A2 tptp.bot_bo7653980558646680370d_enat))) (forall ((A2 tptp.set_real)) (=> (forall ((Y3 tptp.real)) (not (@ (@ tptp.member_real Y3) A2))) (= A2 tptp.bot_bot_set_real))) (forall ((A2 tptp.set_nat)) (=> (forall ((Y3 tptp.nat)) (not (@ (@ tptp.member_nat Y3) A2))) (= A2 tptp.bot_bot_set_nat))) (forall ((A2 tptp.set_int)) (=> (forall ((Y3 tptp.int)) (not (@ (@ tptp.member_int Y3) A2))) (= A2 tptp.bot_bot_set_int))) (forall ((A2 tptp.set_set_nat) (A tptp.set_nat)) (=> (= A2 tptp.bot_bot_set_set_nat) (not (@ (@ tptp.member_set_nat A) A2)))) (forall ((A2 tptp.set_Extended_enat) (A tptp.extended_enat)) (=> (= A2 tptp.bot_bo7653980558646680370d_enat) (not (@ (@ tptp.member_Extended_enat A) A2)))) (forall ((A2 tptp.set_real) (A tptp.real)) (=> (= A2 tptp.bot_bot_set_real) (not (@ (@ tptp.member_real A) A2)))) (forall ((A2 tptp.set_nat) (A tptp.nat)) (=> (= A2 tptp.bot_bot_set_nat) (not (@ (@ tptp.member_nat A) A2)))) (forall ((A2 tptp.set_int) (A tptp.int)) (=> (= A2 tptp.bot_bot_set_int) (not (@ (@ tptp.member_int A) A2)))) (forall ((A tptp.set_nat)) (not (@ (@ tptp.member_set_nat A) tptp.bot_bot_set_set_nat))) (forall ((A tptp.extended_enat)) (not (@ (@ tptp.member_Extended_enat A) tptp.bot_bo7653980558646680370d_enat))) (forall ((A tptp.real)) (not (@ (@ tptp.member_real A) tptp.bot_bot_set_real))) (forall ((A tptp.nat)) (not (@ (@ tptp.member_nat A) tptp.bot_bot_set_nat))) (forall ((A tptp.int)) (not (@ (@ tptp.member_int A) tptp.bot_bot_set_int))) (forall ((A tptp.set_Extended_enat)) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A) tptp.bot_bo7653980558646680370d_enat) (= A tptp.bot_bo7653980558646680370d_enat))) (forall ((A tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A) tptp.bot_bot_set_real) (= A tptp.bot_bot_set_real))) (forall ((A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) tptp.bot_bot_set_nat) (= A tptp.bot_bot_set_nat))) (forall ((A tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) tptp.bot_bot_set_int) (= A tptp.bot_bot_set_int))) (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.bot_bot_nat) (= A tptp.bot_bot_nat))) (forall ((A tptp.set_Extended_enat)) (= (@ (@ tptp.ord_le7203529160286727270d_enat A) tptp.bot_bo7653980558646680370d_enat) (= A tptp.bot_bo7653980558646680370d_enat))) (forall ((A tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real A) tptp.bot_bot_set_real) (= A tptp.bot_bot_set_real))) (forall ((A tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A) tptp.bot_bot_set_nat) (= A tptp.bot_bot_set_nat))) (forall ((A tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A) tptp.bot_bot_set_int) (= A tptp.bot_bot_set_int))) (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.bot_bot_nat) (= A tptp.bot_bot_nat))) (forall ((A tptp.set_Extended_enat)) (@ (@ tptp.ord_le7203529160286727270d_enat tptp.bot_bo7653980558646680370d_enat) A)) (forall ((A tptp.set_real)) (@ (@ tptp.ord_less_eq_set_real tptp.bot_bot_set_real) A)) (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat tptp.bot_bot_set_nat) A)) (forall ((A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int tptp.bot_bot_set_int) A)) (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.bot_bot_nat) A)) (forall ((A tptp.set_Extended_enat)) (= (not (= A tptp.bot_bo7653980558646680370d_enat)) (@ (@ tptp.ord_le2529575680413868914d_enat tptp.bot_bo7653980558646680370d_enat) A))) (forall ((A tptp.set_real)) (= (not (= A tptp.bot_bot_set_real)) (@ (@ tptp.ord_less_set_real tptp.bot_bot_set_real) A))) (forall ((A tptp.set_nat)) (= (not (= A tptp.bot_bot_set_nat)) (@ (@ tptp.ord_less_set_nat tptp.bot_bot_set_nat) A))) (forall ((A tptp.set_int)) (= (not (= A tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_set_int tptp.bot_bot_set_int) A))) (forall ((A tptp.nat)) (= (not (= A tptp.bot_bot_nat)) (@ (@ tptp.ord_less_nat tptp.bot_bot_nat) A))) (forall ((A tptp.extended_enat)) (= (not (= A tptp.bot_bo4199563552545308370d_enat)) (@ (@ tptp.ord_le72135733267957522d_enat tptp.bot_bo4199563552545308370d_enat) A))) (forall ((A tptp.set_Extended_enat)) (not (@ (@ tptp.ord_le2529575680413868914d_enat A) tptp.bot_bo7653980558646680370d_enat))) (forall ((A tptp.set_real)) (not (@ (@ tptp.ord_less_set_real A) tptp.bot_bot_set_real))) (forall ((A tptp.set_nat)) (not (@ (@ tptp.ord_less_set_nat A) tptp.bot_bot_set_nat))) (forall ((A tptp.set_int)) (not (@ (@ tptp.ord_less_set_int A) tptp.bot_bot_set_int))) (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.bot_bot_nat))) (forall ((A tptp.extended_enat)) (not (@ (@ tptp.ord_le72135733267957522d_enat A) tptp.bot_bo4199563552545308370d_enat))) (forall ((A2 tptp.set_VEBT_VEBT)) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (exists ((Xs2 tptp.list_VEBT_VEBT)) (= (@ tptp.set_VEBT_VEBT2 Xs2) A2)))) (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (exists ((Xs2 tptp.list_nat)) (= (@ tptp.set_nat2 Xs2) A2)))) (forall ((A2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A2) (exists ((Xs2 tptp.list_complex)) (= (@ tptp.set_complex2 Xs2) A2)))) (forall ((A2 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (exists ((Xs2 tptp.list_int)) (= (@ tptp.set_int2 Xs2) A2)))) (forall ((A2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (exists ((Xs2 tptp.list_Extended_enat)) (= (@ tptp.set_Extended_enat2 Xs2) A2)))) (forall ((X tptp.real) (Y tptp.real)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_real X) Y)) (@ (@ tptp.ord_less_real Y) X)))) (forall ((X tptp.int) (Y tptp.int)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_int Y) X)))) (forall ((X2 tptp.real)) (exists ((X_12 tptp.real)) (@ (@ tptp.ord_less_real X2) X_12))) (forall ((X2 tptp.real)) (exists ((Y3 tptp.real)) (@ (@ tptp.ord_less_real Y3) X2))) (= tptp.ord_less_eq_set_nat (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat A5) B5) (= A5 B5)))) (= tptp.ord_less_eq_set_int (lambda ((A5 tptp.set_int) (B5 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int A5) B5) (= A5 B5)))) (forall ((A2 tptp.set_nat) (B tptp.set_nat) (C4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B) (=> (@ (@ tptp.ord_less_set_nat B) C4) (@ (@ tptp.ord_less_set_nat A2) C4)))) (forall ((A2 tptp.set_int) (B tptp.set_int) (C4 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B) (=> (@ (@ tptp.ord_less_set_int B) C4) (@ (@ tptp.ord_less_set_int A2) C4)))) (= tptp.ord_less_set_nat (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A5) B5) (not (@ (@ tptp.ord_less_eq_set_nat B5) A5))))) (= tptp.ord_less_set_int (lambda ((A5 tptp.set_int) (B5 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A5) B5) (not (@ (@ tptp.ord_less_eq_set_int B5) A5))))) (forall ((A2 tptp.set_nat) (B tptp.set_nat) (C4 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat A2))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_nat B) C4) (@ _let_1 C4))))) (forall ((A2 tptp.set_int) (B tptp.set_int) (C4 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int A2))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_int B) C4) (@ _let_1 C4))))) (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A2) B) (@ (@ tptp.ord_less_eq_set_nat A2) B))) (forall ((A2 tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A2) B) (@ (@ tptp.ord_less_eq_set_int A2) B))) (forall ((P (-> tptp.real Bool)) (Q (-> tptp.real Bool))) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.collect_real P)) (@ tptp.collect_real Q)) (forall ((X4 tptp.real)) (=> (@ P X4) (@ Q X4))))) (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 ((X4 tptp.list_nat)) (=> (@ P X4) (@ Q X4))))) (forall ((P (-> tptp.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.collect_set_nat P)) (@ tptp.collect_set_nat Q)) (forall ((X4 tptp.set_nat)) (=> (@ P X4) (@ Q X4))))) (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat P)) (@ tptp.collect_nat Q)) (forall ((X4 tptp.nat)) (=> (@ P X4) (@ Q X4))))) (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int P)) (@ tptp.collect_int Q)) (forall ((X4 tptp.int)) (=> (@ P X4) (@ Q X4))))) (= (lambda ((Y4 tptp.set_nat) (Z2 tptp.set_nat)) (= Y4 Z2)) (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A5) B5) (@ (@ tptp.ord_less_eq_set_nat B5) A5)))) (= (lambda ((Y4 tptp.set_int) (Z2 tptp.set_int)) (= Y4 Z2)) (lambda ((A5 tptp.set_int) (B5 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A5) B5) (@ (@ tptp.ord_less_eq_set_int B5) A5)))) (forall ((A2 tptp.set_nat) (B tptp.set_nat) (C4 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A2))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_nat B) C4) (@ _let_1 C4))))) (forall ((A2 tptp.set_int) (B tptp.set_int) (C4 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A2))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_int B) C4) (@ _let_1 C4))))) (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.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (=> (forall ((X5 tptp.set_nat)) (=> (@ P X5) (@ Q X5))) (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.collect_set_nat P)) (@ tptp.collect_set_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_nat)) (@ (@ tptp.ord_less_eq_set_nat A2) A2)) (forall ((A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A2) A2)) _let_274 _let_273 _let_272 _let_271 _let_270 (= tptp.ord_less_set_nat (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A5) B5) (not (= A5 B5))))) (= tptp.ord_less_set_int (lambda ((A5 tptp.set_int) (B5 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A5) B5) (not (= A5 B5))))) (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (=> (= A2 B) (@ (@ tptp.ord_less_eq_set_nat B) A2))) (forall ((A2 tptp.set_int) (B tptp.set_int)) (=> (= A2 B) (@ (@ tptp.ord_less_eq_set_int B) A2))) (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (=> (= A2 B) (@ (@ tptp.ord_less_eq_set_nat A2) B))) (forall ((A2 tptp.set_int) (B tptp.set_int)) (=> (= A2 B) (@ (@ tptp.ord_less_eq_set_int A2) B))) (= tptp.ord_le7203529160286727270d_enat (lambda ((A5 tptp.set_Extended_enat) (B5 tptp.set_Extended_enat)) (forall ((X4 tptp.extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat X4))) (=> (@ _let_1 A5) (@ _let_1 B5)))))) (= tptp.ord_less_eq_set_real (lambda ((A5 tptp.set_real) (B5 tptp.set_real)) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.member_real X4))) (=> (@ _let_1 A5) (@ _let_1 B5)))))) (= tptp.ord_le6893508408891458716et_nat (lambda ((A5 tptp.set_set_nat) (B5 tptp.set_set_nat)) (forall ((X4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X4))) (=> (@ _let_1 A5) (@ _let_1 B5)))))) (= tptp.ord_less_eq_set_nat (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (forall ((X4 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X4))) (=> (@ _let_1 A5) (@ _let_1 B5)))))) (= tptp.ord_less_eq_set_int (lambda ((A5 tptp.set_int) (B5 tptp.set_int)) (forall ((X4 tptp.int)) (let ((_let_1 (@ tptp.member_int X4))) (=> (@ _let_1 A5) (@ _let_1 B5)))))) (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (=> (= A2 B) (not (=> (@ (@ tptp.ord_less_eq_set_nat A2) B) (not (@ (@ tptp.ord_less_eq_set_nat B) A2)))))) (forall ((A2 tptp.set_int) (B tptp.set_int)) (=> (= A2 B) (not (=> (@ (@ tptp.ord_less_eq_set_int A2) B) (not (@ (@ tptp.ord_less_eq_set_int B) A2)))))) (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A2) B) (not (=> (@ (@ tptp.ord_less_eq_set_nat A2) B) (@ (@ tptp.ord_less_eq_set_nat B) A2))))) (forall ((A2 tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A2) B) (not (=> (@ (@ tptp.ord_less_eq_set_int A2) B) (@ (@ tptp.ord_less_eq_set_int B) A2))))) (forall ((A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat C))) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) B) (=> (@ _let_1 A2) (@ _let_1 B))))) (forall ((A2 tptp.set_real) (B tptp.set_real) (C tptp.real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ (@ tptp.ord_less_eq_set_real A2) B) (=> (@ _let_1 A2) (@ _let_1 B))))) (forall ((A2 tptp.set_set_nat) (B tptp.set_set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A2) B) (=> (@ _let_1 A2) (@ _let_1 B))))) (forall ((A2 tptp.set_nat) (B tptp.set_nat) (C tptp.nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B) (=> (@ _let_1 A2) (@ _let_1 B))))) (forall ((A2 tptp.set_int) (B tptp.set_int) (C tptp.int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ (@ tptp.ord_less_eq_set_int A2) B) (=> (@ _let_1 A2) (@ _let_1 B))))) (forall ((A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat) (X tptp.extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat X))) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) B) (=> (@ _let_1 A2) (@ _let_1 B))))) (forall ((A2 tptp.set_real) (B tptp.set_real) (X tptp.real)) (let ((_let_1 (@ tptp.member_real X))) (=> (@ (@ tptp.ord_less_eq_set_real A2) B) (=> (@ _let_1 A2) (@ _let_1 B))))) (forall ((A2 tptp.set_set_nat) (B tptp.set_set_nat) (X tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X))) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A2) B) (=> (@ _let_1 A2) (@ _let_1 B))))) (forall ((A2 tptp.set_nat) (B tptp.set_nat) (X tptp.nat)) (let ((_let_1 (@ tptp.member_nat X))) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B) (=> (@ _let_1 A2) (@ _let_1 B))))) (forall ((A2 tptp.set_int) (B tptp.set_int) (X tptp.int)) (let ((_let_1 (@ tptp.member_int X))) (=> (@ (@ tptp.ord_less_eq_set_int A2) B) (=> (@ _let_1 A2) (@ _let_1 B))))) (forall ((A2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (not (= A2 tptp.bot_bo7653980558646680370d_enat)) (exists ((X5 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X5) A2) (forall ((Xa tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat Xa) A2) (=> (@ (@ tptp.ord_le2932123472753598470d_enat X5) Xa) (= X5 Xa))))))))) (forall ((A2 tptp.set_real)) (=> (@ tptp.finite_finite_real A2) (=> (not (= A2 tptp.bot_bot_set_real)) (exists ((X5 tptp.real)) (and (@ (@ tptp.member_real X5) A2) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A2) (=> (@ (@ tptp.ord_less_eq_real X5) Xa) (= X5 Xa))))))))) (forall ((A2 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A2) (=> (not (= A2 tptp.bot_bot_set_set_nat)) (exists ((X5 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X5) A2) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_nat X5) Xa) (= X5 Xa))))))))) (forall ((A2 tptp.set_set_int)) (=> (@ tptp.finite6197958912794628473et_int A2) (=> (not (= A2 tptp.bot_bot_set_set_int)) (exists ((X5 tptp.set_int)) (and (@ (@ tptp.member_set_int X5) A2) (forall ((Xa tptp.set_int)) (=> (@ (@ tptp.member_set_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_int X5) Xa) (= X5 Xa))))))))) (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (=> (not (= A2 tptp.bot_bot_set_nat)) (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) A2) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_nat X5) Xa) (= X5 Xa))))))))) (forall ((A2 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (=> (not (= A2 tptp.bot_bot_set_int)) (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) A2) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_int X5) Xa) (= X5 Xa))))))))) (forall ((A2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (not (= A2 tptp.bot_bo7653980558646680370d_enat)) (exists ((X5 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X5) A2) (forall ((Xa tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat Xa) A2) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Xa) X5) (= X5 Xa))))))))) (forall ((A2 tptp.set_real)) (=> (@ tptp.finite_finite_real A2) (=> (not (= A2 tptp.bot_bot_set_real)) (exists ((X5 tptp.real)) (and (@ (@ tptp.member_real X5) A2) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A2) (=> (@ (@ tptp.ord_less_eq_real Xa) X5) (= X5 Xa))))))))) (forall ((A2 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A2) (=> (not (= A2 tptp.bot_bot_set_set_nat)) (exists ((X5 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X5) A2) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_nat Xa) X5) (= X5 Xa))))))))) (forall ((A2 tptp.set_set_int)) (=> (@ tptp.finite6197958912794628473et_int A2) (=> (not (= A2 tptp.bot_bot_set_set_int)) (exists ((X5 tptp.set_int)) (and (@ (@ tptp.member_set_int X5) A2) (forall ((Xa tptp.set_int)) (=> (@ (@ tptp.member_set_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_int Xa) X5) (= X5 Xa))))))))) (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (=> (not (= A2 tptp.bot_bot_set_nat)) (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) A2) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_nat Xa) X5) (= X5 Xa))))))))) (forall ((A2 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (=> (not (= A2 tptp.bot_bot_set_int)) (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) A2) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_int Xa) X5) (= X5 Xa))))))))) _let_269 (forall ((S2 tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S2)) (forall ((M tptp.nat)) (exists ((N tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.member_nat N) S2)))))) (= tptp.finite_finite_nat (lambda ((N5 tptp.set_nat)) (exists ((M tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) N5) (@ (@ tptp.ord_less_nat X4) M)))))) (forall ((S2 tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S2)) (forall ((M tptp.nat)) (exists ((N tptp.nat)) (and (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.member_nat N) S2)))))) (forall ((N6 tptp.set_nat) (N2 tptp.nat)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) N6) (@ (@ tptp.ord_less_nat X5) N2))) (@ tptp.finite_finite_nat N6))) (forall ((K tptp.nat) (S2 tptp.set_nat)) (=> (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) M3) (exists ((N7 tptp.nat)) (and (@ (@ tptp.ord_less_nat M3) N7) (@ (@ tptp.member_nat N7) S2))))) (not (@ tptp.finite_finite_nat S2)))) (forall ((A2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat A2) (=> (forall ((A6 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A6) (=> (forall ((B6 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B6) A6) (@ P B6))) (@ P A6)))) (@ P A2)))) (forall ((A2 tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((A6 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A6) (=> (forall ((B6 tptp.set_complex)) (=> (@ (@ tptp.ord_less_set_complex B6) A6) (@ P B6))) (@ P A6)))) (@ P A2)))) (forall ((A2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((A6 tptp.set_int)) (=> (@ tptp.finite_finite_int A6) (=> (forall ((B6 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int B6) A6) (@ P B6))) (@ P A6)))) (@ P A2)))) (forall ((A2 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (forall ((A6 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A6) (=> (forall ((B6 tptp.set_Extended_enat)) (=> (@ (@ tptp.ord_le2529575680413868914d_enat B6) A6) (@ P B6))) (@ P A6)))) (@ P A2)))) (forall ((S2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (not (= S2 tptp.bot_bot_set_complex)) (not (exists ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) S2) (@ (@ tptp.ord_less_nat (@ F X2)) (@ F (@ (@ tptp.lattic5364784637807008409ex_nat F) S2))))))))) (forall ((S2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat S2) (=> (not (= S2 tptp.bot_bo7653980558646680370d_enat)) (not (exists ((X2 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X2) S2) (@ (@ tptp.ord_less_nat (@ F X2)) (@ F (@ (@ tptp.lattic3845382081240766429at_nat F) S2))))))))) (forall ((S2 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real S2) (=> (not (= S2 tptp.bot_bot_set_real)) (not (exists ((X2 tptp.real)) (and (@ (@ tptp.member_real X2) S2) (@ (@ tptp.ord_less_nat (@ F X2)) (@ F (@ (@ tptp.lattic5055836439445974935al_nat F) S2))))))))) (forall ((S2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat S2) (=> (not (= S2 tptp.bot_bot_set_nat)) (not (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) S2) (@ (@ tptp.ord_less_nat (@ F X2)) (@ F (@ (@ tptp.lattic7446932960582359483at_nat F) S2))))))))) (forall ((S2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int S2) (=> (not (= S2 tptp.bot_bot_set_int)) (not (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) S2) (@ (@ tptp.ord_less_nat (@ F X2)) (@ F (@ (@ tptp.lattic8446286672483414039nt_nat F) S2))))))))) (forall ((S2 tptp.set_complex) (F (-> tptp.complex tptp.extended_enat))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (not (= S2 tptp.bot_bot_set_complex)) (not (exists ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) S2) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X2)) (@ F (@ (@ tptp.lattic7796887085614042845d_enat F) S2))))))))) (forall ((S2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.extended_enat))) (=> (@ tptp.finite4001608067531595151d_enat S2) (=> (not (= S2 tptp.bot_bo7653980558646680370d_enat)) (not (exists ((X2 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X2) S2) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X2)) (@ F (@ (@ tptp.lattic1996716550891908761d_enat F) S2))))))))) (forall ((S2 tptp.set_real) (F (-> tptp.real tptp.extended_enat))) (=> (@ tptp.finite_finite_real S2) (=> (not (= S2 tptp.bot_bot_set_real)) (not (exists ((X2 tptp.real)) (and (@ (@ tptp.member_real X2) S2) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X2)) (@ F (@ (@ tptp.lattic9066027731366277983d_enat F) S2))))))))) (forall ((S2 tptp.set_nat) (F (-> tptp.nat tptp.extended_enat))) (=> (@ tptp.finite_finite_nat S2) (=> (not (= S2 tptp.bot_bot_set_nat)) (not (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) S2) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X2)) (@ F (@ (@ tptp.lattic8926238025367240251d_enat F) S2))))))))) (forall ((S2 tptp.set_int) (F (-> tptp.int tptp.extended_enat))) (=> (@ tptp.finite_finite_int S2) (=> (not (= S2 tptp.bot_bot_set_int)) (not (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) S2) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X2)) (@ F (@ (@ tptp.lattic6042659972569420511d_enat F) S2))))))))) _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 (forall ((M7 tptp.set_list_VEBT_VEBT)) (=> (@ tptp.finite3004134309566078307T_VEBT M7) (exists ((N3 tptp.nat)) (forall ((X2 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member2936631157270082147T_VEBT X2) M7) (@ (@ tptp.ord_less_nat (@ tptp.size_s6755466524823107622T_VEBT X2)) N3)))))) (forall ((M7 tptp.set_list_int)) (=> (@ tptp.finite3922522038869484883st_int M7) (exists ((N3 tptp.nat)) (forall ((X2 tptp.list_int)) (=> (@ (@ tptp.member_list_int X2) M7) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_int X2)) N3)))))) (forall ((M7 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat M7) (exists ((N3 tptp.nat)) (forall ((X2 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat X2) M7) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_nat X2)) N3)))))) (forall ((P (-> tptp.nat Bool)) (X tptp.nat) (M7 tptp.nat)) (=> (@ P X) (=> (forall ((X5 tptp.nat)) (=> (@ P X5) (@ (@ tptp.ord_less_eq_nat X5) M7))) (not (forall ((M3 tptp.nat)) (=> (@ P M3) (not (forall ((X2 tptp.nat)) (=> (@ P X2) (@ (@ tptp.ord_less_eq_nat X2) M3)))))))))) (forall ((A2 tptp.set_Extended_enat) (A tptp.extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ (@ tptp.member_Extended_enat A) A2) (exists ((X5 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat A) X5) (forall ((Xa tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat Xa) A2) (=> (@ (@ tptp.ord_le2932123472753598470d_enat X5) Xa) (= X5 Xa))))))))) (forall ((A2 tptp.set_real) (A tptp.real)) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real A) A2) (exists ((X5 tptp.real)) (and (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_less_eq_real A) X5) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A2) (=> (@ (@ tptp.ord_less_eq_real X5) Xa) (= X5 Xa))))))))) (forall ((A2 tptp.set_set_nat) (A tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A2) (=> (@ (@ tptp.member_set_nat A) A2) (exists ((X5 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X5) A2) (@ (@ tptp.ord_less_eq_set_nat A) X5) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_nat X5) Xa) (= X5 Xa))))))))) (forall ((A2 tptp.set_set_int) (A tptp.set_int)) (=> (@ tptp.finite6197958912794628473et_int A2) (=> (@ (@ tptp.member_set_int A) A2) (exists ((X5 tptp.set_int)) (and (@ (@ tptp.member_set_int X5) A2) (@ (@ tptp.ord_less_eq_set_int A) X5) (forall ((Xa tptp.set_int)) (=> (@ (@ tptp.member_set_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_int X5) Xa) (= X5 Xa))))))))) (forall ((A2 tptp.set_nat) (A tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.member_nat A) A2) (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_less_eq_nat A) X5) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_nat X5) Xa) (= X5 Xa))))))))) (forall ((A2 tptp.set_int) (A tptp.int)) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int A) A2) (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_eq_int A) X5) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_int X5) Xa) (= X5 Xa))))))))) (forall ((A2 tptp.set_Extended_enat) (A tptp.extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ (@ tptp.member_Extended_enat A) A2) (exists ((X5 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat X5) A) (forall ((Xa tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat Xa) A2) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Xa) X5) (= X5 Xa))))))))) (forall ((A2 tptp.set_real) (A tptp.real)) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real A) A2) (exists ((X5 tptp.real)) (and (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_less_eq_real X5) A) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A2) (=> (@ (@ tptp.ord_less_eq_real Xa) X5) (= X5 Xa))))))))) (forall ((A2 tptp.set_set_nat) (A tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A2) (=> (@ (@ tptp.member_set_nat A) A2) (exists ((X5 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X5) A2) (@ (@ tptp.ord_less_eq_set_nat X5) A) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_nat Xa) X5) (= X5 Xa))))))))) (forall ((A2 tptp.set_set_int) (A tptp.set_int)) (=> (@ tptp.finite6197958912794628473et_int A2) (=> (@ (@ tptp.member_set_int A) A2) (exists ((X5 tptp.set_int)) (and (@ (@ tptp.member_set_int X5) A2) (@ (@ tptp.ord_less_eq_set_int X5) A) (forall ((Xa tptp.set_int)) (=> (@ (@ tptp.member_set_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_int Xa) X5) (= X5 Xa))))))))) (forall ((A2 tptp.set_nat) (A tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.member_nat A) A2) (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_less_eq_nat X5) A) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_nat Xa) X5) (= X5 Xa))))))))) (forall ((A2 tptp.set_int) (A tptp.int)) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int A) A2) (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_eq_int X5) A) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_int Xa) X5) (= X5 Xa))))))))) (@ tptp.finite3207457112153483333omplex tptp.bot_bot_set_complex) (@ tptp.finite4001608067531595151d_enat tptp.bot_bo7653980558646680370d_enat) (@ tptp.finite_finite_real tptp.bot_bot_set_real) (@ tptp.finite_finite_nat tptp.bot_bot_set_nat) (@ tptp.finite_finite_int tptp.bot_bot_set_int) (forall ((S2 tptp.set_complex)) (=> (not (@ tptp.finite3207457112153483333omplex S2)) (not (= S2 tptp.bot_bot_set_complex)))) (forall ((S2 tptp.set_Extended_enat)) (=> (not (@ tptp.finite4001608067531595151d_enat S2)) (not (= S2 tptp.bot_bo7653980558646680370d_enat)))) (forall ((S2 tptp.set_real)) (=> (not (@ tptp.finite_finite_real S2)) (not (= S2 tptp.bot_bot_set_real)))) (forall ((S2 tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat S2)) (not (= S2 tptp.bot_bot_set_nat)))) (forall ((S2 tptp.set_int)) (=> (not (@ tptp.finite_finite_int S2)) (not (= S2 tptp.bot_bot_set_int)))) (forall ((A2 tptp.set_set_nat) (R (-> tptp.set_nat tptp.set_nat Bool))) (=> (@ tptp.finite1152437895449049373et_nat A2) (=> (forall ((X5 tptp.set_nat)) (not (@ (@ R X5) X5))) (=> (forall ((X5 tptp.set_nat) (Y3 tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ R X5))) (=> (@ _let_1 Y3) (=> (@ (@ R Y3) Z) (@ _let_1 Z))))) (=> (forall ((X5 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X5) A2) (exists ((Y6 tptp.set_nat)) (and (@ (@ tptp.member_set_nat Y6) A2) (@ (@ R X5) Y6))))) (= A2 tptp.bot_bot_set_set_nat)))))) (forall ((A2 tptp.set_complex) (R (-> tptp.complex tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X5 tptp.complex)) (not (@ (@ R X5) X5))) (=> (forall ((X5 tptp.complex) (Y3 tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ R X5))) (=> (@ _let_1 Y3) (=> (@ (@ R Y3) Z) (@ _let_1 Z))))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (exists ((Y6 tptp.complex)) (and (@ (@ tptp.member_complex Y6) A2) (@ (@ R X5) Y6))))) (= A2 tptp.bot_bot_set_complex)))))) (forall ((A2 tptp.set_Extended_enat) (R (-> tptp.extended_enat tptp.extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (forall ((X5 tptp.extended_enat)) (not (@ (@ R X5) X5))) (=> (forall ((X5 tptp.extended_enat) (Y3 tptp.extended_enat) (Z tptp.extended_enat)) (let ((_let_1 (@ R X5))) (=> (@ _let_1 Y3) (=> (@ (@ R Y3) Z) (@ _let_1 Z))))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) A2) (exists ((Y6 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat Y6) A2) (@ (@ R X5) Y6))))) (= A2 tptp.bot_bo7653980558646680370d_enat)))))) (forall ((A2 tptp.set_real) (R (-> tptp.real tptp.real Bool))) (=> (@ tptp.finite_finite_real A2) (=> (forall ((X5 tptp.real)) (not (@ (@ R X5) X5))) (=> (forall ((X5 tptp.real) (Y3 tptp.real) (Z tptp.real)) (let ((_let_1 (@ R X5))) (=> (@ _let_1 Y3) (=> (@ (@ R Y3) Z) (@ _let_1 Z))))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (exists ((Y6 tptp.real)) (and (@ (@ tptp.member_real Y6) A2) (@ (@ R X5) Y6))))) (= A2 tptp.bot_bot_set_real)))))) (forall ((A2 tptp.set_nat) (R (-> tptp.nat tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A2) (=> (forall ((X5 tptp.nat)) (not (@ (@ R X5) X5))) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ R X5))) (=> (@ _let_1 Y3) (=> (@ (@ R Y3) Z) (@ _let_1 Z))))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (exists ((Y6 tptp.nat)) (and (@ (@ tptp.member_nat Y6) A2) (@ (@ R X5) Y6))))) (= A2 tptp.bot_bot_set_nat)))))) (forall ((A2 tptp.set_int) (R (-> tptp.int tptp.int Bool))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X5 tptp.int)) (not (@ (@ R X5) X5))) (=> (forall ((X5 tptp.int) (Y3 tptp.int) (Z tptp.int)) (let ((_let_1 (@ R X5))) (=> (@ _let_1 Y3) (=> (@ (@ R Y3) Z) (@ _let_1 Z))))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (exists ((Y6 tptp.int)) (and (@ (@ tptp.member_int Y6) A2) (@ (@ R X5) Y6))))) (= A2 tptp.bot_bot_set_int)))))) (forall ((A2 tptp.set_complex) (B tptp.set_complex)) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B) (=> (@ tptp.finite3207457112153483333omplex B) (@ tptp.finite3207457112153483333omplex A2)))) (forall ((A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat)) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) B) (=> (@ tptp.finite4001608067531595151d_enat B) (@ tptp.finite4001608067531595151d_enat A2)))) (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B) (=> (@ tptp.finite_finite_nat B) (@ tptp.finite_finite_nat A2)))) (forall ((A2 tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B) (=> (@ tptp.finite_finite_int B) (@ tptp.finite_finite_int A2)))) (forall ((S2 tptp.set_complex) (T3 tptp.set_complex)) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (not (@ tptp.finite3207457112153483333omplex S2)) (not (@ tptp.finite3207457112153483333omplex T3))))) (forall ((S2 tptp.set_Extended_enat) (T3 tptp.set_Extended_enat)) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (not (@ tptp.finite4001608067531595151d_enat S2)) (not (@ tptp.finite4001608067531595151d_enat T3))))) (forall ((S2 tptp.set_nat) (T3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat S2) T3) (=> (not (@ tptp.finite_finite_nat S2)) (not (@ tptp.finite_finite_nat T3))))) (forall ((S2 tptp.set_int) (T3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int S2) T3) (=> (not (@ tptp.finite_finite_int S2)) (not (@ tptp.finite_finite_int T3))))) (forall ((B tptp.set_complex) (A2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex B) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B) (@ tptp.finite3207457112153483333omplex A2)))) (forall ((B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat B) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) B) (@ tptp.finite4001608067531595151d_enat A2)))) (forall ((B tptp.set_nat) (A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B) (@ tptp.finite_finite_nat A2)))) (forall ((B tptp.set_int) (A2 tptp.set_int)) (=> (@ tptp.finite_finite_int B) (=> (@ (@ tptp.ord_less_eq_set_int A2) B) (@ tptp.finite_finite_int A2)))) (forall ((S2 tptp.set_complex) (Y tptp.complex) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (not (= S2 tptp.bot_bot_set_complex)) (=> (@ (@ tptp.member_complex Y) S2) (@ (@ tptp.ord_less_eq_real (@ F (@ (@ tptp.lattic8794016678065449205x_real F) S2))) (@ F Y)))))) (forall ((S2 tptp.set_Extended_enat) (Y tptp.extended_enat) (F (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat S2) (=> (not (= S2 tptp.bot_bo7653980558646680370d_enat)) (=> (@ (@ tptp.member_Extended_enat Y) S2) (@ (@ tptp.ord_less_eq_real (@ F (@ (@ tptp.lattic1189837152898106425t_real F) S2))) (@ F Y)))))) (forall ((S2 tptp.set_real) (Y tptp.real) (F (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real S2) (=> (not (= S2 tptp.bot_bot_set_real)) (=> (@ (@ tptp.member_real Y) S2) (@ (@ tptp.ord_less_eq_real (@ F (@ (@ tptp.lattic8440615504127631091l_real F) S2))) (@ F Y)))))) (forall ((S2 tptp.set_nat) (Y tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat S2) (=> (not (= S2 tptp.bot_bot_set_nat)) (=> (@ (@ tptp.member_nat Y) S2) (@ (@ tptp.ord_less_eq_real (@ F (@ (@ tptp.lattic488527866317076247t_real F) S2))) (@ F Y)))))) (forall ((S2 tptp.set_int) (Y tptp.int) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int S2) (=> (not (= S2 tptp.bot_bot_set_int)) (=> (@ (@ tptp.member_int Y) S2) (@ (@ tptp.ord_less_eq_real (@ F (@ (@ tptp.lattic2675449441010098035t_real F) S2))) (@ F Y)))))) (forall ((S2 tptp.set_complex) (Y tptp.complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (not (= S2 tptp.bot_bot_set_complex)) (=> (@ (@ tptp.member_complex Y) S2) (@ (@ tptp.ord_less_eq_nat (@ F (@ (@ tptp.lattic5364784637807008409ex_nat F) S2))) (@ F Y)))))) (forall ((S2 tptp.set_Extended_enat) (Y tptp.extended_enat) (F (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat S2) (=> (not (= S2 tptp.bot_bo7653980558646680370d_enat)) (=> (@ (@ tptp.member_Extended_enat Y) S2) (@ (@ tptp.ord_less_eq_nat (@ F (@ (@ tptp.lattic3845382081240766429at_nat F) S2))) (@ F Y)))))) (forall ((S2 tptp.set_real) (Y tptp.real) (F (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real S2) (=> (not (= S2 tptp.bot_bot_set_real)) (=> (@ (@ tptp.member_real Y) S2) (@ (@ tptp.ord_less_eq_nat (@ F (@ (@ tptp.lattic5055836439445974935al_nat F) S2))) (@ F Y)))))) (forall ((S2 tptp.set_nat) (Y tptp.nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat S2) (=> (not (= S2 tptp.bot_bot_set_nat)) (=> (@ (@ tptp.member_nat Y) S2) (@ (@ tptp.ord_less_eq_nat (@ F (@ (@ tptp.lattic7446932960582359483at_nat F) S2))) (@ F Y)))))) (forall ((S2 tptp.set_int) (Y tptp.int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int S2) (=> (not (= S2 tptp.bot_bot_set_int)) (=> (@ (@ tptp.member_int Y) S2) (@ (@ tptp.ord_less_eq_nat (@ F (@ (@ tptp.lattic8446286672483414039nt_nat F) S2))) (@ F Y)))))) (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B2 tptp.nat)) (=> (forall ((A4 tptp.nat) (B4 tptp.nat)) (= (@ (@ P A4) B4) (@ (@ P B4) A4))) (=> (forall ((A4 tptp.nat)) (@ (@ P A4) tptp.zero_zero_nat)) (=> (forall ((A4 tptp.nat) (B4 tptp.nat)) (let ((_let_1 (@ P A4))) (=> (@ _let_1 B4) (@ _let_1 (@ (@ tptp.plus_plus_nat A4) B4))))) (@ (@ P A) B2))))) (forall ((N2 tptp.nat) (P (-> tptp.nat Bool)) (M2 tptp.nat)) (=> (forall ((K3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K3) (@ P K3))) (=> (forall ((K3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N2) (=> (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K3) I5) (@ P I5))) (@ P K3)))) (@ P M2)))) (forall ((A2 tptp.set_set_nat)) (=> (forall ((X5 tptp.set_nat)) (not (@ (@ tptp.member_set_nat X5) A2))) (@ (@ tptp.ord_le6893508408891458716et_nat A2) tptp.bot_bot_set_set_nat))) (forall ((A2 tptp.set_Extended_enat)) (=> (forall ((X5 tptp.extended_enat)) (not (@ (@ tptp.member_Extended_enat X5) A2))) (@ (@ tptp.ord_le7203529160286727270d_enat A2) tptp.bot_bo7653980558646680370d_enat))) (forall ((A2 tptp.set_real)) (=> (forall ((X5 tptp.real)) (not (@ (@ tptp.member_real X5) A2))) (@ (@ tptp.ord_less_eq_set_real A2) tptp.bot_bot_set_real))) (forall ((A2 tptp.set_nat)) (=> (forall ((X5 tptp.nat)) (not (@ (@ tptp.member_nat X5) A2))) (@ (@ tptp.ord_less_eq_set_nat A2) tptp.bot_bot_set_nat))) (forall ((A2 tptp.set_int)) (=> (forall ((X5 tptp.int)) (not (@ (@ tptp.member_int X5) A2))) (@ (@ tptp.ord_less_eq_set_int A2) tptp.bot_bot_set_int))) (forall ((X tptp.nat)) (=> (not (= X tptp.zero_zero_nat)) (not (forall ((N3 tptp.nat)) (not (= X (@ tptp.suc N3))))))) (forall ((X tptp.nat)) (=> (not (= X tptp.zero_zero_nat)) (=> (not (= X (@ tptp.suc tptp.zero_zero_nat))) (not (forall ((Va tptp.nat)) (not (= X (@ tptp.suc (@ tptp.suc Va))))))))) (forall ((P (-> tptp.nat Bool))) (=> (not (@ P tptp.zero_zero_nat)) (=> (exists ((X_1 tptp.nat)) (@ P X_1)) (exists ((N3 tptp.nat)) (and (not (@ P N3)) (@ P (@ tptp.suc N3))))))) (forall ((B2 tptp.nat) (A tptp.nat)) (= (= B2 (@ (@ tptp.plus_plus_nat B2) A)) (= A tptp.zero_zero_nat))) (forall ((B2 tptp.real) (A tptp.real)) (= (= B2 (@ (@ tptp.plus_plus_real B2) A)) (= A tptp.zero_zero_real))) (forall ((B2 tptp.int) (A tptp.int)) (= (= B2 (@ (@ tptp.plus_plus_int B2) A)) (= A tptp.zero_zero_int))) (forall ((B2 tptp.complex) (A tptp.complex)) (= (= B2 (@ (@ tptp.plus_plus_complex B2) A)) (= A tptp.zero_zero_complex))) (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)) (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)) (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)) (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)) (not (@ _let_212 tptp.zero_zero_nat)) (not (@ _let_223 tptp.zero_z5237406670263579293d_enat)) (not (@ _let_167 tptp.zero_zero_real)) (not (@ _let_168 tptp.zero_zero_int)) (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 ((A tptp.real) (B2 tptp.real)) (or (= A B2) (not (@ (@ tptp.ord_less_eq_real A) B2)) (not (@ (@ tptp.ord_less_eq_real B2) A)))) (forall ((A tptp.nat) (B2 tptp.nat)) (or (= A B2) (not (@ (@ tptp.ord_less_eq_nat A) B2)) (not (@ (@ tptp.ord_less_eq_nat B2) A)))) (forall ((A tptp.int) (B2 tptp.int)) (or (= A B2) (not (@ (@ tptp.ord_less_eq_int A) B2)) (not (@ (@ tptp.ord_less_eq_int B2) A)))) (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real A) A)) (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A) A)) (forall ((A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A) A)) (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)) (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) A)) (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))) (forall ((A tptp.extended_enat)) (not (@ (@ tptp.ord_le72135733267957522d_enat A) A))) (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real A) A))) (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int A) A))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B2) C))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_real B2) C))))) (@ _let_235 tptp.zero_z5237406670263579293d_enat) (@ _let_172 tptp.zero_zero_real) (@ _let_232 tptp.zero_zero_nat) (@ _let_171 tptp.zero_zero_int) (forall ((B7 tptp.extended_enat) (A7 tptp.extended_enat)) (= (not (@ (@ tptp.ord_le2932123472753598470d_enat B7) A7)) (@ (@ tptp.ord_le72135733267957522d_enat A7) B7))) (forall ((B7 tptp.real) (A7 tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real B7) A7)) (@ (@ tptp.ord_less_real A7) B7))) (forall ((B7 tptp.nat) (A7 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat B7) A7)) (@ (@ tptp.ord_less_nat A7) B7))) (forall ((B7 tptp.int) (A7 tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int B7) A7)) (@ (@ tptp.ord_less_int A7) B7))) (forall ((P (-> tptp.list_nat Bool))) (= (= (@ tptp.collect_list_nat P) tptp.bot_bot_set_list_nat) (= P tptp.bot_bot_list_nat_o))) (forall ((P (-> tptp.set_nat Bool))) (= (= (@ tptp.collect_set_nat P) tptp.bot_bot_set_set_nat) (= P tptp.bot_bot_set_nat_o))) (forall ((P (-> tptp.extended_enat Bool))) (= (= (@ tptp.collec4429806609662206161d_enat P) tptp.bot_bo7653980558646680370d_enat) (= P tptp.bot_bo1954855461789132331enat_o))) (forall ((P (-> tptp.real Bool))) (= (= (@ tptp.collect_real P) tptp.bot_bot_set_real) (= P tptp.bot_bot_real_o))) (forall ((P (-> tptp.nat Bool))) (= (= (@ tptp.collect_nat P) tptp.bot_bot_set_nat) (= P tptp.bot_bot_nat_o))) (forall ((P (-> tptp.int Bool))) (= (= (@ tptp.collect_int P) tptp.bot_bot_set_int) (= P tptp.bot_bot_int_o))) (= tptp.bot_bot_set_nat_o (lambda ((X4 tptp.set_nat)) (@ (@ tptp.member_set_nat X4) tptp.bot_bot_set_set_nat))) (= tptp.bot_bo1954855461789132331enat_o (lambda ((X4 tptp.extended_enat)) (@ (@ tptp.member_Extended_enat X4) tptp.bot_bo7653980558646680370d_enat))) (= tptp.bot_bot_real_o (lambda ((X4 tptp.real)) (@ (@ tptp.member_real X4) tptp.bot_bot_set_real))) (= tptp.bot_bot_nat_o (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) tptp.bot_bot_set_nat))) (= tptp.bot_bot_int_o (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) tptp.bot_bot_set_int))) (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.extended_enat) (B2 tptp.extended_enat) (P (-> tptp.extended_enat Bool))) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B2) (=> (@ P A) (=> (not (@ P B2)) (exists ((C2 tptp.extended_enat)) (and (@ (@ tptp.ord_le2932123472753598470d_enat A) C2) (@ (@ tptp.ord_le2932123472753598470d_enat C2) B2) (forall ((X2 tptp.extended_enat)) (=> (and (@ (@ tptp.ord_le2932123472753598470d_enat A) X2) (@ (@ tptp.ord_le72135733267957522d_enat X2) C2)) (@ P X2))) (forall ((D3 tptp.extended_enat)) (=> (forall ((X5 tptp.extended_enat)) (=> (and (@ (@ tptp.ord_le2932123472753598470d_enat A) X5) (@ (@ tptp.ord_le72135733267957522d_enat X5) D3)) (@ P X5))) (@ (@ tptp.ord_le2932123472753598470d_enat D3) C2))))))))) (forall ((A tptp.real) (B2 tptp.real) (P (-> tptp.real Bool))) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ P A) (=> (not (@ P B2)) (exists ((C2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A) C2) (@ (@ tptp.ord_less_eq_real C2) B2) (forall ((X2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A) X2) (@ (@ tptp.ord_less_real X2) C2)) (@ P X2))) (forall ((D3 tptp.real)) (=> (forall ((X5 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A) X5) (@ (@ tptp.ord_less_real X5) D3)) (@ P X5))) (@ (@ tptp.ord_less_eq_real D3) C2))))))))) (forall ((A tptp.nat) (B2 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat A) B2) (=> (@ P A) (=> (not (@ P B2)) (exists ((C2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A) C2) (@ (@ tptp.ord_less_eq_nat C2) B2) (forall ((X2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat A) X2) (@ (@ tptp.ord_less_nat X2) C2)) (@ P X2))) (forall ((D3 tptp.nat)) (=> (forall ((X5 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat A) X5) (@ (@ tptp.ord_less_nat X5) D3)) (@ P X5))) (@ (@ tptp.ord_less_eq_nat D3) C2))))))))) (forall ((A tptp.int) (B2 tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int A) B2) (=> (@ P A) (=> (not (@ P B2)) (exists ((C2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A) C2) (@ (@ tptp.ord_less_eq_int C2) B2) (forall ((X2 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int A) X2) (@ (@ tptp.ord_less_int X2) C2)) (@ P X2))) (forall ((D3 tptp.int)) (=> (forall ((X5 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int A) X5) (@ (@ tptp.ord_less_int X5) D3)) (@ P X5))) (@ (@ tptp.ord_less_eq_int D3) C2))))))))) (forall ((T tptp.extended_enat)) (exists ((Z tptp.extended_enat)) (forall ((X2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z) X2) (not (@ (@ tptp.ord_le2932123472753598470d_enat X2) T)))))) (forall ((T tptp.real)) (exists ((Z tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X2) (not (@ (@ tptp.ord_less_eq_real X2) T)))))) (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z) X2) (not (@ (@ tptp.ord_less_eq_nat X2) T)))))) (forall ((T tptp.int)) (exists ((Z tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int Z) X2) (not (@ (@ tptp.ord_less_eq_int X2) T)))))) (forall ((T tptp.extended_enat)) (exists ((Z tptp.extended_enat)) (forall ((X2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z) X2) (@ (@ tptp.ord_le2932123472753598470d_enat T) X2))))) (forall ((T tptp.real)) (exists ((Z tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X2) (@ (@ tptp.ord_less_eq_real T) X2))))) (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z) X2) (@ (@ tptp.ord_less_eq_nat T) X2))))) (forall ((T tptp.int)) (exists ((Z tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int Z) X2) (@ (@ tptp.ord_less_eq_int T) X2))))) (forall ((T tptp.extended_enat)) (exists ((Z tptp.extended_enat)) (forall ((X2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X2) Z) (@ (@ tptp.ord_le2932123472753598470d_enat X2) T))))) (forall ((T tptp.real)) (exists ((Z tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Z) (@ (@ tptp.ord_less_eq_real X2) T))))) (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Z) (@ (@ tptp.ord_less_eq_nat X2) T))))) (forall ((T tptp.int)) (exists ((Z tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Z) (@ (@ tptp.ord_less_eq_int X2) T))))) (forall ((T tptp.extended_enat)) (exists ((Z tptp.extended_enat)) (forall ((X2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X2) Z) (not (@ (@ tptp.ord_le2932123472753598470d_enat T) X2)))))) (forall ((T tptp.real)) (exists ((Z tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Z) (not (@ (@ tptp.ord_less_eq_real T) X2)))))) (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Z) (not (@ (@ tptp.ord_less_eq_nat T) X2)))))) (forall ((T tptp.int)) (exists ((Z tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Z) (not (@ (@ tptp.ord_less_eq_int T) X2)))))) (forall ((X tptp.extended_enat) (Xs tptp.list_Extended_enat)) (=> (not (@ (@ tptp.member_Extended_enat X) (@ tptp.set_Extended_enat2 Xs))) (= (@ (@ tptp.count_101369445342291426d_enat Xs) X) tptp.zero_zero_nat))) (forall ((X tptp.real) (Xs tptp.list_real)) (=> (not (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs))) (= (@ (@ tptp.count_list_real Xs) X) tptp.zero_zero_nat))) (forall ((X tptp.set_nat) (Xs tptp.list_set_nat)) (=> (not (@ (@ tptp.member_set_nat X) (@ tptp.set_set_nat2 Xs))) (= (@ (@ tptp.count_list_set_nat Xs) X) tptp.zero_zero_nat))) (forall ((X tptp.vEBT_VEBT) (Xs tptp.list_VEBT_VEBT)) (=> (not (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs))) (= (@ (@ tptp.count_list_VEBT_VEBT Xs) X) tptp.zero_zero_nat))) (forall ((X tptp.int) (Xs tptp.list_int)) (=> (not (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs))) (= (@ (@ tptp.count_list_int Xs) X) tptp.zero_zero_nat))) (forall ((X tptp.nat) (Xs tptp.list_nat)) (=> (not (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs))) (= (@ (@ tptp.count_list_nat Xs) X) tptp.zero_zero_nat))) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat tptp.mi) tptp.ma))) tptp.deg) tptp.treeList) tptp.summary)) tptp.xa) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat tptp.xa) (@ (@ tptp.ord_max_nat tptp.mi) tptp.ma)))) tptp.deg) _let_7) _let_261)) (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList2) Summary)) N2) (= Deg N2))) (forall ((Tree tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt Tree) (@ tptp.suc (@ tptp.suc N2))) (exists ((Info2 tptp.option4927543243414619207at_nat) (TreeList3 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (= Tree (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc (@ tptp.suc N2))) TreeList3) S3))))) (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) Deg) (=> (= Mi Ma) (and (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X_1))))) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_1))))))) (forall ((X tptp.set_Extended_enat)) (= (@ (@ tptp.ord_ma4205026669011143323d_enat X) tptp.bot_bo7653980558646680370d_enat) X)) (forall ((X tptp.set_real)) (= (@ (@ tptp.ord_max_set_real X) tptp.bot_bot_set_real) X)) (forall ((X tptp.set_nat)) (= (@ (@ tptp.ord_max_set_nat X) tptp.bot_bot_set_nat) X)) (forall ((X tptp.set_int)) (= (@ (@ tptp.ord_max_set_int X) tptp.bot_bot_set_int) X)) (forall ((X tptp.nat)) (= (@ (@ tptp.ord_max_nat X) tptp.bot_bot_nat) X)) (forall ((X tptp.set_Extended_enat)) (= (@ (@ tptp.ord_ma4205026669011143323d_enat tptp.bot_bo7653980558646680370d_enat) X) X)) (forall ((X tptp.set_real)) (= (@ (@ tptp.ord_max_set_real tptp.bot_bot_set_real) X) X)) (forall ((X tptp.set_nat)) (= (@ (@ tptp.ord_max_set_nat tptp.bot_bot_set_nat) X) X)) (forall ((X tptp.set_int)) (= (@ (@ tptp.ord_max_set_int tptp.bot_bot_set_int) X) X)) (forall ((X tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.bot_bot_nat) X) X)) (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_max_nat (@ tptp.suc M2)) (@ tptp.suc N2)) (@ tptp.suc (@ (@ tptp.ord_max_nat M2) N2)))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (= (@ (@ tptp.ord_max_nat A) B2) tptp.zero_zero_nat) (and (= A tptp.zero_zero_nat) (= B2 tptp.zero_zero_nat)))) (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) A) A)) (forall ((A tptp.nat) (B2 tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.ord_max_nat A) B2)) (and (= A tptp.zero_zero_nat) (= B2 tptp.zero_zero_nat)))) (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat A) tptp.zero_zero_nat) A)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) N2) N2)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_max_nat N2) tptp.zero_zero_nat) N2)) (= (@ tptp.nat_triangle tptp.zero_zero_nat) tptp.zero_zero_nat) (forall ((Mi tptp.nat) (Ma tptp.nat) (Va2 tptp.list_VEBT_VEBT) (Vb tptp.vEBT_VEBT) (X tptp.nat)) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) tptp.zero_zero_nat) Va2) Vb)) X) (or (= X Mi) (= X Ma)))) _let_258 _let_257 _let_256 _let_255 _let_254 (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y) X) (= (@ (@ tptp.ord_max_real X) Y) X))) (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X) (= (@ (@ tptp.ord_max_set_nat X) Y) X))) (forall ((Y tptp.set_int) (X tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y) X) (= (@ (@ tptp.ord_max_set_int X) Y) X))) (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= (@ (@ tptp.ord_max_nat X) Y) X))) (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= (@ (@ tptp.ord_max_int X) Y) X))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (= (@ (@ tptp.ord_max_real X) Y) Y))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (= (@ (@ tptp.ord_max_set_nat X) Y) Y))) (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X) Y) (= (@ (@ tptp.ord_max_set_int X) Y) Y))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (= (@ (@ tptp.ord_max_nat X) Y) Y))) (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (= (@ (@ tptp.ord_max_int X) Y) Y))) (forall ((X tptp.real) (Y tptp.real) (Z3 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.ord_max_real X) Y)) Z3) (@ (@ tptp.ord_max_real (@ (@ tptp.plus_plus_real X) Z3)) (@ (@ tptp.plus_plus_real Y) Z3)))) (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat X) Y)) Z3) (@ (@ tptp.ord_max_nat (@ (@ tptp.plus_plus_nat X) Z3)) (@ (@ tptp.plus_plus_nat Y) Z3)))) (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.ord_max_int X) Y)) Z3) (@ (@ tptp.ord_max_int (@ (@ tptp.plus_plus_int X) Z3)) (@ (@ tptp.plus_plus_int Y) Z3)))) (forall ((X tptp.real) (Y tptp.real) (Z3 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real X))) (= (@ _let_1 (@ (@ tptp.ord_max_real Y) Z3)) (@ (@ tptp.ord_max_real (@ _let_1 Y)) (@ _let_1 Z3))))) (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat X))) (= (@ _let_1 (@ (@ tptp.ord_max_nat Y) Z3)) (@ (@ tptp.ord_max_nat (@ _let_1 Y)) (@ _let_1 Z3))))) (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X))) (= (@ _let_1 (@ (@ tptp.ord_max_int Y) Z3)) (@ (@ tptp.ord_max_int (@ _let_1 Y)) (@ _let_1 Z3))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (Q3 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat M2) N2)) Q3) (@ (@ tptp.ord_max_nat (@ (@ tptp.plus_plus_nat M2) Q3)) (@ (@ tptp.plus_plus_nat N2) Q3)))) (forall ((M2 tptp.nat) (N2 tptp.nat) (Q3 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M2))) (= (@ _let_1 (@ (@ tptp.ord_max_nat N2) Q3)) (@ (@ tptp.ord_max_nat (@ _let_1 N2)) (@ _let_1 Q3))))) (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 ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Z) (not (@ (@ tptp.ord_less_nat T) X2)))))) (forall ((T tptp.extended_enat)) (exists ((Z tptp.extended_enat)) (forall ((X2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X2) Z) (not (@ (@ tptp.ord_le72135733267957522d_enat T) X2)))))) (forall ((T tptp.real)) (exists ((Z tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Z) (not (@ (@ tptp.ord_less_real T) X2)))))) (forall ((T tptp.int)) (exists ((Z tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Z) (not (@ (@ tptp.ord_less_int T) X2)))))) (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X2))) (=> (@ _let_1 Z) (@ _let_1 T)))))) (forall ((T tptp.extended_enat)) (exists ((Z tptp.extended_enat)) (forall ((X2 tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat X2))) (=> (@ _let_1 Z) (@ _let_1 T)))))) (forall ((T tptp.real)) (exists ((Z tptp.real)) (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X2))) (=> (@ _let_1 Z) (@ _let_1 T)))))) (forall ((T tptp.int)) (exists ((Z tptp.int)) (forall ((X2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X2))) (=> (@ _let_1 Z) (@ _let_1 T)))))) (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Z) (not (= X2 T)))))) (forall ((T tptp.extended_enat)) (exists ((Z tptp.extended_enat)) (forall ((X2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X2) Z) (not (= X2 T)))))) (forall ((T tptp.real)) (exists ((Z tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Z) (not (= X2 T)))))) (forall ((T tptp.int)) (exists ((Z tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Z) (not (= X2 T)))))) (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Z) (not (= X2 T)))))) (forall ((T tptp.extended_enat)) (exists ((Z tptp.extended_enat)) (forall ((X2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X2) Z) (not (= X2 T)))))) (forall ((T tptp.real)) (exists ((Z tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Z) (not (= X2 T)))))) (forall ((T tptp.int)) (exists ((Z tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Z) (not (= X2 T)))))) (forall ((P (-> tptp.nat Bool)) (P4 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q4 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z4) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z4) (= (@ Q X5) (@ Q4 X5))))) (exists ((Z tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Z) (= (or (@ P X2) (@ Q X2)) (or (@ P4 X2) (@ Q4 X2))))))))) (forall ((P (-> tptp.extended_enat Bool)) (P4 (-> tptp.extended_enat Bool)) (Q (-> tptp.extended_enat Bool)) (Q4 (-> tptp.extended_enat Bool))) (=> (exists ((Z4 tptp.extended_enat)) (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Z4) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z4 tptp.extended_enat)) (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Z4) (= (@ Q X5) (@ Q4 X5))))) (exists ((Z tptp.extended_enat)) (forall ((X2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X2) Z) (= (or (@ P X2) (@ Q X2)) (or (@ P4 X2) (@ Q4 X2))))))))) (forall ((P (-> tptp.real Bool)) (P4 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q4 (-> tptp.real Bool))) (=> (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z4) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z4) (= (@ Q X5) (@ Q4 X5))))) (exists ((Z tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Z) (= (or (@ P X2) (@ Q X2)) (or (@ P4 X2) (@ Q4 X2))))))))) (forall ((P (-> tptp.int Bool)) (P4 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q4 (-> tptp.int Bool))) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z4) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z4) (= (@ Q X5) (@ Q4 X5))))) (exists ((Z tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Z) (= (or (@ P X2) (@ Q X2)) (or (@ P4 X2) (@ Q4 X2))))))))) (forall ((P (-> tptp.nat Bool)) (P4 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q4 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z4) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z4) (= (@ Q X5) (@ Q4 X5))))) (exists ((Z tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Z) (= (and (@ P X2) (@ Q X2)) (and (@ P4 X2) (@ Q4 X2))))))))) (forall ((P (-> tptp.extended_enat Bool)) (P4 (-> tptp.extended_enat Bool)) (Q (-> tptp.extended_enat Bool)) (Q4 (-> tptp.extended_enat Bool))) (=> (exists ((Z4 tptp.extended_enat)) (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Z4) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z4 tptp.extended_enat)) (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Z4) (= (@ Q X5) (@ Q4 X5))))) (exists ((Z tptp.extended_enat)) (forall ((X2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X2) Z) (= (and (@ P X2) (@ Q X2)) (and (@ P4 X2) (@ Q4 X2))))))))) (forall ((P (-> tptp.real Bool)) (P4 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q4 (-> tptp.real Bool))) (=> (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z4) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z4) (= (@ Q X5) (@ Q4 X5))))) (exists ((Z tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Z) (= (and (@ P X2) (@ Q X2)) (and (@ P4 X2) (@ Q4 X2))))))))) (forall ((P (-> tptp.int Bool)) (P4 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q4 (-> tptp.int Bool))) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z4) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z4) (= (@ Q X5) (@ Q4 X5))))) (exists ((Z tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Z) (= (and (@ P X2) (@ Q X2)) (and (@ P4 X2) (@ Q4 X2))))))))) (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z) X2) (@ (@ tptp.ord_less_nat T) X2))))) (forall ((T tptp.extended_enat)) (exists ((Z tptp.extended_enat)) (forall ((X2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z) X2) (@ (@ tptp.ord_le72135733267957522d_enat T) X2))))) (forall ((T tptp.real)) (exists ((Z tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X2) (@ (@ tptp.ord_less_real T) X2))))) (forall ((T tptp.int)) (exists ((Z tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int Z) X2) (@ (@ tptp.ord_less_int T) X2))))) (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z) X2) (not (@ (@ tptp.ord_less_nat X2) T)))))) (forall ((T tptp.extended_enat)) (exists ((Z tptp.extended_enat)) (forall ((X2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z) X2) (not (@ (@ tptp.ord_le72135733267957522d_enat X2) T)))))) (forall ((T tptp.real)) (exists ((Z tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X2) (not (@ (@ tptp.ord_less_real X2) T)))))) (forall ((T tptp.int)) (exists ((Z tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int Z) X2) (not (@ (@ tptp.ord_less_int X2) T)))))) (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z) X2) (not (= X2 T)))))) (forall ((T tptp.extended_enat)) (exists ((Z tptp.extended_enat)) (forall ((X2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z) X2) (not (= X2 T)))))) (forall ((T tptp.real)) (exists ((Z tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X2) (not (= X2 T)))))) (forall ((T tptp.int)) (exists ((Z tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int Z) X2) (not (= X2 T)))))) (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z) X2) (not (= X2 T)))))) (forall ((T tptp.extended_enat)) (exists ((Z tptp.extended_enat)) (forall ((X2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z) X2) (not (= X2 T)))))) (forall ((T tptp.real)) (exists ((Z tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X2) (not (= X2 T)))))) (forall ((T tptp.int)) (exists ((Z tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int Z) X2) (not (= X2 T)))))) (forall ((P (-> tptp.nat Bool)) (P4 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q4 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X5) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X5) (= (@ Q X5) (@ Q4 X5))))) (exists ((Z tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z) X2) (= (or (@ P X2) (@ Q X2)) (or (@ P4 X2) (@ Q4 X2))))))))) (forall ((P (-> tptp.extended_enat Bool)) (P4 (-> tptp.extended_enat Bool)) (Q (-> tptp.extended_enat Bool)) (Q4 (-> tptp.extended_enat Bool))) (=> (exists ((Z4 tptp.extended_enat)) (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z4) X5) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z4 tptp.extended_enat)) (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z4) X5) (= (@ Q X5) (@ Q4 X5))))) (exists ((Z tptp.extended_enat)) (forall ((X2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z) X2) (= (or (@ P X2) (@ Q X2)) (or (@ P4 X2) (@ Q4 X2))))))))) (forall ((P (-> tptp.real Bool)) (P4 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q4 (-> tptp.real Bool))) (=> (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X5) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X5) (= (@ Q X5) (@ Q4 X5))))) (exists ((Z tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X2) (= (or (@ P X2) (@ Q X2)) (or (@ P4 X2) (@ Q4 X2))))))))) (forall ((P (-> tptp.int Bool)) (P4 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q4 (-> tptp.int Bool))) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X5) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X5) (= (@ Q X5) (@ Q4 X5))))) (exists ((Z tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int Z) X2) (= (or (@ P X2) (@ Q X2)) (or (@ P4 X2) (@ Q4 X2))))))))) (forall ((P (-> tptp.nat Bool)) (P4 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q4 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X5) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X5) (= (@ Q X5) (@ Q4 X5))))) (exists ((Z tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z) X2) (= (and (@ P X2) (@ Q X2)) (and (@ P4 X2) (@ Q4 X2))))))))) (forall ((P (-> tptp.extended_enat Bool)) (P4 (-> tptp.extended_enat Bool)) (Q (-> tptp.extended_enat Bool)) (Q4 (-> tptp.extended_enat Bool))) (=> (exists ((Z4 tptp.extended_enat)) (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z4) X5) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z4 tptp.extended_enat)) (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z4) X5) (= (@ Q X5) (@ Q4 X5))))) (exists ((Z tptp.extended_enat)) (forall ((X2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z) X2) (= (and (@ P X2) (@ Q X2)) (and (@ P4 X2) (@ Q4 X2))))))))) (forall ((P (-> tptp.real Bool)) (P4 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q4 (-> tptp.real Bool))) (=> (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X5) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X5) (= (@ Q X5) (@ Q4 X5))))) (exists ((Z tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X2) (= (and (@ P X2) (@ Q X2)) (and (@ P4 X2) (@ Q4 X2))))))))) (forall ((P (-> tptp.int Bool)) (P4 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q4 (-> tptp.int Bool))) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X5) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X5) (= (@ Q X5) (@ Q4 X5))))) (exists ((Z tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int Z) X2) (= (and (@ P X2) (@ Q X2)) (and (@ P4 X2) (@ Q4 X2))))))))) (forall ((A tptp.real)) (exists ((B4 tptp.real)) (or (@ (@ tptp.ord_less_real A) B4) (@ (@ tptp.ord_less_real B4) A)))) (forall ((Xs tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.count_list_VEBT_VEBT Xs) X)) (@ tptp.size_s6755466524823107622T_VEBT Xs))) (forall ((Xs tptp.list_int) (X tptp.int)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.count_list_int Xs) X)) (@ tptp.size_size_list_int Xs))) (forall ((Xs tptp.list_nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.count_list_nat Xs) X)) (@ tptp.size_size_list_nat Xs))) (forall ((V tptp.product_prod_nat_nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vb) Vc)) X))) (forall ((B2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B2) A) (= (@ (@ tptp.ord_max_nat A) B2) A))) (forall ((B2 tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B2) A) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B2) A))) (forall ((B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B2) A) (= (@ (@ tptp.ord_max_real A) B2) A))) (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B2) A) (= (@ (@ tptp.ord_max_int A) B2) A))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (= (@ (@ tptp.ord_max_nat A) B2) B2))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B2) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B2) B2))) (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (= (@ (@ tptp.ord_max_real A) B2) B2))) (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B2) (= (@ (@ tptp.ord_max_int A) B2) B2))) (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.ord_max_nat X) Y)) Z3) (and (@ (@ tptp.ord_less_nat X) Z3) (@ (@ tptp.ord_less_nat Y) Z3)))) (forall ((X tptp.extended_enat) (Y tptp.extended_enat) (Z3 tptp.extended_enat)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.ord_ma741700101516333627d_enat X) Y)) Z3) (and (@ (@ tptp.ord_le72135733267957522d_enat X) Z3) (@ (@ tptp.ord_le72135733267957522d_enat Y) Z3)))) (forall ((X tptp.real) (Y tptp.real) (Z3 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.ord_max_real X) Y)) Z3) (and (@ (@ tptp.ord_less_real X) Z3) (@ (@ tptp.ord_less_real Y) Z3)))) (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.ord_max_int X) Y)) Z3) (and (@ (@ tptp.ord_less_int X) Z3) (@ (@ tptp.ord_less_int Y) Z3)))) (forall ((B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B2) A) (= (@ (@ tptp.ord_max_real A) B2) A))) (forall ((B2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B2) A) (= (@ (@ tptp.ord_max_nat A) B2) A))) (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B2) A) (= (@ (@ tptp.ord_max_int A) B2) A))) (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (= (@ (@ tptp.ord_max_real A) B2) B2))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (= (@ (@ tptp.ord_max_nat A) B2) B2))) (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (= (@ (@ tptp.ord_max_int A) B2) B2))) (forall ((B2 tptp.real) (C tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.ord_max_real B2) C)) A) (and (@ (@ tptp.ord_less_eq_real B2) A) (@ (@ tptp.ord_less_eq_real C) A)))) (forall ((B2 tptp.nat) (C tptp.nat) (A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat B2) C)) A) (and (@ (@ tptp.ord_less_eq_nat B2) A) (@ (@ tptp.ord_less_eq_nat C) A)))) (forall ((B2 tptp.int) (C tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int B2) C)) A) (and (@ (@ tptp.ord_less_eq_int B2) A) (@ (@ tptp.ord_less_eq_int C) A)))) (forall ((V tptp.product_prod_nat_nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT) (X tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Uy) Uz)) X))) (forall ((Info tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) (@ tptp.suc tptp.zero_zero_nat)) Ts) S))) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X) _let_1))) (forall ((Uz tptp.product_prod_nat_nat) (Va2 tptp.nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz)) Va2) Vb) Vc)))) (forall ((C tptp.real) (B2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.ord_max_real A) B2))))) (forall ((C tptp.nat) (B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.ord_max_nat A) B2))))) (forall ((C tptp.int) (B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.ord_max_int A) B2))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_real A) B2))))) (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_nat A) B2))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_int A) B2))))) (= tptp.ord_less_eq_real (lambda ((A3 tptp.real) (B3 tptp.real)) (= (@ (@ tptp.ord_max_real A3) B3) B3))) (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (= (@ (@ tptp.ord_max_nat A3) B3) B3))) (= tptp.ord_less_eq_int (lambda ((A3 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.ord_max_int A3) B3) B3))) (= tptp.ord_less_eq_real (lambda ((B3 tptp.real) (A3 tptp.real)) (= (@ (@ tptp.ord_max_real A3) B3) A3))) (= tptp.ord_less_eq_nat (lambda ((B3 tptp.nat) (A3 tptp.nat)) (= (@ (@ tptp.ord_max_nat A3) B3) A3))) (= tptp.ord_less_eq_int (lambda ((B3 tptp.int) (A3 tptp.int)) (= (@ (@ tptp.ord_max_int A3) B3) A3))) (forall ((Z3 tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real Z3))) (= (@ _let_1 (@ (@ tptp.ord_max_real X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))) (forall ((Z3 tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat Z3))) (= (@ _let_1 (@ (@ tptp.ord_max_nat X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))) (forall ((Z3 tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int Z3))) (= (@ _let_1 (@ (@ tptp.ord_max_int X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))) (forall ((B2 tptp.real) (A tptp.real)) (@ (@ tptp.ord_less_eq_real B2) (@ (@ tptp.ord_max_real A) B2))) (forall ((B2 tptp.nat) (A tptp.nat)) (@ (@ tptp.ord_less_eq_nat B2) (@ (@ tptp.ord_max_nat A) B2))) (forall ((B2 tptp.int) (A tptp.int)) (@ (@ tptp.ord_less_eq_int B2) (@ (@ tptp.ord_max_int A) B2))) (forall ((A tptp.real) (B2 tptp.real)) (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.ord_max_real A) B2))) (forall ((A tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.ord_max_nat A) B2))) (forall ((A tptp.int) (B2 tptp.int)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.ord_max_int A) B2))) (= tptp.ord_less_eq_real (lambda ((B3 tptp.real) (A3 tptp.real)) (= A3 (@ (@ tptp.ord_max_real A3) B3)))) (= tptp.ord_less_eq_nat (lambda ((B3 tptp.nat) (A3 tptp.nat)) (= A3 (@ (@ tptp.ord_max_nat A3) B3)))) (= tptp.ord_less_eq_int (lambda ((B3 tptp.int) (A3 tptp.int)) (= A3 (@ (@ tptp.ord_max_int A3) B3)))) (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B2) A) (=> (@ (@ tptp.ord_less_eq_real C) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.ord_max_real B2) C)) A)))) (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B2) A) (=> (@ (@ tptp.ord_less_eq_nat C) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat B2) C)) A)))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B2) A) (=> (@ (@ tptp.ord_less_eq_int C) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int B2) C)) A)))) (forall ((B2 tptp.real) (C tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.ord_max_real B2) C)) A) (not (=> (@ (@ tptp.ord_less_eq_real B2) A) (not (@ (@ tptp.ord_less_eq_real C) A)))))) (forall ((B2 tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat B2) C)) A) (not (=> (@ (@ tptp.ord_less_eq_nat B2) A) (not (@ (@ tptp.ord_less_eq_nat C) A)))))) (forall ((B2 tptp.int) (C tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int B2) C)) A) (not (=> (@ (@ tptp.ord_less_eq_int B2) A) (not (@ (@ tptp.ord_less_eq_int C) A)))))) (forall ((A tptp.real) (B2 tptp.real)) (=> (= A (@ (@ tptp.ord_max_real A) B2)) (@ (@ tptp.ord_less_eq_real B2) A))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (= A (@ (@ tptp.ord_max_nat A) B2)) (@ (@ tptp.ord_less_eq_nat B2) A))) (forall ((A tptp.int) (B2 tptp.int)) (=> (= A (@ (@ tptp.ord_max_int A) B2)) (@ (@ tptp.ord_less_eq_int B2) A))) (forall ((B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B2) A) (= A (@ (@ tptp.ord_max_real A) B2)))) (forall ((B2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B2) A) (= A (@ (@ tptp.ord_max_nat A) B2)))) (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B2) A) (= A (@ (@ tptp.ord_max_int A) B2)))) (forall ((C tptp.real) (A tptp.real) (D tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real C) A) (=> (@ (@ tptp.ord_less_eq_real D) B2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.ord_max_real C) D)) (@ (@ tptp.ord_max_real A) B2))))) (forall ((C tptp.nat) (A tptp.nat) (D tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) A) (=> (@ (@ tptp.ord_less_eq_nat D) B2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat C) D)) (@ (@ tptp.ord_max_nat A) B2))))) (forall ((C tptp.int) (A tptp.int) (D tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C) A) (=> (@ (@ tptp.ord_less_eq_int D) B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int C) D)) (@ (@ tptp.ord_max_int A) B2))))) (forall ((C tptp.nat) (B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.ord_max_nat A) B2))))) (forall ((C tptp.extended_enat) (B2 tptp.extended_enat) (A tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat A) B2))))) (forall ((C tptp.real) (B2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.ord_max_real A) B2))))) (forall ((C tptp.int) (B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.ord_max_int A) B2))))) (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_nat A) B2))))) (forall ((C tptp.extended_enat) (A tptp.extended_enat) (B2 tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat A) B2))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_real A) B2))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_int A) B2))))) (= tptp.ord_less_nat (lambda ((B3 tptp.nat) (A3 tptp.nat)) (and (= A3 (@ (@ tptp.ord_max_nat A3) B3)) (not (= A3 B3))))) (= tptp.ord_le72135733267957522d_enat (lambda ((B3 tptp.extended_enat) (A3 tptp.extended_enat)) (and (= A3 (@ (@ tptp.ord_ma741700101516333627d_enat A3) B3)) (not (= A3 B3))))) (= tptp.ord_less_real (lambda ((B3 tptp.real) (A3 tptp.real)) (and (= A3 (@ (@ tptp.ord_max_real A3) B3)) (not (= A3 B3))))) (= tptp.ord_less_int (lambda ((B3 tptp.int) (A3 tptp.int)) (and (= A3 (@ (@ tptp.ord_max_int A3) B3)) (not (= A3 B3))))) (forall ((B2 tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.ord_max_nat B2) C)) A) (not (=> (@ (@ tptp.ord_less_nat B2) A) (not (@ (@ tptp.ord_less_nat C) A)))))) (forall ((B2 tptp.extended_enat) (C tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.ord_ma741700101516333627d_enat B2) C)) A) (not (=> (@ (@ tptp.ord_le72135733267957522d_enat B2) A) (not (@ (@ tptp.ord_le72135733267957522d_enat C) A)))))) (forall ((B2 tptp.real) (C tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.ord_max_real B2) C)) A) (not (=> (@ (@ tptp.ord_less_real B2) A) (not (@ (@ tptp.ord_less_real C) A)))))) (forall ((B2 tptp.int) (C tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.ord_max_int B2) C)) A) (not (=> (@ (@ tptp.ord_less_int B2) A) (not (@ (@ tptp.ord_less_int C) A)))))) (forall ((Z3 tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat Z3))) (= (@ _let_1 (@ (@ tptp.ord_max_nat X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))) (forall ((Z3 tptp.extended_enat) (X tptp.extended_enat) (Y tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat Z3))) (= (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))) (forall ((Z3 tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real Z3))) (= (@ _let_1 (@ (@ tptp.ord_max_real X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))) (forall ((Z3 tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_int Z3))) (= (@ _let_1 (@ (@ tptp.ord_max_int X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))) (forall ((Info tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) tptp.zero_zero_nat) Ts) S))) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X) _let_1))) (forall ((X22 tptp.product_prod_nat_nat)) (= (@ tptp.size_s170228958280169651at_nat (@ tptp.some_P7363390416028606310at_nat X22)) (@ tptp.suc tptp.zero_zero_nat))) (forall ((X22 tptp.num)) (= (@ tptp.size_size_option_num (@ tptp.some_num X22)) (@ tptp.suc tptp.zero_zero_nat))) (forall ((M2 tptp.nat) (Xs tptp.list_VEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.nth_Pr744662078594809490T_VEBT (@ (@ tptp.enumerate_VEBT_VEBT N2) Xs)) M2) (@ (@ tptp.produc599794634098209291T_VEBT (@ (@ tptp.plus_plus_nat N2) M2)) (@ (@ tptp.nth_VEBT_VEBT Xs) M2))))) (forall ((M2 tptp.nat) (Xs tptp.list_int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_Pr3440142176431000676at_int (@ (@ tptp.enumerate_int N2) Xs)) M2) (@ (@ tptp.product_Pair_nat_int (@ (@ tptp.plus_plus_nat N2) M2)) (@ (@ tptp.nth_int Xs) M2))))) (forall ((M2 tptp.nat) (Xs tptp.list_nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_Pr7617993195940197384at_nat (@ (@ tptp.enumerate_nat N2) Xs)) M2) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat N2) M2)) (@ (@ tptp.nth_nat Xs) M2))))) (forall ((X tptp.product_prod_nat_nat) (P (-> tptp.product_prod_nat_nat Bool)) (Xs tptp.list_P6011104703257516679at_nat)) (= (= (@ tptp.some_P7363390416028606310at_nat X) (@ (@ tptp.find_P8199882355184865565at_nat P) Xs)) (exists ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs) I3))) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s5460976970255530739at_nat Xs)) (@ P _let_1) (= X _let_1) (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J2) I3) (not (@ P (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs) J2)))))))))) (forall ((X tptp.num) (P (-> tptp.num Bool)) (Xs tptp.list_num)) (= (= (@ tptp.some_num X) (@ (@ tptp.find_num P) Xs)) (exists ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_num Xs) I3))) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_num Xs)) (@ P _let_1) (= X _let_1) (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J2) I3) (not (@ P (@ (@ tptp.nth_num Xs) J2)))))))))) (forall ((X tptp.vEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool)) (Xs tptp.list_VEBT_VEBT)) (= (= (@ tptp.some_VEBT_VEBT X) (@ (@ tptp.find_VEBT_VEBT P) Xs)) (exists ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_VEBT_VEBT Xs) I3))) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ P _let_1) (= X _let_1) (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J2) I3) (not (@ P (@ (@ tptp.nth_VEBT_VEBT Xs) J2)))))))))) (forall ((X tptp.int) (P (-> tptp.int Bool)) (Xs tptp.list_int)) (= (= (@ tptp.some_int X) (@ (@ tptp.find_int P) Xs)) (exists ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_int Xs) I3))) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_int Xs)) (@ P _let_1) (= X _let_1) (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J2) I3) (not (@ P (@ (@ tptp.nth_int Xs) J2)))))))))) (forall ((X tptp.nat) (P (-> tptp.nat Bool)) (Xs tptp.list_nat)) (= (= (@ tptp.some_nat X) (@ (@ tptp.find_nat P) Xs)) (exists ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_nat Xs) I3))) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs)) (@ P _let_1) (= X _let_1) (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J2) I3) (not (@ P (@ (@ tptp.nth_nat Xs) J2)))))))))) (forall ((P (-> tptp.product_prod_nat_nat Bool)) (Xs tptp.list_P6011104703257516679at_nat) (X tptp.product_prod_nat_nat)) (= (= (@ (@ tptp.find_P8199882355184865565at_nat P) Xs) (@ tptp.some_P7363390416028606310at_nat X)) (exists ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs) I3))) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s5460976970255530739at_nat Xs)) (@ P _let_1) (= X _let_1) (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J2) I3) (not (@ P (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs) J2)))))))))) (forall ((P (-> tptp.num Bool)) (Xs tptp.list_num) (X tptp.num)) (= (= (@ (@ tptp.find_num P) Xs) (@ tptp.some_num X)) (exists ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_num Xs) I3))) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_num Xs)) (@ P _let_1) (= X _let_1) (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J2) I3) (not (@ P (@ (@ tptp.nth_num Xs) J2)))))))))) (forall ((P (-> tptp.vEBT_VEBT Bool)) (Xs tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (= (= (@ (@ tptp.find_VEBT_VEBT P) Xs) (@ tptp.some_VEBT_VEBT X)) (exists ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_VEBT_VEBT Xs) I3))) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ P _let_1) (= X _let_1) (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J2) I3) (not (@ P (@ (@ tptp.nth_VEBT_VEBT Xs) J2)))))))))) (forall ((P (-> tptp.int Bool)) (Xs tptp.list_int) (X tptp.int)) (= (= (@ (@ tptp.find_int P) Xs) (@ tptp.some_int X)) (exists ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_int Xs) I3))) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_int Xs)) (@ P _let_1) (= X _let_1) (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J2) I3) (not (@ P (@ (@ tptp.nth_int Xs) J2)))))))))) (forall ((P (-> tptp.nat Bool)) (Xs tptp.list_nat) (X tptp.nat)) (= (= (@ (@ tptp.find_nat P) Xs) (@ tptp.some_nat X)) (exists ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_nat Xs) I3))) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs)) (@ P _let_1) (= X _let_1) (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J2) I3) (not (@ P (@ (@ tptp.nth_nat Xs) J2)))))))))) (=> (not _let_253) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high tptp.ma) tptp.na) I5) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I5)) (@ (@ tptp.vEBT_VEBT_low tptp.ma) tptp.na))) (forall ((Y6 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high Y6) tptp.na) I5) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I5)) (@ (@ tptp.vEBT_VEBT_low Y6) tptp.na))) (and (@ (@ tptp.ord_less_nat tptp.mi) Y6) (@ (@ tptp.ord_less_eq_nat Y6) tptp.ma)))))))) (forall ((Xs tptp.list_P6011104703257516679at_nat) (Ys tptp.list_P6011104703257516679at_nat) (R2 tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.member6693912407220327184at_nat (@ (@ tptp.produc5943733680697469783at_nat Xs) Ys)) (@ tptp.listre4828114922151135584at_nat R2)) (exists ((Y5 tptp.product_prod_nat_nat) (N tptp.nat)) (and (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs) N)) Y5)) R2) (@ (@ tptp.ord_less_nat N) (@ tptp.size_s5460976970255530739at_nat Xs)) (= Ys (@ (@ (@ tptp.list_u6180841689913720943at_nat Xs) N) Y5)))))) (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT) (R2 tptp.set_Pr6192946355708809607T_VEBT)) (= (@ (@ tptp.member4439316823752958928T_VEBT (@ (@ tptp.produc3897820843166775703T_VEBT Xs) Ys)) (@ tptp.listrel1_VEBT_VEBT R2)) (exists ((Y5 tptp.vEBT_VEBT) (N tptp.nat)) (and (@ (@ tptp.member568628332442017744T_VEBT (@ (@ tptp.produc537772716801021591T_VEBT (@ (@ tptp.nth_VEBT_VEBT Xs) N)) Y5)) R2) (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= Ys (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) N) Y5)))))) (forall ((Xs tptp.list_int) (Ys tptp.list_int) (R2 tptp.set_Pr958786334691620121nt_int)) (= (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int Xs) Ys)) (@ tptp.listrel1_int R2)) (exists ((Y5 tptp.int) (N tptp.nat)) (and (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int (@ (@ tptp.nth_int Xs) N)) Y5)) R2) (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs)) (= Ys (@ (@ (@ tptp.list_update_int Xs) N) Y5)))))) (forall ((Xs tptp.list_nat) (Ys tptp.list_nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat Xs) Ys)) (@ tptp.listrel1_nat R2)) (exists ((Y5 tptp.nat) (N tptp.nat)) (and (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.nth_nat Xs) N)) Y5)) R2) (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (= Ys (@ (@ (@ tptp.list_update_nat Xs) N) Y5)))))) (forall ((X (-> tptp.product_prod_nat_nat tptp.nat)) (X22 tptp.product_prod_nat_nat)) (= (@ (@ tptp.size_o8335143837870341156at_nat X) (@ tptp.some_P7363390416028606310at_nat X22)) (@ (@ tptp.plus_plus_nat (@ X X22)) (@ tptp.suc tptp.zero_zero_nat)))) (forall ((X (-> tptp.num tptp.nat)) (X22 tptp.num)) (= (@ (@ tptp.size_option_num X) (@ tptp.some_num X22)) (@ (@ tptp.plus_plus_nat (@ X X22)) (@ tptp.suc tptp.zero_zero_nat)))) (forall ((I tptp.nat) (N2 tptp.nat) (P (-> tptp.nat Bool)) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) N2) (=> (@ P X) (@ P (@ (@ tptp.nth_nat (@ (@ tptp.replicate_nat N2) X)) I))))) (forall ((I tptp.nat) (N2 tptp.nat) (P (-> tptp.int Bool)) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat I) N2) (=> (@ P X) (@ P (@ (@ tptp.nth_int (@ (@ tptp.replicate_int N2) X)) I))))) (forall ((I tptp.nat) (N2 tptp.nat) (P (-> tptp.vEBT_VEBT Bool)) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I) N2) (=> (@ P X) (@ P (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.replicate_VEBT_VEBT N2) X)) I))))) (forall ((V tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc V)))) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat X) X))) _let_1) TreeList2) Summary)))) _let_252 _let_251 _let_250 (= (@ tptp.size_s6755466524823107622T_VEBT tptp.treeList) _let_245) _let_247 (@ _let_249 _let_246) (@ (@ tptp.ord_less_nat tptp.i) _let_245) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 tptp.treeList)) (and (@ (@ tptp.vEBT_invar_vebt X2) tptp.na) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.ord_less_nat Xa) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.na)) (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_vebt_insert X2) Xa)) tptp.na)))))) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (= (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I5)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions tptp.summary) I5)))) (forall ((Ma tptp.nat) (N2 tptp.nat) (M2 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) M2))) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high Ma) N2)) (@ _let_1 M2))))) (forall ((Tree tptp.vEBT_VEBT) (X tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member Tree) X) (=> (@ (@ tptp.vEBT_invar_vebt Tree) N2) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))) (forall ((M2 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat M2)) (@ tptp.numera1916890842035813515d_enat N2)) (@ (@ tptp.ord_less_eq_num M2) N2))) (forall ((M2 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M2)) (@ tptp.numeral_numeral_real N2)) (@ (@ tptp.ord_less_eq_num M2) N2))) (forall ((M2 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat M2)) (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.ord_less_eq_num M2) N2))) (forall ((M2 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M2)) (@ tptp.numeral_numeral_int N2)) (@ (@ tptp.ord_less_eq_num M2) N2))) (forall ((M2 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat M2)) (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.ord_less_num M2) N2))) (forall ((M2 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat M2)) (@ tptp.numera1916890842035813515d_enat N2)) (@ (@ tptp.ord_less_num M2) N2))) (forall ((M2 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M2)) (@ tptp.numeral_numeral_int N2)) (@ (@ tptp.ord_less_num M2) N2))) (forall ((M2 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M2)) (@ tptp.numeral_numeral_real N2)) (@ (@ tptp.ord_less_num M2) N2))) (forall ((M2 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat M2)) (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M2) N2)))) (forall ((M2 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.numera1916890842035813515d_enat M2)) (@ tptp.numera1916890842035813515d_enat N2)) (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.plus_plus_num M2) N2)))) (forall ((M2 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int M2)) (@ tptp.numeral_numeral_int N2)) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M2) N2)))) (forall ((M2 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real M2)) (@ tptp.numeral_numeral_real N2)) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M2) N2)))) (forall ((V tptp.num) (W2 tptp.num) (Z3 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat V)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat W2)) Z3)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num V) W2))) Z3))) (forall ((V tptp.num) (W2 tptp.num) (Z3 tptp.extended_enat)) (= (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.numera1916890842035813515d_enat V)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.numera1916890842035813515d_enat W2)) Z3)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.plus_plus_num V) W2))) Z3))) (forall ((V tptp.num) (W2 tptp.num) (Z3 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int V)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int W2)) Z3)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num V) W2))) Z3))) (forall ((V tptp.num) (W2 tptp.num) (Z3 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real V)) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real W2)) Z3)) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num V) W2))) Z3))) (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary))) (=> (or (= X Mi) (= X Ma)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X) _let_1))))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.vEBT_vebt_insert T) X)) X)))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (@ (@ tptp.ord_less_nat X) _let_1) (=> (@ (@ tptp.ord_less_nat Y) _let_1) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions T) X) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.vEBT_vebt_insert T) Y)) X))))))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (@ (@ tptp.ord_less_nat X) _let_1) (=> (@ (@ tptp.ord_less_nat Y) _let_1) (=> (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.vEBT_vebt_insert T) X)) Y) (or (@ (@ tptp.vEBT_vebt_member T) Y) (= X Y)))))))) (forall ((M2 tptp.nat) (X tptp.vEBT_VEBT) (N2 tptp.nat) (Y tptp.vEBT_VEBT)) (= (= (@ (@ tptp.replicate_VEBT_VEBT M2) X) (@ (@ tptp.replicate_VEBT_VEBT N2) Y)) (and (= M2 N2) (=> (not (= M2 tptp.zero_zero_nat)) (= X Y))))) (forall ((N2 tptp.nat) (X tptp.vEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ tptp.replicate_VEBT_VEBT N2) X)) N2)) (forall ((N2 tptp.nat) (X tptp.int)) (= (@ tptp.size_size_list_int (@ (@ tptp.replicate_int N2) X)) N2)) (forall ((N2 tptp.nat) (X tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.replicate_nat N2) X)) N2)) (forall ((N2 tptp.nat) (Xs tptp.list_VEBT_VEBT)) (= (@ tptp.size_s4762443039079500285T_VEBT (@ (@ tptp.enumerate_VEBT_VEBT N2) Xs)) (@ tptp.size_s6755466524823107622T_VEBT Xs))) (forall ((N2 tptp.nat) (Xs tptp.list_int)) (= (@ tptp.size_s2970893825323803983at_int (@ (@ tptp.enumerate_int N2) Xs)) (@ tptp.size_size_list_int Xs))) (forall ((N2 tptp.nat) (Xs tptp.list_nat)) (= (@ tptp.size_s5460976970255530739at_nat (@ (@ tptp.enumerate_nat N2) Xs)) (@ tptp.size_size_list_nat Xs))) (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 ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_vebt_insert tptp.summary) X)) tptp.m))) (forall ((N2 tptp.num)) (= (@ tptp.suc (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num N2) tptp.one)))) (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat U))) (let ((_let_2 (@ tptp.numera1916890842035813515d_enat V))) (let ((_let_3 (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_le2932123472753598470d_enat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real U))) (let ((_let_2 (@ tptp.numeral_numeral_real V))) (let ((_let_3 (@ (@ tptp.ord_max_real _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_real _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat U))) (let ((_let_2 (@ tptp.numeral_numeral_nat V))) (let ((_let_3 (@ (@ tptp.ord_max_nat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_nat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int U))) (let ((_let_2 (@ tptp.numeral_numeral_int V))) (let ((_let_3 (@ (@ tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X))) (= (@ (@ tptp.ord_max_nat _let_1) tptp.zero_zero_nat) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) tptp.zero_z5237406670263579293d_enat) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X))) (= (@ (@ tptp.ord_max_int _let_1) tptp.zero_zero_int) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X))) (= (@ (@ tptp.ord_max_real _let_1) tptp.zero_zero_real) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X))) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) _let_1) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) _let_1) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X))) (= (@ (@ tptp.ord_max_int tptp.zero_zero_int) _let_1) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X))) (= (@ (@ tptp.ord_max_real tptp.zero_zero_real) _let_1) _let_1))) (and _let_248 _let_247) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 tptp.treeList)) (=> (@ (@ tptp.vEBT_invar_vebt X) tptp.na) (=> (@ (@ tptp.ord_less_nat Xa2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.na)) (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_vebt_insert X) Xa2)) tptp.na))))) (forall ((X tptp.extended_enat) (N2 tptp.nat) (Y tptp.extended_enat)) (= (@ (@ tptp.member_Extended_enat X) (@ tptp.set_Extended_enat2 (@ (@ tptp.replic7216382294607269926d_enat N2) Y))) (and (= X Y) (not (= N2 tptp.zero_zero_nat))))) (forall ((X tptp.real) (N2 tptp.nat) (Y tptp.real)) (= (@ (@ tptp.member_real X) (@ tptp.set_real2 (@ (@ tptp.replicate_real N2) Y))) (and (= X Y) (not (= N2 tptp.zero_zero_nat))))) (forall ((X tptp.set_nat) (N2 tptp.nat) (Y tptp.set_nat)) (= (@ (@ tptp.member_set_nat X) (@ tptp.set_set_nat2 (@ (@ tptp.replicate_set_nat N2) Y))) (and (= X Y) (not (= N2 tptp.zero_zero_nat))))) (forall ((X tptp.int) (N2 tptp.nat) (Y tptp.int)) (= (@ (@ tptp.member_int X) (@ tptp.set_int2 (@ (@ tptp.replicate_int N2) Y))) (and (= X Y) (not (= N2 tptp.zero_zero_nat))))) (forall ((X tptp.nat) (N2 tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.member_nat X) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N2) Y))) (and (= X Y) (not (= N2 tptp.zero_zero_nat))))) (forall ((X tptp.vEBT_VEBT) (N2 tptp.nat) (Y tptp.vEBT_VEBT)) (= (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N2) Y))) (and (= X Y) (not (= N2 tptp.zero_zero_nat))))) (forall ((N2 tptp.nat) (A tptp.int) (P (-> tptp.int Bool))) (= (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) (@ tptp.set_int2 (@ (@ tptp.replicate_int N2) A))) (@ P X4))) (and (@ P A) (not (= N2 tptp.zero_zero_nat))))) (forall ((N2 tptp.nat) (A tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N2) A))) (@ P X4))) (and (@ P A) (not (= N2 tptp.zero_zero_nat))))) (forall ((N2 tptp.nat) (A tptp.vEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (exists ((X4 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N2) A))) (@ P X4))) (and (@ P A) (not (= N2 tptp.zero_zero_nat))))) (forall ((N2 tptp.nat) (A tptp.int) (P (-> tptp.int Bool))) (= (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) (@ tptp.set_int2 (@ (@ tptp.replicate_int N2) A))) (@ P X4))) (or (@ P A) (= N2 tptp.zero_zero_nat)))) (forall ((N2 tptp.nat) (A tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N2) A))) (@ P X4))) (or (@ P A) (= N2 tptp.zero_zero_nat)))) (forall ((N2 tptp.nat) (A tptp.vEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N2) A))) (@ P X4))) (or (@ P A) (= N2 tptp.zero_zero_nat)))) (forall ((I tptp.nat) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) N2) (= (@ (@ tptp.nth_nat (@ (@ tptp.replicate_nat N2) X)) I) X))) (forall ((I tptp.nat) (N2 tptp.nat) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat I) N2) (= (@ (@ tptp.nth_int (@ (@ tptp.replicate_int N2) X)) I) X))) (forall ((I tptp.nat) (N2 tptp.nat) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I) N2) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.replicate_VEBT_VEBT N2) X)) I) X))) (and (@ (@ tptp.ord_less_nat _let_2) _let_245) (@ (@ tptp.ord_less_nat _let_1) (@ _let_244 tptp.na))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (@ tptp.suc (@ tptp.suc N2)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc N2)))) (forall ((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.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.numeral_numeral_int N2))) (= (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_int _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 ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT) (R2 tptp.set_Pr6192946355708809607T_VEBT)) (=> (@ (@ tptp.member4439316823752958928T_VEBT (@ (@ tptp.produc3897820843166775703T_VEBT Xs) Ys)) (@ tptp.listrel1_VEBT_VEBT R2)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_s6755466524823107622T_VEBT Ys)))) (forall ((Xs tptp.list_int) (Ys tptp.list_int) (R2 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member6698963635872716290st_int (@ (@ tptp.produc364263696895485585st_int Xs) Ys)) (@ tptp.listrel1_int R2)) (= (@ tptp.size_size_list_int Xs) (@ tptp.size_size_list_int Ys)))) (forall ((Xs tptp.list_nat) (Ys tptp.list_nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member7340969449405702474st_nat (@ (@ tptp.produc2694037385005941721st_nat Xs) Ys)) (@ tptp.listrel1_nat R2)) (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys)))) (= _let_194 _let_81) (forall ((P (-> tptp.extended_enat Bool)) (Xs tptp.list_Extended_enat)) (= (= (@ (@ tptp.find_Extended_enat P) Xs) tptp.none_Extended_enat) (not (exists ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) (@ tptp.set_Extended_enat2 Xs)) (@ P X4)))))) (forall ((P (-> tptp.real Bool)) (Xs tptp.list_real)) (= (= (@ (@ tptp.find_real P) Xs) tptp.none_real) (not (exists ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) (@ tptp.set_real2 Xs)) (@ P X4)))))) (forall ((P (-> tptp.set_nat Bool)) (Xs tptp.list_set_nat)) (= (= (@ (@ tptp.find_set_nat P) Xs) tptp.none_set_nat) (not (exists ((X4 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X4) (@ tptp.set_set_nat2 Xs)) (@ P X4)))))) (forall ((P (-> tptp.vEBT_VEBT Bool)) (Xs tptp.list_VEBT_VEBT)) (= (= (@ (@ tptp.find_VEBT_VEBT P) Xs) tptp.none_VEBT_VEBT) (not (exists ((X4 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Xs)) (@ P X4)))))) (forall ((P (-> tptp.int Bool)) (Xs tptp.list_int)) (= (= (@ (@ tptp.find_int P) Xs) tptp.none_int) (not (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) (@ tptp.set_int2 Xs)) (@ P X4)))))) (forall ((P (-> tptp.nat Bool)) (Xs tptp.list_nat)) (= (= (@ (@ tptp.find_nat P) Xs) tptp.none_nat) (not (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) (@ tptp.set_nat2 Xs)) (@ P X4)))))) (forall ((P (-> tptp.product_prod_nat_nat Bool)) (Xs tptp.list_P6011104703257516679at_nat)) (= (= (@ (@ tptp.find_P8199882355184865565at_nat P) Xs) tptp.none_P5556105721700978146at_nat) (not (exists ((X4 tptp.product_prod_nat_nat)) (and (@ (@ tptp.member8440522571783428010at_nat X4) (@ tptp.set_Pr5648618587558075414at_nat Xs)) (@ P X4)))))) (forall ((P (-> tptp.num Bool)) (Xs tptp.list_num)) (= (= (@ (@ tptp.find_num P) Xs) tptp.none_num) (not (exists ((X4 tptp.num)) (and (@ (@ tptp.member_num X4) (@ tptp.set_num2 Xs)) (@ P X4)))))) (forall ((P (-> tptp.extended_enat Bool)) (Xs tptp.list_Extended_enat)) (= (= tptp.none_Extended_enat (@ (@ tptp.find_Extended_enat P) Xs)) (not (exists ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) (@ tptp.set_Extended_enat2 Xs)) (@ P X4)))))) (forall ((P (-> tptp.real Bool)) (Xs tptp.list_real)) (= (= tptp.none_real (@ (@ tptp.find_real P) Xs)) (not (exists ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) (@ tptp.set_real2 Xs)) (@ P X4)))))) (forall ((P (-> tptp.set_nat Bool)) (Xs tptp.list_set_nat)) (= (= tptp.none_set_nat (@ (@ tptp.find_set_nat P) Xs)) (not (exists ((X4 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X4) (@ tptp.set_set_nat2 Xs)) (@ P X4)))))) (forall ((P (-> tptp.vEBT_VEBT Bool)) (Xs tptp.list_VEBT_VEBT)) (= (= tptp.none_VEBT_VEBT (@ (@ tptp.find_VEBT_VEBT P) Xs)) (not (exists ((X4 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Xs)) (@ P X4)))))) (forall ((P (-> tptp.int Bool)) (Xs tptp.list_int)) (= (= tptp.none_int (@ (@ tptp.find_int P) Xs)) (not (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) (@ tptp.set_int2 Xs)) (@ P X4)))))) (forall ((P (-> tptp.nat Bool)) (Xs tptp.list_nat)) (= (= tptp.none_nat (@ (@ tptp.find_nat P) Xs)) (not (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) (@ tptp.set_nat2 Xs)) (@ P X4)))))) (forall ((P (-> tptp.product_prod_nat_nat Bool)) (Xs tptp.list_P6011104703257516679at_nat)) (= (= tptp.none_P5556105721700978146at_nat (@ (@ tptp.find_P8199882355184865565at_nat P) Xs)) (not (exists ((X4 tptp.product_prod_nat_nat)) (and (@ (@ tptp.member8440522571783428010at_nat X4) (@ tptp.set_Pr5648618587558075414at_nat Xs)) (@ P X4)))))) (forall ((P (-> tptp.num Bool)) (Xs tptp.list_num)) (= (= tptp.none_num (@ (@ tptp.find_num P) Xs)) (not (exists ((X4 tptp.num)) (and (@ (@ tptp.member_num X4) (@ tptp.set_num2 Xs)) (@ P X4)))))) (forall ((X tptp.nat) (N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat X) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M2))) (=> (@ _let_2 N2) (=> (@ _let_2 M2) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high X) N2)) (@ _let_1 M2)))))))) (forall ((X (-> tptp.product_prod_nat_nat tptp.nat))) (= (@ (@ tptp.size_o8335143837870341156at_nat X) tptp.none_P5556105721700978146at_nat) (@ tptp.suc tptp.zero_zero_nat))) (forall ((X (-> tptp.num tptp.nat))) (= (@ (@ tptp.size_option_num X) tptp.none_num) (@ tptp.suc tptp.zero_zero_nat))) (forall ((X tptp.nat) (N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat X) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M2))) (=> (@ _let_2 N2) (=> (@ _let_2 M2) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_low X) N2)) (@ _let_1 N2)))))))) (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 ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary tptp.vEBT_VEBT) (M2 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) M2) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)) (=> (= M2 N2) (=> (= Deg (@ (@ tptp.plus_plus_nat N2) M2)) (=> (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.numeral_numeral_nat tptp.one) _let_80) (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)) (not (= tptp.zero_zero_complex (@ tptp.numera6690914467698888265omplex N2)))) (forall ((N2 tptp.num)) (not (= tptp.zero_zero_nat (@ tptp.numeral_numeral_nat N2)))) (forall ((N2 tptp.num)) (not (= tptp.zero_z5237406670263579293d_enat (@ tptp.numera1916890842035813515d_enat N2)))) (forall ((N2 tptp.num)) (not (= tptp.zero_zero_int (@ tptp.numeral_numeral_int N2)))) (forall ((N2 tptp.num)) (not (= tptp.zero_zero_real (@ tptp.numeral_numeral_real N2)))) (forall ((X tptp.produc4471711990508489141at_nat)) (not (forall ((F2 (-> tptp.nat tptp.nat tptp.nat)) (A4 tptp.nat) (B4 tptp.nat) (Acc tptp.nat)) (not (= X (@ (@ tptp.produc3209952032786966637at_nat F2) (@ (@ tptp.produc487386426758144856at_nat A4) (@ (@ tptp.product_Pair_nat_nat B4) Acc)))))))) (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary tptp.vEBT_VEBT) (M2 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) M2) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)) (=> (= M2 (@ tptp.suc N2)) (=> (= Deg (@ (@ tptp.plus_plus_nat N2) M2)) (=> (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))))))))) _let_243 (= (@ tptp.size_s170228958280169651at_nat tptp.none_P5556105721700978146at_nat) _let_80) (= (@ tptp.size_size_option_num tptp.none_num) _let_80) (forall ((Xs tptp.list_Extended_enat) (Ys tptp.list_Extended_enat) (P (-> tptp.extended_enat Bool)) (Q (-> tptp.extended_enat Bool))) (=> (= Xs Ys) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ tptp.set_Extended_enat2 Ys)) (= (@ P X5) (@ Q X5)))) (= (@ (@ tptp.find_Extended_enat P) Xs) (@ (@ tptp.find_Extended_enat Q) Ys))))) (forall ((Xs tptp.list_real) (Ys tptp.list_real) (P (-> tptp.real Bool)) (Q (-> tptp.real Bool))) (=> (= Xs Ys) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ tptp.set_real2 Ys)) (= (@ P X5) (@ Q X5)))) (= (@ (@ tptp.find_real P) Xs) (@ (@ tptp.find_real Q) Ys))))) (forall ((Xs tptp.list_set_nat) (Ys tptp.list_set_nat) (P (-> tptp.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (=> (= Xs Ys) (=> (forall ((X5 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X5) (@ tptp.set_set_nat2 Ys)) (= (@ P X5) (@ Q X5)))) (= (@ (@ tptp.find_set_nat P) Xs) (@ (@ tptp.find_set_nat Q) Ys))))) (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool)) (Q (-> tptp.vEBT_VEBT Bool))) (=> (= Xs Ys) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 Ys)) (= (@ P X5) (@ Q X5)))) (= (@ (@ tptp.find_VEBT_VEBT P) Xs) (@ (@ tptp.find_VEBT_VEBT Q) Ys))))) (forall ((Xs tptp.list_int) (Ys tptp.list_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (= Xs Ys) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ tptp.set_int2 Ys)) (= (@ P X5) (@ Q X5)))) (= (@ (@ tptp.find_int P) Xs) (@ (@ tptp.find_int Q) Ys))))) (forall ((Xs tptp.list_nat) (Ys tptp.list_nat) (P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (= Xs Ys) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) (@ tptp.set_nat2 Ys)) (= (@ P X5) (@ Q X5)))) (= (@ (@ tptp.find_nat P) Xs) (@ (@ tptp.find_nat Q) Ys))))) (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat N2)) tptp.zero_z5237406670263579293d_enat))) (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N2)) tptp.zero_zero_real))) (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N2)) tptp.zero_zero_nat))) (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N2)) tptp.zero_zero_int))) (forall ((N2 tptp.num)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ tptp.numera1916890842035813515d_enat N2))) (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N2))) (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N2))) (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N2))) (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N2)) tptp.zero_zero_nat))) (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_int (@ tptp.numeral_numeral_int N2)) tptp.zero_zero_int))) (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N2)) tptp.zero_zero_real))) (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N2))) (forall ((N2 tptp.num)) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ tptp.numera1916890842035813515d_enat N2))) (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N2))) (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N2))) (forall ((Xs tptp.list_Extended_enat) (N2 tptp.nat) (X tptp.extended_enat)) (=> (= (@ tptp.size_s3941691890525107288d_enat Xs) N2) (=> (forall ((Y3 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat Y3) (@ tptp.set_Extended_enat2 Xs)) (= Y3 X))) (= Xs (@ (@ tptp.replic7216382294607269926d_enat N2) X))))) (forall ((Xs tptp.list_real) (N2 tptp.nat) (X tptp.real)) (=> (= (@ tptp.size_size_list_real Xs) N2) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.member_real Y3) (@ tptp.set_real2 Xs)) (= Y3 X))) (= Xs (@ (@ tptp.replicate_real N2) X))))) (forall ((Xs tptp.list_set_nat) (N2 tptp.nat) (X tptp.set_nat)) (=> (= (@ tptp.size_s3254054031482475050et_nat Xs) N2) (=> (forall ((Y3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Y3) (@ tptp.set_set_nat2 Xs)) (= Y3 X))) (= Xs (@ (@ tptp.replicate_set_nat N2) X))))) (forall ((Xs tptp.list_VEBT_VEBT) (N2 tptp.nat) (X 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 X))) (= Xs (@ (@ tptp.replicate_VEBT_VEBT N2) X))))) (forall ((Xs tptp.list_int) (N2 tptp.nat) (X tptp.int)) (=> (= (@ tptp.size_size_list_int Xs) N2) (=> (forall ((Y3 tptp.int)) (=> (@ (@ tptp.member_int Y3) (@ tptp.set_int2 Xs)) (= Y3 X))) (= Xs (@ (@ tptp.replicate_int N2) X))))) (forall ((Xs tptp.list_nat) (N2 tptp.nat) (X tptp.nat)) (=> (= (@ tptp.size_size_list_nat Xs) N2) (=> (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.member_nat Y3) (@ tptp.set_nat2 Xs)) (= Y3 X))) (= Xs (@ (@ tptp.replicate_nat N2) X))))) (forall ((Xs tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 Xs)) (= X5 X))) (= (@ (@ tptp.replicate_VEBT_VEBT (@ tptp.size_s6755466524823107622T_VEBT Xs)) X) Xs))) (forall ((Xs tptp.list_int) (X tptp.int)) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ tptp.set_int2 Xs)) (= X5 X))) (= (@ (@ tptp.replicate_int (@ tptp.size_size_list_int Xs)) X) Xs))) (forall ((Xs tptp.list_nat) (X tptp.nat)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) (@ tptp.set_nat2 Xs)) (= X5 X))) (= (@ (@ tptp.replicate_nat (@ tptp.size_size_list_nat Xs)) X) Xs))) (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT) (X tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)) X))) (forall ((Uw tptp.nat) (Ux tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT)) (@ tptp.vEBT_VEBT_minNull (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw) Ux) Uy))) (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary tptp.vEBT_VEBT) (M2 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) M2) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _let_2 M2)) (=> (= M2 N2) (=> (= Deg (@ (@ tptp.plus_plus_nat N2) M2)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)) (= (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) X6)) (@ (@ 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))) M2)) (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 ((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 ((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 ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary tptp.vEBT_VEBT) (M2 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) M2) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _let_2 M2)) (=> (= M2 (@ tptp.suc N2)) (=> (= Deg (@ (@ tptp.plus_plus_nat N2) M2)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)) (= (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) X6)) (@ (@ 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))) M2)) (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)))))))))))))) (= tptp.size_s6755466524823107622T_VEBT (@ tptp.gen_length_VEBT_VEBT tptp.zero_zero_nat)) (= tptp.size_size_list_int (@ tptp.gen_length_int tptp.zero_zero_nat)) (= tptp.size_size_list_nat (@ tptp.gen_length_nat tptp.zero_zero_nat)) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int))))) (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (= A tptp.zero_zero_real)))) (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (= A tptp.zero_zero_int)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_real X) _let_1) (@ (@ tptp.power_power_real Y) _let_1)) (= X Y))))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_nat X) _let_1) (@ (@ tptp.power_power_nat Y) _let_1)) (= X Y))))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_int X) _let_1) (@ (@ tptp.power_power_int Y) _let_1)) (= X Y))))))) (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_int) (= A tptp.zero_zero_int))) (forall ((A tptp.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.complex)) (= (= (@ (@ tptp.power_power_complex A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))) (forall ((A tptp.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) (B2 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B2) N2)) (@ (@ tptp.ord_less_eq_real A) B2))))))) (forall ((A tptp.nat) (B2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B2) N2)) (@ (@ tptp.ord_less_eq_nat A) B2))))))) (forall ((A tptp.int) (B2 tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B2) N2)) (@ (@ tptp.ord_less_eq_int A) B2))))))) (forall ((X tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Mi tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3))) (let ((_let_5 (@ tptp.product_Pair_nat_nat Mi))) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (=> (@ (@ tptp.ord_less_nat Mi) X) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (not (= X Ma)) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 (@ (@ tptp.ord_max_nat X) Ma)))) Deg) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) _let_3) (@ (@ tptp.vEBT_vebt_insert _let_4) (@ (@ tptp.vEBT_VEBT_low X) _let_2)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_4)) (@ (@ tptp.vEBT_vebt_insert Summary) _let_3)) Summary))))))))))))) (forall ((Mi tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (X tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Mi) _let_2))) (let ((_let_4 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3))) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (=> (@ (@ tptp.ord_less_nat X) Mi) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (not (= X Ma)) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat X) (@ (@ tptp.ord_max_nat Mi) Ma)))) Deg) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) _let_3) (@ (@ tptp.vEBT_vebt_insert _let_4) (@ (@ tptp.vEBT_VEBT_low Mi) _let_2)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_4)) (@ (@ tptp.vEBT_vebt_insert Summary) _let_3)) Summary)))))))))))) (forall ((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.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.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 ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (=> (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (and (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (or (= X Mi) (= X Ma) (and (@ (@ tptp.ord_less_nat X) Ma) (@ (@ tptp.ord_less_nat Mi) X) (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2)))))))))) (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.divide_divide_nat (@ _let_1 (@ (@ tptp.plus_plus_nat A) B2))) (@ _let_1 A)) (@ _let_1 B2)))) _let_241 (= (@ (@ tptp.divide_divide_nat tptp.deg) _let_194) tptp.na) (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)) (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)) (forall ((A tptp.complex) (C tptp.complex) (B2 tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) C) (@ (@ tptp.divide1717551699836669952omplex B2) C)) (or (= C tptp.zero_zero_complex) (= A B2)))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (= (@ (@ tptp.divide_divide_real A) C) (@ (@ tptp.divide_divide_real B2) C)) (or (= C tptp.zero_zero_real) (= A B2)))) (forall ((C tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex C))) (= (= (@ _let_1 A) (@ _let_1 B2)) (or (= C tptp.zero_zero_complex) (= A B2))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (= (= (@ _let_1 A) (@ _let_1 B2)) (or (= C tptp.zero_zero_real) (= A B2))))) (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)) (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) (B2 tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B2) tptp.zero_zero_complex) (or (= A tptp.zero_zero_complex) (= B2 tptp.zero_zero_complex)))) (forall ((A tptp.real) (B2 tptp.real)) (= (= (@ (@ tptp.divide_divide_real A) B2) tptp.zero_zero_real) (or (= A tptp.zero_zero_real) (= B2 tptp.zero_zero_real)))) (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex tptp.zero_zero_complex) A) tptp.zero_zero_complex)) (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 ((N2 tptp.nat)) (= (@ (@ tptp.power_8040749407984259932d_enat tptp.zero_z5237406670263579293d_enat) (@ tptp.suc N2)) tptp.zero_z5237406670263579293d_enat)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.suc N2)) tptp.zero_zero_nat)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.suc N2)) tptp.zero_zero_real)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.suc N2)) tptp.zero_zero_complex)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.suc N2)) tptp.zero_zero_int)) (forall ((K tptp.num)) (= (@ (@ tptp.power_8040749407984259932d_enat tptp.zero_z5237406670263579293d_enat) (@ tptp.numeral_numeral_nat K)) tptp.zero_z5237406670263579293d_enat)) (forall ((K tptp.num)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_nat)) (forall ((K tptp.num)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_real)) (forall ((K tptp.num)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_complex)) (forall ((K tptp.num)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_int)) (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.suc tptp.zero_zero_nat)) A)) (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.suc tptp.zero_zero_nat)) A)) (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex 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 ((X tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.power_power_nat X) M2) _let_1) (or (= M2 tptp.zero_zero_nat) (= X _let_1))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.power_power_nat _let_1) N2) _let_1))) (forall ((X tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat X) N2)) (or (@ _let_1 X) (= N2 tptp.zero_zero_nat))))) (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList2) Summary))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat Deg) _let_2))) (=> (@ (@ tptp.vEBT_invar_vebt _let_1) N2) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_2) Deg)) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) (@ (@ tptp.vEBT_VEBT_high X) _let_3))) (@ (@ tptp.vEBT_VEBT_low X) _let_3)) (@ (@ tptp.vEBT_V8194947554948674370ptions _let_1) X)))))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) B2)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B2) C)))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A) B2)) tptp.zero_zero_real) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ _let_1 B2)))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B2) C))))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real A) B2)) (or (and (@ _let_1 A) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_real X) Y)))))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X) Y))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B2) C)) (@ (@ tptp.divide_divide_real A) C))))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X) Y))))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_real X) Y)))))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A) B2)) tptp.zero_zero_real) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_real B2) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ _let_1 B2)))))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B2) C)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B2)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B2) A)) (not (= C tptp.zero_zero_real))))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real A) B2)) (or (and (@ _let_1 A) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B2) tptp.zero_zero_real)))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B2) C))))) (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real B2) A) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B2) C))))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X) Y))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ _let_1 (@ (@ tptp.divide_divide_real X) Y)))))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B2) C)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B2)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B2) A))))) (forall ((X tptp.real) (Y tptp.real) (W2 tptp.real) (Z3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ _let_1 W2) (=> (@ (@ tptp.ord_less_real W2) Z3) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Z3)) (@ (@ tptp.divide_divide_real Y) W2)))))))) (forall ((X tptp.real) (Y tptp.real) (W2 tptp.real) (Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) Y) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) W2) (=> (@ (@ tptp.ord_less_eq_real W2) Z3) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Z3)) (@ (@ tptp.divide_divide_real Y) W2))))))) (forall ((Y tptp.real) (X tptp.real) (W2 tptp.real) (Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) W2) (=> (@ (@ tptp.ord_less_eq_real W2) Z3) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Z3)) (@ (@ tptp.divide_divide_real Y) W2))))))) (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real X) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.plus_plus_real _let_1) _let_1) X))) (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.divide_divide_real A) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))) (forall ((A tptp.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 ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X))) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) Y)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))) (forall ((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.complex) (N2 tptp.nat)) (=> (not (= A tptp.zero_zero_complex)) (not (= (@ (@ tptp.power_power_complex A) N2) tptp.zero_zero_complex)))) (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.real) (B2 tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B2) N2))))) (forall ((A tptp.nat) (B2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B2) N2))))) (forall ((A tptp.int) (B2 tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B2) 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.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N2))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N2))))) (forall ((A tptp.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.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.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 ((I tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) I) (=> (@ (@ tptp.ord_less_nat (@ _let_1 M2)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M2) N2))))) (forall ((A tptp.real) (N2 tptp.nat) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B2) N2)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B2) (@ (@ tptp.ord_less_real A) B2)))) (forall ((A tptp.nat) (N2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B2) N2)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B2) (@ (@ tptp.ord_less_nat A) B2)))) (forall ((A tptp.int) (N2 tptp.nat) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B2) N2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B2) (@ (@ tptp.ord_less_int A) B2)))) (forall ((A tptp.real) (N2 tptp.nat) (B2 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 B2) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= A B2))))))) (forall ((A tptp.nat) (N2 tptp.nat) (B2 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 B2) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= A B2))))))) (forall ((A tptp.int) (N2 tptp.nat) (B2 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 B2) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= A B2))))))) (forall ((A tptp.real) (N2 tptp.nat) (B2 tptp.real)) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) _let_1)) (@ (@ tptp.power_power_real B2) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B2) (@ (@ tptp.ord_less_eq_real A) B2))))) (forall ((A tptp.nat) (N2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) _let_1)) (@ (@ tptp.power_power_nat B2) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B2) (@ (@ tptp.ord_less_eq_nat A) B2))))) (forall ((A tptp.int) (N2 tptp.nat) (B2 tptp.int)) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) _let_1)) (@ (@ tptp.power_power_int B2) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B2) (@ (@ tptp.ord_less_eq_int A) B2))))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.power_8040749407984259932d_enat tptp.zero_z5237406670263579293d_enat) N2) tptp.zero_z5237406670263579293d_enat))) (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_complex tptp.zero_zero_complex) N2) tptp.zero_zero_complex))) (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) (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 ((I tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)))) (=> (@ _let_1 I) (@ _let_1 (@ (@ tptp.power_power_nat I) N2))))) (forall ((A tptp.real) (N2 tptp.nat) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (= (@ (@ tptp.power_power_real A) N2) (@ (@ tptp.power_power_real B2) N2)) (=> (@ _let_1 A) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= A B2))))))) (forall ((A tptp.nat) (N2 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (= (@ (@ tptp.power_power_nat A) N2) (@ (@ tptp.power_power_nat B2) N2)) (=> (@ _let_1 A) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= A B2))))))) (forall ((A tptp.int) (N2 tptp.nat) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (= (@ (@ tptp.power_power_int A) N2) (@ (@ tptp.power_power_int B2) N2)) (=> (@ _let_1 A) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= A B2))))))) (forall ((N2 tptp.nat) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= (= (@ (@ tptp.power_power_real A) N2) (@ (@ tptp.power_power_real B2) N2)) (= A B2))))))) (forall ((N2 tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= (= (@ (@ tptp.power_power_nat A) N2) (@ (@ tptp.power_power_nat B2) N2)) (= A B2))))))) (forall ((N2 tptp.nat) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= (= (@ (@ tptp.power_power_int A) N2) (@ (@ tptp.power_power_int B2) N2)) (= A B2))))))) (= (@ _let_240 _let_194) tptp.zero_z5237406670263579293d_enat) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) _let_194) tptp.zero_zero_nat) (= (@ _let_105 _let_194) tptp.zero_zero_real) (= (@ _let_104 _let_194) tptp.zero_zero_complex) (= (@ _let_103 _let_194) tptp.zero_zero_int) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (forall ((K tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K) (@ (@ tptp.ord_less_eq_nat M2) (@ (@ tptp.power_power_nat K) M2)))) (forall ((M2 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 M2) _let_1)) (@ (@ tptp.power_power_nat N2) _let_1)) (@ (@ tptp.ord_less_eq_nat M2) N2)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat M2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) N2) (@ (@ tptp.ord_less_eq_nat M2) N2))) (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_real X) _let_2) (@ (@ tptp.power_power_real Y) _let_2)) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= X Y))))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_nat X) _let_2) (@ (@ tptp.power_power_nat Y) _let_2)) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= X Y))))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_int X) _let_2) (@ (@ tptp.power_power_int Y) _let_2)) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= X Y))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_eq_real X) Y))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat X) _let_1)) (@ (@ tptp.power_power_nat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y) (@ (@ tptp.ord_less_eq_nat X) Y))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (@ (@ tptp.ord_less_eq_int X) Y))))) (forall ((A tptp.real) (B2 tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B2) N2)))))) (forall ((A tptp.nat) (B2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B2) N2)))))) (forall ((A tptp.int) (B2 tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_int A) B2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B2) N2)))))) (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))) (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_int))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_real X) Y))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat X) _let_1)) (@ (@ tptp.power_power_nat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y) (@ (@ tptp.ord_less_nat X) Y))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (@ (@ tptp.ord_less_int X) Y))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) tptp.zero_zero_real)))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))) tptp.zero_zero_int)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) (or (not (= X tptp.zero_zero_real)) (not (= Y tptp.zero_zero_real)))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))) (or (not (= X tptp.zero_zero_int)) (not (= Y tptp.zero_zero_int)))))) (forall ((X tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Mi tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high X) _let_1))) (=> (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) Deg) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low X) _let_1)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X))))))) (forall ((M2 tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat M2) M2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)) (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc M2))) _let_1) (@ tptp.suc (@ (@ tptp.divide_divide_nat M2) _let_1))))) (forall ((Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) Deg) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (or (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) (@ (@ tptp.vEBT_VEBT_high X) _let_1))) (@ (@ tptp.vEBT_VEBT_low X) _let_1)) (= X Mi) (= X Ma)))))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N2) (= (@ (@ tptp.divide_divide_nat M2) N2) tptp.zero_zero_nat))) (forall ((M2 tptp.nat)) (= (@ (@ tptp.divide_divide_nat M2) (@ tptp.suc tptp.zero_zero_nat)) M2)) (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (M2 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))) M2)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2)))) (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 ((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 ((A tptp.nat) (M2 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 M2))) (@ _let_1 N2)) (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N2))))))) (forall ((A tptp.int) (M2 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 M2))) (@ _let_1 N2)) (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N2))))))) (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int tptp.zero_zero_int) A) tptp.zero_zero_int)) (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.one_one_complex) 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) (B2 tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B2) tptp.one_one_complex) (and (not (= B2 tptp.zero_zero_complex)) (= A B2)))) (forall ((A tptp.real) (B2 tptp.real)) (= (= (@ (@ tptp.divide_divide_real A) B2) tptp.one_one_real) (and (not (= B2 tptp.zero_zero_real)) (= A B2)))) (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))) (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) (B2 tptp.complex)) (= (= tptp.one_one_complex (@ (@ tptp.divide1717551699836669952omplex A) B2)) (and (not (= B2 tptp.zero_zero_complex)) (= A B2)))) (forall ((A tptp.real) (B2 tptp.real)) (= (= tptp.one_one_real (@ (@ tptp.divide_divide_real A) B2)) (and (not (= B2 tptp.zero_zero_real)) (= A B2)))) (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))) (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) A) tptp.one_one_real))) (forall ((A tptp.complex)) (let ((_let_1 (@ (@ tptp.divide1717551699836669952omplex A) A))) (let ((_let_2 (= A tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 tptp.zero_zero_complex)) (=> (not _let_2) (= _let_1 tptp.one_one_complex)))))) (forall ((A tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real A) A))) (let ((_let_2 (= A tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))) (forall ((B2 tptp.real) (A tptp.real)) (= (= (@ (@ tptp.divide_divide_real B2) A) tptp.one_one_real) (and (not (= A tptp.zero_zero_real)) (= A B2)))) (forall ((B2 tptp.real) (A tptp.real)) (= (= tptp.one_one_real (@ (@ tptp.divide_divide_real B2) A)) (and (not (= A tptp.zero_zero_real)) (= A B2)))) (forall ((A tptp.real)) (= (= (@ (@ tptp.divide_divide_real tptp.one_one_real) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) (= A tptp.zero_zero_real))) (forall ((A tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (= (= (@ _let_1 M2) (@ _let_1 N2)) (= M2 N2))))) (forall ((A tptp.real) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (= (= (@ _let_1 M2) (@ _let_1 N2)) (= M2 N2))))) (forall ((A tptp.int) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (= (= (@ _let_1 M2) (@ _let_1 N2)) (= M2 N2))))) (= (@ (@ tptp.ord_max_real tptp.one_one_real) tptp.zero_zero_real) tptp.one_one_real) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.one_on7984719198319812577d_enat) tptp.zero_z5237406670263579293d_enat) tptp.one_on7984719198319812577d_enat) (= (@ (@ tptp.ord_max_nat tptp.one_one_nat) tptp.zero_zero_nat) tptp.one_one_nat) (= (@ (@ tptp.ord_max_int tptp.one_one_int) tptp.zero_zero_int) tptp.one_one_int) (= (@ (@ tptp.ord_max_real tptp.zero_zero_real) tptp.one_one_real) tptp.one_one_real) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) tptp.one_on7984719198319812577d_enat) tptp.one_on7984719198319812577d_enat) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) tptp.one_one_nat) tptp.one_one_nat) (= (@ (@ tptp.ord_max_int tptp.zero_zero_int) tptp.one_one_int) tptp.one_one_int) (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat N2) tptp.one_one_nat) (= N2 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.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))) (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) (@ _let_1 A)))) (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B2) A)) (@ (@ tptp.ord_less_real A) B2)))) (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B2) A)) (@ (@ tptp.ord_less_real B2) A)))) (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B2) A)) tptp.one_one_real) (@ (@ tptp.ord_less_real B2) A)))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B2) A)) tptp.one_one_real) (@ _let_1 B2))))) (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 ((B2 tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B2) (= (@ (@ tptp.ord_less_nat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))) (forall ((B2 tptp.real) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B2))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B2) (= (@ (@ tptp.ord_less_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))) (forall ((B2 tptp.int) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B2))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B2) (= (@ (@ tptp.ord_less_int (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))) (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B2) A)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real A) B2)))) (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B2) A)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real B2) A)))) (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B2) A)) (@ (@ tptp.ord_less_eq_real B2) A)))) (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B2) A)) (@ (@ tptp.ord_less_eq_real A) B2)))) (= (@ _let_186 tptp.one_one_complex) _let_109) _let_216 (= _let_222 (@ tptp.numera1916890842035813515d_enat _let_29)) (= _let_220 _let_82) (= _let_221 _let_111) (forall ((B2 tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2) (=> (@ (@ tptp.ord_less_nat B2) tptp.one_one_nat) (= (@ (@ tptp.ord_less_nat (@ _let_1 M2)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat N2) M2)))))) (forall ((B2 tptp.real) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B2))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B2) (=> (@ (@ tptp.ord_less_real B2) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ _let_1 M2)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat N2) M2)))))) (forall ((B2 tptp.int) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_int B2) tptp.one_one_int) (= (@ (@ tptp.ord_less_int (@ _let_1 M2)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat N2) M2)))))) (forall ((B2 tptp.real) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B2))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B2) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))) (forall ((B2 tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B2) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))) (forall ((B2 tptp.int) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B2))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B2) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))) (= (@ tptp.suc tptp.one_one_nat) _let_194) (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_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_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_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.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_complex (@ tptp.numera6690914467698888265omplex N2)) tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ (@ 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_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_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_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.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat N2)) tptp.one_on7984719198319812577d_enat) (@ (@ tptp.ord_less_eq_num N2) tptp.one))) (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N2)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_num N2) tptp.one))) (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N2)) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_num N2) tptp.one))) (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N2)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_num N2) tptp.one))) (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat 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_int tptp.one_one_int) (@ tptp.numeral_numeral_int 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))) _let_239 _let_238 _let_239 _let_238 (forall ((B2 tptp.real) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B2))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B2) (=> (@ (@ tptp.ord_less_real B2) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 M2)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat N2) M2)))))) (forall ((B2 tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2) (=> (@ (@ tptp.ord_less_nat B2) tptp.one_one_nat) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M2)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat N2) M2)))))) (forall ((B2 tptp.int) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_int B2) tptp.one_one_int) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 M2)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat N2) M2)))))) (forall ((X tptp.nat)) (= (= tptp.one_one_nat X) (= X tptp.one_one_nat))) (forall ((X tptp.int)) (= (= tptp.one_one_int X) (= X tptp.one_one_int))) (forall ((X tptp.complex)) (= (= tptp.one_one_complex X) (= X tptp.one_one_complex))) (forall ((X tptp.real)) (= (= tptp.one_one_real X) (= X tptp.one_one_real))) (@ _let_178 tptp.one_one_real) (@ _let_237 tptp.one_one_nat) (@ _let_177 tptp.one_one_int) (not (= tptp.zero_zero_nat tptp.one_one_nat)) (not (= tptp.zero_zero_real tptp.one_one_real)) (not (= tptp.zero_zero_int tptp.one_one_int)) (not (= tptp.zero_zero_complex tptp.one_one_complex)) (not (= tptp.zero_z5237406670263579293d_enat tptp.one_on7984719198319812577d_enat)) (not (@ _let_230 tptp.one_one_nat)) (not (@ _let_229 tptp.one_on7984719198319812577d_enat)) (not (@ _let_175 tptp.one_one_real)) (not (@ _let_176 tptp.one_one_int)) (forall ((B2 tptp.nat) (A tptp.nat)) (=> (not (= B2 tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat B2) A)) B2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) B2)) tptp.one_one_nat)))) (forall ((B2 tptp.int) (A tptp.int)) (=> (not (= B2 tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int B2) A)) B2) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) B2)) tptp.one_one_int)))) (forall ((B2 tptp.nat) (A tptp.nat)) (=> (not (= B2 tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B2)) B2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) B2)) tptp.one_one_nat)))) (forall ((B2 tptp.int) (A tptp.int)) (=> (not (= B2 tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B2)) B2) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) B2)) tptp.one_one_int)))) (not (@ (@ tptp.ord_le2932123472753598470d_enat tptp.one_on7984719198319812577d_enat) tptp.zero_z5237406670263579293d_enat)) (not (@ _let_178 tptp.zero_zero_real)) (not (@ _let_237 tptp.zero_zero_nat)) (not (@ _let_177 tptp.zero_zero_int)) _let_236 _let_234 _let_233 _let_231 _let_236 _let_234 _let_233 _let_231 (not (@ _let_230 tptp.zero_zero_nat)) (not (@ _let_229 tptp.zero_z5237406670263579293d_enat)) (not (@ _let_175 tptp.zero_zero_real)) (not (@ _let_176 tptp.zero_zero_int)) _let_228 _let_227 _let_226 _let_225 _let_228 _let_227 _let_226 _let_225 (forall ((N2 tptp.num)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.one_on7984719198319812577d_enat) (@ tptp.numera1916890842035813515d_enat N2))) (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.numeral_numeral_real N2))) (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N2))) (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.numeral_numeral_int N2))) (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N2)) tptp.one_one_nat))) (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_int (@ tptp.numeral_numeral_int N2)) tptp.one_one_int))) (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N2)) tptp.one_one_real))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) (@ (@ tptp.plus_plus_nat B2) tptp.one_one_nat)))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B2) (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) tptp.one_on7984719198319812577d_enat)) (@ (@ tptp.plus_p3455044024723400733d_enat B2) tptp.one_on7984719198319812577d_enat)))) (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) tptp.one_one_real)) (@ (@ tptp.plus_plus_real B2) tptp.one_one_real)))) (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B2) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) (@ (@ tptp.plus_plus_int B2) tptp.one_one_int)))) (forall ((A tptp.nat)) (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat))) (forall ((A tptp.real)) (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real A) tptp.one_one_real))) (forall ((A tptp.int)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int A) tptp.one_one_int))) (forall ((B2 tptp.complex) (A tptp.complex)) (=> (not (= B2 tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B2) tptp.one_one_complex) (= A B2)))) (forall ((B2 tptp.real) (A tptp.real)) (=> (not (= B2 tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real A) B2) tptp.one_one_real) (= A B2)))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex X))) (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X))) (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.plus_p3455044024723400733d_enat tptp.one_on7984719198319812577d_enat) _let_1) (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) tptp.one_on7984719198319812577d_enat)))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X))) (= (@ (@ tptp.plus_plus_int tptp.one_one_int) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X))) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))) (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) N2))))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.one_one_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N2))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.one_one_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N2))))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (= (= (@ (@ tptp.divide_divide_nat M2) N2) M2) (= N2 tptp.one_one_nat)))) (forall ((N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M2) N2)) M2)))) (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.complex)) (= (@ (@ tptp.power_power_complex A) tptp.zero_zero_nat) tptp.one_one_complex)) (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) tptp.zero_zero_nat) tptp.one_one_int)) _let_224 (= tptp.suc (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))) (= _let_214 tptp.suc) (= tptp.suc _let_214) (@ _let_212 _let_215) (@ _let_223 _let_222) (@ _let_167 _let_221) (@ _let_168 _let_220) (forall ((B2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B2) A)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ _let_1 B2)) (and (@ _let_1 tptp.zero_zero_real) (@ (@ tptp.ord_less_real B2) A)))))) (forall ((B2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B2) A)) tptp.one_one_real) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_real B2) A)) (and (@ _let_1 tptp.zero_zero_real) (@ _let_1 B2)) (= A tptp.zero_zero_real))))) (forall ((A tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N2)) tptp.one_one_real)))) (forall ((A tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) N2)) tptp.one_one_nat)))) (forall ((A tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N2)) tptp.one_one_int)))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) B2)) (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real)))))) (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) B2)) (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real))) B2))) _let_219 (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)))))) _let_218 _let_217 (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 ((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.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.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 ((A tptp.nat) (M2 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 M2)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M2) N2))))) (forall ((A tptp.real) (M2 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 M2)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M2) N2))))) (forall ((A tptp.int) (M2 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 M2)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M2) N2))))) (forall ((N2 tptp.nat) (N6 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat N2) N6) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_nat (@ _let_1 N2)) (@ _let_1 N6)))))) (forall ((N2 tptp.nat) (N6 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat N2) N6) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (@ (@ tptp.ord_less_real (@ _let_1 N2)) (@ _let_1 N6)))))) (forall ((N2 tptp.nat) (N6 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat N2) N6) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (@ (@ tptp.ord_less_int (@ _let_1 N2)) (@ _let_1 N6)))))) (forall ((N2 tptp.nat) (N6 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N6) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A) (@ (@ tptp.ord_less_eq_real (@ _let_1 N2)) (@ _let_1 N6)))))) (forall ((N2 tptp.nat) (N6 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N6) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N2)) (@ _let_1 N6)))))) (forall ((N2 tptp.nat) (N6 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N6) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A) (@ (@ tptp.ord_less_eq_int (@ _let_1 N2)) (@ _let_1 N6)))))) (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 ((B2 tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B2) A)) tptp.one_one_real) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real B2) A)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real A) B2)) (= A tptp.zero_zero_real)))) (forall ((B2 tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B2) A)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real A) B2)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B2) A))))) (forall ((A tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) (@ tptp.suc N2))) A)))) (forall ((A tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) (@ tptp.suc N2))) A)))) (forall ((A tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) (@ tptp.suc N2))) A)))) (forall ((A tptp.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.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.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) (N6 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat N2) N6) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ _let_1 N6)) (@ _let_1 N2))))))) (forall ((N2 tptp.nat) (N6 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat N2) N6) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ _let_1 N6)) (@ _let_1 N2))))))) (forall ((N2 tptp.nat) (N6 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat N2) N6) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ _let_1 N6)) (@ _let_1 N2))))))) (forall ((N2 tptp.nat) (N6 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N6) (=> (@ (@ 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 N6)) (@ _let_1 N2))))))) (forall ((N2 tptp.nat) (N6 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N6) (=> (@ (@ 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 N6)) (@ _let_1 N2))))))) (forall ((N2 tptp.nat) (N6 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N6) (=> (@ (@ 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 N6)) (@ _let_1 N2))))))) (forall ((A tptp.real) (M2 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 M2)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M2) N2))))) (forall ((A tptp.nat) (M2 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 M2)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M2) N2))))) (forall ((A tptp.int) (M2 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 M2)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M2) N2))))) (forall ((A tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.power_power_real A) N2))))) (forall ((A tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.power_power_nat A) N2))))) (forall ((A tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int A) N2))))) (forall ((A tptp.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.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.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_216 (forall ((M2 tptp.nat) (N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M2) K)) (@ (@ tptp.divide_divide_nat N2) K)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M2) N2)) M2)) (forall ((B2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ _let_1 B2) (=> (@ _let_1 K) (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (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 ((B2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B2) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) K) (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 N3)) K) (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N3) tptp.one_one_nat))))))))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.divide_divide_nat M2) N2) tptp.zero_zero_nat) (or (@ (@ tptp.ord_less_nat M2) N2) (= N2 tptp.zero_zero_nat)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M2) N2)) (@ (@ tptp.divide_divide_nat (@ tptp.suc M2)) N2))) (forall ((M2 tptp.nat) (N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N2)) (@ _let_1 M2)))))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.divide_divide_nat M2) N2)) (and (@ (@ tptp.ord_less_eq_nat N2) M2) (@ _let_1 N2))))) (forall ((M2 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 M2) N2)) tptp.zero_zero_nat)) (not (= (@ _let_1 M2) tptp.zero_zero_nat))))) (forall ((M2 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 M2) N2)) tptp.zero_zero_int)) (not (= (@ _let_1 M2) tptp.zero_zero_int))))) (forall ((M2 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 M2) N2)) tptp.zero_zero_nat)) (not (= (@ _let_1 N2) tptp.zero_zero_nat))))) (forall ((M2 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 M2) N2)) tptp.zero_zero_int)) (not (= (@ _let_1 N2) tptp.zero_zero_int))))) (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))))) _let_213 (forall ((X tptp.nat) (N2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_nat X) _let_1) (= (@ (@ tptp.vEBT_VEBT_low (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat Y) _let_1)) X)) N2) X)))) (forall ((X tptp.nat) (N2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_nat X) _let_1) (= (@ (@ tptp.vEBT_VEBT_high (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat Y) _let_1)) X)) N2) Y)))) (forall ((A1 tptp.vEBT_VEBT) (A22 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt A1) A22) (=> (=> (exists ((A4 Bool) (B4 Bool)) (= A1 (@ (@ tptp.vEBT_Leaf A4) B4))) (not (= A22 (@ tptp.suc tptp.zero_zero_nat)))) (=> (forall ((TreeList3 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M3 tptp.nat) (Deg2 tptp.nat)) (=> (= A1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList3) Summary2)) (=> (= A22 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 Summary2) M3) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M3)) (=> (= M3 N3) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M3)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) 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) (Summary2 tptp.vEBT_VEBT) (M3 tptp.nat) (Deg2 tptp.nat)) (=> (= A1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList3) Summary2)) (=> (= A22 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 Summary2) M3) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M3)) (=> (= M3 (@ tptp.suc N3)) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M3)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) 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) (Summary2 tptp.vEBT_VEBT) (M3 tptp.nat) (Deg2 tptp.nat) (Mi2 tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (= Mi2 Ma2))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (= A1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Deg2) TreeList3) Summary2)) (=> (= A22 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 Summary2) M3) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ _let_2 M3)) (=> (= M3 N3) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M3)) (=> (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M3)) (= (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I5)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I5)))) (=> (=> _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 Mi2) Ma2) (=> (@ (@ tptp.ord_less_nat Ma2) (@ _let_2 Deg2)) (not (=> (not _let_1) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M3)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma2) N3) I5) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I5)) (@ (@ tptp.vEBT_VEBT_low Ma2) N3))) (forall ((X2 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X2) N3) I5) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I5)) (@ (@ tptp.vEBT_VEBT_low X2) N3))) (and (@ (@ tptp.ord_less_nat Mi2) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma2))))))))))))))))))))))) (not (forall ((TreeList3 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M3 tptp.nat) (Deg2 tptp.nat) (Mi2 tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (= Mi2 Ma2))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (= A1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Deg2) TreeList3) Summary2)) (=> (= A22 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 Summary2) M3) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ _let_2 M3)) (=> (= M3 (@ tptp.suc N3)) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M3)) (=> (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M3)) (= (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I5)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I5)))) (=> (=> _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 Mi2) Ma2) (=> (@ (@ tptp.ord_less_nat Ma2) (@ _let_2 Deg2)) (not (=> (not _let_1) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M3)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma2) N3) I5) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I5)) (@ (@ tptp.vEBT_VEBT_low Ma2) N3))) (forall ((X2 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X2) N3) I5) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I5)) (@ (@ tptp.vEBT_VEBT_low X2) N3))) (and (@ (@ tptp.ord_less_nat Mi2) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma2)))))))))))))))))))))))))))))) (= tptp.vEBT_invar_vebt (lambda ((A12 tptp.vEBT_VEBT) (A23 tptp.nat)) (or (and (exists ((A3 Bool) (B3 Bool)) (= A12 (@ (@ tptp.vEBT_Leaf A3) B3))) (= A23 (@ tptp.suc tptp.zero_zero_nat))) (exists ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary3 tptp.vEBT_VEBT)) (and (= A12 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A23) TreeList) Summary3)) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X4) N))) (@ (@ tptp.vEBT_invar_vebt Summary3) N) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= A23 (@ (@ tptp.plus_plus_nat N) N)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) X6))) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X6))))))) (exists ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc N))) (and (= A12 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A23) TreeList) Summary3)) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X4) N))) (@ (@ tptp.vEBT_invar_vebt Summary3) _let_1) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (= A23 (@ (@ tptp.plus_plus_nat N) _let_1)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) X6))) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X6)))))))) (exists ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary3 tptp.vEBT_VEBT) (Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (= Mi3 Ma3))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (and (= A12 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) A23) TreeList) Summary3)) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X4) N))) (@ (@ tptp.vEBT_invar_vebt Summary3) N) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ _let_2 N)) (= A23 (@ (@ 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 ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I3)))) (=> _let_1 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X6)))))) (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ _let_2 A23)) (=> (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 Ma3) N) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) (@ (@ tptp.vEBT_VEBT_low Ma3) N))) (forall ((X4 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X4) N) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) (@ (@ tptp.vEBT_VEBT_low X4) N))) (and (@ (@ tptp.ord_less_nat Mi3) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma3)))))))))))) (exists ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary3 tptp.vEBT_VEBT) (Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (= Mi3 Ma3))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ tptp.suc N))) (and (= A12 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) A23) TreeList) Summary3)) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X4) N))) (@ (@ tptp.vEBT_invar_vebt Summary3) _let_3) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ _let_2 _let_3)) (= A23 (@ (@ 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 ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I3)))) (=> _let_1 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X6)))))) (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ _let_2 A23)) (=> (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 Ma3) N) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) (@ (@ tptp.vEBT_VEBT_low Ma3) N))) (forall ((X4 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X4) N) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) (@ (@ tptp.vEBT_VEBT_low X4) N))) (and (@ (@ tptp.ord_less_nat Mi3) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma3)))))))))))))))) (forall ((M2 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat M2)) (@ tptp.numera1916890842035813515d_enat N2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat M2)) (@ tptp.numeral_numeral_nat N2)))) (forall ((M2 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat M2)) (@ tptp.numera1916890842035813515d_enat N2)) (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat M2)) (@ tptp.numeral_numeral_nat N2)))) (@ _let_212 _let_194) (forall ((A Bool) (B2 Bool)) (not (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_Leaf A) B2)) tptp.zero_zero_nat))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (= N2 tptp.one_one_nat) (exists ((A4 Bool) (B4 Bool)) (= T (@ (@ tptp.vEBT_Leaf A4) B4)))))) (forall ((T tptp.vEBT_VEBT)) (=> (@ (@ tptp.vEBT_invar_vebt T) tptp.one_one_nat) (exists ((A4 Bool) (B4 Bool)) (= T (@ (@ tptp.vEBT_Leaf A4) B4))))) (forall ((T tptp.vEBT_VEBT)) (= (@ (@ tptp.vEBT_invar_vebt T) tptp.one_one_nat) (exists ((A3 Bool) (B3 Bool)) (= T (@ (@ tptp.vEBT_Leaf A3) B3))))) (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (= (= (@ (@ tptp.times_times_nat A) C) (@ (@ tptp.times_times_nat B2) C)) (or (= C tptp.zero_zero_nat) (= A B2)))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (= (@ (@ tptp.times_times_int A) C) (@ (@ tptp.times_times_int B2) C)) (or (= C tptp.zero_zero_int) (= A B2)))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (= (@ (@ tptp.times_times_real A) C) (@ (@ tptp.times_times_real B2) C)) (or (= C tptp.zero_zero_real) (= A B2)))) (forall ((A tptp.complex) (C tptp.complex) (B2 tptp.complex)) (= (= (@ (@ tptp.times_times_complex A) C) (@ (@ tptp.times_times_complex B2) C)) (or (= C tptp.zero_zero_complex) (= A B2)))) (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (= (= (@ _let_1 A) (@ _let_1 B2)) (or (= C tptp.zero_zero_nat) (= A B2))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (= (@ _let_1 A) (@ _let_1 B2)) (or (= C tptp.zero_zero_int) (= A B2))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (= (@ _let_1 A) (@ _let_1 B2)) (or (= C tptp.zero_zero_real) (= A B2))))) (forall ((C tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C))) (= (= (@ _let_1 A) (@ _let_1 B2)) (or (= C tptp.zero_zero_complex) (= A B2))))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (= (@ (@ tptp.times_times_nat A) B2) tptp.zero_zero_nat) (or (= A tptp.zero_zero_nat) (= B2 tptp.zero_zero_nat)))) (forall ((A tptp.int) (B2 tptp.int)) (= (= (@ (@ tptp.times_times_int A) B2) tptp.zero_zero_int) (or (= A tptp.zero_zero_int) (= B2 tptp.zero_zero_int)))) (forall ((A tptp.real) (B2 tptp.real)) (= (= (@ (@ tptp.times_times_real A) B2) tptp.zero_zero_real) (or (= A tptp.zero_zero_real) (= B2 tptp.zero_zero_real)))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (= (@ (@ tptp.times_times_complex A) B2) tptp.zero_zero_complex) (or (= A tptp.zero_zero_complex) (= B2 tptp.zero_zero_complex)))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (= (= (@ (@ tptp.times_7803423173614009249d_enat A) B2) tptp.zero_z5237406670263579293d_enat) (or (= A tptp.zero_z5237406670263579293d_enat) (= B2 tptp.zero_z5237406670263579293d_enat)))) (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.real)) (= (@ (@ tptp.times_times_real A) tptp.zero_zero_real) tptp.zero_zero_real)) (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.zero_zero_complex) tptp.zero_zero_complex)) (forall ((A tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat A) tptp.zero_z5237406670263579293d_enat) tptp.zero_z5237406670263579293d_enat)) (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.real)) (= (@ (@ tptp.times_times_real tptp.zero_zero_real) A) tptp.zero_zero_real)) (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.zero_zero_complex) A) tptp.zero_zero_complex)) (forall ((A tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat tptp.zero_z5237406670263579293d_enat) A) tptp.zero_z5237406670263579293d_enat)) (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.real)) (= (@ (@ tptp.times_times_real A) tptp.one_one_real) A)) (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.one_one_complex) A)) (forall ((A tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat A) tptp.one_on7984719198319812577d_enat) A)) (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)) (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)) (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A) A)) (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.one_one_complex) A) A)) (forall ((A tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat tptp.one_on7984719198319812577d_enat) A) A)) (forall ((B2 tptp.complex) (C tptp.complex) (A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex B2) C)) A) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex B2) A)) C))) (forall ((B2 tptp.real) (C tptp.real) (A tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real B2) C)) A) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real B2) A)) C))) (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (= (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_times_complex B2) C))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (= (@ (@ tptp.divide_divide_real (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_times_real B2) C))))) (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) (@ (@ tptp.divide1717551699836669952omplex B2) C)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) C)) B2))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (= (@ (@ tptp.divide_divide_real A) (@ (@ tptp.divide_divide_real B2) C)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) C)) B2))) (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ (@ tptp.divide1717551699836669952omplex B2) C)) (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 B2)) C)))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.divide_divide_real B2) C)) (@ (@ tptp.divide_divide_real (@ _let_1 B2)) C)))) (forall ((M2 tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.times_times_nat M2) K) (@ (@ tptp.times_times_nat N2) K)) (or (= M2 N2) (= K tptp.zero_zero_nat)))) (forall ((K tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (= (@ _let_1 M2) (@ _let_1 N2)) (or (= M2 N2) (= K tptp.zero_zero_nat))))) (forall ((M2 tptp.nat)) (= (@ (@ tptp.times_times_nat M2) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.times_times_nat M2) N2) tptp.zero_zero_nat) (or (= M2 tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (= tptp.one_one_nat (@ (@ tptp.times_times_nat M2) N2)) (and (= M2 tptp.one_one_nat) (= N2 tptp.one_one_nat)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.times_times_nat M2) N2) tptp.one_one_nat) (and (= M2 tptp.one_one_nat) (= N2 tptp.one_one_nat)))) (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 ((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.complex) (C tptp.complex)) (= (= (@ (@ tptp.times_times_complex A) C) C) (or (= C tptp.zero_zero_complex) (= A tptp.one_one_complex)))) (forall ((C tptp.int) (B2 tptp.int)) (= (= C (@ (@ tptp.times_times_int B2) C)) (or (= C tptp.zero_zero_int) (= B2 tptp.one_one_int)))) (forall ((C tptp.real) (B2 tptp.real)) (= (= C (@ (@ tptp.times_times_real B2) C)) (or (= C tptp.zero_zero_real) (= B2 tptp.one_one_real)))) (forall ((C tptp.complex) (B2 tptp.complex)) (= (= C (@ (@ tptp.times_times_complex B2) C)) (or (= C tptp.zero_zero_complex) (= B2 tptp.one_one_complex)))) (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.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.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.int) (B2 tptp.int)) (= (= C (@ (@ tptp.times_times_int C) B2)) (or (= C tptp.zero_zero_int) (= B2 tptp.one_one_int)))) (forall ((C tptp.real) (B2 tptp.real)) (= (= C (@ (@ tptp.times_times_real C) B2)) (or (= C tptp.zero_zero_real) (= B2 tptp.one_one_real)))) (forall ((C tptp.complex) (B2 tptp.complex)) (= (= C (@ (@ tptp.times_times_complex C) B2)) (or (= C tptp.zero_zero_complex) (= B2 tptp.one_one_complex)))) (forall ((X tptp.int) (Y tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y)) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))) (forall ((X tptp.real) (Y tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y)) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real)))) (forall ((C tptp.complex) (A tptp.complex) (B2 tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex C) B2)) (@ (@ tptp.divide1717551699836669952omplex A) B2)))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real C) B2)) (@ (@ tptp.divide_divide_real A) B2)))) (forall ((B2 tptp.complex) (A tptp.complex)) (=> (not (= B2 tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) B2)) B2) A))) (forall ((B2 tptp.nat) (A tptp.nat)) (=> (not (= B2 tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) B2)) B2) A))) (forall ((B2 tptp.int) (A tptp.int)) (=> (not (= B2 tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) B2)) B2) A))) (forall ((B2 tptp.real) (A tptp.real)) (=> (not (= B2 tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) B2)) B2) A))) (forall ((C tptp.complex) (A tptp.complex) (B2 tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B2) C)) (@ (@ tptp.divide1717551699836669952omplex A) B2)))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) C)) (@ (@ tptp.divide_divide_real A) B2)))) (forall ((C tptp.complex) (A tptp.complex) (B2 tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex C) A)) (@ (@ tptp.times_times_complex B2) C)) (@ (@ tptp.divide1717551699836669952omplex A) B2)))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real C) A)) (@ (@ tptp.times_times_real B2) C)) (@ (@ tptp.divide_divide_real A) B2)))) (forall ((A tptp.complex) (B2 tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) B2)) A) B2))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) B2)) A) B2))) (forall ((A tptp.int) (B2 tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) B2)) A) B2))) (forall ((A tptp.real) (B2 tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) B2)) A) B2))) (forall ((C tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C))) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.divide1717551699836669952omplex A) B2))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.divide_divide_real A) B2))))) (forall ((C tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C))) (let ((_let_2 (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 A)) (@ _let_1 B2)))) (let ((_let_3 (= C tptp.zero_zero_complex))) (and (=> _let_3 (= _let_2 tptp.zero_zero_complex)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide1717551699836669952omplex A) B2)))))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (let ((_let_2 (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ _let_1 B2)))) (let ((_let_3 (= C tptp.zero_zero_real))) (and (=> _let_3 (= _let_2 tptp.zero_zero_real)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_real A) B2)))))))) (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 A)) (@ _let_1 B2)))) (let ((_let_3 (= C tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_nat A) B2)))))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (let ((_let_2 (@ (@ tptp.divide_divide_int (@ _let_1 A)) (@ _let_1 B2)))) (let ((_let_3 (= C tptp.zero_zero_int))) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_int A) B2)))))))) (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (=> (not (= C tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B2) C)) (@ (@ tptp.divide_divide_nat A) B2)))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (=> (not (= C tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) C)) (@ (@ tptp.divide_divide_int A) B2)))) (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (not (= C tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.divide_divide_nat A) B2))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (not (= C tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.divide_divide_int A) B2))))) (forall ((A tptp.complex) (B2 tptp.complex) (V tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex V))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B2)) _let_1) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) _let_1)) (@ (@ tptp.times_times_complex B2) _let_1))))) (forall ((A tptp.nat) (B2 tptp.nat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat V))) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B2)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) _let_1)) (@ (@ tptp.times_times_nat B2) _let_1))))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (V tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat V))) (= (@ (@ tptp.times_7803423173614009249d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) B2)) _let_1) (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.times_7803423173614009249d_enat A) _let_1)) (@ (@ tptp.times_7803423173614009249d_enat B2) _let_1))))) (forall ((A tptp.int) (B2 tptp.int) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int V))) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B2)) _let_1) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) _let_1)) (@ (@ tptp.times_times_int B2) _let_1))))) (forall ((A tptp.real) (B2 tptp.real) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real V))) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B2)) _let_1) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) _let_1)) (@ (@ tptp.times_times_real B2) _let_1))))) (forall ((V tptp.num) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B2) C)) (@ (@ tptp.plus_plus_complex (@ _let_1 B2)) (@ _let_1 C))))) (forall ((V tptp.num) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B2) C)) (@ (@ tptp.plus_plus_nat (@ _let_1 B2)) (@ _let_1 C))))) (forall ((V tptp.num) (B2 tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat V)))) (= (@ _let_1 (@ (@ tptp.plus_p3455044024723400733d_enat B2) C)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ _let_1 B2)) (@ _let_1 C))))) (forall ((V tptp.num) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B2) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B2)) (@ _let_1 C))))) (forall ((V tptp.num) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B2) C)) (@ (@ tptp.plus_plus_real (@ _let_1 B2)) (@ _let_1 C))))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.times_times_nat M2) N2)) (and (= M2 _let_1) (= N2 _let_1))))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.times_times_nat M2) N2) _let_1) (and (= M2 _let_1) (= N2 _let_1))))) (forall ((M2 tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat M2) K)) (@ (@ tptp.times_times_nat N2) K)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat M2) N2)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.times_times_nat M2) N2)) (and (@ _let_1 M2) (@ _let_1 N2))))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M2))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.plus_plus_nat M2) (@ _let_1 N2))))) (forall ((A tptp.real) (B2 tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.divide_divide_real B2) _let_1)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) _let_1)) B2)))) (forall ((B2 tptp.real) (W2 tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B2) _let_1)) A) (@ (@ tptp.ord_less_eq_real B2) (@ (@ tptp.times_times_real A) _let_1))))) (forall ((B2 tptp.complex) (W2 tptp.num) (A tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W2))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B2) _let_1) A) (and (=> (not _let_2) (= B2 (@ (@ tptp.times_times_complex A) _let_1))) (=> _let_2 (= A tptp.zero_zero_complex))))))) (forall ((B2 tptp.real) (W2 tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B2) _let_1) A) (and (=> (not _let_2) (= B2 (@ (@ tptp.times_times_real A) _let_1))) (=> _let_2 (= A tptp.zero_zero_real))))))) (forall ((A tptp.complex) (B2 tptp.complex) (W2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W2))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= A (@ (@ tptp.divide1717551699836669952omplex B2) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex A) _let_1) B2)) (=> _let_2 (= A tptp.zero_zero_complex))))))) (forall ((A tptp.real) (B2 tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= A (@ (@ tptp.divide_divide_real B2) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real A) _let_1) B2)) (=> _let_2 (= A tptp.zero_zero_real))))))) (forall ((A tptp.real) (B2 tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.divide_divide_real B2) _let_1)) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) _let_1)) B2)))) (forall ((B2 tptp.real) (W2 tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B2) _let_1)) A) (@ (@ tptp.ord_less_real B2) (@ (@ tptp.times_times_real A) _let_1))))) (forall ((A tptp.complex) (B2 tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) (@ (@ tptp.times_times_complex A) B2)) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) B2)))) (forall ((A tptp.real) (B2 tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) (@ (@ tptp.times_times_real A) B2)) (@ (@ tptp.divide_divide_real tptp.one_one_real) B2)))) (forall ((B2 tptp.complex) (A tptp.complex)) (=> (not (= B2 tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex B2) (@ (@ tptp.times_times_complex A) B2)) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) A)))) (forall ((B2 tptp.real) (A tptp.real)) (=> (not (= B2 tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real B2) (@ (@ tptp.times_times_real A) B2)) (@ (@ tptp.divide_divide_real tptp.one_one_real) A)))) (forall ((B2 tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (not (= B2 tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B2) C)) A)) B2) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B2))))) (forall ((B2 tptp.int) (C tptp.int) (A tptp.int)) (=> (not (= B2 tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) C)) A)) B2) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B2))))) (forall ((B2 tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (not (= B2 tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C) B2)) A)) B2) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B2))))) (forall ((B2 tptp.int) (C tptp.int) (A tptp.int)) (=> (not (= B2 tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C) B2)) A)) B2) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B2))))) (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (not (= B2 tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat B2) C))) B2) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B2))))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B2 tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int B2) C))) B2) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B2))))) (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (not (= B2 tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat C) B2))) B2) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B2))))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B2 tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int C) B2))) B2) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B2))))) (forall ((M2 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 M2) N2)) (and (@ _let_1 M2) (@ _let_1 N2))))) (forall ((M2 tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M2) K)) (@ (@ tptp.times_times_nat N2) K)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_eq_nat M2) N2)))) (forall ((N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat M2) N2)) N2) M2))) (forall ((N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N2) M2)) N2) M2))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_times_nat B2) C))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_times_int B2) C))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_times_real B2) C))))) (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_times_complex B2) C))))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.times_7803423173614009249d_enat A))) (= (@ (@ tptp.times_7803423173614009249d_enat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_7803423173614009249d_enat B2) C))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_times_nat B2) C))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_times_int B2) C))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_times_real B2) C))))) (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_times_complex B2) C))))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.times_7803423173614009249d_enat A))) (= (@ (@ tptp.times_7803423173614009249d_enat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_7803423173614009249d_enat B2) C))))) (= tptp.times_times_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.times_times_nat B3) A3))) (= tptp.times_times_int (lambda ((A3 tptp.int) (B3 tptp.int)) (@ (@ tptp.times_times_int B3) A3))) (= tptp.times_times_real (lambda ((A3 tptp.real) (B3 tptp.real)) (@ (@ tptp.times_times_real B3) A3))) (= tptp.times_times_complex (lambda ((A3 tptp.complex) (B3 tptp.complex)) (@ (@ tptp.times_times_complex B3) A3))) (= tptp.times_7803423173614009249d_enat (lambda ((A3 tptp.extended_enat) (B3 tptp.extended_enat)) (@ (@ tptp.times_7803423173614009249d_enat B3) A3))) (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat B2))) (let ((_let_2 (@ tptp.times_times_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int B2))) (let ((_let_2 (@ tptp.times_times_int A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real B2))) (let ((_let_2 (@ tptp.times_times_real A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((B2 tptp.complex) (A tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex B2))) (let ((_let_2 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((B2 tptp.extended_enat) (A tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.times_7803423173614009249d_enat B2))) (let ((_let_2 (@ tptp.times_7803423173614009249d_enat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((X21 Bool) (X222 Bool)) (= (@ tptp.size_size_VEBT_VEBT (@ (@ tptp.vEBT_Leaf X21) X222)) tptp.zero_zero_nat)) (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (=> (not (= C tptp.zero_zero_nat)) (= (= (@ (@ tptp.times_times_nat A) C) (@ (@ tptp.times_times_nat B2) C)) (= A B2)))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (=> (not (= C tptp.zero_zero_int)) (= (= (@ (@ tptp.times_times_int A) C) (@ (@ tptp.times_times_int B2) C)) (= A B2)))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (= (@ (@ tptp.times_times_real A) C) (@ (@ tptp.times_times_real B2) C)) (= A B2)))) (forall ((C tptp.complex) (A tptp.complex) (B2 tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (= (@ (@ tptp.times_times_complex A) C) (@ (@ tptp.times_times_complex B2) C)) (= A B2)))) (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (not (= C tptp.zero_zero_nat)) (= (= (@ _let_1 A) (@ _let_1 B2)) (= A B2))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (not (= C tptp.zero_zero_int)) (= (= (@ _let_1 A) (@ _let_1 B2)) (= A B2))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (not (= C tptp.zero_zero_real)) (= (= (@ _let_1 A) (@ _let_1 B2)) (= A B2))))) (forall ((C tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C))) (=> (not (= C tptp.zero_zero_complex)) (= (= (@ _let_1 A) (@ _let_1 B2)) (= A B2))))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (not (= B2 tptp.zero_zero_nat)) (not (= (@ (@ tptp.times_times_nat A) B2) tptp.zero_zero_nat))))) (forall ((A tptp.int) (B2 tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (not (= B2 tptp.zero_zero_int)) (not (= (@ (@ tptp.times_times_int A) B2) tptp.zero_zero_int))))) (forall ((A tptp.real) (B2 tptp.real)) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B2 tptp.zero_zero_real)) (not (= (@ (@ tptp.times_times_real A) B2) tptp.zero_zero_real))))) (forall ((A tptp.complex) (B2 tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B2 tptp.zero_zero_complex)) (not (= (@ (@ tptp.times_times_complex A) B2) tptp.zero_zero_complex))))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (=> (not (= A tptp.zero_z5237406670263579293d_enat)) (=> (not (= B2 tptp.zero_z5237406670263579293d_enat)) (not (= (@ (@ tptp.times_7803423173614009249d_enat A) B2) tptp.zero_z5237406670263579293d_enat))))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (= (@ (@ tptp.times_times_nat A) B2) tptp.zero_zero_nat) (or (= A tptp.zero_zero_nat) (= B2 tptp.zero_zero_nat)))) (forall ((A tptp.int) (B2 tptp.int)) (=> (= (@ (@ tptp.times_times_int A) B2) tptp.zero_zero_int) (or (= A tptp.zero_zero_int) (= B2 tptp.zero_zero_int)))) (forall ((A tptp.real) (B2 tptp.real)) (=> (= (@ (@ tptp.times_times_real A) B2) tptp.zero_zero_real) (or (= A tptp.zero_zero_real) (= B2 tptp.zero_zero_real)))) (forall ((A tptp.complex) (B2 tptp.complex)) (=> (= (@ (@ tptp.times_times_complex A) B2) tptp.zero_zero_complex) (or (= A tptp.zero_zero_complex) (= B2 tptp.zero_zero_complex)))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (=> (= (@ (@ tptp.times_7803423173614009249d_enat A) B2) tptp.zero_z5237406670263579293d_enat) (or (= A tptp.zero_z5237406670263579293d_enat) (= B2 tptp.zero_z5237406670263579293d_enat)))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (not (= (@ (@ tptp.times_times_nat A) B2) tptp.zero_zero_nat)) (and (not (= A tptp.zero_zero_nat)) (not (= B2 tptp.zero_zero_nat))))) (forall ((A tptp.int) (B2 tptp.int)) (=> (not (= (@ (@ tptp.times_times_int A) B2) tptp.zero_zero_int)) (and (not (= A tptp.zero_zero_int)) (not (= B2 tptp.zero_zero_int))))) (forall ((A tptp.real) (B2 tptp.real)) (=> (not (= (@ (@ tptp.times_times_real A) B2) tptp.zero_zero_real)) (and (not (= A tptp.zero_zero_real)) (not (= B2 tptp.zero_zero_real))))) (forall ((A tptp.complex) (B2 tptp.complex)) (=> (not (= (@ (@ tptp.times_times_complex A) B2) tptp.zero_zero_complex)) (and (not (= A tptp.zero_zero_complex)) (not (= B2 tptp.zero_zero_complex))))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (=> (not (= (@ (@ tptp.times_7803423173614009249d_enat A) B2) tptp.zero_z5237406670263579293d_enat)) (and (not (= A tptp.zero_z5237406670263579293d_enat)) (not (= B2 tptp.zero_z5237406670263579293d_enat))))) (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)) (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)) (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A) A)) (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.one_one_complex) A) A)) (forall ((A tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat tptp.one_on7984719198319812577d_enat) A) 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.real)) (= (@ (@ tptp.times_times_real A) tptp.one_one_real) A)) (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.one_one_complex) A)) (forall ((A tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat A) tptp.one_on7984719198319812577d_enat) A)) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat B2))) (let ((_let_2 (@ tptp.times_times_nat A))) (= (and (not (= A B2)) (not (= C D))) (not (= (@ (@ tptp.plus_plus_nat (@ _let_2 C)) (@ _let_1 D)) (@ (@ tptp.plus_plus_nat (@ _let_2 D)) (@ _let_1 C)))))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.times_times_int B2))) (let ((_let_2 (@ tptp.times_times_int A))) (= (and (not (= A B2)) (not (= C D))) (not (= (@ (@ tptp.plus_plus_int (@ _let_2 C)) (@ _let_1 D)) (@ (@ tptp.plus_plus_int (@ _let_2 D)) (@ _let_1 C)))))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.times_times_real B2))) (let ((_let_2 (@ tptp.times_times_real A))) (= (and (not (= A B2)) (not (= C D))) (not (= (@ (@ tptp.plus_plus_real (@ _let_2 C)) (@ _let_1 D)) (@ (@ tptp.plus_plus_real (@ _let_2 D)) (@ _let_1 C)))))))) (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex) (D tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex B2))) (let ((_let_2 (@ tptp.times_times_complex A))) (= (and (not (= A B2)) (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 ((W2 tptp.nat) (Y tptp.nat) (X tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat X))) (let ((_let_2 (@ tptp.times_times_nat W2))) (= (= (@ (@ tptp.plus_plus_nat (@ _let_2 Y)) (@ _let_1 Z3)) (@ (@ tptp.plus_plus_nat (@ _let_2 Z3)) (@ _let_1 Y))) (or (= W2 X) (= Y Z3)))))) (forall ((W2 tptp.int) (Y tptp.int) (X tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int X))) (let ((_let_2 (@ tptp.times_times_int W2))) (= (= (@ (@ tptp.plus_plus_int (@ _let_2 Y)) (@ _let_1 Z3)) (@ (@ tptp.plus_plus_int (@ _let_2 Z3)) (@ _let_1 Y))) (or (= W2 X) (= Y Z3)))))) (forall ((W2 tptp.real) (Y tptp.real) (X tptp.real) (Z3 tptp.real)) (let ((_let_1 (@ tptp.times_times_real X))) (let ((_let_2 (@ tptp.times_times_real W2))) (= (= (@ (@ tptp.plus_plus_real (@ _let_2 Y)) (@ _let_1 Z3)) (@ (@ tptp.plus_plus_real (@ _let_2 Z3)) (@ _let_1 Y))) (or (= W2 X) (= Y Z3)))))) (forall ((W2 tptp.complex) (Y tptp.complex) (X tptp.complex) (Z3 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex X))) (let ((_let_2 (@ tptp.times_times_complex W2))) (= (= (@ (@ tptp.plus_plus_complex (@ _let_2 Y)) (@ _let_1 Z3)) (@ (@ tptp.plus_plus_complex (@ _let_2 Z3)) (@ _let_1 Y))) (or (= W2 X) (= Y Z3)))))) (forall ((A tptp.nat) (E2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) E2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B2) E2)) C)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B2)) E2)) C))) (forall ((A tptp.int) (E2 tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) E2)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B2)) E2)) C))) (forall ((A tptp.real) (E2 tptp.real) (B2 tptp.real) (C tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B2) E2)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B2)) E2)) C))) (forall ((A tptp.complex) (E2 tptp.complex) (B2 tptp.complex) (C tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) E2)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex B2) E2)) C)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B2)) E2)) C))) (forall ((A tptp.extended_enat) (E2 tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat)) (= (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.times_7803423173614009249d_enat A) E2)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.times_7803423173614009249d_enat B2) E2)) C)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.times_7803423173614009249d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) B2)) E2)) C))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B2)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B2) C)))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B2)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) C)))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B2)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) C)))) (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B2)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B2) C)))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) B2)) C) (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.times_7803423173614009249d_enat A) C)) (@ (@ tptp.times_7803423173614009249d_enat B2) C)))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B2) C)) (@ (@ tptp.plus_plus_nat (@ _let_1 B2)) (@ _let_1 C))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B2) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B2)) (@ _let_1 C))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B2) C)) (@ (@ tptp.plus_plus_real (@ _let_1 B2)) (@ _let_1 C))))) (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B2) C)) (@ (@ tptp.plus_plus_complex (@ _let_1 B2)) (@ _let_1 C))))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.times_7803423173614009249d_enat A))) (= (@ _let_1 (@ (@ tptp.plus_p3455044024723400733d_enat B2) C)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ _let_1 B2)) (@ _let_1 C))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B2)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B2) C)))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B2)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) C)))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B2)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) C)))) (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B2)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B2) C)))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) B2)) C) (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.times_7803423173614009249d_enat A) C)) (@ (@ tptp.times_7803423173614009249d_enat B2) C)))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B2) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B2)) (@ _let_1 C))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B2) C)) (@ (@ tptp.plus_plus_real (@ _let_1 B2)) (@ _let_1 C))))) (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B2) C)) (@ (@ tptp.plus_plus_complex (@ _let_1 B2)) (@ _let_1 C))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B2)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) C)))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B2)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) C)))) (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B2)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B2) C)))) (forall ((X tptp.complex) (Y tptp.complex) (Z3 tptp.complex) (W2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide1717551699836669952omplex Z3) W2)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex X) Z3)) (@ (@ tptp.times_times_complex Y) W2)))) (forall ((X tptp.real) (Y tptp.real) (Z3 tptp.real) (W2 tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real Z3) W2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real X) Z3)) (@ (@ tptp.times_times_real Y) W2)))) (forall ((X tptp.complex) (Y tptp.complex) (Z3 tptp.complex) (W2 tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide1717551699836669952omplex Z3) W2)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex X) W2)) (@ (@ tptp.times_times_complex Y) Z3)))) (forall ((X tptp.real) (Y tptp.real) (Z3 tptp.real) (W2 tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real Z3) W2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real X) W2)) (@ (@ tptp.times_times_real Y) Z3)))) (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (= (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_times_complex C) B2))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (= (@ (@ tptp.divide_divide_real (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_times_real C) B2))))) (forall ((K tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (= (@ _let_1 M2) (@ _let_1 N2)) (= M2 N2)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) N2) tptp.zero_zero_nat)) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I)) (@ _let_1 J))))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I) K)) (@ (@ tptp.times_times_nat J) K)))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ (@ tptp.ord_less_eq_nat K) L) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I) K)) (@ (@ tptp.times_times_nat J) L))))) (forall ((M2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat M2) (@ (@ tptp.times_times_nat M2) M2))) (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M2))) (@ (@ tptp.ord_less_eq_nat M2) (@ _let_1 (@ _let_1 M2))))) (forall ((K tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N2)) (@ (@ tptp.plus_plus_nat (@ _let_1 M2)) (@ _let_1 N2))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat M2) N2)) K) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat M2) K)) (@ (@ tptp.times_times_nat N2) K)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) N2) N2)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.times_times_nat N2) tptp.one_one_nat) N2)) (forall ((Uu Bool) (Uv Bool) (Uw tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.vEBT_Leaf Uu) Uv)) Uw))) (@ tptp.vEBT_VEBT_minNull _let_211) (forall ((Uv Bool)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf true) Uv)))) (forall ((Uu Bool)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf Uu) true)))) (forall ((M2 tptp.nat) (N2 tptp.nat) (Q3 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.ord_max_nat M2) N2)) Q3) (@ (@ tptp.ord_max_nat (@ (@ tptp.times_times_nat M2) Q3)) (@ (@ tptp.times_times_nat N2) Q3)))) (forall ((M2 tptp.nat) (N2 tptp.nat) (Q3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M2))) (= (@ _let_1 (@ (@ tptp.ord_max_nat N2) Q3)) (@ (@ tptp.ord_max_nat (@ _let_1 N2)) (@ _let_1 Q3))))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat) (D tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B2) (=> (@ (@ tptp.ord_le2932123472753598470d_enat C) D) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.times_7803423173614009249d_enat A) C)) (@ (@ tptp.times_7803423173614009249d_enat B2) D)))))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_eq_real C) D) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) D)))))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ tptp.ord_less_eq_nat C) D) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B2) D)))))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (@ (@ tptp.ord_less_eq_int C) D) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) D)))))))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat) (D tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B2) (=> (@ (@ tptp.ord_le2932123472753598470d_enat C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.times_7803423173614009249d_enat A) C)) (@ (@ tptp.times_7803423173614009249d_enat B2) D)))))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_eq_real C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) D)))))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ tptp.ord_less_eq_nat C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B2) D)))))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (@ (@ tptp.ord_less_eq_int C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) D)))))))) (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) A))) (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) A))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (@ _let_1 A) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real))) (@ _let_1 (@ (@ tptp.times_times_real A) B2))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (@ _let_1 A) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int))) (@ _let_1 (@ (@ tptp.times_times_int A) B2))))) (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_eq_real B2) A) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B2)))))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int B2) A) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B2)))))) (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B2))))) (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) B2))))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.times_7803423173614009249d_enat C))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B2) (=> (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) C) (@ (@ tptp.ord_le2932123472753598470d_enat (@ _let_1 A)) (@ _let_1 B2)))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B2)))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B2)))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B2)))))) (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B2) A) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) C))))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B2) A) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) C))))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B2) (=> (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) C) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.times_7803423173614009249d_enat A) C)) (@ (@ tptp.times_7803423173614009249d_enat B2) C))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) C))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B2) C))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) C))))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B2)) tptp.zero_zero_real) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ _let_1 B2)))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B2)) tptp.zero_zero_int) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (@ _let_1 B2)))))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ _let_1 B2))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B2)) tptp.zero_zero_real)))) (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_nat B2) tptp.zero_zero_nat)) (and (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (@ _let_1 B2))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) B2)) tptp.zero_zero_nat)))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (@ _let_1 B2))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B2)) tptp.zero_zero_int)))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_real A) B2)))))) (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_nat A) B2)))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_int A) B2)))))) (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B2)) tptp.zero_zero_real)))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat B2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) B2)) tptp.zero_zero_nat)))) (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B2)) tptp.zero_zero_int)))) (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B2)) tptp.zero_zero_real)))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) B2)) tptp.zero_zero_nat)))) (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B2)) tptp.zero_zero_int)))) (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real B2) A)) tptp.zero_zero_real)))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat B2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat B2) A)) tptp.zero_zero_nat)))) (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int B2) A)) tptp.zero_zero_int)))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.times_times_real A) B2)) (or (and (@ _let_1 A) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real)))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.times_times_int A) B2)) (or (and (@ _let_1 A) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int)))))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.times_7803423173614009249d_enat C))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B2) (=> (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) C) (@ (@ tptp.ord_le2932123472753598470d_enat (@ _let_1 A)) (@ _let_1 B2)))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B2)))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B2)))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B2)))))) (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real B2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B2))))) (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) B2))))) (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) A)) tptp.zero_zero_real))) (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) A)) tptp.zero_zero_int))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) B2)) tptp.zero_zero_real) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_real B2) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ _let_1 B2)))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) B2)) tptp.zero_zero_int) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (@ _let_1 B2)))))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) B2)) tptp.zero_zero_nat)))) (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B2) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) B2)) tptp.zero_zero_real)))) (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) B2)) tptp.zero_zero_int)))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat B2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) B2)) tptp.zero_zero_nat)))) (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real B2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) B2)) tptp.zero_zero_real)))) (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) B2)) tptp.zero_zero_int)))) (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_nat A) B2)))))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_real A) B2)))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_int A) B2)))))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat B2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat B2) A)) tptp.zero_zero_nat)))) (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real B2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real B2) A)) tptp.zero_zero_real)))) (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int B2) A)) tptp.zero_zero_int)))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.times_times_real A) B2)) (or (and (@ _let_1 A) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B2) tptp.zero_zero_real)))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.times_times_int A) B2)) (or (and (@ _let_1 A) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int)))))) (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 (@ (@ tptp.times_times_nat A) B2)) (=> (@ _let_1 A) (@ _let_1 B2))))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ (@ tptp.times_times_real A) B2)) (=> (@ _let_1 A) (@ _let_1 B2))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.times_times_int A) B2)) (=> (@ _let_1 A) (@ _let_1 B2))))) (forall ((B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 (@ (@ tptp.times_times_nat B2) A)) (=> (@ _let_1 A) (@ _let_1 B2))))) (forall ((B2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ (@ tptp.times_times_real B2) A)) (=> (@ _let_1 A) (@ _let_1 B2))))) (forall ((B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.times_times_int B2) A)) (=> (@ _let_1 A) (@ _let_1 B2))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_real B2) A))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_int B2) A))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_real A) B2))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_int A) B2))))) (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real B2) A) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B2)))))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int B2) A) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B2)))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat A) B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B2)))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B2)))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int A) B2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B2)))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B2)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B2)) (and (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B2) A)))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B2)) (or (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B2)) (and (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B2) A)))))) (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real B2) A) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) C))))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int B2) A) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) C))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B2) C))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) C))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) C))))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) C)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B2)) (and (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B2) A))))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) C)) (or (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B2)) (and (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B2) A))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat A) B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B2)))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B2)))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int A) B2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B2)))))) (forall ((R2 tptp.nat) (A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat R2))) (=> (not (= R2 tptp.zero_zero_nat)) (=> (and (= A B2) (not (= C D))) (not (= (@ (@ tptp.plus_plus_nat A) (@ _let_1 C)) (@ (@ tptp.plus_plus_nat B2) (@ _let_1 D)))))))) (forall ((R2 tptp.int) (A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.times_times_int R2))) (=> (not (= R2 tptp.zero_zero_int)) (=> (and (= A B2) (not (= C D))) (not (= (@ (@ tptp.plus_plus_int A) (@ _let_1 C)) (@ (@ tptp.plus_plus_int B2) (@ _let_1 D)))))))) (forall ((R2 tptp.real) (A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.times_times_real R2))) (=> (not (= R2 tptp.zero_zero_real)) (=> (and (= A B2) (not (= C D))) (not (= (@ (@ tptp.plus_plus_real A) (@ _let_1 C)) (@ (@ tptp.plus_plus_real B2) (@ _let_1 D)))))))) (forall ((R2 tptp.complex) (A tptp.complex) (B2 tptp.complex) (C tptp.complex) (D tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex R2))) (=> (not (= R2 tptp.zero_zero_complex)) (=> (and (= A B2) (not (= C D))) (not (= (@ (@ tptp.plus_plus_complex A) (@ _let_1 C)) (@ (@ tptp.plus_plus_complex B2) (@ _let_1 D)))))))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 M2) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.times_times_nat M2) N2)))))) (forall ((M2 tptp.real) (N2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 M2) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.times_times_real M2) N2)))))) (forall ((M2 tptp.int) (N2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 M2) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.times_times_int M2) N2)))))) (forall ((Y tptp.complex) (Z3 tptp.complex) (X tptp.complex) (W2 tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z3 tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex X) Y) (@ (@ tptp.divide1717551699836669952omplex W2) Z3)) (= (@ (@ tptp.times_times_complex X) Z3) (@ (@ tptp.times_times_complex W2) Y)))))) (forall ((Y tptp.real) (Z3 tptp.real) (X tptp.real) (W2 tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z3 tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real X) Y) (@ (@ tptp.divide_divide_real W2) Z3)) (= (@ (@ tptp.times_times_real X) Z3) (@ (@ tptp.times_times_real W2) Y)))))) (forall ((B2 tptp.complex) (C tptp.complex) (A tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B2) C) A) (and (=> (not _let_1) (= B2 (@ (@ tptp.times_times_complex A) C))) (=> _let_1 (= A tptp.zero_zero_complex)))))) (forall ((B2 tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B2) C) A) (and (=> (not _let_1) (= B2 (@ (@ tptp.times_times_real A) C))) (=> _let_1 (= A tptp.zero_zero_real)))))) (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= A (@ (@ tptp.divide1717551699836669952omplex B2) C)) (and (=> (not _let_1) (= (@ (@ tptp.times_times_complex A) C) B2)) (=> _let_1 (= A tptp.zero_zero_complex)))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= A (@ (@ tptp.divide_divide_real B2) C)) (and (=> (not _let_1) (= (@ (@ tptp.times_times_real A) C) B2)) (=> _let_1 (= A tptp.zero_zero_real)))))) (forall ((C tptp.complex) (B2 tptp.complex) (A tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (=> (= B2 (@ (@ tptp.times_times_complex A) C)) (= (@ (@ tptp.divide1717551699836669952omplex B2) C) A)))) (forall ((C tptp.real) (B2 tptp.real) (A tptp.real)) (=> (not (= C tptp.zero_zero_real)) (=> (= B2 (@ (@ tptp.times_times_real A) C)) (= (@ (@ tptp.divide_divide_real B2) C) A)))) (forall ((C tptp.complex) (A tptp.complex) (B2 tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (=> (= (@ (@ tptp.times_times_complex A) C) B2) (= A (@ (@ tptp.divide1717551699836669952omplex B2) C))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (not (= C tptp.zero_zero_real)) (=> (= (@ (@ tptp.times_times_real A) C) B2) (= A (@ (@ tptp.divide_divide_real B2) C))))) (forall ((C tptp.complex) (B2 tptp.complex) (A tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex B2) C) A) (= B2 (@ (@ tptp.times_times_complex A) C))))) (forall ((C tptp.real) (B2 tptp.real) (A tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real B2) C) A) (= B2 (@ (@ tptp.times_times_real A) C))))) (forall ((C tptp.complex) (A tptp.complex) (B2 tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (= A (@ (@ tptp.divide1717551699836669952omplex B2) C)) (= (@ (@ tptp.times_times_complex A) C) B2)))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (= A (@ (@ tptp.divide_divide_real B2) C)) (= (@ (@ tptp.times_times_real A) C) B2)))) (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.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.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.extended_enat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8040749407984259932d_enat A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_7803423173614009249d_enat 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 (@ _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.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.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.extended_enat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8040749407984259932d_enat A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_7803423173614009249d_enat (@ _let_1 N2)) A)))) (forall ((K tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M2)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M2) N2)))) (forall ((A tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N2)) (@ (@ tptp.times_times_nat (@ _let_1 M2)) (@ _let_1 N2))))) (forall ((A tptp.int) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N2)) (@ (@ tptp.times_times_int (@ _let_1 M2)) (@ _let_1 N2))))) (forall ((A tptp.real) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N2)) (@ (@ tptp.times_times_real (@ _let_1 M2)) (@ _let_1 N2))))) (forall ((A tptp.complex) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N2)) (@ (@ tptp.times_times_complex (@ _let_1 M2)) (@ _let_1 N2))))) (forall ((A tptp.extended_enat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8040749407984259932d_enat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N2)) (@ (@ tptp.times_7803423173614009249d_enat (@ _let_1 M2)) (@ _let_1 N2))))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat I) K)) (@ (@ tptp.times_times_nat J) K))))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat (@ _let_1 I)) (@ _let_1 J)))))) (= (@ tptp.vEBT_vebt_buildup tptp.zero_zero_nat) _let_211) (forall ((K tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M2)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M2) N2)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.suc M2)) N2) (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.times_times_nat M2) N2)))) (forall ((Uu Bool) (Uv Bool) (D tptp.nat)) (= (@ (@ tptp.vEBT_VEBT_valid (@ (@ tptp.vEBT_Leaf Uu) Uv)) D) (= D tptp.one_one_nat))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (= M2 (@ (@ tptp.times_times_nat M2) N2)) (or (= N2 tptp.one_one_nat) (= M2 tptp.zero_zero_nat)))) (forall ((M2 tptp.nat) (I tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.times_times_nat I) N2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M2) N2)) I))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M2) N2)) N2)) M2)) (forall ((N2 tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat N2) (@ (@ tptp.divide_divide_nat M2) N2))) M2)) (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 ((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.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.extended_enat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_8040749407984259932d_enat A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N2))) (@ (@ tptp.times_7803423173614009249d_enat A) (@ (@ tptp.power_8040749407984259932d_enat (@ _let_2 N2)) _let_1)))))) (forall ((M2 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 M2)) (@ _let_1 N2))))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (not (= (@ _let_1 M2) (@ tptp.suc (@ _let_1 N2)))))) (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A4 Bool) (B4 Bool) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A4) B4)) X5)))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT) (Ux2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2)) Ux2)))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList3) S3)) X5)))))))) (forall ((A Bool) (B2 Bool)) (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_Leaf A) B2)) (@ tptp.suc tptp.zero_zero_nat))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.ord_less_eq_real C) D) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) D))))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (=> (@ (@ tptp.ord_less_eq_nat C) D) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B2) D))))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A) B2) (=> (@ (@ tptp.ord_less_eq_int C) D) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) D))))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_real C) D) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) D))))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ tptp.ord_less_nat C) D) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B2) D))))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (@ (@ tptp.ord_less_int C) D) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) D))))))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) C)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B2)))) (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B2) C)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat A) B2)))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) C)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) B2)))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B2))))) (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat A) B2))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B2)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) B2))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_real A) B2))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_int A) B2))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_real B2) A))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_int B2) A))))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) C)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B2)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B2) A))))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) C)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B2)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B2) A))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.ord_less_real C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) D)))))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat A) B2) (=> (@ (@ tptp.ord_less_nat C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B2) D)))))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int A) B2) (=> (@ (@ tptp.ord_less_int C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) D)))))))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) C)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B2)))) (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B2) C)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat A) B2)))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) C)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B2)))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B2)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B2)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B2) A)))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B2)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B2)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B2) A)))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.ord_less_real C) D) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) D))))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (=> (@ (@ tptp.ord_less_nat C) D) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B2) D))))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A) B2) (=> (@ (@ tptp.ord_less_int C) D) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) D))))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B2)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B2))))) (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B2)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat A) B2))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B2))))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) C)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B2)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B2) A))))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) C)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) B2)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B2) A))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B2)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B2)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B2) A)))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B2)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) B2)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B2) A)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Y) X)) X)))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int Y) X)) X)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X) Y)) X)))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X) Y)) X)))))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) tptp.one_on7984719198319812577d_enat) (=> (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) B2) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B2) tptp.one_on7984719198319812577d_enat) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.times_7803423173614009249d_enat A) B2)) tptp.one_on7984719198319812577d_enat))))) (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B2) (=> (@ (@ tptp.ord_less_eq_real B2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B2)) tptp.one_one_real))))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B2) (=> (@ (@ tptp.ord_less_eq_nat B2) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) B2)) tptp.one_one_nat))))) (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_eq_int B2) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B2)) tptp.one_one_int))))) (forall ((C tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat C) tptp.one_on7984719198319812577d_enat) (=> (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) A) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.times_7803423173614009249d_enat A) C)) A)))) (forall ((C tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) A)))) (forall ((C tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) tptp.one_one_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) A)))) (forall ((C tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.one_one_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) A)))) (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y))) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real)))) (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y))) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))) (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y)))) (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y)))) (forall ((X tptp.nat) (A Bool) (B2 Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A))) (let ((_let_2 (@ _let_1 B2))) (let ((_let_3 (@ (@ tptp.vEBT_vebt_insert _let_2) X))) (let ((_let_4 (= X tptp.one_one_nat))) (let ((_let_5 (= X tptp.zero_zero_nat))) (and (=> _let_5 (= _let_3 (@ (@ tptp.vEBT_Leaf true) B2))) (=> (not _let_5) (and (=> _let_4 (= _let_3 (@ _let_1 true))) (=> (not _let_4) (= _let_3 _let_2))))))))))) (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y))) (or (not (= X tptp.zero_zero_real)) (not (= Y tptp.zero_zero_real))))) (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y))) (or (not (= X tptp.zero_zero_int)) (not (= Y tptp.zero_zero_int))))) (forall ((X tptp.real) (Y tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y))) tptp.zero_zero_real))) (forall ((X tptp.int) (Y tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y))) tptp.zero_zero_int))) (forall ((B2 tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ _let_1 C))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B2) C)) A) (and (=> _let_4 (@ (@ tptp.ord_less_real B2) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_real _let_3) B2)) (=> (not _let_2) (@ _let_1 A))))))))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_1 (@ (@ tptp.divide_divide_real B2) C)) (and (=> _let_4 (@ (@ tptp.ord_less_real _let_3) B2)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_real B2) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_real))))))))))) (forall ((C tptp.real) (B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B2) C)) A) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) B2)))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.divide_divide_real B2) C)) (@ (@ tptp.ord_less_real B2) (@ (@ tptp.times_times_real A) C))))) (forall ((C tptp.real) (B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B2) C)) A) (@ (@ tptp.ord_less_real B2) (@ (@ tptp.times_times_real A) C))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.divide_divide_real B2) C)) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) B2)))) (forall ((Y tptp.real) (X tptp.real) (Z3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.times_times_real Z3) Y)) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y)) Z3)))) (forall ((Y tptp.real) (Z3 tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real Z3) Y)) X) (@ (@ tptp.ord_less_real Z3) (@ (@ tptp.divide_divide_real X) Y))))) (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real B2) A) (=> (@ _let_2 C) (=> (@ _let_2 (@ (@ tptp.times_times_real A) B2)) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B2)))))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B2)) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B2))))))) (= (@ tptp.vEBT_vebt_buildup _let_80) _let_211) (forall ((B2 tptp.complex) (C tptp.complex) (W2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W2))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B2) C) _let_1) (and (=> (not _let_2) (= B2 (@ (@ tptp.times_times_complex _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))) (forall ((B2 tptp.real) (C tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B2) C) _let_1) (and (=> (not _let_2) (= B2 (@ (@ tptp.times_times_real _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))) (forall ((W2 tptp.num) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W2))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= _let_1 (@ (@ tptp.divide1717551699836669952omplex B2) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex _let_1) C) B2)) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))) (forall ((W2 tptp.num) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= _let_1 (@ (@ tptp.divide_divide_real B2) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real _let_1) C) B2)) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))) (forall ((A Bool) (B2 Bool) (X tptp.nat)) (let ((_let_1 (= X tptp.one_one_nat))) (let ((_let_2 (= X tptp.zero_zero_nat))) (= (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.vEBT_Leaf A) B2)) X) (and (=> _let_2 A) (=> (not _let_2) (and (=> _let_1 B2) _let_1))))))) (forall ((Z3 tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z3 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X) Z3)) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.times_times_complex Y) Z3))) Z3)))) (forall ((Z3 tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z3 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X) Z3)) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real Y) Z3))) Z3)))) (forall ((Z3 tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z3 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.divide1717551699836669952omplex Y) Z3)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex X) Z3)) Y)) Z3)))) (forall ((Z3 tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z3 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real X) (@ (@ tptp.divide_divide_real Y) Z3)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) Z3)) Y)) Z3)))) (forall ((Y tptp.complex) (Z3 tptp.complex) (X tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex Z3) (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.times_times_complex Z3) Y))) Y)))) (forall ((Y tptp.real) (Z3 tptp.real) (X tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real Z3) (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real Z3) Y))) Y)))) (forall ((Y tptp.complex) (X tptp.complex) (Z3 tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X) Y)) Z3) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.times_times_complex Z3) Y))) Y)))) (forall ((Y tptp.real) (X tptp.real) (Z3 tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X) Y)) Z3) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real Z3) Y))) Y)))) (forall ((Y tptp.complex) (Z3 tptp.complex) (X tptp.complex) (W2 tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z3 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide1717551699836669952omplex W2) Z3)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex X) Z3)) (@ (@ tptp.times_times_complex W2) Y))) (@ (@ tptp.times_times_complex Y) Z3)))))) (forall ((Y tptp.real) (Z3 tptp.real) (X tptp.real) (W2 tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z3 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real W2) Z3)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) Z3)) (@ (@ tptp.times_times_real W2) Y))) (@ (@ tptp.times_times_real Y) Z3)))))) (forall ((Z3 tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.divide1717551699836669952omplex B2) Z3)))) (let ((_let_2 (= Z3 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) Z3)) B2)) Z3))))))) (forall ((Z3 tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real A) (@ (@ tptp.divide_divide_real B2) Z3)))) (let ((_let_2 (= Z3 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) Z3)) B2)) Z3))))))) (forall ((Z3 tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex A) Z3)) B2))) (let ((_let_2 (= Z3 tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 B2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.times_times_complex B2) Z3))) Z3))))))) (forall ((Z3 tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real A) Z3)) B2))) (let ((_let_2 (= Z3 tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 B2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) (@ (@ tptp.times_times_real B2) Z3))) Z3))))))) (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.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.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_times_int A) (@ (@ tptp.power_power_int A) N2)))))) (forall ((A tptp.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.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.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 Bool) (B2 Bool) (X tptp.nat)) (let ((_let_1 (= X tptp.one_one_nat))) (let ((_let_2 (= X tptp.zero_zero_nat))) (= (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.vEBT_Leaf A) B2)) X) (and (=> _let_2 A) (=> (not _let_2) (and (=> _let_1 B2) _let_1))))))) (forall ((N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)))) (=> (@ _let_1 N2) (=> (@ _let_1 M2) (@ _let_1 (@ (@ tptp.times_times_nat M2) N2)))))) (forall ((N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M2) (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat M2) N2))))) (forall ((N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M2) (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat N2) M2))))) (forall ((X tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull X)) (=> (forall ((Uv2 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf true) Uv2)))) (=> (forall ((Uu2 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf Uu2) true)))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc2))))))))) (forall ((Q3 tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q3) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M2) Q3)) N2) (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.times_times_nat N2) Q3))))) (forall ((X tptp.vEBT_VEBT)) (=> (@ tptp.vEBT_VEBT_minNull X) (=> (not (= X (@ (@ tptp.vEBT_Leaf false) false))) (not (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2)))))))) (forall ((A tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (exists ((R3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (= (@ (@ tptp.power_power_real R3) (@ tptp.suc N2)) A))))) (forall ((X tptp.real) (Y tptp.real)) (=> (forall ((Z tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (=> (@ (@ tptp.ord_less_real Z) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Z) X)) Y)))) (@ (@ tptp.ord_less_eq_real X) 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.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) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real C) (@ (@ tptp.times_times_real B2) C)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real tptp.one_one_real) B2)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B2) tptp.one_one_real))))) (forall ((C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int C) (@ (@ tptp.times_times_int B2) C)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int tptp.one_one_int) B2)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B2) tptp.one_one_int))))) (forall ((C tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real C) A)) C) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) tptp.one_one_real)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.one_one_real) A))))) (forall ((C tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int C) A)) C) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) A))))) (forall ((C tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real C) (@ (@ tptp.times_times_real C) B2)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real tptp.one_one_real) B2)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B2) tptp.one_one_real))))) (forall ((C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int C) (@ (@ tptp.times_times_int C) B2)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int tptp.one_one_int) B2)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B2) tptp.one_one_int))))) (forall ((A tptp.real) (C tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) C) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A))))) (forall ((A tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) C) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A))))) (forall ((C tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real C) (@ (@ tptp.times_times_real B2) C)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) B2)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B2) tptp.one_one_real))))) (forall ((C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.times_times_int B2) C)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) B2)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B2) tptp.one_one_int))))) (forall ((C tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real C) A)) C) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A))))) (forall ((C tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int C) A)) C) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A))))) (forall ((C tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real C) (@ (@ tptp.times_times_real C) B2)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) B2)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B2) tptp.one_one_real))))) (forall ((C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.times_times_int C) B2)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) B2)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B2) tptp.one_one_int))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B2)) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B2))))))) (forall ((Y tptp.real) (Z3 tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Z3) Y)) X) (@ (@ tptp.ord_less_eq_real Z3) (@ (@ tptp.divide_divide_real X) Y))))) (forall ((Y tptp.real) (X tptp.real) (Z3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.times_times_real Z3) Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) Z3)))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.divide_divide_real B2) C)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) B2)))) (forall ((C tptp.real) (B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B2) C)) A) (@ (@ tptp.ord_less_eq_real B2) (@ (@ tptp.times_times_real A) C))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.divide_divide_real B2) C)) (@ (@ tptp.ord_less_eq_real B2) (@ (@ tptp.times_times_real A) C))))) (forall ((C tptp.real) (B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B2) C)) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) B2)))) (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (=> (@ (@ tptp.ord_less_eq_real B2) A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B2)) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B2))))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_1 (@ (@ tptp.divide_divide_real B2) C)) (and (=> _let_4 (@ (@ tptp.ord_less_eq_real _let_3) B2)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_real B2) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_real))))))))))) (forall ((B2 tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.times_times_real A) C))) (let ((_let_3 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B2) C)) A) (and (=> _let_3 (@ (@ tptp.ord_less_eq_real B2) _let_2)) (=> (not _let_3) (and (=> _let_1 (@ (@ tptp.ord_less_eq_real _let_2) B2)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A)))))))))) (forall ((X tptp.real) (A tptp.real) (Y tptp.real) (U tptp.real) (V tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real X) A) (=> (@ (@ tptp.ord_less_eq_real Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_real U) V) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real U) X)) (@ (@ tptp.times_times_real V) Y))) A)))))))) (forall ((X tptp.int) (A tptp.int) (Y tptp.int) (U tptp.int) (V tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int X) A) (=> (@ (@ tptp.ord_less_eq_int Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_int U) V) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U) X)) (@ (@ tptp.times_times_int V) Y))) A)))))))) (forall ((B2 tptp.real) (C tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ _let_2 C))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B2) C)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_real B2) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real _let_4) B2)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))) (forall ((W2 tptp.num) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (let ((_let_2 (@ tptp.ord_less_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B2) C)) (and (=> _let_5 (@ (@ tptp.ord_less_real _let_4) B2)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real B2) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))) (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.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.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 ((Z3 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) Z3) (@ (@ tptp.plus_plus_complex Z3) Z3))) (forall ((Z3 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z3) (@ (@ tptp.plus_plus_nat Z3) Z3))) (forall ((Z3 tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))) Z3) (@ (@ tptp.plus_p3455044024723400733d_enat Z3) Z3))) (forall ((Z3 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Z3) (@ (@ tptp.plus_plus_int Z3) Z3))) (forall ((Z3 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) Z3) (@ (@ tptp.plus_plus_real Z3) Z3))) (forall ((Z3 tptp.complex)) (= (@ (@ tptp.times_times_complex Z3) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_complex Z3) Z3))) (forall ((Z3 tptp.nat)) (= (@ (@ tptp.times_times_nat Z3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_nat Z3) Z3))) (forall ((Z3 tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat Z3) (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_p3455044024723400733d_enat Z3) Z3))) (forall ((Z3 tptp.int)) (= (@ (@ tptp.times_times_int Z3) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_int Z3) Z3))) (forall ((Z3 tptp.real)) (= (@ (@ tptp.times_times_real Z3) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real Z3) Z3))) (forall ((A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex A))) (= (@ _let_1 (@ _let_1 B2)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) A)) B2)))) (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ _let_1 (@ _let_1 B2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)) B2)))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat A))) (= (@ _let_1 (@ _let_1 B2)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))) A)) B2)))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ _let_1 (@ _let_1 B2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)) B2)))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ _let_1 (@ _let_1 B2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) A)) B2)))) (forall ((N2 tptp.nat) (Q3 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 Q3)) M2) (=> (@ (@ tptp.ord_less_nat M2) (@ _let_1 (@ tptp.suc Q3))) (= (@ (@ tptp.divide_divide_nat M2) N2) Q3))))) (forall ((Q3 tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q3) (= (@ (@ tptp.ord_less_eq_nat M2) (@ (@ tptp.divide_divide_nat N2) Q3)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M2) Q3)) N2)))) (forall ((P (-> tptp.nat Bool)) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (= N2 tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.divide_divide_nat M2) N2)) (and (=> _let_1 (@ P tptp.zero_zero_nat)) (=> (not _let_1) (forall ((I3 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J2) N2) (=> (= M2 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N2) I3)) J2)) (@ P I3))))))))) (forall ((N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M2) N2)) N2))))) (forall ((N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.times_times_nat N2) (@ (@ tptp.divide_divide_nat M2) N2)))))) (forall ((X tptp.vEBT_VEBT) (Y Bool)) (let ((_let_1 (not Y))) (=> (= (@ tptp.vEBT_VEBT_minNull X) Y) (=> (=> (= X (@ (@ tptp.vEBT_Leaf false) false)) _let_1) (=> (=> (exists ((Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf true) Uv2))) Y) (=> (=> (exists ((Uu2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) true))) Y) (=> (=> (exists ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2))) _let_1) (not (=> (exists ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc2))) Y))))))))) (forall ((X tptp.real) (A tptp.real) (Y tptp.real) (U tptp.real) (V tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real X) A) (=> (@ (@ tptp.ord_less_real Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_real U) V) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real U) X)) (@ (@ tptp.times_times_real V) Y))) A)))))))) (forall ((X tptp.int) (A tptp.int) (Y tptp.int) (U tptp.int) (V tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int X) A) (=> (@ (@ tptp.ord_less_int Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_int U) V) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U) X)) (@ (@ tptp.times_times_int V) Y))) A)))))))) (forall ((B2 tptp.real) (C tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B2) C)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_real B2) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_real _let_3) B2)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1))))))))))) (forall ((W2 tptp.num) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (let ((_let_2 (@ tptp.ord_less_eq_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B2) C)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_real _let_4) B2)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_real B2) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X)) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y) _let_2)))))) (forall ((P (-> tptp.nat Bool)) (M2 tptp.nat) (N2 tptp.nat)) (= (@ P (@ (@ tptp.divide_divide_nat M2) 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)) M2) (@ (@ tptp.ord_less_nat M2) (@ _let_1 (@ tptp.suc Q5))) (@ P Q5))))))) (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A4 Bool) (B4 Bool) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A4) B4)) X5)))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2)) X5)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2)) X5)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2)) X5)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList3) Summary2)) X5)))))))))) (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A4 Bool) (B4 Bool) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A4) B4)) X5)))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts2) S3)) X5)))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S3)) X5)))) (=> (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc (@ tptp.suc V2))) TreeList3) Summary2)) X5)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList3) Summary2)) X5)))))))))) (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (Uv2 Bool) (Uw2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) Uv2)) Uw2)))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT) (Uz2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2)) Uz2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2)) X5)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList3) Vc2)) X5)))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList3) Vd)) X5)))))))))) (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex X) Y)) _let_2) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex X) _let_2)) (@ (@ tptp.power_power_complex Y) _let_2))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X)) Y)))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat X) Y)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat X) _let_1)) (@ (@ tptp.power_power_nat Y) _let_1))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat _let_1) X)) Y))))) (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_8040749407984259932d_enat (@ (@ tptp.plus_p3455044024723400733d_enat X) Y)) _let_2) (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.power_8040749407984259932d_enat X) _let_2)) (@ (@ tptp.power_8040749407984259932d_enat Y) _let_2))) (@ (@ tptp.times_7803423173614009249d_enat (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat _let_1)) X)) Y)))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int X) Y)) _let_2) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_2)) (@ (@ tptp.power_power_int Y) _let_2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int _let_1)) X)) Y)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X) Y)) _let_2) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X)) Y)))))) (forall ((A tptp.real) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (forall ((A tptp.int) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((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 ((U tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (= (@ (@ tptp.power_power_real U) (@ tptp.numeral_numeral_nat _let_1)) (@ (@ tptp.times_times_real X) Y)) (=> (@ _let_2 X) (=> (@ _let_2 Y) (@ (@ tptp.ord_less_eq_real U) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) Y)) (@ tptp.numeral_numeral_real _let_1))))))))) _let_210 (forall ((N2 tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (exists ((R3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (= (@ (@ tptp.power_power_real R3) N2) A)))))) (forall ((N2 tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (exists ((X5 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X5) (= (@ (@ tptp.power_power_real X5) N2) A) (forall ((Y6 tptp.real)) (=> (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y6) (= (@ (@ tptp.power_power_real Y6) N2) A)) (= Y6 X5)))))))) (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 (@ (@ tptp.power_power_real A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ _let_1 A)))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.power_power_int A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ _let_1 A)))) (forall ((A tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) tptp.zero_zero_real))) (forall ((A tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) tptp.zero_zero_int))) (forall ((K tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M2)) (@ _let_1 N2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_eq_nat M2) N2))))) (forall ((K tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 M2)) (@ _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 M2) N2)))))))) (forall ((K tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M2)) (@ _let_1 N2)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat M2) N2))))) (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 ((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_se4205575877204974255it_nat tptp.zero_zero_nat) A) (@ (@ tptp.times_times_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.bit_se4203085406695923979it_int tptp.zero_zero_nat) A) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.divide_divide_int A) _let_1))))) (forall ((K tptp.nat) (M2 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 M2)) (@ _let_1 N2)) (@ (@ tptp.divide_divide_nat M2) N2))))) (forall ((K tptp.nat) (M2 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 M2)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M2) N2))))) (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (= (@ _let_1 (@ (@ tptp.times_times_nat B2) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B2)) C))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (= (@ _let_1 (@ (@ tptp.times_times_int B2) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B2)) C))))) (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A3) tptp.one_one_nat)) __flatten_var_0))) (= tptp.ord_less_int (lambda ((A3 tptp.int) (__flatten_var_0 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A3) tptp.one_one_int)) __flatten_var_0))) (forall ((K tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (= (@ _let_1 M2) (@ _let_1 N2)) (or (= K tptp.zero_zero_nat) (= M2 N2))))) (forall ((I tptp.nat) (U tptp.nat) (J tptp.nat) (K tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) K)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat I) J)) U)) K))) (forall ((K tptp.nat) (M2 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 M2)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M2) N2))))) (forall ((K tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ _let_1 M2) (@ _let_1 N2)) (= M2 N2))))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) B2) (= (@ (@ tptp.divide_divide_nat A) B2) tptp.zero_zero_nat)))) (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) B2) (= (@ (@ tptp.divide_divide_int A) B2) tptp.zero_zero_int)))) (forall ((B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_nat B2) A) (@ _let_1 (@ (@ tptp.divide_divide_nat A) B2)))))) (forall ((B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_int B2) A) (@ _let_1 (@ (@ tptp.divide_divide_int A) B2)))))) (forall ((Z3 tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z3) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X) Z3)) (@ (@ tptp.times_times_real Y) Z3)) (@ (@ tptp.ord_less_eq_real X) Y)))) (forall ((Z3 tptp.int) (X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z3) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X) Z3)) (@ (@ tptp.times_times_int Y) Z3)) (@ (@ tptp.ord_less_eq_int X) Y)))) (forall ((Z3 tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.times_times_real Z3))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z3) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_real X) Y))))) (forall ((Z3 tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.times_times_int Z3))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z3) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_int X) Y))))) (forall ((Q3 tptp.nat) (R2 tptp.nat)) (= (@ tptp.unique6322359934112328802ux_nat (@ (@ tptp.product_Pair_nat_nat Q3) R2)) (= R2 tptp.zero_zero_nat))) (forall ((Q3 tptp.int) (R2 tptp.int)) (= (@ tptp.unique6319869463603278526ux_int (@ (@ tptp.product_Pair_int_int Q3) R2)) (= R2 tptp.zero_zero_int))) _let_209 (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 ((N2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.member_nat (@ tptp.suc N2)) (@ tptp.nat_set_decode X)) (@ (@ tptp.member_nat N2) (@ tptp.nat_set_decode (@ (@ tptp.divide_divide_nat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_insert X) Xa2) Y) (=> (forall ((A4 Bool) (B4 Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A4))) (let ((_let_2 (@ _let_1 B4))) (let ((_let_3 (= Xa2 tptp.one_one_nat))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_2) (not (and (=> _let_4 (= Y (@ (@ tptp.vEBT_Leaf true) B4))) (=> (not _let_4) (and (=> _let_3 (= Y (@ _let_1 true))) (=> (not _let_3) (= Y _let_2)))))))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts2) S3))) (=> (= X _let_1) (not (= Y _let_1))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S3))) (=> (= X _let_1) (not (= Y _let_1))))) (=> (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc V2)))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Summary2)) (not (= Y (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Xa2) Xa2))) _let_1) TreeList3) Summary2)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_5 (@ (@ _let_4 Mi2) Xa2))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_6))) (=> (= X _let_2) (not (= Y (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_4 Xa2) Mi2)) (@ (@ tptp.ord_max_nat _let_5) Ma2)))) _let_1) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList3) _let_6) (@ (@ tptp.vEBT_vebt_insert _let_7) (@ (@ tptp.vEBT_VEBT_low _let_5) _let_3)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_7)) (@ (@ tptp.vEBT_vebt_insert Summary2) _let_6)) Summary2))) _let_2))))))))))))))))))) (forall ((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_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_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_int) (Ys tptp.list_VEBT_VEBT)) (= (@ tptp.size_s6639371672096860321T_VEBT (@ (@ tptp.produc662631939642741121T_VEBT Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_int Xs)) (@ tptp.size_s6755466524823107622T_VEBT Ys)))) (forall ((Xs tptp.list_int) (Ys tptp.list_int)) (= (@ tptp.size_s5157815400016825771nt_int (@ (@ tptp.product_int_int Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_int Xs)) (@ tptp.size_size_list_int Ys)))) (forall ((Xs tptp.list_int) (Ys tptp.list_nat)) (= (@ tptp.size_s7647898544948552527nt_nat (@ (@ tptp.product_int_nat Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_int Xs)) (@ tptp.size_size_list_nat 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_int)) (= (@ tptp.size_s2970893825323803983at_int (@ (@ tptp.product_nat_int Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs)) (@ tptp.size_size_list_int Ys)))) (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (= (@ tptp.size_s5460976970255530739at_nat (@ (@ tptp.product_nat_nat Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs)) (@ tptp.size_size_list_nat Ys)))) (forall ((Z3 tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z3) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real X) Z3)) (@ (@ tptp.times_times_real Y) Z3)) (@ (@ tptp.ord_less_real X) Y)))) (forall ((Z3 tptp.int) (X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z3) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int X) Z3)) (@ (@ tptp.times_times_int Y) Z3)) (@ (@ tptp.ord_less_int X) Y)))) _let_208 (forall ((M2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat M2) tptp.one_one_nat) (= M2 tptp.one_one_nat))) (forall ((P (-> tptp.real Bool)) (Q (-> tptp.real Bool))) (= (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((X4 tptp.real)) (or (@ P X4) (@ Q X4))))) (and (@ tptp.finite_finite_real (@ tptp.collect_real P)) (@ tptp.finite_finite_real (@ tptp.collect_real Q))))) (forall ((P (-> tptp.list_nat Bool)) (Q (-> tptp.list_nat Bool))) (= (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (or (@ P X4) (@ Q X4))))) (and (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat P)) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat Q))))) (forall ((P (-> tptp.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (= (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (or (@ P X4) (@ Q X4))))) (and (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat P)) (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat Q))))) (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (= (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (or (@ P X4) (@ Q X4))))) (and (@ tptp.finite_finite_nat (@ tptp.collect_nat P)) (@ tptp.finite_finite_nat (@ tptp.collect_nat Q))))) (forall ((P (-> tptp.complex Bool)) (Q (-> tptp.complex Bool))) (= (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (or (@ P X4) (@ Q X4))))) (and (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex P)) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex Q))))) (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (= (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((X4 tptp.int)) (or (@ P X4) (@ Q X4))))) (and (@ tptp.finite_finite_int (@ tptp.collect_int P)) (@ tptp.finite_finite_int (@ tptp.collect_int Q))))) (forall ((P (-> tptp.extended_enat Bool)) (Q (-> tptp.extended_enat Bool))) (= (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (or (@ P X4) (@ Q X4))))) (and (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat P)) (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat Q))))) (forall ((P (-> tptp.real Bool)) (Q (-> tptp.real Bool))) (=> (or (@ tptp.finite_finite_real (@ tptp.collect_real P)) (@ tptp.finite_finite_real (@ tptp.collect_real Q))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((X4 tptp.real)) (and (@ P X4) (@ Q X4))))))) (forall ((P (-> tptp.list_nat Bool)) (Q (-> tptp.list_nat Bool))) (=> (or (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat P)) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat Q))) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (and (@ P X4) (@ Q X4))))))) (forall ((P (-> tptp.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (=> (or (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat P)) (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat Q))) (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (and (@ P X4) (@ Q X4))))))) (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (or (@ tptp.finite_finite_nat (@ tptp.collect_nat P)) (@ tptp.finite_finite_nat (@ tptp.collect_nat Q))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ P X4) (@ Q X4))))))) (forall ((P (-> tptp.complex Bool)) (Q (-> tptp.complex Bool))) (=> (or (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex P)) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex Q))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (and (@ P X4) (@ Q X4))))))) (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (or (@ tptp.finite_finite_int (@ tptp.collect_int P)) (@ tptp.finite_finite_int (@ tptp.collect_int Q))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ P X4) (@ Q X4))))))) (forall ((P (-> tptp.extended_enat Bool)) (Q (-> tptp.extended_enat Bool))) (=> (or (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat P)) (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat Q))) (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (and (@ P X4) (@ Q X4))))))) (forall ((A tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))) (forall ((A tptp.real)) (= (@ (@ tptp.dvd_dvd_real tptp.zero_zero_real) A) (= A tptp.zero_zero_real))) (forall ((A tptp.int)) (= (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) A) (= A tptp.zero_zero_int))) (forall ((A tptp.complex)) (= (@ (@ tptp.dvd_dvd_complex tptp.zero_zero_complex) A) (= A tptp.zero_zero_complex))) (forall ((A tptp.extended_enat)) (= (@ (@ tptp.dvd_dv3785147216227455552d_enat tptp.zero_z5237406670263579293d_enat) A) (= A tptp.zero_z5237406670263579293d_enat))) (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) tptp.zero_zero_nat)) (forall ((A tptp.real)) (@ (@ tptp.dvd_dvd_real A) tptp.zero_zero_real)) (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int A) tptp.zero_zero_int)) (forall ((A tptp.complex)) (@ (@ tptp.dvd_dvd_complex A) tptp.zero_zero_complex)) (forall ((A tptp.extended_enat)) (@ (@ tptp.dvd_dv3785147216227455552d_enat A) tptp.zero_z5237406670263579293d_enat)) (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B2) A)) (@ _let_1 B2)))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B2) A)) (@ _let_1 B2)))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B2) A)) (@ _let_1 B2)))) (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat A) B2)) (@ _let_1 B2)))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) B2)) (@ _let_1 B2)))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real A) B2)) (@ _let_1 B2)))) (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.dvd_dvd_nat M2) _let_1) (= M2 _let_1)))) (forall ((K tptp.nat)) (@ (@ tptp.dvd_dvd_nat (@ tptp.suc tptp.zero_zero_nat)) K)) (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.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.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int tptp.zero_zero_int) A) tptp.zero_zero_int)) (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int tptp.zero_zero_int) A) tptp.zero_zero_int)) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B2) (=> (@ _let_1 C) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat B2) A)) (@ (@ tptp.divide_divide_nat C) A)) (@ (@ tptp.dvd_dvd_nat B2) C)))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B2) (=> (@ _let_1 C) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int B2) A)) (@ (@ tptp.divide_divide_int C) A)) (@ (@ tptp.dvd_dvd_int B2) C)))))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B2)) B2) (@ (@ tptp.modulo_modulo_nat A) B2))) (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B2)) B2) (@ (@ tptp.modulo_modulo_int A) B2))) (forall ((B2 tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat B2) A)) B2) (@ (@ tptp.modulo_modulo_nat A) B2))) (forall ((B2 tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int B2) A)) B2) (@ (@ tptp.modulo_modulo_int A) B2))) (forall ((K tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M2)) (@ _let_1 N2)) (or (= K tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat M2) N2))))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N2) (= (@ (@ tptp.modulo_modulo_nat M2) N2) M2))) (forall ((A2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A2) (@ tptp.finite6551019134538273531omplex (@ tptp.collect_set_complex (lambda ((B5 tptp.set_complex)) (@ (@ tptp.ord_le211207098394363844omplex B5) A2)))))) (forall ((A2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (@ tptp.finite5468666774076196335d_enat (@ tptp.collec2260605976452661553d_enat (lambda ((B5 tptp.set_Extended_enat)) (@ (@ tptp.ord_le7203529160286727270d_enat B5) A2)))))) (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat (lambda ((B5 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat B5) A2)))))) (forall ((A2 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (@ tptp.finite6197958912794628473et_int (@ tptp.collect_set_int (lambda ((B5 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int B5) A2)))))) (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) K))))) (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) K))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat B2) A)) (@ (@ tptp.times_times_nat C) A)) (@ (@ tptp.dvd_dvd_nat B2) C)))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int B2) A)) (@ (@ tptp.times_times_int C) A)) (@ (@ tptp.dvd_dvd_int B2) C)))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 B2)) (@ _let_1 C)) (@ (@ tptp.dvd_dvd_nat B2) C))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 B2)) (@ _let_1 C)) (@ (@ tptp.dvd_dvd_int B2) C))))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) C)) (or (= C tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int A) B2)))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) C)) (or (= C tptp.zero_zero_real) (@ (@ tptp.dvd_dvd_real A) B2)))) (forall ((A tptp.complex) (C tptp.complex) (B2 tptp.complex)) (= (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B2) C)) (or (= C tptp.zero_zero_complex) (@ (@ tptp.dvd_dvd_complex A) B2)))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 A)) (@ _let_1 B2)) (or (= C tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int A) B2))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (@ (@ tptp.dvd_dvd_real (@ _let_1 A)) (@ _let_1 B2)) (or (= C tptp.zero_zero_real) (@ (@ tptp.dvd_dvd_real A) B2))))) (forall ((C tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C))) (= (@ (@ tptp.dvd_dvd_complex (@ _let_1 A)) (@ _let_1 B2)) (or (= C tptp.zero_zero_complex) (@ (@ tptp.dvd_dvd_complex A) B2))))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B2)) tptp.one_one_nat)))) (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B2)) tptp.one_one_int)))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B2) (@ (@ tptp.times_times_nat C) A))) (@ _let_1 B2)))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B2) (@ (@ tptp.times_times_int C) A))) (@ _let_1 B2)))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B2) (@ (@ tptp.times_times_real C) A))) (@ _let_1 B2)))) (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B2) (@ (@ tptp.times_times_complex C) A))) (@ _let_1 B2)))) (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C) A)) B2)) (@ _let_1 B2)))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C) A)) B2)) (@ _let_1 B2)))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real C) A)) B2)) (@ _let_1 B2)))) (forall ((A tptp.complex) (C tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex C) A)) B2)) (@ _let_1 B2)))) (forall ((B2 tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat B2) A)) B2) tptp.zero_zero_nat)) (forall ((B2 tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int B2) A)) B2) tptp.zero_zero_int)) (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B2)) B2) tptp.zero_zero_nat)) (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B2)) B2) tptp.zero_zero_int)) (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.one_one_int) tptp.zero_zero_int)) (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.one_one_int) tptp.zero_zero_int)) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B2) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat B2) A)) A) B2))) (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B2) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int B2) A)) A) B2))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B2) (= (@ (@ tptp.times_times_nat A) (@ (@ tptp.divide_divide_nat B2) A)) B2))) (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B2) (= (@ (@ tptp.times_times_int A) (@ (@ tptp.divide_divide_int B2) A)) B2))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat A) B2)) tptp.one_one_nat)))) (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int A) B2)) tptp.one_one_int)))) (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.nat)) (let ((_let_1 (@ tptp.divide_divide_nat tptp.one_one_nat))) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (@ _let_1 (@ _let_1 A)) A)))) (forall ((A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int tptp.one_one_int))) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (@ _let_1 (@ _let_1 A)) A)))) (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B2)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) C)) (@ (@ tptp.divide_divide_nat B2) C))))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B2)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B2) C))))))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) B2)) B2) tptp.zero_zero_nat)) (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) B2)) B2) tptp.zero_zero_int)) (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) B2)) B2) tptp.zero_zero_nat)) (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) B2)) B2) tptp.zero_zero_int)) (forall ((B2 tptp.nat) (C tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B2) C)) A)) B2) (@ (@ tptp.modulo_modulo_nat A) B2))) (forall ((B2 tptp.int) (C tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) C)) A)) B2) (@ (@ tptp.modulo_modulo_int A) B2))) (forall ((C tptp.nat) (B2 tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C) B2)) A)) B2) (@ (@ tptp.modulo_modulo_nat A) B2))) (forall ((C tptp.int) (B2 tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C) B2)) A)) B2) (@ (@ tptp.modulo_modulo_int A) B2))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat B2) C))) B2) (@ (@ tptp.modulo_modulo_nat A) B2))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int B2) C))) B2) (@ (@ tptp.modulo_modulo_int A) B2))) (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat C) B2))) B2) (@ (@ tptp.modulo_modulo_nat A) B2))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int C) B2))) B2) (@ (@ tptp.modulo_modulo_int A) B2))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B2) (= (@ (@ tptp.modulo_modulo_nat B2) A) tptp.zero_zero_nat))) (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B2) (= (@ (@ tptp.modulo_modulo_int B2) A) tptp.zero_zero_int))) (forall ((M2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat M2) (@ tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)) (= (@ tptp.nat_set_decode tptp.zero_zero_nat) tptp.bot_bot_set_nat) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat B2) A)) A) B2))) (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int B2) A)) A) B2))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat B2) (@ (@ tptp.divide_divide_nat tptp.one_one_nat) A)) (@ (@ tptp.divide_divide_nat B2) A)))) (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (@ (@ tptp.times_times_int B2) (@ (@ tptp.divide_divide_int tptp.one_one_int) A)) (@ (@ tptp.divide_divide_int B2) A)))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.suc N2)) (not (@ _let_1 N2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc N2))) (@ _let_1 N2)))) (forall ((N2 tptp.nat) (A tptp.nat) (B2 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 B2) N2)) (@ (@ tptp.dvd_dvd_nat A) B2)))) (forall ((N2 tptp.nat) (A tptp.int) (B2 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 B2) N2)) (@ (@ tptp.dvd_dvd_int A) B2)))) (forall ((N2 tptp.nat) (K tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N2) K)) M2))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M2)) N2))) (forall ((K tptp.nat) (N2 tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K) N2)) M2))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M2)) N2))) (forall ((M2 tptp.nat) (N2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat M2) (@ (@ tptp.times_times_nat N2) K)))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M2)) N2))) (forall ((M2 tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat M2) (@ (@ tptp.times_times_nat K) N2)))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M2)) N2))) (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat A) B2)) (= (@ _let_1 A) (@ _let_1 B2))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) B2)) (= (@ _let_1 A) (@ _let_1 B2))))) (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_nat A) B2))) (not (= (not (@ _let_1 A)) (not (@ _let_1 B2))))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_int A) B2))) (not (= (not (@ _let_1 A)) (not (@ _let_1 B2))))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) N2)) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc N2)) _let_1) (@ tptp.suc (@ (@ tptp.divide_divide_nat N2) _let_1)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) N2) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc N2)) _let_1) (@ (@ tptp.divide_divide_nat N2) _let_1))))) (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc M2))) _let_1) (@ (@ tptp.modulo_modulo_nat M2) _let_1)))) (forall ((K tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat K))) (=> (not (= _let_1 tptp.one_one_nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N2))) _let_1) tptp.one_one_nat)))) (forall ((X tptp.nat)) (= (@ (@ tptp.member_nat tptp.zero_zero_nat) (@ tptp.nat_set_decode X)) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X)))) (forall ((A tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.numeral_numeral_nat W2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_real A) _let_2)) (or _let_3 (and (not _let_3) (@ _let_1 A)))))))) (forall ((A tptp.int) (W2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.numeral_numeral_nat W2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_int A) _let_2)) (or _let_3 (and (not _let_3) (@ _let_1 A)))))))) (forall ((A tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W2))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) _let_1)) tptp.zero_zero_real) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))) (forall ((A tptp.int) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W2))) (= (@ (@ 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.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.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) (not (@ _let_1 A))))) (forall ((A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) (not (@ _let_1 A))))) (forall ((A tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.one_one_nat)) (= _let_1 tptp.zero_zero_nat)))) (forall ((A tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.one_one_int)) (= _let_1 tptp.zero_zero_int)))) (forall ((A tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.zero_zero_nat)) (= _let_1 tptp.one_one_nat)))) (forall ((A tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.zero_zero_int)) (= _let_1 tptp.one_one_int)))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 (@ tptp.suc tptp.zero_zero_nat))) (= _let_1 tptp.zero_zero_nat)))) (forall ((M2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat M2) M2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat)) (forall ((A tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.numeral_numeral_nat W2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_real A) _let_2)) (or (= _let_2 tptp.zero_zero_nat) (and _let_3 (not (= A tptp.zero_zero_real))) (and (not _let_3) (@ _let_1 A)))))))) (forall ((A tptp.int) (W2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.numeral_numeral_nat W2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_int A) _let_2)) (or (= _let_2 tptp.zero_zero_nat) (and _let_3 (not (= A tptp.zero_zero_int))) (and (not _let_3) (@ _let_1 A)))))))) (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat 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.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.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.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 ((M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat M2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (= _let_1 tptp.one_one_nat)))) (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) A)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat A) _let_1))) tptp.one_one_nat) A)))) (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_int _let_1) A)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.divide_divide_int A) _let_1))) tptp.one_one_int) A)))) (forall ((A tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W2))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) _let_1)) tptp.zero_zero_real) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (or (and (not _let_2) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real)) (and _let_2 (= A tptp.zero_zero_real)))))))) (forall ((A tptp.int) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W2))) (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 ((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.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_set_real (@ tptp.collect_real (lambda ((C3 tptp.real)) (@ (@ tptp.dvd_dvd_real C3) A)))) (@ tptp.collect_real (lambda ((C3 tptp.real)) (@ (@ tptp.dvd_dvd_real C3) B2)))) (and (@ (@ tptp.dvd_dvd_real A) B2) (not (@ (@ tptp.dvd_dvd_real B2) A))))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_set_nat (@ tptp.collect_nat (lambda ((C3 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C3) A)))) (@ tptp.collect_nat (lambda ((C3 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C3) B2)))) (and (@ (@ tptp.dvd_dvd_nat A) B2) (not (@ (@ tptp.dvd_dvd_nat B2) A))))) (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_set_int (@ tptp.collect_int (lambda ((C3 tptp.int)) (@ (@ tptp.dvd_dvd_int C3) A)))) (@ tptp.collect_int (lambda ((C3 tptp.int)) (@ (@ tptp.dvd_dvd_int C3) B2)))) (and (@ (@ tptp.dvd_dvd_int A) B2) (not (@ (@ tptp.dvd_dvd_int B2) A))))) _let_207 _let_206 _let_205 (= tptp.ord_less_set_nat (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (@ (@ tptp.ord_less_nat_o (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) A5))) (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) B5))))) (= tptp.ord_less_set_int (lambda ((A5 tptp.set_int) (B5 tptp.set_int)) (@ (@ tptp.ord_less_int_o (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) A5))) (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) B5))))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat A) B2) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat B2) A))) (forall ((A tptp.int) (B2 tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int A) B2) tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int B2) A))) _let_204 _let_203 (forall ((A tptp.nat) (B2 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) B2) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat B2) A))) (forall ((A tptp.int) (B2 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) B2) tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int B2) A))) (= tptp.bot_bot_set_list_nat (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) false))) (= tptp.bot_bot_set_set_nat (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) false))) (= tptp.bot_bo7653980558646680370d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) false))) (= tptp.bot_bot_set_real (@ tptp.collect_real (lambda ((X4 tptp.real)) false))) (= tptp.bot_bot_set_nat (@ tptp.collect_nat (lambda ((X4 tptp.nat)) false))) (= tptp.bot_bot_set_int (@ tptp.collect_int (lambda ((X4 tptp.int)) false))) (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) A)) (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int A) A)) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B2) (=> (@ (@ tptp.dvd_dvd_nat B2) C) (@ _let_1 C))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B2) (=> (@ (@ tptp.dvd_dvd_int B2) C) (@ _let_1 C))))) (forall ((C tptp.nat) (B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C))) (=> (@ _let_1 B2) (= (@ _let_1 (@ (@ tptp.modulo_modulo_nat A) B2)) (@ _let_1 A))))) (forall ((C tptp.int) (B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (@ _let_1 B2) (= (@ _let_1 (@ (@ tptp.modulo_modulo_int A) B2)) (@ _let_1 A))))) (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C))) (=> (@ _let_1 (@ (@ tptp.modulo_modulo_nat A) B2)) (=> (@ _let_1 B2) (@ _let_1 A))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (@ _let_1 (@ (@ tptp.modulo_modulo_int A) B2)) (=> (@ _let_1 B2) (@ _let_1 A))))) (forall ((P (-> tptp.real Bool))) (=> (not (@ tptp.finite_finite_real (@ tptp.collect_real P))) (exists ((X_12 tptp.real)) (@ P X_12)))) (forall ((P (-> tptp.list_nat Bool))) (=> (not (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat P))) (exists ((X_12 tptp.list_nat)) (@ P X_12)))) (forall ((P (-> tptp.set_nat Bool))) (=> (not (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat P))) (exists ((X_12 tptp.set_nat)) (@ P X_12)))) (forall ((P (-> tptp.nat Bool))) (=> (not (@ tptp.finite_finite_nat (@ tptp.collect_nat P))) (exists ((X_12 tptp.nat)) (@ P X_12)))) (forall ((P (-> tptp.complex Bool))) (=> (not (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex P))) (exists ((X_12 tptp.complex)) (@ P X_12)))) (forall ((P (-> tptp.int Bool))) (=> (not (@ tptp.finite_finite_int (@ tptp.collect_int P))) (exists ((X_12 tptp.int)) (@ P X_12)))) (forall ((P (-> tptp.extended_enat Bool))) (=> (not (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat P))) (exists ((X_12 tptp.extended_enat)) (@ P X_12)))) (forall ((A2 tptp.set_real) (B tptp.set_nat) (R (-> tptp.real tptp.nat Bool))) (=> (not (@ tptp.finite_finite_real A2)) (=> (@ tptp.finite_finite_nat B) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) B) (@ (@ R X5) Xa))))) (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) B) (not (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((A3 tptp.real)) (and (@ (@ tptp.member_real A3) A2) (@ (@ R A3) X5)))))))))))) (forall ((A2 tptp.set_real) (B tptp.set_complex) (R (-> tptp.real tptp.complex Bool))) (=> (not (@ tptp.finite_finite_real A2)) (=> (@ tptp.finite3207457112153483333omplex B) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) B) (@ (@ R X5) Xa))))) (exists ((X5 tptp.complex)) (and (@ (@ tptp.member_complex X5) B) (not (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((A3 tptp.real)) (and (@ (@ tptp.member_real A3) A2) (@ (@ R A3) X5)))))))))))) (forall ((A2 tptp.set_real) (B tptp.set_int) (R (-> tptp.real tptp.int Bool))) (=> (not (@ tptp.finite_finite_real A2)) (=> (@ tptp.finite_finite_int B) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) B) (@ (@ R X5) Xa))))) (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) B) (not (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((A3 tptp.real)) (and (@ (@ tptp.member_real A3) A2) (@ (@ R A3) X5)))))))))))) (forall ((A2 tptp.set_real) (B tptp.set_Extended_enat) (R (-> tptp.real tptp.extended_enat Bool))) (=> (not (@ tptp.finite_finite_real A2)) (=> (@ tptp.finite4001608067531595151d_enat B) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (exists ((Xa tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat Xa) B) (@ (@ R X5) Xa))))) (exists ((X5 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X5) B) (not (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((A3 tptp.real)) (and (@ (@ tptp.member_real A3) A2) (@ (@ R A3) X5)))))))))))) (forall ((A2 tptp.set_nat) (B tptp.set_nat) (R (-> tptp.nat tptp.nat Bool))) (=> (not (@ tptp.finite_finite_nat A2)) (=> (@ tptp.finite_finite_nat B) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) B) (@ (@ R X5) Xa))))) (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) B) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A3 tptp.nat)) (and (@ (@ tptp.member_nat A3) A2) (@ (@ R A3) X5)))))))))))) (forall ((A2 tptp.set_nat) (B tptp.set_complex) (R (-> tptp.nat tptp.complex Bool))) (=> (not (@ tptp.finite_finite_nat A2)) (=> (@ tptp.finite3207457112153483333omplex B) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) B) (@ (@ R X5) Xa))))) (exists ((X5 tptp.complex)) (and (@ (@ tptp.member_complex X5) B) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A3 tptp.nat)) (and (@ (@ tptp.member_nat A3) A2) (@ (@ R A3) X5)))))))))))) (forall ((A2 tptp.set_nat) (B tptp.set_int) (R (-> tptp.nat tptp.int Bool))) (=> (not (@ tptp.finite_finite_nat A2)) (=> (@ tptp.finite_finite_int B) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) B) (@ (@ R X5) Xa))))) (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) B) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A3 tptp.nat)) (and (@ (@ tptp.member_nat A3) A2) (@ (@ R A3) X5)))))))))))) (forall ((A2 tptp.set_nat) (B tptp.set_Extended_enat) (R (-> tptp.nat tptp.extended_enat Bool))) (=> (not (@ tptp.finite_finite_nat A2)) (=> (@ tptp.finite4001608067531595151d_enat B) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (exists ((Xa tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat Xa) B) (@ (@ R X5) Xa))))) (exists ((X5 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X5) B) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A3 tptp.nat)) (and (@ (@ tptp.member_nat A3) A2) (@ (@ R A3) X5)))))))))))) (forall ((A2 tptp.set_complex) (B tptp.set_nat) (R (-> tptp.complex tptp.nat Bool))) (=> (not (@ tptp.finite3207457112153483333omplex A2)) (=> (@ tptp.finite_finite_nat B) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) B) (@ (@ R X5) Xa))))) (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) B) (not (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((A3 tptp.complex)) (and (@ (@ tptp.member_complex A3) A2) (@ (@ R A3) X5)))))))))))) (forall ((A2 tptp.set_complex) (B tptp.set_complex) (R (-> tptp.complex tptp.complex Bool))) (=> (not (@ tptp.finite3207457112153483333omplex A2)) (=> (@ tptp.finite3207457112153483333omplex B) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) B) (@ (@ R X5) Xa))))) (exists ((X5 tptp.complex)) (and (@ (@ tptp.member_complex X5) B) (not (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((A3 tptp.complex)) (and (@ (@ tptp.member_complex A3) A2) (@ (@ R A3) X5)))))))))))) (forall ((R tptp.set_Extended_enat) (S2 tptp.set_Extended_enat)) (= (@ (@ tptp.ord_le100613205991271927enat_o (lambda ((X4 tptp.extended_enat)) (@ (@ tptp.member_Extended_enat X4) R))) (lambda ((X4 tptp.extended_enat)) (@ (@ tptp.member_Extended_enat X4) S2))) (@ (@ tptp.ord_le7203529160286727270d_enat R) S2))) (forall ((R tptp.set_real) (S2 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_real_o (lambda ((X4 tptp.real)) (@ (@ tptp.member_real X4) R))) (lambda ((X4 tptp.real)) (@ (@ tptp.member_real X4) S2))) (@ (@ tptp.ord_less_eq_set_real R) S2))) (forall ((R tptp.set_set_nat) (S2 tptp.set_set_nat)) (= (@ (@ tptp.ord_le3964352015994296041_nat_o (lambda ((X4 tptp.set_nat)) (@ (@ tptp.member_set_nat X4) R))) (lambda ((X4 tptp.set_nat)) (@ (@ tptp.member_set_nat X4) S2))) (@ (@ tptp.ord_le6893508408891458716et_nat R) S2))) (forall ((R tptp.set_nat) (S2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_nat_o (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) R))) (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) S2))) (@ (@ tptp.ord_less_eq_set_nat R) S2))) (forall ((R tptp.set_int) (S2 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_int_o (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) R))) (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) S2))) (@ (@ tptp.ord_less_eq_set_int R) S2))) (= tptp.ord_le7203529160286727270d_enat (lambda ((A5 tptp.set_Extended_enat) (B5 tptp.set_Extended_enat)) (@ (@ tptp.ord_le100613205991271927enat_o (lambda ((X4 tptp.extended_enat)) (@ (@ tptp.member_Extended_enat X4) A5))) (lambda ((X4 tptp.extended_enat)) (@ (@ tptp.member_Extended_enat X4) B5))))) (= tptp.ord_less_eq_set_real (lambda ((A5 tptp.set_real) (B5 tptp.set_real)) (@ (@ tptp.ord_less_eq_real_o (lambda ((X4 tptp.real)) (@ (@ tptp.member_real X4) A5))) (lambda ((X4 tptp.real)) (@ (@ tptp.member_real X4) B5))))) (= tptp.ord_le6893508408891458716et_nat (lambda ((A5 tptp.set_set_nat) (B5 tptp.set_set_nat)) (@ (@ tptp.ord_le3964352015994296041_nat_o (lambda ((X4 tptp.set_nat)) (@ (@ tptp.member_set_nat X4) A5))) (lambda ((X4 tptp.set_nat)) (@ (@ tptp.member_set_nat X4) B5))))) (= tptp.ord_less_eq_set_nat (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat_o (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) A5))) (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) B5))))) (= tptp.ord_less_eq_set_int (lambda ((A5 tptp.set_int) (B5 tptp.set_int)) (@ (@ tptp.ord_less_eq_int_o (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) A5))) (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) B5))))) (forall ((A2 tptp.set_Extended_enat) (P (-> tptp.extended_enat Bool))) (@ (@ tptp.ord_le7203529160286727270d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) A2) (@ P X4))))) A2)) (forall ((A2 tptp.set_real) (P (-> tptp.real Bool))) (@ (@ tptp.ord_less_eq_set_real (@ tptp.collect_real (lambda ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) A2) (@ P X4))))) A2)) (forall ((A2 tptp.set_list_nat) (P (-> tptp.list_nat Bool))) (@ (@ tptp.ord_le6045566169113846134st_nat (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (and (@ (@ tptp.member_list_nat X4) A2) (@ P X4))))) A2)) (forall ((A2 tptp.set_set_nat) (P (-> tptp.set_nat Bool))) (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X4) A2) (@ P X4))))) A2)) (forall ((A2 tptp.set_nat) (P (-> tptp.nat Bool))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A2) (@ P X4))))) A2)) (forall ((A2 tptp.set_int) (P (-> tptp.int Bool))) (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A2) (@ P X4))))) A2)) (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.collect_real (lambda ((C3 tptp.real)) (@ (@ tptp.dvd_dvd_real C3) A)))) (@ tptp.collect_real (lambda ((C3 tptp.real)) (@ (@ tptp.dvd_dvd_real C3) B2)))) (@ (@ tptp.dvd_dvd_real A) B2))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat (lambda ((C3 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C3) A)))) (@ tptp.collect_nat (lambda ((C3 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C3) B2)))) (@ (@ tptp.dvd_dvd_nat A) B2))) (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int (lambda ((C3 tptp.int)) (@ (@ tptp.dvd_dvd_int C3) A)))) (@ tptp.collect_int (lambda ((C3 tptp.int)) (@ (@ tptp.dvd_dvd_int C3) B2)))) (@ (@ tptp.dvd_dvd_int A) B2))) (forall ((X8 tptp.set_Extended_enat) (P (-> tptp.extended_enat Bool))) (@ (@ tptp.ord_le7203529160286727270d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) X8) (@ P X4))))) X8)) (forall ((X8 tptp.set_real) (P (-> tptp.real Bool))) (@ (@ tptp.ord_less_eq_set_real (@ tptp.collect_real (lambda ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) X8) (@ P X4))))) X8)) (forall ((X8 tptp.set_list_nat) (P (-> tptp.list_nat Bool))) (@ (@ tptp.ord_le6045566169113846134st_nat (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (and (@ (@ tptp.member_list_nat X4) X8) (@ P X4))))) X8)) (forall ((X8 tptp.set_set_nat) (P (-> tptp.set_nat Bool))) (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X4) X8) (@ P X4))))) X8)) (forall ((X8 tptp.set_nat) (P (-> tptp.nat Bool))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) X8) (@ P X4))))) X8)) (forall ((X8 tptp.set_int) (P (-> tptp.int Bool))) (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) X8) (@ P X4))))) X8)) (forall ((X tptp.extended_enat) (Z5 tptp.set_Extended_enat) (X8 tptp.set_Extended_enat) (P (-> tptp.extended_enat Bool))) (=> (@ (@ tptp.member_Extended_enat X) Z5) (=> (@ (@ tptp.ord_le7203529160286727270d_enat Z5) (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) X8) (@ P X4))))) (@ P X)))) (forall ((X tptp.real) (Z5 tptp.set_real) (X8 tptp.set_real) (P (-> tptp.real Bool))) (=> (@ (@ tptp.member_real X) Z5) (=> (@ (@ tptp.ord_less_eq_set_real Z5) (@ tptp.collect_real (lambda ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) X8) (@ P X4))))) (@ P X)))) (forall ((X tptp.list_nat) (Z5 tptp.set_list_nat) (X8 tptp.set_list_nat) (P (-> tptp.list_nat Bool))) (=> (@ (@ tptp.member_list_nat X) Z5) (=> (@ (@ tptp.ord_le6045566169113846134st_nat Z5) (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (and (@ (@ tptp.member_list_nat X4) X8) (@ P X4))))) (@ P X)))) (forall ((X tptp.set_nat) (Z5 tptp.set_set_nat) (X8 tptp.set_set_nat) (P (-> tptp.set_nat Bool))) (=> (@ (@ tptp.member_set_nat X) Z5) (=> (@ (@ tptp.ord_le6893508408891458716et_nat Z5) (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X4) X8) (@ P X4))))) (@ P X)))) (forall ((X tptp.nat) (Z5 tptp.set_nat) (X8 tptp.set_nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.member_nat X) Z5) (=> (@ (@ tptp.ord_less_eq_set_nat Z5) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) X8) (@ P X4))))) (@ P X)))) (forall ((X tptp.int) (Z5 tptp.set_int) (X8 tptp.set_int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.member_int X) Z5) (=> (@ (@ tptp.ord_less_eq_set_int Z5) (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) X8) (@ P X4))))) (@ P X)))) (= (lambda ((H tptp.nat)) tptp.zero_zero_nat) (@ tptp.times_times_nat tptp.zero_zero_nat)) (= (lambda ((H tptp.int)) tptp.zero_zero_int) (@ tptp.times_times_int tptp.zero_zero_int)) (= (lambda ((H tptp.real)) tptp.zero_zero_real) (@ tptp.times_times_real tptp.zero_zero_real)) (= (lambda ((H tptp.complex)) tptp.zero_zero_complex) (@ tptp.times_times_complex tptp.zero_zero_complex)) (= (lambda ((H tptp.extended_enat)) tptp.zero_z5237406670263579293d_enat) (@ tptp.times_7803423173614009249d_enat tptp.zero_z5237406670263579293d_enat)) (= (lambda ((X4 tptp.nat)) X4) (@ tptp.times_times_nat tptp.one_one_nat)) (= (lambda ((X4 tptp.int)) X4) (@ tptp.times_times_int tptp.one_one_int)) (= (lambda ((X4 tptp.real)) X4) (@ tptp.times_times_real tptp.one_one_real)) (= (lambda ((X4 tptp.complex)) X4) (@ tptp.times_times_complex tptp.one_one_complex)) (= (lambda ((X4 tptp.extended_enat)) X4) (@ tptp.times_7803423173614009249d_enat tptp.one_on7984719198319812577d_enat)) (= tptp.ord_max_real (lambda ((A3 tptp.real) (B3 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_eq_real A3) B3)) B3) A3))) (= tptp.ord_max_set_nat (lambda ((A3 tptp.set_nat) (B3 tptp.set_nat)) (@ (@ (@ tptp.if_set_nat (@ (@ tptp.ord_less_eq_set_nat A3) B3)) B3) A3))) (= tptp.ord_max_set_int (lambda ((A3 tptp.set_int) (B3 tptp.set_int)) (@ (@ (@ tptp.if_set_int (@ (@ tptp.ord_less_eq_set_int A3) B3)) B3) A3))) (= tptp.ord_max_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_eq_nat A3) B3)) B3) A3))) (= tptp.ord_max_int (lambda ((A3 tptp.int) (B3 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int A3) B3)) B3) A3))) (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((D4 tptp.nat)) (@ (@ tptp.dvd_dvd_nat D4) M2)))))) (forall ((B2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (= (@ (@ tptp.modulo_modulo_nat A) B2) tptp.zero_zero_nat))) (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (= (@ (@ tptp.modulo_modulo_int A) B2) tptp.zero_zero_int))) _let_202 _let_201 _let_200 _let_199 (forall ((P (-> tptp.nat Bool)) (I tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (and (@ P K2) (@ (@ tptp.ord_less_nat K2) I)))))) (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 ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.modulo_modulo_nat M2) N2)) (not (@ (@ tptp.dvd_dvd_nat N2) M2)))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.modulo_modulo_nat (@ _let_1 (@ (@ tptp.modulo_modulo_nat B2) C))) C) (@ (@ tptp.modulo_modulo_nat (@ _let_1 B2)) C)))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.modulo_modulo_int (@ _let_1 (@ (@ tptp.modulo_modulo_int B2) C))) C) (@ (@ tptp.modulo_modulo_int (@ _let_1 B2)) C)))) (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) C)) B2)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B2)) C))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) C)) B2)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B2)) C))) (forall ((A tptp.nat) (C tptp.nat) (A7 tptp.nat) (B2 tptp.nat) (B7 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) C) (@ (@ tptp.modulo_modulo_nat A7) C)) (=> (= (@ (@ tptp.modulo_modulo_nat B2) C) (@ (@ tptp.modulo_modulo_nat B7) C)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B2)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A7) B7)) C))))) (forall ((A tptp.int) (C tptp.int) (A7 tptp.int) (B2 tptp.int) (B7 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A7) C)) (=> (= (@ (@ tptp.modulo_modulo_int B2) C) (@ (@ tptp.modulo_modulo_int B7) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B2)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A7) B7)) C))))) (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) C)) (@ (@ tptp.modulo_modulo_nat B2) C))) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B2)) C))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) C)) (@ (@ tptp.modulo_modulo_int B2) C))) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B2)) C))) (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))) (forall ((A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real tptp.zero_zero_real) A) (= A tptp.zero_zero_real))) (forall ((A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) A) (= A tptp.zero_zero_int))) (forall ((A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex tptp.zero_zero_complex) A) (= A tptp.zero_zero_complex))) (forall ((A tptp.extended_enat)) (=> (@ (@ tptp.dvd_dv3785147216227455552d_enat tptp.zero_z5237406670263579293d_enat) A) (= A tptp.zero_z5237406670263579293d_enat))) _let_198 _let_197 (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M2) N2)))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc M2))) N2))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M2) N2))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M2)) N2))) (forall ((B2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) A) (not (forall ((K3 tptp.nat)) (not (= A (@ (@ tptp.times_times_nat B2) K3))))))) (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B2) A) (not (forall ((K3 tptp.int)) (not (= A (@ (@ tptp.times_times_int B2) K3))))))) (forall ((B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real B2) A) (not (forall ((K3 tptp.real)) (not (= A (@ (@ tptp.times_times_real B2) K3))))))) (forall ((B2 tptp.complex) (A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex B2) A) (not (forall ((K3 tptp.complex)) (not (= A (@ (@ tptp.times_times_complex B2) K3))))))) (forall ((B2 tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.dvd_dv3785147216227455552d_enat B2) A) (not (forall ((K3 tptp.extended_enat)) (not (= A (@ (@ tptp.times_7803423173614009249d_enat B2) K3))))))) (forall ((A tptp.nat) (B2 tptp.nat) (K tptp.nat)) (=> (= A (@ (@ tptp.times_times_nat B2) K)) (@ (@ tptp.dvd_dvd_nat B2) A))) (forall ((A tptp.int) (B2 tptp.int) (K tptp.int)) (=> (= A (@ (@ tptp.times_times_int B2) K)) (@ (@ tptp.dvd_dvd_int B2) A))) (forall ((A tptp.real) (B2 tptp.real) (K tptp.real)) (=> (= A (@ (@ tptp.times_times_real B2) K)) (@ (@ tptp.dvd_dvd_real B2) A))) (forall ((A tptp.complex) (B2 tptp.complex) (K tptp.complex)) (=> (= A (@ (@ tptp.times_times_complex B2) K)) (@ (@ tptp.dvd_dvd_complex B2) A))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (K tptp.extended_enat)) (=> (= A (@ (@ tptp.times_7803423173614009249d_enat B2) K)) (@ (@ tptp.dvd_dv3785147216227455552d_enat B2) A))) (= tptp.dvd_dvd_nat (lambda ((B3 tptp.nat) (A3 tptp.nat)) (exists ((K2 tptp.nat)) (= A3 (@ (@ tptp.times_times_nat B3) K2))))) (= tptp.dvd_dvd_int (lambda ((B3 tptp.int) (A3 tptp.int)) (exists ((K2 tptp.int)) (= A3 (@ (@ tptp.times_times_int B3) K2))))) (= tptp.dvd_dvd_real (lambda ((B3 tptp.real) (A3 tptp.real)) (exists ((K2 tptp.real)) (= A3 (@ (@ tptp.times_times_real B3) K2))))) (= tptp.dvd_dvd_complex (lambda ((B3 tptp.complex) (A3 tptp.complex)) (exists ((K2 tptp.complex)) (= A3 (@ (@ tptp.times_times_complex B3) K2))))) _let_196 (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_nat B2) C))))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_int B2) C))))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_real B2) C))))) (forall ((A tptp.complex) (C tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_complex B2) C))))) (forall ((A tptp.extended_enat) (C tptp.extended_enat) (B2 tptp.extended_enat)) (let ((_let_1 (@ tptp.dvd_dv3785147216227455552d_enat A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_7803423173614009249d_enat B2) C))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_nat B2) C))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_int B2) C))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_real B2) C))))) (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_complex B2) C))))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.dvd_dv3785147216227455552d_enat A))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_7803423173614009249d_enat B2) C))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B2)) C) (@ (@ tptp.dvd_dvd_nat A) C))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B2)) C) (@ (@ tptp.dvd_dvd_int A) C))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) B2)) C) (@ (@ tptp.dvd_dvd_real A) C))) (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.times_times_complex A) B2)) C) (@ (@ tptp.dvd_dvd_complex A) C))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat)) (=> (@ (@ tptp.dvd_dv3785147216227455552d_enat (@ (@ tptp.times_7803423173614009249d_enat A) B2)) C) (@ (@ tptp.dvd_dv3785147216227455552d_enat A) C))) (forall ((A tptp.nat) (B2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat A) B2))) (forall ((A tptp.int) (B2 tptp.int)) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int A) B2))) (forall ((A tptp.real) (B2 tptp.real)) (@ (@ tptp.dvd_dvd_real A) (@ (@ tptp.times_times_real A) B2))) (forall ((A tptp.complex) (B2 tptp.complex)) (@ (@ tptp.dvd_dvd_complex A) (@ (@ tptp.times_times_complex A) B2))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (@ (@ tptp.dvd_dv3785147216227455552d_enat A) (@ (@ tptp.times_7803423173614009249d_enat A) B2))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B2) (=> (@ (@ tptp.dvd_dvd_nat C) D) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B2) D))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B2) (=> (@ (@ tptp.dvd_dvd_int C) D) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) D))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.dvd_dvd_real A) B2) (=> (@ (@ tptp.dvd_dvd_real C) D) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) D))))) (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex) (D tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex A) B2) (=> (@ (@ tptp.dvd_dvd_complex C) D) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B2) D))))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat) (D tptp.extended_enat)) (=> (@ (@ tptp.dvd_dv3785147216227455552d_enat A) B2) (=> (@ (@ tptp.dvd_dv3785147216227455552d_enat C) D) (@ (@ tptp.dvd_dv3785147216227455552d_enat (@ (@ tptp.times_7803423173614009249d_enat A) C)) (@ (@ tptp.times_7803423173614009249d_enat B2) D))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B2)) C) (@ (@ tptp.dvd_dvd_nat B2) C))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B2)) C) (@ (@ tptp.dvd_dvd_int B2) C))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) B2)) C) (@ (@ tptp.dvd_dvd_real B2) C))) (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.times_times_complex A) B2)) C) (@ (@ tptp.dvd_dvd_complex B2) C))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat)) (=> (@ (@ tptp.dvd_dv3785147216227455552d_enat (@ (@ tptp.times_7803423173614009249d_enat A) B2)) C) (@ (@ tptp.dvd_dv3785147216227455552d_enat B2) C))) (forall ((A tptp.nat) (B2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat B2) A))) (forall ((A tptp.int) (B2 tptp.int)) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int B2) A))) (forall ((A tptp.real) (B2 tptp.real)) (@ (@ tptp.dvd_dvd_real A) (@ (@ tptp.times_times_real B2) A))) (forall ((A tptp.complex) (B2 tptp.complex)) (@ (@ tptp.dvd_dvd_complex A) (@ (@ tptp.times_times_complex B2) A))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (@ (@ tptp.dvd_dv3785147216227455552d_enat A) (@ (@ tptp.times_7803423173614009249d_enat B2) 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.complex)) (@ (@ tptp.dvd_dvd_complex tptp.one_one_complex) A)) (forall ((A tptp.real)) (@ (@ tptp.dvd_dvd_real tptp.one_one_real) A)) (forall ((B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat B2))) (=> (@ _let_1 tptp.one_one_nat) (@ _let_1 A)))) (forall ((B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int B2))) (=> (@ _let_1 tptp.one_one_int) (@ _let_1 A)))) (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B2) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (@ _let_1 tptp.one_one_nat))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B2) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (@ _let_1 tptp.one_one_int))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B2) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B2) C)) (@ _let_1 C))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B2) (= (@ _let_1 (@ (@ tptp.plus_plus_int B2) C)) (@ _let_1 C))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 B2) (= (@ _let_1 (@ (@ tptp.plus_plus_real B2) C)) (@ _let_1 C))))) (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 C) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B2) C)) (@ _let_1 B2))))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 C) (= (@ _let_1 (@ (@ tptp.plus_plus_int B2) C)) (@ _let_1 B2))))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 C) (= (@ _let_1 (@ (@ tptp.plus_plus_real B2) C)) (@ _let_1 B2))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat B2) C)))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int B2) C)))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_real B2) C)))))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.dvd_dv3785147216227455552d_enat A))) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_p3455044024723400733d_enat B2) C)))))) (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= (= (@ (@ tptp.divide_divide_nat A) C) (@ (@ tptp.divide_divide_nat B2) C)) (= A B2)))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= (= (@ (@ tptp.divide_divide_int A) C) (@ (@ tptp.divide_divide_int B2) C)) (= A B2)))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real C))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= (= (@ (@ tptp.divide_divide_real A) C) (@ (@ tptp.divide_divide_real B2) C)) (= A B2)))))) (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C))) (=> (= (@ (@ tptp.divide_divide_nat A) C) (@ (@ tptp.divide_divide_nat B2) C)) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= A B2)))))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (= (@ (@ tptp.divide_divide_int A) C) (@ (@ tptp.divide_divide_int B2) C)) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= A B2)))))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real C))) (=> (= (@ (@ tptp.divide_divide_real A) C) (@ (@ tptp.divide_divide_real B2) C)) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= A B2)))))) (forall ((D tptp.nat) (B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat D) B2) (=> (@ (@ tptp.dvd_dvd_nat B2) A) (= (@ (@ tptp.divide_divide_nat (@ _let_1 D)) (@ (@ tptp.divide_divide_nat B2) D)) (@ _let_1 B2)))))) (forall ((D tptp.int) (B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int D) B2) (=> (@ (@ tptp.dvd_dvd_int B2) A) (= (@ (@ tptp.divide_divide_int (@ _let_1 D)) (@ (@ tptp.divide_divide_int B2) D)) (@ _let_1 B2)))))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M2) N2)) M2)) (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))) (forall ((A tptp.nat)) (let ((_let_1 (not (= A tptp.zero_zero_nat)))) (= _let_1 (and (@ (@ tptp.dvd_dvd_nat A) tptp.zero_zero_nat) _let_1)))) (forall ((A tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))) (forall ((A tptp.nat)) (not (and (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (not (= tptp.zero_zero_nat A))))) (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) tptp.zero_zero_nat)) (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.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.numeral_numeral_int N2))) (= (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_int _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)))) _let_195 (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 ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.nat_set_decode M2)) (@ tptp.nat_set_decode N2)) (@ (@ tptp.ord_less_eq_nat M2) N2))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat A) B2)) A))) (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.modulo_modulo_int A) B2)) A))) (forall ((B2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2) (@ (@ tptp.ord_less_nat (@ (@ tptp.modulo_modulo_nat A) B2)) B2))) (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (@ (@ tptp.ord_less_int (@ (@ tptp.modulo_modulo_int A) B2)) B2))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat A) B2) A) (= (@ (@ tptp.divide_divide_nat A) B2) tptp.zero_zero_nat))) (forall ((A tptp.int) (B2 tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int A) B2) A) (= (@ (@ tptp.divide_divide_int A) B2) tptp.zero_zero_int))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int B2) C)) (not (forall ((D5 tptp.int)) (not (= B2 (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int C) D5)))))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B2)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) C)) (@ (@ tptp.divide_divide_nat B2) C))) (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) C)) (@ (@ tptp.modulo_modulo_nat B2) C))) C)))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B2)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B2) C))) (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) C)) (@ (@ tptp.modulo_modulo_int B2) C))) C)))) (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 ((D tptp.nat) (S tptp.nat)) (exists ((Z 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) Z) (= _let_1 _let_1)))))) (forall ((D tptp.extended_enat) (S tptp.extended_enat)) (exists ((Z tptp.extended_enat)) (forall ((X2 tptp.extended_enat)) (let ((_let_1 (not (@ (@ tptp.dvd_dv3785147216227455552d_enat D) (@ (@ tptp.plus_p3455044024723400733d_enat X2) S))))) (=> (@ (@ tptp.ord_le72135733267957522d_enat X2) Z) (= _let_1 _let_1)))))) (forall ((D tptp.real) (S tptp.real)) (exists ((Z 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) Z) (= _let_1 _let_1)))))) (forall ((D tptp.int) (S tptp.int)) (exists ((Z 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) Z) (= _let_1 _let_1)))))) (forall ((D tptp.nat) (S tptp.nat)) (exists ((Z 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) Z) (= _let_1 _let_1)))))) (forall ((D tptp.extended_enat) (S tptp.extended_enat)) (exists ((Z tptp.extended_enat)) (forall ((X2 tptp.extended_enat)) (let ((_let_1 (@ (@ tptp.dvd_dv3785147216227455552d_enat D) (@ (@ tptp.plus_p3455044024723400733d_enat X2) S)))) (=> (@ (@ tptp.ord_le72135733267957522d_enat X2) Z) (= _let_1 _let_1)))))) (forall ((D tptp.real) (S tptp.real)) (exists ((Z 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) Z) (= _let_1 _let_1)))))) (forall ((D tptp.int) (S tptp.int)) (exists ((Z 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) Z) (= _let_1 _let_1)))))) (forall ((D tptp.nat) (S tptp.nat)) (exists ((Z 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 Z) X2) (= _let_1 _let_1)))))) (forall ((D tptp.extended_enat) (S tptp.extended_enat)) (exists ((Z tptp.extended_enat)) (forall ((X2 tptp.extended_enat)) (let ((_let_1 (not (@ (@ tptp.dvd_dv3785147216227455552d_enat D) (@ (@ tptp.plus_p3455044024723400733d_enat X2) S))))) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z) X2) (= _let_1 _let_1)))))) (forall ((D tptp.real) (S tptp.real)) (exists ((Z 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 Z) X2) (= _let_1 _let_1)))))) (forall ((D tptp.int) (S tptp.int)) (exists ((Z 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 Z) X2) (= _let_1 _let_1)))))) (forall ((D tptp.nat) (S tptp.nat)) (exists ((Z tptp.nat)) (forall ((X2 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X2) S)))) (=> (@ (@ tptp.ord_less_nat Z) X2) (= _let_1 _let_1)))))) (forall ((D tptp.extended_enat) (S tptp.extended_enat)) (exists ((Z tptp.extended_enat)) (forall ((X2 tptp.extended_enat)) (let ((_let_1 (@ (@ tptp.dvd_dv3785147216227455552d_enat D) (@ (@ tptp.plus_p3455044024723400733d_enat X2) S)))) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z) X2) (= _let_1 _let_1)))))) (forall ((D tptp.real) (S tptp.real)) (exists ((Z tptp.real)) (forall ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X2) S)))) (=> (@ (@ tptp.ord_less_real Z) X2) (= _let_1 _let_1)))))) (forall ((D tptp.int) (S tptp.int)) (exists ((Z tptp.int)) (forall ((X2 tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X2) S)))) (=> (@ (@ tptp.ord_less_int Z) X2) (= _let_1 _let_1)))))) (forall ((B2 tptp.complex) (A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex B2) A) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B2) tptp.zero_zero_complex) (= A tptp.zero_zero_complex)))) (forall ((B2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) A) (= (= (@ (@ tptp.divide_divide_nat A) B2) tptp.zero_zero_nat) (= A tptp.zero_zero_nat)))) (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B2) A) (= (= (@ (@ tptp.divide_divide_int A) B2) tptp.zero_zero_int) (= A tptp.zero_zero_int)))) (forall ((B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real B2) A) (= (= (@ (@ tptp.divide_divide_real A) B2) tptp.zero_zero_real) (= A tptp.zero_zero_real)))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (= (@ (@ tptp.times_times_nat B2) A) (@ (@ tptp.times_times_nat C) A)) (= B2 C)))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (= (@ (@ tptp.times_times_int B2) A) (@ (@ tptp.times_times_int C) A)) (= B2 C)))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B2)) C) (@ (@ tptp.dvd_dvd_nat B2) C)))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B2)) C) (@ (@ tptp.dvd_dvd_int B2) C)))) (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.times_times_nat B2) C)) (@ _let_1 C))))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.times_times_int B2) C)) (@ _let_1 C))))) (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B2)) C) (@ (@ tptp.dvd_dvd_nat A) C)))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B2)) C) (@ (@ tptp.dvd_dvd_int A) C)))) (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.times_times_nat C) B2)) (@ _let_1 C))))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.times_times_int C) B2)) (@ _let_1 C))))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B2)) tptp.one_one_nat) (and (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat)))) (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B2)) tptp.one_one_int) (and (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M2) N2)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M2)) 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)) (@ tptp.finite_finite_nat (@ tptp.nat_set_decode N2))) (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat) (P5 tptp.nat) (M2 tptp.nat)) (=> (@ P N2) (=> (@ (@ tptp.ord_less_nat N2) P5) (=> (@ (@ tptp.ord_less_nat M2) P5) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N3) P5) (=> (@ P N3) (@ P (@ (@ tptp.modulo_modulo_nat (@ tptp.suc N3)) P5))))) (@ P M2)))))) (forall ((C tptp.nat) (B2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat C) B2) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat B2) C)) A) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat B2) A)) C)))) (forall ((C tptp.int) (B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int C) B2) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int B2) C)) A) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int B2) A)) C)))) (forall ((C tptp.nat) (B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) B2) (= (@ _let_1 (@ (@ tptp.divide_divide_nat B2) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B2)) C))))) (forall ((C tptp.int) (B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.dvd_dvd_int C) B2) (= (@ _let_1 (@ (@ tptp.divide_divide_int B2) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B2)) C))))) (forall ((C tptp.nat) (B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) B2) (=> (@ (@ tptp.dvd_dvd_nat B2) A) (= (@ _let_1 (@ (@ tptp.divide_divide_nat B2) C)) (@ (@ tptp.times_times_nat (@ _let_1 B2)) C)))))) (forall ((C tptp.int) (B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int C) B2) (=> (@ (@ tptp.dvd_dvd_int B2) A) (= (@ _let_1 (@ (@ tptp.divide_divide_int B2) C)) (@ (@ tptp.times_times_int (@ _let_1 B2)) C)))))) (forall ((B2 tptp.nat) (C tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (let ((_let_2 (@ (@ tptp.times_times_nat B2) C))) (=> (@ (@ tptp.dvd_dvd_nat _let_2) A) (= (@ _let_1 _let_2) (@ (@ tptp.divide_divide_nat (@ _let_1 B2)) C)))))) (forall ((B2 tptp.int) (C tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (let ((_let_2 (@ (@ tptp.times_times_int B2) C))) (=> (@ (@ tptp.dvd_dvd_int _let_2) A) (= (@ _let_1 _let_2) (@ (@ tptp.divide_divide_int (@ _let_1 B2)) C)))))) (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) C)) B2) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.divide_divide_nat B2) C)))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) B2) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.divide_divide_int B2) C)))) (forall ((B2 tptp.nat) (A tptp.nat) (D tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) A) (=> (@ (@ tptp.dvd_dvd_nat D) C) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B2)) (@ (@ tptp.divide_divide_nat C) D)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B2) D)))))) (forall ((B2 tptp.int) (A tptp.int) (D tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B2) A) (=> (@ (@ tptp.dvd_dvd_int D) C) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B2)) (@ (@ tptp.divide_divide_int C) D)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) D)))))) (forall ((P (-> tptp.nat tptp.nat Bool)) (M2 tptp.nat) (N2 tptp.nat)) (=> (forall ((M3 tptp.nat)) (@ (@ P M3) tptp.zero_zero_nat)) (=> (forall ((M3 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (=> (@ (@ P N3) (@ (@ tptp.modulo_modulo_nat M3) N3)) (@ (@ P M3) N3)))) (@ (@ P M2) N2)))) (forall ((N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_nat (@ (@ tptp.modulo_modulo_nat M2) N2)) N2))) (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.divide_divide_nat C) B2)) (@ _let_1 C))))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.divide_divide_int C) B2)) (@ _let_1 C))))) (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat A) B2)) C) (@ (@ tptp.dvd_dvd_nat A) C)))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int A) B2)) C) (@ (@ tptp.dvd_dvd_int A) C)))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (= (@ (@ tptp.divide_divide_nat B2) A) (@ (@ tptp.divide_divide_nat C) A)) (= B2 C)))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (= (@ (@ tptp.divide_divide_int B2) A) (@ (@ tptp.divide_divide_int C) A)) (= B2 C)))) (forall ((C tptp.nat) (B2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat C) B2) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B2)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) C)) (@ (@ tptp.divide_divide_nat B2) C))))) (forall ((C tptp.int) (B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int C) B2) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B2)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B2) C))))) (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat C) A) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B2)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) C)) (@ (@ tptp.divide_divide_nat B2) C))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int C) A) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B2)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B2) C))))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M2) (@ tptp.suc N2))) N2)) (forall ((M2 tptp.nat) (D tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M2) D) tptp.zero_zero_nat) (exists ((Q2 tptp.nat)) (= M2 (@ (@ tptp.times_times_nat D) Q2))))) (forall ((X tptp.nat) (Y tptp.nat) (N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X) Y) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X) N2)) (@ (@ tptp.power_power_nat Y) M2))))) (forall ((X tptp.real) (Y tptp.real) (N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_real X) Y) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.power_power_real X) N2)) (@ (@ tptp.power_power_real Y) M2))))) (forall ((X tptp.complex) (Y tptp.complex) (N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_complex X) Y) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.power_power_complex X) N2)) (@ (@ tptp.power_power_complex Y) M2))))) (forall ((X tptp.int) (Y tptp.int) (N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int X) Y) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int X) N2)) (@ (@ tptp.power_power_int Y) M2))))) (forall ((A tptp.nat) (N2 tptp.nat) (B2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 N2)) B2) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.dvd_dvd_nat (@ _let_1 M2)) B2))))) (forall ((A tptp.real) (N2 tptp.nat) (B2 tptp.real) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.dvd_dvd_real (@ _let_1 N2)) B2) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.dvd_dvd_real (@ _let_1 M2)) B2))))) (forall ((A tptp.complex) (N2 tptp.nat) (B2 tptp.complex) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (@ (@ tptp.dvd_dvd_complex (@ _let_1 N2)) B2) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.dvd_dvd_complex (@ _let_1 M2)) B2))))) (forall ((A tptp.int) (N2 tptp.nat) (B2 tptp.int) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.dvd_dvd_int (@ _let_1 N2)) B2) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.dvd_dvd_int (@ _let_1 M2)) B2))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.dvd_dvd_nat (@ _let_1 M2)) (@ _let_1 N2))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.dvd_dvd_real (@ _let_1 M2)) (@ _let_1 N2))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.dvd_dvd_complex (@ _let_1 M2)) (@ _let_1 N2))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.dvd_dvd_int (@ _let_1 M2)) (@ _let_1 N2))))) (forall ((X tptp.nat) (N2 tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat X) N2) (@ (@ tptp.modulo_modulo_nat Y) N2)) (exists ((Q1 tptp.nat) (Q22 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N2))) (= (@ (@ tptp.plus_plus_nat X) (@ _let_1 Q1)) (@ (@ tptp.plus_plus_nat Y) (@ _let_1 Q22))))))) (forall ((N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N2) (=> (@ (@ tptp.dvd_dvd_nat M2) N2) (@ _let_1 M2))))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_nat M2) N2) (not (@ (@ tptp.dvd_dvd_nat N2) M2))))) (forall ((A tptp.nat) (B2 tptp.nat)) (exists ((D5 tptp.nat) (X5 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ tptp.times_times_nat B2))) (let ((_let_3 (@ tptp.dvd_dvd_nat D5))) (and (@ _let_3 A) (@ _let_3 B2) (or (= (@ _let_1 X5) (@ (@ tptp.plus_plus_nat (@ _let_2 Y3)) D5)) (= (@ _let_2 X5) (@ (@ tptp.plus_plus_nat (@ _let_1 Y3)) D5))))))))) (forall ((D tptp.nat) (A tptp.nat) (B2 tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ tptp.times_times_nat B2))) (let ((_let_3 (@ tptp.dvd_dvd_nat D))) (=> (@ _let_3 A) (=> (@ _let_3 B2) (=> (or (= (@ _let_1 X) (@ (@ tptp.plus_plus_nat (@ _let_2 Y)) D)) (= (@ _let_2 X) (@ (@ 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) B2))) (let ((_let_3 (@ tptp.times_times_nat _let_2))) (let ((_let_4 (@ tptp.dvd_dvd_nat D))) (and (@ _let_4 A) (@ _let_4 _let_2) (or (= (@ _let_1 X5) (@ (@ tptp.plus_plus_nat (@ _let_3 Y3)) D)) (= (@ _let_3 X5) (@ (@ tptp.plus_plus_nat (@ _let_1 Y3)) D)))))))))))))))) (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.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 ((A2 tptp.set_complex) (N2 tptp.nat)) (=> (@ tptp.finite3207457112153483333omplex A2) (@ tptp.finite8712137658972009173omplex (@ tptp.collect_list_complex (lambda ((Xs3 tptp.list_complex)) (and (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs3)) A2) (= (@ tptp.size_s3451745648224563538omplex Xs3) N2))))))) (forall ((A2 tptp.set_Extended_enat) (N2 tptp.nat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (@ tptp.finite1862508098717546133d_enat (@ tptp.collec8433460942617342167d_enat (lambda ((Xs3 tptp.list_Extended_enat)) (and (@ (@ tptp.ord_le7203529160286727270d_enat (@ tptp.set_Extended_enat2 Xs3)) A2) (= (@ tptp.size_s3941691890525107288d_enat Xs3) N2))))))) (forall ((A2 tptp.set_VEBT_VEBT) (N2 tptp.nat)) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (@ tptp.finite3004134309566078307T_VEBT (@ tptp.collec5608196760682091941T_VEBT (lambda ((Xs3 tptp.list_VEBT_VEBT)) (and (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs3)) A2) (= (@ tptp.size_s6755466524823107622T_VEBT Xs3) N2))))))) (forall ((A2 tptp.set_nat) (N2 tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((Xs3 tptp.list_nat)) (and (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs3)) A2) (= (@ tptp.size_size_list_nat Xs3) N2))))))) (forall ((A2 tptp.set_int) (N2 tptp.nat)) (=> (@ tptp.finite_finite_int A2) (@ tptp.finite3922522038869484883st_int (@ tptp.collect_list_int (lambda ((Xs3 tptp.list_int)) (and (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs3)) A2) (= (@ tptp.size_size_list_int Xs3) N2))))))) (forall ((Va2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_1))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_2))) (let ((_let_8 (@ tptp.vEBT_vebt_buildup _let_2))) (let ((_let_9 (@ (@ tptp.dvd_dvd_nat _let_1) _let_2))) (and (=> _let_9 (= _let_8 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_9) (= _let_8 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4))))))))))))))) (forall ((B2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.modulo_modulo_nat A) B2)))) (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.modulo_modulo_int A) B2)))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) B2) (= (@ (@ tptp.modulo_modulo_nat A) B2) A)))) (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) B2) (= (@ (@ tptp.modulo_modulo_int A) B2) A)))) (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)) (= (@ (@ 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 ((A2 tptp.set_complex) (N2 tptp.nat)) (=> (@ tptp.finite3207457112153483333omplex A2) (@ tptp.finite8712137658972009173omplex (@ tptp.collect_list_complex (lambda ((Xs3 tptp.list_complex)) (and (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs3)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s3451745648224563538omplex Xs3)) N2))))))) (forall ((A2 tptp.set_Extended_enat) (N2 tptp.nat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (@ tptp.finite1862508098717546133d_enat (@ tptp.collec8433460942617342167d_enat (lambda ((Xs3 tptp.list_Extended_enat)) (and (@ (@ tptp.ord_le7203529160286727270d_enat (@ tptp.set_Extended_enat2 Xs3)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s3941691890525107288d_enat Xs3)) N2))))))) (forall ((A2 tptp.set_VEBT_VEBT) (N2 tptp.nat)) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (@ tptp.finite3004134309566078307T_VEBT (@ tptp.collec5608196760682091941T_VEBT (lambda ((Xs3 tptp.list_VEBT_VEBT)) (and (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs3)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT Xs3)) N2))))))) (forall ((A2 tptp.set_nat) (N2 tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((Xs3 tptp.list_nat)) (and (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs3)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs3)) N2))))))) (forall ((A2 tptp.set_int) (N2 tptp.nat)) (=> (@ tptp.finite_finite_int A2) (@ tptp.finite3922522038869484883st_int (@ tptp.collect_list_int (lambda ((Xs3 tptp.list_int)) (and (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs3)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs3)) N2))))))) (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B2) (@ (@ tptp.divide_divide_nat A) B2))) (@ (@ tptp.modulo_modulo_nat A) B2))) C) (@ (@ tptp.plus_plus_nat A) C))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) (@ (@ tptp.divide_divide_int A) B2))) (@ (@ tptp.modulo_modulo_int A) B2))) C) (@ (@ tptp.plus_plus_int A) C))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B2)) B2)) (@ (@ tptp.modulo_modulo_nat A) B2))) C) (@ (@ tptp.plus_plus_nat A) C))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B2)) B2)) (@ (@ tptp.modulo_modulo_int A) B2))) C) (@ (@ tptp.plus_plus_int A) C))) (forall ((A tptp.nat) (B2 tptp.nat)) (= A (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B2)) B2)) (@ (@ tptp.modulo_modulo_nat A) B2)))) (forall ((A tptp.int) (B2 tptp.int)) (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B2)) B2)) (@ (@ tptp.modulo_modulo_int A) B2)))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B2)) B2)) (@ (@ tptp.modulo_modulo_nat A) B2)) A)) (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B2)) B2)) (@ (@ tptp.modulo_modulo_int A) B2)) A)) (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) B2)) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B2)) B2)) A)) (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) B2)) (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B2)) B2)) A)) (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) B2)) (@ (@ tptp.times_times_nat B2) (@ (@ tptp.divide_divide_nat A) B2))) A)) (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) B2)) (@ (@ tptp.times_times_int B2) (@ (@ tptp.divide_divide_int A) B2))) A)) (forall ((B2 tptp.nat) (A tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B2) (@ (@ tptp.divide_divide_nat A) B2))) (@ (@ tptp.modulo_modulo_nat A) B2)) A)) (forall ((B2 tptp.int) (A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) (@ (@ tptp.divide_divide_int A) B2))) (@ (@ tptp.modulo_modulo_int A) B2)) A)) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.divide_divide_nat (@ _let_1 B2)) C) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.divide_divide_nat B2) C))) (@ (@ tptp.divide_divide_nat (@ _let_1 (@ (@ tptp.modulo_modulo_nat B2) C))) C))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.divide_divide_int (@ _let_1 B2)) C) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.divide_divide_int B2) C))) (@ (@ tptp.divide_divide_int (@ _let_1 (@ (@ tptp.modulo_modulo_int B2) C))) C))))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (not (=> (not (= A tptp.zero_zero_nat)) (forall ((C2 tptp.nat)) (not (= B2 (@ (@ tptp.times_times_nat A) C2)))))))) (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (not (=> (not (= A tptp.zero_zero_int)) (forall ((C2 tptp.int)) (not (= B2 (@ (@ tptp.times_times_int A) C2)))))))) (forall ((P (-> tptp.nat Bool)) (L tptp.nat)) (= (exists ((X4 tptp.nat)) (@ P (@ (@ tptp.times_times_nat L) X4))) (exists ((X4 tptp.nat)) (and (@ (@ tptp.dvd_dvd_nat L) (@ (@ tptp.plus_plus_nat X4) tptp.zero_zero_nat)) (@ P X4))))) (forall ((P (-> tptp.int Bool)) (L tptp.int)) (= (exists ((X4 tptp.int)) (@ P (@ (@ tptp.times_times_int L) X4))) (exists ((X4 tptp.int)) (and (@ (@ tptp.dvd_dvd_int L) (@ (@ tptp.plus_plus_int X4) tptp.zero_zero_int)) (@ P X4))))) (forall ((P (-> tptp.real Bool)) (L tptp.real)) (= (exists ((X4 tptp.real)) (@ P (@ (@ tptp.times_times_real L) X4))) (exists ((X4 tptp.real)) (and (@ (@ tptp.dvd_dvd_real L) (@ (@ tptp.plus_plus_real X4) tptp.zero_zero_real)) (@ P X4))))) (forall ((P (-> tptp.complex Bool)) (L tptp.complex)) (= (exists ((X4 tptp.complex)) (@ P (@ (@ tptp.times_times_complex L) X4))) (exists ((X4 tptp.complex)) (and (@ (@ tptp.dvd_dvd_complex L) (@ (@ tptp.plus_plus_complex X4) tptp.zero_zero_complex)) (@ P X4))))) (forall ((P (-> tptp.extended_enat Bool)) (L tptp.extended_enat)) (= (exists ((X4 tptp.extended_enat)) (@ P (@ (@ tptp.times_7803423173614009249d_enat L) X4))) (exists ((X4 tptp.extended_enat)) (and (@ (@ tptp.dvd_dv3785147216227455552d_enat L) (@ (@ tptp.plus_p3455044024723400733d_enat X4) tptp.zero_z5237406670263579293d_enat)) (@ P X4))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B2) (= (= (@ (@ tptp.divide_divide_nat B2) A) C) (= B2 (@ (@ tptp.times_times_nat C) A)))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int A) B2) (= (= (@ (@ tptp.divide_divide_int B2) A) C) (= B2 (@ (@ tptp.times_times_int C) A)))))) (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (not (= B2 tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) A) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat A) B2)) C) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat C) B2)))))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B2 tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B2) A) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int A) B2)) C) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int C) B2)))))) (forall ((C tptp.nat) (B2 tptp.nat) (A tptp.nat)) (=> (not (= C tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat C) B2) (= (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.divide_divide_nat B2) C)) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) C)) B2))))) (forall ((C tptp.int) (B2 tptp.int) (A tptp.int)) (=> (not (= C tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int C) B2) (= (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.divide_divide_int B2) C)) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) B2))))) (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat) (D tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (not (= C tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B2) (=> (@ (@ tptp.dvd_dvd_nat C) D) (= (= (@ (@ tptp.divide_divide_nat B2) A) (@ (@ tptp.divide_divide_nat D) C)) (= (@ (@ tptp.times_times_nat B2) C) (@ (@ tptp.times_times_nat A) D)))))))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int) (D tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (not (= C tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int A) B2) (=> (@ (@ tptp.dvd_dvd_int C) D) (= (= (@ (@ tptp.divide_divide_int B2) A) (@ (@ tptp.divide_divide_int D) C)) (= (@ (@ tptp.times_times_int B2) C) (@ (@ tptp.times_times_int A) D)))))))) (forall ((B2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (= (= (@ (@ tptp.divide_divide_nat A) B2) tptp.zero_zero_nat) (= A tptp.zero_zero_nat)))) (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (= (= (@ (@ tptp.divide_divide_int A) B2) tptp.zero_zero_int) (= A tptp.zero_zero_int)))) (forall ((B2 tptp.nat) (C tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat C) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.times_times_nat B2) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B2)) C)))))) (forall ((B2 tptp.int) (C tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int C) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.times_times_int B2) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B2)) C)))))) (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.divide_divide_nat B2) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B2)) C))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.dvd_dvd_int C) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.divide_divide_int B2) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B2)) C))))) (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B2)) C) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) C)) B2)))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B2)) C) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) C)) B2)))) (forall ((C tptp.nat) (B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat B2) A) (= (@ _let_1 (@ (@ tptp.times_times_nat B2) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B2)) C)))))) (forall ((C tptp.int) (B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int C) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int B2) A) (= (@ _let_1 (@ (@ tptp.times_times_int B2) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B2)) C)))))) (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (= (= A (@ (@ tptp.divide_divide_nat C) B2)) (= (@ (@ tptp.times_times_nat A) B2) C)))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (= (= A (@ (@ tptp.divide_divide_int C) B2)) (= (@ (@ tptp.times_times_int A) B2) C)))) (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (= (= (@ (@ tptp.divide_divide_nat A) B2) C) (= A (@ (@ tptp.times_times_nat C) B2))))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (= (= (@ (@ tptp.divide_divide_int A) B2) C) (= A (@ (@ tptp.times_times_int C) B2))))) (forall ((N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M2) N2)) N2))) (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 ((A2 tptp.nat) (B tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (= (@ (@ tptp.modulo_modulo_nat A2) N2) tptp.zero_zero_nat) (=> (= (@ (@ tptp.modulo_modulo_nat B) N2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat A2) N2)) (@ (@ tptp.divide_divide_nat B) N2))))))) (forall ((M2 tptp.nat) (Q3 tptp.nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M2) Q3) (@ (@ tptp.modulo_modulo_nat N2) Q3)) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (not (forall ((S3 tptp.nat)) (not (= M2 (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.times_times_nat Q3) S3))))))))) (forall ((M2 tptp.nat) (Q3 tptp.nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M2) Q3) (@ (@ tptp.modulo_modulo_nat N2) Q3)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (not (forall ((S3 tptp.nat)) (not (= N2 (@ (@ tptp.plus_plus_nat M2) (@ (@ tptp.times_times_nat Q3) S3))))))))) (forall ((X tptp.nat) (N2 tptp.nat) (Y tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat X) N2) (@ (@ tptp.modulo_modulo_nat Y) N2)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (exists ((Q2 tptp.nat)) (= X (@ (@ tptp.plus_plus_nat Y) (@ (@ tptp.times_times_nat N2) Q2))))))) (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 ((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 ((M2 tptp.nat) (N2 tptp.nat) (Q3 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat M2))) (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 M2) N2)) Q3))) (@ _let_1 N2)))))) (forall ((K tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M2)) (@ _let_1 N2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.dvd_dvd_nat M2) N2))))) (forall ((K tptp.nat) (M2 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 M2)) (@ _let_1 N2)) (@ (@ tptp.dvd_dvd_nat M2) N2))))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (exists ((D5 tptp.nat) (X5 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat D5))) (and (@ _let_1 A) (@ _let_1 B2) (= (@ (@ tptp.times_times_nat A) X5) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B2) Y3)) D5))))))) (forall ((X tptp.nat) (Y tptp.vEBT_VEBT)) (let ((_let_1 (not (= Y (@ (@ tptp.vEBT_Leaf false) false))))) (=> (= (@ tptp.vEBT_vebt_buildup X) Y) (=> (=> (= X tptp.zero_zero_nat) _let_1) (=> (=> (= X (@ tptp.suc tptp.zero_zero_nat)) _let_1) (not (forall ((Va tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_1))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_2))) (let ((_let_8 (@ (@ tptp.dvd_dvd_nat _let_1) _let_2))) (=> (= X _let_2) (not (and (=> _let_8 (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_8) (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4)))))))))))))))))))))) (@ (@ tptp.dvd_dvd_nat _let_194) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_int _let_82) tptp.zero_zero_int) (forall ((A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (not (=> (not (= A tptp.zero_zero_nat)) (forall ((B4 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat tptp.one_one_nat))) (=> (not (= B4 tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B4) tptp.one_one_nat) (=> (= (@ _let_1 A) B4) (=> (= (@ _let_1 B4) A) (=> (= (@ (@ tptp.times_times_nat A) B4) tptp.one_one_nat) (not (= (@ (@ tptp.divide_divide_nat C) A) (@ (@ tptp.times_times_nat C) B4)))))))))))))) (forall ((A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (not (=> (not (= A tptp.zero_zero_int)) (forall ((B4 tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int tptp.one_one_int))) (=> (not (= B4 tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B4) tptp.one_one_int) (=> (= (@ _let_1 A) B4) (=> (= (@ _let_1 B4) A) (=> (= (@ (@ tptp.times_times_int A) B4) tptp.one_one_int) (not (= (@ (@ tptp.divide_divide_int C) A) (@ (@ tptp.times_times_int C) B4)))))))))))))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (= (@ (@ tptp.divide_divide_nat A) (@ (@ tptp.times_times_nat A) B2)) (@ (@ tptp.divide_divide_nat tptp.one_one_nat) B2))))) (forall ((A tptp.int) (B2 tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (= (@ (@ tptp.divide_divide_int A) (@ (@ tptp.times_times_int A) B2)) (@ (@ tptp.divide_divide_int tptp.one_one_int) B2))))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (= (@ (@ tptp.divide_divide_nat A) (@ (@ tptp.times_times_nat B2) A)) (@ (@ tptp.divide_divide_nat tptp.one_one_nat) B2))))) (forall ((A tptp.int) (B2 tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (= (@ (@ tptp.divide_divide_int A) (@ (@ tptp.times_times_int B2) A)) (@ (@ tptp.divide_divide_int tptp.one_one_int) B2))))) (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (not (@ _let_1 A)) (=> (not (@ _let_1 B2)) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B2)))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (not (@ _let_1 A)) (=> (not (@ _let_1 B2)) (@ _let_1 (@ (@ tptp.plus_plus_int A) B2)))))) (forall ((X tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat X))) (=> (not (= X tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M2)) (@ _let_1 N2)) (or (@ (@ tptp.dvd_dvd_nat X) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat M2) N2)))))) (forall ((X tptp.int) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X))) (=> (not (= X tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 M2)) (@ _let_1 N2)) (or (@ (@ tptp.dvd_dvd_int X) tptp.one_one_int) (@ (@ tptp.ord_less_eq_nat M2) N2)))))) (forall ((N2 tptp.nat) (X tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X tptp.one_one_nat)) (@ (@ tptp.dvd_dvd_nat X) (@ (@ tptp.power_power_nat X) N2)))) (forall ((N2 tptp.nat) (X tptp.real)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X tptp.one_one_real)) (@ (@ tptp.dvd_dvd_real X) (@ (@ tptp.power_power_real X) N2)))) (forall ((N2 tptp.nat) (X tptp.complex)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X tptp.one_one_complex)) (@ (@ tptp.dvd_dvd_complex X) (@ (@ tptp.power_power_complex X) N2)))) (forall ((N2 tptp.nat) (X tptp.int)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X tptp.one_one_int)) (@ (@ tptp.dvd_dvd_int X) (@ (@ tptp.power_power_int X) N2)))) (forall ((P (-> tptp.nat Bool)) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (= N2 tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.modulo_modulo_nat M2) N2)) (and (=> _let_1 (@ P M2)) (=> (not _let_1) (forall ((I3 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J2) N2) (=> (= M2 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N2) I3)) J2)) (@ P J2))))))))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat M2) N2)) M2) (= N2 tptp.one_one_nat)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat N2) M2)) M2) (= N2 tptp.one_one_nat)))) (forall ((I tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M2)) (@ _let_1 N2)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) I) (@ (@ tptp.ord_less_eq_nat M2) N2))))) (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat A))) (let ((_let_2 (@ tptp.times_times_nat B2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (= (@ _let_1 (@ _let_2 C)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat A) B2)) C))) (@ _let_1 B2))))))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ tptp.times_times_int B2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (= (@ _let_1 (@ _let_2 C)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A) B2)) C))) (@ _let_1 B2))))))) (forall ((N2 tptp.nat) (Xs tptp.list_P6011104703257516679at_nat) (Ys tptp.list_P6011104703257516679at_nat)) (let ((_let_1 (@ tptp.size_s5460976970255530739at_nat Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_s5460976970255530739at_nat Xs)) _let_1)) (= (@ (@ tptp.nth_Pr6744343527793145070at_nat (@ (@ tptp.produc3544356994491977349at_nat Xs) Ys)) N2) (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_Pr7617993195940197384at_nat 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_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_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_int) (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_int Xs)) _let_1)) (= (@ (@ tptp.nth_Pr3474266648193625910T_VEBT (@ (@ tptp.produc662631939642741121T_VEBT Xs) Ys)) N2) (@ (@ tptp.produc3329399203697025711T_VEBT (@ (@ tptp.nth_int 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_int) (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_int Xs)) _let_1)) (= (@ (@ tptp.nth_Pr4439495888332055232nt_int (@ (@ tptp.product_int_int Xs) Ys)) N2) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.nth_int 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_int) (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_int Xs)) _let_1)) (= (@ (@ tptp.nth_Pr8617346907841251940nt_nat (@ (@ tptp.product_int_nat Xs) Ys)) N2) (@ (@ tptp.product_Pair_int_nat (@ (@ tptp.nth_int 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_nat) (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_nat Xs)) _let_1)) (= (@ (@ tptp.nth_Pr744662078594809490T_VEBT (@ (@ tptp.produc7156399406898700509T_VEBT Xs) Ys)) N2) (@ (@ tptp.produc599794634098209291T_VEBT (@ (@ tptp.nth_nat 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_nat) (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_nat Xs)) _let_1)) (= (@ (@ tptp.nth_Pr3440142176431000676at_int (@ (@ tptp.product_nat_int Xs) Ys)) N2) (@ (@ tptp.product_Pair_nat_int (@ (@ tptp.nth_nat 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_nat) (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_nat Xs)) _let_1)) (= (@ (@ tptp.nth_Pr7617993195940197384at_nat (@ (@ tptp.product_nat_nat Xs) Ys)) N2) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.nth_nat Xs) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_nat Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))) (forall ((N2 tptp.nat) (A tptp.real) (B2 tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B2) N2))))) (forall ((N2 tptp.nat) (A tptp.int) (B2 tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B2) N2))))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M2) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.times_times_nat M2) N2))) M2) tptp.one_one_nat))) (forall ((N2 tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))) (forall ((K tptp.nat) (M2 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 M2)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M2) N2))))) (forall ((M2 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 M2) A)) (or (@ _let_1 A) (= M2 tptp.zero_zero_nat))))) (forall ((M2 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 M2) A)) (or (@ _let_1 A) (= M2 tptp.zero_zero_nat))))) (forall ((M2 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 M2) A)) (and (@ _let_1 A) (not (= M2 tptp.zero_zero_nat)))))) (forall ((M2 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 M2) A)) (and (@ _let_1 A) (not (= M2 tptp.zero_zero_nat)))))) (forall ((B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B2)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2) (=> (@ (@ tptp.ord_less_nat _let_2) B2) (= _let_2 (@ _let_1 B2))))))) (forall ((B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B2)))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_int _let_2) B2) (= _let_2 (@ _let_1 B2))))))) (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 ((Uy tptp.option4927543243414619207at_nat) (V tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (= (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ (@ (@ tptp.vEBT_Node Uy) _let_1) TreeList2) S)) X) (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) _let_4))))))) (forall ((A tptp.nat) (N2 tptp.nat) (M2 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 M2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M2)))) _let_2))))) (forall ((A tptp.int) (N2 tptp.nat) (M2 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 M2)) (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M2)))) _let_2))))) (forall ((A tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)) (not (forall ((B4 tptp.nat)) (not (= A (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B4)) tptp.one_one_nat))))))) (forall ((A tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)) (not (forall ((B4 tptp.int)) (not (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B4)) tptp.one_one_int))))))) (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ _let_1 (@ (@ tptp.power_power_real A) N2)) (or _let_2 (and (not _let_2) (@ _let_1 A))))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ _let_1 (@ (@ tptp.power_power_int A) N2)) (or _let_2 (and (not _let_2) (@ _let_1 A))))))) (forall ((N2 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ _let_1 (@ (@ tptp.power_power_real A) N2)) (@ _let_1 A))))) (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ _let_1 (@ (@ tptp.power_power_int A) N2)) (@ _let_1 A))))) (forall ((N2 tptp.nat) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A) N2)))) (forall ((N2 tptp.nat) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A) N2)))) (forall ((A2 tptp.nat) (B tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B) (=> (@ (@ 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 B) N2) tptp.zero_zero_nat)) tptp.one_one_nat) tptp.zero_zero_nat))) (@ (@ tptp.divide_divide_nat B) N2))))) (forall ((V tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Vd2)) X) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) _let_4))))))) (forall ((B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (let ((_let_2 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.modulo_modulo_nat A) _let_3)) B2) (= (@ _let_2 (@ _let_1 _let_3)) (@ _let_1 B2)))))))) (forall ((B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (let ((_let_2 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.modulo_modulo_int A) _let_3)) B2) (= (@ _let_2 (@ _let_1 _let_3)) (@ _let_1 B2)))))))) (forall ((Mi tptp.nat) (Ma tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Ma) X)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat X) Mi)))) (= (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList2) Summary)) X) (=> (not (= X Mi)) (=> (not (= X Ma)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) _let_4))))))))))))))) (forall ((Mi tptp.nat) (Ma tptp.nat) (V tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList2) Vc)) X) (or (= X Mi) (= X Ma) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) _let_4)))))))) (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ _let_1 (@ (@ tptp.power_power_real A) N2)) (or (= N2 tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_zero_real))) (and (not _let_2) (@ _let_1 A))))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ _let_1 (@ (@ tptp.power_power_int A) N2)) (or (= N2 tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_zero_int))) (and (not _let_2) (@ _let_1 A))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2) Y) (=> (forall ((A4 Bool) (B4 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A4) B4)) (= Y (not (and (=> _let_2 A4) (=> (not _let_2) (and (=> _let_1 B4) _let_1))))))))) (=> (=> (exists ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2))) Y) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((S3 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ 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 Xa2) _let_1))) _let_3))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2) (=> (forall ((A4 Bool) (B4 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A4) B4)) (not (and (=> _let_2 A4) (=> (not _let_2) (and (=> _let_1 B4) _let_1)))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((S3 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ 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 Xa2) _let_1))) _let_3))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2)) (=> (forall ((A4 Bool) (B4 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A4) B4)) (and (=> _let_2 A4) (=> (not _let_2) (and (=> _let_1 B4) _let_1))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2)))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((S3 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ 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 Xa2) _let_1))) _let_3))))))))))) (forall ((M2 tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat X))) (let ((_let_2 (@ _let_1 M2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_plus_nat _let_2) M2))))))))) (forall ((M2 tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int X))) (let ((_let_2 (@ _let_1 M2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) M2)))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_plus_int _let_2) M2))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_membermima X) Xa2) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList3) Vc2))) (not (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3)))))))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vd tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList3) Vd))) (not (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3)))))))))))) (forall ((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.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_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 ((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 ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N2)) tptp.zero_zero_real) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (or (and (not _let_1) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real)) (and _let_1 (= A tptp.zero_zero_real))))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N2)) tptp.zero_zero_int) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (or (and (not _let_1) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)) (and _let_1 (= A tptp.zero_zero_int))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member X) Xa2) (=> (forall ((A4 Bool) (B4 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A4) B4)) (not (and (=> _let_2 A4) (=> (not _let_2) (and (=> _let_1 B4) _let_1)))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList3) Summary2))) (not (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X) Xa2) Y) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) Y) (=> (=> (exists ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2))) Y) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (= Y (not (or (= Xa2 Mi2) (= Xa2 Ma2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList3) Vc2))) (= Y (not (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vd tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList3) Vd))) (= Y (not (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_membermima X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2)))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (or (= Xa2 Mi2) (= Xa2 Ma2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList3) Vc2))) (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vd tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList3) Vd))) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))) (forall ((Mi tptp.nat) (Ma tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList2) Summary))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ tptp.if_nat (@ (@ tptp.ord_less_nat X) Mi)))) (let ((_let_5 (@ (@ _let_4 Mi) X))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_6))) (= (@ (@ tptp.vEBT_vebt_insert _let_2) X) (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (not (or (= X Mi) (= X Ma))))) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_4 X) Mi)) (@ (@ tptp.ord_max_nat _let_5) Ma)))) _let_1) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) _let_6) (@ (@ tptp.vEBT_vebt_insert _let_7) (@ (@ tptp.vEBT_VEBT_low _let_5) _let_3)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_7)) (@ (@ tptp.vEBT_vebt_insert Summary) _let_6)) Summary))) _let_2)))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_vebt_member X) Xa2)) (=> (forall ((A4 Bool) (B4 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A4) B4)) (and (=> _let_2 A4) (=> (not _let_2) (and (=> _let_1 B4) _let_1))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList3) Summary2))) (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_vebt_member X) Xa2) Y) (=> (forall ((A4 Bool) (B4 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A4) B4)) (= Y (not (and (=> _let_2 A4) (=> (not _let_2) (and (=> _let_1 B4) _let_1))))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) Y) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) Y) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) Y) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList3) Summary2))) (= Y (not (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))))))))) (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (let ((_let_2 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2) (=> (@ (@ tptp.ord_less_eq_nat B2) (@ (@ tptp.modulo_modulo_nat A) _let_3)) (= (@ (@ tptp.plus_plus_nat (@ _let_2 (@ _let_1 _let_3))) tptp.one_one_nat) (@ _let_1 B2))))))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (let ((_let_2 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_eq_int B2) (@ (@ tptp.modulo_modulo_int A) _let_3)) (= (@ (@ tptp.plus_plus_int (@ _let_2 (@ _let_1 _let_3))) tptp.one_one_int) (@ _let_1 B2))))))))) (forall ((N2 tptp.nat) (C tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z6 tptp.complex)) (= (@ (@ tptp.power_power_complex Z6) N2) C)))))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((Z6 tptp.real)) (= (@ (@ tptp.power_power_real Z6) N2) tptp.one_one_real)))))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z6 tptp.complex)) (= (@ (@ tptp.power_power_complex Z6) N2) tptp.one_one_complex)))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_insert X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A4 Bool) (B4 Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A4))) (let ((_let_2 (@ _let_1 B4))) (let ((_let_3 (= Xa2 tptp.one_one_nat))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_2) (=> (and (=> _let_4 (= Y (@ (@ tptp.vEBT_Leaf true) B4))) (=> (not _let_4) (and (=> _let_3 (= Y (@ _let_1 true))) (=> (not _let_3) (= Y _let_2))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2)))))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts2) S3))) (=> (= X _let_1) (=> (= Y _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S3))) (=> (= X _let_1) (=> (= Y _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc V2)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Summary2))) (=> (= X _let_2) (=> (= Y (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Xa2) Xa2))) _let_1) TreeList3) Summary2)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2)))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_5 (@ (@ _let_4 Mi2) Xa2))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_6))) (=> (= X _let_2) (=> (= Y (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_4 Xa2) Mi2)) (@ (@ tptp.ord_max_nat _let_5) Ma2)))) _let_1) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList3) _let_6) (@ (@ tptp.vEBT_vebt_insert _let_7) (@ (@ tptp.vEBT_VEBT_low _let_5) _let_3)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_7)) (@ (@ tptp.vEBT_vebt_insert Summary2) _let_6)) Summary2))) _let_2)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))) (forall ((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.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 ((I6 tptp.set_real) (X (-> tptp.real tptp.nat)) (Y (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I6) (not (= (@ X I3) tptp.one_one_nat)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I6) (not (= (@ Y I3) tptp.one_one_nat)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I6) (not (= (@ (@ tptp.times_times_nat (@ X I3)) (@ Y I3)) tptp.one_one_nat))))))))) (forall ((I6 tptp.set_nat) (X (-> tptp.nat tptp.nat)) (Y (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I6) (not (= (@ X I3) tptp.one_one_nat)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I6) (not (= (@ Y I3) tptp.one_one_nat)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I6) (not (= (@ (@ tptp.times_times_nat (@ X I3)) (@ Y I3)) tptp.one_one_nat))))))))) (forall ((I6 tptp.set_complex) (X (-> tptp.complex tptp.nat)) (Y (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I3 tptp.complex)) (and (@ (@ tptp.member_complex I3) I6) (not (= (@ X I3) tptp.one_one_nat)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I3 tptp.complex)) (and (@ (@ tptp.member_complex I3) I6) (not (= (@ Y I3) tptp.one_one_nat)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I3 tptp.complex)) (and (@ (@ tptp.member_complex I3) I6) (not (= (@ (@ tptp.times_times_nat (@ X I3)) (@ Y I3)) tptp.one_one_nat))))))))) (forall ((I6 tptp.set_int) (X (-> tptp.int tptp.nat)) (Y (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.member_int I3) I6) (not (= (@ X I3) tptp.one_one_nat)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.member_int I3) I6) (not (= (@ Y I3) tptp.one_one_nat)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.member_int I3) I6) (not (= (@ (@ tptp.times_times_nat (@ X I3)) (@ Y I3)) tptp.one_one_nat))))))))) (forall ((I6 tptp.set_Extended_enat) (X (-> tptp.extended_enat tptp.nat)) (Y (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I3 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I3) I6) (not (= (@ X I3) tptp.one_one_nat)))))) (=> (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I3 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I3) I6) (not (= (@ Y I3) tptp.one_one_nat)))))) (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I3 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I3) I6) (not (= (@ (@ tptp.times_times_nat (@ X I3)) (@ Y I3)) tptp.one_one_nat))))))))) (forall ((I6 tptp.set_real) (X (-> tptp.real tptp.int)) (Y (-> tptp.real tptp.int))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I6) (not (= (@ X I3) tptp.one_one_int)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I6) (not (= (@ Y I3) tptp.one_one_int)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I6) (not (= (@ (@ tptp.times_times_int (@ X I3)) (@ Y I3)) tptp.one_one_int))))))))) (forall ((I6 tptp.set_nat) (X (-> tptp.nat tptp.int)) (Y (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I6) (not (= (@ X I3) tptp.one_one_int)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I6) (not (= (@ Y I3) tptp.one_one_int)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I6) (not (= (@ (@ tptp.times_times_int (@ X I3)) (@ Y I3)) tptp.one_one_int))))))))) (forall ((I6 tptp.set_complex) (X (-> tptp.complex tptp.int)) (Y (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I3 tptp.complex)) (and (@ (@ tptp.member_complex I3) I6) (not (= (@ X I3) tptp.one_one_int)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I3 tptp.complex)) (and (@ (@ tptp.member_complex I3) I6) (not (= (@ Y I3) tptp.one_one_int)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I3 tptp.complex)) (and (@ (@ tptp.member_complex I3) I6) (not (= (@ (@ tptp.times_times_int (@ X I3)) (@ Y I3)) tptp.one_one_int))))))))) (forall ((I6 tptp.set_int) (X (-> tptp.int tptp.int)) (Y (-> tptp.int tptp.int))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.member_int I3) I6) (not (= (@ X I3) tptp.one_one_int)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.member_int I3) I6) (not (= (@ Y I3) tptp.one_one_int)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.member_int I3) I6) (not (= (@ (@ tptp.times_times_int (@ X I3)) (@ Y I3)) tptp.one_one_int))))))))) (forall ((I6 tptp.set_Extended_enat) (X (-> tptp.extended_enat tptp.int)) (Y (-> tptp.extended_enat tptp.int))) (=> (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I3 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I3) I6) (not (= (@ X I3) tptp.one_one_int)))))) (=> (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I3 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I3) I6) (not (= (@ Y I3) tptp.one_one_int)))))) (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I3 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I3) I6) (not (= (@ (@ tptp.times_times_int (@ X I3)) (@ Y I3)) tptp.one_one_int))))))))) (forall ((I6 tptp.set_real) (X (-> tptp.real tptp.nat)) (Y (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I6) (not (= (@ X I3) tptp.zero_zero_nat)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I6) (not (= (@ Y I3) tptp.zero_zero_nat)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I6) (not (= (@ (@ tptp.plus_plus_nat (@ X I3)) (@ Y I3)) tptp.zero_zero_nat))))))))) (forall ((I6 tptp.set_nat) (X (-> tptp.nat tptp.nat)) (Y (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I6) (not (= (@ X I3) tptp.zero_zero_nat)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I6) (not (= (@ Y I3) tptp.zero_zero_nat)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I6) (not (= (@ (@ tptp.plus_plus_nat (@ X I3)) (@ Y I3)) tptp.zero_zero_nat))))))))) (forall ((I6 tptp.set_complex) (X (-> tptp.complex tptp.nat)) (Y (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I3 tptp.complex)) (and (@ (@ tptp.member_complex I3) I6) (not (= (@ X I3) tptp.zero_zero_nat)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I3 tptp.complex)) (and (@ (@ tptp.member_complex I3) I6) (not (= (@ Y I3) tptp.zero_zero_nat)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I3 tptp.complex)) (and (@ (@ tptp.member_complex I3) I6) (not (= (@ (@ tptp.plus_plus_nat (@ X I3)) (@ Y I3)) tptp.zero_zero_nat))))))))) (forall ((I6 tptp.set_int) (X (-> tptp.int tptp.nat)) (Y (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.member_int I3) I6) (not (= (@ X I3) tptp.zero_zero_nat)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.member_int I3) I6) (not (= (@ Y I3) tptp.zero_zero_nat)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.member_int I3) I6) (not (= (@ (@ tptp.plus_plus_nat (@ X I3)) (@ Y I3)) tptp.zero_zero_nat))))))))) (forall ((I6 tptp.set_Extended_enat) (X (-> tptp.extended_enat tptp.nat)) (Y (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I3 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I3) I6) (not (= (@ X I3) tptp.zero_zero_nat)))))) (=> (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I3 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I3) I6) (not (= (@ Y I3) tptp.zero_zero_nat)))))) (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I3 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I3) I6) (not (= (@ (@ tptp.plus_plus_nat (@ X I3)) (@ Y I3)) tptp.zero_zero_nat))))))))) (forall ((I6 tptp.set_real) (X (-> tptp.real tptp.real)) (Y (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I6) (not (= (@ X I3) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I6) (not (= (@ Y I3) tptp.zero_zero_real)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I6) (not (= (@ (@ tptp.plus_plus_real (@ X I3)) (@ Y I3)) tptp.zero_zero_real))))))))) (forall ((I6 tptp.set_nat) (X (-> tptp.nat tptp.real)) (Y (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I6) (not (= (@ X I3) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I6) (not (= (@ Y I3) tptp.zero_zero_real)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I6) (not (= (@ (@ tptp.plus_plus_real (@ X I3)) (@ Y I3)) tptp.zero_zero_real))))))))) (forall ((I6 tptp.set_complex) (X (-> tptp.complex tptp.real)) (Y (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I3 tptp.complex)) (and (@ (@ tptp.member_complex I3) I6) (not (= (@ X I3) tptp.zero_zero_real)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I3 tptp.complex)) (and (@ (@ tptp.member_complex I3) I6) (not (= (@ Y I3) tptp.zero_zero_real)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I3 tptp.complex)) (and (@ (@ tptp.member_complex I3) I6) (not (= (@ (@ tptp.plus_plus_real (@ X I3)) (@ Y I3)) tptp.zero_zero_real))))))))) (forall ((I6 tptp.set_int) (X (-> tptp.int tptp.real)) (Y (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.member_int I3) I6) (not (= (@ X I3) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.member_int I3) I6) (not (= (@ Y I3) tptp.zero_zero_real)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.member_int I3) I6) (not (= (@ (@ tptp.plus_plus_real (@ X I3)) (@ Y I3)) tptp.zero_zero_real))))))))) (forall ((I6 tptp.set_Extended_enat) (X (-> tptp.extended_enat tptp.real)) (Y (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I3 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I3) I6) (not (= (@ X I3) tptp.zero_zero_real)))))) (=> (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I3 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I3) I6) (not (= (@ Y I3) tptp.zero_zero_real)))))) (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I3 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I3) I6) (not (= (@ (@ tptp.plus_plus_real (@ X I3)) (@ Y I3)) tptp.zero_zero_real))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_vebt_member X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A4 Bool) (B4 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A4) B4))) (let ((_let_2 (= Xa2 tptp.one_one_nat))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_1) (=> (= Y (and (=> _let_3 A4) (=> (not _let_3) (and (=> _let_2 B4) _let_2)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_7 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (= X _let_2) (=> (= Y (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_7 (=> _let_7 (and _let_6 (=> _let_6 (and (=> _let_5 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5)))))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_vebt_member X) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A4 Bool) (B4 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A4) B4))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (and (=> _let_2 A4) (=> (not _let_2) (and (=> _let_1 B4) _let_1))))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Summary2))) (=> (= X _let_7) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_7) Xa2)) (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member X) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A4 Bool) (B4 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A4) B4))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (=> _let_2 A4) (=> (not _let_2) (and (=> _let_1 B4) _let_1)))))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Summary2))) (=> (= X _let_7) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_7) Xa2)) (not (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))))))))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat M2) N2) (=> (@ (@ tptp.dvd_dvd_nat N2) M2) (= M2 N2)))) (forall ((M2 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 M2) A)) (not (= (@ _let_1 A) (= M2 tptp.zero_zero_nat)))))) (forall ((M2 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 M2) A)) (not (= (@ _let_1 A) (= M2 tptp.zero_zero_nat)))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A4 Bool) (B4 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A4) B4))) (let ((_let_2 (= Xa2 tptp.one_one_nat))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_1) (=> (= Y (and (=> _let_3 A4) (=> (not _let_3) (and (=> _let_2 B4) _let_2)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (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 Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (= X _let_2) (=> (= Y (and (=> _let_5 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A4 Bool) (B4 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A4) B4))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (=> _let_2 A4) (=> (not _let_2) (and (=> _let_1 B4) _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 Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList3) S3))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (not (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A4 Bool) (B4 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A4) B4))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (and (=> _let_2 A4) (=> (not _let_2) (and (=> _let_1 B4) _let_1))))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (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 Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList3) S3))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (=> (= X _let_1) (=> (= Y (or (= Xa2 Mi2) (= Xa2 Ma2))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Vc2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (= X _let_2) (=> (= Y (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_5 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Vd))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (= X _let_2) (=> (= Y (and (=> _let_5 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_membermima X) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)) (or (= Xa2 Mi2) (= Xa2 Ma2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Vc2))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4)))))))))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Vd))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_membermima X) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Vc2))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (not (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Vd))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (not (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4)))))))))))))))) (= (@ tptp.arcosh_real tptp.one_one_real) tptp.zero_zero_real) (= (@ tptp.arsinh_real tptp.zero_zero_real) tptp.zero_zero_real) (= (@ tptp.artanh_real tptp.zero_zero_real) tptp.zero_zero_real) (forall ((X tptp.nat) (Y tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.accp_nat tptp.vEBT_v4011308405150292612up_rel))) (let ((_let_3 (= Y (@ (@ tptp.vEBT_Leaf false) false)))) (=> (= (@ tptp.vEBT_vebt_buildup X) Y) (=> (@ _let_2 X) (=> (=> (= X tptp.zero_zero_nat) (=> _let_3 (not (@ _let_2 tptp.zero_zero_nat)))) (=> (=> (= X _let_1) (=> _let_3 (not (@ _let_2 _let_1)))) (not (forall ((Va tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) _let_2))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_2))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1))) (let ((_let_8 (@ (@ tptp.dvd_dvd_nat _let_2) _let_1))) (=> (= X _let_1) (=> (and (=> _let_8 (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_8) (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4))))) (not (@ (@ tptp.accp_nat tptp.vEBT_v4011308405150292612up_rel) _let_1)))))))))))))))))))))) (forall ((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.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 ((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 ((A tptp.nat) (M2 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 M2))) _let_4)) (or (@ (@ tptp.ord_less_nat N2) M2) (= _let_4 tptp.zero_zero_nat) (and (@ (@ tptp.ord_less_eq_nat M2) N2) (@ _let_3 (@ (@ tptp.divide_divide_nat A) (@ _let_2 (@ (@ tptp.minus_minus_nat N2) M2)))))))))))) (forall ((A tptp.int) (M2 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 M2))) _let_4)) (or (@ (@ tptp.ord_less_nat N2) M2) (= _let_4 tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_nat M2) N2) (@ _let_3 (@ (@ tptp.divide_divide_int A) (@ _let_2 (@ (@ tptp.minus_minus_nat N2) M2)))))))))))) (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 ((X22 tptp.num)) (= (@ tptp.size_num (@ tptp.bit0 X22)) (@ (@ tptp.plus_plus_nat (@ tptp.size_num X22)) (@ tptp.suc tptp.zero_zero_nat)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) A) tptp.zero_zero_complex)) (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) A) tptp.zero_zero_int)) (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) A) tptp.zero_zero_real)) (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) tptp.zero_zero_complex) A)) (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) tptp.zero_zero_int) A)) (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) tptp.zero_zero_real) 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.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.real)) (= (@ (@ tptp.minus_minus_real A) tptp.zero_zero_real) A)) (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) A) tptp.zero_zero_complex)) (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) A) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) A) tptp.zero_zero_int)) (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) A) tptp.zero_zero_real)) (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B2)) B2) A)) (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B2)) B2) A)) (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B2)) B2) A)) (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B2)) B2) A)) (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.minus_minus_nat A) B2)))) (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (= (@ (@ tptp.minus_minus_int (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.minus_minus_int A) B2)))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (= (@ (@ tptp.minus_minus_real (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.minus_minus_real A) B2)))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B2)) A) B2)) (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B2)) A) B2)) (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B2)) A) B2)) (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B2) C)) (@ (@ tptp.minus_minus_nat A) B2))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B2) C)) (@ (@ tptp.minus_minus_int A) B2))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B2) C)) (@ (@ tptp.minus_minus_real A) B2))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B2)) B2) A)) (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B2)) B2) A)) (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B2)) B2) A)) (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M2)) (@ tptp.suc N2)) (@ (@ tptp.minus_minus_nat M2) N2))) (forall ((M2 tptp.nat) (N2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat (@ tptp.suc M2)) N2)) (@ tptp.suc K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat M2) N2)) K))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) N2) tptp.zero_zero_nat)) (forall ((M2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat M2) M2) tptp.zero_zero_nat)) (forall ((I tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat I) N2) (= (@ _let_1 (@ _let_1 I)) I)))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ _let_1 (@ (@ tptp.plus_plus_nat J) K))))) (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.zero_n3304061248610475627l_real P)) (@ tptp.zero_n3304061248610475627l_real 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))) _let_193 _let_192 _let_191 (= (@ tptp.zero_n2687167440665602831ol_nat false) tptp.zero_zero_nat) (= (@ tptp.zero_n2684676970156552555ol_int false) tptp.zero_zero_int) (forall ((P Bool)) (= (= (@ tptp.zero_n3304061248610475627l_real P) tptp.zero_zero_real) (not P))) (forall ((P Bool)) (= (= (@ tptp.zero_n1201886186963655149omplex P) tptp.zero_zero_complex) (not P))) (forall ((P Bool)) (= (= (@ tptp.zero_n1046097342994218471d_enat P) tptp.zero_z5237406670263579293d_enat) (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) (Q Bool)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.zero_n1046097342994218471d_enat P)) (@ tptp.zero_n1046097342994218471d_enat Q)) (and (not P) Q))) (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_real (@ tptp.zero_n3304061248610475627l_real P)) (@ tptp.zero_n3304061248610475627l_real Q)) (and (not P) Q))) (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)) (and (not P) Q))) (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)) (and (not P) Q))) (forall ((P Bool)) (= (= (@ tptp.zero_n1201886186963655149omplex P) tptp.one_one_complex) P)) (forall ((P Bool)) (= (= (@ tptp.zero_n3304061248610475627l_real P) tptp.one_one_real) P)) (forall ((P Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P) tptp.one_one_nat) P)) (forall ((P Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P) tptp.one_one_int) P)) (= (@ tptp.zero_n1201886186963655149omplex true) tptp.one_one_complex) (= (@ tptp.zero_n3304061248610475627l_real true) tptp.one_one_real) (= (@ tptp.zero_n2687167440665602831ol_nat true) tptp.one_one_nat) _let_190 (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_ri631733984087533419it_int N2) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n2687167440665602831ol_nat (or P Q)) (@ (@ tptp.ord_max_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)))) (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n2684676970156552555ol_int (or P Q)) (@ (@ tptp.ord_max_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)))) (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real A) B2)) (@ (@ tptp.ord_less_eq_real B2) A))) (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int A) B2)) (@ (@ tptp.ord_less_eq_int B2) A))) (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real A) B2)) (@ (@ tptp.ord_less_real B2) A))) (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int A) B2)) (@ (@ tptp.ord_less_int B2) A))) (forall ((B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B2) A) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B2)) B2) A))) (forall ((B2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B2) A) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat A) B2)) B2) A))) (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B2) A) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B2)) B2) A))) (forall ((B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B2) A) (= (@ (@ tptp.plus_plus_real B2) (@ (@ tptp.minus_minus_real A) B2)) A))) (forall ((B2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B2) A) (= (@ (@ tptp.plus_plus_nat B2) (@ (@ tptp.minus_minus_nat A) B2)) A))) (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B2) A) (= (@ (@ tptp.plus_plus_int B2) (@ (@ tptp.minus_minus_int A) B2)) A))) (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) tptp.one_one_complex) tptp.zero_zero_complex) (= (@ (@ tptp.minus_minus_int tptp.one_one_int) tptp.one_one_int) tptp.zero_zero_int) (= (@ (@ tptp.minus_minus_real tptp.one_one_real) tptp.one_one_real) tptp.zero_zero_real) (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.plus_plus_nat A) B2)) tptp.zero_zero_nat)) (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 ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int A) B2)) C) (@ (@ tptp.minus_minus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B2) C))))))) (forall ((P Bool)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.zero_n3304061248610475627l_real P)) P)) (forall ((P Bool)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.zero_n2687167440665602831ol_nat P)) P)) (forall ((P Bool)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.zero_n2684676970156552555ol_int P)) P)) (forall ((N2 tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) M2)) (@ (@ tptp.ord_less_nat M2) N2))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ (@ tptp.minus_minus_nat M2) N2) tptp.zero_zero_nat))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.minus_minus_nat M2) N2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat M2) N2))) (forall ((P Bool)) (= (@ (@ tptp.ord_less_real (@ tptp.zero_n3304061248610475627l_real P)) tptp.one_one_real) (not P))) (forall ((P Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.zero_n2687167440665602831ol_nat P)) tptp.one_one_nat) (not P))) (forall ((P Bool)) (= (@ (@ tptp.ord_less_int (@ tptp.zero_n2684676970156552555ol_int P)) tptp.one_one_int) (not P))) (forall ((P Bool)) (= (@ tptp.zero_n1201886186963655149omplex (not P)) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.zero_n1201886186963655149omplex P)))) (forall ((P Bool)) (= (@ tptp.zero_n3304061248610475627l_real (not P)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ tptp.zero_n3304061248610475627l_real P)))) (forall ((P Bool)) (= (@ tptp.zero_n2684676970156552555ol_int (not P)) (@ (@ tptp.minus_minus_int tptp.one_one_int) (@ tptp.zero_n2684676970156552555ol_int P)))) (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat I) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat I) K)) J)))) (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J) K)) I) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J) I)) K)))) (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I))) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ _let_1 (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K))))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N2)) tptp.one_one_nat) N2)) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.modulo_modulo_nat _let_1) N2) (@ tptp.zero_n2687167440665602831ol_nat (not (= N2 _let_1)))))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N2)) tptp.one_one_int) tptp.one_one_int)) (= (@ tptp.nat_set_encode tptp.bot_bot_set_nat) tptp.zero_zero_nat) (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (= (@ tptp.nat_set_decode (@ tptp.nat_set_encode A2)) A2))) (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) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc (@ (@ tptp.minus_minus_nat J) K))) I) (@ (@ tptp.minus_minus_nat (@ tptp.suc J)) (@ (@ tptp.plus_plus_nat K) I))))) (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat I) (@ tptp.suc (@ (@ tptp.minus_minus_nat J) K))) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat I) K)) (@ tptp.suc J))))) (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.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.minus_minus_int A) B2)) (@ _let_1 (@ (@ tptp.plus_plus_int A) B2))))) (forall ((B2 Bool)) (= (@ (@ tptp.divide_divide_nat (@ tptp.zero_n2687167440665602831ol_nat B2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat)) (forall ((B2 Bool)) (= (@ (@ tptp.divide_divide_int (@ tptp.zero_n2684676970156552555ol_int B2)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int)) (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 ((M2 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 M2) N2)) (or (@ (@ tptp.ord_less_nat M2) N2) (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N2)))))) (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)) (= (@ (@ 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.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 ((P5 Bool) (Q3 Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P5) (@ tptp.zero_n2687167440665602831ol_nat Q3)) (= P5 Q3))) (forall ((P5 Bool) (Q3 Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P5) (@ tptp.zero_n2684676970156552555ol_int Q3)) (= P5 Q3))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ (@ tptp.minus_minus_nat (@ _let_1 K)) J)))) (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat A))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 C)) B2) (@ (@ tptp.minus_minus_nat (@ _let_1 B2)) C)))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (= (@ (@ tptp.minus_minus_int (@ _let_1 C)) B2) (@ (@ tptp.minus_minus_int (@ _let_1 B2)) C)))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (= (@ (@ tptp.minus_minus_real (@ _let_1 C)) B2) (@ (@ tptp.minus_minus_real (@ _let_1 B2)) C)))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B2) (@ (@ tptp.minus_minus_int C) D)) (= (= A B2) (= C D)))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A) B2) (@ (@ tptp.minus_minus_real C) D)) (= (= A B2) (= C D)))) (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_n1201886186963655149omplex (and P Q)) (@ (@ tptp.times_times_complex (@ tptp.zero_n1201886186963655149omplex P)) (@ tptp.zero_n1201886186963655149omplex Q)))) (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n1046097342994218471d_enat (and P Q)) (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.zero_n1046097342994218471d_enat P)) (@ tptp.zero_n1046097342994218471d_enat 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 ((A tptp.real) (B2 tptp.real) (D tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_eq_real D) C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B2) D))))) (forall ((A tptp.int) (B2 tptp.int) (D tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (@ (@ tptp.ord_less_eq_int D) C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B2) D))))) (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real C))) (=> (@ (@ tptp.ord_less_eq_real B2) A) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B2))))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int C))) (=> (@ (@ tptp.ord_less_eq_int B2) A) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B2))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B2) C)))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B2) C)))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A) B2) (@ (@ tptp.minus_minus_real C) D)) (= (@ (@ tptp.ord_less_eq_real A) B2) (@ (@ tptp.ord_less_eq_real C) D)))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B2) (@ (@ tptp.minus_minus_int C) D)) (= (@ (@ tptp.ord_less_eq_int A) B2) (@ (@ tptp.ord_less_eq_int C) D)))) (= (lambda ((Y4 tptp.complex) (Z2 tptp.complex)) (= Y4 Z2)) (lambda ((A3 tptp.complex) (B3 tptp.complex)) (= (@ (@ tptp.minus_minus_complex A3) B3) tptp.zero_zero_complex))) (= (lambda ((Y4 tptp.int) (Z2 tptp.int)) (= Y4 Z2)) (lambda ((A3 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.minus_minus_int A3) B3) tptp.zero_zero_int))) (= (lambda ((Y4 tptp.real) (Z2 tptp.real)) (= Y4 Z2)) (lambda ((A3 tptp.real) (B3 tptp.real)) (= (@ (@ tptp.minus_minus_real A3) B3) tptp.zero_zero_real))) (forall ((A tptp.real) (B2 tptp.real) (D tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.ord_less_real D) C) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B2) D))))) (forall ((A tptp.int) (B2 tptp.int) (D tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B2) (=> (@ (@ tptp.ord_less_int D) C) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B2) D))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A) B2) (@ (@ tptp.minus_minus_real C) D)) (= (@ (@ tptp.ord_less_real A) B2) (@ (@ tptp.ord_less_real C) D)))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B2) (@ (@ tptp.minus_minus_int C) D)) (= (@ (@ tptp.ord_less_int A) B2) (@ (@ tptp.ord_less_int C) D)))) (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real C))) (=> (@ (@ tptp.ord_less_real B2) A) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B2))))) (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int C))) (=> (@ (@ tptp.ord_less_int B2) A) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B2))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B2) C)))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B2) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B2) C)))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat B2) C)) (@ (@ tptp.minus_minus_nat (@ _let_1 B2)) (@ _let_1 C))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B2) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B2)) (@ _let_1 C))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B2) C)) (@ (@ tptp.minus_minus_real (@ _let_1 B2)) (@ _let_1 C))))) (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ (@ tptp.minus_minus_complex B2) C)) (@ (@ tptp.minus_minus_complex (@ _let_1 B2)) (@ _let_1 C))))) (forall ((B2 tptp.nat) (C tptp.nat) (A tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat B2) C)) A) (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat B2) A)) (@ (@ tptp.times_times_nat C) A)))) (forall ((B2 tptp.int) (C tptp.int) (A tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B2) C)) A) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int B2) A)) (@ (@ tptp.times_times_int C) A)))) (forall ((B2 tptp.real) (C tptp.real) (A tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B2) C)) A) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real B2) A)) (@ (@ tptp.times_times_real C) A)))) (forall ((B2 tptp.complex) (C tptp.complex) (A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex B2) C)) A) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex B2) A)) (@ (@ tptp.times_times_complex C) A)))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B2) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B2)) (@ _let_1 C))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B2) C)) (@ (@ tptp.minus_minus_real (@ _let_1 B2)) (@ _let_1 C))))) (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ (@ tptp.minus_minus_complex B2) C)) (@ (@ tptp.minus_minus_complex (@ _let_1 B2)) (@ _let_1 C))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B2)) C) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) C)))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B2)) C) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) C)))) (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex A) B2)) C) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B2) C)))) (forall ((A2 tptp.int) (K tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_int A2) B2) (@ _let_1 (@ (@ tptp.minus_minus_int A) B2)))))) (forall ((A2 tptp.real) (K tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_real A2) B2) (@ _let_1 (@ (@ tptp.minus_minus_real A) B2)))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (= (= (@ (@ tptp.minus_minus_int A) B2) C) (= A (@ (@ tptp.plus_plus_int C) B2)))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (= (= (@ (@ tptp.minus_minus_real A) B2) C) (= A (@ (@ tptp.plus_plus_real C) B2)))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (= A (@ (@ tptp.minus_minus_int C) B2)) (= (@ (@ tptp.plus_plus_int A) B2) C))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (= A (@ (@ tptp.minus_minus_real C) B2)) (= (@ (@ tptp.plus_plus_real A) B2) C))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B2) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B2)) C)))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B2) C)) (@ (@ tptp.minus_minus_real (@ _let_1 B2)) C)))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.minus_minus_int B2) C)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C)) B2))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (= (@ (@ tptp.minus_minus_real A) (@ (@ tptp.minus_minus_real B2) C)) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) C)) B2))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B2)) C) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C)) B2))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B2)) C) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) C)) B2))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B2) C)) (@ (@ tptp.minus_minus_int (@ _let_1 C)) B2)))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B2) C)) (@ (@ tptp.minus_minus_real (@ _let_1 C)) B2)))) (forall ((C tptp.nat) (B2 tptp.nat) (A tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat C) B2) A) (= C (@ (@ tptp.minus_minus_nat A) B2)))) (forall ((C tptp.int) (B2 tptp.int) (A tptp.int)) (=> (= (@ (@ tptp.plus_plus_int C) B2) A) (= C (@ (@ tptp.minus_minus_int A) B2)))) (forall ((C tptp.real) (B2 tptp.real) (A tptp.real)) (=> (= (@ (@ tptp.plus_plus_real C) B2) A) (= C (@ (@ tptp.minus_minus_real A) B2)))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat A))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B2) C))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (= (@ (@ tptp.minus_minus_int (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B2) C))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (= (@ (@ tptp.minus_minus_real (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_real B2) C))))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int) (D tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B2) D)) (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B2)) (@ (@ tptp.minus_minus_int C) D)))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real) (D tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B2) D)) (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B2)) (@ (@ tptp.minus_minus_real C) D)))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real A) B2)) C) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B2) C)))) (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z3) (@ _let_1 (@ (@ tptp.minus_minus_int Y) Z3)))))) (forall ((X tptp.real) (Y tptp.real) (Z3 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z3) (@ _let_1 (@ (@ tptp.minus_minus_real Y) Z3)))))) (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (I tptp.nat)) (=> (@ P K) (=> (forall ((N3 tptp.nat)) (=> (@ P (@ tptp.suc N3)) (@ P N3))) (@ P (@ (@ tptp.minus_minus_nat K) I))))) (forall ((M2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat M2) tptp.zero_zero_nat) M2)) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.minus_minus_nat M2) N2) tptp.zero_zero_nat) (=> (= (@ (@ tptp.minus_minus_nat N2) M2) tptp.zero_zero_nat) (= M2 N2)))) (forall ((M2 tptp.nat) (N2 tptp.nat) (L tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (let ((_let_2 (@ tptp.ord_less_nat M2))) (=> (@ _let_2 N2) (=> (@ _let_2 L) (@ (@ tptp.ord_less_nat (@ _let_1 N2)) (@ _let_1 M2))))))) (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 ((K tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M2) (=> (@ _let_1 N2) (= (= (@ (@ tptp.minus_minus_nat M2) K) (@ (@ tptp.minus_minus_nat N2) K)) (= M2 N2)))))) (forall ((K tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M2) (=> (@ _let_1 N2) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M2) K)) (@ (@ tptp.minus_minus_nat N2) K)) (@ (@ tptp.ord_less_eq_nat M2) N2)))))) (forall ((K tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M2))) (let ((_let_2 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_2 M2) (=> (@ _let_2 N2) (= (@ (@ tptp.minus_minus_nat (@ _let_1 K)) (@ (@ tptp.minus_minus_nat N2) K)) (@ _let_1 N2))))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M2) L)) (@ (@ tptp.minus_minus_nat N2) L)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M2) N2)) M2)) (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B2))) (let ((_let_2 (@ tptp.minus_minus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) C) (=> (@ _let_1 C) (= (@ (@ tptp.ord_less_eq_nat (@ _let_2 A)) (@ _let_2 B2)) (@ _let_1 A))))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (L tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N2)) (@ _let_1 M2))))) (forall ((K tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 M2)) (@ _let_1 N2)) (@ (@ tptp.minus_minus_nat M2) N2)))) (forall ((M2 tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M2) K)) (@ (@ tptp.plus_plus_nat N2) K)) (@ (@ tptp.minus_minus_nat M2) N2))) (forall ((N2 tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N2) M2)) N2) M2)) (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M2) N2)) N2) M2)) (forall ((K tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N2)) (@ (@ tptp.minus_minus_nat (@ _let_1 M2)) (@ _let_1 N2))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M2) N2)) K) (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat M2) K)) (@ (@ tptp.times_times_nat N2) K)))) (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.ord_max_int X) Y)) Z3) (@ (@ tptp.ord_max_int (@ (@ tptp.minus_minus_int X) Z3)) (@ (@ tptp.minus_minus_int Y) Z3)))) (forall ((X tptp.real) (Y tptp.real) (Z3 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.ord_max_real X) Y)) Z3) (@ (@ tptp.ord_max_real (@ (@ tptp.minus_minus_real X) Z3)) (@ (@ tptp.minus_minus_real Y) Z3)))) (forall ((K tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 M2) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N2)))))) (forall ((P Bool)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.zero_n3304061248610475627l_real P))) (forall ((P Bool)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.zero_n2687167440665602831ol_nat P))) (forall ((P Bool)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.zero_n2684676970156552555ol_int P))) (forall ((P Bool)) (@ (@ tptp.ord_less_eq_real (@ tptp.zero_n3304061248610475627l_real P)) tptp.one_one_real)) (forall ((P Bool)) (@ (@ tptp.ord_less_eq_nat (@ tptp.zero_n2687167440665602831ol_nat P)) tptp.one_one_nat)) (forall ((P Bool)) (@ (@ tptp.ord_less_eq_int (@ tptp.zero_n2684676970156552555ol_int P)) tptp.one_one_int)) (forall ((P (-> tptp.real Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n3304061248610475627l_real P5)) (not (or (and P5 (not (@ P tptp.one_one_real))) (and (not P5) (not (@ P tptp.zero_zero_real))))))) (forall ((P (-> tptp.complex Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n1201886186963655149omplex P5)) (not (or (and P5 (not (@ P tptp.one_one_complex))) (and (not P5) (not (@ P tptp.zero_zero_complex))))))) (forall ((P (-> tptp.extended_enat Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n1046097342994218471d_enat P5)) (not (or (and P5 (not (@ P tptp.one_on7984719198319812577d_enat))) (and (not P5) (not (@ P tptp.zero_z5237406670263579293d_enat))))))) (forall ((P (-> tptp.nat Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n2687167440665602831ol_nat P5)) (not (or (and P5 (not (@ P tptp.one_one_nat))) (and (not P5) (not (@ P tptp.zero_zero_nat))))))) (forall ((P (-> tptp.int Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n2684676970156552555ol_int P5)) (not (or (and P5 (not (@ P tptp.one_one_int))) (and (not P5) (not (@ P tptp.zero_zero_int))))))) (forall ((P (-> tptp.real Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n3304061248610475627l_real P5)) (and (=> P5 (@ P tptp.one_one_real)) (=> (not P5) (@ P tptp.zero_zero_real))))) (forall ((P (-> tptp.complex Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n1201886186963655149omplex P5)) (and (=> P5 (@ P tptp.one_one_complex)) (=> (not P5) (@ P tptp.zero_zero_complex))))) (forall ((P (-> tptp.extended_enat Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n1046097342994218471d_enat P5)) (and (=> P5 (@ P tptp.one_on7984719198319812577d_enat)) (=> (not P5) (@ P tptp.zero_z5237406670263579293d_enat))))) (forall ((P (-> tptp.nat Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n2687167440665602831ol_nat P5)) (and (=> P5 (@ P tptp.one_one_nat)) (=> (not P5) (@ P tptp.zero_zero_nat))))) (forall ((P (-> tptp.int Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n2684676970156552555ol_int P5)) (and (=> P5 (@ P tptp.one_one_int)) (=> (not P5) (@ P tptp.zero_zero_int))))) (= tptp.zero_n3304061248610475627l_real (lambda ((P6 Bool)) (@ (@ (@ tptp.if_real P6) tptp.one_one_real) tptp.zero_zero_real))) (= tptp.zero_n1201886186963655149omplex (lambda ((P6 Bool)) (@ (@ (@ tptp.if_complex P6) tptp.one_one_complex) tptp.zero_zero_complex))) (= tptp.zero_n1046097342994218471d_enat (lambda ((P6 Bool)) (@ (@ (@ tptp.if_Extended_enat P6) tptp.one_on7984719198319812577d_enat) tptp.zero_z5237406670263579293d_enat))) _let_188 (= tptp.zero_n2684676970156552555ol_int (lambda ((P6 Bool)) (@ (@ (@ tptp.if_int P6) tptp.one_one_int) tptp.zero_zero_int))) (= tptp.ord_less_eq_real (lambda ((A3 tptp.real) (B3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A3) B3)) tptp.zero_zero_real))) (= tptp.ord_less_eq_int (lambda ((A3 tptp.int) (B3 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A3) B3)) tptp.zero_zero_int))) (= tptp.ord_less_real (lambda ((A3 tptp.real) (B3 tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A3) B3)) tptp.zero_zero_real))) (= tptp.ord_less_int (lambda ((A3 tptp.int) (B3 tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A3) B3)) tptp.zero_zero_int))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_nat A) B2))) (=> _let_1 (=> _let_1 (= (= (@ (@ tptp.minus_minus_nat B2) A) C) (= B2 (@ (@ tptp.plus_plus_nat C) A))))))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (= (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.minus_minus_nat B2) A)) B2))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (= (@ (@ tptp.minus_minus_nat C) (@ (@ tptp.minus_minus_nat B2) A)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat C) A)) B2)))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B2) C)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B2) A)) C)))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B2) A)) C) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B2) C)) A)))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (= (@ (@ tptp.minus_minus_nat (@ _let_1 B2)) A) (@ _let_1 (@ (@ tptp.minus_minus_nat B2) A)))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat B2) A)) (@ (@ tptp.minus_minus_nat (@ _let_1 B2)) A))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (= (@ (@ tptp.ord_less_eq_nat C) (@ (@ tptp.minus_minus_nat B2) A)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat C) A)) B2)))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (@ (@ tptp.ord_less_eq_nat C) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B2) C)) A)))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B2) A)) A) B2))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.minus_minus_real C) B2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) B2)) C))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.minus_minus_int C) B2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) B2)) C))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) B2)) C) (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.plus_plus_real C) B2)))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) B2)) C) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.plus_plus_int C) B2)))) (forall ((I 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 I) K)) N2))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real N2) K)) J)))))))) (forall ((I 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 I) K)) N2))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat N2) K)) J)))))))) (forall ((I 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 I) K)) N2))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int N2) K)) J)))))))) (forall ((I tptp.real) (K tptp.real) (N2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I) K)) N2) (@ (@ tptp.ord_less_eq_real I) (@ (@ tptp.minus_minus_real N2) K)))) (forall ((I tptp.nat) (K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) N2) (@ (@ tptp.ord_less_eq_nat I) (@ (@ tptp.minus_minus_nat N2) K)))) (forall ((I tptp.int) (K tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K)) N2) (@ (@ tptp.ord_less_eq_int I) (@ (@ tptp.minus_minus_int N2) K)))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.minus_minus_real C) B2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B2)) C))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ (@ tptp.minus_minus_int C) B2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B2)) C))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) B2)) C) (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real C) B2)))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) B2)) C) (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int C) B2)))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat A) B2)) (= (@ (@ tptp.plus_plus_nat B2) (@ (@ tptp.minus_minus_nat A) B2)) A))) (forall ((A tptp.real) (B2 tptp.real)) (=> (not (@ (@ tptp.ord_less_real A) B2)) (= (@ (@ tptp.plus_plus_real B2) (@ (@ tptp.minus_minus_real A) B2)) A))) (forall ((A tptp.int) (B2 tptp.int)) (=> (not (@ (@ tptp.ord_less_int A) B2)) (= (@ (@ tptp.plus_plus_int B2) (@ (@ tptp.minus_minus_int A) B2)) A))) (forall ((A tptp.int) (E2 tptp.int) (C tptp.int) (B2 tptp.int) (D tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E2)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) E2)) D)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B2)) E2)) C) D))) (forall ((A tptp.real) (E2 tptp.real) (C tptp.real) (B2 tptp.real) (D tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E2)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B2) E2)) D)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B2)) E2)) C) D))) (forall ((A tptp.complex) (E2 tptp.complex) (C tptp.complex) (B2 tptp.complex) (D tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) E2)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex B2) E2)) D)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex A) B2)) E2)) C) D))) (forall ((A tptp.int) (E2 tptp.int) (C tptp.int) (B2 tptp.int) (D tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E2)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) E2)) D)) (= C (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B2) A)) E2)) D)))) (forall ((A tptp.real) (E2 tptp.real) (C tptp.real) (B2 tptp.real) (D tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E2)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B2) E2)) D)) (= C (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B2) A)) E2)) D)))) (forall ((A tptp.complex) (E2 tptp.complex) (C tptp.complex) (B2 tptp.complex) (D tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) E2)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex B2) E2)) D)) (= C (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex B2) A)) E2)) D)))) (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X) Y)) (@ (@ tptp.minus_minus_int X) Y)))) (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.minus_minus_real X) Y)))) (forall ((X tptp.complex) (Y tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X) X)) (@ (@ tptp.times_times_complex Y) Y)) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex X) Y)) (@ (@ tptp.minus_minus_complex X) Y)))) (forall ((X tptp.int) (Y tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int X))) (= (@ (@ tptp.minus_minus_int (@ _let_1 Y)) (@ (@ tptp.times_times_int A) B2)) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_minus_int Y) B2))) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) A)) B2))))) (forall ((X tptp.real) (Y tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real X))) (= (@ (@ tptp.minus_minus_real (@ _let_1 Y)) (@ (@ tptp.times_times_real A) B2)) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_minus_real Y) B2))) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X) A)) B2))))) (forall ((X tptp.complex) (Y tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex X))) (= (@ (@ tptp.minus_minus_complex (@ _let_1 Y)) (@ (@ tptp.times_times_complex A) B2)) (@ (@ tptp.plus_plus_complex (@ _let_1 (@ (@ tptp.minus_minus_complex Y) B2))) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X) A)) B2))))) (forall ((B2 tptp.nat) (A tptp.nat)) (@ (@ tptp.dvd_dvd_nat B2) (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.modulo_modulo_nat A) B2)))) (forall ((B2 tptp.int) (A tptp.int)) (@ (@ tptp.dvd_dvd_int B2) (@ (@ tptp.minus_minus_int A) (@ (@ tptp.modulo_modulo_int A) B2)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M2) N2)) (@ tptp.suc M2))) (forall ((N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M2))) (=> (@ (@ tptp.ord_less_nat N2) M2) (= (@ tptp.suc (@ _let_1 (@ tptp.suc N2))) (@ _let_1 N2))))) (forall ((N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N2) (=> (@ _let_1 M2) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M2) N2)) M2))))) (forall ((N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M2)) N2) (@ tptp.suc (@ (@ tptp.minus_minus_nat M2) N2))))) (forall ((K tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M2) (=> (@ _let_1 N2) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M2) K)) (@ (@ tptp.minus_minus_nat N2) K)) (@ (@ tptp.ord_less_nat M2) N2)))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (=> (@ (@ tptp.ord_less_eq_nat C) A) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat A) C)) (@ (@ tptp.minus_minus_nat B2) C))))) (forall ((N2 tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat N2) (@ (@ tptp.plus_plus_nat N2) M2)) tptp.zero_zero_nat)) (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (=> (@ tptp.finite_finite_nat B) (= (= (@ tptp.nat_set_encode A2) (@ tptp.nat_set_encode B)) (= A2 B))))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M2) N2)) (= (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.minus_minus_nat M2) N2)) M2))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (= (@ (@ tptp.ord_less_nat I) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) J))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (= (@ (@ tptp.minus_minus_nat J) I) K) (= J (@ (@ tptp.plus_plus_nat K) I))))) (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J) I)) K) (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J) K)) I)))) (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I))) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ _let_1 (@ (@ tptp.minus_minus_nat J) K)))))) (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.ord_less_eq_nat I) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) J)))) (forall ((J tptp.nat) (K tptp.nat) (I tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat J) K)) I) (@ (@ tptp.ord_less_eq_nat J) (@ (@ tptp.plus_plus_nat I) K)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M2))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.minus_minus_nat (@ _let_1 tptp.one_one_nat)) N2)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat M2))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M2)) (or (@ (@ tptp.ord_less_nat N2) M2) (@ _let_1 N2))))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ _let_1 N2) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M2)))))) (forall ((K tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N2)) (=> (@ _let_1 M2) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (@ _let_1 N2)))))) (forall ((K tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N2)) (=> (@ _let_1 N2) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (@ _let_1 M2)))))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M2) N2)) (= (@ (@ tptp.modulo_modulo_nat M2) N2) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M2) N2)) N2)))) (= tptp.modulo_modulo_nat (lambda ((M tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat M) N)) M) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M) N)) N)))) (forall ((N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (= (@ (@ tptp.modulo_modulo_nat M2) N2) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M2) N2)) N2)))) (forall ((N2 tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat N2) M2)) M2) (@ (@ tptp.ord_max_nat N2) M2))) (forall ((A tptp.real) (E2 tptp.real) (C tptp.real) (B2 tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E2)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B2) E2)) D)) (@ (@ tptp.ord_less_eq_real C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B2) A)) E2)) D)))) (forall ((A tptp.int) (E2 tptp.int) (C tptp.int) (B2 tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E2)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) E2)) D)) (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B2) A)) E2)) D)))) (forall ((A tptp.real) (E2 tptp.real) (C tptp.real) (B2 tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E2)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B2) E2)) D)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B2)) E2)) C)) D))) (forall ((A tptp.int) (E2 tptp.int) (C tptp.int) (B2 tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E2)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) E2)) D)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B2)) E2)) C)) D))) (forall ((A tptp.real) (E2 tptp.real) (C tptp.real) (B2 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 B2) E2)) D)) (@ (@ tptp.ord_less_real C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B2) A)) E2)) D)))) (forall ((A tptp.int) (E2 tptp.int) (C tptp.int) (B2 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 B2) E2)) D)) (@ (@ tptp.ord_less_int C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B2) A)) E2)) D)))) (forall ((A tptp.real) (E2 tptp.real) (C tptp.real) (B2 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 B2) E2)) D)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B2)) E2)) C)) D))) (forall ((A tptp.int) (E2 tptp.int) (C tptp.int) (B2 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 B2) E2)) D)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B2)) E2)) C)) D))) (forall ((Z3 tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z3 tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex X) Z3)) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex X) (@ (@ tptp.times_times_complex Y) Z3))) Z3)))) (forall ((Z3 tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z3 tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real X) Z3)) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X) (@ (@ tptp.times_times_real Y) Z3))) Z3)))) (forall ((Z3 tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z3 tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex X) (@ (@ tptp.divide1717551699836669952omplex Y) Z3)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X) Z3)) Y)) Z3)))) (forall ((Z3 tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z3 tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real X) (@ (@ tptp.divide_divide_real Y) Z3)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z3)) Y)) Z3)))) (forall ((Y tptp.complex) (Z3 tptp.complex) (X tptp.complex) (W2 tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z3 tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide1717551699836669952omplex W2) Z3)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X) Z3)) (@ (@ tptp.times_times_complex W2) Y))) (@ (@ tptp.times_times_complex Y) Z3)))))) (forall ((Y tptp.real) (Z3 tptp.real) (X tptp.real) (W2 tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z3 tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real W2) Z3)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z3)) (@ (@ tptp.times_times_real W2) Y))) (@ (@ tptp.times_times_real Y) Z3)))))) (forall ((Z3 tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex A) (@ (@ tptp.divide1717551699836669952omplex B2) Z3)))) (let ((_let_2 (= Z3 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) Z3)) B2)) Z3))))))) (forall ((Z3 tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real A) (@ (@ tptp.divide_divide_real B2) Z3)))) (let ((_let_2 (= Z3 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) Z3)) B2)) Z3))))))) (forall ((X tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X) X)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X) tptp.one_one_int)) (@ (@ tptp.minus_minus_int X) tptp.one_one_int)))) (forall ((X tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) X)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)) (@ (@ tptp.minus_minus_real X) tptp.one_one_real)))) (forall ((X tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X) X)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex X) tptp.one_one_complex)) (@ (@ tptp.minus_minus_complex X) tptp.one_one_complex)))) (forall ((D tptp.int) (D6 tptp.int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D6) (forall ((X2 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_int X2) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X2) (@ (@ tptp.times_times_int K4) D6))) T)))))))) (forall ((D tptp.real) (D6 tptp.real) (T tptp.real)) (=> (@ (@ tptp.dvd_dvd_real D) D6) (forall ((X2 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_real X2) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real X2) (@ (@ tptp.times_times_real K4) D6))) T)))))))) (forall ((D tptp.complex) (D6 tptp.complex) (T tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex D) D6) (forall ((X2 tptp.complex) (K4 tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_complex X2) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex X2) (@ (@ tptp.times_times_complex K4) D6))) T)))))))) (forall ((D tptp.int) (D6 tptp.int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D6) (forall ((X2 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (= (@ _let_1 (@ (@ tptp.plus_plus_int X2) T)) (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X2) (@ (@ tptp.times_times_int K4) D6))) T))))))) (forall ((D tptp.real) (D6 tptp.real) (T tptp.real)) (=> (@ (@ tptp.dvd_dvd_real D) D6) (forall ((X2 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real D))) (= (@ _let_1 (@ (@ tptp.plus_plus_real X2) T)) (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real X2) (@ (@ tptp.times_times_real K4) D6))) T))))))) (forall ((D tptp.complex) (D6 tptp.complex) (T tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex D) D6) (forall ((X2 tptp.complex) (K4 tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex D))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex X2) T)) (@ _let_1 (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex X2) (@ (@ tptp.times_times_complex K4) D6))) T))))))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.times_times_nat B2) (@ (@ tptp.divide_divide_nat A) B2))) (@ (@ tptp.modulo_modulo_nat A) B2))) (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.times_times_int B2) (@ (@ tptp.divide_divide_int A) B2))) (@ (@ tptp.modulo_modulo_int A) B2))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.modulo_modulo_nat A) B2)) (@ (@ tptp.times_times_nat B2) (@ (@ tptp.divide_divide_nat A) B2)))) (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.modulo_modulo_int A) B2)) (@ (@ tptp.times_times_int B2) (@ (@ tptp.divide_divide_int A) B2)))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.modulo_modulo_nat A) B2)) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B2)) B2))) (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.modulo_modulo_int A) B2)) (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B2)) B2))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B2)) B2)) (@ (@ tptp.modulo_modulo_nat A) B2))) (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B2)) B2)) (@ (@ tptp.modulo_modulo_int A) B2))) (forall ((M2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.power_power_int K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (= (@ (@ tptp.divide_divide_int (@ _let_1 M2)) K) (@ _let_1 (@ (@ tptp.minus_minus_nat M2) (@ tptp.suc tptp.zero_zero_nat)))))))) (forall ((N2 tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I))) N2))) (forall ((P (-> tptp.nat Bool)) (A tptp.nat) (B2 tptp.nat)) (= (@ P (@ (@ tptp.minus_minus_nat A) B2)) (not (or (and (@ (@ tptp.ord_less_nat A) B2) (not (@ P tptp.zero_zero_nat))) (exists ((D4 tptp.nat)) (and (= A (@ (@ tptp.plus_plus_nat B2) D4)) (not (@ P D4)))))))) (forall ((P (-> tptp.nat Bool)) (A tptp.nat) (B2 tptp.nat)) (= (@ P (@ (@ tptp.minus_minus_nat A) B2)) (and (=> (@ (@ tptp.ord_less_nat A) B2) (@ P tptp.zero_zero_nat)) (forall ((D4 tptp.nat)) (=> (= A (@ (@ tptp.plus_plus_nat B2) D4)) (@ P D4)))))) (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J) K)) I) (@ (@ tptp.ord_less_nat J) (@ (@ tptp.plus_plus_nat I) K))))) (forall ((I tptp.nat) (J tptp.nat) (U tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.minus_minus_nat M2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I)) U)) N2))))) (forall ((J tptp.nat) (I tptp.nat) (U tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M2)) (@ (@ 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 I) J)) U)) M2)) N2)))) (forall ((I tptp.nat) (J tptp.nat) (U tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.ord_less_eq_nat M2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I)) U)) N2))))) (forall ((J tptp.nat) (I tptp.nat) (U tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M2)) (@ (@ 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 I) J)) U)) M2)) N2)))) (forall ((I tptp.nat) (J tptp.nat) (U tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (= M2 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I)) U)) N2))))) (forall ((J tptp.nat) (I tptp.nat) (U tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I) J)) U)) M2) N2)))) (forall ((N2 tptp.nat) (M2 tptp.nat) (Q3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (= (= (@ (@ tptp.modulo_modulo_nat M2) Q3) (@ (@ tptp.modulo_modulo_nat N2) Q3)) (@ (@ tptp.dvd_dvd_nat Q3) (@ (@ tptp.minus_minus_nat M2) N2))))) (forall ((A2 tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat A2)) (= (@ tptp.nat_set_encode A2) tptp.zero_zero_nat))) (forall ((M2 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 M2))) (= (@ (@ 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) M2)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N2))))))) (forall ((M2 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 M2))) (= (@ (@ 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) M2)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N2))))))) (forall ((Y tptp.real) (Z3 tptp.real) (X tptp.real) (W2 tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z3 tptp.zero_zero_real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real W2) Z3)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z3)) (@ (@ tptp.times_times_real W2) Y))) (@ (@ tptp.times_times_real Y) Z3))) tptp.zero_zero_real))))) (forall ((Y tptp.real) (Z3 tptp.real) (X tptp.real) (W2 tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z3 tptp.zero_zero_real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real W2) Z3)) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z3)) (@ (@ tptp.times_times_real W2) Y))) (@ (@ tptp.times_times_real Y) Z3))) tptp.zero_zero_real))))) (forall ((A tptp.complex) (N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (not (= A tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N2)) (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 M2)) (@ _let_1 N2))))))) (forall ((A tptp.nat) (N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N2)) (@ (@ tptp.divide_divide_nat (@ _let_1 M2)) (@ _let_1 N2))))))) (forall ((A tptp.int) (N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N2)) (@ (@ tptp.divide_divide_int (@ _let_1 M2)) (@ _let_1 N2))))))) (forall ((A tptp.real) (N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N2)) (@ (@ tptp.divide_divide_real (@ _let_1 M2)) (@ _let_1 N2))))))) (forall ((N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M2)) N2) (@ (@ tptp.minus_minus_nat M2) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= N2 (@ tptp.suc (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))))) (forall ((N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (not (@ (@ tptp.ord_less_nat M2) N2)) (= (@ (@ tptp.divide_divide_nat M2) N2) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M2) N2)) N2)))))) (= tptp.divide_divide_nat (lambda ((M tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_nat (or (@ (@ tptp.ord_less_nat M) N) (= N tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M) N)) N))))) (= tptp.plus_plus_nat (lambda ((M tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_nat (= M tptp.zero_zero_nat)) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)) N))))) (forall ((J tptp.nat) (I tptp.nat) (U tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M2)) (@ (@ 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 I) J)) U)) M2)) N2)))) (forall ((I tptp.nat) (J tptp.nat) (U tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I)) U)) N2))))) (= tptp.times_times_nat (lambda ((M tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_nat (= M tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)) N))))) (forall ((Q3 tptp.nat) (N2 tptp.nat) (R2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat R2) M2))) (let ((_let_2 (@ tptp.dvd_dvd_nat M2))) (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 ((R2 tptp.nat) (N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat R2) N2) (=> (@ (@ tptp.ord_less_eq_nat R2) M2) (=> (@ (@ tptp.dvd_dvd_nat N2) (@ (@ tptp.minus_minus_nat M2) R2)) (= (@ (@ tptp.modulo_modulo_nat M2) N2) R2))))) (forall ((U tptp.real) (V tptp.real) (R2 tptp.real) (S tptp.real)) (=> (@ (@ tptp.ord_less_eq_real U) V) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) R2) (=> (@ (@ tptp.ord_less_eq_real R2) S) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real U) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real R2) (@ (@ tptp.minus_minus_real V) U))) S))) V))))) (forall ((N2 tptp.nat) (M2 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) M2)) tptp.zero_zero_nat))))) (forall ((N2 tptp.nat) (M2 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) M2)) tptp.zero_zero_int))))) (forall ((A tptp.nat) (N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 M2)) (@ _let_1 N2)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N2) M2))) (=> (not (= A tptp.zero_zero_nat)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N2)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M2))))))))))) (forall ((A tptp.int) (N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (let ((_let_2 (@ (@ tptp.divide_divide_int (@ _let_1 M2)) (@ _let_1 N2)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N2) M2))) (=> (not (= A tptp.zero_zero_int)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N2)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M2))))))))))) (= tptp.power_power_nat (lambda ((P6 tptp.nat) (M tptp.nat)) (@ (@ (@ tptp.if_nat (= M tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.times_times_nat P6) (@ (@ tptp.power_power_nat P6) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)))))) (= tptp.power_power_int (lambda ((P6 tptp.int) (M tptp.nat)) (@ (@ (@ tptp.if_int (= M tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ tptp.times_times_int P6) (@ (@ tptp.power_power_int P6) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)))))) (= tptp.power_power_real (lambda ((P6 tptp.real) (M tptp.nat)) (@ (@ (@ tptp.if_real (= M tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.times_times_real P6) (@ (@ tptp.power_power_real P6) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)))))) (= tptp.power_power_complex (lambda ((P6 tptp.complex) (M tptp.nat)) (@ (@ (@ tptp.if_complex (= M tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.times_times_complex P6) (@ (@ tptp.power_power_complex P6) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)))))) (= tptp.power_8040749407984259932d_enat (lambda ((P6 tptp.extended_enat) (M tptp.nat)) (@ (@ (@ tptp.if_Extended_enat (= M tptp.zero_zero_nat)) tptp.one_on7984719198319812577d_enat) (@ (@ tptp.times_7803423173614009249d_enat P6) (@ (@ tptp.power_8040749407984259932d_enat P6) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)))))) (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 ((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.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.extended_enat)) (let ((_let_1 (@ tptp.power_8040749407984259932d_enat A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_7803423173614009249d_enat (@ _let_1 (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))) A) (@ _let_1 N2))))) (forall ((K tptp.nat) (M2 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 M2) N2)) (@ (@ tptp.minus_minus_nat (@ _let_1 M2)) (@ _let_1 N2)))))) (forall ((N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (= (@ (@ tptp.divide_divide_nat M2) N2) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M2) N2)) N2)))))) (= (@ tptp.size_num tptp.one) tptp.zero_zero_nat) (forall ((P (-> tptp.nat Bool)) (A tptp.nat)) (=> (forall ((A4 tptp.nat)) (=> (= (@ (@ tptp.divide_divide_nat A4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A4) (@ P A4))) (=> (forall ((A4 tptp.nat) (B4 Bool)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat B4)) (@ (@ tptp.times_times_nat _let_1) A4)))) (=> (@ P A4) (=> (= (@ (@ tptp.divide_divide_nat _let_2) _let_1) A4) (@ P _let_2)))))) (@ P A)))) (forall ((P (-> tptp.int Bool)) (A tptp.int)) (=> (forall ((A4 tptp.int)) (=> (= (@ (@ tptp.divide_divide_int A4) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A4) (@ P A4))) (=> (forall ((A4 tptp.int) (B4 Bool)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int B4)) (@ (@ tptp.times_times_int _let_1) A4)))) (=> (@ P A4) (=> (= (@ (@ tptp.divide_divide_int _let_2) _let_1) A4) (@ P _let_2)))))) (@ P A)))) (forall ((M2 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 M2))) (= (@ (@ tptp.modulo_modulo_nat _let_2) (@ _let_1 N2)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat M2) N2))) _let_2))))) (forall ((M2 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 M2))) (= (@ (@ tptp.modulo_modulo_int _let_2) (@ _let_1 N2)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat M2) N2))) _let_2))))) (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex X) Y)) _let_2) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex X) _let_2)) (@ (@ tptp.power_power_complex Y) _let_2))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X)) Y)))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int X) Y)) _let_2) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_2)) (@ (@ tptp.power_power_int Y) _let_2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int _let_1)) X)) Y)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) Y)) _let_2) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X)) Y)))))) (forall ((M2 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 M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) 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) M2)))) _let_2)))))) (forall ((M2 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 M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) 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) M2)))) _let_2)))))) (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B2)))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2) (=> (@ (@ tptp.ord_less_eq_nat B2) _let_2) (= (@ (@ tptp.minus_minus_nat _let_2) B2) (@ _let_1 B2)))))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B2)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_eq_int B2) _let_2) (= (@ (@ tptp.minus_minus_int _let_2) B2) (@ _let_1 B2)))))))) (forall ((M2 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 M2)) tptp.one_one_nat)) (@ _let_2 N2))) (@ (@ tptp.ord_less_eq_nat M2) N2))))) (forall ((M2 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 M2)) tptp.one_one_int)) (@ _let_2 N2))) (@ (@ tptp.ord_less_eq_nat M2) 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 ((M2 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 M2)) tptp.one_one_nat)) _let_3)) (or (= _let_3 tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat M2) N2))))))) (forall ((M2 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 M2)) tptp.one_one_int)) _let_3)) (or (= _let_3 tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_nat M2) N2))))))) (forall ((L tptp.num) (R2 tptp.int) (Q3 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q3))) (let ((_let_2 (@ (@ tptp.unique5024387138958732305ep_int L) (@ (@ tptp.product_Pair_int_int Q3) R2)))) (let ((_let_3 (@ tptp.numeral_numeral_int L))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_3) R2))) (and (=> _let_4 (= _let_2 (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R2) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.product_Pair_int_int _let_1) R2))))))))) (forall ((L tptp.num) (R2 tptp.nat) (Q3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q3))) (let ((_let_2 (@ (@ tptp.unique5026877609467782581ep_nat L) (@ (@ tptp.product_Pair_nat_nat Q3) R2)))) (let ((_let_3 (@ tptp.numeral_numeral_nat L))) (let ((_let_4 (@ (@ tptp.ord_less_eq_nat _let_3) R2))) (and (=> _let_4 (= _let_2 (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R2) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.product_Pair_nat_nat _let_1) R2))))))))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.vEBT_VEBT_set_vebt T)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_nat))))) _let_187 (= 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))))))))) (forall ((X tptp.set_Extended_enat) (Y tptp.set_Extended_enat)) (= (= (@ (@ tptp.minus_925952699566721837d_enat X) Y) tptp.bot_bo7653980558646680370d_enat) (@ (@ tptp.ord_le7203529160286727270d_enat X) Y))) (forall ((X tptp.set_real) (Y tptp.set_real)) (= (= (@ (@ tptp.minus_minus_set_real X) Y) tptp.bot_bot_set_real) (@ (@ tptp.ord_less_eq_set_real X) Y))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (= (@ (@ tptp.minus_minus_set_nat X) Y) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat X) Y))) (forall ((X tptp.set_int) (Y tptp.set_int)) (= (= (@ (@ tptp.minus_minus_set_int X) Y) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int X) Y))) (= 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)))))) (= 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)))))) (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 ((A tptp.int)) (= (@ tptp.uminus_uminus_int (@ tptp.uminus_uminus_int A)) A)) (forall ((A tptp.real)) (= (@ tptp.uminus_uminus_real (@ tptp.uminus_uminus_real A)) A)) (forall ((A tptp.int) (B2 tptp.int)) (= (= (@ tptp.uminus_uminus_int A) (@ tptp.uminus_uminus_int B2)) (= A B2))) (forall ((A tptp.real) (B2 tptp.real)) (= (= (@ tptp.uminus_uminus_real A) (@ tptp.uminus_uminus_real B2)) (= A B2))) (forall ((A2 tptp.set_Extended_enat)) (= (@ (@ tptp.minus_925952699566721837d_enat A2) A2) tptp.bot_bo7653980558646680370d_enat)) (forall ((A2 tptp.set_real)) (= (@ (@ tptp.minus_minus_set_real A2) A2) tptp.bot_bot_set_real)) (forall ((A2 tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int A2) A2) tptp.bot_bot_set_int)) (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat A2) A2) tptp.bot_bot_set_nat)) (forall ((A2 tptp.set_Extended_enat)) (= (@ (@ tptp.minus_925952699566721837d_enat tptp.bot_bo7653980558646680370d_enat) A2) tptp.bot_bo7653980558646680370d_enat)) (forall ((A2 tptp.set_real)) (= (@ (@ tptp.minus_minus_set_real tptp.bot_bot_set_real) A2) tptp.bot_bot_set_real)) (forall ((A2 tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int tptp.bot_bot_set_int) A2) tptp.bot_bot_set_int)) (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat tptp.bot_bot_set_nat) A2) tptp.bot_bot_set_nat)) (forall ((A2 tptp.set_Extended_enat)) (= (@ (@ tptp.minus_925952699566721837d_enat A2) tptp.bot_bo7653980558646680370d_enat) A2)) (forall ((A2 tptp.set_real)) (= (@ (@ tptp.minus_minus_set_real A2) tptp.bot_bot_set_real) A2)) (forall ((A2 tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int A2) tptp.bot_bot_set_int) A2)) (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat A2) tptp.bot_bot_set_nat) A2)) (forall ((B tptp.set_complex) (A2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex B) (= (@ tptp.finite3207457112153483333omplex (@ (@ tptp.minus_811609699411566653omplex A2) B)) (@ tptp.finite3207457112153483333omplex A2)))) (forall ((B tptp.set_int) (A2 tptp.set_int)) (=> (@ tptp.finite_finite_int B) (= (@ tptp.finite_finite_int (@ (@ tptp.minus_minus_set_int A2) B)) (@ tptp.finite_finite_int A2)))) (forall ((B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat B) (= (@ tptp.finite4001608067531595151d_enat (@ (@ tptp.minus_925952699566721837d_enat A2) B)) (@ tptp.finite4001608067531595151d_enat A2)))) (forall ((B tptp.set_nat) (A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B) (= (@ tptp.finite_finite_nat (@ (@ tptp.minus_minus_set_nat A2) B)) (@ tptp.finite_finite_nat A2)))) (forall ((A2 tptp.set_complex) (B tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A2) (@ tptp.finite3207457112153483333omplex (@ (@ tptp.minus_811609699411566653omplex A2) B)))) (forall ((A2 tptp.set_int) (B tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (@ tptp.finite_finite_int (@ (@ tptp.minus_minus_set_int A2) B)))) (forall ((A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (@ tptp.finite4001608067531595151d_enat (@ (@ tptp.minus_925952699566721837d_enat A2) B)))) (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (@ tptp.finite_finite_nat (@ (@ tptp.minus_minus_set_nat A2) B)))) (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat A2)) (@ tptp.uminus5710092332889474511et_nat B)) (@ (@ tptp.ord_less_eq_set_nat B) A2))) (forall ((A2 tptp.set_int) (B tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int A2)) (@ tptp.uminus1532241313380277803et_int B)) (@ (@ tptp.ord_less_eq_set_int B) A2))) (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat B)) (@ tptp.uminus5710092332889474511et_nat A2)))) (forall ((A2 tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B) (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int B)) (@ tptp.uminus1532241313380277803et_int A2)))) (forall ((W2 tptp.int) (Z3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int W2) (@ (@ tptp.minus_minus_int Z3) tptp.one_one_int)) (@ (@ tptp.ord_less_int W2) Z3))) (forall ((W2 tptp.int) (Z3 tptp.int)) (= (@ (@ tptp.ord_less_int W2) (@ (@ tptp.plus_plus_int Z3) tptp.one_one_int)) (@ (@ tptp.ord_less_eq_int W2) Z3))) (forall ((A tptp.int) (B2 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) B2)))))) (forall ((A tptp.int) (B2 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) B2)))))) (forall ((A tptp.int) (B2 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) B2)))))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat X)) (@ tptp.uminus5710092332889474511et_nat Y)) (@ (@ tptp.ord_less_eq_set_nat Y) X))) (forall ((X tptp.set_int) (Y tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int X)) (@ tptp.uminus1532241313380277803et_int Y)) (@ (@ tptp.ord_less_eq_set_int Y) X))) (forall ((B2 tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B2)) (@ tptp.uminus_uminus_real A)) (@ (@ tptp.ord_less_eq_real A) B2))) (forall ((B2 tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int B2)) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_eq_int A) B2))) (forall ((A tptp.int)) (= (= (@ tptp.uminus_uminus_int A) A) (= A tptp.zero_zero_int))) (forall ((A tptp.real)) (= (= (@ tptp.uminus_uminus_real A) A) (= A tptp.zero_zero_real))) (forall ((A tptp.int)) (= (= A (@ tptp.uminus_uminus_int A)) (= A tptp.zero_zero_int))) (forall ((A tptp.real)) (= (= A (@ tptp.uminus_uminus_real A)) (= A tptp.zero_zero_real))) (forall ((A tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))) (forall ((A tptp.int)) (= (= (@ tptp.uminus_uminus_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))) (forall ((A tptp.real)) (= (= (@ tptp.uminus_uminus_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((A tptp.complex)) (= (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex A)) (= tptp.zero_zero_complex A))) (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ tptp.uminus_uminus_int A)) (= tptp.zero_zero_int A))) (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ tptp.uminus_uminus_real A)) (= tptp.zero_zero_real A))) (= (@ tptp.uminus1482373934393186551omplex tptp.zero_zero_complex) tptp.zero_zero_complex) _let_180 (= (@ tptp.uminus_uminus_real tptp.zero_zero_real) tptp.zero_zero_real) (forall ((B2 tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B2)) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_int A) B2))) (forall ((B2 tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B2)) (@ tptp.uminus_uminus_real A)) (@ (@ tptp.ord_less_real A) B2))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) B2) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.times_times_complex A) B2)))) (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int A)) B2) (@ tptp.uminus_uminus_int (@ (@ tptp.times_times_int A) B2)))) (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real A)) B2) (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real A) B2)))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B2)) (@ (@ tptp.times_times_complex A) B2))) (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B2)) (@ (@ tptp.times_times_int A) B2))) (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B2)) (@ (@ tptp.times_times_real A) B2))) (forall ((A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ tptp.uminus1482373934393186551omplex B2)) (@ tptp.uminus1482373934393186551omplex (@ _let_1 B2))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ tptp.uminus_uminus_int B2)) (@ tptp.uminus_uminus_int (@ _let_1 B2))))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ tptp.uminus_uminus_real B2)) (@ tptp.uminus_uminus_real (@ _let_1 B2))))) (forall ((A tptp.int) (B2 tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int A) B2)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B2)))) (forall ((A tptp.real) (B2 tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real A) B2)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B2)))) (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) (@ (@ tptp.plus_plus_int A) B2)) B2)) (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.plus_plus_real A) B2)) B2)) (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B2)) B2)) (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) B2)) B2)) (forall ((A tptp.int) (B2 tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.minus_minus_int A) B2)) (@ (@ tptp.minus_minus_int B2) A))) (forall ((A tptp.real) (B2 tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.minus_minus_real A) B2)) (@ (@ tptp.minus_minus_real B2) A))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int X))) (= (@ _let_1 (@ tptp.uminus_uminus_int Y)) (@ _let_1 Y)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real X))) (= (@ _let_1 (@ tptp.uminus_uminus_real Y)) (@ _let_1 Y)))) (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.uminus_uminus_int X)) Y) (@ (@ tptp.dvd_dvd_int X) Y))) (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.dvd_dvd_real (@ tptp.uminus_uminus_real X)) Y) (@ (@ tptp.dvd_dvd_real X) Y))) (forall ((A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat)) (= (= (@ (@ tptp.minus_925952699566721837d_enat A2) B) tptp.bot_bo7653980558646680370d_enat) (@ (@ tptp.ord_le7203529160286727270d_enat A2) B))) (forall ((A2 tptp.set_real) (B tptp.set_real)) (= (= (@ (@ tptp.minus_minus_set_real A2) B) tptp.bot_bot_set_real) (@ (@ tptp.ord_less_eq_set_real A2) B))) (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (= (= (@ (@ tptp.minus_minus_set_nat A2) B) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat A2) B))) (forall ((A2 tptp.set_int) (B tptp.set_int)) (= (= (@ (@ tptp.minus_minus_set_int A2) B) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int A2) B))) (forall ((I tptp.extended_enat) (L tptp.extended_enat) (U tptp.extended_enat)) (= (@ (@ tptp.member_Extended_enat I) (@ (@ tptp.set_or5403411693681687835d_enat L) U)) (and (@ (@ tptp.ord_le2932123472753598470d_enat L) I) (@ (@ tptp.ord_le2932123472753598470d_enat I) U)))) (forall ((I tptp.set_nat) (L tptp.set_nat) (U tptp.set_nat)) (= (@ (@ tptp.member_set_nat I) (@ (@ tptp.set_or4548717258645045905et_nat L) U)) (and (@ (@ tptp.ord_less_eq_set_nat L) I) (@ (@ tptp.ord_less_eq_set_nat I) U)))) (forall ((I tptp.set_int) (L tptp.set_int) (U tptp.set_int)) (= (@ (@ tptp.member_set_int I) (@ (@ tptp.set_or370866239135849197et_int L) U)) (and (@ (@ tptp.ord_less_eq_set_int L) I) (@ (@ tptp.ord_less_eq_set_int I) U)))) (forall ((I tptp.nat) (L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.member_nat I) (@ (@ tptp.set_or1269000886237332187st_nat L) U)) (and (@ (@ tptp.ord_less_eq_nat L) I) (@ (@ tptp.ord_less_eq_nat I) U)))) (forall ((I tptp.int) (L tptp.int) (U tptp.int)) (= (@ (@ tptp.member_int I) (@ (@ tptp.set_or1266510415728281911st_int L) U)) (and (@ (@ tptp.ord_less_eq_int L) I) (@ (@ tptp.ord_less_eq_int I) U)))) (forall ((I tptp.real) (L tptp.real) (U tptp.real)) (= (@ (@ tptp.member_real I) (@ (@ tptp.set_or1222579329274155063t_real L) U)) (and (@ (@ tptp.ord_less_eq_real L) I) (@ (@ tptp.ord_less_eq_real I) U)))) (forall ((L tptp.set_nat) (H2 tptp.set_nat) (L3 tptp.set_nat) (H3 tptp.set_nat)) (= (= (@ (@ tptp.set_or4548717258645045905et_nat L) H2) (@ (@ tptp.set_or4548717258645045905et_nat L3) H3)) (or (and (= L L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_set_nat L) H2)) (not (@ (@ tptp.ord_less_eq_set_nat L3) H3)))))) (forall ((L tptp.set_int) (H2 tptp.set_int) (L3 tptp.set_int) (H3 tptp.set_int)) (= (= (@ (@ tptp.set_or370866239135849197et_int L) H2) (@ (@ tptp.set_or370866239135849197et_int L3) H3)) (or (and (= L L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_set_int L) H2)) (not (@ (@ tptp.ord_less_eq_set_int L3) H3)))))) (forall ((L tptp.nat) (H2 tptp.nat) (L3 tptp.nat) (H3 tptp.nat)) (= (= (@ (@ tptp.set_or1269000886237332187st_nat L) H2) (@ (@ tptp.set_or1269000886237332187st_nat L3) H3)) (or (and (= L L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_nat L) H2)) (not (@ (@ tptp.ord_less_eq_nat L3) H3)))))) (forall ((L tptp.int) (H2 tptp.int) (L3 tptp.int) (H3 tptp.int)) (= (= (@ (@ tptp.set_or1266510415728281911st_int L) H2) (@ (@ tptp.set_or1266510415728281911st_int L3) H3)) (or (and (= L L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_int L) H2)) (not (@ (@ tptp.ord_less_eq_int L3) H3)))))) (forall ((L tptp.real) (H2 tptp.real) (L3 tptp.real) (H3 tptp.real)) (= (= (@ (@ tptp.set_or1222579329274155063t_real L) H2) (@ (@ tptp.set_or1222579329274155063t_real L3) H3)) (or (and (= L L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_real L) H2)) (not (@ (@ tptp.ord_less_eq_real L3) H3)))))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N2) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((L tptp.nat) (U tptp.nat)) (@ tptp.finite_finite_nat (@ (@ tptp.set_or1269000886237332187st_nat L) U))) (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.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int))) (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A))) (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A))) (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (= (@ _let_1 (@ tptp.uminus_uminus_real A)) (@ _let_1 tptp.zero_zero_real)))) (forall ((A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (= (@ _let_1 (@ tptp.uminus_uminus_int A)) (@ _let_1 tptp.zero_zero_int)))) (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) A) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A))) (forall ((A tptp.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.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (= (@ _let_1 (@ tptp.uminus_uminus_int A)) (@ _let_1 tptp.zero_zero_int)))) (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (= (@ _let_1 (@ tptp.uminus_uminus_real A)) (@ _let_1 tptp.zero_zero_real)))) (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) A) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))) (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) A) (@ (@ tptp.ord_less_real tptp.zero_zero_real) A))) (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))) (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real A)) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))) (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))) (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) A))) (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)) (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)) (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)) (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) (@ tptp.uminus1482373934393186551omplex A)) tptp.zero_zero_complex)) (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ tptp.uminus_uminus_int A)) tptp.zero_zero_int)) (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real)) (forall ((B2 tptp.complex)) (= (@ (@ tptp.minus_minus_complex tptp.zero_zero_complex) B2) (@ tptp.uminus1482373934393186551omplex B2))) (forall ((B2 tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) B2) (@ tptp.uminus_uminus_int B2))) (forall ((B2 tptp.real)) (= (@ (@ tptp.minus_minus_real tptp.zero_zero_real) B2) (@ tptp.uminus_uminus_real B2))) (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex tptp.zero_zero_complex) A) (@ tptp.uminus1482373934393186551omplex A))) (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) A) (@ tptp.uminus_uminus_int A))) (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real tptp.zero_zero_real) A) (@ tptp.uminus_uminus_real A))) (forall ((M2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.numeral_numeral_int M2))) (= (@ (@ 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 ((M2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N2))) (let ((_let_2 (@ tptp.numeral_numeral_real M2))) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real _let_2)) (@ tptp.uminus_uminus_real _let_1)) (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real _let_2) _let_1)))))) (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B2) (@ (@ tptp.minus_minus_int B2) A))) (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) B2) (@ (@ tptp.minus_minus_real B2) A))) (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ tptp.uminus_uminus_int B2)) (@ (@ tptp.plus_plus_int A) B2))) (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.minus_minus_real A) (@ tptp.uminus_uminus_real B2)) (@ (@ tptp.plus_plus_real A) B2))) (forall ((X tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex X) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex X))) (forall ((X tptp.real)) (= (@ (@ tptp.divide_divide_real X) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real X))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (= (= (@ (@ tptp.set_or5403411693681687835d_enat A) B2) tptp.bot_bo7653980558646680370d_enat) (not (@ (@ tptp.ord_le2932123472753598470d_enat A) B2)))) (forall ((A tptp.set_nat) (B2 tptp.set_nat)) (= (= (@ (@ tptp.set_or4548717258645045905et_nat A) B2) tptp.bot_bot_set_set_nat) (not (@ (@ tptp.ord_less_eq_set_nat A) B2)))) (forall ((A tptp.set_int) (B2 tptp.set_int)) (= (= (@ (@ tptp.set_or370866239135849197et_int A) B2) tptp.bot_bot_set_set_int) (not (@ (@ tptp.ord_less_eq_set_int A) B2)))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (= (@ (@ tptp.set_or1269000886237332187st_nat A) B2) tptp.bot_bot_set_nat) (not (@ (@ tptp.ord_less_eq_nat A) B2)))) (forall ((A tptp.int) (B2 tptp.int)) (= (= (@ (@ tptp.set_or1266510415728281911st_int A) B2) tptp.bot_bot_set_int) (not (@ (@ tptp.ord_less_eq_int A) B2)))) (forall ((A tptp.real) (B2 tptp.real)) (= (= (@ (@ tptp.set_or1222579329274155063t_real A) B2) tptp.bot_bot_set_real) (not (@ (@ tptp.ord_less_eq_real A) B2)))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (= (= tptp.bot_bo7653980558646680370d_enat (@ (@ tptp.set_or5403411693681687835d_enat A) B2)) (not (@ (@ tptp.ord_le2932123472753598470d_enat A) B2)))) (forall ((A tptp.set_nat) (B2 tptp.set_nat)) (= (= tptp.bot_bot_set_set_nat (@ (@ tptp.set_or4548717258645045905et_nat A) B2)) (not (@ (@ tptp.ord_less_eq_set_nat A) B2)))) (forall ((A tptp.set_int) (B2 tptp.set_int)) (= (= tptp.bot_bot_set_set_int (@ (@ tptp.set_or370866239135849197et_int A) B2)) (not (@ (@ tptp.ord_less_eq_set_int A) B2)))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (= tptp.bot_bot_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A) B2)) (not (@ (@ tptp.ord_less_eq_nat A) B2)))) (forall ((A tptp.int) (B2 tptp.int)) (= (= tptp.bot_bot_set_int (@ (@ tptp.set_or1266510415728281911st_int A) B2)) (not (@ (@ tptp.ord_less_eq_int A) B2)))) (forall ((A tptp.real) (B2 tptp.real)) (= (= tptp.bot_bot_set_real (@ (@ tptp.set_or1222579329274155063t_real A) B2)) (not (@ (@ tptp.ord_less_eq_real A) B2)))) (forall ((A tptp.set_nat) (B2 tptp.set_nat) (C tptp.set_nat) (D tptp.set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.set_or4548717258645045905et_nat A) B2)) (@ (@ tptp.set_or4548717258645045905et_nat C) D)) (or (not (@ (@ tptp.ord_less_eq_set_nat A) B2)) (and (@ (@ tptp.ord_less_eq_set_nat C) A) (@ (@ tptp.ord_less_eq_set_nat B2) D))))) (forall ((A tptp.set_int) (B2 tptp.set_int) (C tptp.set_int) (D tptp.set_int)) (= (@ (@ tptp.ord_le4403425263959731960et_int (@ (@ tptp.set_or370866239135849197et_int A) B2)) (@ (@ tptp.set_or370866239135849197et_int C) D)) (or (not (@ (@ tptp.ord_less_eq_set_int A) B2)) (and (@ (@ tptp.ord_less_eq_set_int C) A) (@ (@ tptp.ord_less_eq_set_int B2) D))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A) B2)) (@ (@ tptp.set_or1269000886237332187st_nat C) D)) (or (not (@ (@ tptp.ord_less_eq_nat A) B2)) (and (@ (@ tptp.ord_less_eq_nat C) A) (@ (@ tptp.ord_less_eq_nat B2) D))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.set_or1266510415728281911st_int A) B2)) (@ (@ tptp.set_or1266510415728281911st_int C) D)) (or (not (@ (@ tptp.ord_less_eq_int A) B2)) (and (@ (@ tptp.ord_less_eq_int C) A) (@ (@ tptp.ord_less_eq_int B2) D))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.set_or1222579329274155063t_real A) B2)) (@ (@ tptp.set_or1222579329274155063t_real C) D)) (or (not (@ (@ tptp.ord_less_eq_real A) B2)) (and (@ (@ tptp.ord_less_eq_real C) A) (@ (@ tptp.ord_less_eq_real B2) D))))) (forall ((B2 tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B2) A) (= (@ (@ tptp.set_or5403411693681687835d_enat A) B2) tptp.bot_bo7653980558646680370d_enat))) (forall ((B2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B2) A) (= (@ (@ tptp.set_or1269000886237332187st_nat A) B2) tptp.bot_bot_set_nat))) (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B2) A) (= (@ (@ tptp.set_or1266510415728281911st_int A) B2) tptp.bot_bot_set_int))) (forall ((B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B2) A) (= (@ (@ tptp.set_or1222579329274155063t_real A) B2) tptp.bot_bot_set_real))) (forall ((A tptp.real) (B2 tptp.real)) (= (not (@ tptp.finite_finite_real (@ (@ tptp.set_or1222579329274155063t_real A) B2))) (@ (@ tptp.ord_less_real A) B2))) (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int tptp.zero_zero_nat) A) tptp.zero_zero_int)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N2)) 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)) (= (@ tptp.ln_ln_real tptp.one_one_real) tptp.zero_zero_real) (= (@ _let_186 _let_108) tptp.zero_zero_complex) (= (@ _let_185 _let_107) tptp.zero_zero_int) (= (@ _let_184 _let_106) tptp.zero_zero_real) (= (@ _let_183 tptp.one_one_complex) tptp.zero_zero_complex) (= (@ _let_182 tptp.one_one_int) tptp.zero_zero_int) (= (@ _let_181 tptp.one_one_real) tptp.zero_zero_real) (= (@ (@ tptp.minus_minus_complex _let_108) _let_108) tptp.zero_zero_complex) (= (@ (@ tptp.minus_minus_int _let_107) _let_107) tptp.zero_zero_int) (= (@ (@ tptp.minus_minus_real _let_106) _let_106) tptp.zero_zero_real) (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int)) (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real U))) (let ((_let_2 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V)))) (let ((_let_3 (@ (@ tptp.ord_max_real _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_real _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int U))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))) (let ((_let_3 (@ (@ tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real U)))) (let ((_let_2 (@ tptp.numeral_numeral_real V))) (let ((_let_3 (@ (@ tptp.ord_max_real _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_real _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int U)))) (let ((_let_2 (@ tptp.numeral_numeral_int V))) (let ((_let_3 (@ (@ tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real U)))) (let ((_let_2 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V)))) (let ((_let_3 (@ (@ tptp.ord_max_real _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_real _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int U)))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))) (let ((_let_3 (@ (@ tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((N2 tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) tptp.one_one_nat) tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N2) tptp.one_one_int) tptp.zero_zero_int) (= N2 tptp.zero_zero_nat))) (forall ((V tptp.num) (W2 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 W2))) Y)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num V) W2)))) Y))) (forall ((V tptp.num) (W2 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 W2))) Y)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num V) W2)))) Y))) (forall ((M2 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ (@ tptp.ord_less_eq_num N2) M2))) (forall ((M2 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ (@ tptp.ord_less_eq_num N2) M2))) (forall ((M2 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ (@ tptp.ord_less_num N2) M2))) (forall ((M2 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ (@ tptp.ord_less_num N2) M2))) (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 ((M2 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2)))) (not (= M2 tptp.one)))) (forall ((M2 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2)))) (not (= M2 tptp.one)))) (forall ((A tptp.real) (B2 tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.divide_divide_real B2) _let_1)) (@ (@ tptp.ord_less_eq_real B2) (@ (@ tptp.times_times_real A) _let_1))))) (forall ((B2 tptp.real) (W2 tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B2) _let_1)) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) _let_1)) B2)))) (forall ((B2 tptp.complex) (W2 tptp.num) (A tptp.complex)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W2)))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B2) _let_1) A) (and (=> (not _let_2) (= B2 (@ (@ tptp.times_times_complex A) _let_1))) (=> _let_2 (= A tptp.zero_zero_complex))))))) (forall ((B2 tptp.real) (W2 tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B2) _let_1) A) (and (=> (not _let_2) (= B2 (@ (@ tptp.times_times_real A) _let_1))) (=> _let_2 (= A tptp.zero_zero_real))))))) (forall ((A tptp.complex) (B2 tptp.complex) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W2)))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= A (@ (@ tptp.divide1717551699836669952omplex B2) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex A) _let_1) B2)) (=> _let_2 (= A tptp.zero_zero_complex))))))) (forall ((A tptp.real) (B2 tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= A (@ (@ tptp.divide_divide_real B2) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real A) _let_1) B2)) (=> _let_2 (= A tptp.zero_zero_real))))))) (forall ((M2 tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.uminus_uminus_int tptp.one_one_int)) (not (= M2 tptp.one)))) (forall ((M2 tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) (@ tptp.uminus_uminus_real tptp.one_one_real)) (not (= M2 tptp.one)))) (forall ((A tptp.real) (B2 tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.divide_divide_real B2) _let_1)) (@ (@ tptp.ord_less_real B2) (@ (@ tptp.times_times_real A) _let_1))))) (forall ((B2 tptp.real) (W2 tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B2) _let_1)) A) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) _let_1)) B2)))) (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)))) (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)))) (= (@ _let_183 _let_108) (@ tptp.uminus1482373934393186551omplex _let_109)) (= (@ _let_182 _let_107) (@ tptp.uminus_uminus_int _let_82)) (= (@ _let_181 _let_106) (@ tptp.uminus_uminus_real _let_111)) (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 ((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 ((M2 tptp.nat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat V))) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M2)))) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M2)) _let_1)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat M2))) (= (@ _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 ((M2 tptp.nat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat V))) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M2)))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M2)) _let_1)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat M2))) (= (@ _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 ((A tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc tptp.zero_zero_nat)) A) (@ (@ tptp.modulo_modulo_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (forall ((A tptp.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.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 ((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.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 ((M2 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 M2) _let_1) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat N2) M2))) _let_1)))) (forall ((M2 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 M2) _let_1) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat N2) M2))) _let_1)))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) _let_1) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_eq_nat _let_1) N2))) _let_1)))) (forall ((N2 tptp.nat)) (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 ((L tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) L) (@ tptp.uminus_uminus_int L))) (forall ((K tptp.int)) (= (@ (@ tptp.minus_minus_int K) tptp.zero_zero_int) K)) (forall ((Z1 tptp.int) (Z22 tptp.int) (W2 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int Z1) Z22)) W2) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int Z1) W2)) (@ (@ tptp.times_times_int Z22) W2)))) (forall ((W2 tptp.int) (Z1 tptp.int) (Z22 tptp.int)) (let ((_let_1 (@ tptp.times_times_int W2))) (= (@ _let_1 (@ (@ tptp.minus_minus_int Z1) Z22)) (@ (@ tptp.minus_minus_int (@ _let_1 Z1)) (@ _let_1 Z22))))) (forall ((I tptp.int) (K tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int I) K) (=> (@ P (@ (@ tptp.minus_minus_int K) tptp.one_one_int)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.ord_less_int I4) K) (=> (@ P I4) (@ P (@ (@ tptp.minus_minus_int I4) tptp.one_one_int))))) (@ P I))))) (forall ((K tptp.int) (M2 tptp.int) (N2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (=> (@ (@ tptp.dvd_dvd_int (@ _let_1 M2)) (@ _let_1 N2)) (=> (not (= K tptp.zero_zero_int)) (@ (@ tptp.dvd_dvd_int M2) N2))))) (forall ((Z3 tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int Z3) N2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N2) (@ (@ tptp.ord_less_eq_int Z3) N2)))) (forall ((M2 tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M2) (=> (@ (@ tptp.ord_less_int M2) N2) (not (@ (@ tptp.dvd_dvd_int N2) M2))))) (forall ((M2 tptp.int) (N2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 M2) (=> (@ _let_1 N2) (=> (@ (@ tptp.dvd_dvd_int M2) N2) (=> (@ (@ tptp.dvd_dvd_int N2) M2) (= M2 N2))))))) (forall ((K tptp.int) (N2 tptp.int) (M2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int K))) (= (@ _let_1 (@ (@ tptp.plus_plus_int N2) (@ (@ tptp.times_times_int K) M2))) (@ _let_1 N2)))) (forall ((A tptp.int) (D tptp.int) (X tptp.int) (T tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X))) (let ((_let_2 (@ tptp.dvd_dvd_int A))) (=> (@ _let_2 D) (= (@ _let_2 (@ _let_1 T)) (@ _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.times_times_int C) D))) T))))))) (forall ((I tptp.int)) (=> (not (= I tptp.zero_zero_int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((D4 tptp.int)) (@ (@ tptp.dvd_dvd_int D4) I)))))) (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat Y)) X) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat X)) Y))) (forall ((Y tptp.set_int) (X tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int Y)) X) (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int X)) Y))) (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) (@ tptp.uminus5710092332889474511et_nat X)) (@ (@ tptp.ord_less_eq_set_nat X) (@ tptp.uminus5710092332889474511et_nat Y)))) (forall ((Y tptp.set_int) (X tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y) (@ tptp.uminus1532241313380277803et_int X)) (@ (@ tptp.ord_less_eq_set_int X) (@ tptp.uminus1532241313380277803et_int Y)))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat Y)) (@ tptp.uminus5710092332889474511et_nat X)))) (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X) Y) (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int Y)) (@ tptp.uminus1532241313380277803et_int X)))) (forall ((I tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (=> (@ (@ tptp.ord_less_int I) J) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (@ (@ tptp.ord_less_int (@ _let_1 I)) (@ _let_1 J)))))) (forall ((W2 tptp.int) (Z3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int W2) tptp.one_one_int)) Z3) (@ (@ tptp.ord_less_int W2) Z3))) (forall ((K tptp.int) (I tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int K) I) (=> (@ P (@ (@ tptp.plus_plus_int K) tptp.one_one_int)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.ord_less_int K) I4) (=> (@ P I4) (@ P (@ (@ tptp.plus_plus_int I4) tptp.one_one_int))))) (@ P I))))) (forall ((Z3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z3) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) Z3)))) (forall ((W2 tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int W2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int Z3) tptp.one_one_int)) (or (@ _let_1 Z3) (= W2 Z3))))) (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) Z3)) Z3)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Z3) tptp.zero_zero_int))) (forall ((M2 tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M2) (= (= (@ (@ tptp.times_times_int M2) N2) tptp.one_one_int) (and (= M2 tptp.one_one_int) (= N2 tptp.one_one_int))))) (forall ((W2 tptp.int) (Z3 tptp.int)) (=> (@ (@ tptp.ord_less_int W2) Z3) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int W2) tptp.one_one_int)) Z3))) (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z3) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z3))) (forall ((Z3 tptp.int)) (not (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) Z3)) Z3) tptp.zero_zero_int))) (forall ((M2 tptp.int) (N2 tptp.int)) (=> (= (@ (@ tptp.times_times_int M2) N2) tptp.one_one_int) (or (= M2 tptp.one_one_int) (= M2 (@ tptp.uminus_uminus_int tptp.one_one_int))))) (forall ((M2 tptp.int) (N2 tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (= (@ (@ tptp.times_times_int M2) N2) tptp.one_one_int) (or (and (= M2 tptp.one_one_int) (= N2 tptp.one_one_int)) (and (= M2 _let_1) (= N2 _let_1)))))) (forall ((L tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) L) tptp.zero_zero_int)) (forall ((K tptp.int)) (= (@ (@ tptp.times_times_int K) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((Z1 tptp.int) (Z22 tptp.int) (W2 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int Z1) Z22)) W2) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Z1) W2)) (@ (@ tptp.times_times_int Z22) W2)))) (forall ((W2 tptp.int) (Z1 tptp.int) (Z22 tptp.int)) (let ((_let_1 (@ tptp.times_times_int W2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int Z1) Z22)) (@ (@ tptp.plus_plus_int (@ _let_1 Z1)) (@ _let_1 Z22))))) _let_180 (forall ((A tptp.int) (B2 tptp.int)) (= (= A (@ tptp.uminus_uminus_int B2)) (= B2 (@ tptp.uminus_uminus_int A)))) (forall ((A tptp.real) (B2 tptp.real)) (= (= A (@ tptp.uminus_uminus_real B2)) (= B2 (@ tptp.uminus_uminus_real A)))) (forall ((A tptp.int) (B2 tptp.int)) (= (= (@ tptp.uminus_uminus_int A) B2) (= (@ tptp.uminus_uminus_int B2) A))) (forall ((A tptp.real) (B2 tptp.real)) (= (= (@ tptp.uminus_uminus_real A) B2) (= (@ tptp.uminus_uminus_real B2) A))) (forall ((N2 tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat (@ _let_1 A)) (@ _let_1 B2))) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B2))))) (forall ((N2 tptp.nat) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ _let_1 A)) (@ _let_1 B2))) (@ _let_1 (@ (@ tptp.plus_plus_int A) B2))))) (forall ((N2 tptp.nat) (A tptp.nat) (B2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat M2))) (let ((_let_2 (@ tptp.bit_se2925701944663578781it_nat N2))) (=> (= (@ _let_2 A) (@ _let_2 B2)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ _let_1 A) (@ _let_1 B2))))))) (forall ((N2 tptp.nat) (A tptp.int) (B2 tptp.int) (M2 tptp.nat)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int M2))) (let ((_let_2 (@ tptp.bit_se2923211474154528505it_int N2))) (=> (= (@ _let_2 A) (@ _let_2 B2)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ _let_1 A) (@ _let_1 B2))))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (Q3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.bit_se2925701944663578781it_nat M2) Q3)) (@ (@ tptp.bit_se2925701944663578781it_nat N2) Q3)))) (forall ((N2 tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.bit_se2925701944663578781it_nat N2) M2)) M2)) (forall ((M2 tptp.nat) (N2 tptp.nat) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int M2) K)) (@ (@ tptp.bit_se2923211474154528505it_int N2) K)))) (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B2)) (@ tptp.uminus_uminus_real A)))) (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int B2)) (@ tptp.uminus_uminus_int A)))) (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) B2) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B2)) A))) (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) B2) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int B2)) A))) (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ tptp.uminus_uminus_real B2)) (@ (@ tptp.ord_less_eq_real B2) (@ tptp.uminus_uminus_real A)))) (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ tptp.uminus_uminus_int B2)) (@ (@ tptp.ord_less_eq_int B2) (@ tptp.uminus_uminus_int A)))) (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B2) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B2)) (@ tptp.uminus_uminus_int A)))) (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B2)) (@ tptp.uminus_uminus_real A)))) (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) B2) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B2)) A))) (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) B2) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B2)) A))) (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ tptp.uminus_uminus_int B2)) (@ (@ tptp.ord_less_int B2) (@ tptp.uminus_uminus_int A)))) (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ tptp.uminus_uminus_real B2)) (@ (@ tptp.ord_less_real B2) (@ tptp.uminus_uminus_real A)))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (= (@ (@ tptp.times_times_complex A) A) (@ (@ tptp.times_times_complex B2) B2)) (or (= A B2) (= A (@ tptp.uminus1482373934393186551omplex B2))))) (forall ((A tptp.int) (B2 tptp.int)) (= (= (@ (@ tptp.times_times_int A) A) (@ (@ tptp.times_times_int B2) B2)) (or (= A B2) (= A (@ tptp.uminus_uminus_int B2))))) (forall ((A tptp.real) (B2 tptp.real)) (= (= (@ (@ tptp.times_times_real A) A) (@ (@ tptp.times_times_real B2) B2)) (or (= A B2) (= A (@ tptp.uminus_uminus_real B2))))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) B2) (@ (@ tptp.times_times_complex A) (@ tptp.uminus1482373934393186551omplex B2)))) (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int A)) B2) (@ (@ tptp.times_times_int A) (@ tptp.uminus_uminus_int B2)))) (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real A)) B2) (@ (@ tptp.times_times_real A) (@ tptp.uminus_uminus_real B2)))) (forall ((A tptp.int) (B2 tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int A) B2)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int B2)) (@ tptp.uminus_uminus_int A)))) (forall ((A tptp.real) (B2 tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real A) B2)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real B2)) (@ tptp.uminus_uminus_real A)))) (forall ((A tptp.int) (B2 tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int A) B2)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int B2)) (@ tptp.uminus_uminus_int A)))) (forall ((A tptp.real) (B2 tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real A) B2)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real B2)) (@ tptp.uminus_uminus_real A)))) (forall ((A2 tptp.int) (K tptp.int) (A tptp.int)) (=> (= A2 (@ (@ tptp.plus_plus_int K) A)) (= (@ tptp.uminus_uminus_int A2) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int K)) (@ tptp.uminus_uminus_int A))))) (forall ((A2 tptp.real) (K tptp.real) (A tptp.real)) (=> (= A2 (@ (@ tptp.plus_plus_real K) A)) (= (@ tptp.uminus_uminus_real A2) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real K)) (@ tptp.uminus_uminus_real A))))) (forall ((B2 tptp.int) (A tptp.int)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int B2)) A) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int A)) B2))) (forall ((B2 tptp.real) (A tptp.real)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real B2)) A) (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real A)) B2))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (= (@ tptp.uminus_uminus_real (@ _let_1 B2)) (@ _let_1 (@ tptp.uminus_uminus_real B2))))) (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B2)) (@ (@ tptp.divide_divide_real A) B2))) (forall ((A tptp.real) (B2 tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) B2)) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real A)) B2))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (not (@ tptp.finite3207457112153483333omplex S2)) (not (@ tptp.finite3207457112153483333omplex (@ (@ tptp.minus_811609699411566653omplex S2) T3)))))) (forall ((T3 tptp.set_int) (S2 tptp.set_int)) (=> (@ tptp.finite_finite_int T3) (=> (not (@ tptp.finite_finite_int S2)) (not (@ tptp.finite_finite_int (@ (@ tptp.minus_minus_set_int S2) T3)))))) (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (not (@ tptp.finite4001608067531595151d_enat S2)) (not (@ tptp.finite4001608067531595151d_enat (@ (@ tptp.minus_925952699566721837d_enat S2) T3)))))) (forall ((T3 tptp.set_nat) (S2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat T3) (=> (not (@ tptp.finite_finite_nat S2)) (not (@ tptp.finite_finite_nat (@ (@ tptp.minus_minus_set_nat S2) T3)))))) (forall ((A2 tptp.set_nat) (B tptp.set_nat) (C4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B) (=> (@ (@ tptp.ord_less_eq_set_nat B) C4) (= (@ (@ tptp.minus_minus_set_nat B) (@ (@ tptp.minus_minus_set_nat C4) A2)) A2)))) (forall ((A2 tptp.set_int) (B tptp.set_int) (C4 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B) (=> (@ (@ tptp.ord_less_eq_set_int B) C4) (= (@ (@ tptp.minus_minus_set_int B) (@ (@ tptp.minus_minus_set_int C4) A2)) A2)))) (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A2) B)) A2)) (forall ((A2 tptp.set_int) (B tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A2) B)) A2)) (forall ((A2 tptp.set_nat) (C4 tptp.set_nat) (D6 tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) C4) (=> (@ (@ tptp.ord_less_eq_set_nat D6) B) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A2) B)) (@ (@ tptp.minus_minus_set_nat C4) D6))))) (forall ((A2 tptp.set_int) (C4 tptp.set_int) (D6 tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) C4) (=> (@ (@ tptp.ord_less_eq_set_int D6) B) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A2) B)) (@ (@ tptp.minus_minus_set_int C4) D6))))) (forall ((A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat)) (=> (@ (@ tptp.ord_le2529575680413868914d_enat A2) B) (exists ((B4 tptp.extended_enat)) (@ (@ tptp.member_Extended_enat B4) (@ (@ tptp.minus_925952699566721837d_enat B) A2))))) (forall ((A2 tptp.set_real) (B tptp.set_real)) (=> (@ (@ tptp.ord_less_set_real A2) B) (exists ((B4 tptp.real)) (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real B) A2))))) (forall ((A2 tptp.set_set_nat) (B tptp.set_set_nat)) (=> (@ (@ tptp.ord_less_set_set_nat A2) B) (exists ((B4 tptp.set_nat)) (@ (@ tptp.member_set_nat B4) (@ (@ tptp.minus_2163939370556025621et_nat B) A2))))) (forall ((A2 tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A2) B) (exists ((B4 tptp.int)) (@ (@ tptp.member_int B4) (@ (@ tptp.minus_minus_set_int B) A2))))) (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A2) B) (exists ((B4 tptp.nat)) (@ (@ tptp.member_nat B4) (@ (@ tptp.minus_minus_set_nat B) A2))))) _let_179 (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 ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_eq_int _let_1) K) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) (@ (@ tptp.minus_minus_int K) _let_1)))))) (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (not (@ tptp.finite_finite_real (@ (@ tptp.set_or1222579329274155063t_real A) B2))))) (forall ((N2 tptp.nat) (A tptp.int) (B2 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 B2)) (= (@ _let_1 A) (@ _let_1 B2)))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int M2))) (let ((_let_2 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ _let_2 A)) (@ (@ (@ (@ tptp.if_int_int (@ (@ tptp.ord_less_eq_nat N2) M2)) _let_2) _let_1) A))))) (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ P M))) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ P X4))))) (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M) N2) (@ P M))) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ P X4))))) (forall ((M2 tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M2)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))) (forall ((M2 tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))) (forall ((M2 tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) (@ tptp.numeral_numeral_real N2))) (forall ((M2 tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ 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_zero_int (@ 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 ((M2 tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))) (forall ((M2 tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M2)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))) (forall ((M2 tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.numeral_numeral_int N2))) (forall ((M2 tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) (@ tptp.numeral_numeral_real N2))) (not (@ _let_178 _let_106)) (not (@ _let_177 _let_107)) (@ _let_170 tptp.one_one_real) (@ _let_169 tptp.one_one_int) (not (= tptp.zero_zero_complex _let_108)) (not (= tptp.zero_zero_int _let_107)) (not (= tptp.zero_zero_real _let_106)) (forall ((A tptp.complex) (B2 tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) B2) (= (@ (@ tptp.plus_plus_complex A) B2) tptp.zero_zero_complex))) (forall ((A tptp.int) (B2 tptp.int)) (= (= (@ tptp.uminus_uminus_int A) B2) (= (@ (@ tptp.plus_plus_int A) B2) tptp.zero_zero_int))) (forall ((A tptp.real) (B2 tptp.real)) (= (= (@ tptp.uminus_uminus_real A) B2) (= (@ (@ tptp.plus_plus_real A) B2) tptp.zero_zero_real))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (= A (@ tptp.uminus1482373934393186551omplex B2)) (= (@ (@ tptp.plus_plus_complex A) B2) tptp.zero_zero_complex))) (forall ((A tptp.int) (B2 tptp.int)) (= (= A (@ tptp.uminus_uminus_int B2)) (= (@ (@ tptp.plus_plus_int A) B2) tptp.zero_zero_int))) (forall ((A tptp.real) (B2 tptp.real)) (= (= A (@ tptp.uminus_uminus_real B2)) (= (@ (@ tptp.plus_plus_real A) B2) tptp.zero_zero_real))) (forall ((A tptp.complex) (B2 tptp.complex)) (=> (= (@ (@ tptp.plus_plus_complex A) B2) tptp.zero_zero_complex) (= (@ tptp.uminus1482373934393186551omplex A) B2))) (forall ((A tptp.int) (B2 tptp.int)) (=> (= (@ (@ tptp.plus_plus_int A) B2) tptp.zero_zero_int) (= (@ tptp.uminus_uminus_int A) B2))) (forall ((A tptp.real) (B2 tptp.real)) (=> (= (@ (@ tptp.plus_plus_real A) B2) tptp.zero_zero_real) (= (@ tptp.uminus_uminus_real A) B2))) (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)) (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)) (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)) (forall ((A tptp.complex) (B2 tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex A) B2) tptp.zero_zero_complex) (= B2 (@ tptp.uminus1482373934393186551omplex A)))) (forall ((A tptp.int) (B2 tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) B2) tptp.zero_zero_int) (= B2 (@ tptp.uminus_uminus_int A)))) (forall ((A tptp.real) (B2 tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) B2) tptp.zero_zero_real) (= B2 (@ tptp.uminus_uminus_real A)))) (not (@ _let_176 _let_107)) (not (@ _let_175 _let_106)) (@ _let_166 tptp.one_one_int) (@ _let_165 tptp.one_one_real) (forall ((B2 tptp.complex) (A tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (=> (not (= B2 tptp.zero_zero_complex)) (= (@ tptp.uminus1482373934393186551omplex (@ _let_1 B2)) (@ _let_1 (@ tptp.uminus1482373934393186551omplex B2)))))) (forall ((B2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (=> (not (= B2 tptp.zero_zero_real)) (= (@ tptp.uminus_uminus_real (@ _let_1 B2)) (@ _let_1 (@ tptp.uminus_uminus_real B2)))))) (forall ((B2 tptp.complex) (A tptp.complex)) (=> (not (= B2 tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B2)) (@ (@ tptp.divide1717551699836669952omplex A) B2)))) (forall ((B2 tptp.real) (A tptp.real)) (=> (not (= B2 tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B2)) (@ (@ tptp.divide_divide_real A) B2)))) (forall ((X tptp.complex)) (= (= (@ (@ tptp.times_times_complex X) X) tptp.one_one_complex) (or (= X tptp.one_one_complex) (= X (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))) (forall ((X tptp.int)) (= (= (@ (@ tptp.times_times_int X) X) tptp.one_one_int) (or (= X tptp.one_one_int) (= X (@ tptp.uminus_uminus_int tptp.one_one_int))))) (forall ((X tptp.real)) (= (= (@ (@ tptp.times_times_real X) X) tptp.one_one_real) (or (= X tptp.one_one_real) (= X (@ tptp.uminus_uminus_real tptp.one_one_real))))) (forall ((B tptp.int) (K tptp.int) (B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (=> (= B (@ (@ tptp.plus_plus_int K) B2)) (= (@ _let_1 B) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int K)) (@ _let_1 B2)))))) (forall ((B tptp.real) (K tptp.real) (B2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (=> (= B (@ (@ tptp.plus_plus_real K) B2)) (= (@ _let_1 B) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real K)) (@ _let_1 B2)))))) _let_174 _let_173 (= tptp.minus_minus_int (lambda ((A3 tptp.int) (B3 tptp.int)) (@ (@ tptp.plus_plus_int A3) (@ tptp.uminus_uminus_int B3)))) (= tptp.minus_minus_real (lambda ((A3 tptp.real) (B3 tptp.real)) (@ (@ tptp.plus_plus_real A3) (@ tptp.uminus_uminus_real B3)))) (forall ((N2 tptp.nat) (M2 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 M2))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N2) M2))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))) (forall ((N2 tptp.nat) (M2 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 M2))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N2) M2))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))) (forall ((N2 tptp.nat) (M2 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 M2))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N2) M2))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))) (forall ((N2 tptp.nat) (M2 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 M2))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N2) M2))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))) (forall ((N2 tptp.nat) (M2 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 M2))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N2) M2))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))) (forall ((N2 tptp.nat) (M2 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 M2))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N2) M2))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))) (forall ((B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int B2) A) (= (@ _let_1 (@ tptp.uminus_uminus_int B2)) (@ tptp.uminus_uminus_int (@ _let_1 B2)))))) (forall ((B2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (=> (@ (@ tptp.dvd_dvd_real B2) A) (= (@ _let_1 (@ tptp.uminus_uminus_real B2)) (@ tptp.uminus_uminus_real (@ _let_1 B2)))))) (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B2) A) (= (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) B2) (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int A) B2))))) (forall ((B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real B2) A) (= (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real A)) B2) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) B2))))) (forall ((A2 tptp.set_Extended_enat)) (= (@ (@ tptp.ord_le7203529160286727270d_enat A2) (@ tptp.uminus417252749190364093d_enat A2)) (= A2 tptp.bot_bo7653980558646680370d_enat))) (forall ((A2 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real A2) (@ tptp.uminus612125837232591019t_real A2)) (= A2 tptp.bot_bot_set_real))) (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A2) (@ tptp.uminus5710092332889474511et_nat A2)) (= A2 tptp.bot_bot_set_nat))) (forall ((A2 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A2) (@ tptp.uminus1532241313380277803et_int A2)) (= A2 tptp.bot_bot_set_int))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat) (D tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat C))) (= (@ (@ tptp.ord_le2529575680413868914d_enat (@ (@ tptp.set_or5403411693681687835d_enat A) B2)) (@ (@ tptp.set_or5403411693681687835d_enat C) D)) (and (or (not (@ (@ tptp.ord_le2932123472753598470d_enat A) B2)) (and (@ _let_1 A) (@ (@ tptp.ord_le2932123472753598470d_enat B2) D) (or (@ (@ tptp.ord_le72135733267957522d_enat C) A) (@ (@ tptp.ord_le72135733267957522d_enat B2) D)))) (@ _let_1 D))))) (forall ((A tptp.set_nat) (B2 tptp.set_nat) (C tptp.set_nat) (D tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat C))) (= (@ (@ tptp.ord_less_set_set_nat (@ (@ tptp.set_or4548717258645045905et_nat A) B2)) (@ (@ tptp.set_or4548717258645045905et_nat C) D)) (and (or (not (@ (@ tptp.ord_less_eq_set_nat A) B2)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_set_nat B2) D) (or (@ (@ tptp.ord_less_set_nat C) A) (@ (@ tptp.ord_less_set_nat B2) D)))) (@ _let_1 D))))) (forall ((A tptp.set_int) (B2 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) B2)) (@ (@ tptp.set_or370866239135849197et_int C) D)) (and (or (not (@ (@ tptp.ord_less_eq_set_int A) B2)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_set_int B2) D) (or (@ (@ tptp.ord_less_set_int C) A) (@ (@ tptp.ord_less_set_int B2) D)))) (@ _let_1 D))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (= (@ (@ tptp.ord_less_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A) B2)) (@ (@ tptp.set_or1269000886237332187st_nat C) D)) (and (or (not (@ (@ tptp.ord_less_eq_nat A) B2)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_nat B2) D) (or (@ (@ tptp.ord_less_nat C) A) (@ (@ tptp.ord_less_nat B2) D)))) (@ _let_1 D))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (= (@ (@ tptp.ord_less_set_int (@ (@ tptp.set_or1266510415728281911st_int A) B2)) (@ (@ tptp.set_or1266510415728281911st_int C) D)) (and (or (not (@ (@ tptp.ord_less_eq_int A) B2)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_int B2) D) (or (@ (@ tptp.ord_less_int C) A) (@ (@ tptp.ord_less_int B2) D)))) (@ _let_1 D))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real C))) (= (@ (@ tptp.ord_less_set_real (@ (@ tptp.set_or1222579329274155063t_real A) B2)) (@ (@ tptp.set_or1222579329274155063t_real C) D)) (and (or (not (@ (@ tptp.ord_less_eq_real A) B2)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real B2) D) (or (@ (@ tptp.ord_less_real C) A) (@ (@ tptp.ord_less_real B2) D)))) (@ _let_1 D))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) (@ 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_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_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))) (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_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) tptp.zero_zero_real)) (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_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))) (not (@ _let_172 _let_106)) (not (@ _let_171 _let_107)) (@ _let_170 tptp.zero_zero_real) (@ _let_169 tptp.zero_zero_int) (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_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.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.numeral_numeral_int N2))) (= (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int _let_1) _let_1)) tptp.one_one_int)))) (forall ((N2 tptp.num)) (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)))) (not (@ _let_168 _let_107)) (not (@ _let_167 _let_106)) (@ _let_166 tptp.zero_zero_int) (@ _let_165 tptp.zero_zero_real) (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))))) (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))))) (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M2)) (@ tptp.uminus_uminus_real tptp.one_one_real)))) (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M2)) (@ tptp.uminus_uminus_int tptp.one_one_int)))) (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) (@ tptp.uminus_uminus_real tptp.one_one_real))) (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.uminus_uminus_int tptp.one_one_int))) (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real M2))) (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M2))) (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) tptp.one_one_real)) (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) tptp.one_one_int)) (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))))) (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))))) (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))))) (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))))) (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M2)) (@ tptp.uminus_uminus_int tptp.one_one_int)))) (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M2)) (@ tptp.uminus_uminus_real tptp.one_one_real)))) (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M2))) (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real M2))) (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) tptp.one_one_int)) (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) tptp.one_one_real)) (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= A (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex B2) C))) (and (=> (not _let_1) (= (@ (@ tptp.times_times_complex A) C) (@ tptp.uminus1482373934393186551omplex B2))) (=> _let_1 (= A tptp.zero_zero_complex)))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= A (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B2) C))) (and (=> (not _let_1) (= (@ (@ tptp.times_times_real A) C) (@ tptp.uminus_uminus_real B2))) (=> _let_1 (= A tptp.zero_zero_real)))))) (forall ((B2 tptp.complex) (C tptp.complex) (A tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex B2) C)) A) (and (=> (not _let_1) (= (@ tptp.uminus1482373934393186551omplex B2) (@ (@ tptp.times_times_complex A) C))) (=> _let_1 (= A tptp.zero_zero_complex)))))) (forall ((B2 tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B2) C)) A) (and (=> (not _let_1) (= (@ tptp.uminus_uminus_real B2) (@ (@ tptp.times_times_real A) C))) (=> _let_1 (= A tptp.zero_zero_real)))))) (forall ((B2 tptp.complex) (A tptp.complex) (C tptp.complex)) (=> (not (= B2 tptp.zero_zero_complex)) (= (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B2)) C) (= (@ tptp.uminus1482373934393186551omplex A) (@ (@ tptp.times_times_complex C) B2))))) (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (=> (not (= B2 tptp.zero_zero_real)) (= (= (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) B2)) C) (= (@ tptp.uminus_uminus_real A) (@ (@ tptp.times_times_real C) B2))))) (forall ((B2 tptp.complex) (C tptp.complex) (A tptp.complex)) (=> (not (= B2 tptp.zero_zero_complex)) (= (= C (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B2))) (= (@ (@ tptp.times_times_complex C) B2) (@ tptp.uminus1482373934393186551omplex A))))) (forall ((B2 tptp.real) (C tptp.real) (A tptp.real)) (=> (not (= B2 tptp.zero_zero_real)) (= (= C (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) B2))) (= (@ (@ tptp.times_times_real C) B2) (@ tptp.uminus_uminus_real A))))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B2) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (and (not (= B2 tptp.zero_zero_complex)) (= A (@ tptp.uminus1482373934393186551omplex B2))))) (forall ((A tptp.real) (B2 tptp.real)) (= (= (@ (@ tptp.divide_divide_real A) B2) (@ tptp.uminus_uminus_real tptp.one_one_real)) (and (not (= B2 tptp.zero_zero_real)) (= A (@ tptp.uminus_uminus_real B2))))) (forall ((N2 tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2)) (@ tptp.suc (@ tptp.numeral_numeral_nat (@ tptp.bit0 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 ((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) (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) (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)) (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 ((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_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.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.numeral_numeral_int N2))) (= (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int _let_1) _let_1)) tptp.one_one_int)))) (forall ((N2 tptp.num)) (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 ((N6 tptp.set_nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N6) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ tptp.finite_finite_nat N6))) (forall ((C tptp.real) (B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B2) C))) A) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B2)) (@ (@ tptp.times_times_real A) C))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B2) C))) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ tptp.uminus_uminus_real B2))))) (forall ((C tptp.real) (B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B2) C))) A) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ tptp.uminus_uminus_real B2))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B2) C))) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B2)) (@ (@ tptp.times_times_real A) C))))) (forall ((B2 tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ tptp.uminus_uminus_real B2))) (let ((_let_4 (@ (@ tptp.times_times_real A) C))) (let ((_let_5 (@ _let_1 C))) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B2) C))) A) (and (=> _let_5 (@ (@ tptp.ord_less_real _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_real _let_4) _let_3)) (=> (not _let_2) (@ _let_1 A)))))))))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ tptp.uminus_uminus_real B2))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_1 (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B2) C))) (and (=> _let_5 (@ (@ tptp.ord_less_real _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_real _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_real)))))))))))) (forall ((B2 tptp.complex) (C tptp.complex) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W2)))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B2) C) _let_1) (and (=> (not _let_2) (= B2 (@ (@ tptp.times_times_complex _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))) (forall ((B2 tptp.real) (C tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B2) C) _let_1) (and (=> (not _let_2) (= B2 (@ (@ tptp.times_times_real _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))) (forall ((W2 tptp.num) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W2)))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= _let_1 (@ (@ tptp.divide1717551699836669952omplex B2) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex _let_1) C) B2)) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))) (forall ((W2 tptp.num) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= _let_1 (@ (@ tptp.divide_divide_real B2) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real _let_1) C) B2)) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))) (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 ((Z3 tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) Z3))) B2))) (let ((_let_2 (= Z3 tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 B2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ (@ tptp.times_times_complex B2) Z3))) Z3))))))) (forall ((Z3 tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) Z3))) B2))) (let ((_let_2 (= Z3 tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 B2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.times_times_real B2) Z3))) Z3))))))) (forall ((Z3 tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z3 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex X) Z3))) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex X)) (@ (@ tptp.times_times_complex Y) Z3))) Z3)))) (forall ((Z3 tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z3 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real X) Z3))) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real X)) (@ (@ tptp.times_times_real Y) Z3))) Z3)))) (forall ((Z3 tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) Z3))) B2))) (let ((_let_2 (= Z3 tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 (@ tptp.uminus1482373934393186551omplex B2))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ (@ tptp.times_times_complex B2) Z3))) Z3))))))) (forall ((Z3 tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) Z3))) B2))) (let ((_let_2 (= Z3 tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_real B2))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.times_times_real B2) Z3))) Z3))))))) (forall ((Z3 tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex A) Z3)) B2))) (let ((_let_2 (= Z3 tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 (@ tptp.uminus1482373934393186551omplex B2))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex A) (@ (@ tptp.times_times_complex B2) Z3))) Z3))))))) (forall ((Z3 tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real A) Z3)) B2))) (let ((_let_2 (= Z3 tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_real B2))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real A) (@ (@ tptp.times_times_real B2) Z3))) Z3))))))) (forall ((Z3 tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z3 tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex X) Z3))) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex X)) (@ (@ tptp.times_times_complex Y) Z3))) Z3)))) (forall ((Z3 tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z3 tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real X) Z3))) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X)) (@ (@ tptp.times_times_real Y) Z3))) Z3)))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one)) (@ tptp.suc _let_81)) (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 ((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))))) (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 ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) M2) M2))) (forall ((N2 tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.bit_se2925701944663578781it_nat N2) M2)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (forall ((N2 tptp.nat) (M2 tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) M2) M2) (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (forall ((X32 tptp.num)) (= (@ tptp.size_size_num (@ tptp.bit1 X32)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_num X32)) (@ tptp.suc tptp.zero_zero_nat)))) (forall ((X32 tptp.num)) (= (@ tptp.size_num (@ tptp.bit1 X32)) (@ (@ tptp.plus_plus_nat (@ tptp.size_num X32)) (@ tptp.suc tptp.zero_zero_nat)))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ tptp.uminus_uminus_real B2))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_1 (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B2) C))) (and (=> _let_5 (@ (@ tptp.ord_less_eq_real _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_eq_real _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_real)))))))))))) (forall ((B2 tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_2 (@ tptp.uminus_uminus_real B2))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B2) C))) A) (and (=> _let_4 (@ (@ tptp.ord_less_eq_real _let_2) _let_3)) (=> (not _let_4) (and (=> _let_1 (@ (@ tptp.ord_less_eq_real _let_3) _let_2)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A))))))))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B2) C))) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B2)) (@ (@ tptp.times_times_real A) C))))) (forall ((C tptp.real) (B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B2) C))) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ tptp.uminus_uminus_real B2))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B2) C))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ tptp.uminus_uminus_real B2))))) (forall ((C tptp.real) (B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B2) C))) A) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B2)) (@ (@ tptp.times_times_real A) C))))) (forall ((B2 tptp.real) (C tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ _let_2 C))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B2) C)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_real B2) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real _let_4) B2)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))) (forall ((W2 tptp.num) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (let ((_let_2 (@ tptp.ord_less_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B2) C)) (and (=> _let_5 (@ (@ tptp.ord_less_real _let_4) B2)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real B2) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))) (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 ((M2 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 M2))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat tptp.one)) _let_1)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M2)) (@ tptp.numeral_numeral_nat Q3)) tptp.zero_zero_nat)))) (forall ((M2 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 M2))) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int tptp.one)) _let_1)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M2)) (@ tptp.numeral_numeral_int Q3)) tptp.zero_zero_int)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M2)))) N2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M2)) N2))) (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_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_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 ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M2)))) N2) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M2)) N2))) (forall ((N2 tptp.nat) (A tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) A) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) A))) (forall ((N2 tptp.nat) (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) (M2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.bit_se2925701944663578781it_nat N2) M2)) M2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) M2))) (forall ((B2 tptp.real) (C tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B2) C)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_real B2) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_real _let_3) B2)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1))))))))))) (forall ((W2 tptp.num) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (let ((_let_2 (@ tptp.ord_less_eq_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B2) C)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_real _let_4) B2)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_real B2) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) X) (=> (@ (@ tptp.ord_less_eq_int X) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int)))) (forall ((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.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.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) (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 ((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 ((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.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 ((M2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ (@ tptp.modulo_modulo_nat M2) (@ 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 ((M2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (let ((_let_2 (@ tptp.bit1 M2))) (let ((_let_3 (@ tptp.unique5052692396658037445od_int _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_num M2) 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 ((M2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (let ((_let_2 (@ tptp.bit1 M2))) (let ((_let_3 (@ tptp.unique5055182867167087721od_nat _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_num M2) 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 ((M2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (let ((_let_2 (@ tptp.bit0 M2))) (let ((_let_3 (@ tptp.unique5052692396658037445od_int _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_eq_num M2) 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 ((M2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (let ((_let_2 (@ tptp.bit0 M2))) (let ((_let_3 (@ tptp.unique5055182867167087721od_nat _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_eq_num M2) 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)))))))))))) _let_164 _let_163 (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 ((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))) (= tptp.unique5052692396658037445od_int (lambda ((M tptp.num) (N tptp.num)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_num M) N)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int M))) (@ (@ tptp.unique5024387138958732305ep_int N) (@ (@ tptp.unique5052692396658037445od_int M) (@ tptp.bit0 N)))))) (= tptp.unique5055182867167087721od_nat (lambda ((M tptp.num) (N tptp.num)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_num M) N)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.unique5026877609467782581ep_nat N) (@ (@ tptp.unique5055182867167087721od_nat M) (@ tptp.bit0 N)))))) (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 ((X tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X))) (let ((_let_2 (@ _let_1 A2))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int X))) (let ((_let_2 (@ _let_1 A2))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X tptp.real) (A2 tptp.set_real)) (let ((_let_1 (@ tptp.insert_real X))) (let ((_let_2 (@ _let_1 A2))) (= (@ _let_1 _let_2) _let_2)))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (A2 tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat A))) (= (@ _let_1 (@ (@ tptp.insert_Extended_enat B2) A2)) (or (= A B2) (@ _let_1 A2))))) (forall ((A tptp.real) (B2 tptp.real) (A2 tptp.set_real)) (let ((_let_1 (@ tptp.member_real A))) (= (@ _let_1 (@ (@ tptp.insert_real B2) A2)) (or (= A B2) (@ _let_1 A2))))) (forall ((A tptp.set_nat) (B2 tptp.set_nat) (A2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat A))) (= (@ _let_1 (@ (@ tptp.insert_set_nat B2) A2)) (or (= A B2) (@ _let_1 A2))))) (forall ((A tptp.nat) (B2 tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat A))) (= (@ _let_1 (@ (@ tptp.insert_nat B2) A2)) (or (= A B2) (@ _let_1 A2))))) (forall ((A tptp.int) (B2 tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ tptp.member_int A))) (= (@ _let_1 (@ (@ tptp.insert_int B2) A2)) (or (= A B2) (@ _let_1 A2))))) (forall ((A tptp.extended_enat) (B tptp.set_Extended_enat) (B2 tptp.extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat A))) (=> (=> (not (@ _let_1 B)) (= A B2)) (@ _let_1 (@ (@ tptp.insert_Extended_enat B2) B))))) (forall ((A tptp.real) (B tptp.set_real) (B2 tptp.real)) (let ((_let_1 (@ tptp.member_real A))) (=> (=> (not (@ _let_1 B)) (= A B2)) (@ _let_1 (@ (@ tptp.insert_real B2) B))))) (forall ((A tptp.set_nat) (B tptp.set_set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat A))) (=> (=> (not (@ _let_1 B)) (= A B2)) (@ _let_1 (@ (@ tptp.insert_set_nat B2) B))))) (forall ((A tptp.nat) (B tptp.set_nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat A))) (=> (=> (not (@ _let_1 B)) (= A B2)) (@ _let_1 (@ (@ tptp.insert_nat B2) B))))) (forall ((A tptp.int) (B tptp.set_int) (B2 tptp.int)) (let ((_let_1 (@ tptp.member_int A))) (=> (=> (not (@ _let_1 B)) (= A B2)) (@ _let_1 (@ (@ tptp.insert_int B2) B))))) (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ (@ tptp.minus_minus_set_nat A2) B))) (= (@ (@ tptp.minus_minus_set_nat _let_1) B) _let_1))) (forall ((C tptp.extended_enat) (A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat C))) (= (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) B)) (and (@ _let_1 A2) (not (@ _let_1 B)))))) (forall ((C tptp.real) (A2 tptp.set_real) (B tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) B)) (and (@ _let_1 A2) (not (@ _let_1 B)))))) (forall ((C tptp.set_nat) (A2 tptp.set_set_nat) (B tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (= (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A2) B)) (and (@ _let_1 A2) (not (@ _let_1 B)))))) (forall ((C tptp.int) (A2 tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B)) (and (@ _let_1 A2) (not (@ _let_1 B)))))) (forall ((C tptp.nat) (A2 tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B)) (and (@ _let_1 A2) (not (@ _let_1 B)))))) (forall ((C tptp.extended_enat) (A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat C))) (=> (@ _let_1 A2) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) B)))))) (forall ((C tptp.real) (A2 tptp.set_real) (B tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ _let_1 A2) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) B)))))) (forall ((C tptp.set_nat) (A2 tptp.set_set_nat) (B tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 A2) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A2) B)))))) (forall ((C tptp.int) (A2 tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 A2) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B)))))) (forall ((C tptp.nat) (A2 tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 A2) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B)))))) (forall ((C tptp.extended_enat) (A2 tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat C))) (=> (not (@ _let_1 A2)) (@ _let_1 (@ tptp.uminus417252749190364093d_enat A2))))) (forall ((C tptp.real) (A2 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (=> (not (@ _let_1 A2)) (@ _let_1 (@ tptp.uminus612125837232591019t_real A2))))) (forall ((C tptp.set_nat) (A2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (not (@ _let_1 A2)) (@ _let_1 (@ tptp.uminus613421341184616069et_nat A2))))) (forall ((C tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (not (@ _let_1 A2)) (@ _let_1 (@ tptp.uminus5710092332889474511et_nat A2))))) (forall ((C tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (not (@ _let_1 A2)) (@ _let_1 (@ tptp.uminus1532241313380277803et_int A2))))) (forall ((C tptp.extended_enat) (A2 tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat C))) (= (@ _let_1 (@ tptp.uminus417252749190364093d_enat A2)) (not (@ _let_1 A2))))) (forall ((C tptp.real) (A2 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (= (@ _let_1 (@ tptp.uminus612125837232591019t_real A2)) (not (@ _let_1 A2))))) (forall ((C tptp.set_nat) (A2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (= (@ _let_1 (@ tptp.uminus613421341184616069et_nat A2)) (not (@ _let_1 A2))))) (forall ((C tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (= (@ _let_1 (@ tptp.uminus5710092332889474511et_nat A2)) (not (@ _let_1 A2))))) (forall ((C tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (= (@ _let_1 (@ tptp.uminus1532241313380277803et_int A2)) (not (@ _let_1 A2))))) (forall ((L tptp.int) (U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or1266510415728281911st_int L) U))) (forall ((A tptp.set_nat)) (@ (@ tptp.member_set_nat A) (@ (@ tptp.insert_set_nat A) tptp.bot_bot_set_set_nat))) (forall ((A tptp.extended_enat)) (@ (@ tptp.member_Extended_enat A) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat))) (forall ((A tptp.real)) (@ (@ tptp.member_real A) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))) (forall ((A tptp.nat)) (@ (@ tptp.member_nat A) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))) (forall ((A tptp.int)) (@ (@ tptp.member_int A) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))) (forall ((A tptp.real) (A2 tptp.set_real)) (= (@ tptp.finite_finite_real (@ (@ tptp.insert_real A) A2)) (@ tptp.finite_finite_real A2))) (forall ((A tptp.nat) (A2 tptp.set_nat)) (= (@ tptp.finite_finite_nat (@ (@ tptp.insert_nat A) A2)) (@ tptp.finite_finite_nat A2))) (forall ((A tptp.complex) (A2 tptp.set_complex)) (= (@ tptp.finite3207457112153483333omplex (@ (@ tptp.insert_complex A) A2)) (@ tptp.finite3207457112153483333omplex A2))) (forall ((A tptp.int) (A2 tptp.set_int)) (= (@ tptp.finite_finite_int (@ (@ tptp.insert_int A) A2)) (@ tptp.finite_finite_int A2))) (forall ((A tptp.extended_enat) (A2 tptp.set_Extended_enat)) (= (@ tptp.finite4001608067531595151d_enat (@ (@ tptp.insert_Extended_enat A) A2)) (@ tptp.finite4001608067531595151d_enat A2))) (forall ((X tptp.extended_enat) (A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat)) (= (@ (@ tptp.ord_le7203529160286727270d_enat (@ (@ tptp.insert_Extended_enat X) A2)) B) (and (@ (@ tptp.member_Extended_enat X) B) (@ (@ tptp.ord_le7203529160286727270d_enat A2) B)))) (forall ((X tptp.real) (A2 tptp.set_real) (B tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.insert_real X) A2)) B) (and (@ (@ tptp.member_real X) B) (@ (@ tptp.ord_less_eq_set_real A2) B)))) (forall ((X tptp.set_nat) (A2 tptp.set_set_nat) (B tptp.set_set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.insert_set_nat X) A2)) B) (and (@ (@ tptp.member_set_nat X) B) (@ (@ tptp.ord_le6893508408891458716et_nat A2) B)))) (forall ((X tptp.nat) (A2 tptp.set_nat) (B tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.insert_nat X) A2)) B) (and (@ (@ tptp.member_nat X) B) (@ (@ tptp.ord_less_eq_set_nat A2) B)))) (forall ((X tptp.int) (A2 tptp.set_int) (B tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.insert_int X) A2)) B) (and (@ (@ tptp.member_int X) B) (@ (@ tptp.ord_less_eq_set_int A2) B)))) (forall ((X tptp.extended_enat) (B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat)) (=> (@ (@ tptp.member_Extended_enat X) B) (= (@ (@ tptp.minus_925952699566721837d_enat (@ (@ tptp.insert_Extended_enat X) A2)) B) (@ (@ tptp.minus_925952699566721837d_enat A2) B)))) (forall ((X tptp.real) (B tptp.set_real) (A2 tptp.set_real)) (=> (@ (@ tptp.member_real X) B) (= (@ (@ tptp.minus_minus_set_real (@ (@ tptp.insert_real X) A2)) B) (@ (@ tptp.minus_minus_set_real A2) B)))) (forall ((X tptp.set_nat) (B tptp.set_set_nat) (A2 tptp.set_set_nat)) (=> (@ (@ tptp.member_set_nat X) B) (= (@ (@ tptp.minus_2163939370556025621et_nat (@ (@ tptp.insert_set_nat X) A2)) B) (@ (@ tptp.minus_2163939370556025621et_nat A2) B)))) (forall ((X tptp.int) (B tptp.set_int) (A2 tptp.set_int)) (=> (@ (@ tptp.member_int X) B) (= (@ (@ tptp.minus_minus_set_int (@ (@ tptp.insert_int X) A2)) B) (@ (@ tptp.minus_minus_set_int A2) B)))) (forall ((X tptp.nat) (B tptp.set_nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.member_nat X) B) (= (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.insert_nat X) A2)) B) (@ (@ tptp.minus_minus_set_nat A2) B)))) (forall ((X tptp.extended_enat) (A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.minus_925952699566721837d_enat A2))) (=> (not (@ (@ tptp.member_Extended_enat X) A2)) (= (@ _let_1 (@ (@ tptp.insert_Extended_enat X) B)) (@ _let_1 B))))) (forall ((X tptp.real) (A2 tptp.set_real) (B tptp.set_real)) (let ((_let_1 (@ tptp.minus_minus_set_real A2))) (=> (not (@ (@ tptp.member_real X) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X) B)) (@ _let_1 B))))) (forall ((X tptp.set_nat) (A2 tptp.set_set_nat) (B tptp.set_set_nat)) (let ((_let_1 (@ tptp.minus_2163939370556025621et_nat A2))) (=> (not (@ (@ tptp.member_set_nat X) A2)) (= (@ _let_1 (@ (@ tptp.insert_set_nat X) B)) (@ _let_1 B))))) (forall ((X tptp.int) (A2 tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.minus_minus_set_int A2))) (=> (not (@ (@ tptp.member_int X) A2)) (= (@ _let_1 (@ (@ tptp.insert_int X) B)) (@ _let_1 B))))) (forall ((X tptp.nat) (A2 tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat A2))) (=> (not (@ (@ tptp.member_nat X) A2)) (= (@ _let_1 (@ (@ tptp.insert_nat X) B)) (@ _let_1 B))))) (forall ((A tptp.list_nat)) (= (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (= X4 A))) (@ (@ tptp.insert_list_nat A) tptp.bot_bot_set_list_nat))) (forall ((A tptp.set_nat)) (= (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (= X4 A))) (@ (@ tptp.insert_set_nat A) tptp.bot_bot_set_set_nat))) (forall ((A tptp.extended_enat)) (= (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (= X4 A))) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat))) (forall ((A tptp.real)) (= (@ tptp.collect_real (lambda ((X4 tptp.real)) (= X4 A))) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))) (forall ((A tptp.nat)) (= (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (= X4 A))) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))) (forall ((A tptp.int)) (= (@ tptp.collect_int (lambda ((X4 tptp.int)) (= X4 A))) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))) (forall ((A tptp.list_nat)) (= (@ tptp.collect_list_nat (@ (lambda ((Y4 tptp.list_nat) (Z2 tptp.list_nat)) (= Y4 Z2)) A)) (@ (@ tptp.insert_list_nat A) tptp.bot_bot_set_list_nat))) (forall ((A tptp.set_nat)) (= (@ tptp.collect_set_nat (@ (lambda ((Y4 tptp.set_nat) (Z2 tptp.set_nat)) (= Y4 Z2)) A)) (@ (@ tptp.insert_set_nat A) tptp.bot_bot_set_set_nat))) (forall ((A tptp.extended_enat)) (= (@ tptp.collec4429806609662206161d_enat (@ (lambda ((Y4 tptp.extended_enat) (Z2 tptp.extended_enat)) (= Y4 Z2)) A)) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat))) (forall ((A tptp.real)) (= (@ tptp.collect_real (@ (lambda ((Y4 tptp.real) (Z2 tptp.real)) (= Y4 Z2)) A)) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))) (forall ((A tptp.nat)) (= (@ tptp.collect_nat (@ (lambda ((Y4 tptp.nat) (Z2 tptp.nat)) (= Y4 Z2)) A)) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))) (forall ((A tptp.int)) (= (@ tptp.collect_int (@ (lambda ((Y4 tptp.int) (Z2 tptp.int)) (= Y4 Z2)) A)) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))) (forall ((A tptp.int) (B2 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) B2)))))) (forall ((A tptp.extended_enat) (A2 tptp.set_Extended_enat) (B2 tptp.extended_enat)) (let ((_let_1 (@ (@ tptp.insert_Extended_enat B2) tptp.bot_bo7653980558646680370d_enat))) (= (= (@ (@ tptp.insert_Extended_enat A) A2) _let_1) (and (= A B2) (@ (@ tptp.ord_le7203529160286727270d_enat A2) _let_1))))) (forall ((A tptp.real) (A2 tptp.set_real) (B2 tptp.real)) (let ((_let_1 (@ (@ tptp.insert_real B2) tptp.bot_bot_set_real))) (= (= (@ (@ tptp.insert_real A) A2) _let_1) (and (= A B2) (@ (@ tptp.ord_less_eq_set_real A2) _let_1))))) (forall ((A tptp.nat) (A2 tptp.set_nat) (B2 tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat B2) tptp.bot_bot_set_nat))) (= (= (@ (@ tptp.insert_nat A) A2) _let_1) (and (= A B2) (@ (@ tptp.ord_less_eq_set_nat A2) _let_1))))) (forall ((A tptp.int) (A2 tptp.set_int) (B2 tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int B2) tptp.bot_bot_set_int))) (= (= (@ (@ tptp.insert_int A) A2) _let_1) (and (= A B2) (@ (@ tptp.ord_less_eq_set_int A2) _let_1))))) (forall ((B2 tptp.extended_enat) (A tptp.extended_enat) (A2 tptp.set_Extended_enat)) (let ((_let_1 (@ (@ tptp.insert_Extended_enat B2) tptp.bot_bo7653980558646680370d_enat))) (= (= _let_1 (@ (@ tptp.insert_Extended_enat A) A2)) (and (= A B2) (@ (@ tptp.ord_le7203529160286727270d_enat A2) _let_1))))) (forall ((B2 tptp.real) (A tptp.real) (A2 tptp.set_real)) (let ((_let_1 (@ (@ tptp.insert_real B2) tptp.bot_bot_set_real))) (= (= _let_1 (@ (@ tptp.insert_real A) A2)) (and (= A B2) (@ (@ tptp.ord_less_eq_set_real A2) _let_1))))) (forall ((B2 tptp.nat) (A tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.insert_nat B2) tptp.bot_bot_set_nat))) (= (= _let_1 (@ (@ tptp.insert_nat A) A2)) (and (= A B2) (@ (@ tptp.ord_less_eq_set_nat A2) _let_1))))) (forall ((B2 tptp.int) (A tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ (@ tptp.insert_int B2) tptp.bot_bot_set_int))) (= (= _let_1 (@ (@ tptp.insert_int A) A2)) (and (= A B2) (@ (@ tptp.ord_less_eq_set_int A2) _let_1))))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat)) (= (= (@ (@ tptp.set_or5403411693681687835d_enat A) B2) (@ (@ tptp.insert_Extended_enat C) tptp.bot_bo7653980558646680370d_enat)) (and (= A B2) (= B2 C)))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (= (= (@ (@ tptp.set_or1269000886237332187st_nat A) B2) (@ (@ tptp.insert_nat C) tptp.bot_bot_set_nat)) (and (= A B2) (= B2 C)))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (= (= (@ (@ tptp.set_or1266510415728281911st_int A) B2) (@ (@ tptp.insert_int C) tptp.bot_bot_set_int)) (and (= A B2) (= B2 C)))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (= (= (@ (@ tptp.set_or1222579329274155063t_real A) B2) (@ (@ tptp.insert_real C) tptp.bot_bot_set_real)) (and (= A B2) (= B2 C)))) (forall ((A tptp.extended_enat)) (= (@ (@ tptp.set_or5403411693681687835d_enat A) A) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat))) (forall ((A tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat A) A) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))) (forall ((A tptp.int)) (= (@ (@ tptp.set_or1266510415728281911st_int A) A) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))) (forall ((A tptp.real)) (= (@ (@ tptp.set_or1222579329274155063t_real A) A) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))) (forall ((A tptp.extended_enat) (A2 tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.insert_Extended_enat A))) (= (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ _let_1 tptp.bot_bo7653980558646680370d_enat))) (@ _let_1 A2)))) (forall ((A tptp.real) (A2 tptp.set_real)) (let ((_let_1 (@ tptp.insert_real A))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ _let_1 tptp.bot_bot_set_real))) (@ _let_1 A2)))) (forall ((A tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ _let_1 tptp.bot_bot_set_int))) (@ _let_1 A2)))) (forall ((A tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) (@ _let_1 tptp.bot_bot_set_nat))) (@ _let_1 A2)))) (forall ((A2 tptp.set_real) (A tptp.real) (B tptp.set_real)) (let ((_let_1 (@ tptp.minus_minus_set_real A2))) (= (@ tptp.finite_finite_real (@ _let_1 (@ (@ tptp.insert_real A) B))) (@ tptp.finite_finite_real (@ _let_1 B))))) (forall ((A2 tptp.set_complex) (A tptp.complex) (B tptp.set_complex)) (let ((_let_1 (@ tptp.minus_811609699411566653omplex A2))) (= (@ tptp.finite3207457112153483333omplex (@ _let_1 (@ (@ tptp.insert_complex A) B))) (@ tptp.finite3207457112153483333omplex (@ _let_1 B))))) (forall ((A2 tptp.set_int) (A tptp.int) (B tptp.set_int)) (let ((_let_1 (@ tptp.minus_minus_set_int A2))) (= (@ tptp.finite_finite_int (@ _let_1 (@ (@ tptp.insert_int A) B))) (@ tptp.finite_finite_int (@ _let_1 B))))) (forall ((A2 tptp.set_Extended_enat) (A tptp.extended_enat) (B tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.minus_925952699566721837d_enat A2))) (= (@ tptp.finite4001608067531595151d_enat (@ _let_1 (@ (@ tptp.insert_Extended_enat A) B))) (@ tptp.finite4001608067531595151d_enat (@ _let_1 B))))) (forall ((A2 tptp.set_nat) (A tptp.nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat A2))) (= (@ tptp.finite_finite_nat (@ _let_1 (@ (@ tptp.insert_nat A) B))) (@ tptp.finite_finite_nat (@ _let_1 B))))) (= (@ tptp.pred_numeral tptp.one) tptp.zero_zero_nat) (forall ((K tptp.num) (N2 tptp.nat)) (= (= (@ tptp.numeral_numeral_nat K) (@ tptp.suc N2)) (= (@ tptp.pred_numeral K) N2))) (forall ((N2 tptp.nat) (K tptp.num)) (= (= (@ tptp.suc N2) (@ tptp.numeral_numeral_nat K)) (= N2 (@ tptp.pred_numeral K)))) (forall ((A2 tptp.set_set_nat) (B2 tptp.set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat A2) (@ tptp.uminus613421341184616069et_nat (@ (@ tptp.insert_set_nat B2) tptp.bot_bot_set_set_nat))) (not (@ (@ tptp.member_set_nat B2) A2)))) (forall ((A2 tptp.set_Extended_enat) (B2 tptp.extended_enat)) (= (@ (@ tptp.ord_le7203529160286727270d_enat A2) (@ tptp.uminus417252749190364093d_enat (@ (@ tptp.insert_Extended_enat B2) tptp.bot_bo7653980558646680370d_enat))) (not (@ (@ tptp.member_Extended_enat B2) A2)))) (forall ((A2 tptp.set_real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real A2) (@ tptp.uminus612125837232591019t_real (@ (@ tptp.insert_real B2) tptp.bot_bot_set_real))) (not (@ (@ tptp.member_real B2) A2)))) (forall ((A2 tptp.set_nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat A2) (@ tptp.uminus5710092332889474511et_nat (@ (@ tptp.insert_nat B2) tptp.bot_bot_set_nat))) (not (@ (@ tptp.member_nat B2) A2)))) (forall ((A2 tptp.set_int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int A2) (@ tptp.uminus1532241313380277803et_int (@ (@ tptp.insert_int B2) tptp.bot_bot_set_int))) (not (@ (@ tptp.member_int B2) A2)))) (forall ((K tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N2)) (@ (@ tptp.ord_less_nat (@ tptp.pred_numeral K)) N2))) (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.ord_less_nat N2) (@ tptp.pred_numeral K)))) (forall ((K tptp.num) (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.ord_less_eq_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.pred_numeral K)))) (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.minus_minus_nat N2) (@ tptp.pred_numeral K)))) (forall ((K tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N2)) (@ (@ tptp.minus_minus_nat (@ tptp.pred_numeral K)) N2))) (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_max_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat K)) (@ tptp.suc (@ (@ tptp.ord_max_nat N2) (@ tptp.pred_numeral K))))) (forall ((K tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_max_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N2)) (@ tptp.suc (@ (@ tptp.ord_max_nat (@ tptp.pred_numeral K)) N2)))) (forall ((M2 tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int M2) tptp.one) (@ (@ tptp.product_Pair_int_int (@ tptp.numeral_numeral_int M2)) tptp.zero_zero_int))) (forall ((M2 tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat M2) tptp.one) (@ (@ tptp.product_Pair_nat_nat (@ tptp.numeral_numeral_nat M2)) tptp.zero_zero_nat))) (forall ((N2 tptp.nat) (X tptp.vEBT_VEBT)) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N2) X)) (@ (@ tptp.insert_VEBT_VEBT X) tptp.bot_bo8194388402131092736T_VEBT)))) (forall ((N2 tptp.nat) (X tptp.extended_enat)) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ tptp.set_Extended_enat2 (@ (@ tptp.replic7216382294607269926d_enat N2) X)) (@ (@ tptp.insert_Extended_enat X) tptp.bot_bo7653980558646680370d_enat)))) (forall ((N2 tptp.nat) (X tptp.real)) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ tptp.set_real2 (@ (@ tptp.replicate_real N2) X)) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real)))) (forall ((N2 tptp.nat) (X tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N2) X)) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat)))) (forall ((N2 tptp.nat) (X tptp.int)) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ tptp.set_int2 (@ (@ tptp.replicate_int N2) X)) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int)))) (forall ((N2 tptp.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.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 ((M2 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int (@ tptp.bit1 M2)) (@ tptp.bit0 N2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q5 tptp.int) (R4 tptp.int)) (@ (@ tptp.product_Pair_int_int Q5) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) R4)) tptp.one_one_int)))) (@ (@ tptp.unique5052692396658037445od_int M2) N2)))) (forall ((M2 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat (@ tptp.bit1 M2)) (@ tptp.bit0 N2)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q5 tptp.nat) (R4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Q5) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) R4)) tptp.one_one_nat)))) (@ (@ tptp.unique5055182867167087721od_nat M2) N2)))) _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 (= tptp.minus_925952699566721837d_enat (lambda ((A5 tptp.set_Extended_enat) (B5 tptp.set_Extended_enat)) (@ tptp.collec4429806609662206161d_enat (@ (@ tptp.minus_2020553357622893040enat_o (lambda ((X4 tptp.extended_enat)) (@ (@ tptp.member_Extended_enat X4) A5))) (lambda ((X4 tptp.extended_enat)) (@ (@ tptp.member_Extended_enat X4) B5)))))) (= tptp.minus_minus_set_real (lambda ((A5 tptp.set_real) (B5 tptp.set_real)) (@ tptp.collect_real (@ (@ tptp.minus_minus_real_o (lambda ((X4 tptp.real)) (@ (@ tptp.member_real X4) A5))) (lambda ((X4 tptp.real)) (@ (@ tptp.member_real X4) B5)))))) (= tptp.minus_7954133019191499631st_nat (lambda ((A5 tptp.set_list_nat) (B5 tptp.set_list_nat)) (@ tptp.collect_list_nat (@ (@ tptp.minus_1139252259498527702_nat_o (lambda ((X4 tptp.list_nat)) (@ (@ tptp.member_list_nat X4) A5))) (lambda ((X4 tptp.list_nat)) (@ (@ tptp.member_list_nat X4) B5)))))) (= tptp.minus_2163939370556025621et_nat (lambda ((A5 tptp.set_set_nat) (B5 tptp.set_set_nat)) (@ tptp.collect_set_nat (@ (@ tptp.minus_6910147592129066416_nat_o (lambda ((X4 tptp.set_nat)) (@ (@ tptp.member_set_nat X4) A5))) (lambda ((X4 tptp.set_nat)) (@ (@ tptp.member_set_nat X4) B5)))))) (= tptp.minus_minus_set_int (lambda ((A5 tptp.set_int) (B5 tptp.set_int)) (@ tptp.collect_int (@ (@ tptp.minus_minus_int_o (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) A5))) (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) B5)))))) (= tptp.minus_minus_set_nat (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (@ tptp.collect_nat (@ (@ tptp.minus_minus_nat_o (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) A5))) (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) B5)))))) (forall ((X tptp.extended_enat) (B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat)) (let ((_let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) B))) (let ((_let_2 (@ tptp.insert_Extended_enat X))) (let ((_let_3 (@ (@ tptp.minus_925952699566721837d_enat (@ _let_2 A2)) B))) (let ((_let_4 (@ (@ tptp.member_Extended_enat X) B))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))) (forall ((X tptp.real) (B tptp.set_real) (A2 tptp.set_real)) (let ((_let_1 (@ (@ tptp.minus_minus_set_real A2) B))) (let ((_let_2 (@ tptp.insert_real X))) (let ((_let_3 (@ (@ tptp.minus_minus_set_real (@ _let_2 A2)) B))) (let ((_let_4 (@ (@ tptp.member_real X) B))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))) (forall ((X tptp.set_nat) (B tptp.set_set_nat) (A2 tptp.set_set_nat)) (let ((_let_1 (@ (@ tptp.minus_2163939370556025621et_nat A2) B))) (let ((_let_2 (@ tptp.insert_set_nat X))) (let ((_let_3 (@ (@ tptp.minus_2163939370556025621et_nat (@ _let_2 A2)) B))) (let ((_let_4 (@ (@ tptp.member_set_nat X) B))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))) (forall ((X tptp.int) (B tptp.set_int) (A2 tptp.set_int)) (let ((_let_1 (@ (@ tptp.minus_minus_set_int A2) B))) (let ((_let_2 (@ tptp.insert_int X))) (let ((_let_3 (@ (@ tptp.minus_minus_set_int (@ _let_2 A2)) B))) (let ((_let_4 (@ (@ tptp.member_int X) B))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))) (forall ((X tptp.nat) (B tptp.set_nat) (A2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.minus_minus_set_nat A2) B))) (let ((_let_2 (@ tptp.insert_nat X))) (let ((_let_3 (@ (@ tptp.minus_minus_set_nat (@ _let_2 A2)) B))) (let ((_let_4 (@ (@ tptp.member_nat X) B))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))) (forall ((C tptp.extended_enat) (A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat C))) (=> (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) B)) (not (@ _let_1 B))))) (forall ((C tptp.real) (A2 tptp.set_real) (B tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) B)) (not (@ _let_1 B))))) (forall ((C tptp.set_nat) (A2 tptp.set_set_nat) (B tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A2) B)) (not (@ _let_1 B))))) (forall ((C tptp.int) (A2 tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B)) (not (@ _let_1 B))))) (forall ((C tptp.nat) (A2 tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B)) (not (@ _let_1 B))))) (forall ((C tptp.extended_enat) (A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat C))) (=> (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) B)) (@ _let_1 A2)))) (forall ((C tptp.real) (A2 tptp.set_real) (B tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) B)) (@ _let_1 A2)))) (forall ((C tptp.set_nat) (A2 tptp.set_set_nat) (B tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A2) B)) (@ _let_1 A2)))) (forall ((C tptp.int) (A2 tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B)) (@ _let_1 A2)))) (forall ((C tptp.nat) (A2 tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B)) (@ _let_1 A2)))) (forall ((C tptp.extended_enat) (A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat C))) (=> (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) B)) (not (=> (@ _let_1 A2) (@ _let_1 B)))))) (forall ((C tptp.real) (A2 tptp.set_real) (B tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) B)) (not (=> (@ _let_1 A2) (@ _let_1 B)))))) (forall ((C tptp.set_nat) (A2 tptp.set_set_nat) (B tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A2) B)) (not (=> (@ _let_1 A2) (@ _let_1 B)))))) (forall ((C tptp.int) (A2 tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B)) (not (=> (@ _let_1 A2) (@ _let_1 B)))))) (forall ((C tptp.nat) (A2 tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B)) (not (=> (@ _let_1 A2) (@ _let_1 B)))))) (forall ((P (-> tptp.int Bool)) (K tptp.int) (I 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 I))))) (forall ((I tptp.int) (K tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_int I) 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 I))))) (forall ((K tptp.int) (M2 tptp.int) (N2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int K))) (=> (@ _let_1 (@ (@ tptp.minus_minus_int M2) N2)) (=> (@ _let_1 N2) (@ _let_1 M2))))) (forall ((C tptp.extended_enat) (A2 tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat C))) (=> (@ _let_1 (@ tptp.uminus417252749190364093d_enat A2)) (not (@ _let_1 A2))))) (forall ((C tptp.real) (A2 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ _let_1 (@ tptp.uminus612125837232591019t_real A2)) (not (@ _let_1 A2))))) (forall ((C tptp.set_nat) (A2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 (@ tptp.uminus613421341184616069et_nat A2)) (not (@ _let_1 A2))))) (forall ((C tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ tptp.uminus5710092332889474511et_nat A2)) (not (@ _let_1 A2))))) (forall ((C tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ tptp.uminus1532241313380277803et_int A2)) (not (@ _let_1 A2))))) _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 (forall ((P (-> tptp.real Bool))) (= (@ tptp.collect_real (lambda ((X4 tptp.real)) (not (@ P X4)))) (@ tptp.uminus612125837232591019t_real (@ tptp.collect_real P)))) (forall ((P (-> tptp.list_nat Bool))) (= (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (not (@ P X4)))) (@ tptp.uminus3195874150345416415st_nat (@ tptp.collect_list_nat P)))) (forall ((P (-> tptp.set_nat Bool))) (= (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (not (@ P X4)))) (@ tptp.uminus613421341184616069et_nat (@ tptp.collect_set_nat P)))) (forall ((P (-> tptp.nat Bool))) (= (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (not (@ P X4)))) (@ tptp.uminus5710092332889474511et_nat (@ tptp.collect_nat P)))) (forall ((P (-> tptp.int Bool))) (= (@ tptp.collect_int (lambda ((X4 tptp.int)) (not (@ P X4)))) (@ tptp.uminus1532241313380277803et_int (@ tptp.collect_int P)))) (= tptp.uminus417252749190364093d_enat (lambda ((A5 tptp.set_Extended_enat)) (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (not (@ (@ tptp.member_Extended_enat X4) A5)))))) (= tptp.uminus612125837232591019t_real (lambda ((A5 tptp.set_real)) (@ tptp.collect_real (lambda ((X4 tptp.real)) (not (@ (@ tptp.member_real X4) A5)))))) (= tptp.uminus3195874150345416415st_nat (lambda ((A5 tptp.set_list_nat)) (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (not (@ (@ tptp.member_list_nat X4) A5)))))) (= tptp.uminus613421341184616069et_nat (lambda ((A5 tptp.set_set_nat)) (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (not (@ (@ tptp.member_set_nat X4) A5)))))) (= tptp.uminus5710092332889474511et_nat (lambda ((A5 tptp.set_nat)) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (not (@ (@ tptp.member_nat X4) A5)))))) (= tptp.uminus1532241313380277803et_int (lambda ((A5 tptp.set_int)) (@ tptp.collect_int (lambda ((X4 tptp.int)) (not (@ (@ tptp.member_int X4) A5)))))) _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 (forall ((A tptp.real) (P (-> tptp.real Bool))) (= (@ (@ tptp.insert_real A) (@ tptp.collect_real P)) (@ tptp.collect_real (lambda ((U2 tptp.real)) (=> (not (= U2 A)) (@ P U2)))))) (forall ((A tptp.list_nat) (P (-> tptp.list_nat Bool))) (= (@ (@ tptp.insert_list_nat A) (@ tptp.collect_list_nat P)) (@ tptp.collect_list_nat (lambda ((U2 tptp.list_nat)) (=> (not (= U2 A)) (@ P U2)))))) (forall ((A tptp.set_nat) (P (-> tptp.set_nat Bool))) (= (@ (@ tptp.insert_set_nat A) (@ tptp.collect_set_nat P)) (@ tptp.collect_set_nat (lambda ((U2 tptp.set_nat)) (=> (not (= U2 A)) (@ P U2)))))) (forall ((A tptp.nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.insert_nat A) (@ tptp.collect_nat P)) (@ tptp.collect_nat (lambda ((U2 tptp.nat)) (=> (not (= U2 A)) (@ P U2)))))) (forall ((A tptp.int) (P (-> tptp.int Bool))) (= (@ (@ tptp.insert_int A) (@ tptp.collect_int P)) (@ tptp.collect_int (lambda ((U2 tptp.int)) (=> (not (= U2 A)) (@ P U2)))))) (forall ((A tptp.extended_enat) (A2 tptp.set_Extended_enat)) (=> (@ (@ tptp.member_Extended_enat A) A2) (exists ((B8 tptp.set_Extended_enat)) (and (= A2 (@ (@ tptp.insert_Extended_enat A) B8)) (not (@ (@ tptp.member_Extended_enat A) B8)))))) (forall ((A tptp.real) (A2 tptp.set_real)) (=> (@ (@ tptp.member_real A) A2) (exists ((B8 tptp.set_real)) (and (= A2 (@ (@ tptp.insert_real A) B8)) (not (@ (@ tptp.member_real A) B8)))))) (forall ((A tptp.set_nat) (A2 tptp.set_set_nat)) (=> (@ (@ tptp.member_set_nat A) A2) (exists ((B8 tptp.set_set_nat)) (and (= A2 (@ (@ tptp.insert_set_nat A) B8)) (not (@ (@ tptp.member_set_nat A) B8)))))) (forall ((A tptp.nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.member_nat A) A2) (exists ((B8 tptp.set_nat)) (and (= A2 (@ (@ tptp.insert_nat A) B8)) (not (@ (@ tptp.member_nat A) B8)))))) (forall ((A tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.member_int A) A2) (exists ((B8 tptp.set_int)) (and (= A2 (@ (@ tptp.insert_int A) B8)) (not (@ (@ tptp.member_int A) B8)))))) (forall ((X tptp.nat) (Y tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X))) (let ((_let_2 (@ tptp.insert_nat Y))) (= (@ _let_1 (@ _let_2 A2)) (@ _let_2 (@ _let_1 A2)))))) (forall ((X tptp.int) (Y tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int X))) (let ((_let_2 (@ tptp.insert_int Y))) (= (@ _let_1 (@ _let_2 A2)) (@ _let_2 (@ _let_1 A2)))))) (forall ((X tptp.real) (Y tptp.real) (A2 tptp.set_real)) (let ((_let_1 (@ tptp.insert_real X))) (let ((_let_2 (@ tptp.insert_real Y))) (= (@ _let_1 (@ _let_2 A2)) (@ _let_2 (@ _let_1 A2)))))) (forall ((A tptp.extended_enat) (A2 tptp.set_Extended_enat) (B2 tptp.extended_enat) (B tptp.set_Extended_enat)) (let ((_let_1 (= A B2))) (=> (not (@ (@ tptp.member_Extended_enat A) A2)) (=> (not (@ (@ tptp.member_Extended_enat B2) B)) (= (= (@ (@ tptp.insert_Extended_enat A) A2) (@ (@ tptp.insert_Extended_enat B2) B)) (and (=> _let_1 (= A2 B)) (=> (not _let_1) (exists ((C5 tptp.set_Extended_enat)) (and (= A2 (@ (@ tptp.insert_Extended_enat B2) C5)) (not (@ (@ tptp.member_Extended_enat B2) C5)) (= B (@ (@ tptp.insert_Extended_enat A) C5)) (not (@ (@ tptp.member_Extended_enat A) C5))))))))))) (forall ((A tptp.real) (A2 tptp.set_real) (B2 tptp.real) (B tptp.set_real)) (let ((_let_1 (= A B2))) (=> (not (@ (@ tptp.member_real A) A2)) (=> (not (@ (@ tptp.member_real B2) B)) (= (= (@ (@ tptp.insert_real A) A2) (@ (@ tptp.insert_real B2) B)) (and (=> _let_1 (= A2 B)) (=> (not _let_1) (exists ((C5 tptp.set_real)) (and (= A2 (@ (@ tptp.insert_real B2) C5)) (not (@ (@ tptp.member_real B2) C5)) (= B (@ (@ tptp.insert_real A) C5)) (not (@ (@ tptp.member_real A) C5))))))))))) (forall ((A tptp.set_nat) (A2 tptp.set_set_nat) (B2 tptp.set_nat) (B tptp.set_set_nat)) (let ((_let_1 (= A B2))) (=> (not (@ (@ tptp.member_set_nat A) A2)) (=> (not (@ (@ tptp.member_set_nat B2) B)) (= (= (@ (@ tptp.insert_set_nat A) A2) (@ (@ tptp.insert_set_nat B2) B)) (and (=> _let_1 (= A2 B)) (=> (not _let_1) (exists ((C5 tptp.set_set_nat)) (and (= A2 (@ (@ tptp.insert_set_nat B2) C5)) (not (@ (@ tptp.member_set_nat B2) C5)) (= B (@ (@ tptp.insert_set_nat A) C5)) (not (@ (@ tptp.member_set_nat A) C5))))))))))) (forall ((A tptp.nat) (A2 tptp.set_nat) (B2 tptp.nat) (B tptp.set_nat)) (let ((_let_1 (= A B2))) (=> (not (@ (@ tptp.member_nat A) A2)) (=> (not (@ (@ tptp.member_nat B2) B)) (= (= (@ (@ tptp.insert_nat A) A2) (@ (@ tptp.insert_nat B2) B)) (and (=> _let_1 (= A2 B)) (=> (not _let_1) (exists ((C5 tptp.set_nat)) (and (= A2 (@ (@ tptp.insert_nat B2) C5)) (not (@ (@ tptp.member_nat B2) C5)) (= B (@ (@ tptp.insert_nat A) C5)) (not (@ (@ tptp.member_nat A) C5))))))))))) (forall ((A tptp.int) (A2 tptp.set_int) (B2 tptp.int) (B tptp.set_int)) (let ((_let_1 (= A B2))) (=> (not (@ (@ tptp.member_int A) A2)) (=> (not (@ (@ tptp.member_int B2) B)) (= (= (@ (@ tptp.insert_int A) A2) (@ (@ tptp.insert_int B2) B)) (and (=> _let_1 (= A2 B)) (=> (not _let_1) (exists ((C5 tptp.set_int)) (and (= A2 (@ (@ tptp.insert_int B2) C5)) (not (@ (@ tptp.member_int B2) C5)) (= B (@ (@ tptp.insert_int A) C5)) (not (@ (@ tptp.member_int A) C5))))))))))) (forall ((A tptp.extended_enat) (A2 tptp.set_Extended_enat)) (=> (@ (@ tptp.member_Extended_enat A) A2) (= (@ (@ tptp.insert_Extended_enat A) A2) A2))) (forall ((A tptp.real) (A2 tptp.set_real)) (=> (@ (@ tptp.member_real A) A2) (= (@ (@ tptp.insert_real A) A2) A2))) (forall ((A tptp.set_nat) (A2 tptp.set_set_nat)) (=> (@ (@ tptp.member_set_nat A) A2) (= (@ (@ tptp.insert_set_nat A) A2) A2))) (forall ((A tptp.nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.member_nat A) A2) (= (@ (@ tptp.insert_nat A) A2) A2))) (forall ((A tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.member_int A) A2) (= (@ (@ tptp.insert_int A) A2) A2))) (forall ((X tptp.extended_enat) (A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.insert_Extended_enat X))) (let ((_let_2 (@ tptp.member_Extended_enat X))) (=> (not (@ _let_2 A2)) (=> (not (@ _let_2 B)) (= (= (@ _let_1 A2) (@ _let_1 B)) (= A2 B))))))) (forall ((X tptp.real) (A2 tptp.set_real) (B tptp.set_real)) (let ((_let_1 (@ tptp.insert_real X))) (let ((_let_2 (@ tptp.member_real X))) (=> (not (@ _let_2 A2)) (=> (not (@ _let_2 B)) (= (= (@ _let_1 A2) (@ _let_1 B)) (= A2 B))))))) (forall ((X tptp.set_nat) (A2 tptp.set_set_nat) (B tptp.set_set_nat)) (let ((_let_1 (@ tptp.insert_set_nat X))) (let ((_let_2 (@ tptp.member_set_nat X))) (=> (not (@ _let_2 A2)) (=> (not (@ _let_2 B)) (= (= (@ _let_1 A2) (@ _let_1 B)) (= A2 B))))))) (forall ((X tptp.nat) (A2 tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X))) (let ((_let_2 (@ tptp.member_nat X))) (=> (not (@ _let_2 A2)) (=> (not (@ _let_2 B)) (= (= (@ _let_1 A2) (@ _let_1 B)) (= A2 B))))))) (forall ((X tptp.int) (A2 tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.insert_int X))) (let ((_let_2 (@ tptp.member_int X))) (=> (not (@ _let_2 A2)) (=> (not (@ _let_2 B)) (= (= (@ _let_1 A2) (@ _let_1 B)) (= A2 B))))))) (forall ((X tptp.extended_enat) (A2 tptp.set_Extended_enat)) (=> (@ (@ tptp.member_Extended_enat X) A2) (not (forall ((B8 tptp.set_Extended_enat)) (=> (= A2 (@ (@ tptp.insert_Extended_enat X) B8)) (@ (@ tptp.member_Extended_enat X) B8)))))) (forall ((X tptp.real) (A2 tptp.set_real)) (=> (@ (@ tptp.member_real X) A2) (not (forall ((B8 tptp.set_real)) (=> (= A2 (@ (@ tptp.insert_real X) B8)) (@ (@ tptp.member_real X) B8)))))) (forall ((X tptp.set_nat) (A2 tptp.set_set_nat)) (=> (@ (@ tptp.member_set_nat X) A2) (not (forall ((B8 tptp.set_set_nat)) (=> (= A2 (@ (@ tptp.insert_set_nat X) B8)) (@ (@ tptp.member_set_nat X) B8)))))) (forall ((X tptp.nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.member_nat X) A2) (not (forall ((B8 tptp.set_nat)) (=> 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((_let_1 (@ tptp.member_int A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.insert_int B2) B))))) (forall ((A tptp.extended_enat) (B tptp.set_Extended_enat)) (@ (@ tptp.member_Extended_enat A) (@ (@ tptp.insert_Extended_enat A) B))) (forall ((A tptp.real) (B tptp.set_real)) (@ (@ tptp.member_real A) (@ (@ tptp.insert_real A) B))) (forall ((A tptp.set_nat) (B tptp.set_set_nat)) (@ (@ tptp.member_set_nat A) (@ (@ tptp.insert_set_nat A) B))) (forall ((A tptp.nat) (B tptp.set_nat)) (@ (@ tptp.member_nat A) (@ (@ tptp.insert_nat A) B))) (forall ((A tptp.int) (B tptp.set_int)) (@ (@ tptp.member_int A) (@ (@ tptp.insert_int A) B))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (A2 tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat A))) (=> (@ _let_1 (@ (@ tptp.insert_Extended_enat B2) A2)) (=> (not (= A B2)) (@ _let_1 A2))))) (forall ((A tptp.real) (B2 tptp.real) (A2 tptp.set_real)) (let ((_let_1 (@ tptp.member_real A))) (=> (@ _let_1 (@ (@ tptp.insert_real B2) A2)) (=> 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tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B2) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat)) (= B2 A))) (forall ((B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real)) (= B2 A))) (forall ((B2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.member_nat B2) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat)) (= B2 A))) (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int)) (= B2 A))) (forall ((B2 tptp.set_nat) (A tptp.set_nat)) (= (@ (@ tptp.member_set_nat B2) (@ (@ tptp.insert_set_nat A) tptp.bot_bot_set_set_nat)) (= B2 A))) (forall ((B2 tptp.extended_enat) (A tptp.extended_enat)) (= (@ (@ tptp.member_Extended_enat B2) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat)) (= B2 A))) (forall ((B2 tptp.real) (A tptp.real)) (= (@ (@ tptp.member_real B2) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real)) (= B2 A))) (forall ((B2 tptp.nat) (A tptp.nat)) (= (@ (@ tptp.member_nat B2) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat)) (= B2 A))) (forall ((B2 tptp.int) (A tptp.int)) (= (@ (@ tptp.member_int B2) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int)) (= B2 A))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat) (D tptp.extended_enat)) (= (= (@ (@ tptp.insert_Extended_enat A) (@ (@ tptp.insert_Extended_enat B2) tptp.bot_bo7653980558646680370d_enat)) (@ (@ tptp.insert_Extended_enat C) (@ (@ tptp.insert_Extended_enat D) tptp.bot_bo7653980558646680370d_enat))) (or (and (= A C) (= B2 D)) (and (= A D) (= B2 C))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (= (= (@ (@ tptp.insert_real A) (@ (@ tptp.insert_real B2) tptp.bot_bot_set_real)) (@ (@ tptp.insert_real C) (@ (@ tptp.insert_real D) tptp.bot_bot_set_real))) (or (and (= A C) (= B2 D)) (and (= A D) (= B2 C))))) (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (= (= (@ (@ 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tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat) (@ (@ tptp.insert_Extended_enat B2) tptp.bot_bo7653980558646680370d_enat)) (= A B2))) (forall ((A tptp.real) (B2 tptp.real)) (=> (= (@ (@ tptp.insert_real A) tptp.bot_bot_set_real) (@ (@ tptp.insert_real B2) tptp.bot_bot_set_real)) (= A B2))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (= (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat) (@ (@ tptp.insert_nat B2) tptp.bot_bot_set_nat)) (= A B2))) (forall ((A tptp.int) (B2 tptp.int)) (=> (= (@ (@ tptp.insert_int A) tptp.bot_bot_set_int) (@ (@ tptp.insert_int B2) tptp.bot_bot_set_int)) (= A B2))) (forall ((X tptp.extended_enat) (A2 tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.insert_Extended_enat X))) (= (@ tptp.uminus417252749190364093d_enat (@ _let_1 A2)) (@ (@ tptp.minus_925952699566721837d_enat (@ tptp.uminus417252749190364093d_enat A2)) (@ _let_1 tptp.bot_bo7653980558646680370d_enat))))) (forall ((X tptp.real) (A2 tptp.set_real)) (let ((_let_1 (@ tptp.insert_real X))) (= (@ tptp.uminus612125837232591019t_real (@ _let_1 A2)) (@ (@ tptp.minus_minus_set_real (@ tptp.uminus612125837232591019t_real A2)) (@ _let_1 tptp.bot_bot_set_real))))) (forall ((X tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int X))) (= (@ tptp.uminus1532241313380277803et_int (@ _let_1 A2)) (@ (@ tptp.minus_minus_set_int (@ tptp.uminus1532241313380277803et_int A2)) (@ _let_1 tptp.bot_bot_set_int))))) (forall ((X tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X))) (= (@ tptp.uminus5710092332889474511et_nat (@ _let_1 A2)) (@ (@ tptp.minus_minus_set_nat (@ tptp.uminus5710092332889474511et_nat A2)) (@ _let_1 tptp.bot_bot_set_nat))))) (forall ((A2 tptp.set_Extended_enat) (A tptp.extended_enat) (B tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.insert_Extended_enat A))) (let ((_let_2 (@ tptp.minus_925952699566721837d_enat A2))) (= (@ _let_2 (@ _let_1 B)) (@ (@ tptp.minus_925952699566721837d_enat (@ _let_2 B)) (@ _let_1 tptp.bot_bo7653980558646680370d_enat)))))) (forall ((A2 tptp.set_real) (A tptp.real) (B tptp.set_real)) (let ((_let_1 (@ tptp.insert_real A))) (let ((_let_2 (@ tptp.minus_minus_set_real A2))) (= (@ _let_2 (@ _let_1 B)) (@ (@ tptp.minus_minus_set_real (@ _let_2 B)) (@ _let_1 tptp.bot_bot_set_real)))))) (forall ((A2 tptp.set_int) (A tptp.int) (B tptp.set_int)) (let ((_let_1 (@ tptp.insert_int A))) (let ((_let_2 (@ tptp.minus_minus_set_int A2))) (= (@ _let_2 (@ _let_1 B)) (@ (@ tptp.minus_minus_set_int (@ _let_2 B)) (@ _let_1 tptp.bot_bot_set_int)))))) (forall ((A2 tptp.set_nat) (A tptp.nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat A))) (let ((_let_2 (@ tptp.minus_minus_set_nat A2))) (= (@ _let_2 (@ _let_1 B)) (@ (@ tptp.minus_minus_set_nat (@ _let_2 B)) (@ _let_1 tptp.bot_bot_set_nat)))))) (forall ((A tptp.set_nat) (A2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.insert_set_nat A))) (=> (@ (@ tptp.member_set_nat A) A2) (= (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A2) (@ _let_1 tptp.bot_bot_set_set_nat))) A2)))) (forall ((A tptp.extended_enat) (A2 tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.insert_Extended_enat A))) (=> (@ (@ tptp.member_Extended_enat A) A2) (= (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ _let_1 tptp.bot_bo7653980558646680370d_enat))) A2)))) (forall ((A tptp.real) (A2 tptp.set_real)) (let ((_let_1 (@ tptp.insert_real A))) (=> (@ (@ tptp.member_real A) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ _let_1 tptp.bot_bot_set_real))) A2)))) (forall ((A tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int A))) (=> (@ (@ tptp.member_int A) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ _let_1 tptp.bot_bot_set_int))) A2)))) (forall ((A tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat A))) (=> (@ (@ tptp.member_nat A) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) (@ _let_1 tptp.bot_bot_set_nat))) A2)))) (forall ((A2 tptp.set_Extended_enat) (A tptp.extended_enat) (B tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.insert_Extended_enat A))) (let ((_let_2 (@ tptp.minus_925952699566721837d_enat A2))) (= (@ _let_2 (@ _let_1 B)) (@ (@ tptp.minus_925952699566721837d_enat (@ _let_2 (@ _let_1 tptp.bot_bo7653980558646680370d_enat))) B))))) (forall ((A2 tptp.set_real) (A tptp.real) (B tptp.set_real)) (let ((_let_1 (@ tptp.insert_real A))) (let ((_let_2 (@ tptp.minus_minus_set_real A2))) (= (@ _let_2 (@ _let_1 B)) (@ (@ tptp.minus_minus_set_real (@ _let_2 (@ _let_1 tptp.bot_bot_set_real))) B))))) (forall ((A2 tptp.set_int) (A tptp.int) (B tptp.set_int)) (let ((_let_1 (@ tptp.insert_int A))) (let ((_let_2 (@ tptp.minus_minus_set_int A2))) (= (@ _let_2 (@ _let_1 B)) (@ (@ tptp.minus_minus_set_int (@ _let_2 (@ _let_1 tptp.bot_bot_set_int))) B))))) (forall ((A2 tptp.set_nat) (A tptp.nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat A))) (let ((_let_2 (@ tptp.minus_minus_set_nat A2))) (= (@ _let_2 (@ _let_1 B)) (@ (@ tptp.minus_minus_set_nat (@ _let_2 (@ _let_1 tptp.bot_bot_set_nat))) B))))) (forall ((X tptp.set_nat) (A2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.insert_set_nat X))) (=> (not (@ (@ tptp.member_set_nat X) A2)) (= (@ (@ tptp.minus_2163939370556025621et_nat (@ _let_1 A2)) (@ _let_1 tptp.bot_bot_set_set_nat)) A2)))) (forall ((X tptp.extended_enat) (A2 tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.insert_Extended_enat X))) (=> (not (@ (@ tptp.member_Extended_enat X) A2)) (= (@ (@ tptp.minus_925952699566721837d_enat (@ _let_1 A2)) (@ _let_1 tptp.bot_bo7653980558646680370d_enat)) A2)))) (forall ((X tptp.real) (A2 tptp.set_real)) (let ((_let_1 (@ tptp.insert_real X))) (=> (not (@ (@ tptp.member_real X) A2)) (= (@ (@ tptp.minus_minus_set_real (@ _let_1 A2)) (@ _let_1 tptp.bot_bot_set_real)) A2)))) (forall ((X tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int X))) (=> (not (@ (@ tptp.member_int X) A2)) (= (@ (@ tptp.minus_minus_set_int (@ _let_1 A2)) (@ _let_1 tptp.bot_bot_set_int)) A2)))) (forall ((X tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X))) (=> (not (@ (@ tptp.member_nat X) A2)) (= (@ (@ tptp.minus_minus_set_nat (@ _let_1 A2)) (@ _let_1 tptp.bot_bot_set_nat)) A2)))) (forall ((A2 tptp.set_real) (A tptp.real)) (=> (@ tptp.finite_finite_real A2) (@ tptp.finite_finite_real (@ (@ tptp.insert_real A) A2)))) (forall ((A2 tptp.set_nat) (A tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (@ tptp.finite_finite_nat (@ (@ tptp.insert_nat A) A2)))) (forall ((A2 tptp.set_complex) (A tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex A2) (@ tptp.finite3207457112153483333omplex (@ (@ tptp.insert_complex A) A2)))) (forall ((A2 tptp.set_int) (A tptp.int)) (=> (@ tptp.finite_finite_int A2) (@ tptp.finite_finite_int (@ (@ tptp.insert_int A) A2)))) (forall ((A2 tptp.set_Extended_enat) (A tptp.extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (@ tptp.finite4001608067531595151d_enat (@ (@ tptp.insert_Extended_enat A) A2)))) (forall ((C4 tptp.set_real) (D6 tptp.set_real) (A tptp.real)) (let ((_let_1 (@ tptp.insert_real A))) (=> (@ (@ tptp.ord_less_eq_set_real C4) D6) (@ (@ tptp.ord_less_eq_set_real (@ _let_1 C4)) (@ _let_1 D6))))) (forall ((C4 tptp.set_nat) (D6 tptp.set_nat) (A tptp.nat)) (let ((_let_1 (@ tptp.insert_nat A))) (=> (@ (@ tptp.ord_less_eq_set_nat C4) D6) (@ (@ tptp.ord_less_eq_set_nat (@ _let_1 C4)) (@ _let_1 D6))))) (forall ((C4 tptp.set_int) (D6 tptp.set_int) (A tptp.int)) (let ((_let_1 (@ tptp.insert_int A))) (=> (@ (@ tptp.ord_less_eq_set_int C4) D6) (@ (@ tptp.ord_less_eq_set_int (@ _let_1 C4)) (@ _let_1 D6))))) (forall ((X tptp.extended_enat) (A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.ord_le7203529160286727270d_enat A2))) (=> (not (@ (@ tptp.member_Extended_enat X) A2)) (= (@ _let_1 (@ (@ tptp.insert_Extended_enat X) B)) (@ _let_1 B))))) (forall ((X tptp.real) (A2 tptp.set_real) (B tptp.set_real)) (let ((_let_1 (@ tptp.ord_less_eq_set_real A2))) (=> (not (@ (@ tptp.member_real X) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X) B)) (@ _let_1 B))))) (forall ((X tptp.set_nat) (A2 tptp.set_set_nat) (B tptp.set_set_nat)) (let ((_let_1 (@ tptp.ord_le6893508408891458716et_nat A2))) (=> (not (@ (@ tptp.member_set_nat X) A2)) (= (@ _let_1 (@ (@ tptp.insert_set_nat X) B)) (@ _let_1 B))))) (forall ((X tptp.nat) (A2 tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A2))) (=> (not (@ (@ tptp.member_nat X) A2)) (= (@ _let_1 (@ (@ tptp.insert_nat X) B)) (@ _let_1 B))))) (forall ((X tptp.int) (A2 tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A2))) (=> (not (@ (@ tptp.member_int X) A2)) (= (@ _let_1 (@ (@ tptp.insert_int X) B)) (@ _let_1 B))))) (forall ((B tptp.set_real) (A tptp.real)) (@ (@ tptp.ord_less_eq_set_real B) (@ (@ tptp.insert_real A) B))) (forall ((B tptp.set_nat) (A tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat B) (@ (@ tptp.insert_nat A) B))) (forall ((B tptp.set_int) (A tptp.int)) (@ (@ tptp.ord_less_eq_set_int B) (@ (@ tptp.insert_int A) B))) (forall ((A2 tptp.set_real) (B tptp.set_real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_set_real A2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.insert_real B2) B))))) (forall ((A2 tptp.set_nat) (B tptp.set_nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.insert_nat B2) B))))) (forall ((A2 tptp.set_int) (B tptp.set_int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.insert_int B2) B))))) (forall ((X tptp.extended_enat) (A2 tptp.set_Extended_enat) (X8 tptp.set_Extended_enat)) (=> (@ (@ tptp.member_Extended_enat X) A2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat X8) A2) (@ (@ tptp.ord_le7203529160286727270d_enat (@ (@ tptp.insert_Extended_enat X) X8)) A2)))) (forall ((X tptp.real) (A2 tptp.set_real) (X8 tptp.set_real)) (=> (@ (@ tptp.member_real X) A2) (=> (@ (@ tptp.ord_less_eq_set_real X8) A2) (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.insert_real X) X8)) A2)))) (forall ((X tptp.set_nat) (A2 tptp.set_set_nat) (X8 tptp.set_set_nat)) (=> (@ (@ tptp.member_set_nat X) A2) (=> (@ (@ tptp.ord_le6893508408891458716et_nat X8) A2) (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.insert_set_nat X) X8)) A2)))) (forall ((X tptp.nat) (A2 tptp.set_nat) (X8 tptp.set_nat)) (=> (@ (@ tptp.member_nat X) A2) (=> (@ (@ tptp.ord_less_eq_set_nat X8) A2) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.insert_nat X) X8)) A2)))) (forall ((X tptp.int) (A2 tptp.set_int) (X8 tptp.set_int)) (=> (@ (@ tptp.member_int X) A2) (=> (@ (@ tptp.ord_less_eq_set_int X8) A2) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.insert_int X) X8)) A2)))) (forall ((A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat) (X tptp.extended_enat) (C4 tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.minus_925952699566721837d_enat B))) (let ((_let_2 (@ tptp.ord_le7203529160286727270d_enat A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_Extended_enat X) C4))) (and (@ _let_2 (@ _let_1 C4)) (not (@ (@ tptp.member_Extended_enat X) A2))))))) (forall ((A2 tptp.set_real) (B tptp.set_real) (X tptp.real) (C4 tptp.set_real)) (let ((_let_1 (@ tptp.minus_minus_set_real B))) (let ((_let_2 (@ tptp.ord_less_eq_set_real A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_real X) C4))) (and (@ _let_2 (@ _let_1 C4)) (not (@ (@ tptp.member_real X) A2))))))) (forall ((A2 tptp.set_set_nat) (B tptp.set_set_nat) (X tptp.set_nat) (C4 tptp.set_set_nat)) (let ((_let_1 (@ tptp.minus_2163939370556025621et_nat B))) (let ((_let_2 (@ tptp.ord_le6893508408891458716et_nat A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_set_nat X) C4))) (and (@ _let_2 (@ _let_1 C4)) (not (@ (@ tptp.member_set_nat X) A2))))))) (forall ((A2 tptp.set_nat) (B tptp.set_nat) (X tptp.nat) (C4 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat B))) (let ((_let_2 (@ tptp.ord_less_eq_set_nat A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_nat X) C4))) (and (@ _let_2 (@ _let_1 C4)) (not (@ (@ tptp.member_nat X) A2))))))) (forall ((A2 tptp.set_int) (B tptp.set_int) (X tptp.int) (C4 tptp.set_int)) (let ((_let_1 (@ tptp.minus_minus_set_int B))) (let ((_let_2 (@ tptp.ord_less_eq_set_int A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_int X) C4))) (and (@ _let_2 (@ _let_1 C4)) (not (@ (@ tptp.member_int X) A2))))))) (forall ((P (-> tptp.list_nat Bool)) (A tptp.list_nat)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (and (= X4 A) (@ P X4)))) (@ (@ tptp.insert_list_nat A) tptp.bot_bot_set_list_nat))) (=> (not _let_1) (= (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (and (= X4 A) (@ P X4)))) tptp.bot_bot_set_list_nat))))) (forall ((P (-> tptp.set_nat Bool)) (A tptp.set_nat)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (and (= X4 A) (@ P X4)))) (@ (@ tptp.insert_set_nat A) tptp.bot_bot_set_set_nat))) (=> (not _let_1) (= (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (and (= X4 A) (@ P X4)))) tptp.bot_bot_set_set_nat))))) (forall ((P (-> tptp.extended_enat Bool)) (A tptp.extended_enat)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (and (= X4 A) (@ P X4)))) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat))) (=> (not _let_1) (= (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (and (= X4 A) (@ P X4)))) tptp.bot_bo7653980558646680370d_enat))))) (forall ((P (-> tptp.real Bool)) (A tptp.real)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collect_real (lambda ((X4 tptp.real)) (and (= X4 A) (@ P X4)))) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))) (=> (not _let_1) (= (@ tptp.collect_real (lambda ((X4 tptp.real)) (and (= X4 A) (@ P X4)))) tptp.bot_bot_set_real))))) (forall ((P (-> tptp.nat Bool)) (A tptp.nat)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (= X4 A) (@ P X4)))) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))) (=> (not _let_1) (= (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (= X4 A) (@ P X4)))) tptp.bot_bot_set_nat))))) (forall ((P (-> tptp.int Bool)) (A tptp.int)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (= X4 A) (@ P X4)))) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))) (=> (not _let_1) (= (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (= X4 A) (@ P X4)))) tptp.bot_bot_set_int))))) (forall ((P (-> tptp.list_nat Bool)) (A tptp.list_nat)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (and (= A X4) (@ P X4)))) (@ (@ tptp.insert_list_nat A) tptp.bot_bot_set_list_nat))) (=> (not _let_1) (= (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (and (= A X4) (@ P X4)))) tptp.bot_bot_set_list_nat))))) (forall ((P (-> tptp.set_nat Bool)) (A tptp.set_nat)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (and (= A X4) (@ P X4)))) (@ (@ tptp.insert_set_nat A) tptp.bot_bot_set_set_nat))) (=> (not _let_1) (= (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (and (= A X4) (@ P X4)))) tptp.bot_bot_set_set_nat))))) (forall ((P (-> tptp.extended_enat Bool)) (A tptp.extended_enat)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (and (= A X4) (@ P X4)))) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat))) (=> (not _let_1) (= (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (and (= A X4) (@ P X4)))) tptp.bot_bo7653980558646680370d_enat))))) (forall ((P (-> tptp.real Bool)) (A tptp.real)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collect_real (lambda ((X4 tptp.real)) (and (= A X4) (@ P X4)))) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))) (=> (not _let_1) (= (@ tptp.collect_real (lambda ((X4 tptp.real)) (and (= A X4) (@ P X4)))) tptp.bot_bot_set_real))))) (forall ((P (-> tptp.nat Bool)) (A tptp.nat)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (= A X4) (@ P X4)))) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))) (=> (not _let_1) (= (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (= A X4) (@ P X4)))) tptp.bot_bot_set_nat))))) (forall ((P (-> tptp.int Bool)) (A tptp.int)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (= A X4) (@ P X4)))) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))) (=> (not _let_1) (= (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (= A X4) (@ P X4)))) tptp.bot_bot_set_int))))) (forall ((A tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A) (=> (not (= A tptp.bot_bot_set_complex)) (not (forall ((A6 tptp.set_complex)) (=> (exists ((A4 tptp.complex)) (= A (@ (@ tptp.insert_complex A4) A6))) (not (@ tptp.finite3207457112153483333omplex A6)))))))) (forall ((A tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A) (=> (not (= A tptp.bot_bo7653980558646680370d_enat)) (not (forall ((A6 tptp.set_Extended_enat)) (=> (exists ((A4 tptp.extended_enat)) (= A (@ (@ tptp.insert_Extended_enat A4) A6))) (not (@ tptp.finite4001608067531595151d_enat A6)))))))) (forall ((A tptp.set_real)) (=> (@ tptp.finite_finite_real A) (=> (not (= A tptp.bot_bot_set_real)) (not (forall ((A6 tptp.set_real)) (=> (exists ((A4 tptp.real)) (= A (@ (@ tptp.insert_real A4) A6))) (not (@ tptp.finite_finite_real A6)))))))) (forall ((A tptp.set_nat)) (=> (@ tptp.finite_finite_nat A) (=> (not (= A tptp.bot_bot_set_nat)) (not (forall ((A6 tptp.set_nat)) (=> (exists ((A4 tptp.nat)) (= A (@ (@ tptp.insert_nat A4) A6))) (not (@ tptp.finite_finite_nat A6)))))))) (forall ((A tptp.set_int)) (=> (@ tptp.finite_finite_int A) (=> (not (= A tptp.bot_bot_set_int)) (not (forall ((A6 tptp.set_int)) (=> (exists ((A4 tptp.int)) (= A (@ (@ tptp.insert_int A4) A6))) (not (@ tptp.finite_finite_int A6)))))))) (= tptp.finite3207457112153483333omplex (lambda ((A3 tptp.set_complex)) (or (= A3 tptp.bot_bot_set_complex) (exists ((A5 tptp.set_complex) (B3 tptp.complex)) (and (= A3 (@ (@ tptp.insert_complex B3) A5)) (@ tptp.finite3207457112153483333omplex A5)))))) (= tptp.finite4001608067531595151d_enat (lambda ((A3 tptp.set_Extended_enat)) (or (= A3 tptp.bot_bo7653980558646680370d_enat) (exists ((A5 tptp.set_Extended_enat) (B3 tptp.extended_enat)) (and (= A3 (@ (@ tptp.insert_Extended_enat B3) A5)) (@ tptp.finite4001608067531595151d_enat A5)))))) (= tptp.finite_finite_real (lambda ((A3 tptp.set_real)) (or (= A3 tptp.bot_bot_set_real) (exists ((A5 tptp.set_real) (B3 tptp.real)) (and (= A3 (@ (@ tptp.insert_real B3) A5)) (@ tptp.finite_finite_real A5)))))) (= tptp.finite_finite_nat (lambda ((A3 tptp.set_nat)) (or (= A3 tptp.bot_bot_set_nat) (exists ((A5 tptp.set_nat) (B3 tptp.nat)) (and (= A3 (@ (@ tptp.insert_nat B3) A5)) (@ tptp.finite_finite_nat A5)))))) (= tptp.finite_finite_int (lambda ((A3 tptp.set_int)) (or (= A3 tptp.bot_bot_set_int) (exists ((A5 tptp.set_int) (B3 tptp.int)) (and (= A3 (@ (@ tptp.insert_int B3) A5)) (@ tptp.finite_finite_int A5)))))) (forall ((F3 tptp.set_set_nat) (P (-> tptp.set_set_nat Bool))) (=> (@ tptp.finite1152437895449049373et_nat F3) (=> (@ P tptp.bot_bot_set_set_nat) (=> (forall ((X5 tptp.set_nat) (F4 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat F4) (=> (not (@ (@ tptp.member_set_nat X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_set_nat X5) F4)))))) (@ P F3))))) (forall ((F3 tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex F3) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((X5 tptp.complex) (F4 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex F4) (=> (not (@ (@ tptp.member_complex X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_complex X5) F4)))))) (@ P F3))))) (forall ((F3 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat F3) (=> (@ P tptp.bot_bo7653980558646680370d_enat) (=> (forall ((X5 tptp.extended_enat) (F4 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat F4) (=> (not (@ (@ tptp.member_Extended_enat X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_Extended_enat X5) F4)))))) (@ P F3))))) (forall ((F3 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real F3) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((X5 tptp.real) (F4 tptp.set_real)) (=> (@ tptp.finite_finite_real F4) (=> (not (@ (@ tptp.member_real X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_real X5) F4)))))) (@ P F3))))) (forall ((F3 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat F3) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((X5 tptp.nat) (F4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat F4) (=> (not (@ (@ tptp.member_nat X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_nat X5) F4)))))) (@ P F3))))) (forall ((F3 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int F3) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((X5 tptp.int) (F4 tptp.set_int)) (=> (@ tptp.finite_finite_int F4) (=> (not (@ (@ tptp.member_int X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_int X5) F4)))))) (@ P F3))))) (forall ((F3 tptp.set_set_nat) (P (-> tptp.set_set_nat Bool))) (=> (@ tptp.finite1152437895449049373et_nat F3) (=> (not (= F3 tptp.bot_bot_set_set_nat)) (=> (forall ((X5 tptp.set_nat)) (@ P (@ (@ tptp.insert_set_nat X5) tptp.bot_bot_set_set_nat))) (=> (forall ((X5 tptp.set_nat) (F4 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat F4) (=> (not (= F4 tptp.bot_bot_set_set_nat)) (=> (not (@ (@ tptp.member_set_nat X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_set_nat X5) F4))))))) (@ P F3)))))) (forall ((F3 tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex F3) (=> (not (= F3 tptp.bot_bot_set_complex)) (=> (forall ((X5 tptp.complex)) (@ P (@ (@ tptp.insert_complex X5) tptp.bot_bot_set_complex))) (=> (forall ((X5 tptp.complex) (F4 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex F4) (=> (not (= F4 tptp.bot_bot_set_complex)) (=> (not (@ (@ tptp.member_complex X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_complex X5) F4))))))) (@ P F3)))))) (forall ((F3 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat F3) (=> (not (= F3 tptp.bot_bo7653980558646680370d_enat)) (=> (forall ((X5 tptp.extended_enat)) (@ P (@ (@ tptp.insert_Extended_enat X5) tptp.bot_bo7653980558646680370d_enat))) (=> (forall ((X5 tptp.extended_enat) (F4 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat F4) (=> (not (= F4 tptp.bot_bo7653980558646680370d_enat)) (=> (not (@ (@ tptp.member_Extended_enat X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_Extended_enat X5) F4))))))) (@ P F3)))))) (forall ((F3 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real F3) (=> (not (= F3 tptp.bot_bot_set_real)) (=> (forall ((X5 tptp.real)) (@ P (@ (@ tptp.insert_real X5) tptp.bot_bot_set_real))) (=> (forall ((X5 tptp.real) (F4 tptp.set_real)) (=> (@ tptp.finite_finite_real F4) (=> (not (= F4 tptp.bot_bot_set_real)) (=> (not (@ (@ tptp.member_real X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_real X5) F4))))))) (@ P F3)))))) (forall ((F3 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat F3) (=> (not (= F3 tptp.bot_bot_set_nat)) (=> (forall ((X5 tptp.nat)) (@ P (@ (@ tptp.insert_nat X5) tptp.bot_bot_set_nat))) (=> (forall ((X5 tptp.nat) (F4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat F4) (=> (not (= F4 tptp.bot_bot_set_nat)) (=> (not (@ (@ tptp.member_nat X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_nat X5) F4))))))) (@ P F3)))))) (forall ((F3 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int F3) (=> (not (= F3 tptp.bot_bot_set_int)) (=> (forall ((X5 tptp.int)) (@ P (@ (@ tptp.insert_int X5) tptp.bot_bot_set_int))) (=> (forall ((X5 tptp.int) (F4 tptp.set_int)) (=> (@ tptp.finite_finite_int F4) (=> (not (= F4 tptp.bot_bot_set_int)) (=> (not (@ (@ tptp.member_int X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_int X5) F4))))))) (@ P F3)))))) (forall ((P (-> tptp.set_set_nat Bool)) (A2 tptp.set_set_nat)) (=> (forall ((A6 tptp.set_set_nat)) (=> (not (@ tptp.finite1152437895449049373et_nat A6)) (@ P A6))) (=> (@ P tptp.bot_bot_set_set_nat) (=> (forall ((X5 tptp.set_nat) (F4 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat F4) (=> (not (@ (@ tptp.member_set_nat X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_set_nat X5) F4)))))) (@ P A2))))) (forall ((P (-> tptp.set_complex Bool)) (A2 tptp.set_complex)) (=> (forall ((A6 tptp.set_complex)) (=> (not (@ tptp.finite3207457112153483333omplex A6)) (@ P A6))) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((X5 tptp.complex) (F4 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex F4) (=> (not (@ (@ tptp.member_complex X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_complex X5) F4)))))) (@ P A2))))) (forall ((P (-> tptp.set_Extended_enat Bool)) (A2 tptp.set_Extended_enat)) (=> (forall ((A6 tptp.set_Extended_enat)) (=> (not (@ tptp.finite4001608067531595151d_enat A6)) (@ P A6))) (=> (@ P tptp.bot_bo7653980558646680370d_enat) (=> (forall ((X5 tptp.extended_enat) (F4 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat F4) (=> (not (@ (@ tptp.member_Extended_enat X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_Extended_enat X5) F4)))))) (@ P A2))))) (forall ((P (-> tptp.set_real Bool)) (A2 tptp.set_real)) (=> (forall ((A6 tptp.set_real)) (=> (not (@ tptp.finite_finite_real A6)) (@ P A6))) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((X5 tptp.real) (F4 tptp.set_real)) (=> (@ tptp.finite_finite_real F4) (=> (not (@ (@ tptp.member_real X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_real X5) F4)))))) (@ P A2))))) (forall ((P (-> tptp.set_nat Bool)) (A2 tptp.set_nat)) (=> (forall ((A6 tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat A6)) (@ P A6))) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((X5 tptp.nat) (F4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat F4) (=> (not (@ (@ tptp.member_nat X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_nat X5) F4)))))) (@ P A2))))) (forall ((P (-> tptp.set_int Bool)) (A2 tptp.set_int)) (=> (forall ((A6 tptp.set_int)) (=> (not (@ tptp.finite_finite_int A6)) (@ P A6))) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((X5 tptp.int) (F4 tptp.set_int)) (=> (@ tptp.finite_finite_int F4) (=> (not (@ (@ tptp.member_int X5) F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_int X5) F4)))))) (@ P A2))))) (forall ((S2 tptp.set_complex) (A tptp.complex)) (=> (not (@ tptp.finite3207457112153483333omplex S2)) (not (@ tptp.finite3207457112153483333omplex (@ (@ tptp.minus_811609699411566653omplex S2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex)))))) (forall ((S2 tptp.set_Extended_enat) (A tptp.extended_enat)) (=> (not (@ tptp.finite4001608067531595151d_enat S2)) (not (@ tptp.finite4001608067531595151d_enat (@ (@ tptp.minus_925952699566721837d_enat S2) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat)))))) (forall ((S2 tptp.set_real) (A tptp.real)) (=> (not (@ tptp.finite_finite_real S2)) (not (@ tptp.finite_finite_real (@ (@ tptp.minus_minus_set_real S2) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real)))))) (forall ((S2 tptp.set_int) (A tptp.int)) (=> (not (@ tptp.finite_finite_int S2)) (not (@ tptp.finite_finite_int (@ (@ tptp.minus_minus_set_int S2) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int)))))) (forall ((S2 tptp.set_nat) (A tptp.nat)) (=> (not (@ tptp.finite_finite_nat S2)) (not (@ tptp.finite_finite_nat (@ (@ tptp.minus_minus_set_nat S2) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat)))))) (forall ((X8 (-> tptp.set_complex Bool)) (A2 tptp.set_complex)) (=> (@ X8 A2) (=> (forall ((A6 tptp.set_complex)) (=> (@ X8 A6) (exists ((X2 tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_811609699411566653omplex A6) (@ (@ tptp.insert_complex X2) tptp.bot_bot_set_complex)))) (and (@ (@ tptp.member_complex X2) A6) (or (@ X8 _let_1) (not (@ tptp.finite3207457112153483333omplex _let_1)))))))) (not (@ tptp.finite3207457112153483333omplex A2))))) (forall ((X8 (-> tptp.set_Extended_enat Bool)) (A2 tptp.set_Extended_enat)) (=> (@ X8 A2) (=> (forall ((A6 tptp.set_Extended_enat)) (=> (@ X8 A6) (exists ((X2 tptp.extended_enat)) (let ((_let_1 (@ (@ tptp.minus_925952699566721837d_enat A6) (@ (@ tptp.insert_Extended_enat X2) tptp.bot_bo7653980558646680370d_enat)))) (and (@ (@ tptp.member_Extended_enat X2) A6) (or (@ X8 _let_1) (not (@ tptp.finite4001608067531595151d_enat _let_1)))))))) (not (@ tptp.finite4001608067531595151d_enat A2))))) (forall ((X8 (-> tptp.set_real Bool)) (A2 tptp.set_real)) (=> (@ X8 A2) (=> (forall ((A6 tptp.set_real)) (=> (@ X8 A6) (exists ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_set_real A6) (@ (@ tptp.insert_real X2) tptp.bot_bot_set_real)))) (and (@ (@ tptp.member_real X2) A6) (or (@ X8 _let_1) (not (@ tptp.finite_finite_real _let_1)))))))) (not (@ tptp.finite_finite_real A2))))) (forall ((X8 (-> tptp.set_int Bool)) (A2 tptp.set_int)) (=> (@ X8 A2) (=> (forall ((A6 tptp.set_int)) (=> (@ X8 A6) (exists ((X2 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_set_int A6) (@ (@ tptp.insert_int X2) tptp.bot_bot_set_int)))) (and (@ (@ tptp.member_int X2) A6) (or (@ X8 _let_1) (not (@ tptp.finite_finite_int _let_1)))))))) (not (@ tptp.finite_finite_int A2))))) (forall ((X8 (-> tptp.set_nat Bool)) (A2 tptp.set_nat)) (=> (@ X8 A2) (=> (forall ((A6 tptp.set_nat)) (=> (@ X8 A6) (exists ((X2 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_set_nat A6) (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat)))) (and (@ (@ tptp.member_nat X2) A6) (or (@ X8 _let_1) (not (@ tptp.finite_finite_nat _let_1)))))))) (not (@ tptp.finite_finite_nat A2))))) (forall ((A2 tptp.set_set_nat) (P (-> tptp.set_set_nat Bool))) (=> (@ tptp.finite1152437895449049373et_nat A2) (=> (@ P A2) (=> (forall ((A4 tptp.set_nat) (A6 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A6) (=> (@ (@ tptp.member_set_nat A4) A6) (=> (@ P A6) (@ P (@ (@ tptp.minus_2163939370556025621et_nat A6) (@ (@ tptp.insert_set_nat A4) tptp.bot_bot_set_set_nat))))))) (@ P tptp.bot_bot_set_set_nat))))) (forall ((A2 tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ P A2) (=> (forall ((A4 tptp.complex) (A6 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A6) (=> (@ (@ tptp.member_complex A4) A6) (=> (@ P A6) (@ P (@ (@ tptp.minus_811609699411566653omplex A6) (@ (@ tptp.insert_complex A4) tptp.bot_bot_set_complex))))))) (@ P tptp.bot_bot_set_complex))))) (forall ((A2 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ P A2) (=> (forall ((A4 tptp.extended_enat) (A6 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A6) (=> (@ (@ tptp.member_Extended_enat A4) A6) (=> (@ P A6) (@ P (@ (@ tptp.minus_925952699566721837d_enat A6) (@ (@ tptp.insert_Extended_enat A4) tptp.bot_bo7653980558646680370d_enat))))))) (@ P tptp.bot_bo7653980558646680370d_enat))))) (forall ((A2 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real A2) (=> (@ P A2) (=> (forall ((A4 tptp.real) (A6 tptp.set_real)) (=> (@ tptp.finite_finite_real A6) (=> (@ (@ tptp.member_real A4) A6) (=> (@ P A6) (@ P (@ (@ tptp.minus_minus_set_real A6) (@ (@ tptp.insert_real A4) tptp.bot_bot_set_real))))))) (@ P tptp.bot_bot_set_real))))) (forall ((A2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int A2) (=> (@ P A2) (=> (forall ((A4 tptp.int) (A6 tptp.set_int)) (=> (@ tptp.finite_finite_int A6) (=> (@ (@ tptp.member_int A4) A6) (=> (@ P A6) (@ P (@ (@ tptp.minus_minus_set_int A6) (@ (@ tptp.insert_int A4) tptp.bot_bot_set_int))))))) (@ P tptp.bot_bot_set_int))))) (forall ((A2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat A2) (=> (@ P A2) (=> (forall ((A4 tptp.nat) (A6 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A6) (=> (@ (@ tptp.member_nat A4) A6) (=> (@ P A6) (@ P (@ (@ tptp.minus_minus_set_nat A6) (@ (@ tptp.insert_nat A4) tptp.bot_bot_set_nat))))))) (@ P tptp.bot_bot_set_nat))))) (forall ((X8 tptp.set_Extended_enat) (A tptp.extended_enat)) (let ((_let_1 (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat))) (= (@ (@ tptp.ord_le7203529160286727270d_enat X8) _let_1) (or (= X8 tptp.bot_bo7653980558646680370d_enat) (= X8 _let_1))))) (forall ((X8 tptp.set_real) (A tptp.real)) (let ((_let_1 (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))) (= (@ (@ tptp.ord_less_eq_set_real X8) _let_1) (or (= X8 tptp.bot_bot_set_real) (= X8 _let_1))))) (forall ((X8 tptp.set_nat) (A tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))) (= (@ (@ tptp.ord_less_eq_set_nat X8) _let_1) (or (= X8 tptp.bot_bot_set_nat) (= X8 _let_1))))) (forall ((X8 tptp.set_int) (A tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))) (= (@ (@ tptp.ord_less_eq_set_int X8) _let_1) (or (= X8 tptp.bot_bot_set_int) (= X8 _let_1))))) (forall ((A2 tptp.set_Extended_enat) (X tptp.extended_enat)) (let ((_let_1 (@ (@ tptp.insert_Extended_enat X) tptp.bot_bo7653980558646680370d_enat))) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) _let_1) (or (= A2 tptp.bot_bo7653980558646680370d_enat) (= A2 _let_1))))) (forall ((A2 tptp.set_real) (X tptp.real)) (let ((_let_1 (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))) (=> (@ (@ tptp.ord_less_eq_set_real A2) _let_1) (or (= A2 tptp.bot_bot_set_real) (= A2 _let_1))))) (forall ((A2 tptp.set_nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))) (=> (@ (@ tptp.ord_less_eq_set_nat A2) _let_1) (or (= A2 tptp.bot_bot_set_nat) (= A2 _let_1))))) (forall ((A2 tptp.set_int) (X tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))) (=> (@ (@ tptp.ord_less_eq_set_int A2) _let_1) (or (= A2 tptp.bot_bot_set_int) (= A2 _let_1))))) (forall ((A2 tptp.set_Extended_enat) (X tptp.extended_enat) (B tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.insert_Extended_enat X))) (=> (@ (@ tptp.ord_le7203529160286727270d_enat (@ (@ tptp.minus_925952699566721837d_enat A2) (@ _let_1 tptp.bot_bo7653980558646680370d_enat))) B) (@ (@ tptp.ord_le7203529160286727270d_enat A2) (@ _let_1 B))))) (forall ((A2 tptp.set_real) (X tptp.real) (B tptp.set_real)) (let ((_let_1 (@ tptp.insert_real X))) (=> (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.minus_minus_set_real A2) (@ _let_1 tptp.bot_bot_set_real))) B) (@ (@ tptp.ord_less_eq_set_real A2) (@ _let_1 B))))) (forall ((A2 tptp.set_nat) (X tptp.nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X))) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A2) (@ _let_1 tptp.bot_bot_set_nat))) B) (@ (@ tptp.ord_less_eq_set_nat A2) (@ _let_1 B))))) (forall ((A2 tptp.set_int) (X tptp.int) (B tptp.set_int)) (let ((_let_1 (@ tptp.insert_int X))) (=> (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A2) (@ _let_1 tptp.bot_bot_set_int))) B) (@ (@ tptp.ord_less_eq_set_int A2) (@ _let_1 B))))) (forall ((A2 tptp.set_set_nat) (X tptp.set_nat) (B tptp.set_set_nat)) (let ((_let_1 (@ tptp.ord_le6893508408891458716et_nat A2))) (let ((_let_2 (@ (@ tptp.member_set_nat X) A2))) (let ((_let_3 (@ tptp.insert_set_nat X))) (= (@ _let_1 (@ _let_3 B)) (and (=> _let_2 (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.minus_2163939370556025621et_nat A2) (@ _let_3 tptp.bot_bot_set_set_nat))) B)) (=> (not _let_2) (@ _let_1 B)))))))) (forall ((A2 tptp.set_Extended_enat) (X tptp.extended_enat) (B tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.ord_le7203529160286727270d_enat A2))) (let ((_let_2 (@ (@ tptp.member_Extended_enat X) A2))) (let ((_let_3 (@ tptp.insert_Extended_enat X))) (= (@ _let_1 (@ _let_3 B)) (and (=> _let_2 (@ (@ tptp.ord_le7203529160286727270d_enat (@ (@ tptp.minus_925952699566721837d_enat A2) (@ _let_3 tptp.bot_bo7653980558646680370d_enat))) B)) (=> (not _let_2) (@ _let_1 B)))))))) (forall ((A2 tptp.set_real) (X tptp.real) (B tptp.set_real)) (let ((_let_1 (@ tptp.ord_less_eq_set_real A2))) (let ((_let_2 (@ (@ tptp.member_real X) A2))) (let ((_let_3 (@ tptp.insert_real X))) (= (@ _let_1 (@ _let_3 B)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.minus_minus_set_real A2) (@ _let_3 tptp.bot_bot_set_real))) B)) (=> (not _let_2) (@ _let_1 B)))))))) (forall ((A2 tptp.set_nat) (X tptp.nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A2))) (let ((_let_2 (@ (@ tptp.member_nat X) A2))) (let ((_let_3 (@ tptp.insert_nat X))) (= (@ _let_1 (@ _let_3 B)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A2) (@ _let_3 tptp.bot_bot_set_nat))) B)) (=> (not _let_2) (@ _let_1 B)))))))) (forall ((A2 tptp.set_int) (X tptp.int) (B tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A2))) (let ((_let_2 (@ (@ tptp.member_int X) A2))) (let ((_let_3 (@ tptp.insert_int X))) (= (@ _let_1 (@ _let_3 B)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A2) (@ _let_3 tptp.bot_bot_set_int))) B)) (=> (not _let_2) (@ _let_1 B)))))))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (=> (= A B2) (= (@ (@ tptp.set_or5403411693681687835d_enat A) B2) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat)))) (forall ((A tptp.nat) (B2 tptp.nat)) (=> (= A B2) (= (@ (@ tptp.set_or1269000886237332187st_nat A) B2) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat)))) (forall ((A tptp.int) (B2 tptp.int)) (=> (= A B2) (= (@ (@ tptp.set_or1266510415728281911st_int A) B2) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int)))) (forall ((A tptp.real) (B2 tptp.real)) (=> (= A B2) (= (@ (@ tptp.set_or1222579329274155063t_real A) B2) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real)))) _let_144 (forall ((S2 tptp.set_complex) (P (-> tptp.set_complex Bool)) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((X5 tptp.complex) (S4 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex S4) (=> (forall ((Y6 tptp.complex)) (=> (@ (@ tptp.member_complex Y6) S4) (@ (@ tptp.ord_less_eq_real (@ F Y6)) (@ F X5)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_complex X5) S4)))))) (@ P S2))))) (forall ((S2 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool)) (F (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat S2) (=> (@ P tptp.bot_bo7653980558646680370d_enat) (=> (forall ((X5 tptp.extended_enat) (S4 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat S4) (=> (forall ((Y6 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat Y6) S4) (@ (@ tptp.ord_less_eq_real (@ F Y6)) (@ F X5)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_Extended_enat X5) S4)))))) (@ P S2))))) (forall ((S2 tptp.set_real) (P (-> tptp.set_real Bool)) (F (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real S2) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((X5 tptp.real) (S4 tptp.set_real)) (=> (@ tptp.finite_finite_real S4) (=> (forall ((Y6 tptp.real)) (=> (@ (@ tptp.member_real Y6) S4) (@ (@ tptp.ord_less_eq_real (@ F Y6)) (@ F X5)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_real X5) S4)))))) (@ P S2))))) (forall ((S2 tptp.set_nat) (P (-> tptp.set_nat Bool)) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat S2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((X5 tptp.nat) (S4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S4) (=> (forall ((Y6 tptp.nat)) (=> (@ (@ tptp.member_nat Y6) S4) (@ (@ tptp.ord_less_eq_real (@ F Y6)) (@ F X5)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_nat X5) S4)))))) (@ P S2))))) (forall ((S2 tptp.set_int) (P (-> tptp.set_int Bool)) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int S2) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((X5 tptp.int) (S4 tptp.set_int)) (=> (@ tptp.finite_finite_int S4) (=> (forall ((Y6 tptp.int)) (=> (@ (@ tptp.member_int Y6) S4) (@ (@ tptp.ord_less_eq_real (@ F Y6)) (@ F X5)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_int X5) S4)))))) (@ P S2))))) (forall ((S2 tptp.set_complex) (P (-> tptp.set_complex Bool)) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((X5 tptp.complex) (S4 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex S4) (=> (forall ((Y6 tptp.complex)) (=> (@ (@ tptp.member_complex Y6) S4) (@ (@ tptp.ord_less_eq_nat (@ F Y6)) (@ F X5)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_complex X5) S4)))))) (@ P S2))))) (forall ((S2 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool)) (F (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat S2) (=> (@ P tptp.bot_bo7653980558646680370d_enat) (=> (forall ((X5 tptp.extended_enat) (S4 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat S4) (=> (forall ((Y6 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat Y6) S4) (@ (@ tptp.ord_less_eq_nat (@ F Y6)) (@ F X5)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_Extended_enat X5) S4)))))) (@ P S2))))) (forall ((S2 tptp.set_real) (P (-> tptp.set_real Bool)) (F (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real S2) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((X5 tptp.real) (S4 tptp.set_real)) (=> (@ tptp.finite_finite_real S4) (=> (forall ((Y6 tptp.real)) (=> (@ (@ tptp.member_real Y6) S4) (@ (@ tptp.ord_less_eq_nat (@ F Y6)) (@ F X5)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_real X5) S4)))))) (@ P S2))))) (forall ((S2 tptp.set_nat) (P (-> tptp.set_nat Bool)) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat S2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((X5 tptp.nat) (S4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S4) (=> (forall ((Y6 tptp.nat)) (=> (@ (@ tptp.member_nat Y6) S4) (@ (@ tptp.ord_less_eq_nat (@ F Y6)) (@ F X5)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_nat X5) S4)))))) (@ P S2))))) (forall ((S2 tptp.set_int) (P (-> tptp.set_int Bool)) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int S2) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((X5 tptp.int) (S4 tptp.set_int)) (=> (@ tptp.finite_finite_int S4) (=> (forall ((Y6 tptp.int)) (=> (@ (@ tptp.member_int Y6) S4) (@ (@ tptp.ord_less_eq_nat (@ F Y6)) (@ F X5)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_int X5) S4)))))) (@ P S2))))) (forall ((A2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat A2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((B4 tptp.nat) (A6 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A6) (=> (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A6) (@ (@ tptp.ord_less_nat X2) B4))) (=> (@ P A6) (@ P (@ (@ tptp.insert_nat B4) A6)))))) (@ P A2))))) (forall ((A2 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ P tptp.bot_bo7653980558646680370d_enat) (=> (forall ((B4 tptp.extended_enat) (A6 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A6) (=> (forall ((X2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X2) A6) (@ (@ tptp.ord_le72135733267957522d_enat X2) B4))) (=> (@ P A6) (@ P (@ (@ tptp.insert_Extended_enat B4) A6)))))) (@ P A2))))) (forall ((A2 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real A2) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((B4 tptp.real) (A6 tptp.set_real)) (=> (@ tptp.finite_finite_real A6) (=> (forall ((X2 tptp.real)) (=> (@ (@ tptp.member_real X2) A6) (@ (@ tptp.ord_less_real X2) B4))) (=> (@ P A6) (@ P (@ (@ tptp.insert_real B4) A6)))))) (@ P A2))))) (forall ((A2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int A2) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((B4 tptp.int) (A6 tptp.set_int)) (=> (@ tptp.finite_finite_int A6) (=> (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) A6) (@ (@ tptp.ord_less_int X2) B4))) (=> (@ P A6) (@ P (@ (@ tptp.insert_int B4) A6)))))) (@ P A2))))) (forall ((A2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat A2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((B4 tptp.nat) (A6 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A6) (=> (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A6) (@ (@ tptp.ord_less_nat B4) X2))) (=> (@ P A6) (@ P (@ (@ tptp.insert_nat B4) A6)))))) (@ P A2))))) (forall ((A2 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ P tptp.bot_bo7653980558646680370d_enat) (=> (forall ((B4 tptp.extended_enat) (A6 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A6) (=> (forall ((X2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X2) A6) (@ (@ tptp.ord_le72135733267957522d_enat B4) X2))) (=> (@ P A6) (@ P (@ (@ tptp.insert_Extended_enat B4) A6)))))) (@ P A2))))) (forall ((A2 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real A2) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((B4 tptp.real) (A6 tptp.set_real)) (=> (@ tptp.finite_finite_real A6) (=> (forall ((X2 tptp.real)) (=> (@ (@ tptp.member_real X2) A6) (@ (@ tptp.ord_less_real B4) X2))) (=> (@ P A6) (@ P (@ (@ tptp.insert_real B4) A6)))))) (@ P A2))))) (forall ((A2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int A2) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((B4 tptp.int) (A6 tptp.set_int)) (=> (@ tptp.finite_finite_int A6) (=> (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) A6) (@ (@ tptp.ord_less_int B4) X2))) (=> (@ P A6) (@ P (@ (@ tptp.insert_int B4) A6)))))) (@ P A2))))) (forall ((F3 tptp.set_set_nat) (A2 tptp.set_set_nat) (P (-> tptp.set_set_nat Bool))) (=> (@ tptp.finite1152437895449049373et_nat F3) (=> (@ (@ tptp.ord_le6893508408891458716et_nat F3) A2) (=> (@ P tptp.bot_bot_set_set_nat) (=> (forall ((A4 tptp.set_nat) (F4 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat A4))) (=> (@ tptp.finite1152437895449049373et_nat F4) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_le6893508408891458716et_nat F4) A2) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_set_nat A4) F4))))))))) (@ P F3)))))) (forall ((F3 tptp.set_complex) (A2 tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex F3) (=> (@ (@ tptp.ord_le211207098394363844omplex F3) A2) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((A4 tptp.complex) (F4 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex A4))) (=> (@ tptp.finite3207457112153483333omplex F4) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_le211207098394363844omplex F4) A2) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_complex A4) F4))))))))) (@ P F3)))))) (forall ((F3 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat F3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat F3) A2) (=> (@ P tptp.bot_bo7653980558646680370d_enat) (=> (forall ((A4 tptp.extended_enat) (F4 tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat A4))) (=> (@ tptp.finite4001608067531595151d_enat F4) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat F4) A2) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_Extended_enat A4) F4))))))))) (@ P F3)))))) (forall ((F3 tptp.set_real) (A2 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real F3) (=> (@ (@ tptp.ord_less_eq_set_real F3) A2) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((A4 tptp.real) (F4 tptp.set_real)) (let ((_let_1 (@ tptp.member_real A4))) (=> (@ tptp.finite_finite_real F4) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_less_eq_set_real F4) A2) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_real A4) F4))))))))) (@ P F3)))))) (forall ((F3 tptp.set_nat) (A2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat F3) (=> (@ (@ tptp.ord_less_eq_set_nat F3) A2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((A4 tptp.nat) (F4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat A4))) (=> (@ tptp.finite_finite_nat F4) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_less_eq_set_nat F4) A2) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_nat A4) F4))))))))) (@ P F3)))))) (forall ((F3 tptp.set_int) (A2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int F3) (=> (@ (@ tptp.ord_less_eq_set_int F3) A2) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((A4 tptp.int) (F4 tptp.set_int)) (let ((_let_1 (@ tptp.member_int A4))) (=> (@ tptp.finite_finite_int F4) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_less_eq_set_int F4) A2) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_int A4) F4))))))))) (@ P F3)))))) (forall ((F3 tptp.set_set_nat) (A2 tptp.set_set_nat) (P (-> tptp.set_set_nat Bool))) (=> (@ tptp.finite1152437895449049373et_nat F3) (=> (@ (@ tptp.ord_le6893508408891458716et_nat F3) A2) (=> (@ P tptp.bot_bot_set_set_nat) (=> (forall ((A4 tptp.set_nat) (F4 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat A4))) (=> (@ tptp.finite1152437895449049373et_nat F4) (=> (@ _let_1 A2) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_set_nat A4) F4)))))))) (@ P F3)))))) (forall ((F3 tptp.set_complex) (A2 tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex F3) (=> (@ (@ tptp.ord_le211207098394363844omplex F3) A2) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((A4 tptp.complex) (F4 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex A4))) (=> (@ tptp.finite3207457112153483333omplex F4) (=> (@ _let_1 A2) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_complex A4) F4)))))))) (@ P F3)))))) (forall ((F3 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat F3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat F3) A2) (=> (@ P tptp.bot_bo7653980558646680370d_enat) (=> (forall ((A4 tptp.extended_enat) (F4 tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat A4))) (=> (@ tptp.finite4001608067531595151d_enat F4) (=> (@ _let_1 A2) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_Extended_enat A4) F4)))))))) (@ P F3)))))) (forall ((F3 tptp.set_real) (A2 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real F3) (=> (@ (@ tptp.ord_less_eq_set_real F3) A2) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((A4 tptp.real) (F4 tptp.set_real)) (let ((_let_1 (@ tptp.member_real A4))) (=> (@ tptp.finite_finite_real F4) (=> (@ _let_1 A2) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_real A4) F4)))))))) (@ P F3)))))) (forall ((F3 tptp.set_nat) (A2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat F3) (=> (@ (@ tptp.ord_less_eq_set_nat F3) A2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((A4 tptp.nat) (F4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat A4))) (=> (@ tptp.finite_finite_nat F4) (=> (@ _let_1 A2) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_nat A4) F4)))))))) (@ P F3)))))) (forall ((F3 tptp.set_int) (A2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int F3) (=> (@ (@ tptp.ord_less_eq_set_int F3) A2) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((A4 tptp.int) (F4 tptp.set_int)) (let ((_let_1 (@ tptp.member_int A4))) (=> (@ tptp.finite_finite_int F4) (=> (@ _let_1 A2) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_int A4) F4)))))))) (@ P F3)))))) (forall ((B tptp.set_set_nat) (P (-> tptp.set_set_nat Bool))) (=> (@ tptp.finite1152437895449049373et_nat B) (=> (@ P tptp.bot_bot_set_set_nat) (=> (forall ((A6 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A6) (=> (not (= A6 tptp.bot_bot_set_set_nat)) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A6) B) (=> (forall ((X2 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X2) A6) (@ P (@ (@ tptp.minus_2163939370556025621et_nat A6) (@ (@ tptp.insert_set_nat X2) tptp.bot_bot_set_set_nat))))) (@ P A6)))))) (@ P B))))) (forall ((B tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex B) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((A6 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A6) (=> (not (= A6 tptp.bot_bot_set_complex)) (=> (@ (@ tptp.ord_le211207098394363844omplex A6) B) (=> (forall ((X2 tptp.complex)) (=> (@ (@ tptp.member_complex X2) A6) (@ P (@ (@ tptp.minus_811609699411566653omplex A6) (@ (@ tptp.insert_complex X2) tptp.bot_bot_set_complex))))) (@ P A6)))))) (@ P B))))) (forall ((B tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat B) (=> (@ P tptp.bot_bo7653980558646680370d_enat) (=> (forall ((A6 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A6) (=> (not (= A6 tptp.bot_bo7653980558646680370d_enat)) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A6) B) (=> (forall ((X2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X2) A6) (@ P (@ (@ tptp.minus_925952699566721837d_enat A6) (@ (@ tptp.insert_Extended_enat X2) tptp.bot_bo7653980558646680370d_enat))))) (@ P A6)))))) (@ P B))))) (forall ((B tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real B) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((A6 tptp.set_real)) (=> (@ tptp.finite_finite_real A6) (=> (not (= A6 tptp.bot_bot_set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A6) B) (=> (forall ((X2 tptp.real)) (=> (@ (@ tptp.member_real X2) A6) (@ P (@ (@ tptp.minus_minus_set_real A6) (@ (@ tptp.insert_real X2) tptp.bot_bot_set_real))))) (@ P A6)))))) (@ P B))))) (forall ((B tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat B) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((A6 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A6) (=> (not (= A6 tptp.bot_bot_set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A6) B) (=> (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A6) (@ P (@ (@ tptp.minus_minus_set_nat A6) (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat))))) (@ P A6)))))) (@ P B))))) (forall ((B tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int B) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((A6 tptp.set_int)) (=> (@ tptp.finite_finite_int A6) (=> (not (= A6 tptp.bot_bot_set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A6) B) (=> (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) A6) (@ P (@ (@ tptp.minus_minus_set_int A6) (@ (@ tptp.insert_int X2) tptp.bot_bot_set_int))))) (@ P A6)))))) (@ P B))))) (forall ((P (-> tptp.set_set_nat Bool)) (B tptp.set_set_nat)) (let ((_let_1 (@ P B))) (=> (@ P tptp.bot_bot_set_set_nat) (=> (=> (not (@ tptp.finite1152437895449049373et_nat B)) _let_1) (=> (forall ((A6 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A6) (=> (not (= A6 tptp.bot_bot_set_set_nat)) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A6) B) (=> (forall ((X2 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X2) A6) (@ P (@ (@ tptp.minus_2163939370556025621et_nat A6) (@ (@ tptp.insert_set_nat X2) tptp.bot_bot_set_set_nat))))) (@ P A6)))))) _let_1))))) (forall ((P (-> tptp.set_complex Bool)) (B tptp.set_complex)) (let ((_let_1 (@ P B))) (=> (@ P tptp.bot_bot_set_complex) (=> (=> (not (@ tptp.finite3207457112153483333omplex B)) _let_1) (=> (forall ((A6 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A6) (=> (not (= A6 tptp.bot_bot_set_complex)) (=> (@ (@ tptp.ord_le211207098394363844omplex A6) B) (=> (forall ((X2 tptp.complex)) (=> (@ (@ tptp.member_complex X2) A6) (@ P (@ (@ tptp.minus_811609699411566653omplex A6) (@ (@ tptp.insert_complex X2) tptp.bot_bot_set_complex))))) (@ P A6)))))) _let_1))))) (forall ((P (-> tptp.set_Extended_enat Bool)) (B tptp.set_Extended_enat)) (let ((_let_1 (@ P B))) (=> (@ P tptp.bot_bo7653980558646680370d_enat) (=> (=> (not (@ tptp.finite4001608067531595151d_enat B)) _let_1) (=> (forall ((A6 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A6) (=> (not (= A6 tptp.bot_bo7653980558646680370d_enat)) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A6) B) (=> (forall ((X2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X2) A6) (@ P (@ (@ tptp.minus_925952699566721837d_enat A6) (@ (@ tptp.insert_Extended_enat X2) tptp.bot_bo7653980558646680370d_enat))))) (@ P A6)))))) _let_1))))) (forall ((P (-> tptp.set_real Bool)) (B tptp.set_real)) (let ((_let_1 (@ P B))) (=> (@ P tptp.bot_bot_set_real) (=> (=> (not (@ tptp.finite_finite_real B)) _let_1) (=> (forall ((A6 tptp.set_real)) (=> (@ tptp.finite_finite_real A6) (=> (not (= A6 tptp.bot_bot_set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A6) B) (=> (forall ((X2 tptp.real)) (=> (@ (@ tptp.member_real X2) A6) (@ P (@ (@ tptp.minus_minus_set_real A6) (@ (@ tptp.insert_real X2) tptp.bot_bot_set_real))))) (@ P A6)))))) _let_1))))) (forall ((P (-> tptp.set_nat Bool)) (B tptp.set_nat)) (let ((_let_1 (@ P B))) (=> (@ P tptp.bot_bot_set_nat) (=> (=> (not (@ tptp.finite_finite_nat B)) _let_1) (=> (forall ((A6 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A6) (=> (not (= A6 tptp.bot_bot_set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A6) B) (=> (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A6) (@ P (@ (@ tptp.minus_minus_set_nat A6) (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat))))) (@ P A6)))))) _let_1))))) (forall ((P (-> tptp.set_int Bool)) (B tptp.set_int)) (let ((_let_1 (@ P B))) (=> (@ P tptp.bot_bot_set_int) (=> (=> (not (@ tptp.finite_finite_int B)) _let_1) (=> (forall ((A6 tptp.set_int)) (=> (@ tptp.finite_finite_int A6) (=> (not (= A6 tptp.bot_bot_set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A6) B) (=> (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) A6) (@ P (@ (@ tptp.minus_minus_set_int A6) (@ (@ tptp.insert_int X2) tptp.bot_bot_set_int))))) (@ P A6)))))) _let_1))))) (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 ((S2 tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((T4 tptp.set_complex)) (=> (@ (@ tptp.ord_less_set_complex T4) S2) (=> (@ P T4) (exists ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) (@ (@ tptp.minus_811609699411566653omplex S2) T4)) (@ P (@ (@ tptp.insert_complex X2) T4))))))) (@ P S2))))) (forall ((S2 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat S2) (=> (@ P tptp.bot_bo7653980558646680370d_enat) (=> (forall ((T4 tptp.set_Extended_enat)) (=> (@ (@ tptp.ord_le2529575680413868914d_enat T4) S2) (=> (@ P T4) (exists ((X2 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X2) (@ (@ tptp.minus_925952699566721837d_enat S2) T4)) (@ P (@ (@ tptp.insert_Extended_enat X2) T4))))))) (@ P S2))))) (forall ((S2 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real S2) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((T4 tptp.set_real)) (=> (@ (@ tptp.ord_less_set_real T4) S2) (=> (@ P T4) (exists ((X2 tptp.real)) (and (@ (@ tptp.member_real X2) (@ (@ tptp.minus_minus_set_real S2) T4)) (@ P (@ (@ tptp.insert_real X2) T4))))))) (@ P S2))))) (forall ((S2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int S2) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((T4 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int T4) S2) (=> (@ P T4) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.minus_minus_set_int S2) T4)) (@ P (@ (@ tptp.insert_int X2) T4))))))) (@ P S2))))) (forall ((S2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat S2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((T4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat T4) S2) (=> (@ P T4) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) (@ (@ tptp.minus_minus_set_nat S2) T4)) (@ P (@ (@ tptp.insert_nat X2) T4))))))) (@ P S2))))) (forall ((A2 tptp.set_set_nat) (X tptp.set_nat) (B tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat X))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_set_nat X))) (let ((_let_4 (@ _let_1 B))) (let ((_let_5 (@ tptp.ord_less_set_set_nat A2))) (= (@ _let_5 (@ _let_3 B)) (and (=> _let_4 (@ _let_5 B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_set_nat (@ (@ tptp.minus_2163939370556025621et_nat A2) (@ _let_3 tptp.bot_bot_set_set_nat))) B)) (=> (not _let_2) (@ (@ tptp.ord_le6893508408891458716et_nat A2) B)))))))))))) (forall ((A2 tptp.set_Extended_enat) (X tptp.extended_enat) (B tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat X))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_Extended_enat X))) (let ((_let_4 (@ _let_1 B))) (let ((_let_5 (@ tptp.ord_le2529575680413868914d_enat A2))) (= (@ _let_5 (@ _let_3 B)) (and (=> _let_4 (@ _let_5 B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_le2529575680413868914d_enat (@ (@ tptp.minus_925952699566721837d_enat A2) (@ _let_3 tptp.bot_bo7653980558646680370d_enat))) B)) (=> (not _let_2) (@ (@ tptp.ord_le7203529160286727270d_enat A2) B)))))))))))) (forall ((A2 tptp.set_real) (X tptp.real) (B tptp.set_real)) (let ((_let_1 (@ tptp.member_real X))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_real X))) (let ((_let_4 (@ _let_1 B))) (let ((_let_5 (@ tptp.ord_less_set_real A2))) (= (@ _let_5 (@ _let_3 B)) (and (=> _let_4 (@ _let_5 B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_real (@ (@ tptp.minus_minus_set_real A2) (@ _let_3 tptp.bot_bot_set_real))) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_real A2) B)))))))))))) (forall ((A2 tptp.set_nat) (X tptp.nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat X))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_nat X))) (let ((_let_4 (@ _let_1 B))) (let ((_let_5 (@ tptp.ord_less_set_nat A2))) (= (@ _let_5 (@ _let_3 B)) (and (=> _let_4 (@ _let_5 B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_nat (@ (@ tptp.minus_minus_set_nat A2) (@ _let_3 tptp.bot_bot_set_nat))) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_nat A2) B)))))))))))) (forall ((A2 tptp.set_int) (X tptp.int) (B tptp.set_int)) (let ((_let_1 (@ tptp.member_int X))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_int X))) (let ((_let_4 (@ _let_1 B))) (let ((_let_5 (@ tptp.ord_less_set_int A2))) (= (@ _let_5 (@ _let_3 B)) (and (=> _let_4 (@ _let_5 B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_int (@ (@ tptp.minus_minus_set_int A2) (@ _let_3 tptp.bot_bot_set_int))) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_int A2) B)))))))))))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ (@ tptp.insert_nat M2) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N2)) (@ (@ tptp.set_or1269000886237332187st_nat M2) N2)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.insert_nat _let_2) (@ _let_1 N2))))))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ (@ tptp.set_or1269000886237332187st_nat M2) N2) (@ (@ tptp.insert_nat M2) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N2))))) (forall ((Xs tptp.list_real) (I tptp.nat) (X tptp.real)) (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real Xs) I) X))) (@ (@ tptp.insert_real X) (@ tptp.set_real2 Xs)))) (forall ((Xs tptp.list_VEBT_VEBT) (I tptp.nat) (X tptp.vEBT_VEBT)) (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) X))) (@ (@ tptp.insert_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs)))) (forall ((Xs tptp.list_nat) (I tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs) I) X))) (@ (@ tptp.insert_nat X) (@ tptp.set_nat2 Xs)))) (forall ((Xs tptp.list_int) (I tptp.nat) (X tptp.int)) (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs) I) X))) (@ (@ tptp.insert_int X) (@ tptp.set_int2 Xs)))) (forall ((N2 tptp.nat) (X tptp.vEBT_VEBT)) (= (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT (@ tptp.suc N2)) X)) (@ (@ tptp.insert_VEBT_VEBT X) tptp.bot_bo8194388402131092736T_VEBT))) (forall ((N2 tptp.nat) (X tptp.extended_enat)) (= (@ tptp.set_Extended_enat2 (@ (@ tptp.replic7216382294607269926d_enat (@ tptp.suc N2)) X)) (@ (@ tptp.insert_Extended_enat X) tptp.bot_bo7653980558646680370d_enat))) (forall ((N2 tptp.nat) (X tptp.real)) (= (@ tptp.set_real2 (@ (@ tptp.replicate_real (@ tptp.suc N2)) X)) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))) (forall ((N2 tptp.nat) (X tptp.nat)) (= (@ tptp.set_nat2 (@ (@ tptp.replicate_nat (@ tptp.suc N2)) X)) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))) (forall ((N2 tptp.nat) (X tptp.int)) (= (@ tptp.set_int2 (@ (@ tptp.replicate_int (@ tptp.suc N2)) X)) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))) (forall ((N2 tptp.nat) (X tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N2) X)))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.bot_bo8194388402131092736T_VEBT)) (=> (not _let_2) (= _let_1 (@ (@ tptp.insert_VEBT_VEBT X) tptp.bot_bo8194388402131092736T_VEBT))))))) (forall ((N2 tptp.nat) (X tptp.extended_enat)) (let ((_let_1 (@ tptp.set_Extended_enat2 (@ (@ tptp.replic7216382294607269926d_enat N2) X)))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.bot_bo7653980558646680370d_enat)) (=> (not _let_2) (= _let_1 (@ (@ tptp.insert_Extended_enat X) tptp.bot_bo7653980558646680370d_enat))))))) (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.set_real2 (@ (@ tptp.replicate_real N2) X)))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.bot_bot_set_real)) (=> (not _let_2) (= _let_1 (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))))))) (forall ((N2 tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N2) X)))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.bot_bot_set_nat)) (=> (not _let_2) (= _let_1 (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))))))) (forall ((N2 tptp.nat) (X tptp.int)) (let ((_let_1 (@ tptp.set_int2 (@ (@ tptp.replicate_int N2) X)))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.bot_bot_set_int)) (=> (not _let_2) (= _let_1 (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))))))) (forall ((N2 tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.nat_set_decode Z3))) (=> (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)) Z3)) (@ (@ tptp.insert_nat N2) _let_1))))) (= tptp.unique5026877609467782581ep_nat (lambda ((L2 tptp.num) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q5 tptp.nat) (R4 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) R4)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R4) _let_2))) (@ (@ tptp.product_Pair_nat_nat _let_1) R4)))))) __flatten_var_0))) (forall ((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))) (= tptp.divmod_nat (lambda ((M tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (or (= N tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat M) N))) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) M)) (@ (@ 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 M) N)) N))))) (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 ((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)))))) (= tptp.ring_17405671764205052669omplex (lambda ((K2 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.divide_divide_int K2) _let_2))))) (@ (@ (@ tptp.if_complex (= K2 tptp.zero_zero_int)) tptp.zero_zero_complex) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int)) (@ tptp.uminus1482373934393186551omplex (@ tptp.ring_17405671764205052669omplex (@ tptp.uminus_uminus_int K2)))) (@ (@ (@ tptp.if_complex (= (@ (@ tptp.modulo_modulo_int K2) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_plus_complex _let_3) tptp.one_one_complex))))))))) (= tptp.ring_1_of_int_int (lambda ((K2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_int _let_1) (@ tptp.ring_1_of_int_int (@ (@ tptp.divide_divide_int K2) _let_1))))) (@ (@ (@ tptp.if_int (= K2 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int (@ tptp.ring_1_of_int_int (@ tptp.uminus_uminus_int K2)))) (@ (@ (@ tptp.if_int (= (@ (@ tptp.modulo_modulo_int K2) _let_1) tptp.zero_zero_int)) _let_2) (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)))))))) (= tptp.ring_1_of_int_real (lambda ((K2 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int K2) _let_2))))) (@ (@ (@ tptp.if_real (= K2 tptp.zero_zero_int)) tptp.zero_zero_real) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int)) (@ tptp.uminus_uminus_real (@ tptp.ring_1_of_int_real (@ tptp.uminus_uminus_int K2)))) (@ (@ (@ tptp.if_real (= (@ (@ tptp.modulo_modulo_int K2) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_plus_real _let_3) tptp.one_one_real))))))))) (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 ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_int A) _let_1)))) (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N2)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)))) (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))) (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N2)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)) A))) (forall ((W2 tptp.int) (Z3 tptp.int)) (= (= (@ tptp.ring_1_of_int_real W2) (@ tptp.ring_1_of_int_real Z3)) (= W2 Z3))) (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 ((P Bool)) (= (@ tptp.ring_1_of_int_real (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n3304061248610475627l_real P))) (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n2684676970156552555ol_int P))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))) (forall ((K tptp.int) (L tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit tptp.zero_zero_nat) K) L) L)) (forall ((Z3 tptp.int)) (= (= (@ tptp.ring_1_of_int_int Z3) tptp.zero_zero_int) (= Z3 tptp.zero_zero_int))) (forall ((Z3 tptp.int)) (= (= (@ tptp.ring_17405671764205052669omplex Z3) tptp.zero_zero_complex) (= Z3 tptp.zero_zero_int))) (forall ((Z3 tptp.int)) (= (= (@ tptp.ring_1_of_int_real Z3) tptp.zero_zero_real) (= Z3 tptp.zero_zero_int))) (forall ((Z3 tptp.int)) (= (= tptp.zero_zero_int (@ tptp.ring_1_of_int_int Z3)) (= Z3 tptp.zero_zero_int))) (forall ((Z3 tptp.int)) (= (= tptp.zero_zero_complex (@ tptp.ring_17405671764205052669omplex Z3)) (= Z3 tptp.zero_zero_int))) (forall ((Z3 tptp.int)) (= (= tptp.zero_zero_real (@ tptp.ring_1_of_int_real Z3)) (= Z3 tptp.zero_zero_int))) (= (@ tptp.ring_1_of_int_int tptp.zero_zero_int) tptp.zero_zero_int) (= (@ tptp.ring_17405671764205052669omplex tptp.zero_zero_int) tptp.zero_zero_complex) (= (@ tptp.ring_1_of_int_real tptp.zero_zero_int) tptp.zero_zero_real) (forall ((W2 tptp.int) (Z3 tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real W2)) (@ tptp.ring_1_of_int_real Z3)) (@ (@ tptp.ord_less_eq_int W2) Z3))) (forall ((W2 tptp.int) (Z3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int W2)) (@ tptp.ring_1_of_int_int Z3)) (@ (@ tptp.ord_less_eq_int W2) Z3))) (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int K))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))) (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_real (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_real K))) (forall ((Z3 tptp.int) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (= (@ tptp.ring_1_of_int_int Z3) _let_1) (= Z3 _let_1)))) (forall ((Z3 tptp.int) (N2 tptp.num)) (= (= (@ tptp.ring_1_of_int_real Z3) (@ tptp.numeral_numeral_real N2)) (= Z3 (@ tptp.numeral_numeral_int N2)))) (forall ((W2 tptp.int) (Z3 tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real W2)) (@ tptp.ring_1_of_int_real Z3)) (@ (@ tptp.ord_less_int W2) Z3))) (forall ((W2 tptp.int) (Z3 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int W2)) (@ tptp.ring_1_of_int_int Z3)) (@ (@ tptp.ord_less_int W2) Z3))) (= (@ tptp.ring_1_of_int_int tptp.one_one_int) tptp.one_one_int) (= (@ tptp.ring_17405671764205052669omplex tptp.one_one_int) tptp.one_one_complex) (= (@ tptp.ring_1_of_int_real tptp.one_one_int) tptp.one_one_real) (forall ((Z3 tptp.int)) (= (= (@ tptp.ring_1_of_int_int Z3) tptp.one_one_int) (= Z3 tptp.one_one_int))) (forall ((Z3 tptp.int)) (= (= (@ tptp.ring_17405671764205052669omplex Z3) tptp.one_one_complex) (= Z3 tptp.one_one_int))) (forall ((Z3 tptp.int)) (= (= (@ tptp.ring_1_of_int_real Z3) tptp.one_one_real) (= Z3 tptp.one_one_int))) (forall ((W2 tptp.int) (Z3 tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.times_times_int W2) Z3)) (@ (@ tptp.times_times_int (@ tptp.ring_1_of_int_int W2)) (@ tptp.ring_1_of_int_int Z3)))) (forall ((W2 tptp.int) (Z3 tptp.int)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int W2) Z3)) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real W2)) (@ tptp.ring_1_of_int_real Z3)))) (forall ((W2 tptp.int) (Z3 tptp.int)) (= (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.times_times_int W2) Z3)) (@ (@ tptp.times_times_complex (@ tptp.ring_17405671764205052669omplex W2)) (@ tptp.ring_17405671764205052669omplex Z3)))) (forall ((W2 tptp.int) (Z3 tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.plus_plus_int W2) Z3)) (@ (@ tptp.plus_plus_int (@ tptp.ring_1_of_int_int W2)) (@ tptp.ring_1_of_int_int Z3)))) (forall ((W2 tptp.int) (Z3 tptp.int)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int W2) Z3)) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real W2)) (@ tptp.ring_1_of_int_real Z3)))) (forall ((Z3 tptp.int)) (= (@ tptp.ring_1_of_int_int (@ tptp.uminus_uminus_int Z3)) (@ tptp.uminus_uminus_int (@ tptp.ring_1_of_int_int Z3)))) (forall ((Z3 tptp.int)) (= (@ tptp.ring_1_of_int_real (@ tptp.uminus_uminus_int Z3)) (@ tptp.uminus_uminus_real (@ tptp.ring_1_of_int_real Z3)))) (= (@ tptp.bit_se2000444600071755411sk_int tptp.zero_zero_nat) tptp.zero_zero_int) (= (@ tptp.bit_se2002935070580805687sk_nat tptp.zero_zero_nat) tptp.zero_zero_nat) (forall ((N2 tptp.nat)) (= (= (@ tptp.bit_se2000444600071755411sk_int N2) tptp.zero_zero_int) (= N2 tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (= (= (@ tptp.bit_se2002935070580805687sk_nat N2) tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat))) (forall ((W2 tptp.int) (Z3 tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.minus_minus_int W2) Z3)) (@ (@ tptp.minus_minus_int (@ tptp.ring_1_of_int_int W2)) (@ tptp.ring_1_of_int_int Z3)))) (forall ((W2 tptp.int) (Z3 tptp.int)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.minus_minus_int W2) Z3)) (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real W2)) (@ tptp.ring_1_of_int_real Z3)))) (forall ((Z3 tptp.int) (N2 tptp.nat)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.power_power_int Z3) N2)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real Z3)) N2))) (forall ((Z3 tptp.int) (N2 tptp.nat)) (= (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.power_power_int Z3) N2)) (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex Z3)) N2))) (forall ((Z3 tptp.int) (N2 tptp.nat)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.power_power_int Z3) N2)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int Z3)) N2))) (forall ((B2 tptp.int) (W2 tptp.nat) (X tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B2)) W2) (@ tptp.ring_1_of_int_real X)) (= (@ (@ tptp.power_power_int B2) W2) X))) (forall ((B2 tptp.int) (W2 tptp.nat) (X tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex B2)) W2) (@ tptp.ring_17405671764205052669omplex X)) (= (@ (@ tptp.power_power_int B2) W2) X))) (forall ((B2 tptp.int) (W2 tptp.nat) (X tptp.int)) (= (= (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B2)) W2) (@ tptp.ring_1_of_int_int X)) (= (@ (@ tptp.power_power_int B2) W2) X))) (forall ((X tptp.int) (B2 tptp.int) (W2 tptp.nat)) (= (= (@ tptp.ring_1_of_int_real X) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B2)) W2)) (= X (@ (@ tptp.power_power_int B2) W2)))) (forall ((X tptp.int) (B2 tptp.int) (W2 tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex X) (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex B2)) W2)) (= X (@ (@ tptp.power_power_int B2) W2)))) (forall ((X tptp.int) (B2 tptp.int) (W2 tptp.nat)) (= (= (@ tptp.ring_1_of_int_int X) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B2)) W2)) (= X (@ (@ tptp.power_power_int B2) W2)))) (= (@ tptp.bit_se2000444600071755411sk_int _let_80) tptp.one_one_int) (= (@ tptp.bit_se2002935070580805687sk_nat _let_80) tptp.one_one_nat) (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ring_1_of_int_real Z3)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z3))) (forall ((Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z3)) (@ _let_1 Z3)))) (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z3)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_int Z3) tptp.zero_zero_int))) (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int Z3)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int Z3) tptp.zero_zero_int))) (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.ring_1_of_int_real Z3)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z3))) (forall ((Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z3)) (@ _let_1 Z3)))) (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z3)) tptp.zero_zero_real) (@ (@ tptp.ord_less_int Z3) tptp.zero_zero_int))) (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int Z3)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Z3) tptp.zero_zero_int))) (forall ((N2 tptp.num) (Z3 tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N2)) (@ tptp.ring_1_of_int_real Z3)) (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N2)) Z3))) (forall ((N2 tptp.num) (Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z3)) (@ _let_1 Z3)))) (forall ((Z3 tptp.int) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z3)) (@ tptp.numeral_numeral_real N2)) (@ (@ tptp.ord_less_eq_int Z3) (@ tptp.numeral_numeral_int N2)))) (forall ((Z3 tptp.int) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int Z3)) _let_1) (@ (@ tptp.ord_less_eq_int Z3) _let_1)))) (forall ((Z3 tptp.int) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int Z3)) _let_1) (@ (@ tptp.ord_less_int Z3) _let_1)))) (forall ((Z3 tptp.int) (N2 tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z3)) (@ tptp.numeral_numeral_real N2)) (@ (@ tptp.ord_less_int Z3) (@ tptp.numeral_numeral_int N2)))) (forall ((N2 tptp.num) (Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z3)) (@ _let_1 Z3)))) (forall ((N2 tptp.num) (Z3 tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N2)) (@ tptp.ring_1_of_int_real Z3)) (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N2)) Z3))) (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.ring_1_of_int_real Z3)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z3))) (forall ((Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.one_one_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z3)) (@ _let_1 Z3)))) (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z3)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_int Z3) tptp.one_one_int))) (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int Z3)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int Z3) tptp.one_one_int))) (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z3)) tptp.one_one_real) (@ (@ tptp.ord_less_int Z3) tptp.one_one_int))) (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int Z3)) tptp.one_one_int) (@ (@ tptp.ord_less_int Z3) tptp.one_one_int))) (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.ring_1_of_int_real Z3)) (@ (@ tptp.ord_less_int tptp.one_one_int) Z3))) (forall ((Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z3)) (@ _let_1 Z3)))) (forall ((X tptp.int) (B2 tptp.int) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real X)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B2)) W2)) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.power_power_int B2) W2)))) (forall ((X tptp.int) (B2 tptp.int) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int X)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B2)) W2)) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.power_power_int B2) W2)))) (forall ((B2 tptp.int) (W2 tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B2)) W2)) (@ tptp.ring_1_of_int_real X)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B2) W2)) X))) (forall ((B2 tptp.int) (W2 tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B2)) W2)) (@ tptp.ring_1_of_int_int X)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B2) W2)) X))) (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X)) N2) (@ tptp.ring_17405671764205052669omplex Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2) Y))) (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2))) (= (= _let_1 (@ tptp.ring_1_of_int_int Y)) (= _let_1 Y)))) (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N2) (@ tptp.ring_1_of_int_real Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2) Y))) (forall ((Y tptp.int) (X tptp.num) (N2 tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex Y) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X)) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))) (forall ((Y tptp.int) (X tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2))) (= (= (@ tptp.ring_1_of_int_int Y) _let_1) (= Y _let_1)))) (forall ((Y tptp.int) (X tptp.num) (N2 tptp.nat)) (= (= (@ tptp.ring_1_of_int_real Y) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))) (forall ((M2 tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M2))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.inc M2))))) (forall ((M2 tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc M2))))) (forall ((M2 tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.inc M2))))) (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_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_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 ((B2 tptp.int) (W2 tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B2)) W2)) (@ tptp.ring_1_of_int_real X)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B2) W2)) X))) (forall ((B2 tptp.int) (W2 tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B2)) W2)) (@ tptp.ring_1_of_int_int X)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B2) W2)) X))) (forall ((X tptp.int) (B2 tptp.int) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real X)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B2)) W2)) (@ (@ tptp.ord_less_int X) (@ (@ tptp.power_power_int B2) W2)))) (forall ((X tptp.int) (B2 tptp.int) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int X)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B2)) W2)) (@ (@ tptp.ord_less_int X) (@ (@ tptp.power_power_int B2) W2)))) (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N2)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))) (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_eq_int A) _let_1)))) (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N2)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)) A))) (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))) (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))) (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N2)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)) A))) (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_int A) _let_1)))) (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N2)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))) (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex X))) N2) (@ tptp.ring_17405671764205052669omplex Y)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2) Y))) (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2))) (= (= _let_1 (@ tptp.ring_1_of_int_int Y)) (= _let_1 Y)))) (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N2) (@ tptp.ring_1_of_int_real Y)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2) Y))) (forall ((Y tptp.int) (X tptp.num) (N2 tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex Y) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex X))) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)))) (forall ((Y tptp.int) (X tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2))) (= (= (@ tptp.ring_1_of_int_int Y) _let_1) (= Y _let_1)))) (forall ((Y tptp.int) (X tptp.num) (N2 tptp.nat)) (= (= (@ tptp.ring_1_of_int_real Y) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)))) (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N2)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)))) (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_eq_int A) _let_1)))) (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N2)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)) A))) (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))) (forall ((X tptp.real)) (exists ((Z tptp.int)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.ring_1_of_int_real Z)))) (forall ((X tptp.real)) (exists ((Z tptp.int)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z)) X))) (forall ((X tptp.real)) (exists ((Z tptp.int)) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real Z)))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_int X))) (= (@ (@ tptp.times_times_int _let_1) Y) (@ (@ tptp.times_times_int Y) _let_1)))) (forall ((X tptp.int) (Y tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real X))) (= (@ (@ tptp.times_times_real _let_1) Y) (@ (@ tptp.times_times_real Y) _let_1)))) (forall ((X tptp.int) (Y tptp.complex)) (let ((_let_1 (@ tptp.ring_17405671764205052669omplex X))) (= (@ (@ tptp.times_times_complex _let_1) Y) (@ (@ tptp.times_times_complex Y) _let_1)))) (forall ((X tptp.int) (Y tptp.int)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.ord_max_int X) Y)) (@ (@ tptp.ord_max_real (@ tptp.ring_1_of_int_real X)) (@ tptp.ring_1_of_int_real Y)))) (forall ((X tptp.int) (Y tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.ord_max_int X) Y)) (@ (@ tptp.ord_max_int (@ tptp.ring_1_of_int_int X)) (@ tptp.ring_1_of_int_int Y)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.bit_se2002935070580805687sk_nat N2))) (forall ((N2 tptp.nat) (K tptp.int) (M2 tptp.nat) (L tptp.int) (R2 tptp.int)) (let ((_let_1 (@ (@ tptp.bit_concat_bit N2) K))) (= (@ _let_1 (@ (@ (@ tptp.bit_concat_bit M2) L) R2)) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.plus_plus_nat M2) N2)) (@ _let_1 L)) R2)))) (forall ((M2 tptp.int) (N2 tptp.int)) (let ((_let_1 (@ tptp.set_or1266510415728281911st_int M2))) (let ((_let_2 (@ (@ tptp.plus_plus_int tptp.one_one_int) N2))) (=> (@ (@ tptp.ord_less_eq_int M2) _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.insert_int _let_2) (@ _let_1 N2))))))) (= tptp.set_or1266510415728281911st_int (lambda ((I3 tptp.int) (J2 tptp.int)) (@ (@ (@ tptp.if_set_int (@ (@ tptp.ord_less_int J2) I3)) tptp.bot_bot_set_int) (@ (@ tptp.insert_int I3) (@ (@ tptp.set_or1266510415728281911st_int (@ (@ tptp.plus_plus_int I3) tptp.one_one_int)) J2))))) (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 ((Z3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z3) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ring_1_of_int_real Z3)))) (forall ((Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z3) (@ _let_1 (@ tptp.ring_1_of_int_int Z3))))) (forall ((Z3 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z3) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.ring_1_of_int_real Z3)))) (forall ((Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 Z3) (@ _let_1 (@ tptp.ring_1_of_int_int Z3))))) (forall ((X tptp.real)) (exists ((X5 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real X5)) X) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int X5) tptp.one_one_int))) (forall ((Y6 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Y6)) X) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Y6) tptp.one_one_int)))) (= Y6 X5)))))) (forall ((X tptp.real)) (exists ((Z tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z)) X) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Z) tptp.one_one_int)))))) (forall ((X tptp.num)) (= (@ tptp.numera6690914467698888265omplex (@ tptp.inc X)) (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex X)) tptp.one_one_complex))) (forall ((X tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.inc X)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat X)) tptp.one_one_nat))) (forall ((X tptp.num)) (= (@ tptp.numera1916890842035813515d_enat (@ tptp.inc X)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.numera1916890842035813515d_enat X)) tptp.one_on7984719198319812577d_enat))) (forall ((X tptp.num)) (= (@ tptp.numeral_numeral_int (@ tptp.inc X)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int X)) tptp.one_one_int))) (forall ((X tptp.num)) (= (@ tptp.numeral_numeral_real (@ tptp.inc X)) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real X)) tptp.one_one_real))) (forall ((K tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))) (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_real (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real K)))) (forall ((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 ((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.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2002935070580805687sk_nat N2)) (= N2 tptp.zero_zero_nat))) (forall ((X tptp.real) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ring_1_of_int_real Y))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real X) _let_1)) _let_2) (=> (@ (@ tptp.ord_less_eq_real _let_2) (@ (@ tptp.plus_plus_real X) _let_1)) (= (@ tptp.archim8280529875227126926d_real X) Y)))))) (forall ((X tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X)))) (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X)))) (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X))) (@ (@ tptp.plus_plus_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))) (forall ((M2 tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int M2) N2) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X4 tptp.int)) X4)) (@ (@ tptp.set_or1266510415728281911st_int M2) 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 M2) (@ (@ tptp.minus_minus_int M2) tptp.one_one_int)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))) (forall ((X tptp.int) (Xa2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_3 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 X)) (not (@ _let_2 Xa2)))))) (let ((_let_4 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_5 (and (@ (@ tptp.member_int X) _let_4) (@ (@ tptp.member_int Xa2) _let_4)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X) Xa2) Y) (and (=> _let_5 (= Y (@ tptp.uminus_uminus_int _let_3))) (=> (not _let_5) (= Y (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int X) _let_1)) (@ (@ tptp.divide_divide_int Xa2) _let_1)))))))))))))) (= tptp.bit_se725231765392027082nd_int (lambda ((K2 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_3 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 K2)) (not (@ _let_2 L2)))))) (let ((_let_4 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (@ (@ (@ tptp.if_int (and (@ (@ tptp.member_int K2) _let_4) (@ (@ tptp.member_int L2) _let_4))) (@ tptp.uminus_uminus_int _let_3)) (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1))))))))))) (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 ((X tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.zero_zero_int) X) tptp.zero_zero_int)) (forall ((X tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int X) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((A2 tptp.set_int)) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((Uu3 tptp.int)) tptp.zero_zero_int)) A2) tptp.zero_zero_int)) (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Uu3 tptp.nat)) tptp.zero_zero_nat)) A2) tptp.zero_zero_nat)) (forall ((A2 tptp.set_complex)) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((Uu3 tptp.complex)) tptp.zero_zero_complex)) A2) tptp.zero_zero_complex)) (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((Uu3 tptp.nat)) tptp.zero_zero_real)) A2) tptp.zero_zero_real)) (forall ((G (-> tptp.extended_enat tptp.nat))) (= (@ (@ tptp.groups2027974829824023292at_nat G) tptp.bot_bo7653980558646680370d_enat) tptp.zero_zero_nat)) (forall ((G (-> tptp.extended_enat tptp.real))) (= (@ (@ tptp.groups4148127829035722712t_real G) tptp.bot_bo7653980558646680370d_enat) tptp.zero_zero_real)) (forall ((G (-> tptp.extended_enat tptp.int))) (= (@ (@ tptp.groups2025484359314973016at_int G) tptp.bot_bo7653980558646680370d_enat) tptp.zero_zero_int)) (forall ((G (-> tptp.extended_enat tptp.complex))) (= (@ (@ tptp.groups6818542070133387226omplex G) tptp.bot_bo7653980558646680370d_enat) tptp.zero_zero_complex)) (forall ((G (-> tptp.extended_enat tptp.extended_enat))) (= (@ (@ tptp.groups2433450451889696826d_enat G) tptp.bot_bo7653980558646680370d_enat) tptp.zero_z5237406670263579293d_enat)) (forall ((G (-> tptp.real tptp.nat))) (= (@ (@ tptp.groups1935376822645274424al_nat G) tptp.bot_bot_set_real) tptp.zero_zero_nat)) (forall ((G (-> tptp.real tptp.real))) (= (@ (@ tptp.groups8097168146408367636l_real G) tptp.bot_bot_set_real) tptp.zero_zero_real)) (forall ((G (-> tptp.real tptp.int))) (= (@ (@ tptp.groups1932886352136224148al_int G) tptp.bot_bot_set_real) tptp.zero_zero_int)) (forall ((G (-> tptp.real tptp.complex))) (= (@ (@ tptp.groups5754745047067104278omplex G) tptp.bot_bot_set_real) tptp.zero_zero_complex)) (forall ((G (-> tptp.real tptp.extended_enat))) (= (@ (@ tptp.groups2800946370649118462d_enat G) tptp.bot_bot_set_real) tptp.zero_z5237406670263579293d_enat)) (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (=> (not (@ tptp.finite3207457112153483333omplex A2)) (= (@ (@ tptp.groups5693394587270226106ex_nat G) A2) tptp.zero_zero_nat))) (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.nat))) (=> (not (@ tptp.finite_finite_int A2)) (= (@ (@ tptp.groups4541462559716669496nt_nat G) A2) tptp.zero_zero_nat))) (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.nat))) (=> (not (@ tptp.finite4001608067531595151d_enat A2)) (= (@ (@ tptp.groups2027974829824023292at_nat G) A2) tptp.zero_zero_nat))) (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.real))) (=> (not (@ tptp.finite3207457112153483333omplex A2)) (= (@ (@ tptp.groups5808333547571424918x_real G) A2) tptp.zero_zero_real))) (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.real))) (=> (not (@ tptp.finite_finite_int A2)) (= (@ (@ tptp.groups8778361861064173332t_real G) A2) tptp.zero_zero_real))) (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.real))) (=> (not (@ tptp.finite4001608067531595151d_enat A2)) (= (@ (@ tptp.groups4148127829035722712t_real G) A2) tptp.zero_zero_real))) (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.int))) (=> (not (@ tptp.finite_finite_nat A2)) (= (@ (@ tptp.groups3539618377306564664at_int G) A2) tptp.zero_zero_int))) (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.int))) (=> (not (@ tptp.finite3207457112153483333omplex A2)) (= (@ (@ tptp.groups5690904116761175830ex_int G) A2) tptp.zero_zero_int))) (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.int))) (=> (not (@ tptp.finite4001608067531595151d_enat A2)) (= (@ (@ tptp.groups2025484359314973016at_int G) A2) tptp.zero_zero_int))) (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.complex))) (=> (not (@ tptp.finite_finite_nat A2)) (= (@ (@ tptp.groups2073611262835488442omplex G) A2) tptp.zero_zero_complex))) (forall ((F3 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex F3) (= (= (@ (@ tptp.groups5693394587270226106ex_nat F) F3) tptp.zero_zero_nat) (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) F3) (= (@ F X4) tptp.zero_zero_nat)))))) (forall ((F3 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int F3) (= (= (@ (@ tptp.groups4541462559716669496nt_nat F) F3) tptp.zero_zero_nat) (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) F3) (= (@ F X4) tptp.zero_zero_nat)))))) (forall ((F3 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat F3) (= (= (@ (@ tptp.groups2027974829824023292at_nat F) F3) tptp.zero_zero_nat) (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) F3) (= (@ F X4) tptp.zero_zero_nat)))))) (forall ((F3 tptp.set_nat) (F (-> tptp.nat tptp.extended_enat))) (=> (@ tptp.finite_finite_nat F3) (= (= (@ (@ tptp.groups7108830773950497114d_enat F) F3) tptp.zero_z5237406670263579293d_enat) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) F3) (= (@ F X4) tptp.zero_z5237406670263579293d_enat)))))) (forall ((F3 tptp.set_complex) (F (-> tptp.complex tptp.extended_enat))) (=> (@ tptp.finite3207457112153483333omplex F3) (= (= (@ (@ tptp.groups1752964319039525884d_enat F) F3) tptp.zero_z5237406670263579293d_enat) (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) F3) (= (@ F X4) tptp.zero_z5237406670263579293d_enat)))))) (forall ((F3 tptp.set_int) (F (-> tptp.int tptp.extended_enat))) (=> (@ tptp.finite_finite_int F3) (= (= (@ (@ tptp.groups4225252721152677374d_enat F) F3) tptp.zero_z5237406670263579293d_enat) (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) F3) (= (@ F X4) tptp.zero_z5237406670263579293d_enat)))))) (forall ((F3 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.extended_enat))) (=> (@ tptp.finite4001608067531595151d_enat F3) (= (= (@ (@ tptp.groups2433450451889696826d_enat F) F3) tptp.zero_z5237406670263579293d_enat) (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) F3) (= (@ F X4) tptp.zero_z5237406670263579293d_enat)))))) (forall ((F3 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat F3) (= (= (@ (@ tptp.groups3542108847815614940at_nat F) F3) tptp.zero_zero_nat) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) F3) (= (@ F X4) tptp.zero_zero_nat)))))) (= (@ tptp.archim8280529875227126926d_real tptp.zero_zero_real) tptp.zero_zero_int) (forall ((S2 tptp.set_real) (A tptp.real) (B2 (-> tptp.real tptp.nat))) (let ((_let_1 (@ (@ tptp.member_real A) S2))) (=> (@ tptp.finite_finite_real S2) (and (=> _let_1 (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) tptp.zero_zero_nat))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) tptp.zero_zero_nat))) S2) tptp.zero_zero_nat)))))) (forall ((S2 tptp.set_complex) (A tptp.complex) (B2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_1 (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) tptp.zero_zero_nat))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) tptp.zero_zero_nat))) S2) tptp.zero_zero_nat)))))) (forall ((S2 tptp.set_int) (A tptp.int) (B2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ (@ tptp.member_int A) S2))) (=> (@ tptp.finite_finite_int S2) (and (=> _let_1 (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) tptp.zero_zero_nat))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) tptp.zero_zero_nat))) S2) tptp.zero_zero_nat)))))) (forall ((S2 tptp.set_Extended_enat) (A tptp.extended_enat) (B2 (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ (@ tptp.member_Extended_enat A) S2))) (=> (@ tptp.finite4001608067531595151d_enat S2) (and (=> _let_1 (= (@ (@ tptp.groups2027974829824023292at_nat (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) tptp.zero_zero_nat))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups2027974829824023292at_nat (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) tptp.zero_zero_nat))) S2) tptp.zero_zero_nat)))))) (forall ((S2 tptp.set_real) (A tptp.real) (B2 (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.member_real A) S2))) (=> (@ tptp.finite_finite_real S2) (and (=> _let_1 (= (@ (@ tptp.groups8097168146408367636l_real (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B2 K2)) tptp.zero_zero_real))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups8097168146408367636l_real (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B2 K2)) tptp.zero_zero_real))) S2) tptp.zero_zero_real)))))) (forall ((S2 tptp.set_complex) (A tptp.complex) (B2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_1 (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B2 K2)) tptp.zero_zero_real))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B2 K2)) tptp.zero_zero_real))) S2) tptp.zero_zero_real)))))) (forall ((S2 tptp.set_int) (A tptp.int) (B2 (-> tptp.int tptp.real))) (let ((_let_1 (@ (@ tptp.member_int A) S2))) (=> (@ tptp.finite_finite_int S2) (and (=> _let_1 (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B2 K2)) tptp.zero_zero_real))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B2 K2)) tptp.zero_zero_real))) S2) tptp.zero_zero_real)))))) (forall ((S2 tptp.set_Extended_enat) (A tptp.extended_enat) (B2 (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ (@ tptp.member_Extended_enat A) S2))) (=> (@ tptp.finite4001608067531595151d_enat S2) (and (=> _let_1 (= (@ (@ tptp.groups4148127829035722712t_real (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B2 K2)) tptp.zero_zero_real))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups4148127829035722712t_real (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B2 K2)) tptp.zero_zero_real))) S2) tptp.zero_zero_real)))))) (forall ((S2 tptp.set_real) (A tptp.real) (B2 (-> tptp.real tptp.int))) (let ((_let_1 (@ (@ tptp.member_real A) S2))) (=> (@ tptp.finite_finite_real S2) (and (=> _let_1 (= (@ (@ tptp.groups1932886352136224148al_int (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B2 K2)) tptp.zero_zero_int))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups1932886352136224148al_int (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B2 K2)) tptp.zero_zero_int))) S2) tptp.zero_zero_int)))))) (forall ((S2 tptp.set_nat) (A tptp.nat) (B2 (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.member_nat A) S2))) (=> (@ tptp.finite_finite_nat S2) (and (=> _let_1 (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B2 K2)) tptp.zero_zero_int))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B2 K2)) tptp.zero_zero_int))) S2) tptp.zero_zero_int)))))) (forall ((S2 tptp.set_real) (A tptp.real) (B2 (-> tptp.real tptp.nat))) (let ((_let_1 (@ (@ tptp.member_real A) S2))) (=> (@ tptp.finite_finite_real S2) (and (=> _let_1 (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_nat (= A K2)) (@ B2 K2)) tptp.zero_zero_nat))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_nat (= A K2)) (@ B2 K2)) tptp.zero_zero_nat))) S2) tptp.zero_zero_nat)))))) (forall ((S2 tptp.set_complex) (A tptp.complex) (B2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_1 (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_nat (= A K2)) (@ B2 K2)) tptp.zero_zero_nat))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_nat (= A K2)) (@ B2 K2)) tptp.zero_zero_nat))) S2) tptp.zero_zero_nat)))))) (forall ((S2 tptp.set_int) (A tptp.int) (B2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ (@ tptp.member_int A) S2))) (=> (@ tptp.finite_finite_int S2) (and (=> _let_1 (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_nat (= A K2)) (@ B2 K2)) tptp.zero_zero_nat))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_nat (= A K2)) (@ B2 K2)) tptp.zero_zero_nat))) S2) tptp.zero_zero_nat)))))) (forall ((S2 tptp.set_Extended_enat) (A tptp.extended_enat) (B2 (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ (@ tptp.member_Extended_enat A) S2))) (=> (@ tptp.finite4001608067531595151d_enat S2) (and (=> _let_1 (= (@ (@ tptp.groups2027974829824023292at_nat (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_nat (= A K2)) (@ B2 K2)) tptp.zero_zero_nat))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups2027974829824023292at_nat (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_nat (= A K2)) (@ B2 K2)) tptp.zero_zero_nat))) S2) tptp.zero_zero_nat)))))) (forall ((S2 tptp.set_real) (A tptp.real) (B2 (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.member_real A) S2))) (=> (@ tptp.finite_finite_real S2) (and (=> _let_1 (= (@ (@ tptp.groups8097168146408367636l_real (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_real (= A K2)) (@ B2 K2)) tptp.zero_zero_real))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups8097168146408367636l_real (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_real (= A K2)) (@ B2 K2)) tptp.zero_zero_real))) S2) tptp.zero_zero_real)))))) (forall ((S2 tptp.set_complex) (A tptp.complex) (B2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_1 (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_real (= A K2)) (@ B2 K2)) tptp.zero_zero_real))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_real (= A K2)) (@ B2 K2)) tptp.zero_zero_real))) S2) tptp.zero_zero_real)))))) (forall ((S2 tptp.set_int) (A tptp.int) (B2 (-> tptp.int tptp.real))) (let ((_let_1 (@ (@ tptp.member_int A) S2))) (=> (@ tptp.finite_finite_int S2) (and (=> _let_1 (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_real (= A K2)) (@ B2 K2)) tptp.zero_zero_real))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_real (= A K2)) (@ B2 K2)) tptp.zero_zero_real))) S2) tptp.zero_zero_real)))))) (forall ((S2 tptp.set_Extended_enat) (A tptp.extended_enat) (B2 (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ (@ tptp.member_Extended_enat A) S2))) (=> (@ tptp.finite4001608067531595151d_enat S2) (and (=> _let_1 (= (@ (@ tptp.groups4148127829035722712t_real (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_real (= A K2)) (@ B2 K2)) tptp.zero_zero_real))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups4148127829035722712t_real (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_real (= A K2)) (@ B2 K2)) tptp.zero_zero_real))) S2) tptp.zero_zero_real)))))) (forall ((S2 tptp.set_real) (A tptp.real) (B2 (-> tptp.real tptp.int))) (let ((_let_1 (@ (@ tptp.member_real A) S2))) (=> (@ tptp.finite_finite_real S2) (and (=> _let_1 (= (@ (@ tptp.groups1932886352136224148al_int (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_int (= A K2)) (@ B2 K2)) tptp.zero_zero_int))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups1932886352136224148al_int (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_int (= A K2)) (@ B2 K2)) tptp.zero_zero_int))) S2) tptp.zero_zero_int)))))) (forall ((S2 tptp.set_nat) (A tptp.nat) (B2 (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.member_nat A) S2))) (=> (@ tptp.finite_finite_nat S2) (and (=> _let_1 (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_int (= A K2)) (@ B2 K2)) tptp.zero_zero_int))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_int (= A K2)) (@ B2 K2)) tptp.zero_zero_int))) S2) tptp.zero_zero_int)))))) (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat G))) (=> (@ tptp.finite_finite_real A2) (=> (not (@ (@ tptp.member_real X) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X) A2)) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_1 A2))))))) (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (@ (@ tptp.member_complex X) A2)) (= (@ _let_1 (@ (@ tptp.insert_complex X) A2)) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_1 A2))))))) (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G))) (=> (@ tptp.finite_finite_int A2) (=> (not (@ (@ tptp.member_int X) A2)) (= (@ _let_1 (@ (@ tptp.insert_int X) A2)) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_1 A2))))))) (forall ((A2 tptp.set_Extended_enat) (X tptp.extended_enat) (G (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2027974829824023292at_nat G))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (not (@ (@ tptp.member_Extended_enat X) A2)) (= (@ _let_1 (@ (@ tptp.insert_Extended_enat X) A2)) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_1 A2))))))) (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int G))) (=> (@ tptp.finite_finite_real A2) (=> (not (@ (@ tptp.member_real X) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X) A2)) (@ (@ tptp.plus_plus_int (@ G X)) (@ _let_1 A2))))))) (forall ((A2 tptp.set_nat) (X tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ tptp.finite_finite_nat A2) (=> (not (@ (@ tptp.member_nat X) A2)) (= (@ _let_1 (@ (@ tptp.insert_nat X) A2)) (@ (@ tptp.plus_plus_int (@ G X)) (@ _let_1 A2))))))) (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (@ (@ tptp.member_complex X) A2)) (= (@ _let_1 (@ (@ tptp.insert_complex X) A2)) (@ (@ tptp.plus_plus_int (@ G X)) (@ _let_1 A2))))))) (forall ((A2 tptp.set_Extended_enat) (X tptp.extended_enat) (G (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2025484359314973016at_int G))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (not (@ (@ tptp.member_Extended_enat X) A2)) (= (@ _let_1 (@ (@ tptp.insert_Extended_enat X) A2)) (@ (@ tptp.plus_plus_int (@ G X)) (@ _let_1 A2))))))) (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real G))) (=> (@ tptp.finite_finite_real A2) (=> (not (@ (@ tptp.member_real X) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X) A2)) (@ (@ tptp.plus_plus_real (@ G X)) (@ _let_1 A2))))))) (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (@ (@ tptp.member_complex X) A2)) (= (@ _let_1 (@ (@ tptp.insert_complex X) A2)) (@ (@ tptp.plus_plus_real (@ G X)) (@ _let_1 A2))))))) (forall ((F (-> tptp.complex tptp.int)) (A2 tptp.set_complex)) (= (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.groups5690904116761175830ex_int F) A2)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((X4 tptp.complex)) (@ tptp.ring_17405671764205052669omplex (@ F X4)))) A2))) (forall ((F (-> tptp.nat tptp.int)) (A2 tptp.set_nat)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.groups3539618377306564664at_int F) A2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((X4 tptp.nat)) (@ tptp.ring_1_of_int_real (@ F X4)))) A2))) (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.groups4538972089207619220nt_int F) A2)) (@ (@ tptp.groups8778361861064173332t_real (lambda ((X4 tptp.int)) (@ tptp.ring_1_of_int_real (@ F X4)))) A2))) (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X4 tptp.int)) (@ tptp.ring_1_of_int_int (@ F X4)))) A2))) (forall ((X tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X))) tptp.one_one_int) tptp.zero_zero_int)) (forall ((X tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) tptp.one_one_nat) tptp.zero_zero_nat)) (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) tptp.zero_zero_int)) (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) tptp.zero_zero_nat)) (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y)))))) (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y)))))) (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.int))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (= (@ G X5) tptp.zero_zero_int))) (= (@ (@ tptp.groups4538972089207619220nt_int G) A2) tptp.zero_zero_int))) (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.nat))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (= (@ G X5) tptp.zero_zero_nat))) (= (@ (@ tptp.groups3542108847815614940at_nat G) A2) tptp.zero_zero_nat))) (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.complex))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (= (@ G X5) tptp.zero_zero_complex))) (= (@ (@ tptp.groups7754918857620584856omplex G) A2) tptp.zero_zero_complex))) (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.real))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (= (@ G X5) tptp.zero_zero_real))) (= (@ (@ tptp.groups6591440286371151544t_real G) A2) tptp.zero_zero_real))) (forall ((G (-> tptp.extended_enat tptp.nat)) (A2 tptp.set_Extended_enat)) (=> (not (= (@ (@ tptp.groups2027974829824023292at_nat G) A2) tptp.zero_zero_nat)) (not (forall ((A4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A4) A2) (= (@ G A4) tptp.zero_zero_nat)))))) (forall ((G (-> tptp.real tptp.nat)) (A2 tptp.set_real)) (=> (not (= (@ (@ tptp.groups1935376822645274424al_nat G) A2) tptp.zero_zero_nat)) (not (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) A2) (= (@ G A4) tptp.zero_zero_nat)))))) (forall ((G (-> tptp.int tptp.nat)) (A2 tptp.set_int)) (=> (not (= (@ (@ tptp.groups4541462559716669496nt_nat G) A2) tptp.zero_zero_nat)) (not (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) A2) (= (@ G A4) tptp.zero_zero_nat)))))) (forall ((G (-> tptp.extended_enat tptp.real)) (A2 tptp.set_Extended_enat)) (=> (not (= (@ (@ tptp.groups4148127829035722712t_real G) A2) tptp.zero_zero_real)) (not (forall ((A4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A4) A2) (= (@ G A4) tptp.zero_zero_real)))))) (forall ((G (-> tptp.real tptp.real)) (A2 tptp.set_real)) (=> (not (= (@ (@ tptp.groups8097168146408367636l_real G) A2) tptp.zero_zero_real)) (not (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) A2) (= (@ G A4) tptp.zero_zero_real)))))) (forall ((G (-> tptp.int tptp.real)) (A2 tptp.set_int)) (=> (not (= (@ (@ tptp.groups8778361861064173332t_real G) A2) tptp.zero_zero_real)) (not (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) A2) (= (@ G A4) tptp.zero_zero_real)))))) (forall ((G (-> tptp.extended_enat tptp.int)) (A2 tptp.set_Extended_enat)) (=> (not (= (@ (@ tptp.groups2025484359314973016at_int G) A2) tptp.zero_zero_int)) (not (forall ((A4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A4) A2) (= (@ G A4) tptp.zero_zero_int)))))) (forall ((G (-> tptp.real tptp.int)) (A2 tptp.set_real)) (=> (not (= (@ (@ tptp.groups1932886352136224148al_int G) A2) tptp.zero_zero_int)) (not (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) A2) (= (@ G A4) tptp.zero_zero_int)))))) (forall ((G (-> tptp.nat tptp.int)) (A2 tptp.set_nat)) (=> (not (= (@ (@ tptp.groups3539618377306564664at_int G) A2) tptp.zero_zero_int)) (not (forall ((A4 tptp.nat)) (=> (@ (@ tptp.member_nat A4) A2) (= (@ G A4) tptp.zero_zero_int)))))) (forall ((G (-> tptp.extended_enat tptp.complex)) (A2 tptp.set_Extended_enat)) (=> (not (= (@ (@ tptp.groups6818542070133387226omplex G) A2) tptp.zero_zero_complex)) (not (forall ((A4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A4) A2) (= (@ G A4) tptp.zero_zero_complex)))))) (forall ((K5 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real)) (G (-> tptp.extended_enat tptp.real))) (=> (forall ((I4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I4) K5) (@ (@ tptp.ord_less_eq_real (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups4148127829035722712t_real F) K5)) (@ (@ tptp.groups4148127829035722712t_real G) K5)))) (forall ((K5 tptp.set_real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) K5) (@ (@ tptp.ord_less_eq_real (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8097168146408367636l_real F) K5)) (@ (@ tptp.groups8097168146408367636l_real G) K5)))) (forall ((K5 tptp.set_int) (F (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) K5) (@ (@ tptp.ord_less_eq_real (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8778361861064173332t_real F) K5)) (@ (@ tptp.groups8778361861064173332t_real G) K5)))) (forall ((K5 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat)) (G (-> tptp.extended_enat tptp.nat))) (=> (forall ((I4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I4) K5) (@ (@ tptp.ord_less_eq_nat (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups2027974829824023292at_nat F) K5)) (@ (@ tptp.groups2027974829824023292at_nat G) K5)))) (forall ((K5 tptp.set_real) (F (-> tptp.real tptp.nat)) (G (-> tptp.real tptp.nat))) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) K5) (@ (@ tptp.ord_less_eq_nat (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups1935376822645274424al_nat F) K5)) (@ (@ tptp.groups1935376822645274424al_nat G) K5)))) (forall ((K5 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) K5) (@ (@ tptp.ord_less_eq_nat (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4541462559716669496nt_nat F) K5)) (@ (@ tptp.groups4541462559716669496nt_nat G) K5)))) (forall ((K5 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.int)) (G (-> tptp.extended_enat tptp.int))) (=> (forall ((I4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I4) K5) (@ (@ tptp.ord_less_eq_int (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups2025484359314973016at_int F) K5)) (@ (@ tptp.groups2025484359314973016at_int G) K5)))) (forall ((K5 tptp.set_real) (F (-> tptp.real tptp.int)) (G (-> tptp.real tptp.int))) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) K5) (@ (@ tptp.ord_less_eq_int (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups1932886352136224148al_int F) K5)) (@ (@ tptp.groups1932886352136224148al_int G) K5)))) (forall ((K5 tptp.set_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_int) (F (-> tptp.int tptp.int)) (G (-> tptp.int tptp.int))) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) K5) (@ (@ tptp.ord_less_eq_int (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups4538972089207619220nt_int F) K5)) (@ (@ tptp.groups4538972089207619220nt_int G) K5)))) (forall ((G (-> tptp.int tptp.int)) (H2 (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X4 tptp.int)) (@ (@ tptp.plus_plus_int (@ G X4)) (@ H2 X4)))) A2) (@ (@ tptp.plus_plus_int (@ (@ tptp.groups4538972089207619220nt_int G) A2)) (@ (@ tptp.groups4538972089207619220nt_int H2) A2)))) (forall ((G (-> tptp.nat tptp.nat)) (H2 (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ G X4)) (@ H2 X4)))) A2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups3542108847815614940at_nat G) A2)) (@ (@ tptp.groups3542108847815614940at_nat H2) A2)))) (forall ((G (-> tptp.complex tptp.complex)) (H2 (-> tptp.complex tptp.complex)) (A2 tptp.set_complex)) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X4 tptp.complex)) (@ (@ tptp.plus_plus_complex (@ G X4)) (@ H2 X4)))) A2) (@ (@ tptp.plus_plus_complex (@ (@ tptp.groups7754918857620584856omplex G) A2)) (@ (@ tptp.groups7754918857620584856omplex H2) A2)))) (forall ((G (-> tptp.nat tptp.real)) (H2 (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((X4 tptp.nat)) (@ (@ tptp.plus_plus_real (@ G X4)) (@ H2 X4)))) A2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real G) A2)) (@ (@ tptp.groups6591440286371151544t_real H2) A2)))) (forall ((A2 tptp.set_real) (B tptp.set_int) (G (-> tptp.real tptp.int tptp.int)) (R (-> tptp.real tptp.int Bool))) (=> (@ tptp.finite_finite_real A2) (=> (@ tptp.finite_finite_int B) (= (@ (@ tptp.groups1932886352136224148al_int (lambda ((X4 tptp.real)) (@ (@ tptp.groups4538972089207619220nt_int (@ G X4)) (@ tptp.collect_int (lambda ((Y5 tptp.int)) (and (@ (@ tptp.member_int Y5) B) (@ (@ R X4) Y5))))))) A2) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((Y5 tptp.int)) (@ (@ tptp.groups1932886352136224148al_int (lambda ((X4 tptp.real)) (@ (@ G X4) Y5))) (@ tptp.collect_real (lambda ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) A2) (@ (@ R X4) Y5))))))) B))))) (forall ((A2 tptp.set_nat) (B tptp.set_int) (G (-> tptp.nat tptp.int tptp.int)) (R (-> tptp.nat tptp.int Bool))) (=> (@ tptp.finite_finite_nat A2) (=> (@ tptp.finite_finite_int B) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((X4 tptp.nat)) (@ (@ tptp.groups4538972089207619220nt_int (@ G X4)) (@ tptp.collect_int (lambda ((Y5 tptp.int)) (and (@ (@ tptp.member_int Y5) B) (@ (@ R X4) Y5))))))) A2) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((Y5 tptp.int)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((X4 tptp.nat)) (@ (@ G X4) Y5))) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A2) (@ (@ R X4) Y5))))))) B))))) (forall ((A2 tptp.set_complex) (B tptp.set_int) (G (-> tptp.complex tptp.int tptp.int)) (R (-> tptp.complex tptp.int Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ tptp.finite_finite_int B) (= (@ (@ tptp.groups5690904116761175830ex_int (lambda ((X4 tptp.complex)) (@ (@ tptp.groups4538972089207619220nt_int (@ G X4)) (@ tptp.collect_int (lambda ((Y5 tptp.int)) (and (@ (@ tptp.member_int Y5) B) (@ (@ R X4) Y5))))))) A2) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((Y5 tptp.int)) (@ (@ tptp.groups5690904116761175830ex_int (lambda ((X4 tptp.complex)) (@ (@ G X4) Y5))) (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A2) (@ (@ R X4) Y5))))))) B))))) (forall ((A2 tptp.set_Extended_enat) (B tptp.set_int) (G (-> tptp.extended_enat tptp.int tptp.int)) (R (-> tptp.extended_enat tptp.int Bool))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ tptp.finite_finite_int B) (= (@ (@ tptp.groups2025484359314973016at_int (lambda ((X4 tptp.extended_enat)) (@ (@ tptp.groups4538972089207619220nt_int (@ G X4)) (@ tptp.collect_int (lambda ((Y5 tptp.int)) (and (@ (@ tptp.member_int Y5) B) (@ (@ R X4) Y5))))))) A2) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((Y5 tptp.int)) (@ (@ tptp.groups2025484359314973016at_int (lambda ((X4 tptp.extended_enat)) (@ (@ G X4) Y5))) (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) A2) (@ (@ R X4) Y5))))))) B))))) (forall ((A2 tptp.set_real) (B tptp.set_nat) (G (-> tptp.real tptp.nat tptp.nat)) (R (-> tptp.real tptp.nat Bool))) (=> (@ tptp.finite_finite_real A2) (=> (@ tptp.finite_finite_nat B) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((X4 tptp.real)) (@ (@ tptp.groups3542108847815614940at_nat (@ G X4)) (@ tptp.collect_nat (lambda ((Y5 tptp.nat)) (and (@ (@ tptp.member_nat Y5) B) (@ (@ R X4) Y5))))))) A2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Y5 tptp.nat)) (@ (@ tptp.groups1935376822645274424al_nat (lambda ((X4 tptp.real)) (@ (@ G X4) Y5))) (@ tptp.collect_real (lambda ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) A2) (@ (@ R X4) Y5))))))) B))))) (forall ((A2 tptp.set_complex) (B tptp.set_nat) (G (-> tptp.complex tptp.nat tptp.nat)) (R (-> tptp.complex tptp.nat Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ tptp.finite_finite_nat B) (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((X4 tptp.complex)) (@ (@ tptp.groups3542108847815614940at_nat (@ G X4)) (@ tptp.collect_nat (lambda ((Y5 tptp.nat)) (and (@ (@ tptp.member_nat Y5) B) (@ (@ R X4) Y5))))))) A2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Y5 tptp.nat)) (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((X4 tptp.complex)) (@ (@ G X4) Y5))) (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A2) (@ (@ R X4) Y5))))))) B))))) (forall ((A2 tptp.set_int) (B tptp.set_nat) (G (-> tptp.int tptp.nat tptp.nat)) (R (-> tptp.int tptp.nat Bool))) (=> (@ tptp.finite_finite_int A2) (=> (@ tptp.finite_finite_nat B) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X4 tptp.int)) (@ (@ tptp.groups3542108847815614940at_nat (@ G X4)) (@ tptp.collect_nat (lambda ((Y5 tptp.nat)) (and (@ (@ tptp.member_nat Y5) B) (@ (@ R X4) Y5))))))) A2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Y5 tptp.nat)) (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X4 tptp.int)) (@ (@ G X4) Y5))) (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A2) (@ (@ R X4) Y5))))))) B))))) (forall ((A2 tptp.set_Extended_enat) (B tptp.set_nat) (G (-> tptp.extended_enat tptp.nat tptp.nat)) (R (-> tptp.extended_enat tptp.nat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ tptp.finite_finite_nat B) (= (@ (@ tptp.groups2027974829824023292at_nat (lambda ((X4 tptp.extended_enat)) (@ (@ tptp.groups3542108847815614940at_nat (@ G X4)) (@ tptp.collect_nat (lambda ((Y5 tptp.nat)) (and (@ (@ tptp.member_nat Y5) B) (@ (@ R X4) Y5))))))) A2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Y5 tptp.nat)) (@ (@ tptp.groups2027974829824023292at_nat (lambda ((X4 tptp.extended_enat)) (@ (@ G X4) Y5))) (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) A2) (@ (@ R X4) Y5))))))) B))))) (forall ((A2 tptp.set_real) (B tptp.set_complex) (G (-> tptp.real tptp.complex tptp.complex)) (R (-> tptp.real tptp.complex Bool))) (=> (@ tptp.finite_finite_real A2) (=> (@ tptp.finite3207457112153483333omplex B) (= (@ (@ tptp.groups5754745047067104278omplex (lambda ((X4 tptp.real)) (@ (@ tptp.groups7754918857620584856omplex (@ G X4)) (@ tptp.collect_complex (lambda ((Y5 tptp.complex)) (and (@ (@ tptp.member_complex Y5) B) (@ (@ R X4) Y5))))))) A2) (@ (@ tptp.groups7754918857620584856omplex (lambda ((Y5 tptp.complex)) (@ (@ tptp.groups5754745047067104278omplex (lambda ((X4 tptp.real)) (@ (@ G X4) Y5))) (@ tptp.collect_real (lambda ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) A2) (@ (@ R X4) Y5))))))) B))))) (forall ((A2 tptp.set_nat) (B tptp.set_complex) (G (-> tptp.nat tptp.complex tptp.complex)) (R (-> tptp.nat tptp.complex Bool))) (=> (@ tptp.finite_finite_nat A2) (=> (@ tptp.finite3207457112153483333omplex B) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((X4 tptp.nat)) (@ (@ tptp.groups7754918857620584856omplex (@ G X4)) (@ tptp.collect_complex (lambda ((Y5 tptp.complex)) (and (@ (@ tptp.member_complex Y5) B) (@ (@ R X4) Y5))))))) A2) (@ (@ tptp.groups7754918857620584856omplex (lambda ((Y5 tptp.complex)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((X4 tptp.nat)) (@ (@ G X4) Y5))) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A2) (@ (@ R X4) Y5))))))) B))))) (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.extended_enat))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) tptp.zero_z5237406670263579293d_enat))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups2433450451889696826d_enat F) A2)) tptp.zero_z5237406670263579293d_enat))) (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.extended_enat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) tptp.zero_z5237406670263579293d_enat))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups2800946370649118462d_enat F) A2)) tptp.zero_z5237406670263579293d_enat))) (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.extended_enat))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) tptp.zero_z5237406670263579293d_enat))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups7108830773950497114d_enat F) A2)) tptp.zero_z5237406670263579293d_enat))) (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.extended_enat))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) tptp.zero_z5237406670263579293d_enat))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups4225252721152677374d_enat F) A2)) tptp.zero_z5237406670263579293d_enat))) (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) A2) (@ (@ tptp.ord_less_eq_real (@ F X5)) tptp.zero_zero_real))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups4148127829035722712t_real F) A2)) tptp.zero_zero_real))) (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))) (@ (@ 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(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_Extended_enat) (F (-> tptp.extended_enat tptp.extended_enat))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.groups2433450451889696826d_enat F) A2)))) (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.extended_enat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.groups2800946370649118462d_enat F) A2)))) (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.extended_enat))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.groups7108830773950497114d_enat F) A2)))) (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.extended_enat))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.groups4225252721152677374d_enat F) A2)))) (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ 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((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X5)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups1935376822645274424al_nat F) A2)))) (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X5)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups4541462559716669496nt_nat F) A2)))) (forall ((F (-> tptp.real tptp.real)) (I6 tptp.set_real) (G (-> tptp.real tptp.real)) (I tptp.real)) (=> (= (@ (@ tptp.groups8097168146408367636l_real F) I6) (@ (@ tptp.groups8097168146408367636l_real G) I6)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_real (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_real I) I6) (=> (@ tptp.finite_finite_real I6) (= (@ F I) (@ G I))))))) (forall ((F (-> tptp.complex tptp.real)) (I6 tptp.set_complex) (G (-> tptp.complex tptp.real)) (I tptp.complex)) (=> (= (@ (@ tptp.groups5808333547571424918x_real F) I6) (@ (@ tptp.groups5808333547571424918x_real G) I6)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_eq_real (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_complex I) I6) (=> (@ tptp.finite3207457112153483333omplex I6) (= (@ F I) (@ G I))))))) (forall ((F (-> tptp.int tptp.real)) (I6 tptp.set_int) (G (-> tptp.int tptp.real)) (I tptp.int)) (=> (= (@ (@ tptp.groups8778361861064173332t_real F) I6) (@ (@ tptp.groups8778361861064173332t_real G) I6)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_eq_real (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_int I) I6) (=> (@ tptp.finite_finite_int I6) (= (@ F I) (@ G I))))))) (forall ((F (-> tptp.extended_enat tptp.real)) (I6 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.real)) (I tptp.extended_enat)) (=> (= (@ (@ tptp.groups4148127829035722712t_real F) I6) (@ (@ tptp.groups4148127829035722712t_real G) I6)) (=> (forall ((I4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I4) I6) (@ (@ tptp.ord_less_eq_real (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_Extended_enat I) I6) (=> (@ tptp.finite4001608067531595151d_enat I6) (= (@ F I) (@ G I))))))) (forall ((F (-> tptp.real tptp.nat)) (I6 tptp.set_real) (G (-> tptp.real tptp.nat)) (I tptp.real)) (=> (= (@ (@ tptp.groups1935376822645274424al_nat F) I6) (@ (@ tptp.groups1935376822645274424al_nat G) I6)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_nat (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_real I) I6) (=> (@ tptp.finite_finite_real I6) (= (@ F I) (@ G I))))))) (forall ((F (-> tptp.complex tptp.nat)) (I6 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (I tptp.complex)) (=> (= (@ (@ tptp.groups5693394587270226106ex_nat F) I6) (@ (@ tptp.groups5693394587270226106ex_nat G) I6)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_eq_nat (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_complex I) I6) (=> (@ tptp.finite3207457112153483333omplex I6) (= (@ F I) (@ G I))))))) (forall ((F (-> tptp.int tptp.nat)) (I6 tptp.set_int) (G (-> tptp.int tptp.nat)) (I tptp.int)) (=> (= (@ (@ tptp.groups4541462559716669496nt_nat F) I6) (@ (@ tptp.groups4541462559716669496nt_nat G) I6)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_eq_nat (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_int I) I6) (=> (@ tptp.finite_finite_int I6) (= (@ F I) (@ G I))))))) (forall ((F (-> tptp.extended_enat tptp.nat)) (I6 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.nat)) (I tptp.extended_enat)) (=> (= (@ (@ tptp.groups2027974829824023292at_nat F) I6) (@ (@ tptp.groups2027974829824023292at_nat G) I6)) (=> (forall ((I4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I4) I6) (@ (@ tptp.ord_less_eq_nat (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_Extended_enat I) I6) (=> (@ tptp.finite4001608067531595151d_enat I6) (= (@ F I) (@ G I))))))) (forall ((F (-> tptp.real tptp.int)) (I6 tptp.set_real) (G (-> tptp.real tptp.int)) (I tptp.real)) (=> (= (@ (@ tptp.groups1932886352136224148al_int F) I6) (@ (@ tptp.groups1932886352136224148al_int G) I6)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_int (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_real I) I6) (=> (@ tptp.finite_finite_real I6) (= (@ F I) (@ G I))))))) (forall ((F (-> tptp.nat tptp.int)) (I6 tptp.set_nat) (G (-> tptp.nat tptp.int)) (I tptp.nat)) (=> (= (@ (@ tptp.groups3539618377306564664at_int F) I6) (@ (@ tptp.groups3539618377306564664at_int G) I6)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_eq_int (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_nat I) I6) (=> (@ tptp.finite_finite_nat I6) (= (@ F I) (@ G I))))))) (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.nat)) (P (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A2) (= (@ (@ tptp.groups1935376822645274424al_nat G) (@ tptp.collect_real (lambda ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) A2) (@ P X4))))) (@ (@ tptp.groups1935376822645274424al_nat (lambda ((X4 tptp.real)) (@ (@ (@ tptp.if_nat (@ P X4)) (@ G X4)) tptp.zero_zero_nat))) A2)))) (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (P (-> tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ (@ tptp.groups5693394587270226106ex_nat G) (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A2) (@ P X4))))) (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((X4 tptp.complex)) (@ (@ (@ tptp.if_nat (@ P X4)) (@ G X4)) tptp.zero_zero_nat))) A2)))) (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.nat)) (P (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A2) (= (@ (@ tptp.groups4541462559716669496nt_nat G) (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A2) (@ P X4))))) (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_nat (@ P X4)) (@ G X4)) tptp.zero_zero_nat))) A2)))) (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.nat)) (P (-> tptp.extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ (@ tptp.groups2027974829824023292at_nat G) (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) A2) (@ P X4))))) (@ (@ tptp.groups2027974829824023292at_nat (lambda ((X4 tptp.extended_enat)) (@ (@ (@ tptp.if_nat (@ P X4)) (@ G X4)) tptp.zero_zero_nat))) A2)))) (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.real)) (P (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A2) (= (@ (@ tptp.groups8097168146408367636l_real G) (@ tptp.collect_real (lambda ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) A2) (@ P X4))))) (@ (@ tptp.groups8097168146408367636l_real (lambda ((X4 tptp.real)) (@ (@ (@ tptp.if_real (@ P X4)) (@ G X4)) tptp.zero_zero_real))) A2)))) (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.real)) (P (-> tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ (@ tptp.groups5808333547571424918x_real G) (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A2) (@ P X4))))) (@ (@ tptp.groups5808333547571424918x_real (lambda ((X4 tptp.complex)) (@ (@ (@ tptp.if_real (@ P X4)) (@ G X4)) tptp.zero_zero_real))) A2)))) (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.real)) (P (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A2) (= (@ (@ tptp.groups8778361861064173332t_real G) (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A2) (@ P X4))))) (@ (@ tptp.groups8778361861064173332t_real (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_real (@ P X4)) (@ G X4)) tptp.zero_zero_real))) A2)))) (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.real)) (P (-> tptp.extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ (@ tptp.groups4148127829035722712t_real G) (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) A2) (@ P X4))))) (@ (@ tptp.groups4148127829035722712t_real (lambda ((X4 tptp.extended_enat)) (@ (@ (@ tptp.if_real (@ P X4)) (@ G X4)) tptp.zero_zero_real))) A2)))) (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.int)) (P (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A2) (= (@ (@ tptp.groups1932886352136224148al_int G) (@ tptp.collect_real (lambda ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) A2) (@ P X4))))) (@ (@ tptp.groups1932886352136224148al_int (lambda ((X4 tptp.real)) (@ (@ (@ tptp.if_int (@ P X4)) (@ G X4)) tptp.zero_zero_int))) A2)))) (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.int)) (P (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A2) (@ P X4))))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((X4 tptp.nat)) (@ (@ (@ tptp.if_int (@ P X4)) (@ G X4)) tptp.zero_zero_int))) A2)))) (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.extended_enat))) (=> (@ tptp.finite_finite_real A2) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (= (= (@ (@ tptp.groups2800946370649118462d_enat F) A2) tptp.zero_z5237406670263579293d_enat) (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A2) (= (@ F X4) tptp.zero_z5237406670263579293d_enat))))))) (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.extended_enat))) (=> (@ tptp.finite_finite_nat A2) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (= (= (@ (@ tptp.groups7108830773950497114d_enat F) A2) tptp.zero_z5237406670263579293d_enat) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A2) (= (@ F X4) tptp.zero_z5237406670263579293d_enat))))))) (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.extended_enat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (= (= (@ (@ tptp.groups1752964319039525884d_enat F) A2) tptp.zero_z5237406670263579293d_enat) (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A2) (= (@ F X4) tptp.zero_z5237406670263579293d_enat))))))) (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.extended_enat))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (= (= (@ (@ tptp.groups4225252721152677374d_enat F) A2) tptp.zero_z5237406670263579293d_enat) (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (= (@ F X4) tptp.zero_z5237406670263579293d_enat))))))) (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.extended_enat))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (= (= (@ (@ tptp.groups2433450451889696826d_enat F) A2) tptp.zero_z5237406670263579293d_enat) (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) A2) (= (@ F X4) tptp.zero_z5237406670263579293d_enat))))))) (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real A2) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (= (= (@ (@ tptp.groups8097168146408367636l_real F) A2) tptp.zero_zero_real) (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A2) (= (@ F X4) tptp.zero_zero_real))))))) (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (= (= (@ (@ tptp.groups5808333547571424918x_real F) A2) tptp.zero_zero_real) (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A2) (= (@ F X4) tptp.zero_zero_real))))))) (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (= (= (@ (@ tptp.groups8778361861064173332t_real F) A2) tptp.zero_zero_real) (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (= (@ F X4) tptp.zero_zero_real))))))) (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (= (= (@ (@ tptp.groups4148127829035722712t_real F) A2) tptp.zero_zero_real) (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) A2) (= (@ F X4) tptp.zero_zero_real))))))) (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real A2) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X5)))) (= (= (@ (@ tptp.groups1935376822645274424al_nat F) A2) tptp.zero_zero_nat) (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A2) (= (@ F X4) tptp.zero_zero_nat))))))) (forall ((S tptp.set_nat) (T tptp.set_nat) (G (-> tptp.nat tptp.extended_enat)) (I (-> tptp.nat tptp.nat)) (F (-> tptp.nat tptp.extended_enat))) (=> (@ tptp.finite_finite_nat S) (=> (@ tptp.finite_finite_nat T) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) T) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ G X5)))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) T) (= (@ I Xa) X5) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) (@ G Xa)))))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups7108830773950497114d_enat F) S)) (@ (@ tptp.groups7108830773950497114d_enat G) T))))))) (forall ((S tptp.set_nat) (T tptp.set_complex) (G (-> tptp.complex tptp.extended_enat)) (I (-> tptp.complex tptp.nat)) (F (-> tptp.nat tptp.extended_enat))) (=> (@ tptp.finite_finite_nat S) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) T) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ G X5)))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I Xa) X5) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) (@ G Xa)))))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups7108830773950497114d_enat F) S)) (@ (@ tptp.groups1752964319039525884d_enat G) T))))))) (forall ((S tptp.set_nat) (T tptp.set_int) (G (-> tptp.int tptp.extended_enat)) (I (-> tptp.int tptp.nat)) (F (-> tptp.nat tptp.extended_enat))) (=> (@ tptp.finite_finite_nat S) (=> (@ tptp.finite_finite_int T) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) T) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ G X5)))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) T) (= (@ I Xa) X5) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) (@ G Xa)))))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups7108830773950497114d_enat F) S)) (@ (@ tptp.groups4225252721152677374d_enat G) T))))))) (forall ((S tptp.set_nat) (T tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.extended_enat)) (I (-> tptp.extended_enat tptp.nat)) (F (-> tptp.nat tptp.extended_enat))) (=> (@ tptp.finite_finite_nat S) (=> (@ tptp.finite4001608067531595151d_enat T) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) T) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ G X5)))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S) (exists ((Xa tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat Xa) T) (= (@ I Xa) X5) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) (@ G Xa)))))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups7108830773950497114d_enat F) S)) (@ (@ tptp.groups2433450451889696826d_enat G) T))))))) (forall ((S tptp.set_complex) (T tptp.set_nat) (G (-> tptp.nat tptp.extended_enat)) (I (-> tptp.nat tptp.complex)) (F (-> tptp.complex tptp.extended_enat))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (@ tptp.finite_finite_nat T) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) T) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ G X5)))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) T) (= (@ I Xa) X5) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) (@ G Xa)))))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups1752964319039525884d_enat F) S)) (@ (@ tptp.groups7108830773950497114d_enat G) T))))))) (forall ((S tptp.set_complex) (T tptp.set_complex) (G (-> tptp.complex tptp.extended_enat)) (I (-> tptp.complex tptp.complex)) (F (-> tptp.complex tptp.extended_enat))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) T) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ G X5)))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I Xa) X5) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) (@ G Xa)))))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups1752964319039525884d_enat F) S)) (@ (@ tptp.groups1752964319039525884d_enat G) T))))))) (forall ((S tptp.set_complex) (T tptp.set_int) (G (-> tptp.int tptp.extended_enat)) (I (-> tptp.int tptp.complex)) (F (-> tptp.complex tptp.extended_enat))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (@ tptp.finite_finite_int T) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) T) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ G X5)))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) T) (= (@ I Xa) X5) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) (@ G Xa)))))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups1752964319039525884d_enat F) S)) (@ (@ tptp.groups4225252721152677374d_enat G) T))))))) (forall ((S tptp.set_complex) (T tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.extended_enat)) (I (-> tptp.extended_enat tptp.complex)) (F (-> tptp.complex tptp.extended_enat))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (@ tptp.finite4001608067531595151d_enat T) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) T) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ G X5)))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (exists ((Xa tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat Xa) T) (= (@ I Xa) X5) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) (@ G Xa)))))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups1752964319039525884d_enat F) S)) (@ (@ tptp.groups2433450451889696826d_enat G) T))))))) (forall ((S tptp.set_int) (T tptp.set_nat) (G (-> tptp.nat tptp.extended_enat)) (I (-> tptp.nat tptp.int)) (F (-> tptp.int tptp.extended_enat))) (=> (@ tptp.finite_finite_int S) (=> (@ tptp.finite_finite_nat T) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) T) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ G X5)))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) S) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) T) (= (@ I Xa) X5) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) (@ G Xa)))))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups4225252721152677374d_enat F) S)) (@ (@ tptp.groups7108830773950497114d_enat G) T))))))) (forall ((S tptp.set_int) (T tptp.set_complex) (G (-> tptp.complex tptp.extended_enat)) (I (-> tptp.complex tptp.int)) (F (-> tptp.int tptp.extended_enat))) (=> (@ tptp.finite_finite_int S) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) T) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ G X5)))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) S) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I Xa) X5) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) (@ G Xa)))))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups4225252721152677374d_enat F) S)) (@ (@ tptp.groups1752964319039525884d_enat G) T))))))) (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ G X5)))) (=> (exists ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (@ (@ tptp.ord_less_real (@ F X2)) (@ G X2)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups5808333547571424918x_real F) A2)) (@ (@ tptp.groups5808333547571424918x_real G) A2)))))) (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ G X5)))) (=> (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (@ (@ tptp.ord_less_real (@ F X2)) (@ G X2)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups8778361861064173332t_real F) A2)) (@ (@ tptp.groups8778361861064173332t_real G) A2)))))) (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real)) (G (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) A2) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ G X5)))) (=> (exists ((X2 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X2) A2) (@ (@ tptp.ord_less_real (@ F X2)) (@ G X2)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups4148127829035722712t_real F) A2)) (@ (@ tptp.groups4148127829035722712t_real G) A2)))))) (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ G X5)))) (=> (exists ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (@ (@ tptp.ord_less_nat (@ F X2)) (@ G X2)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups5693394587270226106ex_nat F) A2)) (@ (@ tptp.groups5693394587270226106ex_nat G) A2)))))) (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ G X5)))) (=> (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (@ (@ tptp.ord_less_nat (@ F X2)) (@ G X2)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) (@ (@ tptp.groups4541462559716669496nt_nat G) A2)))))) (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat)) (G (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) A2) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ G X5)))) (=> (exists ((X2 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X2) A2) (@ (@ tptp.ord_less_nat (@ F X2)) (@ G X2)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups2027974829824023292at_nat F) A2)) (@ (@ tptp.groups2027974829824023292at_nat G) A2)))))) (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat A2) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ G X5)))) (=> (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (@ (@ tptp.ord_less_int (@ F X2)) (@ G X2)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups3539618377306564664at_int F) A2)) (@ (@ tptp.groups3539618377306564664at_int G) A2)))))) (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.int)) (G (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ G X5)))) (=> (exists ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (@ (@ tptp.ord_less_int (@ F X2)) (@ G X2)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups5690904116761175830ex_int F) A2)) (@ (@ tptp.groups5690904116761175830ex_int G) A2)))))) (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.int)) (G (-> tptp.extended_enat tptp.int))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) A2) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ G X5)))) (=> (exists ((X2 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X2) A2) (@ (@ tptp.ord_less_int (@ F X2)) (@ G X2)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups2025484359314973016at_int F) A2)) (@ (@ tptp.groups2025484359314973016at_int G) A2)))))) (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.int)) (G (-> tptp.int tptp.int))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ G X5)))) (=> (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (@ (@ tptp.ord_less_int (@ F X2)) (@ G X2)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)) (@ (@ tptp.groups4538972089207619220nt_int G) A2)))))) (forall ((R (-> tptp.nat tptp.nat Bool)) (S2 tptp.set_complex) (H2 (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ (@ R tptp.zero_zero_nat) tptp.zero_zero_nat) (=> (forall ((X1 tptp.nat) (Y1 tptp.nat) (X23 tptp.nat) (Y22 tptp.nat)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.plus_plus_nat X1) Y1)) (@ (@ tptp.plus_plus_nat X23) Y22)))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S2) (@ (@ R (@ H2 X5)) (@ G X5)))) (@ (@ R (@ (@ tptp.groups5693394587270226106ex_nat H2) S2)) (@ (@ 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(forall ((R (-> tptp.real tptp.real Bool)) (S2 tptp.set_int) (H2 (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (@ (@ R tptp.zero_zero_real) tptp.zero_zero_real) (=> (forall ((X1 tptp.real) (Y1 tptp.real) (X23 tptp.real) (Y22 tptp.real)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.plus_plus_real X1) Y1)) (@ (@ tptp.plus_plus_real X23) Y22)))) (=> (@ tptp.finite_finite_int S2) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) S2) (@ (@ R (@ H2 X5)) (@ G X5)))) (@ (@ R (@ (@ tptp.groups8778361861064173332t_real H2) S2)) (@ (@ tptp.groups8778361861064173332t_real G) S2))))))) (forall ((R (-> tptp.real tptp.real Bool)) (S2 tptp.set_Extended_enat) (H2 (-> tptp.extended_enat tptp.real)) (G (-> tptp.extended_enat tptp.real))) (=> (@ (@ R tptp.zero_zero_real) tptp.zero_zero_real) (=> (forall ((X1 tptp.real) (Y1 tptp.real) (X23 tptp.real) (Y22 tptp.real)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.plus_plus_real X1) Y1)) (@ (@ 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(forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) S2) (@ (@ R (@ H2 X5)) (@ G X5)))) (@ (@ R (@ (@ tptp.groups2025484359314973016at_int H2) S2)) (@ (@ tptp.groups2025484359314973016at_int G) S2))))))) (forall ((R (-> tptp.complex tptp.complex Bool)) (S2 tptp.set_nat) (H2 (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.complex))) (=> (@ (@ R tptp.zero_zero_complex) tptp.zero_zero_complex) (=> (forall ((X1 tptp.complex) (Y1 tptp.complex) (X23 tptp.complex) (Y22 tptp.complex)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.plus_plus_complex X1) Y1)) (@ (@ tptp.plus_plus_complex X23) Y22)))) (=> (@ tptp.finite_finite_nat S2) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S2) (@ (@ R (@ H2 X5)) (@ G X5)))) (@ (@ R (@ (@ tptp.groups2073611262835488442omplex H2) S2)) (@ (@ tptp.groups2073611262835488442omplex G) S2))))))) (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ 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(X tptp.complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_complex X) A2)))) (let ((_let_4 (@ (@ tptp.member_complex X) A2))) (=> (@ tptp.finite3207457112153483333omplex A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_int (@ G X)) _let_2)))))))))) (forall ((A2 tptp.set_Extended_enat) (X tptp.extended_enat) (G (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2025484359314973016at_int G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_Extended_enat X) A2)))) (let ((_let_4 (@ (@ tptp.member_Extended_enat X) A2))) (=> (@ tptp.finite4001608067531595151d_enat A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_int (@ G X)) _let_2)))))))))) (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ 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A4)))) (= (@ (@ tptp.groups4541462559716669496nt_nat G) S2) (@ (@ tptp.groups1935376822645274424al_nat H2) T3)))))))))))) (forall ((S5 tptp.set_int) (T5 tptp.set_complex) (S2 tptp.set_int) (I (-> tptp.complex tptp.int)) (J (-> tptp.int tptp.complex)) (T3 tptp.set_complex) (G (-> tptp.int tptp.nat)) (H2 (-> tptp.complex tptp.nat))) (=> (@ tptp.finite_finite_int S5) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) (@ (@ tptp.minus_minus_set_int S2) S5)) (= (@ I (@ J A4)) A4))) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) (@ (@ tptp.minus_minus_set_int S2) S5)) (@ (@ tptp.member_complex (@ J A4)) (@ (@ tptp.minus_811609699411566653omplex T3) T5)))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex T3) T5)) (= (@ J (@ I B4)) B4))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex T3) T5)) (@ (@ tptp.member_int (@ I B4)) (@ (@ tptp.minus_minus_set_int S2) S5)))) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) S5) (= (@ G A4) tptp.zero_zero_nat))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) T5) (= (@ H2 B4) tptp.zero_zero_nat))) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) S2) (= (@ H2 (@ J A4)) (@ G A4)))) (= (@ (@ tptp.groups4541462559716669496nt_nat G) S2) (@ (@ tptp.groups5693394587270226106ex_nat H2) T3)))))))))))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_int (@ tptp.archim8280529875227126926d_real X)) (@ tptp.archim8280529875227126926d_real Y)))) (forall ((S tptp.set_real) (F (-> tptp.real tptp.extended_enat)) (I tptp.real)) (=> (@ tptp.finite_finite_real S) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) S) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (=> (= (@ (@ tptp.groups2800946370649118462d_enat F) S) tptp.zero_z5237406670263579293d_enat) (=> (@ (@ tptp.member_real I) S) (= (@ F I) tptp.zero_z5237406670263579293d_enat)))))) (forall ((S tptp.set_nat) (F (-> tptp.nat tptp.extended_enat)) (I tptp.nat)) (=> (@ tptp.finite_finite_nat S) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) S) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (=> (= (@ (@ tptp.groups7108830773950497114d_enat F) S) tptp.zero_z5237406670263579293d_enat) (=> (@ (@ tptp.member_nat I) S) (= (@ F I) tptp.zero_z5237406670263579293d_enat)))))) (forall ((S tptp.set_complex) (F (-> tptp.complex tptp.extended_enat)) (I tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) S) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (=> (= (@ (@ tptp.groups1752964319039525884d_enat F) S) tptp.zero_z5237406670263579293d_enat) (=> (@ (@ tptp.member_complex I) S) (= (@ F I) tptp.zero_z5237406670263579293d_enat)))))) (forall ((S tptp.set_int) (F (-> tptp.int tptp.extended_enat)) (I tptp.int)) (=> (@ tptp.finite_finite_int S) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) S) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (=> (= (@ (@ tptp.groups4225252721152677374d_enat F) S) tptp.zero_z5237406670263579293d_enat) (=> (@ (@ tptp.member_int I) S) (= (@ F I) tptp.zero_z5237406670263579293d_enat)))))) (forall ((S tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.extended_enat)) (I tptp.extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat S) (=> (forall ((I4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I4) S) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (=> (= (@ (@ tptp.groups2433450451889696826d_enat F) S) tptp.zero_z5237406670263579293d_enat) (=> (@ (@ tptp.member_Extended_enat I) S) (= (@ F I) tptp.zero_z5237406670263579293d_enat)))))) (forall ((S tptp.set_real) (F (-> tptp.real tptp.real)) (I tptp.real)) (=> (@ tptp.finite_finite_real S) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) S) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4)))) (=> (= (@ (@ tptp.groups8097168146408367636l_real F) S) tptp.zero_zero_real) (=> (@ (@ tptp.member_real I) S) (= (@ F I) tptp.zero_zero_real)))))) (forall ((S tptp.set_complex) (F (-> tptp.complex tptp.real)) (I tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) S) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4)))) (=> (= (@ (@ tptp.groups5808333547571424918x_real F) S) tptp.zero_zero_real) (=> (@ (@ tptp.member_complex I) S) (= (@ F I) tptp.zero_zero_real)))))) (forall ((S tptp.set_int) (F (-> tptp.int tptp.real)) (I tptp.int)) (=> (@ tptp.finite_finite_int S) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) S) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4)))) (=> (= (@ (@ tptp.groups8778361861064173332t_real F) S) tptp.zero_zero_real) (=> (@ (@ tptp.member_int I) S) (= (@ F I) tptp.zero_zero_real)))))) (forall ((S tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real)) (I tptp.extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat S) (=> (forall ((I4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I4) S) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4)))) (=> (= (@ (@ tptp.groups4148127829035722712t_real F) S) tptp.zero_zero_real) (=> (@ (@ tptp.member_Extended_enat I) S) (= (@ F I) tptp.zero_zero_real)))))) (forall ((S tptp.set_real) (F (-> tptp.real tptp.nat)) (I tptp.real)) (=> (@ tptp.finite_finite_real S) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) S) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I4)))) (=> (= (@ (@ tptp.groups1935376822645274424al_nat F) S) tptp.zero_zero_nat) (=> (@ (@ tptp.member_real I) S) (= (@ F I) tptp.zero_zero_nat)))))) (forall ((S tptp.set_real) (F (-> tptp.real tptp.extended_enat)) (B tptp.extended_enat) (I tptp.real)) (=> (@ tptp.finite_finite_real S) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) S) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (=> (= (@ (@ tptp.groups2800946370649118462d_enat F) S) B) (=> (@ (@ tptp.member_real I) S) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F I)) B)))))) (forall ((S tptp.set_nat) (F (-> tptp.nat tptp.extended_enat)) (B tptp.extended_enat) (I tptp.nat)) (=> (@ tptp.finite_finite_nat S) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) S) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (=> (= (@ (@ tptp.groups7108830773950497114d_enat F) S) B) (=> (@ (@ tptp.member_nat I) S) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F I)) B)))))) (forall ((S tptp.set_complex) (F (-> tptp.complex tptp.extended_enat)) (B tptp.extended_enat) (I tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) S) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (=> (= (@ (@ tptp.groups1752964319039525884d_enat F) S) B) (=> (@ (@ tptp.member_complex I) S) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F I)) B)))))) (forall ((S tptp.set_int) (F (-> tptp.int tptp.extended_enat)) (B tptp.extended_enat) (I tptp.int)) (=> (@ tptp.finite_finite_int S) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) S) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (=> (= (@ (@ tptp.groups4225252721152677374d_enat F) S) B) (=> (@ (@ tptp.member_int I) S) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F I)) B)))))) (forall ((S tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.extended_enat)) (B tptp.extended_enat) (I tptp.extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat S) (=> (forall ((I4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I4) S) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (=> (= (@ (@ tptp.groups2433450451889696826d_enat F) S) B) (=> (@ (@ tptp.member_Extended_enat I) S) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F I)) B)))))) (forall ((S tptp.set_real) (F (-> tptp.real tptp.real)) (B tptp.real) (I tptp.real)) (=> (@ tptp.finite_finite_real S) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) S) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4)))) (=> (= (@ (@ tptp.groups8097168146408367636l_real F) S) B) (=> (@ (@ tptp.member_real I) S) (@ (@ tptp.ord_less_eq_real (@ F I)) B)))))) (forall ((S tptp.set_complex) (F (-> tptp.complex tptp.real)) (B tptp.real) (I tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) S) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4)))) (=> (= (@ (@ tptp.groups5808333547571424918x_real F) S) B) (=> (@ (@ tptp.member_complex I) S) (@ (@ tptp.ord_less_eq_real (@ F I)) B)))))) (forall ((S tptp.set_int) (F (-> tptp.int tptp.real)) (B tptp.real) (I tptp.int)) (=> (@ tptp.finite_finite_int S) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) S) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4)))) (=> (= (@ (@ tptp.groups8778361861064173332t_real F) S) B) (=> (@ (@ tptp.member_int I) S) (@ (@ tptp.ord_less_eq_real (@ F I)) B)))))) (forall ((S tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real)) (B tptp.real) (I tptp.extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat S) (=> (forall ((I4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I4) S) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4)))) (=> (= (@ (@ tptp.groups4148127829035722712t_real F) S) B) (=> (@ (@ tptp.member_Extended_enat I) S) (@ (@ tptp.ord_less_eq_real (@ F I)) B)))))) (forall ((S tptp.set_real) (F (-> tptp.real tptp.nat)) (B tptp.nat) (I tptp.real)) (=> (@ tptp.finite_finite_real S) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) S) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I4)))) (=> (= (@ (@ tptp.groups1935376822645274424al_nat F) S) B) (=> (@ (@ tptp.member_real I) S) (@ (@ tptp.ord_less_eq_nat (@ F I)) B)))))) (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat G))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ tptp.collect_real (lambda ((X4 tptp.real)) (= (@ G X4) tptp.zero_zero_nat))))) (@ _let_1 A2))))) (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (= (@ G X4) tptp.zero_zero_nat))))) (@ _let_1 A2))))) (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ tptp.collect_int (lambda ((X4 tptp.int)) (= (@ G X4) tptp.zero_zero_nat))))) (@ _let_1 A2))))) (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2027974829824023292at_nat G))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (= (@ G X4) tptp.zero_zero_nat))))) (@ _let_1 A2))))) (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real G))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ tptp.collect_real (lambda ((X4 tptp.real)) (= (@ G X4) tptp.zero_zero_real))))) (@ _let_1 A2))))) (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (= (@ G X4) tptp.zero_zero_real))))) (@ _let_1 A2))))) (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ tptp.collect_int (lambda ((X4 tptp.int)) (= (@ G X4) tptp.zero_zero_real))))) (@ _let_1 A2))))) (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups4148127829035722712t_real G))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (= (@ G X4) tptp.zero_zero_real))))) (@ _let_1 A2))))) (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int G))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ tptp.collect_real (lambda ((X4 tptp.real)) (= (@ G X4) tptp.zero_zero_int))))) (@ _let_1 A2))))) (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (= (@ G X4) tptp.zero_zero_int))))) (@ _let_1 A2))))) (forall ((I6 tptp.set_real) (I tptp.real) (F (-> tptp.real tptp.extended_enat))) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat))) (=> (@ tptp.finite_finite_real I6) (=> (@ (@ tptp.member_real I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups2800946370649118462d_enat F) I6)))))))) (forall ((I6 tptp.set_nat) (I tptp.nat) (F (-> tptp.nat tptp.extended_enat))) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat))) (=> (@ tptp.finite_finite_nat I6) (=> (@ (@ tptp.member_nat I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups7108830773950497114d_enat F) I6)))))))) (forall ((I6 tptp.set_complex) (I tptp.complex) (F (-> tptp.complex tptp.extended_enat))) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (@ (@ tptp.member_complex I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups1752964319039525884d_enat F) I6)))))))) (forall ((I6 tptp.set_int) (I tptp.int) (F (-> tptp.int tptp.extended_enat))) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat))) (=> (@ tptp.finite_finite_int I6) (=> (@ (@ tptp.member_int I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups4225252721152677374d_enat F) I6)))))))) (forall ((I6 tptp.set_Extended_enat) (I tptp.extended_enat) (F (-> tptp.extended_enat tptp.extended_enat))) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat))) (=> (@ tptp.finite4001608067531595151d_enat I6) (=> (@ (@ tptp.member_Extended_enat I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I4) I6) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups2433450451889696826d_enat F) I6)))))))) (forall ((I6 tptp.set_real) (I tptp.real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.finite_finite_real I6) (=> (@ (@ tptp.member_real I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups8097168146408367636l_real F) I6)))))))) (forall ((I6 tptp.set_complex) (I tptp.complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (@ (@ tptp.member_complex I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups5808333547571424918x_real F) I6)))))))) (forall ((I6 tptp.set_int) (I tptp.int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.finite_finite_int I6) (=> (@ (@ tptp.member_int I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups8778361861064173332t_real F) I6)))))))) (forall ((I6 tptp.set_Extended_enat) (I tptp.extended_enat) (F (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.finite4001608067531595151d_enat I6) (=> (@ (@ tptp.member_Extended_enat I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I4) I6) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups4148127829035722712t_real F) I6)))))))) (forall ((I6 tptp.set_real) (I tptp.real) (F (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ tptp.finite_finite_real I6) (=> (@ (@ tptp.member_real I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups1935376822645274424al_nat F) I6)))))))) (forall ((I6 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (not (= I6 tptp.bot_bot_set_complex)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I4)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups5693394587270226106ex_nat F) I6)))))) (forall ((I6 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat I6) (=> (not (= I6 tptp.bot_bo7653980558646680370d_enat)) (=> (forall ((I4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I4) I6) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I4)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups2027974829824023292at_nat F) I6)))))) (forall ((I6 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real I6) (=> (not (= I6 tptp.bot_bot_set_real)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I4)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups1935376822645274424al_nat F) I6)))))) (forall ((I6 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int I6) (=> (not (= I6 tptp.bot_bot_set_int)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I4)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups4541462559716669496nt_nat F) I6)))))) (forall ((I6 tptp.set_complex) (F (-> tptp.complex tptp.extended_enat))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (not (= I6 tptp.bot_bot_set_complex)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.groups1752964319039525884d_enat F) I6)))))) (forall ((I6 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.extended_enat))) (=> (@ tptp.finite4001608067531595151d_enat I6) (=> (not (= I6 tptp.bot_bo7653980558646680370d_enat)) (=> (forall ((I4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I4) I6) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.groups2433450451889696826d_enat F) I6)))))) (forall ((I6 tptp.set_real) (F (-> tptp.real tptp.extended_enat))) (=> (@ tptp.finite_finite_real I6) (=> (not (= I6 tptp.bot_bot_set_real)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.groups2800946370649118462d_enat F) I6)))))) (forall ((I6 tptp.set_nat) (F (-> tptp.nat tptp.extended_enat))) (=> (@ tptp.finite_finite_nat I6) (=> (not (= I6 tptp.bot_bot_set_nat)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.groups7108830773950497114d_enat F) I6)))))) (forall ((I6 tptp.set_int) (F (-> tptp.int tptp.extended_enat))) (=> (@ tptp.finite_finite_int I6) (=> (not (= I6 tptp.bot_bot_set_int)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.groups4225252721152677374d_enat F) I6)))))) (forall ((I6 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (not (= I6 tptp.bot_bot_set_complex)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I4)))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.groups5808333547571424918x_real F) I6)))))) (forall ((T3 tptp.set_real) (S2 tptp.set_real) (G (-> tptp.real tptp.nat)) (H2 (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S2) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S2)) (= (@ G X5) tptp.zero_zero_nat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups1935376822645274424al_nat G) T3) (@ (@ tptp.groups1935376822645274424al_nat H2) S2))))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (H2 (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X5) tptp.zero_zero_nat))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups5693394587270226106ex_nat G) T3) (@ (@ tptp.groups5693394587270226106ex_nat H2) S2))))))) (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.nat)) (H2 (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G X5) tptp.zero_zero_nat))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups2027974829824023292at_nat G) T3) (@ (@ tptp.groups2027974829824023292at_nat H2) S2))))))) (forall ((T3 tptp.set_real) (S2 tptp.set_real) (G (-> tptp.real tptp.real)) (H2 (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S2) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S2)) (= (@ G X5) tptp.zero_zero_real))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups8097168146408367636l_real G) T3) (@ (@ tptp.groups8097168146408367636l_real H2) S2))))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.real)) (H2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X5) tptp.zero_zero_real))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups5808333547571424918x_real G) T3) (@ (@ tptp.groups5808333547571424918x_real H2) S2))))))) (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.real)) (H2 (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G X5) tptp.zero_zero_real))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups4148127829035722712t_real G) T3) (@ (@ tptp.groups4148127829035722712t_real H2) S2))))))) (forall ((T3 tptp.set_real) (S2 tptp.set_real) (G (-> tptp.real tptp.int)) (H2 (-> tptp.real tptp.int))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S2) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S2)) (= (@ G X5) tptp.zero_zero_int))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups1932886352136224148al_int G) T3) (@ (@ tptp.groups1932886352136224148al_int H2) S2))))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.int)) (H2 (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X5) tptp.zero_zero_int))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups5690904116761175830ex_int G) T3) (@ (@ tptp.groups5690904116761175830ex_int H2) S2))))))) (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.int)) (H2 (-> tptp.extended_enat tptp.int))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G X5) tptp.zero_zero_int))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups2025484359314973016at_int G) T3) (@ (@ tptp.groups2025484359314973016at_int H2) S2))))))) (forall ((T3 tptp.set_real) (S2 tptp.set_real) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S2) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S2)) (= (@ G X5) tptp.zero_zero_complex))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups5754745047067104278omplex G) T3) (@ (@ tptp.groups5754745047067104278omplex H2) S2))))))) (forall ((T3 tptp.set_real) (S2 tptp.set_real) (H2 (-> tptp.real tptp.nat)) (G (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S2) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S2)) (= (@ H2 X5) tptp.zero_zero_nat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups1935376822645274424al_nat G) S2) (@ (@ tptp.groups1935376822645274424al_nat H2) T3))))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (H2 (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ H2 X5) tptp.zero_zero_nat))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups5693394587270226106ex_nat G) S2) (@ (@ tptp.groups5693394587270226106ex_nat H2) T3))))))) (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (H2 (-> tptp.extended_enat tptp.nat)) (G (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ H2 X5) tptp.zero_zero_nat))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups2027974829824023292at_nat G) S2) (@ (@ tptp.groups2027974829824023292at_nat H2) T3))))))) (forall ((T3 tptp.set_real) (S2 tptp.set_real) (H2 (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S2) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S2)) (= (@ H2 X5) tptp.zero_zero_real))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups8097168146408367636l_real G) S2) (@ (@ tptp.groups8097168146408367636l_real H2) T3))))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (H2 (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ H2 X5) tptp.zero_zero_real))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups5808333547571424918x_real G) S2) (@ (@ tptp.groups5808333547571424918x_real H2) T3))))))) (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (H2 (-> tptp.extended_enat tptp.real)) (G (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ H2 X5) tptp.zero_zero_real))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups4148127829035722712t_real G) S2) (@ (@ tptp.groups4148127829035722712t_real H2) T3))))))) (forall ((T3 tptp.set_real) (S2 tptp.set_real) (H2 (-> tptp.real tptp.int)) (G (-> tptp.real tptp.int))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S2) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S2)) (= (@ H2 X5) tptp.zero_zero_int))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups1932886352136224148al_int G) S2) (@ (@ tptp.groups1932886352136224148al_int H2) T3))))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (H2 (-> tptp.complex tptp.int)) (G (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ H2 X5) tptp.zero_zero_int))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups5690904116761175830ex_int G) S2) (@ (@ tptp.groups5690904116761175830ex_int H2) T3))))))) (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (H2 (-> tptp.extended_enat tptp.int)) (G (-> tptp.extended_enat tptp.int))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ H2 X5) tptp.zero_zero_int))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups2025484359314973016at_int G) S2) (@ (@ tptp.groups2025484359314973016at_int H2) T3))))))) (forall ((T3 tptp.set_real) (S2 tptp.set_real) (H2 (-> tptp.real tptp.complex)) (G (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S2) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S2)) (= (@ H2 X5) tptp.zero_zero_complex))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups5754745047067104278omplex G) S2) (@ (@ tptp.groups5754745047067104278omplex H2) T3))))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X5) tptp.zero_zero_nat))) (= (@ _let_1 T3) (@ _let_1 S2))))))) (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2027974829824023292at_nat G))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G X5) tptp.zero_zero_nat))) (= (@ _let_1 T3) (@ _let_1 S2))))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X5) tptp.zero_zero_real))) (= (@ _let_1 T3) (@ _let_1 S2))))))) (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups4148127829035722712t_real G))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G X5) tptp.zero_zero_real))) (= (@ _let_1 T3) (@ _let_1 S2))))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X5) tptp.zero_zero_int))) (= (@ _let_1 T3) (@ _let_1 S2))))))) (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2025484359314973016at_int G))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G X5) tptp.zero_zero_int))) (= (@ _let_1 T3) (@ _let_1 S2))))))) (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.complex))) (let ((_let_1 (@ tptp.groups6818542070133387226omplex G))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G X5) tptp.zero_zero_complex))) (= (@ _let_1 T3) (@ _let_1 S2))))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.extended_enat))) (let ((_let_1 (@ tptp.groups1752964319039525884d_enat G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X5) tptp.zero_z5237406670263579293d_enat))) (= (@ _let_1 T3) (@ _let_1 S2))))))) (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.extended_enat))) (let ((_let_1 (@ tptp.groups2433450451889696826d_enat G))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G X5) tptp.zero_z5237406670263579293d_enat))) (= (@ _let_1 T3) (@ _let_1 S2))))))) (forall ((T3 tptp.set_nat) (S2 tptp.set_nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ tptp.finite_finite_nat T3) (=> (@ (@ tptp.ord_less_eq_set_nat S2) T3) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) (@ (@ tptp.minus_minus_set_nat T3) S2)) (= (@ G X5) tptp.zero_zero_int))) (= (@ _let_1 T3) (@ _let_1 S2))))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X5) tptp.zero_zero_nat))) (= (@ _let_1 S2) (@ _let_1 T3))))))) (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2027974829824023292at_nat G))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G X5) tptp.zero_zero_nat))) (= (@ _let_1 S2) (@ _let_1 T3))))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X5) tptp.zero_zero_real))) (= (@ _let_1 S2) (@ _let_1 T3))))))) (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups4148127829035722712t_real G))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G X5) tptp.zero_zero_real))) (= (@ _let_1 S2) (@ _let_1 T3))))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X5) tptp.zero_zero_int))) (= (@ _let_1 S2) (@ _let_1 T3))))))) (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2025484359314973016at_int G))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G X5) tptp.zero_zero_int))) (= (@ _let_1 S2) (@ _let_1 T3))))))) (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.complex))) (let ((_let_1 (@ tptp.groups6818542070133387226omplex G))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G X5) tptp.zero_zero_complex))) (= (@ _let_1 S2) (@ _let_1 T3))))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.extended_enat))) (let ((_let_1 (@ tptp.groups1752964319039525884d_enat G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X5) tptp.zero_z5237406670263579293d_enat))) (= (@ _let_1 S2) (@ _let_1 T3))))))) (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.extended_enat))) (let ((_let_1 (@ tptp.groups2433450451889696826d_enat G))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G X5) tptp.zero_z5237406670263579293d_enat))) (= (@ _let_1 S2) (@ _let_1 T3))))))) (forall ((T3 tptp.set_nat) (S2 tptp.set_nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ tptp.finite_finite_nat T3) (=> (@ (@ tptp.ord_less_eq_set_nat S2) T3) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) (@ (@ tptp.minus_minus_set_nat T3) S2)) (= (@ G X5) tptp.zero_zero_int))) (= (@ _let_1 S2) (@ _let_1 T3))))))) (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B tptp.set_real) (G (-> tptp.real tptp.nat)) (H2 (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat H2))) (let ((_let_2 (@ tptp.groups1935376822645274424al_nat G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B) C4) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A4) tptp.zero_zero_nat))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real C4) B)) (= (@ H2 B4) tptp.zero_zero_nat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B))))))))))) (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B tptp.set_complex) (G (-> tptp.complex tptp.nat)) (H2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat H2))) (let ((_let_2 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B) C4) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A4) tptp.zero_zero_nat))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex C4) B)) (= (@ H2 B4) tptp.zero_zero_nat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B))))))))))) (forall ((C4 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.nat)) (H2 (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2027974829824023292at_nat H2))) (let ((_let_2 (@ tptp.groups2027974829824023292at_nat G))) (=> (@ tptp.finite4001608067531595151d_enat C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B) C4) (=> (forall ((A4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A4) (@ (@ tptp.minus_925952699566721837d_enat C4) A2)) (= (@ G A4) tptp.zero_zero_nat))) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) (@ (@ tptp.minus_925952699566721837d_enat C4) B)) (= (@ H2 B4) tptp.zero_zero_nat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B))))))))))) (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B tptp.set_real) (G (-> tptp.real tptp.real)) (H2 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real H2))) (let ((_let_2 (@ tptp.groups8097168146408367636l_real G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B) C4) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A4) tptp.zero_zero_real))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real C4) B)) (= (@ H2 B4) tptp.zero_zero_real))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B))))))))))) (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B tptp.set_complex) (G (-> tptp.complex tptp.real)) (H2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real H2))) (let ((_let_2 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B) C4) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A4) tptp.zero_zero_real))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex C4) B)) (= (@ H2 B4) tptp.zero_zero_real))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B))))))))))) (forall ((C4 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.real)) (H2 (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups4148127829035722712t_real H2))) (let ((_let_2 (@ tptp.groups4148127829035722712t_real G))) (=> (@ tptp.finite4001608067531595151d_enat C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B) C4) (=> (forall ((A4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A4) (@ (@ tptp.minus_925952699566721837d_enat C4) A2)) (= (@ G A4) tptp.zero_zero_real))) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) (@ (@ tptp.minus_925952699566721837d_enat C4) B)) (= (@ H2 B4) tptp.zero_zero_real))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B))))))))))) (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B tptp.set_real) (G (-> tptp.real tptp.int)) (H2 (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int H2))) (let ((_let_2 (@ tptp.groups1932886352136224148al_int G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B) C4) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A4) tptp.zero_zero_int))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real C4) B)) (= (@ H2 B4) tptp.zero_zero_int))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B))))))))))) (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B tptp.set_complex) (G (-> tptp.complex tptp.int)) (H2 (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int H2))) (let ((_let_2 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B) C4) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A4) tptp.zero_zero_int))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex C4) B)) (= (@ H2 B4) tptp.zero_zero_int))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B))))))))))) (forall ((C4 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.int)) (H2 (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2025484359314973016at_int H2))) (let ((_let_2 (@ tptp.groups2025484359314973016at_int G))) (=> (@ tptp.finite4001608067531595151d_enat C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B) C4) (=> (forall ((A4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A4) (@ (@ tptp.minus_925952699566721837d_enat C4) A2)) (= (@ G A4) tptp.zero_zero_int))) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) (@ (@ tptp.minus_925952699566721837d_enat C4) B)) (= (@ H2 B4) tptp.zero_zero_int))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B))))))))))) (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B tptp.set_real) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups5754745047067104278omplex H2))) (let ((_let_2 (@ tptp.groups5754745047067104278omplex G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B) C4) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A4) tptp.zero_zero_complex))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real C4) B)) (= (@ H2 B4) tptp.zero_zero_complex))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B))))))))))) (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B tptp.set_real) (G (-> tptp.real tptp.nat)) (H2 (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat H2))) (let ((_let_2 (@ tptp.groups1935376822645274424al_nat G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B) C4) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A4) tptp.zero_zero_nat))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real C4) B)) (= (@ H2 B4) tptp.zero_zero_nat))) (= (= (@ _let_2 A2) (@ _let_1 B)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))) (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B tptp.set_complex) (G (-> tptp.complex tptp.nat)) (H2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat H2))) (let ((_let_2 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B) C4) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A4) tptp.zero_zero_nat))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex C4) B)) (= (@ H2 B4) tptp.zero_zero_nat))) (= (= (@ _let_2 A2) (@ _let_1 B)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))) (forall ((C4 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.nat)) (H2 (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2027974829824023292at_nat H2))) (let ((_let_2 (@ tptp.groups2027974829824023292at_nat G))) (=> (@ tptp.finite4001608067531595151d_enat C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B) C4) (=> (forall ((A4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A4) (@ (@ tptp.minus_925952699566721837d_enat C4) A2)) (= (@ G A4) tptp.zero_zero_nat))) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) (@ (@ tptp.minus_925952699566721837d_enat C4) B)) (= (@ H2 B4) tptp.zero_zero_nat))) (= (= (@ _let_2 A2) (@ _let_1 B)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))) (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B tptp.set_real) (G (-> tptp.real tptp.real)) (H2 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real H2))) (let ((_let_2 (@ tptp.groups8097168146408367636l_real G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B) C4) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A4) tptp.zero_zero_real))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real C4) B)) (= (@ H2 B4) tptp.zero_zero_real))) (= (= (@ _let_2 A2) (@ _let_1 B)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))) (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B tptp.set_complex) (G (-> tptp.complex tptp.real)) (H2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real H2))) (let ((_let_2 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B) C4) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A4) tptp.zero_zero_real))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex C4) B)) (= (@ H2 B4) tptp.zero_zero_real))) (= (= (@ _let_2 A2) (@ _let_1 B)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))) (forall ((C4 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.real)) (H2 (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups4148127829035722712t_real H2))) (let ((_let_2 (@ tptp.groups4148127829035722712t_real G))) (=> (@ tptp.finite4001608067531595151d_enat C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B) C4) (=> (forall ((A4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A4) (@ (@ tptp.minus_925952699566721837d_enat C4) A2)) (= (@ G A4) tptp.zero_zero_real))) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) (@ (@ tptp.minus_925952699566721837d_enat C4) B)) (= (@ H2 B4) tptp.zero_zero_real))) (= (= (@ _let_2 A2) (@ _let_1 B)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))) (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B tptp.set_real) (G (-> tptp.real tptp.int)) (H2 (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int H2))) (let ((_let_2 (@ tptp.groups1932886352136224148al_int G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B) C4) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A4) tptp.zero_zero_int))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real C4) B)) (= (@ H2 B4) tptp.zero_zero_int))) (= (= (@ _let_2 A2) (@ _let_1 B)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))) (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B tptp.set_complex) (G (-> tptp.complex tptp.int)) (H2 (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int H2))) (let ((_let_2 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B) C4) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A4) tptp.zero_zero_int))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex C4) B)) (= (@ H2 B4) tptp.zero_zero_int))) (= (= (@ _let_2 A2) (@ _let_1 B)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))) (forall ((C4 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.int)) (H2 (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2025484359314973016at_int H2))) (let ((_let_2 (@ tptp.groups2025484359314973016at_int G))) (=> (@ tptp.finite4001608067531595151d_enat C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B) C4) (=> (forall ((A4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A4) (@ (@ tptp.minus_925952699566721837d_enat C4) A2)) (= (@ G A4) tptp.zero_zero_int))) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) (@ (@ tptp.minus_925952699566721837d_enat C4) B)) (= (@ H2 B4) tptp.zero_zero_int))) (= (= (@ _let_2 A2) (@ _let_1 B)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))) (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B tptp.set_real) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups5754745047067104278omplex H2))) (let ((_let_2 (@ tptp.groups5754745047067104278omplex G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B) C4) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A4) tptp.zero_zero_complex))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real C4) B)) (= (@ H2 B4) tptp.zero_zero_complex))) (= (= (@ _let_2 A2) (@ _let_1 B)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))) (forall ((B tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B))) (@ _let_1 B))))))) (forall ((B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2027974829824023292at_nat G))) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B) A2) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) B))) (@ _let_1 B))))))) (forall ((B tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B))) (@ _let_1 B))))))) (forall ((B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2025484359314973016at_int G))) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B) A2) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) B))) (@ _let_1 B))))))) (forall ((B tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B))) (@ _let_1 B))))))) (forall ((B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups4148127829035722712t_real G))) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B) A2) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) B))) (@ _let_1 B))))))) (forall ((B tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.extended_enat))) (let ((_let_1 (@ tptp.groups1752964319039525884d_enat G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.plus_p3455044024723400733d_enat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B))) (@ _let_1 B))))))) (forall ((B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.extended_enat))) (let ((_let_1 (@ tptp.groups2433450451889696826d_enat G))) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B) A2) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_1 A2) (@ (@ tptp.plus_p3455044024723400733d_enat (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) B))) (@ _let_1 B))))))) (forall ((B tptp.set_nat) (A2 tptp.set_nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ (@ tptp.ord_less_eq_set_nat B) A2) (=> (@ tptp.finite_finite_nat A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B))) (@ _let_1 B))))))) (forall ((B tptp.set_nat) (A2 tptp.set_nat) (G (-> tptp.nat tptp.extended_enat))) (let ((_let_1 (@ tptp.groups7108830773950497114d_enat G))) (=> (@ (@ tptp.ord_less_eq_set_nat B) A2) (=> (@ tptp.finite_finite_nat A2) (= (@ _let_1 A2) (@ (@ tptp.plus_p3455044024723400733d_enat (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B))) (@ _let_1 B))))))) (forall ((A2 tptp.set_complex) (B tptp.set_complex) (F (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int F))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.ord_le211207098394363844omplex B) A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B)) (@ (@ tptp.minus_minus_int (@ _let_1 A2)) (@ _let_1 B))))))) (forall ((A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2025484359314973016at_int F))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B) A2) (= (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) B)) (@ (@ tptp.minus_minus_int (@ _let_1 A2)) (@ _let_1 B))))))) (forall ((A2 tptp.set_complex) (B tptp.set_complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real F))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.ord_le211207098394363844omplex B) A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B)) (@ (@ tptp.minus_minus_real (@ _let_1 A2)) (@ _let_1 B))))))) (forall ((A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups4148127829035722712t_real F))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B) A2) (= (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) B)) (@ (@ tptp.minus_minus_real (@ _let_1 A2)) (@ _let_1 B))))))) (forall ((A2 tptp.set_nat) (B tptp.set_nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int F))) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.ord_less_eq_set_nat B) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B)) (@ (@ tptp.minus_minus_int (@ _let_1 A2)) (@ _let_1 B))))))) (forall ((A2 tptp.set_int) (B tptp.set_int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real F))) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.ord_less_eq_set_int B) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B)) (@ (@ tptp.minus_minus_real (@ _let_1 A2)) (@ _let_1 B))))))) (forall ((A2 tptp.set_int) (B tptp.set_int) (F (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.groups4538972089207619220nt_int F))) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.ord_less_eq_set_int B) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B)) (@ (@ tptp.minus_minus_int (@ _let_1 A2)) (@ _let_1 B))))))) (forall ((A2 tptp.set_complex) (B tptp.set_complex) (F (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups7754918857620584856omplex F))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.ord_le211207098394363844omplex B) A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B)) (@ (@ tptp.minus_minus_complex (@ _let_1 A2)) (@ _let_1 B))))))) (forall ((A2 tptp.set_nat) (B tptp.set_nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups6591440286371151544t_real F))) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.ord_less_eq_set_nat B) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B)) (@ (@ tptp.minus_minus_real (@ _let_1 A2)) (@ _let_1 B))))))) (forall ((B tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.extended_enat))) (let ((_let_1 (@ tptp.groups2800946370649118462d_enat F))) (=> (@ tptp.finite_finite_real B) (=> (@ (@ tptp.ord_less_eq_set_real A2) B) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real B) A2)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F B4)))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ _let_1 A2)) (@ _let_1 B))))))) (forall ((B tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.extended_enat))) (let ((_let_1 (@ tptp.groups1752964319039525884d_enat F))) (=> (@ tptp.finite3207457112153483333omplex B) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex B) A2)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F B4)))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ _let_1 A2)) (@ _let_1 B))))))) (forall ((B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.extended_enat))) (let ((_let_1 (@ tptp.groups2433450451889696826d_enat F))) (=> (@ tptp.finite4001608067531595151d_enat B) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) B) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) (@ (@ tptp.minus_925952699566721837d_enat B) A2)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F B4)))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ _let_1 A2)) (@ _let_1 B))))))) (forall ((B tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real F))) (=> (@ tptp.finite_finite_real B) (=> (@ (@ tptp.ord_less_eq_set_real A2) B) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real B) A2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F B4)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B))))))) (forall ((B tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real F))) (=> (@ tptp.finite3207457112153483333omplex B) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex B) A2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F B4)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B))))))) (forall ((B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups4148127829035722712t_real F))) (=> (@ tptp.finite4001608067531595151d_enat B) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) B) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) (@ (@ tptp.minus_925952699566721837d_enat B) A2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F B4)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B))))))) (forall ((B tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat F))) (=> (@ tptp.finite_finite_real B) (=> (@ (@ tptp.ord_less_eq_set_real A2) B) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real B) A2)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F B4)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B))))))) (forall ((B tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat F))) (=> (@ tptp.finite3207457112153483333omplex B) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex B) A2)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F B4)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B))))))) (forall ((B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2027974829824023292at_nat F))) (=> (@ tptp.finite4001608067531595151d_enat B) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) B) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) (@ (@ tptp.minus_925952699566721837d_enat B) A2)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F B4)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B))))))) (forall ((B tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int F))) (=> (@ tptp.finite_finite_real B) (=> (@ (@ tptp.ord_less_eq_set_real A2) B) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real B) A2)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F B4)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B))))))) (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex))))))))) (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_int (@ G X)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex))))))))) (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_real (@ G X)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex))))))))) (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.extended_enat))) (let ((_let_1 (@ tptp.groups1752964319039525884d_enat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_p3455044024723400733d_enat (@ G X)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex))))))))) (forall ((A2 tptp.set_Extended_enat) (X tptp.extended_enat) (G (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2027974829824023292at_nat G))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ (@ tptp.member_Extended_enat X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ (@ tptp.insert_Extended_enat X) tptp.bot_bo7653980558646680370d_enat))))))))) (forall ((A2 tptp.set_Extended_enat) (X tptp.extended_enat) (G (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2025484359314973016at_int G))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ (@ tptp.member_Extended_enat X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_int (@ G X)) (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ (@ tptp.insert_Extended_enat X) tptp.bot_bo7653980558646680370d_enat))))))))) (forall ((A2 tptp.set_Extended_enat) (X tptp.extended_enat) (G (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups4148127829035722712t_real G))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ (@ tptp.member_Extended_enat X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_real (@ G X)) (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ (@ tptp.insert_Extended_enat X) tptp.bot_bo7653980558646680370d_enat))))))))) (forall ((A2 tptp.set_Extended_enat) (X tptp.extended_enat) (G (-> tptp.extended_enat tptp.extended_enat))) (let ((_let_1 (@ tptp.groups2433450451889696826d_enat G))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ (@ tptp.member_Extended_enat X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_p3455044024723400733d_enat (@ G X)) (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ (@ tptp.insert_Extended_enat X) tptp.bot_bo7653980558646680370d_enat))))))))) (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat G))) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))))))))) (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int G))) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_int (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))))))))) (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (X tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X))) (let ((_let_2 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_1 tptp.bot_bot_set_complex))))))))) (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.int)) (X tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X))) (let ((_let_2 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_int (@ G X)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_1 tptp.bot_bot_set_complex))))))))) (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.real)) (X tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X))) (let ((_let_2 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_real (@ G X)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_1 tptp.bot_bot_set_complex))))))))) (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.extended_enat)) (X tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X))) (let ((_let_2 (@ tptp.groups1752964319039525884d_enat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ G X)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_1 tptp.bot_bot_set_complex))))))))) (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.nat)) (X tptp.extended_enat)) (let ((_let_1 (@ tptp.insert_Extended_enat X))) (let ((_let_2 (@ tptp.groups2027974829824023292at_nat G))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_2 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ _let_1 tptp.bot_bo7653980558646680370d_enat))))))))) (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.int)) (X tptp.extended_enat)) (let ((_let_1 (@ tptp.insert_Extended_enat X))) (let ((_let_2 (@ tptp.groups2025484359314973016at_int G))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_int (@ G X)) (@ _let_2 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ _let_1 tptp.bot_bo7653980558646680370d_enat))))))))) (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.real)) (X tptp.extended_enat)) (let ((_let_1 (@ tptp.insert_Extended_enat X))) (let ((_let_2 (@ tptp.groups4148127829035722712t_real G))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_real (@ G X)) (@ _let_2 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ _let_1 tptp.bot_bo7653980558646680370d_enat))))))))) (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.extended_enat)) (X tptp.extended_enat)) (let ((_let_1 (@ tptp.insert_Extended_enat X))) (let ((_let_2 (@ tptp.groups2433450451889696826d_enat G))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ G X)) (@ _let_2 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ _let_1 tptp.bot_bo7653980558646680370d_enat))))))))) (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.nat)) (X tptp.real)) (let ((_let_1 (@ tptp.insert_real X))) (let ((_let_2 (@ tptp.groups1935376822645274424al_nat G))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_real A2) (@ _let_1 tptp.bot_bot_set_real))))))))) (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.int)) (X tptp.real)) (let ((_let_1 (@ tptp.insert_real X))) (let ((_let_2 (@ tptp.groups1932886352136224148al_int G))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_int (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_real A2) (@ _let_1 tptp.bot_bot_set_real))))))))) (forall ((A2 tptp.set_complex) (A tptp.complex) (F (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_4 (@ (@ tptp.member_complex A) A2))) (=> (@ tptp.finite3207457112153483333omplex A2) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_int _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2))))))))) (forall ((A2 tptp.set_Extended_enat) (A tptp.extended_enat) (F (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2025484359314973016at_int F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat))))) (let ((_let_4 (@ (@ tptp.member_Extended_enat A) A2))) (=> (@ tptp.finite4001608067531595151d_enat A2) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_int _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2))))))))) (forall ((A2 tptp.set_real) (A tptp.real) (F (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_4 (@ (@ tptp.member_real A) A2))) (=> (@ tptp.finite_finite_real A2) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_int _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2))))))))) (forall ((A2 tptp.set_complex) (A tptp.complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_4 (@ (@ tptp.member_complex A) A2))) (=> (@ tptp.finite3207457112153483333omplex A2) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_real _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2))))))))) (forall ((A2 tptp.set_Extended_enat) (A tptp.extended_enat) (F (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups4148127829035722712t_real F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat))))) (let ((_let_4 (@ (@ tptp.member_Extended_enat A) A2))) (=> (@ tptp.finite4001608067531595151d_enat A2) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_real _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2))))))))) (forall ((A2 tptp.set_real) (A tptp.real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_4 (@ (@ tptp.member_real A) A2))) (=> (@ tptp.finite_finite_real A2) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_real _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2))))))))) (forall ((A2 tptp.set_int) (A tptp.int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_4 (@ (@ tptp.member_int A) A2))) (=> (@ tptp.finite_finite_int A2) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_real _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2))))))))) (forall ((A2 tptp.set_nat) (A tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))) (let ((_let_4 (@ (@ tptp.member_nat A) A2))) (=> (@ tptp.finite_finite_nat A2) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_int _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2))))))))) (forall ((A2 tptp.set_int) (A tptp.int) (F (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.groups4538972089207619220nt_int F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_4 (@ (@ tptp.member_int A) A2))) (=> (@ tptp.finite_finite_int A2) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_int _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2))))))))) (forall ((A2 tptp.set_complex) (A tptp.complex) (F (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups7754918857620584856omplex F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_4 (@ (@ tptp.member_complex A) A2))) (=> (@ tptp.finite3207457112153483333omplex A2) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_complex _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2))))))))) (forall ((S2 tptp.set_complex) (A tptp.complex) (B2 (-> tptp.complex tptp.nat)) (C (-> tptp.complex tptp.nat))) (let ((_let_1 (@ (@ tptp.groups5693394587270226106ex_nat C) (@ (@ tptp.minus_811609699411566653omplex S2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_2 (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) (@ (@ tptp.plus_plus_nat (@ B2 A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) _let_1))))))) (forall ((S2 tptp.set_complex) (A tptp.complex) (B2 (-> tptp.complex tptp.int)) (C (-> tptp.complex tptp.int))) (let ((_let_1 (@ (@ tptp.groups5690904116761175830ex_int C) (@ (@ tptp.minus_811609699411566653omplex S2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_2 (= (@ (@ tptp.groups5690904116761175830ex_int (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) (@ (@ tptp.plus_plus_int (@ B2 A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups5690904116761175830ex_int (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) _let_1))))))) (forall ((S2 tptp.set_complex) (A tptp.complex) (B2 (-> tptp.complex tptp.real)) (C (-> tptp.complex tptp.real))) (let ((_let_1 (@ (@ tptp.groups5808333547571424918x_real C) (@ (@ tptp.minus_811609699411566653omplex S2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_2 (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) (@ (@ tptp.plus_plus_real (@ B2 A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) _let_1))))))) (forall ((S2 tptp.set_complex) (A tptp.complex) (B2 (-> tptp.complex tptp.extended_enat)) (C (-> tptp.complex tptp.extended_enat))) (let ((_let_1 (@ (@ tptp.groups1752964319039525884d_enat C) (@ (@ tptp.minus_811609699411566653omplex S2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_2 (= (@ (@ tptp.groups1752964319039525884d_enat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_Extended_enat (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) (@ (@ tptp.plus_p3455044024723400733d_enat (@ B2 A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups1752964319039525884d_enat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_Extended_enat (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) _let_1))))))) (forall ((S2 tptp.set_Extended_enat) (A tptp.extended_enat) (B2 (-> tptp.extended_enat tptp.nat)) (C (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ (@ tptp.groups2027974829824023292at_nat C) (@ (@ tptp.minus_925952699566721837d_enat S2) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat))))) (let ((_let_2 (@ (@ tptp.member_Extended_enat A) S2))) (=> (@ tptp.finite4001608067531595151d_enat S2) (and (=> _let_2 (= (@ (@ tptp.groups2027974829824023292at_nat (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) (@ (@ tptp.plus_plus_nat (@ B2 A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups2027974829824023292at_nat (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) _let_1))))))) (forall ((S2 tptp.set_Extended_enat) (A tptp.extended_enat) (B2 (-> tptp.extended_enat tptp.int)) (C (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ (@ tptp.groups2025484359314973016at_int C) (@ (@ tptp.minus_925952699566721837d_enat S2) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat))))) (let ((_let_2 (@ (@ tptp.member_Extended_enat A) S2))) (=> (@ tptp.finite4001608067531595151d_enat S2) (and (=> _let_2 (= (@ (@ tptp.groups2025484359314973016at_int (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) (@ (@ tptp.plus_plus_int (@ B2 A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups2025484359314973016at_int (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) _let_1))))))) (forall ((S2 tptp.set_Extended_enat) (A tptp.extended_enat) (B2 (-> tptp.extended_enat tptp.real)) (C (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ (@ tptp.groups4148127829035722712t_real C) (@ (@ tptp.minus_925952699566721837d_enat S2) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat))))) (let ((_let_2 (@ (@ tptp.member_Extended_enat A) S2))) (=> (@ tptp.finite4001608067531595151d_enat S2) (and (=> _let_2 (= (@ (@ tptp.groups4148127829035722712t_real (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) (@ (@ tptp.plus_plus_real (@ B2 A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups4148127829035722712t_real (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) _let_1))))))) (forall ((S2 tptp.set_Extended_enat) (A tptp.extended_enat) (B2 (-> tptp.extended_enat tptp.extended_enat)) (C (-> tptp.extended_enat tptp.extended_enat))) (let ((_let_1 (@ (@ tptp.groups2433450451889696826d_enat C) (@ (@ tptp.minus_925952699566721837d_enat S2) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat))))) (let ((_let_2 (@ (@ tptp.member_Extended_enat A) S2))) (=> (@ tptp.finite4001608067531595151d_enat S2) (and (=> _let_2 (= (@ (@ tptp.groups2433450451889696826d_enat (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_Extended_enat (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) (@ (@ tptp.plus_p3455044024723400733d_enat (@ B2 A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups2433450451889696826d_enat (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_Extended_enat (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) _let_1))))))) (forall ((S2 tptp.set_real) (A tptp.real) (B2 (-> tptp.real tptp.nat)) (C (-> tptp.real tptp.nat))) (let ((_let_1 (@ (@ tptp.groups1935376822645274424al_nat C) (@ (@ tptp.minus_minus_set_real S2) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_2 (@ (@ tptp.member_real A) S2))) (=> (@ tptp.finite_finite_real S2) (and (=> _let_2 (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) (@ (@ tptp.plus_plus_nat (@ B2 A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) _let_1))))))) (forall ((S2 tptp.set_real) (A tptp.real) (B2 (-> tptp.real tptp.int)) (C (-> tptp.real tptp.int))) (let ((_let_1 (@ (@ tptp.groups1932886352136224148al_int C) (@ (@ tptp.minus_minus_set_real S2) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_2 (@ (@ tptp.member_real A) S2))) (=> (@ tptp.finite_finite_real S2) (and (=> _let_2 (= (@ (@ tptp.groups1932886352136224148al_int (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) (@ (@ tptp.plus_plus_int (@ B2 A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups1932886352136224148al_int (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) _let_1))))))) (forall ((B tptp.set_real) (A2 tptp.set_real) (B2 tptp.real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real F))) (=> (@ tptp.finite_finite_real B) (=> (@ (@ tptp.ord_less_eq_set_real A2) B) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real B) A2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F B2)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) B) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B))))))))) (forall ((B tptp.set_complex) (A2 tptp.set_complex) (B2 tptp.complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real F))) (=> (@ tptp.finite3207457112153483333omplex B) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex B) A2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F B2)) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) B) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B))))))))) (forall ((B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (B2 tptp.extended_enat) (F (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups4148127829035722712t_real F))) (=> (@ tptp.finite4001608067531595151d_enat B) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) B) (=> (@ (@ tptp.member_Extended_enat B2) (@ (@ tptp.minus_925952699566721837d_enat B) A2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F B2)) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) B) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B))))))))) (forall ((B tptp.set_real) (A2 tptp.set_real) (B2 tptp.real) (F (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat F))) (=> (@ tptp.finite_finite_real B) (=> (@ (@ tptp.ord_less_eq_set_real A2) B) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real B) A2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F B2)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) B) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X5)))) (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B))))))))) (forall ((B tptp.set_complex) (A2 tptp.set_complex) (B2 tptp.complex) (F (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat F))) (=> (@ tptp.finite3207457112153483333omplex B) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex B) A2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F B2)) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) B) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X5)))) (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B))))))))) (forall ((B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (B2 tptp.extended_enat) (F (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2027974829824023292at_nat F))) (=> (@ tptp.finite4001608067531595151d_enat B) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) B) (=> (@ (@ tptp.member_Extended_enat B2) (@ (@ tptp.minus_925952699566721837d_enat B) A2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F B2)) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) B) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X5)))) (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B))))))))) (forall ((B tptp.set_real) (A2 tptp.set_real) (B2 tptp.real) (F (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int F))) (=> (@ tptp.finite_finite_real B) (=> (@ (@ tptp.ord_less_eq_set_real A2) B) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real B) A2)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F B2)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) B) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X5)))) (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B))))))))) (forall ((B tptp.set_complex) (A2 tptp.set_complex) (B2 tptp.complex) (F (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int F))) (=> (@ tptp.finite3207457112153483333omplex B) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex B) A2)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F B2)) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) B) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X5)))) (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B))))))))) (forall ((B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (B2 tptp.extended_enat) (F (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2025484359314973016at_int F))) (=> (@ tptp.finite4001608067531595151d_enat B) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) B) (=> (@ (@ tptp.member_Extended_enat B2) (@ (@ tptp.minus_925952699566721837d_enat B) A2)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F B2)) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) B) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X5)))) (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B))))))))) (forall ((B tptp.set_nat) (A2 tptp.set_nat) (B2 tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int F))) (=> (@ tptp.finite_finite_nat B) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B) (=> (@ (@ tptp.member_nat B2) (@ (@ tptp.minus_minus_set_nat B) A2)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F B2)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) B) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X5)))) (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B))))))))) (forall ((I tptp.complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.extended_enat))) (=> (@ (@ tptp.member_complex I) A2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex I) tptp.bot_bot_set_complex))) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (=> (@ tptp.finite3207457112153483333omplex A2) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F I)) (@ (@ tptp.groups1752964319039525884d_enat F) A2)))))) (forall ((I tptp.extended_enat) (A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.extended_enat))) (=> (@ (@ tptp.member_Extended_enat I) A2) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat A2) (@ (@ tptp.insert_Extended_enat I) tptp.bot_bo7653980558646680370d_enat))) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (=> (@ tptp.finite4001608067531595151d_enat A2) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F I)) (@ (@ tptp.groups2433450451889696826d_enat F) A2)))))) (forall ((I tptp.real) (A2 tptp.set_real) (F (-> tptp.real tptp.extended_enat))) (=> (@ (@ tptp.member_real I) A2) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real I) tptp.bot_bot_set_real))) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (=> (@ tptp.finite_finite_real A2) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F I)) (@ (@ tptp.groups2800946370649118462d_enat F) A2)))))) (forall ((I tptp.int) (A2 tptp.set_int) (F (-> tptp.int tptp.extended_enat))) (=> (@ (@ tptp.member_int I) A2) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int I) tptp.bot_bot_set_int))) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (=> (@ tptp.finite_finite_int A2) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F I)) (@ (@ tptp.groups4225252721152677374d_enat F) A2)))))) (forall ((I tptp.nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.extended_enat))) (=> (@ (@ tptp.member_nat I) A2) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) (@ (@ tptp.minus_minus_set_nat A2) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (=> (@ tptp.finite_finite_nat A2) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F I)) (@ (@ tptp.groups7108830773950497114d_enat F) A2)))))) (forall ((I tptp.complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ (@ tptp.member_complex I) A2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex I) tptp.bot_bot_set_complex))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (=> (@ tptp.finite3207457112153483333omplex A2) (@ (@ tptp.ord_less_eq_real (@ F I)) (@ (@ tptp.groups5808333547571424918x_real F) A2)))))) (forall ((I tptp.extended_enat) (A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real))) (=> (@ (@ tptp.member_Extended_enat I) A2) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat A2) (@ (@ tptp.insert_Extended_enat I) tptp.bot_bo7653980558646680370d_enat))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (=> (@ tptp.finite4001608067531595151d_enat A2) (@ (@ tptp.ord_less_eq_real (@ F I)) (@ (@ tptp.groups4148127829035722712t_real F) A2)))))) (forall ((I tptp.real) (A2 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.member_real I) A2) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real I) tptp.bot_bot_set_real))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (=> (@ tptp.finite_finite_real A2) (@ (@ tptp.ord_less_eq_real (@ F I)) (@ (@ tptp.groups8097168146408367636l_real F) A2)))))) (forall ((I tptp.int) (A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ (@ tptp.member_int I) A2) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int I) tptp.bot_bot_set_int))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (=> (@ tptp.finite_finite_int A2) (@ (@ tptp.ord_less_eq_real (@ F I)) (@ (@ tptp.groups8778361861064173332t_real F) A2)))))) (forall ((I tptp.complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ (@ tptp.member_complex I) A2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex I) tptp.bot_bot_set_complex))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X5)))) (=> (@ tptp.finite3207457112153483333omplex A2) (@ (@ tptp.ord_less_eq_nat (@ F I)) (@ (@ tptp.groups5693394587270226106ex_nat F) A2)))))) (forall ((X tptp.int) (Xa2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int X) Xa2)))) (let ((_let_2 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ tptp.dvd_dvd_int _let_2))) (let ((_let_4 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_3 X)) (not (@ _let_3 Xa2)))))) (let ((_let_5 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_6 (and (@ (@ tptp.member_int X) _let_5) (@ (@ tptp.member_int Xa2) _let_5)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X) Xa2) Y) (=> _let_1 (not (=> (and (=> _let_6 (= Y (@ tptp.uminus_uminus_int _let_4))) (=> (not _let_6) (= Y (@ (@ tptp.plus_plus_int _let_4) (@ (@ tptp.times_times_int _let_2) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int X) _let_2)) (@ (@ tptp.divide_divide_int Xa2) _let_2))))))) (not _let_1)))))))))))) (forall ((K tptp.int) (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))))))))))))))) (= tptp.bit_ri631733984087533419it_int (lambda ((N tptp.nat) (K2 tptp.int)) (let ((_let_1 (@ tptp.suc N))) (@ (@ tptp.minus_minus_int (@ (@ tptp.bit_se2923211474154528505it_int _let_1) K2)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K2) N))))))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat M2) 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 M2) (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat)))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)) X))) (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)))) (forall ((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)))) _let_143 (= (@ tptp.bit_se1148574629649215175it_nat tptp.zero_zero_nat) tptp.bot_bot_nat_o) (= (@ tptp.archim7802044766580827645g_real tptp.zero_zero_real) tptp.zero_zero_int) (forall ((X tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)) (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) tptp.zero_zero_nat)) (forall ((M2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M2))) (@ tptp.suc N2)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int M2)) N2))) (forall ((M2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 M2))) (@ tptp.suc N2)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat M2)) N2))) (forall ((M2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M2))) (@ tptp.suc N2)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int M2)) N2))) (forall ((M2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 M2))) (@ tptp.suc N2)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat M2)) N2))) (forall ((X tptp.real) (Z3 tptp.int)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X) (@ tptp.ring_1_of_int_real Z3))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X)) Z3))) (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) tptp.one_one_nat)) (forall ((X tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat)) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X))) (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.numeral_numeral_real V)))) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X))) (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real V)) X))) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real))) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real tptp.one_one_real) X))) (forall ((X tptp.real) (V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X) (@ tptp.numeral_numeral_real V))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.numeral_numeral_int V)))) (forall ((X tptp.real)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X)) tptp.one_one_int))) (forall ((W2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 W2)))) (@ tptp.suc N2)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W2))) N2))) (forall ((W2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 W2)))) (@ tptp.suc N2)) (not (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W2)) N2)))) (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 ((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.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) (M2 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (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) M2))) (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) (M2 tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_3 (@ tptp.groups2073611262835488442omplex G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M2))) (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) (M2 tptp.nat) (G (-> tptp.nat tptp.extended_enat))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_3 (@ tptp.groups7108830773950497114d_enat G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M2))) (and (=> _let_5 (= _let_4 tptp.zero_z5237406670263579293d_enat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_p3455044024723400733d_enat (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))))) (forall ((N2 tptp.nat) (M2 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (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) M2))) (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) (M2 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (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) M2))) (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 ((X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real X) (@ tptp.uminus_uminus_real tptp.one_one_real)))) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X))) (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.complex))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I3)))) A2) (@ C tptp.zero_zero_nat))) (=> (not _let_1) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I3)))) A2) tptp.zero_zero_complex))))) (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.real))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I3)))) A2) (@ C tptp.zero_zero_nat))) (=> (not _let_1) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I3)))) A2) tptp.zero_zero_real))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.modulo_modulo_int A) _let_1)) N2) (and (= N2 tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_int _let_1) A)))))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) N2) (and (= N2 tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_nat _let_1) A)))))) (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)))) (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)) X))) (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_real X) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))))) (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) X))) (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.complex)) (D (-> tptp.nat tptp.complex))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I3))) (@ D I3)))) A2) (@ (@ tptp.divide1717551699836669952omplex (@ C tptp.zero_zero_nat)) (@ D tptp.zero_zero_nat)))) (=> (not _let_1) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I3))) (@ D I3)))) A2) tptp.zero_zero_complex))))) (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.real)) (D (-> tptp.nat tptp.real))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I3))) (@ D I3)))) A2) (@ (@ tptp.divide_divide_real (@ C tptp.zero_zero_nat)) (@ D tptp.zero_zero_nat)))) (=> (not _let_1) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I3))) (@ D I3)))) A2) tptp.zero_zero_real))))) (forall ((A tptp.int) (B2 tptp.int) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (or (not (@ (@ tptp.bit_se1146084159140164899it_int A) N3)) (not (@ (@ tptp.bit_se1146084159140164899it_int B2) N3)))) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.plus_plus_int A) B2)) N2) (or (@ (@ tptp.bit_se1146084159140164899it_int A) N2) (@ (@ tptp.bit_se1146084159140164899it_int B2) N2))))) (forall ((A tptp.nat) (B2 tptp.nat) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (or (not (@ (@ tptp.bit_se1148574629649215175it_nat A) N3)) (not (@ (@ tptp.bit_se1148574629649215175it_nat B2) N3)))) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.plus_plus_nat A) B2)) N2) (or (@ (@ tptp.bit_se1148574629649215175it_nat A) N2) (@ (@ tptp.bit_se1148574629649215175it_nat B2) 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 ((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 ((M2 tptp.nat) (A tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se2925701944663578781it_nat M2) A)) N2) (and (@ (@ tptp.ord_less_nat N2) M2) (@ (@ tptp.bit_se1148574629649215175it_nat A) N2)))) (forall ((M2 tptp.nat) (A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se2923211474154528505it_int M2) A)) N2) (and (@ (@ tptp.ord_less_nat N2) M2) (@ (@ tptp.bit_se1146084159140164899it_int A) N2)))) (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y) X) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real Y)) (@ tptp.archim7802044766580827645g_real X)))) (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real X)))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.archim7802044766580827645g_real Y)) (@ (@ tptp.ord_less_real X) Y))) (forall ((B2 Bool) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.zero_n2684676970156552555ol_int B2)) N2) (and B2 (= N2 tptp.zero_zero_nat)))) (forall ((B2 Bool) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.zero_n2687167440665602831ol_nat B2)) N2) (and B2 (= N2 tptp.zero_zero_nat)))) (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.nat)) (F (-> tptp.extended_enat tptp.nat))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) A2) (@ (@ tptp.ord_less_eq_nat (@ G X5)) (@ F X5)))) (= (@ (@ tptp.groups2027974829824023292at_nat (lambda ((X4 tptp.extended_enat)) (@ (@ tptp.minus_minus_nat (@ F X4)) (@ G X4)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups2027974829824023292at_nat F) A2)) (@ (@ tptp.groups2027974829824023292at_nat G) A2))))) (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 ((X4 tptp.real)) (@ (@ tptp.minus_minus_nat (@ F X4)) (@ G X4)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups1935376822645274424al_nat F) A2)) (@ (@ tptp.groups1935376822645274424al_nat G) A2))))) (forall ((A2 tptp.set_set_nat) (G (-> tptp.set_nat tptp.nat)) (F (-> tptp.set_nat tptp.nat))) (=> (forall ((X5 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X5) A2) (@ (@ tptp.ord_less_eq_nat (@ G X5)) (@ F X5)))) (= (@ (@ tptp.groups8294997508430121362at_nat (lambda ((X4 tptp.set_nat)) (@ (@ tptp.minus_minus_nat (@ F X4)) (@ G X4)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups8294997508430121362at_nat F) A2)) (@ (@ tptp.groups8294997508430121362at_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 ((X4 tptp.int)) (@ (@ tptp.minus_minus_nat (@ F X4)) (@ G X4)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) (@ (@ tptp.groups4541462559716669496nt_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 ((X4 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ F X4)) (@ G X4)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups3542108847815614940at_nat G) A2))))) (forall ((G (-> tptp.nat tptp.nat)) (M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) (@ tptp.suc N2))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N2)))) (forall ((G (-> tptp.nat tptp.real)) (M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) (@ tptp.suc N2))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N2)))) (forall ((G (-> tptp.nat tptp.nat)) (M2 tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M2) 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 M2) N2)))) (forall ((G (-> tptp.nat tptp.real)) (M2 tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M2) 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 M2) N2)))) (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (= (@ (@ tptp.groups5693394587270226106ex_nat F) A2) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A2) (= (@ F X4) (@ tptp.suc tptp.zero_zero_nat)) (forall ((Y5 tptp.complex)) (=> (@ (@ tptp.member_complex Y5) A2) (=> (not (= X4 Y5)) (= (@ F Y5) tptp.zero_zero_nat))))))))) (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (= (= (@ (@ tptp.groups4541462559716669496nt_nat F) A2) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A2) (= (@ F X4) (@ tptp.suc tptp.zero_zero_nat)) (forall ((Y5 tptp.int)) (=> (@ (@ tptp.member_int Y5) A2) (=> (not (= X4 Y5)) (= (@ F Y5) tptp.zero_zero_nat))))))))) (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (= (@ (@ tptp.groups2027974829824023292at_nat F) A2) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) A2) (= (@ F X4) (@ tptp.suc tptp.zero_zero_nat)) (forall ((Y5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat Y5) A2) (=> (not (= X4 Y5)) (= (@ F Y5) tptp.zero_zero_nat))))))))) (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (= (= (@ (@ tptp.groups3542108847815614940at_nat F) A2) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A2) (= (@ F X4) (@ tptp.suc tptp.zero_zero_nat)) (forall ((Y5 tptp.nat)) (=> (@ (@ tptp.member_nat Y5) A2) (=> (not (= X4 Y5)) (= (@ F Y5) tptp.zero_zero_nat))))))))) (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.groups3542108847815614940at_nat F) A2) (@ tptp.suc N2)) (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X5)))))) (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (= (@ (@ tptp.groups5693394587270226106ex_nat F) A2) tptp.one_one_nat) (exists ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A2) (= (@ F X4) tptp.one_one_nat) (forall ((Y5 tptp.complex)) (=> (@ (@ tptp.member_complex Y5) A2) (=> (not (= X4 Y5)) (= (@ F Y5) tptp.zero_zero_nat))))))))) (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (= (= (@ (@ tptp.groups4541462559716669496nt_nat F) A2) tptp.one_one_nat) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A2) (= (@ F X4) tptp.one_one_nat) (forall ((Y5 tptp.int)) (=> (@ (@ tptp.member_int Y5) A2) (=> (not (= X4 Y5)) (= (@ F Y5) tptp.zero_zero_nat))))))))) (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (= (@ (@ tptp.groups2027974829824023292at_nat F) A2) tptp.one_one_nat) (exists ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) A2) (= (@ F X4) tptp.one_one_nat) (forall ((Y5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat Y5) A2) (=> (not (= X4 Y5)) (= (@ F Y5) tptp.zero_zero_nat))))))))) (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (= (= (@ (@ tptp.groups3542108847815614940at_nat F) A2) tptp.one_one_nat) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A2) (= (@ F X4) tptp.one_one_nat) (forall ((Y5 tptp.nat)) (=> (@ (@ tptp.member_nat Y5) A2) (=> (not (= X4 Y5)) (= (@ F Y5) tptp.zero_zero_nat))))))))) (forall ((X tptp.real) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_real X) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) A))) (forall ((X tptp.real) (Z3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) Z3) (@ (@ tptp.ord_less_eq_real X) (@ tptp.ring_1_of_int_real Z3)))) (forall ((Z3 tptp.int) (X tptp.real)) (= (@ (@ tptp.ord_less_int Z3) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z3)) X))) (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X) Y))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.archim7802044766580827645g_real Y)))) (forall ((X tptp.int) (M2 tptp.nat) (I6 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_int X))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_int X) (@ (@ tptp.plus_plus_nat M2) I3)))) I6) (@ (@ tptp.times_times_int (@ _let_1 M2)) (@ (@ tptp.groups3539618377306564664at_int _let_1) I6))))) (forall ((X tptp.complex) (M2 tptp.nat) (I6 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_complex X))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_complex X) (@ (@ tptp.plus_plus_nat M2) I3)))) I6) (@ (@ tptp.times_times_complex (@ _let_1 M2)) (@ (@ tptp.groups2073611262835488442omplex _let_1) I6))))) (forall ((X tptp.real) (M2 tptp.nat) (I6 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_real X))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_real X) (@ (@ tptp.plus_plus_nat M2) I3)))) I6) (@ (@ tptp.times_times_real (@ _let_1 M2)) (@ (@ tptp.groups6591440286371151544t_real _let_1) I6))))) (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N2) M2))) (= (@ (@ tptp.groups3542108847815614940at_nat G) _let_1) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M2) N2)) I3)))) _let_1)))) (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N2) M2))) (= (@ (@ tptp.groups6591440286371151544t_real G) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M2) N2)) I3)))) _let_1)))) (forall ((N2 tptp.nat) (C tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N2) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X4 tptp.complex)) X4)) (@ tptp.collect_complex (lambda ((Z6 tptp.complex)) (= (@ (@ tptp.power_power_complex Z6) N2) C)))) tptp.zero_zero_complex))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N2) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X4 tptp.complex)) X4)) (@ tptp.collect_complex (lambda ((Z6 tptp.complex)) (= (@ (@ tptp.power_power_complex Z6) N2) tptp.one_one_complex)))) tptp.zero_zero_complex))) (forall ((R2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real R2))) (@ (@ tptp.plus_plus_real R2) tptp.one_one_real))) (forall ((R2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real R2))) tptp.one_one_real)) R2)) (forall ((B tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat F))) (=> (@ tptp.finite3207457112153483333omplex B) (=> (@ (@ tptp.ord_le211207098394363844omplex B) A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B)) (@ (@ tptp.minus_minus_nat (@ _let_1 A2)) (@ _let_1 B))))))) (forall ((B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2027974829824023292at_nat F))) (=> (@ tptp.finite4001608067531595151d_enat B) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B) A2) (= (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) B)) (@ (@ tptp.minus_minus_nat (@ _let_1 A2)) (@ _let_1 B))))))) (forall ((B tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat F))) (=> (@ tptp.finite_finite_int B) (=> (@ (@ tptp.ord_less_eq_set_int B) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B)) (@ (@ tptp.minus_minus_nat (@ _let_1 A2)) (@ _let_1 B))))))) (forall ((B tptp.set_nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat F))) (=> (@ tptp.finite_finite_nat B) (=> (@ (@ tptp.ord_less_eq_set_nat B) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B)) (@ (@ tptp.minus_minus_nat (@ _let_1 A2)) (@ _let_1 B))))))) (forall ((A tptp.set_nat) (A2 tptp.set_set_nat) (F (-> tptp.set_nat tptp.nat))) (let ((_let_1 (@ tptp.groups8294997508430121362at_nat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A2) (@ (@ tptp.insert_set_nat A) tptp.bot_bot_set_set_nat))))) (let ((_let_4 (@ (@ tptp.member_set_nat A) A2))) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2)))))))) (forall ((A tptp.extended_enat) (A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2027974829824023292at_nat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat))))) (let ((_let_4 (@ (@ tptp.member_Extended_enat A) A2))) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2)))))))) (forall ((A tptp.real) (A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_4 (@ (@ tptp.member_real A) A2))) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2)))))))) (forall ((A tptp.int) (A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_4 (@ (@ tptp.member_int A) A2))) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2)))))))) (forall ((A tptp.nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))) (let ((_let_4 (@ (@ tptp.member_nat A) A2))) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2)))))))) (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.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.extended_enat)) (K tptp.nat)) (let ((_let_1 (@ tptp.groups7108830773950497114d_enat F))) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_z5237406670263579293d_enat) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) K)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K)))))) (forall ((F (-> tptp.nat tptp.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.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.extended_enat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups7108830773950497114d_enat G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ _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 ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int G))) (let ((_let_3 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_int (@ G _let_3)) (@ _let_2 (@ _let_1 N2))))))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.extended_enat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.groups7108830773950497114d_enat G))) (let ((_let_3 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ G _let_3)) (@ _let_2 (@ _let_1 N2))))))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.groups3542108847815614940at_nat G))) (let ((_let_3 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_nat (@ G _let_3)) (@ _let_2 (@ _let_1 N2))))))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real G))) (let ((_let_3 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_real (@ G _let_3)) (@ _let_2 (@ _let_1 N2))))))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N2)) (@ (@ tptp.plus_plus_int (@ G M2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N2))))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.extended_enat))) (let ((_let_1 (@ tptp.groups7108830773950497114d_enat G))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N2)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ G M2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N2))))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N2)) (@ (@ tptp.plus_plus_nat (@ G M2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N2))))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups6591440286371151544t_real G))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N2)) (@ (@ tptp.plus_plus_real (@ G M2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N2))))))) (forall ((N2 tptp.nat) (M2 tptp.nat) (K tptp.int)) (=> (@ (@ tptp.ord_less_nat N2) M2) (=> (@ (@ tptp.bit_se1146084159140164899it_int K) N2) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int M2) K))))) (forall ((M2 tptp.nat) (K tptp.int) (L tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ (@ tptp.bit_concat_bit M2) K) L)) N2) (or (and (@ (@ tptp.ord_less_nat N2) M2) (@ (@ tptp.bit_se1146084159140164899it_int K) N2)) (and (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.bit_se1146084159140164899it_int L) (@ (@ tptp.minus_minus_nat N2) M2)))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.groups3539618377306564664at_int G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.plus_plus_int (@ G M2)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.extended_enat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.groups7108830773950497114d_enat G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.plus_p3455044024723400733d_enat (@ G M2)) (@ (@ tptp.groups7108830773950497114d_enat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups3542108847815614940at_nat G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.plus_plus_nat (@ G M2)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.plus_plus_real (@ G M2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_1) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I3))) (@ F I3)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N2)) (@ (@ tptp.minus_minus_int (@ F _let_1)) (@ F M2)))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_1) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F (@ tptp.suc I3))) (@ F I3)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N2)) (@ (@ tptp.minus_minus_real (@ F _let_1)) (@ F M2)))))) (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.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 ((X tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real X)))) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) X) (@ (@ tptp.ord_less_eq_real X) _let_1)))) (forall ((Z3 tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real Z3))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (= (@ tptp.archim7802044766580827645g_real X) Z3))))) (forall ((X tptp.real) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real A))) (= (= (@ tptp.archim7802044766580827645g_real X) A) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) X) (@ (@ tptp.ord_less_eq_real X) _let_1))))) (forall ((P (-> tptp.int Bool)) (T tptp.real)) (= (@ P (@ tptp.archim7802044766580827645g_real T)) (forall ((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)) T) (@ (@ tptp.ord_less_eq_real T) _let_1)) (@ P I3)))))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real (@ (@ tptp.times_times_real A) B2))) (@ (@ tptp.times_times_int (@ tptp.archim7802044766580827645g_real A)) (@ tptp.archim7802044766580827645g_real B2))))))) (forall ((X tptp.real) (Z3 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X)) Z3) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real Z3)) tptp.one_one_real)))) (forall ((Z3 tptp.int) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_int Z3) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real Z3)) tptp.one_one_real)) X))) (forall ((K tptp.int)) (not (forall ((N3 tptp.nat)) (let ((_let_1 (@ tptp.bit_se1146084159140164899it_int K))) (=> (forall ((M5 tptp.nat)) (let ((_let_1 (@ tptp.bit_se1146084159140164899it_int K))) (=> (@ (@ tptp.ord_less_eq_nat N3) M5) (= (@ _let_1 M5) (@ _let_1 N3))))) (not (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)) (not (@ _let_1 N3)))))))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int)) (P5 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (let ((_let_2 (@ _let_1 P5))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups3539618377306564664at_int G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _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 ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.extended_enat)) (P5 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (let ((_let_2 (@ _let_1 P5))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups7108830773950497114d_enat G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ _let_4 (@ _let_5 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat)) (P5 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (let ((_let_2 (@ _let_1 P5))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups3542108847815614940at_nat G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _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 ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.real)) (P5 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (let ((_let_2 (@ _let_1 P5))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups6591440286371151544t_real G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _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 ((Xs tptp.list_complex) (X8 tptp.set_complex)) (=> (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs)) X8) (=> (@ tptp.finite3207457112153483333omplex X8) (= (@ (@ tptp.groups5693394587270226106ex_nat (@ tptp.count_list_complex Xs)) X8) (@ tptp.size_s3451745648224563538omplex Xs))))) (forall ((Xs tptp.list_Extended_enat) (X8 tptp.set_Extended_enat)) (=> (@ (@ tptp.ord_le7203529160286727270d_enat (@ tptp.set_Extended_enat2 Xs)) X8) (=> (@ tptp.finite4001608067531595151d_enat X8) (= (@ (@ tptp.groups2027974829824023292at_nat (@ tptp.count_101369445342291426d_enat Xs)) X8) (@ tptp.size_s3941691890525107288d_enat Xs))))) (forall ((Xs tptp.list_VEBT_VEBT) (X8 tptp.set_VEBT_VEBT)) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) X8) (=> (@ tptp.finite5795047828879050333T_VEBT X8) (= (@ (@ tptp.groups771621172384141258BT_nat (@ tptp.count_list_VEBT_VEBT Xs)) X8) (@ tptp.size_s6755466524823107622T_VEBT Xs))))) (forall ((Xs tptp.list_int) (X8 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) X8) (=> (@ tptp.finite_finite_int X8) (= (@ (@ tptp.groups4541462559716669496nt_nat (@ tptp.count_list_int Xs)) X8) (@ tptp.size_size_list_int Xs))))) (forall ((Xs tptp.list_nat) (X8 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) X8) (=> (@ tptp.finite_finite_nat X8) (= (@ (@ tptp.groups3542108847815614940at_nat (@ tptp.count_list_nat Xs)) X8) (@ tptp.size_size_list_nat Xs))))) (forall ((A tptp.int) (N2 tptp.nat)) (= (= (@ (@ tptp.bit_se725231765392027082nd_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) tptp.zero_zero_int) (not (@ (@ tptp.bit_se1146084159140164899it_int A) N2)))) (forall ((A tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.bit_se727722235901077358nd_nat A) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.zero_zero_nat) (not (@ (@ tptp.bit_se1148574629649215175it_nat A) N2)))) (forall ((Q3 tptp.real) (P5 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q3) (@ (@ tptp.ord_less_eq_real P5) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real (@ (@ tptp.divide_divide_real P5) Q3)))) Q3)))) (forall ((M2 tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N2))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M2) N2))) (and (=> _let_2 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_complex (@ F M2)) (@ F (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) tptp.zero_zero_complex)))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N2))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M2) N2))) (and (=> _let_2 (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_int (@ F M2)) (@ F (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) tptp.zero_zero_int)))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N2))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M2) N2))) (and (=> _let_2 (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_real (@ F M2)) (@ F (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) tptp.zero_zero_real)))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K2)) (@ F (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N2)) (@ (@ tptp.minus_minus_int (@ F N2)) (@ F M2))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K2)) (@ F (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N2)) (@ (@ tptp.minus_minus_real (@ F N2)) (@ F M2))))) (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.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 ((Q3 tptp.real) (P5 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 P5) Q3)))) tptp.one_one_real)) Q3)) P5))) (forall ((N2 tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N2))) (=> (@ (@ tptp.ord_less_real _let_1) X) (=> (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim7802044766580827645g_real X) (@ (@ tptp.plus_plus_int N2) tptp.one_one_int)))))) (forall ((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 ((M2 tptp.nat) (N2 tptp.nat) (X tptp.int)) (let ((_let_1 (@ tptp.power_power_int X))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int tptp.one_one_int) X)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M2) N2))) (@ (@ tptp.minus_minus_int (@ _let_1 M2)) (@ _let_1 (@ tptp.suc N2))))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (X tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex tptp.one_one_complex) X)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M2) N2))) (@ (@ tptp.minus_minus_complex (@ _let_1 M2)) (@ _let_1 (@ tptp.suc N2))))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.power_power_real X))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M2) N2))) (@ (@ tptp.minus_minus_real (@ _let_1 M2)) (@ _let_1 (@ tptp.suc N2))))))) (forall ((G (-> tptp.nat tptp.int)) (M2 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 M2)) (@ 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 M2) N2))))) (forall ((G (-> tptp.nat tptp.extended_enat)) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups7108830773950497114d_enat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M2)) (@ tptp.suc (@ _let_1 N2)))) (@ (@ tptp.groups7108830773950497114d_enat (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.plus_p3455044024723400733d_enat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N2))))) (forall ((G (-> tptp.nat tptp.nat)) (M2 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 M2)) (@ 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 M2) N2))))) (forall ((G (-> tptp.nat tptp.real)) (M2 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 M2)) (@ 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 M2) N2))))) (forall ((A0 tptp.int) (A1 tptp.int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int A0) A1)) (=> (forall ((K3 tptp.int) (L4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int K3) L4)) (=> (=> (not (and (@ (@ tptp.member_int K3) _let_2) (@ (@ tptp.member_int L4) _let_2))) (@ (@ P (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L4) _let_1))) (@ (@ P K3) L4)))))) (@ (@ P A0) A1)))) (forall ((A tptp.int) (B2 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) B2))) (let ((_let_3 (= N2 tptp.zero_zero_nat))) (=> (forall ((J3 tptp.nat)) (not (@ (@ tptp.bit_se1146084159140164899it_int A) (@ tptp.suc J3)))) (= (@ (@ 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) (B2 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) B2))) (let ((_let_3 (= N2 tptp.zero_zero_nat))) (=> (forall ((J3 tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat A) (@ tptp.suc J3)))) (= (@ (@ 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_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)))))))) (= tptp.bit_se727722235901077358nd_nat (lambda ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (or (= M 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 M) _let_1)) (@ (@ tptp.modulo_modulo_nat N) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M) _let_1)) (@ (@ tptp.divide_divide_nat N) _let_1)))))))) (= tptp.bit_se727722235901077358nd_nat (lambda ((M 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 M)) (not (@ _let_2 N))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M) _let_1)) (@ (@ tptp.divide_divide_nat N) _let_1)))))))) (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 ((N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ 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 ((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 ((A0 tptp.int) (A1 tptp.int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int A0) A1)) (=> (forall ((I4 tptp.int) (J3 tptp.int)) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int I4) J3)) (=> (=> (@ (@ tptp.ord_less_eq_int I4) J3) (@ (@ P (@ (@ tptp.plus_plus_int I4) tptp.one_one_int)) J3)) (@ (@ P I4) J3)))) (@ (@ P A0) A1)))) (forall ((N2 tptp.nat) (M2 tptp.nat) (X tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X))) (let ((_let_2 (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M2) N2)))) (let ((_let_3 (= X tptp.one_one_complex))) (let ((_let_4 (@ (@ tptp.ord_less_nat N2) M2))) (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)) M2)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ _let_1 M2)) (@ _let_1 (@ tptp.suc N2)))) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) X)))))))))))) (forall ((N2 tptp.nat) (M2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.power_power_real X))) (let ((_let_2 (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M2) N2)))) (let ((_let_3 (= X tptp.one_one_real))) (let ((_let_4 (@ (@ tptp.ord_less_nat N2) M2))) (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)) M2)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ _let_1 M2)) (@ _let_1 (@ tptp.suc N2)))) (@ (@ tptp.minus_minus_real tptp.one_one_real) X)))))))))))) (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 ((X tptp.complex) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_2 (@ tptp.power_power_complex X))) (let ((_let_3 (@ (@ tptp.groups2073611262835488442omplex _let_2) (@ (@ tptp.set_or1269000886237332187st_nat M2) (@ (@ tptp.plus_plus_nat M2) N2))))) (let ((_let_4 (= X tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex N2)) tptp.one_one_complex))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ _let_2 M2)) (@ _let_1 (@ _let_2 (@ tptp.suc N2))))) (@ _let_1 X)))))))))) (forall ((X tptp.real) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (let ((_let_2 (@ tptp.power_power_real X))) (let ((_let_3 (@ (@ tptp.groups6591440286371151544t_real _let_2) (@ (@ tptp.set_or1269000886237332187st_nat M2) (@ (@ tptp.plus_plus_nat M2) N2))))) (let ((_let_4 (= X tptp.one_one_real))) (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N2)) tptp.one_one_real))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ _let_2 M2)) (@ _let_1 (@ _let_2 (@ tptp.suc N2))))) (@ _let_1 X)))))))))) (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.semiri4216267220026989637d_enat N2))) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups7108830773950497114d_enat tptp.semiri4216267220026989637d_enat) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2))) (@ (@ tptp.times_7803423173614009249d_enat _let_1) (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) tptp.one_on7984719198319812577d_enat))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.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 ((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 ((M2 tptp.nat) (N2 tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real M2) (@ tptp.semiri5074537144036343181t_real N2)) (= M2 N2))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M2) (@ tptp.semiri1314217659103216013at_int N2)) (= M2 N2))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M2) (@ tptp.semiri1316708129612266289at_nat N2)) (= M2 N2))) (forall ((N2 tptp.num) (M2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N2)) (@ tptp.semiri5074537144036343181t_real M2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N2)) M2))) (forall ((M2 tptp.nat) (V tptp.num)) (= (= (@ tptp.semiri1314217659103216013at_int M2) (@ tptp.numeral_numeral_int V)) (= M2 (@ tptp.numeral_numeral_nat V)))) (forall ((N2 tptp.nat) (M2 tptp.nat)) (= (= (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2)) (@ tptp.semiri1314217659103216013at_int M2)) (and (= N2 tptp.zero_zero_nat) (= M2 tptp.zero_zero_nat)))) (forall ((N2 tptp.nat)) (= (@ tptp.ring_1_of_int_real (@ tptp.semiri1314217659103216013at_int N2)) (@ tptp.semiri5074537144036343181t_real N2))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))) (forall ((N2 tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) (@ tptp.semiri1314217659103216013at_int M2))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.dvd_dvd_nat M2) N2))) (= (@ tptp.semiri8010041392384452111omplex tptp.zero_zero_nat) tptp.zero_zero_complex) (= (@ tptp.semiri4216267220026989637d_enat tptp.zero_zero_nat) tptp.zero_z5237406670263579293d_enat) (= (@ tptp.semiri5074537144036343181t_real tptp.zero_zero_nat) tptp.zero_zero_real) _let_141 (= (@ 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_z5237406670263579293d_enat (@ tptp.semiri4216267220026989637d_enat N2)) (= tptp.zero_zero_nat N2))) (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_real (@ tptp.semiri5074537144036343181t_real N2)) (= tptp.zero_zero_nat N2))) (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_int (@ tptp.semiri1314217659103216013at_int N2)) (= tptp.zero_zero_nat N2))) (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_nat (@ tptp.semiri1316708129612266289at_nat N2)) (= tptp.zero_zero_nat N2))) (forall ((M2 tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex M2) tptp.zero_zero_complex) (= M2 tptp.zero_zero_nat))) (forall ((M2 tptp.nat)) (= (= (@ tptp.semiri4216267220026989637d_enat M2) tptp.zero_z5237406670263579293d_enat) (= M2 tptp.zero_zero_nat))) (forall ((M2 tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real M2) tptp.zero_zero_real) (= M2 tptp.zero_zero_nat))) (forall ((M2 tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M2) tptp.zero_zero_int) (= M2 tptp.zero_zero_nat))) (forall ((M2 tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M2) tptp.zero_zero_nat) (= M2 tptp.zero_zero_nat))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.semiri4216267220026989637d_enat M2)) (@ tptp.semiri4216267220026989637d_enat N2)) (@ (@ tptp.ord_less_nat M2) N2))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.ord_less_nat M2) N2))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.ord_less_nat M2) N2))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M2)) (@ tptp.semiri1316708129612266289at_nat N2)) (@ (@ tptp.ord_less_nat M2) N2))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.ord_less_eq_nat M2) N2))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat M2)) (@ tptp.semiri1316708129612266289at_nat N2)) (@ (@ tptp.ord_less_eq_nat M2) N2))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.ord_less_eq_nat M2) N2))) (forall ((W2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real W2)) (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat W2)) N2))) (forall ((N2 tptp.nat) (W2 tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.numeral_numeral_real W2)) (@ (@ tptp.ord_less_nat N2) (@ tptp.numeral_numeral_nat W2)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri4216267220026989637d_enat (@ (@ tptp.plus_plus_nat M2) N2)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.semiri4216267220026989637d_enat M2)) (@ tptp.semiri4216267220026989637d_enat N2)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat M2) N2)) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.semiri5074537144036343181t_real N2)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat M2) N2)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N2)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.plus_plus_nat M2) N2)) (@ (@ tptp.plus_plus_nat (@ tptp.semiri1316708129612266289at_nat M2)) (@ tptp.semiri1316708129612266289at_nat N2)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.times_times_nat M2) N2)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex M2)) (@ tptp.semiri8010041392384452111omplex N2)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri4216267220026989637d_enat (@ (@ tptp.times_times_nat M2) N2)) (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.semiri4216267220026989637d_enat M2)) (@ tptp.semiri4216267220026989637d_enat N2)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.times_times_nat M2) N2)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.semiri5074537144036343181t_real N2)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.times_times_nat M2) N2)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N2)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.times_times_nat M2) N2)) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat M2)) (@ tptp.semiri1316708129612266289at_nat N2)))) (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex N2) tptp.one_one_complex) (= 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_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.semiri5074537144036343181t_real tptp.one_one_nat) tptp.one_one_real) (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int) (= (@ tptp.semiri1316708129612266289at_nat tptp.one_one_nat) tptp.one_one_nat) (forall ((N2 tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2)))) (@ tptp.semiri1314217659103216013at_int M2))) (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 ((F (-> tptp.int tptp.nat)) (A2 tptp.set_int)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X4 tptp.int)) (@ tptp.semiri1314217659103216013at_int (@ F X4)))) A2))) (forall ((F (-> tptp.complex tptp.nat)) (A2 tptp.set_complex)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.groups5693394587270226106ex_nat F) A2)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((X4 tptp.complex)) (@ tptp.semiri8010041392384452111omplex (@ F X4)))) A2))) (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((X4 tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ F X4)))) A2))) (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) (@ tptp.semiri1316708129612266289at_nat (@ F X4)))) A2))) (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((X4 tptp.nat)) (@ tptp.semiri5074537144036343181t_real (@ F X4)))) A2))) (forall ((M2 tptp.nat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.semiri4216267220026989637d_enat M2)) tptp.zero_z5237406670263579293d_enat) (= M2 tptp.zero_zero_nat))) (forall ((M2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real M2)) tptp.zero_zero_real) (= M2 tptp.zero_zero_nat))) (forall ((M2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat M2)) tptp.zero_zero_nat) (= M2 tptp.zero_zero_nat))) (forall ((M2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M2)) tptp.zero_zero_int) (= M2 tptp.zero_zero_nat))) (forall ((M2 tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.suc M2)) (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.semiri8010041392384452111omplex M2)))) (forall ((M2 tptp.nat)) (= (@ tptp.semiri4216267220026989637d_enat (@ tptp.suc M2)) (@ (@ tptp.plus_p3455044024723400733d_enat tptp.one_on7984719198319812577d_enat) (@ tptp.semiri4216267220026989637d_enat M2)))) (forall ((M2 tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M2)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real M2)))) (forall ((M2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc M2)) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.semiri1314217659103216013at_int M2)))) (forall ((M2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc M2)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.semiri1316708129612266289at_nat M2)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ tptp.semiri4216267220026989637d_enat N2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat N2)) (@ _let_1 N2)))) (forall ((B2 tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B2)) W2)) (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B2) W2)) X))) (forall ((B2 tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B2)) W2)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B2) W2)) X))) (forall ((B2 tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B2)) W2)) (@ tptp.semiri1316708129612266289at_nat X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B2) W2)) X))) (forall ((X tptp.nat) (B2 tptp.nat) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B2)) W2)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat B2) W2)))) (forall ((X tptp.nat) (B2 tptp.nat) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B2)) W2)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat B2) W2)))) (forall ((X tptp.nat) (B2 tptp.nat) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat X)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B2)) W2)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat B2) W2)))) (forall ((X tptp.nat) (B2 tptp.nat) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B2)) W2)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B2) W2)))) (forall ((X tptp.nat) (B2 tptp.nat) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat X)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B2)) W2)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B2) W2)))) (forall ((X tptp.nat) (B2 tptp.nat) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B2)) W2)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B2) W2)))) (forall ((B2 tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B2)) W2)) (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B2) W2)) X))) (forall ((B2 tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B2)) W2)) (@ tptp.semiri1316708129612266289at_nat X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B2) W2)) X))) (forall ((B2 tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B2)) W2)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B2) W2)) X))) (forall ((X tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real X)) N2)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X) (= N2 tptp.zero_zero_nat)))) (forall ((X tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int X)) N2)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X) (= N2 tptp.zero_zero_nat)))) (forall ((X tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat X)) N2)) (or (@ _let_1 X) (= N2 tptp.zero_zero_nat))))) (forall ((X tptp.nat) (I tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N2)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N2)))) (forall ((X tptp.nat) (I tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N2)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N2)))) (forall ((X tptp.nat) (I tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N2))) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat X)) _let_1) (@ (@ tptp.ord_less_nat X) _let_1)))) (forall ((I tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N2)) (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N2)) X))) (forall ((I tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N2)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N2)) X))) (forall ((I tptp.num) (N2 tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N2)))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat X)) (@ _let_1 X)))) (forall ((X tptp.nat) (I tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N2)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N2)))) (forall ((X tptp.nat) (I tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N2))) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat X)) _let_1) (@ (@ tptp.ord_less_eq_nat X) _let_1)))) (forall ((X tptp.nat) (I tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N2)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N2)))) (forall ((I tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N2)) (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N2)) X))) (forall ((I tptp.num) (N2 tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N2)))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat X)) (@ _let_1 X)))) (forall ((I tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N2)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N2)) X))) (forall ((X tptp.real)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.semiri5074537144036343181t_real N3)))) (forall ((X tptp.real)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real X) (@ tptp.semiri5074537144036343181t_real N3)))) (forall ((X tptp.nat) (Y tptp.complex)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex X))) (= (@ (@ tptp.times_times_complex _let_1) Y) (@ (@ tptp.times_times_complex Y) _let_1)))) (forall ((X tptp.nat) (Y tptp.extended_enat)) (let ((_let_1 (@ tptp.semiri4216267220026989637d_enat X))) (= (@ (@ tptp.times_7803423173614009249d_enat _let_1) Y) (@ (@ tptp.times_7803423173614009249d_enat Y) _let_1)))) (forall ((X tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real X))) (= (@ (@ tptp.times_times_real _let_1) Y) (@ (@ tptp.times_times_real Y) _let_1)))) (forall ((X tptp.nat) (Y tptp.int)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int X))) (= (@ (@ tptp.times_times_int _let_1) Y) (@ (@ tptp.times_times_int Y) _let_1)))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat X))) (= (@ (@ tptp.times_times_nat _let_1) Y) (@ (@ tptp.times_times_nat Y) _let_1)))) (= tptp.ord_less_nat (lambda ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N)) tptp.one_one_real)) (@ tptp.semiri5074537144036343181t_real M)))) (forall ((Z3 tptp.int)) (=> (forall ((N3 tptp.nat)) (not (= Z3 (@ tptp.semiri1314217659103216013at_int N3)))) (not (forall ((N3 tptp.nat)) (not (= Z3 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N3)))))))) (forall ((Z3 tptp.int)) (not (forall ((M3 tptp.nat) (N3 tptp.nat)) (not (= Z3 (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int M3)) (@ tptp.semiri1314217659103216013at_int N3))))))) (forall ((N2 tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.ring_1_of_int_real X)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N2)) X))) (forall ((N2 tptp.nat) (X tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int X)) (@ _let_1 X)))) (forall ((N2 tptp.nat)) (= (@ (@ 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 ((N2 tptp.nat)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ tptp.semiri4216267220026989637d_enat N2))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.semiri5074537144036343181t_real N2))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_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 ((M2 tptp.nat)) (not (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.semiri4216267220026989637d_enat M2)) tptp.zero_z5237406670263579293d_enat))) (forall ((M2 tptp.nat)) (not (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M2)) tptp.zero_zero_real))) (forall ((M2 tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M2)) tptp.zero_zero_int))) (forall ((M2 tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M2)) tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri8010041392384452111omplex (@ tptp.suc N2)) tptp.zero_zero_complex))) (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri4216267220026989637d_enat (@ tptp.suc N2)) tptp.zero_z5237406670263579293d_enat))) (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2)) tptp.zero_zero_real))) (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2)) tptp.zero_zero_int))) (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc N2)) tptp.zero_zero_nat))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N2) (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.semiri4216267220026989637d_enat M2)) (@ tptp.semiri4216267220026989637d_enat N2)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N2) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.semiri5074537144036343181t_real N2)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N2) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N2)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N2) (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M2)) (@ tptp.semiri1316708129612266289at_nat N2)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.semiri4216267220026989637d_enat M2)) (@ tptp.semiri4216267220026989637d_enat N2)) (@ (@ tptp.ord_less_nat M2) N2))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.ord_less_nat M2) N2))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.ord_less_nat M2) N2))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M2)) (@ tptp.semiri1316708129612266289at_nat N2)) (@ (@ tptp.ord_less_nat M2) N2))) (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real I)) (@ tptp.semiri5074537144036343181t_real J)))) (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat I)) (@ tptp.semiri1316708129612266289at_nat J)))) (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int I)) (@ tptp.semiri1314217659103216013at_int J)))) (= tptp.ord_less_eq_nat (lambda ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M)) tptp.one_one_real)))) _let_141 (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B3)))) (forall ((Z3 tptp.int)) (=> (forall ((N3 tptp.nat)) (not (= Z3 (@ tptp.semiri1314217659103216013at_int N3)))) (not (forall ((N3 tptp.nat)) (not (= Z3 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N3))))))))) (forall ((P (-> tptp.int Bool)) (Z3 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 Z3)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.ord_less_eq_nat M2) N2))) (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B3)))) (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 ((M2 tptp.nat) (N2 tptp.nat) (Z3 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int M2)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N2)) Z3)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat M2) N2))) Z3))) (forall ((N2 tptp.nat) (M2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat N2) M2)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N2)) (@ tptp.semiri1314217659103216013at_int M2)))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat A) B2)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B2)))) _let_140 (forall ((N2 tptp.nat) (M2 tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N2)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int M2))))) (forall ((X tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.ord_max_nat X) Y)) (@ (@ tptp.ord_max_real (@ tptp.semiri5074537144036343181t_real X)) (@ tptp.semiri5074537144036343181t_real Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.ord_max_nat X) Y)) (@ (@ tptp.ord_max_int (@ tptp.semiri1314217659103216013at_int X)) (@ tptp.semiri1314217659103216013at_int Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.ord_max_nat X) Y)) (@ (@ tptp.ord_max_nat (@ tptp.semiri1316708129612266289at_nat X)) (@ tptp.semiri1316708129612266289at_nat Y)))) (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B3)))) (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B3)))) (forall ((N2 tptp.num)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat N2)))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real Y) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) X))))) (forall ((N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat M2) N2)) (@ (@ tptp.minus_minus_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.semiri5074537144036343181t_real N2))))) (forall ((N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat M2) N2)) (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N2))))) (forall ((N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat M2) N2)) (@ (@ tptp.minus_minus_nat (@ tptp.semiri1316708129612266289at_nat M2)) (@ tptp.semiri1316708129612266289at_nat N2))))) (forall ((X tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 C) (=> (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M3) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M3)) X)) C))) (= X tptp.zero_zero_real)))))) (forall ((M2 tptp.int)) (=> (forall ((N3 tptp.nat)) (not (= M2 (@ tptp.semiri1314217659103216013at_int N3)))) (not (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (not (= M2 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N3))))))))) (forall ((N2 tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int N2)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int M2))) (and (= N2 tptp.zero_zero_nat) (= M2 tptp.zero_zero_nat)))) (forall ((A tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc A)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A)) tptp.one_one_int))) (forall ((N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N2)) tptp.one_one_int))) (= tptp.ord_less_int (lambda ((W3 tptp.int) (Z6 tptp.int)) (exists ((N tptp.nat)) (= Z6 (@ (@ tptp.plus_plus_int W3) (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N))))))) (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 ((F (-> tptp.int tptp.nat)) (A2 tptp.set_int)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X4 tptp.int)) (@ tptp.semiri1314217659103216013at_int (@ F X4)))) A2))) (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((X4 tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ F X4)))) A2))) (forall ((A tptp.int) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int M2))) (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) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat M2))) (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)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (exists ((N3 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (= K (@ tptp.semiri1314217659103216013at_int N3)))))) (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (not (forall ((N3 tptp.nat)) (=> (= K (@ tptp.semiri1314217659103216013at_int N3)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3))))))) (forall ((K tptp.int)) (=> (not (= K tptp.zero_zero_int)) (=> (forall ((N3 tptp.nat)) (=> (= K (@ tptp.semiri1314217659103216013at_int N3)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3)))) (not (forall ((N3 tptp.nat)) (=> (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N3))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3)))))))) (forall ((I tptp.int) (J tptp.int) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int K)))) (=> (@ (@ tptp.ord_less_int I) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_int (@ _let_1 I)) (@ _let_1 J)))))) (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 ((X tptp.int)) (=> (@ (@ tptp.ord_less_int X) tptp.zero_zero_int) (exists ((N3 tptp.nat)) (= X (@ 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 ((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 ((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) (M2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (=> (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ tptp.semiri5074537144036343181t_real M2))) (@ _let_1 (@ tptp.semiri5074537144036343181t_real N2))))))) (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (not (forall ((N3 tptp.nat)) (=> (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N3))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3))))))) (forall ((P (-> tptp.int Bool)) (X tptp.nat) (Y tptp.nat)) (= (@ P (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat X) Y))) (and (=> (@ (@ tptp.ord_less_eq_nat Y) X) (@ P (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int X)) (@ tptp.semiri1314217659103216013at_int Y)))) (=> (@ (@ tptp.ord_less_nat X) Y) (@ P tptp.zero_zero_int))))) (forall ((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.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.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.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.semiri4216267220026989637d_enat N2))) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups7108830773950497114d_enat tptp.semiri4216267220026989637d_enat) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_7803423173614009249d_enat _let_1) (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) tptp.one_on7984719198319812577d_enat))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.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 ((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)))))) (= tptp.semiri8010041392384452111omplex (lambda ((N tptp.nat)) (@ (@ (@ tptp.if_complex (= N tptp.zero_zero_nat)) tptp.zero_zero_complex) (@ (@ tptp.produc1917071388513777916omplex (lambda ((M tptp.nat) (Q5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ tptp.semiri8010041392384452111omplex M)))) (@ (@ (@ tptp.if_complex (= Q5 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex))))) (@ (@ tptp.divmod_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (= tptp.semiri4216267220026989637d_enat (lambda ((N tptp.nat)) (@ (@ (@ tptp.if_Extended_enat (= N tptp.zero_zero_nat)) tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.produc2676513652042109336d_enat (lambda ((M tptp.nat) (Q5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))) (@ tptp.semiri4216267220026989637d_enat M)))) (@ (@ (@ tptp.if_Extended_enat (= Q5 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) tptp.one_on7984719198319812577d_enat))))) (@ (@ tptp.divmod_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (= tptp.semiri5074537144036343181t_real (lambda ((N tptp.nat)) (@ (@ (@ tptp.if_real (= N tptp.zero_zero_nat)) tptp.zero_zero_real) (@ (@ tptp.produc1703576794950452218t_real (lambda ((M tptp.nat) (Q5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real M)))) (@ (@ (@ tptp.if_real (= Q5 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))))) (@ (@ tptp.divmod_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (= tptp.semiri1314217659103216013at_int (lambda ((N tptp.nat)) (@ (@ (@ tptp.if_int (= N tptp.zero_zero_nat)) tptp.zero_zero_int) (@ (@ tptp.produc6840382203811409530at_int (lambda ((M tptp.nat) (Q5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.semiri1314217659103216013at_int M)))) (@ (@ (@ tptp.if_int (= Q5 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))) (@ (@ tptp.divmod_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (= tptp.semiri1316708129612266289at_nat (lambda ((N tptp.nat)) (@ (@ (@ tptp.if_nat (= N tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.produc6842872674320459806at_nat (lambda ((M tptp.nat) (Q5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.semiri1316708129612266289at_nat M)))) (@ (@ (@ tptp.if_nat (= Q5 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))) (@ (@ tptp.divmod_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (forall ((H2 tptp.complex) (Z3 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 Z3))) (=> (not (= H2 tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z3) H2)) N2)) (@ _let_2 N2))) H2)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N2)) (@ _let_2 _let_1))) (@ (@ tptp.times_times_complex H2) (@ (@ tptp.groups2073611262835488442omplex (lambda ((P6 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((Q5 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z3) H2)) Q5)) (@ (@ tptp.power_power_complex Z3) (@ (@ 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))) P6))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))) (forall ((H2 tptp.real) (Z3 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 Z3))) (=> (not (= H2 tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z3) H2)) N2)) (@ _let_2 N2))) H2)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ _let_2 _let_1))) (@ (@ tptp.times_times_real H2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((P6 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((Q5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z3) H2)) Q5)) (@ (@ tptp.power_power_real Z3) (@ (@ 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))) P6))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))) (forall ((H2 tptp.real) (Z3 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 Z3))) (let ((_let_5 (@ (@ tptp.plus_plus_real Z3) H2))) (=> (not (= H2 tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real Z3)) K5) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real _let_5)) K5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real _let_5) N2)) (@ _let_4 N2))) H2)) (@ _let_3 (@ _let_4 _let_2))))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real _let_2))) (@ (@ tptp.power_power_real K5) (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ tptp.real_V7735802525324610683m_real H2)))))))))))) (forall ((H2 tptp.complex) (Z3 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 Z3))) (let ((_let_4 (@ (@ tptp.plus_plus_complex Z3) H2))) (=> (not (= H2 tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex Z3)) K5) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex _let_4)) K5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex _let_4) N2)) (@ _let_3 N2))) H2)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N2)) (@ _let_3 _let_2))))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.semiri5074537144036343181t_real _let_2))) (@ (@ tptp.power_power_real K5) (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ tptp.real_V1022390504157884413omplex H2))))))))))) (forall ((Z3 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) Z3)) _let_4) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.power_power_nat _let_3) _let_4))) (@ (@ tptp.comm_s2602460028002588243omplex Z3) N2))) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z3) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_2))) N2)))))))) (forall ((Z3 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) Z3)) _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 Z3) N2))) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z3) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2))) N2)))))))) _let_139 _let_138 _let_137 _let_136 _let_135 (forall ((B2 tptp.nat) (K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B2)) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N2)) tptp.one_one_int)) (and (@ (@ tptp.ord_less_nat (@ _let_1 N2)) K) (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))))))) (forall ((X tptp.nat) (Y tptp.nat)) (= (= (@ tptp.set_ord_lessThan_nat X) (@ tptp.set_ord_lessThan_nat Y)) (= X Y))) (forall ((X tptp.int) (Y tptp.int)) (= (= (@ tptp.set_ord_lessThan_int X) (@ tptp.set_ord_lessThan_int Y)) (= X Y))) (forall ((I tptp.set_nat) (K tptp.set_nat)) (= (@ (@ tptp.member_set_nat I) (@ tptp.set_or890127255671739683et_nat K)) (@ (@ tptp.ord_less_set_nat I) K))) (forall ((I tptp.extended_enat) (K tptp.extended_enat)) (= (@ (@ tptp.member_Extended_enat I) (@ tptp.set_or8419480210114673929d_enat K)) (@ (@ tptp.ord_le72135733267957522d_enat I) K))) (forall ((I tptp.real) (K tptp.real)) (= (@ (@ tptp.member_real I) (@ tptp.set_or5984915006950818249n_real K)) (@ (@ tptp.ord_less_real I) K))) (forall ((I tptp.nat) (K tptp.nat)) (= (@ (@ tptp.member_nat I) (@ tptp.set_ord_lessThan_nat K)) (@ (@ tptp.ord_less_nat I) K))) (forall ((I tptp.int) (K tptp.int)) (= (@ (@ tptp.member_int I) (@ tptp.set_ord_lessThan_int K)) (@ (@ tptp.ord_less_int I) K))) (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.set_ord_lessThan_nat K))) (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_or5984915006950818249n_real X)) (@ tptp.set_or5984915006950818249n_real Y)) (@ (@ tptp.ord_less_eq_real X) Y))) (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_ord_lessThan_nat X)) (@ tptp.set_ord_lessThan_nat Y)) (@ (@ tptp.ord_less_eq_nat X) Y))) (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_lessThan_int X)) (@ tptp.set_ord_lessThan_int Y)) (@ (@ tptp.ord_less_eq_int X) Y))) (forall ((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 ((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)) (= (@ tptp.set_ord_lessThan_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat) (forall ((K tptp.extended_enat)) (let ((_let_1 (@ (@ tptp.insert_Extended_enat K) tptp.bot_bo7653980558646680370d_enat))) (= (@ (@ tptp.minus_925952699566721837d_enat _let_1) (@ tptp.set_or8419480210114673929d_enat K)) _let_1))) (forall ((K tptp.real)) (let ((_let_1 (@ (@ tptp.insert_real K) tptp.bot_bot_set_real))) (= (@ (@ tptp.minus_minus_set_real _let_1) (@ tptp.set_or5984915006950818249n_real K)) _let_1))) (forall ((K tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat K) tptp.bot_bot_set_nat))) (= (@ (@ tptp.minus_minus_set_nat _let_1) (@ tptp.set_ord_lessThan_nat K)) _let_1))) (forall ((K tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int K) tptp.bot_bot_set_int))) (= (@ (@ tptp.minus_minus_set_int _let_1) (@ tptp.set_ord_lessThan_int K)) _let_1))) (forall ((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.extended_enat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups7108830773950497114d_enat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_p3455044024723400733d_enat (@ _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 ((M2 tptp.nat) (N2 tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M2) (@ tptp.semiri1314217659103216013at_int N2)) (= M2 N2))) (forall ((X tptp.real)) (not (= (@ tptp.set_or5984915006950818249n_real X) tptp.bot_bot_set_real))) (forall ((X tptp.int)) (not (= (@ tptp.set_ord_lessThan_int X) tptp.bot_bot_set_int))) (forall ((A tptp.int)) (not (@ tptp.finite_finite_int (@ tptp.set_ord_lessThan_int A)))) _let_134 _let_133 _let_132 _let_131 _let_130 (forall ((N2 tptp.extended_enat)) (= (= (@ tptp.set_or8419480210114673929d_enat N2) tptp.bot_bo7653980558646680370d_enat) (= N2 tptp.bot_bo4199563552545308370d_enat))) (forall ((N2 tptp.nat)) (= (= (@ tptp.set_ord_lessThan_nat N2) tptp.bot_bot_set_nat) (= N2 tptp.bot_bot_nat))) (forall ((M2 tptp.extended_enat) (N2 tptp.extended_enat)) (= (@ (@ tptp.ord_le2529575680413868914d_enat (@ tptp.set_or8419480210114673929d_enat M2)) (@ tptp.set_or8419480210114673929d_enat N2)) (@ (@ tptp.ord_le72135733267957522d_enat M2) N2))) (forall ((M2 tptp.real) (N2 tptp.real)) (= (@ (@ tptp.ord_less_set_real (@ tptp.set_or5984915006950818249n_real M2)) (@ tptp.set_or5984915006950818249n_real N2)) (@ (@ tptp.ord_less_real M2) N2))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_set_nat (@ tptp.set_ord_lessThan_nat M2)) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ tptp.ord_less_nat M2) N2))) (forall ((M2 tptp.int) (N2 tptp.int)) (= (@ (@ tptp.ord_less_set_int (@ tptp.set_ord_lessThan_int M2)) (@ tptp.set_ord_lessThan_int N2)) (@ (@ tptp.ord_less_int M2) N2))) (forall ((X tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.comm_s4663373288045622133er_nat X) N2))))) (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.comm_s7457072308508201937r_real X) N2))))) (forall ((X tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.comm_s4660882817536571857er_int X) N2))))) (forall ((A tptp.real) (N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A))) (=> (= (@ _let_1 N2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (= (@ _let_1 M2) tptp.zero_zero_real))))) (forall ((A tptp.complex) (N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex A))) (=> (= (@ _let_1 N2) tptp.zero_zero_complex) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (= (@ _let_1 M2) tptp.zero_zero_complex))))) (forall ((A tptp.real) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A))) (=> (not (= (@ _let_1 M2) tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (not (= (@ _let_1 N2) tptp.zero_zero_real)))))) (forall ((A tptp.complex) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex A))) (=> (not (= (@ _let_1 M2) tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (not (= (@ _let_1 N2) tptp.zero_zero_complex)))))) (forall ((K tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K)) (@ (@ tptp.insert_nat K) (@ tptp.set_ord_lessThan_nat K)))) (forall ((N2 tptp.nat)) (= (= (@ tptp.set_ord_lessThan_nat N2) tptp.bot_bot_set_nat) (= N2 tptp.zero_zero_nat))) (forall ((S2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S2) (exists ((K3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat S2) (@ tptp.set_ord_lessThan_nat K3))))) (= tptp.finite_finite_nat (lambda ((S6 tptp.set_nat)) (exists ((K2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat S6) (@ tptp.set_ord_lessThan_nat K2))))) (forall ((X tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.comm_s7457072308508201937r_real X) N2)))) (forall ((X tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.comm_s4663373288045622133er_nat X) N2)))) (forall ((X tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.comm_s4660882817536571857er_int X) N2)))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_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_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_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.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_s3181272606743183617d_enat tptp.zero_z5237406670263579293d_enat) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_on7984719198319812577d_enat)) (=> (not _let_2) (= _let_1 tptp.zero_z5237406670263579293d_enat)))))) (forall ((K tptp.num)) (let ((_let_1 (@ tptp.pred_numeral K))) (= (@ tptp.set_ord_lessThan_nat (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.insert_nat _let_1) (@ tptp.set_ord_lessThan_nat _let_1))))) (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((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 ((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 ((X4 tptp.int)) (@ (@ tptp.minus_minus_nat (@ P X4)) (@ Q X4)))) _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 ((X4 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ P X4)) (@ Q X4)))) _let_1))))) (forall ((M2 tptp.nat) (B2 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M2))) (=> (@ (@ tptp.ord_less_eq_real _let_1) (@ (@ tptp.power_power_real B2) N2)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B2) _let_1)) (@ tptp.semiri5074537144036343181t_real N2))))))) (forall ((M2 tptp.nat) (B2 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M2))) (=> (@ (@ tptp.ord_less_real _let_1) (@ (@ tptp.power_power_real B2) N2)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (@ (@ tptp.ord_less_real (@ (@ tptp.log B2) _let_1)) (@ tptp.semiri5074537144036343181t_real N2))))))) (forall ((A tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) (@ tptp.suc N2)) (@ (@ tptp.times_times_nat A) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) N2)))) (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) (@ tptp.suc N2)) (@ (@ tptp.times_times_int A) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) N2)))) (forall ((A tptp.real) (N2 tptp.nat)) (= (@ (@ 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.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.extended_enat) (N2 tptp.nat)) (= (@ (@ tptp.comm_s3181272606743183617d_enat A) (@ tptp.suc N2)) (@ (@ tptp.times_7803423173614009249d_enat A) (@ (@ tptp.comm_s3181272606743183617d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) tptp.one_on7984719198319812577d_enat)) N2)))) (forall ((Z3 tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex Z3))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex Z3) (@ tptp.semiri8010041392384452111omplex N2))) (@ _let_1 N2))))) (forall ((Z3 tptp.extended_enat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s3181272606743183617d_enat Z3))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_7803423173614009249d_enat (@ (@ tptp.plus_p3455044024723400733d_enat Z3) (@ tptp.semiri4216267220026989637d_enat N2))) (@ _let_1 N2))))) (forall ((Z3 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z3))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real Z3) (@ tptp.semiri5074537144036343181t_real N2))) (@ _let_1 N2))))) (forall ((Z3 tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z3))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int Z3) (@ tptp.semiri1314217659103216013at_int N2))) (@ _let_1 N2))))) (forall ((Z3 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z3))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat Z3) (@ tptp.semiri1316708129612266289at_nat N2))) (@ _let_1 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.extended_enat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s3181272606743183617d_enat A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_7803423173614009249d_enat (@ _let_1 N2)) (@ (@ tptp.plus_p3455044024723400733d_enat A) (@ tptp.semiri4216267220026989637d_enat 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_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_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 ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_nat K2) N2) (= A (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex K2))))))) (forall ((A tptp.real) (N2 tptp.nat)) (= (= (@ (@ tptp.comm_s7457072308508201937r_real A) N2) tptp.zero_zero_real) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_nat K2) N2) (= A (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real K2))))))) (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_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 ((Z3 tptp.complex) (N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex Z3))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M2)) (@ (@ tptp.times_times_complex (@ _let_1 N2)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z3) (@ tptp.semiri8010041392384452111omplex N2))) M2))))) (forall ((Z3 tptp.extended_enat) (N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s3181272606743183617d_enat Z3))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M2)) (@ (@ tptp.times_7803423173614009249d_enat (@ _let_1 N2)) (@ (@ tptp.comm_s3181272606743183617d_enat (@ (@ tptp.plus_p3455044024723400733d_enat Z3) (@ tptp.semiri4216267220026989637d_enat N2))) M2))))) (forall ((Z3 tptp.real) (N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z3))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M2)) (@ (@ tptp.times_times_real (@ _let_1 N2)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z3) (@ tptp.semiri5074537144036343181t_real N2))) M2))))) (forall ((Z3 tptp.int) (N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z3))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M2)) (@ (@ tptp.times_times_int (@ _let_1 N2)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int Z3) (@ tptp.semiri1314217659103216013at_int N2))) M2))))) (forall ((Z3 tptp.nat) (N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z3))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M2)) (@ (@ tptp.times_times_nat (@ _let_1 N2)) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat Z3) (@ tptp.semiri1316708129612266289at_nat N2))) M2))))) (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.extended_enat)) (N2 tptp.nat)) (= (@ (@ tptp.groups7108830773950497114d_enat G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_p3455044024723400733d_enat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups7108830773950497114d_enat (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.int)) (M2 tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc N))) (@ F N)))) (@ tptp.set_ord_lessThan_nat M2)) (@ (@ tptp.minus_minus_int (@ F M2)) (@ F tptp.zero_zero_nat)))) (forall ((F (-> tptp.nat tptp.real)) (M2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_real (@ F (@ tptp.suc N))) (@ F N)))) (@ tptp.set_ord_lessThan_nat M2)) (@ (@ tptp.minus_minus_real (@ F M2)) (@ F tptp.zero_zero_nat)))) (forall ((F (-> tptp.nat tptp.int)) (M2 tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_int (@ F N)) (@ F (@ tptp.suc N))))) (@ tptp.set_ord_lessThan_nat M2)) (@ (@ tptp.minus_minus_int (@ F tptp.zero_zero_nat)) (@ F M2)))) (forall ((F (-> tptp.nat tptp.real)) (M2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N)) (@ F (@ tptp.suc N))))) (@ tptp.set_ord_lessThan_nat M2)) (@ (@ tptp.minus_minus_real (@ F tptp.zero_zero_nat)) (@ F M2)))) (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 ((K2 tptp.nat)) (@ G (@ tptp.suc K2)))) (@ 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 ((K2 tptp.nat)) (@ G (@ tptp.suc K2)))) (@ tptp.set_ord_lessThan_nat N2)))) (forall ((N2 tptp.nat) (M2 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)) M2) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M2)))))) (forall ((X tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X))) (let ((_let_2 (@ tptp.minus_minus_int tptp.one_one_int))) (= (@ _let_2 (@ _let_1 N2)) (@ (@ tptp.times_times_int (@ _let_2 X)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.set_ord_lessThan_nat N2))))))) (forall ((X tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X))) (let ((_let_2 (@ tptp.minus_minus_complex tptp.one_one_complex))) (= (@ _let_2 (@ _let_1 N2)) (@ (@ tptp.times_times_complex (@ _let_2 X)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_lessThan_nat N2))))))) (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X))) (let ((_let_2 (@ tptp.minus_minus_real tptp.one_one_real))) (= (@ _let_2 (@ _let_1 N2)) (@ (@ tptp.times_times_real (@ _let_2 X)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_lessThan_nat N2))))))) (forall ((X tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X))) (= (@ (@ tptp.minus_minus_int (@ _let_1 N2)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) tptp.one_one_int)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.set_ord_lessThan_nat N2)))))) (forall ((X tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X))) (= (@ (@ tptp.minus_minus_complex (@ _let_1 N2)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X) tptp.one_one_complex)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_lessThan_nat N2)))))) (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X))) (= (@ (@ tptp.minus_minus_real (@ _let_1 N2)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X) tptp.one_one_real)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_lessThan_nat N2)))))) (forall ((X tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X))) (=> (not (= X tptp.one_one_complex)) (= (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ _let_1 N2)) tptp.one_one_complex)) (@ (@ tptp.minus_minus_complex X) tptp.one_one_complex)))))) (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X))) (=> (not (= X tptp.one_one_real)) (= (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ _let_1 N2)) tptp.one_one_real)) (@ (@ tptp.minus_minus_real X) tptp.one_one_real)))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (Z3 tptp.complex)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex Z3))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ _let_1 N2) (@ (@ tptp.times_times_complex (@ _let_1 M2)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z3) (@ tptp.semiri8010041392384452111omplex M2))) (@ (@ tptp.minus_minus_nat N2) M2))))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (Z3 tptp.extended_enat)) (let ((_let_1 (@ tptp.comm_s3181272606743183617d_enat Z3))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ _let_1 N2) (@ (@ tptp.times_7803423173614009249d_enat (@ _let_1 M2)) (@ (@ tptp.comm_s3181272606743183617d_enat (@ (@ tptp.plus_p3455044024723400733d_enat Z3) (@ tptp.semiri4216267220026989637d_enat M2))) (@ (@ tptp.minus_minus_nat N2) M2))))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (Z3 tptp.real)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z3))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ _let_1 N2) (@ (@ tptp.times_times_real (@ _let_1 M2)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z3) (@ tptp.semiri5074537144036343181t_real M2))) (@ (@ tptp.minus_minus_nat N2) M2))))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (Z3 tptp.int)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z3))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ _let_1 N2) (@ (@ tptp.times_times_int (@ _let_1 M2)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int Z3) (@ tptp.semiri1314217659103216013at_int M2))) (@ (@ tptp.minus_minus_nat N2) M2))))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z3))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ _let_1 N2) (@ (@ tptp.times_times_nat (@ _let_1 M2)) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat Z3) (@ tptp.semiri1316708129612266289at_nat M2))) (@ (@ tptp.minus_minus_nat N2) M2))))))) (forall ((N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) M2) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M2)))))) (forall ((X tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_2 (@ tptp.power_power_complex X))) (let ((_let_3 (@ (@ tptp.groups2073611262835488442omplex _let_2) (@ tptp.set_ord_lessThan_nat N2)))) (let ((_let_4 (= X tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (@ tptp.semiri8010041392384452111omplex N2))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 (@ _let_2 N2))) (@ _let_1 X)))))))))) (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (let ((_let_2 (@ tptp.power_power_real X))) (let ((_let_3 (@ (@ tptp.groups6591440286371151544t_real _let_2) (@ tptp.set_ord_lessThan_nat N2)))) (let ((_let_4 (= X tptp.one_one_real))) (and (=> _let_4 (= _let_3 (@ tptp.semiri5074537144036343181t_real N2))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_real (@ _let_1 (@ _let_2 N2))) (@ _let_1 X)))))))))) (forall ((Z3 tptp.int) (H2 tptp.int) (M2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M2))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((P6 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int Z3))) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int Z3) H2)) (@ (@ tptp.minus_minus_nat M2) P6))) (@ _let_1 P6))) (@ _let_1 M2))))) _let_1) (@ (@ tptp.groups3539618377306564664at_int (lambda ((P6 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M2) P6))) (let ((_let_2 (@ tptp.power_power_int Z3))) (@ (@ tptp.times_times_int (@ _let_2 P6)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int Z3) H2)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))) (forall ((Z3 tptp.complex) (H2 tptp.complex) (M2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M2))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((P6 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex Z3))) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z3) H2)) (@ (@ tptp.minus_minus_nat M2) P6))) (@ _let_1 P6))) (@ _let_1 M2))))) _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((P6 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M2) P6))) (let ((_let_2 (@ tptp.power_power_complex Z3))) (@ (@ tptp.times_times_complex (@ _let_2 P6)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z3) H2)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))) (forall ((Z3 tptp.real) (H2 tptp.real) (M2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M2))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((P6 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real Z3))) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z3) H2)) (@ (@ tptp.minus_minus_nat M2) P6))) (@ _let_1 P6))) (@ _let_1 M2))))) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((P6 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M2) P6))) (let ((_let_2 (@ tptp.power_power_real Z3))) (@ (@ tptp.times_times_real (@ _let_2 P6)) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z3) H2)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))) (forall ((X tptp.int) (N2 tptp.nat) (Y tptp.int)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) Y)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((P6 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X) P6)) (@ (@ tptp.power_power_int Y) (@ (@ tptp.minus_minus_nat N2) P6))))) (@ tptp.set_ord_lessThan_nat _let_1)))))) (forall ((X tptp.complex) (N2 tptp.nat) (Y tptp.complex)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex X) _let_1)) (@ (@ tptp.power_power_complex Y) _let_1)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X) Y)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((P6 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex X) P6)) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat N2) P6))))) (@ tptp.set_ord_lessThan_nat _let_1)))))) (forall ((X tptp.real) (N2 tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X) Y)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((P6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real X) P6)) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat N2) P6))))) (@ tptp.set_ord_lessThan_nat _let_1)))))) (forall ((X tptp.int) (N2 tptp.nat) (Y tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int X) N2)) (@ (@ tptp.power_power_int Y) N2)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) Y)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int Y) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I3)))) (@ (@ tptp.power_power_int X) I3)))) (@ tptp.set_ord_lessThan_nat N2))))) (forall ((X tptp.complex) (N2 tptp.nat) (Y tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex X) N2)) (@ (@ tptp.power_power_complex Y) N2)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X) Y)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I3)))) (@ (@ tptp.power_power_complex X) I3)))) (@ tptp.set_ord_lessThan_nat N2))))) (forall ((X tptp.real) (N2 tptp.nat) (Y tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X) N2)) (@ (@ tptp.power_power_real Y) N2)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X) Y)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I3)))) (@ (@ tptp.power_power_real X) I3)))) (@ tptp.set_ord_lessThan_nat N2))))) (forall ((R2 tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex R2))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex R2) (@ tptp.semiri8010041392384452111omplex K))) (@ (@ tptp.comm_s2602460028002588243omplex _let_1) K)) (@ (@ tptp.times_times_complex R2) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)) K))))) (forall ((R2 tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real R2))) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real R2) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.comm_s7457072308508201937r_real _let_1) K)) (@ (@ tptp.times_times_real R2) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) K))))) (forall ((R2 tptp.int) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int R2))) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int R2) (@ tptp.semiri1314217659103216013at_int K))) (@ (@ tptp.comm_s4660882817536571857er_int _let_1) K)) (@ (@ tptp.times_times_int R2) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) K))))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (@ (@ tptp.ord_less_real (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M2))) (@ tptp.semiri5074537144036343181t_real N2)))))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_nat M2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M2))) (@ tptp.semiri5074537144036343181t_real N2)))))) (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 ((X tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_int tptp.one_one_int))) (= (@ _let_1 (@ (@ tptp.power_power_int X) N2)) (@ (@ tptp.times_times_int (@ _let_1 X)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_int X) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I3))))) (@ tptp.set_ord_lessThan_nat N2)))))) (forall ((X tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (= (@ _let_1 (@ (@ tptp.power_power_complex X) N2)) (@ (@ tptp.times_times_complex (@ _let_1 X)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_complex X) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I3))))) (@ tptp.set_ord_lessThan_nat N2)))))) (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (= (@ _let_1 (@ (@ tptp.power_power_real X) N2)) (@ (@ tptp.times_times_real (@ _let_1 X)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_real X) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I3))))) (@ tptp.set_ord_lessThan_nat 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 ((B2 tptp.complex) (K tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex B2)) K) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex B2) (@ tptp.semiri8010041392384452111omplex K))) tptp.one_one_complex)) K)))) (forall ((B2 tptp.real) (K tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real B2)) K) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real B2) (@ tptp.semiri5074537144036343181t_real K))) tptp.one_one_real)) K)))) (forall ((B2 tptp.int) (K tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int B2)) K) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) K)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int B2) (@ tptp.semiri1314217659103216013at_int K))) tptp.one_one_int)) K)))) (forall ((B2 tptp.complex) (K tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex B2) (@ tptp.semiri8010041392384452111omplex K))) tptp.one_one_complex)) K) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K)) (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex B2)) K)))) (forall ((B2 tptp.real) (K tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real B2) (@ tptp.semiri5074537144036343181t_real K))) tptp.one_one_real)) K) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K)) (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real B2)) K)))) (forall ((B2 tptp.int) (K tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int B2) (@ tptp.semiri1314217659103216013at_int K))) tptp.one_one_int)) K) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) K)) (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int B2)) K)))) (forall ((B2 tptp.nat) (N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (=> (@ (@ 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))) B2) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B2)) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N2)) tptp.one_one_int))))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.log (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_eq_nat _let_2) N2) (= (@ tptp.archim7802044766580827645g_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real N2))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) _let_2)) tptp.one_one_nat))))) tptp.one_one_int))))))) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real X)) tptp.zero_zero_real) (= X tptp.zero_zero_real))) (forall ((X tptp.complex)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X)) tptp.zero_zero_real) (= X tptp.zero_zero_complex))) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.real_V7735802525324610683m_real X)) (not (= X tptp.zero_zero_real)))) (forall ((X tptp.complex)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.real_V1022390504157884413omplex X)) (not (= X tptp.zero_zero_complex)))) (forall ((X tptp.real)) (= (= (@ tptp.real_V7735802525324610683m_real X) tptp.zero_zero_real) (= X tptp.zero_zero_real))) (forall ((X tptp.complex)) (= (= (@ tptp.real_V1022390504157884413omplex X) tptp.zero_zero_real) (= X tptp.zero_zero_complex))) (= (@ tptp.real_V7735802525324610683m_real tptp.zero_zero_real) tptp.zero_zero_real) (= (@ tptp.real_V1022390504157884413omplex tptp.zero_zero_complex) tptp.zero_zero_real) (forall ((B2 tptp.real) (A tptp.real)) (=> (not (= B2 tptp.zero_zero_real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.divide_divide_real A) B2)) (@ (@ tptp.divide_divide_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B2))))) (forall ((B2 tptp.complex) (A tptp.complex)) (=> (not (= B2 tptp.zero_zero_complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.divide1717551699836669952omplex A) B2)) (@ (@ tptp.divide_divide_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B2))))) (forall ((A tptp.real) (B2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B2))) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real A) B2)))) (forall ((A tptp.complex) (B2 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B2))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex A) B2)))) (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X)) Y)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X) Y)))) (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex X)) Y)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X) Y)))) (forall ((W2 tptp.real) (N2 tptp.nat) (Z3 tptp.real)) (=> (= (@ (@ tptp.power_power_real W2) N2) (@ (@ tptp.power_power_real Z3) N2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.real_V7735802525324610683m_real W2) (@ tptp.real_V7735802525324610683m_real Z3))))) (forall ((W2 tptp.complex) (N2 tptp.nat) (Z3 tptp.complex)) (=> (= (@ (@ tptp.power_power_complex W2) N2) (@ (@ tptp.power_power_complex Z3) N2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.real_V1022390504157884413omplex W2) (@ tptp.real_V1022390504157884413omplex Z3))))) (forall ((X tptp.real) (Y tptp.real) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y))) E2) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X) Y))) E2))) (forall ((X tptp.complex) (Y tptp.complex) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y))) E2) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X) Y))) E2))) (forall ((X tptp.real) (R2 tptp.real) (Y tptp.real) (S tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X)) R2) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Y)) S) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X) Y))) (@ (@ tptp.plus_plus_real R2) S))))) (forall ((X tptp.complex) (R2 tptp.real) (Y tptp.complex) (S tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X)) R2) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Y)) S) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X) Y))) (@ (@ tptp.plus_plus_real R2) S))))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real A) B2))) C) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real B2)) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real A)) C)))) (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex A) B2))) C) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex B2)) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex A)) C)))) (forall ((X tptp.real) (Y tptp.real) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y))) E2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X) Y))) E2))) (forall ((X tptp.complex) (Y tptp.complex) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y))) E2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X) Y))) E2))) (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X) Y))) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y)))) (forall ((X tptp.complex) (Y tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X) Y))) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y)))) (forall ((A tptp.real) (R2 tptp.real) (B2 tptp.real) (S tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real A)) R2) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real B2)) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real A) B2))) (@ (@ tptp.plus_plus_real R2) S))))) (forall ((A tptp.complex) (R2 tptp.real) (B2 tptp.complex) (S tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex A)) R2) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex B2)) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex A) B2))) (@ (@ tptp.plus_plus_real R2) S))))) (forall ((W2 tptp.real) (N2 tptp.nat)) (=> (= (@ (@ tptp.power_power_real W2) N2) tptp.one_one_real) (or (= (@ tptp.real_V7735802525324610683m_real W2) tptp.one_one_real) (= N2 tptp.zero_zero_nat)))) (forall ((W2 tptp.complex) (N2 tptp.nat)) (=> (= (@ (@ tptp.power_power_complex W2) N2) tptp.one_one_complex) (or (= (@ tptp.real_V1022390504157884413omplex W2) tptp.one_one_real) (= N2 tptp.zero_zero_nat)))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B2)) (@ (@ tptp.plus_plus_real C) D)))) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A) C))) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real B2) D))))) (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex) (D tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) B2)) (@ (@ tptp.plus_plus_complex C) D)))) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A) C))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex B2) D))))) (forall ((F (-> tptp.nat tptp.nat)) (Mm tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ F (@ tptp.suc K2)))) (@ tptp.set_ord_lessThan_nat Mm)) (@ (@ tptp.groups3542108847815614940at_nat F) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) Mm)))) (forall ((F (-> tptp.nat tptp.real)) (Mm tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ F (@ tptp.suc K2)))) (@ tptp.set_ord_lessThan_nat Mm)) (@ (@ tptp.groups6591440286371151544t_real F) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) Mm)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M)) (@ (@ tptp.power_power_real tptp.zero_zero_real) M)))) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) tptp.one_one_real)) (forall ((Z3 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 Z3) _let_2)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z3) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex _let_1)))) _let_2)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((K2 tptp.nat)) (@ (@ tptp.plus_plus_complex Z3) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri8010041392384452111omplex K2)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) tptp.one_one_nat))))))) (forall ((Z3 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 Z3) _let_2)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z3) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1)))) _let_2)) (@ (@ tptp.groups129246275422532515t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.plus_plus_real Z3) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real K2)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) tptp.one_one_nat))))))) _let_129 _let_128 _let_127 _let_126 _let_125 (forall ((X tptp.real) (B2 tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.powr_real B2))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B2) (= (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log B2) X)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int K)) tptp.one_one_int)) (and (@ (@ tptp.ord_less_real (@ _let_1 (@ tptp.semiri5074537144036343181t_real K))) X) (@ (@ tptp.ord_less_eq_real X) (@ _let_1 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))))))) (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Z3)) 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 Z3) N)))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real tptp.one_one_real) Z3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (forall ((Z3 tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Z3)) tptp.one_one_real) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ tptp.suc N))) (@ (@ tptp.power_power_complex Z3) N)))) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex tptp.one_one_complex) Z3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (forall ((W2 tptp.real) (Z3 tptp.real)) (= (= (@ (@ tptp.powr_real W2) Z3) tptp.zero_zero_real) (= W2 tptp.zero_zero_real))) (forall ((Z3 tptp.real)) (= (@ (@ tptp.powr_real tptp.zero_zero_real) Z3) tptp.zero_zero_real)) (forall ((F (-> tptp.int tptp.nat)) (A2 tptp.set_int)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups1707563613775114915nt_nat F) A2)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X4 tptp.int)) (@ tptp.semiri1314217659103216013at_int (@ F X4)))) A2))) (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.groups708209901874060359at_nat F) A2)) (@ (@ tptp.groups129246275422532515t_real (lambda ((X4 tptp.nat)) (@ tptp.semiri5074537144036343181t_real (@ F X4)))) A2))) (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups708209901874060359at_nat F) A2)) (@ (@ tptp.groups705719431365010083at_int (lambda ((X4 tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ F X4)))) A2))) (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.groups708209901874060359at_nat F) A2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) (@ tptp.semiri1316708129612266289at_nat (@ F X4)))) A2))) (forall ((F (-> tptp.nat tptp.int)) (A2 tptp.set_nat)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.groups705719431365010083at_int F) A2)) (@ (@ tptp.groups129246275422532515t_real (lambda ((X4 tptp.nat)) (@ tptp.ring_1_of_int_real (@ F X4)))) A2))) (forall ((F (-> tptp.nat tptp.int)) (A2 tptp.set_nat)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.groups705719431365010083at_int F) A2)) (@ (@ tptp.groups705719431365010083at_int (lambda ((X4 tptp.nat)) (@ tptp.ring_1_of_int_int (@ F X4)))) A2))) (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.groups1705073143266064639nt_int F) A2)) (@ (@ tptp.groups2316167850115554303t_real (lambda ((X4 tptp.int)) (@ tptp.ring_1_of_int_real (@ F X4)))) A2))) (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.groups1705073143266064639nt_int F) A2)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X4 tptp.int)) (@ tptp.ring_1_of_int_int (@ F X4)))) A2))) (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (= (@ (@ tptp.groups861055069439313189ex_nat F) A2) tptp.zero_zero_nat) (exists ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A2) (= (@ F X4) tptp.zero_zero_nat)))))) (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (= (= (@ (@ tptp.groups1707563613775114915nt_nat F) A2) tptp.zero_zero_nat) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A2) (= (@ F X4) tptp.zero_zero_nat)))))) (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (= (@ (@ tptp.groups2880970938130013265at_nat F) A2) tptp.zero_zero_nat) (exists ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) A2) (= (@ F X4) tptp.zero_zero_nat)))))) (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat A2) (= (= (@ (@ tptp.groups129246275422532515t_real F) A2) tptp.zero_zero_real) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A2) (= (@ F X4) tptp.zero_zero_real)))))) (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (= (@ (@ tptp.groups766887009212190081x_real F) A2) tptp.zero_zero_real) (exists ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A2) (= (@ F X4) tptp.zero_zero_real)))))) (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A2) (= (= (@ (@ tptp.groups2316167850115554303t_real F) A2) tptp.zero_zero_real) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A2) (= (@ F X4) tptp.zero_zero_real)))))) (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (= (@ (@ tptp.groups97031904164794029t_real F) A2) tptp.zero_zero_real) (exists ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) A2) (= (@ F X4) tptp.zero_zero_real)))))) (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (= (@ (@ tptp.groups858564598930262913ex_int F) A2) tptp.zero_zero_int) (exists ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A2) (= (@ F X4) tptp.zero_zero_int)))))) (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.int))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (= (@ (@ tptp.groups2878480467620962989at_int F) A2) tptp.zero_zero_int) (exists ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) A2) (= (@ F X4) tptp.zero_zero_int)))))) (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat A2) (= (= (@ (@ tptp.groups6464643781859351333omplex F) A2) tptp.zero_zero_complex) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A2) (= (@ F X4) tptp.zero_zero_complex)))))) (forall ((G (-> tptp.extended_enat tptp.nat))) (= (@ (@ tptp.groups2880970938130013265at_nat G) tptp.bot_bo7653980558646680370d_enat) tptp.one_one_nat)) (forall ((G (-> tptp.extended_enat tptp.int))) (= (@ (@ tptp.groups2878480467620962989at_int G) tptp.bot_bo7653980558646680370d_enat) tptp.one_one_int)) (forall ((G (-> tptp.extended_enat tptp.complex))) (= (@ (@ tptp.groups4622424608036095791omplex G) tptp.bot_bo7653980558646680370d_enat) tptp.one_one_complex)) (forall ((G (-> tptp.extended_enat tptp.real))) (= (@ (@ tptp.groups97031904164794029t_real G) tptp.bot_bo7653980558646680370d_enat) tptp.one_one_real)) (forall ((G (-> tptp.real tptp.nat))) (= (@ (@ tptp.groups4696554848551431203al_nat G) tptp.bot_bot_set_real) tptp.one_one_nat)) (forall ((G (-> tptp.real tptp.int))) (= (@ (@ tptp.groups4694064378042380927al_int G) tptp.bot_bot_set_real) tptp.one_one_int)) (forall ((G (-> tptp.real tptp.complex))) (= (@ (@ tptp.groups713298508707869441omplex G) tptp.bot_bot_set_real) tptp.one_one_complex)) (forall ((G (-> tptp.real tptp.real))) (= (@ (@ tptp.groups1681761925125756287l_real G) tptp.bot_bot_set_real) tptp.one_one_real)) (forall ((G (-> tptp.nat tptp.complex))) (= (@ (@ tptp.groups6464643781859351333omplex G) tptp.bot_bot_set_nat) tptp.one_one_complex)) (forall ((G (-> tptp.nat tptp.real))) (= (@ (@ tptp.groups129246275422532515t_real G) tptp.bot_bot_set_nat) tptp.one_one_real)) (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (=> (not (@ tptp.finite3207457112153483333omplex A2)) (= (@ (@ tptp.groups861055069439313189ex_nat G) A2) tptp.one_one_nat))) (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.nat))) (=> (not (@ tptp.finite_finite_int A2)) (= (@ (@ tptp.groups1707563613775114915nt_nat G) A2) tptp.one_one_nat))) (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.nat))) (=> (not (@ tptp.finite4001608067531595151d_enat A2)) (= (@ (@ tptp.groups2880970938130013265at_nat G) A2) tptp.one_one_nat))) (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.int))) (=> (not (@ tptp.finite3207457112153483333omplex A2)) (= (@ (@ tptp.groups858564598930262913ex_int G) A2) tptp.one_one_int))) (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.int))) (=> (not (@ tptp.finite4001608067531595151d_enat A2)) (= (@ (@ tptp.groups2878480467620962989at_int G) A2) tptp.one_one_int))) (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.complex))) (=> (not (@ tptp.finite_finite_nat A2)) (= (@ (@ tptp.groups6464643781859351333omplex G) A2) tptp.one_one_complex))) (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.complex))) (=> (not (@ tptp.finite3207457112153483333omplex A2)) (= (@ (@ tptp.groups3708469109370488835omplex G) A2) tptp.one_one_complex))) (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.complex))) (=> (not (@ tptp.finite_finite_int A2)) (= (@ (@ tptp.groups7440179247065528705omplex G) A2) tptp.one_one_complex))) (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.complex))) (=> (not (@ tptp.finite4001608067531595151d_enat A2)) (= (@ (@ tptp.groups4622424608036095791omplex G) A2) tptp.one_one_complex))) (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.real))) (=> (not (@ tptp.finite_finite_nat A2)) (= (@ (@ tptp.groups129246275422532515t_real G) A2) tptp.one_one_real))) (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.powr_real X) tptp.zero_zero_real))) (let ((_let_2 (= X tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))) (forall ((A2 tptp.set_real) (A tptp.real) (F (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real A) A2) (@ (@ tptp.dvd_dvd_nat (@ F A)) (@ (@ tptp.groups4696554848551431203al_nat F) A2))))) (forall ((A2 tptp.set_complex) (A tptp.complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex A) A2) (@ (@ tptp.dvd_dvd_nat (@ F A)) (@ (@ tptp.groups861055069439313189ex_nat F) A2))))) (forall ((A2 tptp.set_int) (A tptp.int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int A) A2) (@ (@ tptp.dvd_dvd_nat (@ F A)) (@ (@ tptp.groups1707563613775114915nt_nat F) A2))))) (forall ((A2 tptp.set_Extended_enat) (A tptp.extended_enat) (F (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ (@ tptp.member_Extended_enat A) A2) (@ (@ tptp.dvd_dvd_nat (@ F A)) (@ (@ tptp.groups2880970938130013265at_nat F) A2))))) (forall ((A2 tptp.set_real) (A tptp.real) (F (-> tptp.real tptp.int))) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real A) A2) (@ (@ tptp.dvd_dvd_int (@ F A)) (@ (@ tptp.groups4694064378042380927al_int F) A2))))) (forall ((A2 tptp.set_complex) (A tptp.complex) (F (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex A) A2) (@ (@ tptp.dvd_dvd_int (@ F A)) (@ (@ tptp.groups858564598930262913ex_int F) A2))))) (forall ((A2 tptp.set_Extended_enat) (A tptp.extended_enat) (F (-> tptp.extended_enat tptp.int))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ (@ tptp.member_Extended_enat A) A2) (@ (@ tptp.dvd_dvd_int (@ F A)) (@ (@ tptp.groups2878480467620962989at_int F) A2))))) (forall ((A2 tptp.set_nat) (A tptp.nat) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.member_nat A) A2) (@ (@ tptp.dvd_dvd_int (@ F A)) (@ (@ tptp.groups705719431365010083at_int F) A2))))) (forall ((A2 tptp.set_int) (A tptp.int) (F (-> tptp.int tptp.int))) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int A) A2) (@ (@ tptp.dvd_dvd_int (@ F A)) (@ (@ tptp.groups1705073143266064639nt_int F) A2))))) (forall ((A2 tptp.set_nat) (A tptp.nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.member_nat A) A2) (@ (@ tptp.dvd_dvd_nat (@ F A)) (@ (@ tptp.groups708209901874060359at_nat F) A2))))) (forall ((A2 tptp.set_real) (A tptp.real) (B2 tptp.nat) (F (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real A) A2) (=> (= B2 (@ F A)) (@ (@ tptp.dvd_dvd_nat B2) (@ (@ tptp.groups4696554848551431203al_nat F) A2)))))) (forall ((A2 tptp.set_complex) (A tptp.complex) (B2 tptp.nat) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex A) A2) (=> (= B2 (@ F A)) (@ (@ tptp.dvd_dvd_nat B2) (@ (@ tptp.groups861055069439313189ex_nat F) A2)))))) (forall ((A2 tptp.set_int) (A tptp.int) (B2 tptp.nat) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int A) A2) (=> (= B2 (@ F A)) (@ (@ tptp.dvd_dvd_nat B2) (@ (@ tptp.groups1707563613775114915nt_nat F) A2)))))) (forall ((A2 tptp.set_Extended_enat) (A tptp.extended_enat) (B2 tptp.nat) (F (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ (@ tptp.member_Extended_enat A) A2) (=> (= B2 (@ F A)) (@ (@ tptp.dvd_dvd_nat B2) (@ (@ tptp.groups2880970938130013265at_nat F) A2)))))) (forall ((A2 tptp.set_real) (A tptp.real) (B2 tptp.int) (F (-> tptp.real tptp.int))) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real A) A2) (=> (= B2 (@ F A)) (@ (@ tptp.dvd_dvd_int B2) (@ (@ tptp.groups4694064378042380927al_int F) A2)))))) (forall ((A2 tptp.set_complex) (A tptp.complex) (B2 tptp.int) (F (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex A) A2) (=> (= B2 (@ F A)) (@ (@ tptp.dvd_dvd_int B2) (@ (@ tptp.groups858564598930262913ex_int F) A2)))))) (forall ((A2 tptp.set_Extended_enat) (A tptp.extended_enat) (B2 tptp.int) (F (-> tptp.extended_enat tptp.int))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ (@ tptp.member_Extended_enat A) A2) (=> (= B2 (@ F A)) (@ (@ tptp.dvd_dvd_int B2) (@ (@ tptp.groups2878480467620962989at_int F) A2)))))) (forall ((A2 tptp.set_nat) (A tptp.nat) (B2 tptp.int) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.member_nat A) A2) (=> (= B2 (@ F A)) (@ (@ tptp.dvd_dvd_int B2) (@ (@ tptp.groups705719431365010083at_int F) A2)))))) (forall ((A2 tptp.set_int) (A tptp.int) (B2 tptp.int) (F (-> tptp.int tptp.int))) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int A) A2) (=> (= B2 (@ F A)) (@ (@ tptp.dvd_dvd_int B2) (@ (@ tptp.groups1705073143266064639nt_int F) A2)))))) (forall ((A2 tptp.set_nat) (A tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.member_nat A) A2) (=> (= B2 (@ F A)) (@ (@ tptp.dvd_dvd_nat B2) (@ (@ tptp.groups708209901874060359at_nat F) A2)))))) (= (@ tptp.cos_coeff tptp.zero_zero_nat) tptp.one_one_real) (forall ((S2 tptp.set_real) (A tptp.real) (B2 (-> tptp.real tptp.nat))) (let ((_let_1 (@ (@ tptp.member_real A) S2))) (=> (@ tptp.finite_finite_real S2) (and (=> _let_1 (= (@ (@ tptp.groups4696554848551431203al_nat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) tptp.one_one_nat))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups4696554848551431203al_nat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) tptp.one_one_nat))) S2) tptp.one_one_nat)))))) (forall ((S2 tptp.set_complex) (A tptp.complex) (B2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_1 (= (@ (@ tptp.groups861055069439313189ex_nat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) tptp.one_one_nat))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups861055069439313189ex_nat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) tptp.one_one_nat))) S2) tptp.one_one_nat)))))) (forall ((S2 tptp.set_int) (A tptp.int) (B2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ (@ tptp.member_int A) S2))) (=> (@ tptp.finite_finite_int S2) (and (=> _let_1 (= (@ (@ tptp.groups1707563613775114915nt_nat (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) tptp.one_one_nat))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups1707563613775114915nt_nat (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) tptp.one_one_nat))) S2) tptp.one_one_nat)))))) (forall ((S2 tptp.set_Extended_enat) (A tptp.extended_enat) (B2 (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ (@ tptp.member_Extended_enat A) S2))) (=> (@ tptp.finite4001608067531595151d_enat S2) (and (=> _let_1 (= (@ (@ tptp.groups2880970938130013265at_nat (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) tptp.one_one_nat))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups2880970938130013265at_nat (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) tptp.one_one_nat))) S2) tptp.one_one_nat)))))) (forall ((S2 tptp.set_real) (A tptp.real) (B2 (-> tptp.real tptp.int))) (let ((_let_1 (@ (@ tptp.member_real A) S2))) (=> (@ tptp.finite_finite_real S2) (and (=> _let_1 (= (@ (@ tptp.groups4694064378042380927al_int (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B2 K2)) tptp.one_one_int))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups4694064378042380927al_int (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B2 K2)) tptp.one_one_int))) S2) tptp.one_one_int)))))) (forall ((S2 tptp.set_complex) (A tptp.complex) (B2 (-> tptp.complex tptp.int))) (let ((_let_1 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_1 (= (@ (@ tptp.groups858564598930262913ex_int (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B2 K2)) tptp.one_one_int))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups858564598930262913ex_int (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B2 K2)) tptp.one_one_int))) S2) tptp.one_one_int)))))) (forall ((S2 tptp.set_Extended_enat) (A tptp.extended_enat) (B2 (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ (@ tptp.member_Extended_enat A) S2))) (=> (@ tptp.finite4001608067531595151d_enat S2) (and (=> _let_1 (= (@ (@ tptp.groups2878480467620962989at_int (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B2 K2)) tptp.one_one_int))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups2878480467620962989at_int (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B2 K2)) tptp.one_one_int))) S2) tptp.one_one_int)))))) (forall ((S2 tptp.set_real) (A tptp.real) (B2 (-> tptp.real tptp.complex))) (let ((_let_1 (@ (@ tptp.member_real A) S2))) (=> (@ tptp.finite_finite_real S2) (and (=> _let_1 (= (@ (@ tptp.groups713298508707869441omplex (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B2 K2)) tptp.one_one_complex))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups713298508707869441omplex (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B2 K2)) tptp.one_one_complex))) S2) tptp.one_one_complex)))))) (forall ((S2 tptp.set_nat) (A tptp.nat) (B2 (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.member_nat A) S2))) (=> (@ tptp.finite_finite_nat S2) (and (=> _let_1 (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B2 K2)) tptp.one_one_complex))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B2 K2)) tptp.one_one_complex))) S2) tptp.one_one_complex)))))) (forall ((S2 tptp.set_complex) (A tptp.complex) (B2 (-> tptp.complex tptp.complex))) (let ((_let_1 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_1 (= (@ (@ tptp.groups3708469109370488835omplex (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B2 K2)) tptp.one_one_complex))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups3708469109370488835omplex (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B2 K2)) tptp.one_one_complex))) S2) tptp.one_one_complex)))))) (forall ((S2 tptp.set_real) (A tptp.real) (B2 (-> tptp.real tptp.nat))) (let ((_let_1 (@ (@ tptp.member_real A) S2))) (=> (@ tptp.finite_finite_real S2) (and (=> _let_1 (= (@ (@ tptp.groups4696554848551431203al_nat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_nat (= A K2)) (@ B2 K2)) tptp.one_one_nat))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups4696554848551431203al_nat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_nat (= A K2)) (@ B2 K2)) tptp.one_one_nat))) S2) tptp.one_one_nat)))))) (forall ((S2 tptp.set_complex) (A tptp.complex) (B2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_1 (= (@ (@ tptp.groups861055069439313189ex_nat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_nat (= A K2)) (@ B2 K2)) tptp.one_one_nat))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups861055069439313189ex_nat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_nat (= A K2)) (@ B2 K2)) tptp.one_one_nat))) S2) tptp.one_one_nat)))))) (forall ((S2 tptp.set_int) (A tptp.int) (B2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ (@ tptp.member_int A) S2))) (=> (@ tptp.finite_finite_int S2) (and (=> _let_1 (= (@ (@ tptp.groups1707563613775114915nt_nat (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_nat (= A K2)) (@ B2 K2)) tptp.one_one_nat))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups1707563613775114915nt_nat (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_nat (= A K2)) (@ B2 K2)) tptp.one_one_nat))) S2) tptp.one_one_nat)))))) (forall ((S2 tptp.set_Extended_enat) (A tptp.extended_enat) (B2 (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ (@ tptp.member_Extended_enat A) S2))) (=> (@ tptp.finite4001608067531595151d_enat S2) (and (=> _let_1 (= (@ (@ tptp.groups2880970938130013265at_nat (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_nat (= A K2)) (@ B2 K2)) tptp.one_one_nat))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups2880970938130013265at_nat (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_nat (= A K2)) (@ B2 K2)) tptp.one_one_nat))) S2) tptp.one_one_nat)))))) (forall ((S2 tptp.set_real) (A tptp.real) (B2 (-> tptp.real tptp.int))) (let ((_let_1 (@ (@ tptp.member_real A) S2))) (=> (@ tptp.finite_finite_real S2) (and (=> _let_1 (= (@ (@ tptp.groups4694064378042380927al_int (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_int (= A K2)) (@ B2 K2)) tptp.one_one_int))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups4694064378042380927al_int (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_int (= A K2)) (@ B2 K2)) tptp.one_one_int))) S2) tptp.one_one_int)))))) (forall ((S2 tptp.set_complex) (A tptp.complex) (B2 (-> tptp.complex tptp.int))) (let ((_let_1 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_1 (= (@ (@ tptp.groups858564598930262913ex_int (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_int (= A K2)) (@ B2 K2)) tptp.one_one_int))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups858564598930262913ex_int (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_int (= A K2)) (@ B2 K2)) tptp.one_one_int))) S2) tptp.one_one_int)))))) (forall ((S2 tptp.set_Extended_enat) (A tptp.extended_enat) (B2 (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ (@ tptp.member_Extended_enat A) S2))) (=> (@ tptp.finite4001608067531595151d_enat S2) (and (=> _let_1 (= (@ (@ tptp.groups2878480467620962989at_int (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_int (= A K2)) (@ B2 K2)) tptp.one_one_int))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups2878480467620962989at_int (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_int (= A K2)) (@ B2 K2)) tptp.one_one_int))) S2) tptp.one_one_int)))))) (forall ((S2 tptp.set_real) (A tptp.real) (B2 (-> tptp.real tptp.complex))) (let ((_let_1 (@ (@ tptp.member_real A) S2))) (=> (@ tptp.finite_finite_real S2) (and (=> _let_1 (= (@ (@ tptp.groups713298508707869441omplex (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B2 K2)) tptp.one_one_complex))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups713298508707869441omplex (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B2 K2)) tptp.one_one_complex))) S2) tptp.one_one_complex)))))) (forall ((S2 tptp.set_nat) (A tptp.nat) (B2 (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.member_nat A) S2))) (=> (@ tptp.finite_finite_nat S2) (and (=> _let_1 (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B2 K2)) tptp.one_one_complex))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B2 K2)) tptp.one_one_complex))) S2) tptp.one_one_complex)))))) (forall ((S2 tptp.set_complex) (A tptp.complex) (B2 (-> tptp.complex tptp.complex))) (let ((_let_1 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_1 (= (@ (@ tptp.groups3708469109370488835omplex (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B2 K2)) tptp.one_one_complex))) S2) (@ B2 A))) (=> (not _let_1) (= (@ (@ tptp.groups3708469109370488835omplex (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B2 K2)) tptp.one_one_complex))) S2) tptp.one_one_complex)))))) (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups4696554848551431203al_nat G))) (=> (@ tptp.finite_finite_real A2) (=> (not (@ (@ tptp.member_real X) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X) A2)) (@ (@ tptp.times_times_nat (@ G X)) (@ _let_1 A2))))))) (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (@ (@ tptp.member_complex X) A2)) (= (@ _let_1 (@ (@ tptp.insert_complex X) A2)) (@ (@ tptp.times_times_nat (@ G X)) (@ _let_1 A2))))))) (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat G))) (=> (@ tptp.finite_finite_int A2) (=> (not (@ (@ tptp.member_int X) A2)) (= (@ _let_1 (@ (@ tptp.insert_int X) A2)) (@ (@ tptp.times_times_nat (@ G X)) (@ _let_1 A2))))))) (forall ((A2 tptp.set_Extended_enat) (X tptp.extended_enat) (G (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2880970938130013265at_nat G))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (not (@ (@ tptp.member_Extended_enat X) A2)) (= (@ _let_1 (@ (@ tptp.insert_Extended_enat X) A2)) (@ (@ tptp.times_times_nat (@ G X)) (@ _let_1 A2))))))) (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups4694064378042380927al_int G))) (=> (@ tptp.finite_finite_real A2) (=> (not (@ (@ tptp.member_real X) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X) A2)) (@ (@ tptp.times_times_int (@ G X)) (@ _let_1 A2))))))) (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (@ (@ tptp.member_complex X) A2)) (= (@ _let_1 (@ (@ tptp.insert_complex X) A2)) (@ (@ tptp.times_times_int (@ G X)) (@ _let_1 A2))))))) (forall ((A2 tptp.set_Extended_enat) (X tptp.extended_enat) (G (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2878480467620962989at_int G))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (not (@ (@ tptp.member_Extended_enat X) A2)) (= (@ _let_1 (@ (@ tptp.insert_Extended_enat X) A2)) (@ (@ tptp.times_times_int (@ G X)) (@ _let_1 A2))))))) (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real G))) (=> (@ tptp.finite_finite_real A2) (=> (not (@ (@ tptp.member_real X) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X) A2)) (@ (@ tptp.times_times_real (@ G X)) (@ _let_1 A2))))))) (forall ((A2 tptp.set_nat) (X tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (=> (@ tptp.finite_finite_nat A2) (=> (not (@ (@ tptp.member_nat X) A2)) (= (@ _let_1 (@ (@ tptp.insert_nat X) A2)) (@ (@ tptp.times_times_real (@ G X)) (@ _let_1 A2))))))) (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (@ (@ tptp.member_complex X) A2)) (= (@ _let_1 (@ (@ tptp.insert_complex X) A2)) (@ (@ tptp.times_times_real (@ G X)) (@ _let_1 A2))))))) (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.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.extended_enat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups7961826882256487087d_enat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.times_7803423173614009249d_enat (@ _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.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 ((A (-> tptp.nat tptp.real)) (X tptp.real)) (= (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ A N)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N)))) X) (= (@ A tptp.zero_zero_nat) X))) (forall ((A (-> tptp.nat tptp.complex)) (X tptp.complex)) (= (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ A N)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N)))) X) (= (@ A tptp.zero_zero_nat) X))) (forall ((N2 tptp.nat) (M2 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (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) M2))) (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) (M2 tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_3 (@ tptp.groups6464643781859351333omplex G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M2))) (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) (M2 tptp.nat) (G (-> tptp.nat tptp.extended_enat))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_3 (@ tptp.groups7961826882256487087d_enat G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M2))) (and (=> _let_5 (= _let_4 tptp.one_on7984719198319812577d_enat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_7803423173614009249d_enat (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))))) (forall ((N2 tptp.nat) (M2 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (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) M2))) (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 ((N2 tptp.nat) (M2 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (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) M2))) (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 ((A2 tptp.set_real) (B tptp.set_nat) (G (-> tptp.real tptp.nat tptp.int)) (R (-> tptp.real tptp.nat Bool))) (=> (@ tptp.finite_finite_real A2) (=> (@ tptp.finite_finite_nat B) (= (@ (@ tptp.groups4694064378042380927al_int (lambda ((X4 tptp.real)) (@ (@ tptp.groups705719431365010083at_int (@ G X4)) (@ tptp.collect_nat (lambda ((Y5 tptp.nat)) (and (@ (@ tptp.member_nat Y5) B) (@ (@ R X4) Y5))))))) A2) (@ (@ tptp.groups705719431365010083at_int (lambda ((Y5 tptp.nat)) (@ (@ tptp.groups4694064378042380927al_int (lambda ((X4 tptp.real)) (@ (@ G X4) Y5))) (@ tptp.collect_real (lambda ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) A2) (@ (@ R X4) Y5))))))) B))))) (forall ((A2 tptp.set_complex) (B tptp.set_nat) (G (-> tptp.complex tptp.nat tptp.int)) (R (-> tptp.complex tptp.nat Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ tptp.finite_finite_nat B) (= (@ (@ tptp.groups858564598930262913ex_int (lambda ((X4 tptp.complex)) (@ (@ tptp.groups705719431365010083at_int (@ G X4)) (@ tptp.collect_nat (lambda ((Y5 tptp.nat)) (and (@ (@ tptp.member_nat Y5) B) (@ (@ R X4) Y5))))))) A2) (@ (@ tptp.groups705719431365010083at_int (lambda ((Y5 tptp.nat)) (@ (@ tptp.groups858564598930262913ex_int (lambda ((X4 tptp.complex)) (@ (@ G X4) Y5))) (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A2) (@ (@ R X4) Y5))))))) B))))) (forall ((A2 tptp.set_Extended_enat) (B tptp.set_nat) (G (-> tptp.extended_enat tptp.nat tptp.int)) (R (-> tptp.extended_enat tptp.nat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ tptp.finite_finite_nat B) (= (@ (@ tptp.groups2878480467620962989at_int (lambda ((X4 tptp.extended_enat)) (@ (@ tptp.groups705719431365010083at_int (@ G X4)) (@ tptp.collect_nat (lambda ((Y5 tptp.nat)) (and (@ (@ tptp.member_nat Y5) B) (@ (@ R X4) Y5))))))) A2) (@ (@ tptp.groups705719431365010083at_int (lambda ((Y5 tptp.nat)) (@ (@ tptp.groups2878480467620962989at_int (lambda ((X4 tptp.extended_enat)) (@ (@ G X4) Y5))) (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) A2) (@ (@ R X4) Y5))))))) B))))) (forall ((A2 tptp.set_real) (B tptp.set_int) (G (-> tptp.real tptp.int tptp.int)) (R (-> tptp.real tptp.int Bool))) (=> (@ tptp.finite_finite_real A2) (=> (@ tptp.finite_finite_int B) (= (@ (@ tptp.groups4694064378042380927al_int (lambda ((X4 tptp.real)) (@ (@ tptp.groups1705073143266064639nt_int (@ G X4)) (@ tptp.collect_int (lambda ((Y5 tptp.int)) (and (@ (@ tptp.member_int Y5) B) (@ (@ R X4) Y5))))))) A2) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((Y5 tptp.int)) (@ (@ tptp.groups4694064378042380927al_int (lambda ((X4 tptp.real)) (@ (@ G X4) Y5))) (@ tptp.collect_real (lambda ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) A2) (@ (@ R X4) Y5))))))) B))))) (forall ((A2 tptp.set_complex) (B tptp.set_int) (G (-> tptp.complex tptp.int tptp.int)) (R (-> tptp.complex tptp.int Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ tptp.finite_finite_int B) (= (@ (@ tptp.groups858564598930262913ex_int (lambda ((X4 tptp.complex)) (@ (@ tptp.groups1705073143266064639nt_int (@ G X4)) (@ tptp.collect_int (lambda ((Y5 tptp.int)) (and (@ (@ tptp.member_int Y5) B) (@ (@ R X4) Y5))))))) A2) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((Y5 tptp.int)) (@ (@ tptp.groups858564598930262913ex_int (lambda ((X4 tptp.complex)) (@ (@ G X4) Y5))) (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A2) (@ (@ R X4) Y5))))))) B))))) (forall ((A2 tptp.set_Extended_enat) (B tptp.set_int) (G (-> tptp.extended_enat tptp.int tptp.int)) (R (-> tptp.extended_enat tptp.int Bool))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ tptp.finite_finite_int B) (= (@ (@ tptp.groups2878480467620962989at_int (lambda ((X4 tptp.extended_enat)) (@ (@ tptp.groups1705073143266064639nt_int (@ G X4)) (@ tptp.collect_int (lambda ((Y5 tptp.int)) (and (@ (@ tptp.member_int Y5) B) (@ (@ R X4) Y5))))))) A2) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((Y5 tptp.int)) (@ (@ tptp.groups2878480467620962989at_int (lambda ((X4 tptp.extended_enat)) (@ (@ G X4) Y5))) (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) A2) (@ (@ R X4) Y5))))))) B))))) (forall ((A2 tptp.set_real) (B tptp.set_nat) (G (-> tptp.real tptp.nat tptp.nat)) (R (-> tptp.real tptp.nat Bool))) (=> (@ tptp.finite_finite_real A2) (=> (@ tptp.finite_finite_nat B) (= (@ (@ tptp.groups4696554848551431203al_nat (lambda ((X4 tptp.real)) (@ (@ tptp.groups708209901874060359at_nat (@ G X4)) (@ tptp.collect_nat (lambda ((Y5 tptp.nat)) (and (@ (@ tptp.member_nat Y5) B) (@ (@ R X4) Y5))))))) A2) (@ (@ tptp.groups708209901874060359at_nat (lambda ((Y5 tptp.nat)) (@ (@ tptp.groups4696554848551431203al_nat (lambda ((X4 tptp.real)) (@ (@ G X4) Y5))) (@ tptp.collect_real (lambda ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) A2) (@ (@ R X4) Y5))))))) B))))) (forall ((A2 tptp.set_complex) (B tptp.set_nat) (G (-> tptp.complex tptp.nat tptp.nat)) (R (-> tptp.complex tptp.nat Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ tptp.finite_finite_nat B) (= (@ (@ tptp.groups861055069439313189ex_nat (lambda ((X4 tptp.complex)) (@ (@ tptp.groups708209901874060359at_nat (@ G X4)) (@ tptp.collect_nat (lambda ((Y5 tptp.nat)) (and (@ (@ tptp.member_nat Y5) B) (@ (@ R X4) Y5))))))) A2) (@ (@ tptp.groups708209901874060359at_nat (lambda ((Y5 tptp.nat)) (@ (@ tptp.groups861055069439313189ex_nat (lambda ((X4 tptp.complex)) (@ (@ G X4) Y5))) (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A2) (@ (@ R X4) Y5))))))) B))))) (forall ((A2 tptp.set_int) (B tptp.set_nat) (G (-> tptp.int tptp.nat tptp.nat)) (R (-> tptp.int tptp.nat Bool))) (=> (@ tptp.finite_finite_int A2) (=> (@ tptp.finite_finite_nat B) (= (@ (@ tptp.groups1707563613775114915nt_nat (lambda ((X4 tptp.int)) (@ (@ tptp.groups708209901874060359at_nat (@ G X4)) (@ tptp.collect_nat (lambda ((Y5 tptp.nat)) (and (@ (@ tptp.member_nat Y5) B) (@ (@ R X4) Y5))))))) A2) (@ (@ tptp.groups708209901874060359at_nat (lambda ((Y5 tptp.nat)) (@ (@ tptp.groups1707563613775114915nt_nat (lambda ((X4 tptp.int)) (@ (@ G X4) Y5))) (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A2) (@ (@ R X4) Y5))))))) B))))) (forall ((A2 tptp.set_Extended_enat) (B tptp.set_nat) (G (-> tptp.extended_enat tptp.nat tptp.nat)) (R (-> tptp.extended_enat tptp.nat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ tptp.finite_finite_nat B) (= (@ (@ tptp.groups2880970938130013265at_nat (lambda ((X4 tptp.extended_enat)) (@ (@ tptp.groups708209901874060359at_nat (@ G X4)) (@ tptp.collect_nat (lambda ((Y5 tptp.nat)) (and (@ (@ tptp.member_nat Y5) B) (@ (@ R X4) Y5))))))) A2) (@ (@ tptp.groups708209901874060359at_nat (lambda ((Y5 tptp.nat)) (@ (@ tptp.groups2880970938130013265at_nat (lambda ((X4 tptp.extended_enat)) (@ (@ G X4) Y5))) (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) A2) (@ (@ R X4) Y5))))))) B))))) (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real)) (G (-> tptp.extended_enat tptp.real))) (=> (forall ((I4 tptp.extended_enat)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_Extended_enat I4) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G I4)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups97031904164794029t_real F) A2)) (@ (@ tptp.groups97031904164794029t_real G) A2)))) (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (forall ((I4 tptp.real)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_real I4) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G I4)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups1681761925125756287l_real F) A2)) (@ (@ tptp.groups1681761925125756287l_real G) A2)))) (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (forall ((I4 tptp.nat)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_nat I4) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G I4)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups129246275422532515t_real F) A2)) (@ (@ tptp.groups129246275422532515t_real G) A2)))) (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (forall ((I4 tptp.int)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_int I4) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G I4)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups2316167850115554303t_real F) A2)) (@ (@ tptp.groups2316167850115554303t_real G) A2)))) (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat)) (G (-> tptp.extended_enat tptp.nat))) (=> (forall ((I4 tptp.extended_enat)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_Extended_enat I4) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) (@ G I4)))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups2880970938130013265at_nat F) A2)) (@ (@ tptp.groups2880970938130013265at_nat G) A2)))) (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat)) (G (-> tptp.real tptp.nat))) (=> (forall ((I4 tptp.real)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_real I4) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) (@ G I4)))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4696554848551431203al_nat F) A2)) (@ (@ tptp.groups4696554848551431203al_nat G) A2)))) (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (forall ((I4 tptp.int)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_int I4) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) (@ G I4)))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups1707563613775114915nt_nat F) A2)) (@ (@ tptp.groups1707563613775114915nt_nat G) A2)))) (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.int)) (G (-> tptp.extended_enat tptp.int))) (=> (forall ((I4 tptp.extended_enat)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_Extended_enat 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.groups2878480467620962989at_int F) A2)) (@ (@ tptp.groups2878480467620962989at_int G) A2)))) (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.int)) (G (-> tptp.real tptp.int))) (=> (forall ((I4 tptp.real)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_real I4) A2) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) _let_1) (@ (@ tptp.ord_less_eq_int _let_1) (@ G I4)))))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups4694064378042380927al_int F) A2)) (@ (@ tptp.groups4694064378042380927al_int G) A2)))) (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (forall ((I4 tptp.nat)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_nat 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.groups705719431365010083at_int F) A2)) (@ (@ tptp.groups705719431365010083at_int G) 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_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_int tptp.zero_zero_int) (@ F X5)))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.groups705719431365010083at_int F) A2)))) (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.int))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F X5)))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.groups1705073143266064639nt_int F) A2)))) (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X5)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups708209901874060359at_nat F) A2)))) (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) A2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X5)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups97031904164794029t_real F) A2)))) (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X5)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups1681761925125756287l_real F) A2)))) (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X5)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups129246275422532515t_real F) A2)))) (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X5)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups2316167850115554303t_real F) A2)))) (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) A2) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ F X5)))) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ (@ tptp.groups2880970938130013265at_nat F) A2)))) (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ F X5)))) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ (@ tptp.groups4696554848551431203al_nat F) A2)))) (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ F X5)))) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ (@ tptp.groups1707563613775114915nt_nat F) A2)))) (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.int))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) A2) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F X5)))) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ (@ tptp.groups2878480467620962989at_int F) A2)))) (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.int))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F X5)))) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ (@ tptp.groups4694064378042380927al_int 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.one_one_int) (@ F X5)))) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ (@ tptp.groups705719431365010083at_int F) A2)))) (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (exists ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (= (@ F X2) tptp.zero_zero_nat))) (= (@ (@ tptp.groups861055069439313189ex_nat F) A2) tptp.zero_zero_nat)))) (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (=> (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (= (@ F X2) tptp.zero_zero_nat))) (= (@ (@ tptp.groups1707563613775114915nt_nat F) A2) tptp.zero_zero_nat)))) (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (exists ((X2 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X2) A2) (= (@ F X2) tptp.zero_zero_nat))) (= (@ (@ tptp.groups2880970938130013265at_nat F) A2) tptp.zero_zero_nat)))) (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat A2) (=> (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (= (@ F X2) tptp.zero_zero_real))) (= (@ (@ tptp.groups129246275422532515t_real F) A2) tptp.zero_zero_real)))) (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (exists ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (= (@ F X2) tptp.zero_zero_real))) (= (@ (@ tptp.groups766887009212190081x_real F) A2) tptp.zero_zero_real)))) (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A2) (=> (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (= (@ F X2) tptp.zero_zero_real))) (= (@ (@ tptp.groups2316167850115554303t_real F) A2) tptp.zero_zero_real)))) (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (exists ((X2 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X2) A2) (= (@ F X2) tptp.zero_zero_real))) (= (@ (@ tptp.groups97031904164794029t_real F) A2) tptp.zero_zero_real)))) (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (exists ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (= (@ F X2) tptp.zero_zero_int))) (= (@ (@ tptp.groups858564598930262913ex_int F) A2) tptp.zero_zero_int)))) (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.int))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (exists ((X2 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X2) A2) (= (@ F X2) tptp.zero_zero_int))) (= (@ (@ tptp.groups2878480467620962989at_int F) A2) tptp.zero_zero_int)))) (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat A2) (=> (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (= (@ F X2) tptp.zero_zero_complex))) (= (@ (@ tptp.groups6464643781859351333omplex F) A2) tptp.zero_zero_complex)))) (forall ((F (-> tptp.nat tptp.real)) (A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real F) (@ (@ tptp.set_or1269000886237332187st_nat A) B2)) (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ F A3)) __flatten_var_0))) A) B2) tptp.one_one_real))) (forall ((F (-> tptp.nat tptp.complex)) (A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.groups6464643781859351333omplex F) (@ (@ tptp.set_or1269000886237332187st_nat A) B2)) (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.times_times_complex (@ F A3)) __flatten_var_0))) A) B2) tptp.one_one_complex))) (forall ((F (-> tptp.nat tptp.extended_enat)) (A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.groups7961826882256487087d_enat F) (@ (@ tptp.set_or1269000886237332187st_nat A) B2)) (@ (@ (@ (@ tptp.set_fo2538466533108834004d_enat (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.extended_enat)) (@ (@ tptp.times_7803423173614009249d_enat (@ F A3)) __flatten_var_0))) A) B2) tptp.one_on7984719198319812577d_enat))) (forall ((F (-> tptp.nat tptp.int)) (A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int F) (@ (@ tptp.set_or1269000886237332187st_nat A) B2)) (@ (@ (@ (@ tptp.set_fo2581907887559384638at_int (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.times_times_int (@ F A3)) __flatten_var_0))) A) B2) tptp.one_one_int))) (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat F) (@ (@ tptp.set_or1269000886237332187st_nat A) B2)) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.times_times_nat (@ F A3)) __flatten_var_0))) A) B2) tptp.one_one_nat))) (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.nat)) (P (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A2) (= (@ (@ tptp.groups4696554848551431203al_nat G) (@ tptp.collect_real (lambda ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) A2) (@ P X4))))) (@ (@ tptp.groups4696554848551431203al_nat (lambda ((X4 tptp.real)) (@ (@ (@ tptp.if_nat (@ P X4)) (@ G X4)) tptp.one_one_nat))) A2)))) (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (P (-> tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ (@ tptp.groups861055069439313189ex_nat G) (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A2) (@ P X4))))) (@ (@ tptp.groups861055069439313189ex_nat (lambda ((X4 tptp.complex)) (@ (@ (@ tptp.if_nat (@ P X4)) (@ G X4)) tptp.one_one_nat))) A2)))) (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.nat)) (P (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A2) (= (@ (@ tptp.groups1707563613775114915nt_nat G) (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A2) (@ P X4))))) (@ (@ tptp.groups1707563613775114915nt_nat (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_nat (@ P X4)) (@ G X4)) tptp.one_one_nat))) A2)))) (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.nat)) (P (-> tptp.extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ (@ tptp.groups2880970938130013265at_nat G) (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) A2) (@ P X4))))) (@ (@ tptp.groups2880970938130013265at_nat (lambda ((X4 tptp.extended_enat)) (@ (@ (@ tptp.if_nat (@ P X4)) (@ G X4)) tptp.one_one_nat))) A2)))) (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.int)) (P (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A2) (= (@ (@ tptp.groups4694064378042380927al_int G) (@ tptp.collect_real (lambda ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) A2) (@ P X4))))) (@ (@ tptp.groups4694064378042380927al_int (lambda ((X4 tptp.real)) (@ (@ (@ tptp.if_int (@ P X4)) (@ G X4)) tptp.one_one_int))) A2)))) (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.int)) (P (-> tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ (@ tptp.groups858564598930262913ex_int G) (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A2) (@ P X4))))) (@ (@ tptp.groups858564598930262913ex_int (lambda ((X4 tptp.complex)) (@ (@ (@ tptp.if_int (@ P X4)) (@ G X4)) tptp.one_one_int))) A2)))) (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.int)) (P (-> tptp.extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ (@ tptp.groups2878480467620962989at_int G) (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) A2) (@ P X4))))) (@ (@ tptp.groups2878480467620962989at_int (lambda ((X4 tptp.extended_enat)) (@ (@ (@ tptp.if_int (@ P X4)) (@ G X4)) tptp.one_one_int))) A2)))) (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.complex)) (P (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A2) (= (@ (@ tptp.groups713298508707869441omplex G) (@ tptp.collect_real (lambda ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) A2) (@ P X4))))) (@ (@ tptp.groups713298508707869441omplex (lambda ((X4 tptp.real)) (@ (@ (@ tptp.if_complex (@ P X4)) (@ G X4)) tptp.one_one_complex))) A2)))) (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.complex)) (P (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.groups6464643781859351333omplex G) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A2) (@ P X4))))) (@ (@ tptp.groups6464643781859351333omplex (lambda ((X4 tptp.nat)) (@ (@ (@ tptp.if_complex (@ P X4)) (@ G X4)) tptp.one_one_complex))) A2)))) (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.complex)) (P (-> tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ (@ tptp.groups3708469109370488835omplex G) (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A2) (@ P X4))))) (@ (@ tptp.groups3708469109370488835omplex (lambda ((X4 tptp.complex)) (@ (@ (@ tptp.if_complex (@ P X4)) (@ G X4)) tptp.one_one_complex))) A2)))) (forall ((G (-> tptp.nat tptp.int)) (M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) (@ tptp.suc N2))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N2)))) (forall ((G (-> tptp.nat tptp.nat)) (M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) (@ tptp.suc N2))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N2)))) (forall ((G (-> tptp.nat tptp.int)) (M2 tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M2) K)) (@ (@ tptp.plus_plus_nat N2) K))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I3) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N2)))) (forall ((G (-> tptp.nat tptp.nat)) (M2 tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M2) K)) (@ (@ tptp.plus_plus_nat N2) K))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I3) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N2)))) (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.extended_enat))) (=> (forall ((X5 tptp.extended_enat)) (let ((_let_1 (@ F X5))) (=> (@ (@ tptp.member_Extended_enat X5) A2) (and (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) _let_1) (@ (@ tptp.ord_le2932123472753598470d_enat _let_1) tptp.one_on7984719198319812577d_enat))))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups8932437906259616549d_enat F) A2)) tptp.one_on7984719198319812577d_enat))) (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.extended_enat))) (=> (forall ((X5 tptp.real)) (let ((_let_1 (@ F X5))) (=> (@ (@ tptp.member_real X5) A2) (and (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) _let_1) (@ (@ tptp.ord_le2932123472753598470d_enat _let_1) tptp.one_on7984719198319812577d_enat))))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups7973222482632965587d_enat F) A2)) tptp.one_on7984719198319812577d_enat))) (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.extended_enat))) (=> (forall ((X5 tptp.nat)) (let ((_let_1 (@ F X5))) (=> (@ (@ tptp.member_nat X5) A2) (and (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) _let_1) (@ (@ tptp.ord_le2932123472753598470d_enat _let_1) tptp.one_on7984719198319812577d_enat))))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups7961826882256487087d_enat F) A2)) tptp.one_on7984719198319812577d_enat))) (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.extended_enat))) (=> (forall ((X5 tptp.int)) (let ((_let_1 (@ F X5))) (=> (@ (@ tptp.member_int X5) A2) (and (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) _let_1) (@ (@ tptp.ord_le2932123472753598470d_enat _let_1) tptp.one_on7984719198319812577d_enat))))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups5078248829458667347d_enat F) A2)) tptp.one_on7984719198319812577d_enat))) (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real))) (=> (forall ((X5 tptp.extended_enat)) (let ((_let_1 (@ F X5))) (=> (@ (@ tptp.member_Extended_enat X5) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.one_one_real))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups97031904164794029t_real F) A2)) tptp.one_one_real))) (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (forall ((X5 tptp.real)) (let ((_let_1 (@ F X5))) (=> (@ (@ tptp.member_real X5) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.one_one_real))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups1681761925125756287l_real F) A2)) tptp.one_one_real))) (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (forall ((X5 tptp.nat)) (let ((_let_1 (@ F X5))) (=> (@ (@ tptp.member_nat X5) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.one_one_real))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups129246275422532515t_real F) A2)) tptp.one_one_real))) (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (forall ((X5 tptp.int)) (let ((_let_1 (@ F X5))) (=> (@ (@ tptp.member_int X5) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.one_one_real))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups2316167850115554303t_real F) A2)) tptp.one_one_real))) (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat))) (=> (forall ((X5 tptp.extended_enat)) (let ((_let_1 (@ F X5))) (=> (@ (@ tptp.member_Extended_enat X5) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) tptp.one_one_nat))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups2880970938130013265at_nat F) A2)) tptp.one_one_nat))) (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (forall ((X5 tptp.real)) (let ((_let_1 (@ F X5))) (=> (@ (@ tptp.member_real X5) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) tptp.one_one_nat))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4696554848551431203al_nat F) A2)) tptp.one_one_nat))) (forall ((R (-> tptp.nat tptp.nat Bool)) (S2 tptp.set_complex) (H2 (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ (@ R tptp.one_one_nat) tptp.one_one_nat) (=> (forall ((X1 tptp.nat) (Y1 tptp.nat) (X23 tptp.nat) (Y22 tptp.nat)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.times_times_nat X1) Y1)) (@ (@ tptp.times_times_nat X23) Y22)))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S2) (@ (@ R (@ H2 X5)) (@ G X5)))) (@ (@ R (@ (@ tptp.groups861055069439313189ex_nat H2) S2)) (@ (@ tptp.groups861055069439313189ex_nat G) S2))))))) (forall ((R (-> tptp.nat tptp.nat Bool)) (S2 tptp.set_int) (H2 (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ (@ R tptp.one_one_nat) tptp.one_one_nat) (=> (forall ((X1 tptp.nat) (Y1 tptp.nat) (X23 tptp.nat) (Y22 tptp.nat)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.times_times_nat X1) Y1)) (@ (@ tptp.times_times_nat X23) Y22)))) (=> (@ tptp.finite_finite_int S2) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) S2) (@ (@ R (@ H2 X5)) (@ G X5)))) (@ (@ R (@ (@ tptp.groups1707563613775114915nt_nat H2) S2)) (@ (@ tptp.groups1707563613775114915nt_nat G) S2))))))) (forall ((R (-> tptp.nat tptp.nat Bool)) (S2 tptp.set_Extended_enat) (H2 (-> tptp.extended_enat tptp.nat)) (G (-> tptp.extended_enat tptp.nat))) (=> (@ (@ R tptp.one_one_nat) tptp.one_one_nat) (=> (forall ((X1 tptp.nat) (Y1 tptp.nat) (X23 tptp.nat) (Y22 tptp.nat)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.times_times_nat X1) Y1)) (@ (@ tptp.times_times_nat X23) Y22)))) (=> (@ tptp.finite4001608067531595151d_enat S2) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) S2) (@ (@ R (@ H2 X5)) (@ G X5)))) (@ (@ R (@ (@ tptp.groups2880970938130013265at_nat H2) S2)) (@ (@ tptp.groups2880970938130013265at_nat G) S2))))))) (forall ((R (-> tptp.int tptp.int Bool)) (S2 tptp.set_complex) (H2 (-> tptp.complex tptp.int)) (G (-> tptp.complex tptp.int))) (=> (@ (@ R tptp.one_one_int) tptp.one_one_int) (=> (forall ((X1 tptp.int) (Y1 tptp.int) (X23 tptp.int) (Y22 tptp.int)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.times_times_int X1) Y1)) (@ (@ tptp.times_times_int X23) Y22)))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S2) (@ (@ R (@ H2 X5)) (@ G X5)))) (@ (@ R (@ (@ tptp.groups858564598930262913ex_int H2) S2)) (@ (@ tptp.groups858564598930262913ex_int G) S2))))))) (forall ((R (-> tptp.int tptp.int Bool)) (S2 tptp.set_Extended_enat) (H2 (-> tptp.extended_enat tptp.int)) (G (-> tptp.extended_enat tptp.int))) (=> (@ (@ R tptp.one_one_int) tptp.one_one_int) (=> (forall ((X1 tptp.int) (Y1 tptp.int) (X23 tptp.int) (Y22 tptp.int)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.times_times_int X1) Y1)) (@ (@ tptp.times_times_int X23) Y22)))) (=> (@ tptp.finite4001608067531595151d_enat S2) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) S2) (@ (@ R (@ H2 X5)) (@ G X5)))) (@ (@ R (@ (@ tptp.groups2878480467620962989at_int H2) S2)) (@ (@ tptp.groups2878480467620962989at_int G) S2))))))) (forall ((R (-> tptp.real tptp.real Bool)) (S2 tptp.set_nat) (H2 (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (@ (@ R tptp.one_one_real) tptp.one_one_real) (=> (forall ((X1 tptp.real) (Y1 tptp.real) (X23 tptp.real) (Y22 tptp.real)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.times_times_real X1) Y1)) (@ (@ tptp.times_times_real X23) Y22)))) (=> (@ tptp.finite_finite_nat S2) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S2) (@ (@ R (@ H2 X5)) (@ G X5)))) (@ (@ R (@ (@ tptp.groups129246275422532515t_real H2) S2)) (@ (@ tptp.groups129246275422532515t_real G) S2))))))) (forall ((R (-> tptp.real tptp.real Bool)) (S2 tptp.set_complex) (H2 (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ (@ R tptp.one_one_real) tptp.one_one_real) (=> (forall ((X1 tptp.real) (Y1 tptp.real) (X23 tptp.real) (Y22 tptp.real)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.times_times_real X1) Y1)) (@ (@ tptp.times_times_real X23) Y22)))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S2) (@ (@ R (@ H2 X5)) (@ G X5)))) (@ (@ R (@ (@ tptp.groups766887009212190081x_real H2) S2)) (@ (@ tptp.groups766887009212190081x_real G) S2))))))) (forall ((R (-> tptp.real tptp.real Bool)) (S2 tptp.set_int) (H2 (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (@ (@ R tptp.one_one_real) tptp.one_one_real) (=> (forall ((X1 tptp.real) (Y1 tptp.real) (X23 tptp.real) (Y22 tptp.real)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.times_times_real X1) Y1)) (@ (@ tptp.times_times_real X23) Y22)))) (=> (@ tptp.finite_finite_int S2) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) S2) (@ (@ R (@ H2 X5)) (@ G X5)))) (@ (@ R (@ (@ tptp.groups2316167850115554303t_real H2) S2)) (@ (@ tptp.groups2316167850115554303t_real G) S2))))))) (forall ((R (-> tptp.real tptp.real Bool)) (S2 tptp.set_Extended_enat) (H2 (-> tptp.extended_enat tptp.real)) (G (-> tptp.extended_enat tptp.real))) (=> (@ (@ R tptp.one_one_real) tptp.one_one_real) (=> (forall ((X1 tptp.real) (Y1 tptp.real) (X23 tptp.real) (Y22 tptp.real)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.times_times_real X1) Y1)) (@ (@ tptp.times_times_real X23) Y22)))) (=> (@ tptp.finite4001608067531595151d_enat S2) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) S2) (@ (@ R (@ H2 X5)) (@ G X5)))) (@ (@ R (@ (@ tptp.groups97031904164794029t_real H2) S2)) (@ (@ tptp.groups97031904164794029t_real G) S2))))))) (forall ((R (-> tptp.complex tptp.complex Bool)) (S2 tptp.set_nat) (H2 (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.complex))) (=> (@ (@ R tptp.one_one_complex) tptp.one_one_complex) (=> (forall ((X1 tptp.complex) (Y1 tptp.complex) (X23 tptp.complex) (Y22 tptp.complex)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y22)) (@ (@ R (@ (@ tptp.times_times_complex X1) Y1)) (@ (@ tptp.times_times_complex X23) Y22)))) (=> (@ tptp.finite_finite_nat S2) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S2) (@ (@ R (@ H2 X5)) (@ G X5)))) (@ (@ R (@ (@ tptp.groups6464643781859351333omplex H2) S2)) (@ (@ tptp.groups6464643781859351333omplex G) S2))))))) (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real 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A2)))) (let ((_let_4 (@ (@ tptp.member_int X) A2))) (=> (@ tptp.finite_finite_int A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_nat (@ G X)) _let_2)))))))))) (forall ((A2 tptp.set_Extended_enat) (X tptp.extended_enat) (G (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2880970938130013265at_nat G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_Extended_enat X) A2)))) (let ((_let_4 (@ (@ tptp.member_Extended_enat X) A2))) (=> (@ tptp.finite4001608067531595151d_enat A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_nat (@ G X)) _let_2)))))))))) (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups4694064378042380927al_int G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_real X) A2)))) (let ((_let_4 (@ (@ tptp.member_real X) A2))) (=> (@ tptp.finite_finite_real A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_int (@ G X)) _let_2)))))))))) (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_complex X) A2)))) (let ((_let_4 (@ (@ tptp.member_complex X) A2))) (=> (@ tptp.finite3207457112153483333omplex A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_int (@ G X)) _let_2)))))))))) (forall ((A2 tptp.set_Extended_enat) (X tptp.extended_enat) (G (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2878480467620962989at_int G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_Extended_enat X) A2)))) (let ((_let_4 (@ (@ tptp.member_Extended_enat X) A2))) (=> (@ tptp.finite4001608067531595151d_enat A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_int (@ G X)) _let_2)))))))))) (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_real X) A2)))) (let ((_let_4 (@ (@ tptp.member_real X) A2))) (=> (@ tptp.finite_finite_real A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_real (@ G X)) _let_2)))))))))) (forall ((A2 tptp.set_nat) (X tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_nat X) A2)))) (let ((_let_4 (@ (@ tptp.member_nat X) A2))) (=> (@ tptp.finite_finite_nat A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_real (@ G X)) _let_2)))))))))) (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_complex X) A2)))) (let ((_let_4 (@ (@ tptp.member_complex X) A2))) (=> (@ tptp.finite3207457112153483333omplex A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_real (@ G X)) _let_2)))))))))) (forall ((B tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat F))) (=> (@ tptp.finite3207457112153483333omplex B) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B) (@ (@ tptp.dvd_dvd_nat (@ _let_1 A2)) (@ _let_1 B)))))) (forall ((B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2880970938130013265at_nat F))) (=> (@ tptp.finite4001608067531595151d_enat B) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) B) (@ (@ tptp.dvd_dvd_nat (@ _let_1 A2)) (@ _let_1 B)))))) (forall ((B tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int F))) (=> (@ tptp.finite3207457112153483333omplex B) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B) (@ (@ tptp.dvd_dvd_int (@ _let_1 A2)) (@ _let_1 B)))))) (forall ((B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2878480467620962989at_int F))) (=> (@ tptp.finite4001608067531595151d_enat B) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) B) (@ (@ tptp.dvd_dvd_int (@ _let_1 A2)) (@ _let_1 B)))))) (forall ((B tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat F))) (=> (@ tptp.finite_finite_int B) (=> (@ (@ tptp.ord_less_eq_set_int A2) B) (@ (@ tptp.dvd_dvd_nat (@ _let_1 A2)) (@ _let_1 B)))))) (forall ((B tptp.set_nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups705719431365010083at_int F))) (=> (@ tptp.finite_finite_nat B) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B) (@ (@ tptp.dvd_dvd_int (@ _let_1 A2)) (@ _let_1 B)))))) (forall ((B tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.groups1705073143266064639nt_int F))) (=> (@ tptp.finite_finite_int B) (=> (@ (@ tptp.ord_less_eq_set_int A2) B) (@ (@ tptp.dvd_dvd_int (@ _let_1 A2)) (@ _let_1 B)))))) (forall ((B tptp.set_nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups708209901874060359at_nat F))) (=> (@ tptp.finite_finite_nat B) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B) (@ (@ tptp.dvd_dvd_nat (@ _let_1 A2)) (@ _let_1 B)))))) (forall ((B tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.nat)) (G (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real B) (=> (@ (@ tptp.ord_less_eq_set_real A2) B) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) A2) (@ (@ tptp.dvd_dvd_nat (@ F A4)) (@ G A4)))) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.groups4696554848551431203al_nat F) A2)) (@ (@ tptp.groups4696554848551431203al_nat G) B)))))) (forall ((B tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex B) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) A2) (@ (@ tptp.dvd_dvd_nat (@ F A4)) (@ G A4)))) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.groups861055069439313189ex_nat F) A2)) (@ (@ tptp.groups861055069439313189ex_nat G) B)))))) (forall ((B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat)) (G (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat B) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) B) (=> (forall ((A4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A4) A2) (@ (@ tptp.dvd_dvd_nat (@ F A4)) (@ G A4)))) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.groups2880970938130013265at_nat F) A2)) (@ (@ tptp.groups2880970938130013265at_nat G) B)))))) (forall ((B tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.int)) (G (-> tptp.real tptp.int))) (=> (@ tptp.finite_finite_real B) (=> (@ (@ tptp.ord_less_eq_set_real A2) B) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) A2) (@ (@ tptp.dvd_dvd_int (@ F A4)) (@ G A4)))) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.groups4694064378042380927al_int F) A2)) (@ (@ tptp.groups4694064378042380927al_int G) B)))))) (forall ((B tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.int)) (G (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex B) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) A2) (@ (@ tptp.dvd_dvd_int (@ F A4)) (@ G A4)))) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.groups858564598930262913ex_int F) A2)) (@ (@ tptp.groups858564598930262913ex_int G) B)))))) (forall ((B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.int)) (G (-> tptp.extended_enat tptp.int))) (=> (@ tptp.finite4001608067531595151d_enat B) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) B) (=> (forall ((A4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A4) A2) (@ (@ tptp.dvd_dvd_int (@ F A4)) (@ G A4)))) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.groups2878480467620962989at_int F) A2)) (@ (@ tptp.groups2878480467620962989at_int G) B)))))) (forall ((B tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int B) (=> (@ (@ tptp.ord_less_eq_set_int A2) B) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) A2) (@ (@ tptp.dvd_dvd_nat (@ F A4)) (@ G A4)))) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.groups1707563613775114915nt_nat F) A2)) (@ (@ tptp.groups1707563613775114915nt_nat G) B)))))) (forall ((B tptp.set_nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat B) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B) (=> (forall ((A4 tptp.nat)) (=> (@ (@ tptp.member_nat A4) A2) (@ (@ tptp.dvd_dvd_int (@ F A4)) (@ G A4)))) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.groups705719431365010083at_int F) A2)) (@ (@ tptp.groups705719431365010083at_int G) B)))))) (forall ((B tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.int)) (G (-> tptp.int tptp.int))) (=> (@ tptp.finite_finite_int B) (=> (@ (@ tptp.ord_less_eq_set_int A2) B) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) A2) (@ (@ tptp.dvd_dvd_int (@ F A4)) (@ G A4)))) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.groups1705073143266064639nt_int F) A2)) (@ (@ tptp.groups1705073143266064639nt_int G) B)))))) (forall ((B tptp.set_nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat B) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B) (=> (forall ((A4 tptp.nat)) (=> (@ (@ tptp.member_nat A4) A2) (@ (@ tptp.dvd_dvd_nat (@ F A4)) (@ G A4)))) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.groups708209901874060359at_nat F) A2)) (@ (@ tptp.groups708209901874060359at_nat G) B)))))) (forall ((S5 tptp.set_real) (T5 tptp.set_real) (S2 tptp.set_real) (I (-> tptp.real tptp.real)) (J (-> tptp.real tptp.real)) (T3 tptp.set_real) (G (-> tptp.real tptp.nat)) (H2 (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real S5) (=> (@ tptp.finite_finite_real T5) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real S2) S5)) (= (@ I (@ J A4)) A4))) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real S2) S5)) (@ (@ tptp.member_real (@ J A4)) (@ (@ tptp.minus_minus_set_real T3) T5)))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real T3) T5)) (= (@ J (@ I B4)) B4))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real T3) T5)) (@ (@ tptp.member_real (@ I B4)) (@ (@ tptp.minus_minus_set_real S2) S5)))) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) S5) (= (@ G A4) tptp.one_one_nat))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) T5) (= (@ H2 B4) tptp.one_one_nat))) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) S2) (= (@ H2 (@ J A4)) (@ G A4)))) (= (@ (@ tptp.groups4696554848551431203al_nat G) S2) (@ (@ tptp.groups4696554848551431203al_nat H2) T3)))))))))))) (forall ((S5 tptp.set_real) (T5 tptp.set_complex) (S2 tptp.set_real) (I (-> tptp.complex tptp.real)) (J (-> tptp.real tptp.complex)) (T3 tptp.set_complex) (G (-> tptp.real tptp.nat)) (H2 (-> tptp.complex tptp.nat))) (=> (@ tptp.finite_finite_real S5) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real S2) S5)) (= (@ I (@ J A4)) A4))) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real S2) S5)) (@ (@ tptp.member_complex (@ J A4)) (@ (@ tptp.minus_811609699411566653omplex T3) T5)))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex T3) T5)) (= (@ J (@ I B4)) B4))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex T3) T5)) (@ (@ tptp.member_real (@ I B4)) (@ (@ tptp.minus_minus_set_real S2) S5)))) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) S5) (= (@ G A4) tptp.one_one_nat))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) T5) (= (@ H2 B4) tptp.one_one_nat))) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) S2) (= (@ H2 (@ J A4)) (@ G A4)))) (= (@ (@ tptp.groups4696554848551431203al_nat G) S2) (@ (@ tptp.groups861055069439313189ex_nat H2) T3)))))))))))) (forall ((S5 tptp.set_real) (T5 tptp.set_int) (S2 tptp.set_real) (I (-> tptp.int tptp.real)) (J (-> tptp.real tptp.int)) (T3 tptp.set_int) (G (-> tptp.real tptp.nat)) (H2 (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_real S5) (=> (@ tptp.finite_finite_int T5) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real S2) S5)) (= (@ I (@ J A4)) A4))) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real S2) S5)) (@ (@ tptp.member_int (@ J A4)) (@ (@ tptp.minus_minus_set_int T3) T5)))) (=> (forall ((B4 tptp.int)) (=> (@ (@ tptp.member_int B4) (@ (@ tptp.minus_minus_set_int T3) T5)) (= (@ J (@ I B4)) B4))) (=> (forall ((B4 tptp.int)) (=> (@ (@ tptp.member_int B4) (@ (@ tptp.minus_minus_set_int T3) T5)) (@ (@ tptp.member_real (@ I B4)) (@ (@ tptp.minus_minus_set_real S2) S5)))) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) S5) (= (@ G A4) tptp.one_one_nat))) (=> (forall ((B4 tptp.int)) (=> (@ (@ tptp.member_int B4) T5) (= (@ H2 B4) tptp.one_one_nat))) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) S2) (= (@ H2 (@ J A4)) (@ G A4)))) (= (@ (@ tptp.groups4696554848551431203al_nat G) S2) (@ (@ tptp.groups1707563613775114915nt_nat H2) T3)))))))))))) (forall ((S5 tptp.set_real) (T5 tptp.set_Extended_enat) (S2 tptp.set_real) (I (-> tptp.extended_enat tptp.real)) (J (-> tptp.real tptp.extended_enat)) (T3 tptp.set_Extended_enat) (G (-> tptp.real tptp.nat)) (H2 (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite_finite_real S5) (=> (@ tptp.finite4001608067531595151d_enat T5) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real S2) S5)) (= (@ I (@ J A4)) A4))) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real S2) S5)) (@ (@ tptp.member_Extended_enat (@ J A4)) (@ (@ tptp.minus_925952699566721837d_enat T3) T5)))) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) (@ (@ tptp.minus_925952699566721837d_enat T3) T5)) (= (@ J (@ I B4)) B4))) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) (@ (@ tptp.minus_925952699566721837d_enat T3) T5)) (@ (@ tptp.member_real (@ I B4)) (@ (@ tptp.minus_minus_set_real S2) S5)))) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) S5) (= (@ G A4) tptp.one_one_nat))) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) T5) (= (@ H2 B4) tptp.one_one_nat))) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) S2) (= (@ H2 (@ J A4)) (@ G A4)))) (= (@ (@ tptp.groups4696554848551431203al_nat G) S2) (@ (@ tptp.groups2880970938130013265at_nat H2) T3)))))))))))) (forall ((S5 tptp.set_complex) (T5 tptp.set_real) (S2 tptp.set_complex) (I (-> tptp.real tptp.complex)) (J (-> tptp.complex tptp.real)) (T3 tptp.set_real) (G (-> tptp.complex tptp.nat)) (H2 (-> tptp.real tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex S5) (=> (@ tptp.finite_finite_real T5) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) (@ (@ tptp.minus_811609699411566653omplex S2) S5)) (= (@ I (@ J A4)) A4))) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) (@ (@ tptp.minus_811609699411566653omplex S2) S5)) (@ (@ tptp.member_real (@ J A4)) (@ (@ tptp.minus_minus_set_real T3) T5)))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real T3) T5)) (= (@ J (@ I B4)) B4))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real T3) T5)) (@ (@ tptp.member_complex (@ I B4)) (@ (@ tptp.minus_811609699411566653omplex S2) S5)))) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) S5) (= (@ G A4) tptp.one_one_nat))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) T5) (= (@ H2 B4) tptp.one_one_nat))) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) S2) (= (@ H2 (@ J A4)) (@ G A4)))) (= (@ (@ tptp.groups861055069439313189ex_nat G) S2) (@ (@ tptp.groups4696554848551431203al_nat H2) T3)))))))))))) (forall ((S5 tptp.set_complex) (T5 tptp.set_complex) (S2 tptp.set_complex) (I (-> tptp.complex tptp.complex)) (J (-> tptp.complex tptp.complex)) (T3 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (H2 (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex S5) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) (@ (@ tptp.minus_811609699411566653omplex S2) S5)) (= (@ I (@ J A4)) A4))) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) (@ (@ tptp.minus_811609699411566653omplex S2) S5)) (@ (@ tptp.member_complex (@ J A4)) (@ (@ tptp.minus_811609699411566653omplex T3) T5)))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex T3) T5)) (= (@ J (@ I B4)) B4))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex T3) T5)) (@ (@ tptp.member_complex (@ I B4)) (@ (@ tptp.minus_811609699411566653omplex S2) S5)))) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) S5) (= (@ G A4) tptp.one_one_nat))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) T5) (= (@ H2 B4) tptp.one_one_nat))) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) S2) (= (@ H2 (@ J A4)) (@ G A4)))) (= (@ (@ tptp.groups861055069439313189ex_nat G) S2) (@ (@ tptp.groups861055069439313189ex_nat H2) T3)))))))))))) (forall ((S5 tptp.set_complex) (T5 tptp.set_int) (S2 tptp.set_complex) (I (-> tptp.int tptp.complex)) (J (-> tptp.complex tptp.int)) (T3 tptp.set_int) (G (-> tptp.complex tptp.nat)) (H2 (-> tptp.int tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex S5) (=> (@ tptp.finite_finite_int T5) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) (@ (@ tptp.minus_811609699411566653omplex S2) S5)) (= (@ I (@ J A4)) A4))) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) (@ (@ tptp.minus_811609699411566653omplex S2) S5)) (@ (@ tptp.member_int (@ J A4)) (@ (@ tptp.minus_minus_set_int T3) T5)))) (=> (forall ((B4 tptp.int)) (=> (@ (@ tptp.member_int B4) (@ (@ tptp.minus_minus_set_int T3) T5)) (= (@ J (@ I B4)) B4))) (=> (forall ((B4 tptp.int)) (=> (@ (@ tptp.member_int B4) (@ (@ tptp.minus_minus_set_int T3) T5)) (@ (@ tptp.member_complex (@ I B4)) (@ (@ tptp.minus_811609699411566653omplex S2) S5)))) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) S5) (= (@ G A4) tptp.one_one_nat))) (=> (forall ((B4 tptp.int)) (=> (@ (@ tptp.member_int B4) T5) (= (@ H2 B4) tptp.one_one_nat))) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) S2) (= (@ H2 (@ J A4)) (@ G A4)))) (= (@ (@ tptp.groups861055069439313189ex_nat G) S2) (@ (@ tptp.groups1707563613775114915nt_nat H2) T3)))))))))))) (forall ((S5 tptp.set_complex) (T5 tptp.set_Extended_enat) (S2 tptp.set_complex) (I (-> tptp.extended_enat tptp.complex)) (J (-> tptp.complex tptp.extended_enat)) (T3 tptp.set_Extended_enat) (G (-> tptp.complex tptp.nat)) (H2 (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex S5) (=> (@ tptp.finite4001608067531595151d_enat T5) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) (@ (@ tptp.minus_811609699411566653omplex S2) S5)) (= (@ I (@ J A4)) A4))) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) (@ (@ tptp.minus_811609699411566653omplex S2) S5)) (@ (@ tptp.member_Extended_enat (@ J A4)) (@ (@ tptp.minus_925952699566721837d_enat T3) T5)))) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) (@ (@ tptp.minus_925952699566721837d_enat T3) T5)) (= (@ J (@ I B4)) B4))) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) (@ (@ tptp.minus_925952699566721837d_enat T3) T5)) (@ (@ tptp.member_complex (@ I B4)) (@ (@ tptp.minus_811609699411566653omplex S2) S5)))) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) S5) (= (@ G A4) tptp.one_one_nat))) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) T5) (= (@ H2 B4) tptp.one_one_nat))) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) S2) (= (@ H2 (@ J A4)) (@ G A4)))) (= (@ (@ tptp.groups861055069439313189ex_nat G) S2) (@ (@ tptp.groups2880970938130013265at_nat H2) T3)))))))))))) (forall ((S5 tptp.set_int) (T5 tptp.set_real) (S2 tptp.set_int) (I (-> tptp.real tptp.int)) (J (-> tptp.int tptp.real)) (T3 tptp.set_real) (G (-> tptp.int tptp.nat)) (H2 (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_int S5) (=> (@ tptp.finite_finite_real T5) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) (@ (@ tptp.minus_minus_set_int S2) S5)) (= (@ I (@ J A4)) A4))) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) (@ (@ tptp.minus_minus_set_int S2) S5)) (@ (@ tptp.member_real (@ J A4)) (@ (@ tptp.minus_minus_set_real T3) T5)))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real T3) T5)) (= (@ J (@ I B4)) B4))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real T3) T5)) (@ (@ tptp.member_int (@ I B4)) (@ (@ tptp.minus_minus_set_int S2) S5)))) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) S5) (= (@ G A4) tptp.one_one_nat))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) T5) (= (@ H2 B4) tptp.one_one_nat))) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) S2) (= (@ H2 (@ J A4)) (@ G A4)))) (= (@ (@ tptp.groups1707563613775114915nt_nat G) S2) (@ (@ tptp.groups4696554848551431203al_nat H2) T3)))))))))))) (forall ((S5 tptp.set_int) (T5 tptp.set_complex) (S2 tptp.set_int) (I (-> tptp.complex tptp.int)) (J (-> tptp.int tptp.complex)) (T3 tptp.set_complex) (G (-> tptp.int tptp.nat)) (H2 (-> tptp.complex tptp.nat))) (=> (@ tptp.finite_finite_int S5) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) (@ (@ tptp.minus_minus_set_int S2) S5)) (= (@ I (@ J A4)) A4))) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) (@ (@ tptp.minus_minus_set_int S2) S5)) (@ (@ tptp.member_complex (@ J A4)) (@ (@ tptp.minus_811609699411566653omplex T3) T5)))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex T3) T5)) (= (@ J (@ I B4)) B4))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex T3) T5)) (@ (@ tptp.member_int (@ I B4)) (@ (@ tptp.minus_minus_set_int S2) S5)))) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) S5) (= (@ G A4) tptp.one_one_nat))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) T5) (= (@ H2 B4) tptp.one_one_nat))) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) S2) (= (@ H2 (@ J A4)) (@ G A4)))) (= (@ (@ tptp.groups1707563613775114915nt_nat G) S2) (@ (@ tptp.groups861055069439313189ex_nat H2) T3)))))))))))) (forall ((X tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (= (@ _let_1 (@ (@ tptp.plus_plus_real A) B2)) (@ (@ tptp.times_times_real (@ _let_1 A)) (@ _let_1 B2))))) (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups4696554848551431203al_nat G))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ tptp.collect_real (lambda ((X4 tptp.real)) (= (@ G X4) tptp.one_one_nat))))) (@ _let_1 A2))))) (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (= (@ G X4) tptp.one_one_nat))))) (@ _let_1 A2))))) (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat G))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ tptp.collect_int (lambda ((X4 tptp.int)) (= (@ G X4) tptp.one_one_nat))))) (@ _let_1 A2))))) (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2880970938130013265at_nat G))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (= (@ G X4) tptp.one_one_nat))))) (@ _let_1 A2))))) (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups4694064378042380927al_int G))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ tptp.collect_real (lambda ((X4 tptp.real)) (= (@ G X4) tptp.one_one_int))))) (@ _let_1 A2))))) (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (= (@ G X4) tptp.one_one_int))))) (@ _let_1 A2))))) (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2878480467620962989at_int G))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ tptp.collec4429806609662206161d_enat (lambda ((X4 tptp.extended_enat)) (= (@ G X4) tptp.one_one_int))))) (@ _let_1 A2))))) (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups713298508707869441omplex G))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ tptp.collect_real (lambda ((X4 tptp.real)) (= (@ G X4) tptp.one_one_complex))))) (@ _let_1 A2))))) (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups3708469109370488835omplex G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (= (@ G X4) tptp.one_one_complex))))) (@ _let_1 A2))))) (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups7440179247065528705omplex G))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ tptp.collect_int (lambda ((X4 tptp.int)) (= (@ G X4) tptp.one_one_complex))))) (@ _let_1 A2))))) (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I3))))) _let_1) (@ (@ tptp.groups705719431365010083at_int G) _let_1)))) (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I3))))) _let_1) (@ (@ tptp.groups708209901874060359at_nat G) _let_1)))) (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N2) M2))) (= (@ (@ tptp.groups705719431365010083at_int G) _let_1) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M2) N2)) I3)))) _let_1)))) (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N2) M2))) (= (@ (@ tptp.groups708209901874060359at_nat G) _let_1) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M2) N2)) I3)))) _let_1)))) (forall ((I6 tptp.set_real) (I tptp.real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ tptp.finite_finite_real I6) (=> (@ (@ tptp.member_real I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups1681761925125756287l_real F) I6)))))))) (forall ((I6 tptp.set_nat) (I tptp.nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ tptp.finite_finite_nat I6) (=> (@ (@ tptp.member_nat I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups129246275422532515t_real F) I6)))))))) (forall ((I6 tptp.set_complex) (I tptp.complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (@ (@ tptp.member_complex I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups766887009212190081x_real F) I6)))))))) (forall ((I6 tptp.set_int) (I tptp.int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ tptp.finite_finite_int I6) (=> (@ (@ tptp.member_int I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups2316167850115554303t_real F) I6)))))))) (forall ((I6 tptp.set_Extended_enat) (I tptp.extended_enat) (F (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ tptp.finite4001608067531595151d_enat I6) (=> (@ (@ tptp.member_Extended_enat I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I4) I6) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups97031904164794029t_real F) I6)))))))) (forall ((I6 tptp.set_real) (I tptp.real) (F (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ tptp.finite_finite_real I6) (=> (@ (@ tptp.member_real I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups4694064378042380927al_int F) I6)))))))) (forall ((I6 tptp.set_complex) (I tptp.complex) (F (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (@ (@ tptp.member_complex I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups858564598930262913ex_int F) I6)))))))) (forall ((I6 tptp.set_Extended_enat) (I tptp.extended_enat) (F (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ tptp.finite4001608067531595151d_enat I6) (=> (@ (@ tptp.member_Extended_enat I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I4) I6) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups2878480467620962989at_int F) I6)))))))) (forall ((I6 tptp.set_nat) (I tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ tptp.finite_finite_nat I6) (=> (@ (@ tptp.member_nat I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups705719431365010083at_int F) I6)))))))) (forall ((I6 tptp.set_int) (I tptp.int) (F (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ tptp.finite_finite_int I6) (=> (@ (@ tptp.member_int I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups1705073143266064639nt_int F) I6)))))))) (forall ((I6 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (not (= I6 tptp.bot_bot_set_complex)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ F I4)))) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.groups766887009212190081x_real F) I6)))))) (forall ((I6 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat I6) (=> (not (= I6 tptp.bot_bo7653980558646680370d_enat)) (=> (forall ((I4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I4) I6) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ F I4)))) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.groups97031904164794029t_real F) I6)))))) (forall ((I6 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real I6) (=> (not (= I6 tptp.bot_bot_set_real)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ F I4)))) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.groups1681761925125756287l_real F) I6)))))) (forall ((I6 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat I6) (=> (not (= I6 tptp.bot_bot_set_nat)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ F I4)))) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.groups129246275422532515t_real F) I6)))))) (forall ((I6 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int I6) (=> (not (= I6 tptp.bot_bot_set_int)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ F I4)))) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.groups2316167850115554303t_real F) I6)))))) (forall ((I6 tptp.set_complex) (F (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (not (= I6 tptp.bot_bot_set_complex)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ F I4)))) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ (@ tptp.groups858564598930262913ex_int F) I6)))))) (forall ((I6 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.int))) (=> (@ tptp.finite4001608067531595151d_enat I6) (=> (not (= I6 tptp.bot_bo7653980558646680370d_enat)) (=> (forall ((I4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I4) I6) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ F I4)))) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ (@ tptp.groups2878480467620962989at_int F) I6)))))) (forall ((I6 tptp.set_real) (F (-> tptp.real tptp.int))) (=> (@ tptp.finite_finite_real I6) (=> (not (= I6 tptp.bot_bot_set_real)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ F I4)))) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ (@ tptp.groups4694064378042380927al_int F) I6)))))) (forall ((I6 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat I6) (=> (not (= I6 tptp.bot_bot_set_nat)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ F I4)))) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ (@ tptp.groups705719431365010083at_int F) I6)))))) (forall ((I6 tptp.set_int) (F (-> tptp.int tptp.int))) (=> (@ tptp.finite_finite_int I6) (=> (not (= I6 tptp.bot_bot_set_int)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ F I4)))) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ (@ tptp.groups1705073143266064639nt_int F) I6)))))) (forall ((B tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B))) (@ _let_1 B))))))) (forall ((B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2880970938130013265at_nat G))) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B) A2) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) B))) (@ _let_1 B))))))) (forall ((B tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B))) (@ _let_1 B))))))) (forall ((B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2878480467620962989at_int G))) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B) A2) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) B))) (@ _let_1 B))))))) (forall ((B tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B))) (@ _let_1 B))))))) (forall ((B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups97031904164794029t_real G))) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B) A2) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) B))) (@ _let_1 B))))))) (forall ((B tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups3708469109370488835omplex G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_complex (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B))) (@ _let_1 B))))))) (forall ((B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.complex))) (let ((_let_1 (@ tptp.groups4622424608036095791omplex G))) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B) A2) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_complex (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) B))) (@ _let_1 B))))))) (forall ((B tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.extended_enat))) (let ((_let_1 (@ tptp.groups8780218893797010257d_enat G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.times_7803423173614009249d_enat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B))) (@ _let_1 B))))))) (forall ((B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.extended_enat))) (let ((_let_1 (@ tptp.groups8932437906259616549d_enat G))) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B) A2) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_1 A2) (@ (@ tptp.times_7803423173614009249d_enat (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) B))) (@ _let_1 B))))))) (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B tptp.set_real) (G (-> tptp.real tptp.nat)) (H2 (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups4696554848551431203al_nat H2))) (let ((_let_2 (@ tptp.groups4696554848551431203al_nat G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B) C4) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A4) tptp.one_one_nat))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real C4) B)) (= (@ H2 B4) tptp.one_one_nat))) (= (= (@ _let_2 A2) (@ _let_1 B)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))) (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B tptp.set_complex) (G (-> tptp.complex tptp.nat)) (H2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat H2))) (let ((_let_2 (@ tptp.groups861055069439313189ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B) C4) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A4) tptp.one_one_nat))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex C4) B)) (= (@ H2 B4) tptp.one_one_nat))) (= (= (@ _let_2 A2) (@ _let_1 B)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))) (forall ((C4 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.nat)) (H2 (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2880970938130013265at_nat H2))) (let ((_let_2 (@ tptp.groups2880970938130013265at_nat G))) (=> (@ tptp.finite4001608067531595151d_enat C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B) C4) (=> (forall ((A4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A4) (@ (@ tptp.minus_925952699566721837d_enat C4) A2)) (= (@ G A4) tptp.one_one_nat))) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) (@ (@ tptp.minus_925952699566721837d_enat C4) B)) (= (@ H2 B4) tptp.one_one_nat))) (= (= (@ _let_2 A2) (@ _let_1 B)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))) (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B tptp.set_real) (G (-> tptp.real tptp.int)) (H2 (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups4694064378042380927al_int H2))) (let ((_let_2 (@ tptp.groups4694064378042380927al_int G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B) C4) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A4) tptp.one_one_int))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real C4) B)) (= (@ H2 B4) tptp.one_one_int))) (= (= (@ _let_2 A2) (@ _let_1 B)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))) (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B tptp.set_complex) (G (-> tptp.complex tptp.int)) (H2 (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int H2))) (let ((_let_2 (@ tptp.groups858564598930262913ex_int G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B) C4) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A4) tptp.one_one_int))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex C4) B)) (= (@ H2 B4) tptp.one_one_int))) (= (= (@ _let_2 A2) (@ _let_1 B)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))) (forall ((C4 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.int)) (H2 (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2878480467620962989at_int H2))) (let ((_let_2 (@ tptp.groups2878480467620962989at_int G))) (=> (@ tptp.finite4001608067531595151d_enat C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B) C4) (=> (forall ((A4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A4) (@ (@ tptp.minus_925952699566721837d_enat C4) A2)) (= (@ G A4) tptp.one_one_int))) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) (@ (@ tptp.minus_925952699566721837d_enat C4) B)) (= (@ H2 B4) tptp.one_one_int))) (= (= (@ _let_2 A2) (@ _let_1 B)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))) (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B tptp.set_real) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups713298508707869441omplex H2))) (let ((_let_2 (@ tptp.groups713298508707869441omplex G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B) C4) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A4) tptp.one_one_complex))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real C4) B)) (= (@ H2 B4) tptp.one_one_complex))) (= (= (@ _let_2 A2) (@ _let_1 B)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))) (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B tptp.set_complex) (G (-> tptp.complex tptp.complex)) (H2 (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups3708469109370488835omplex H2))) (let ((_let_2 (@ tptp.groups3708469109370488835omplex G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B) C4) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A4) tptp.one_one_complex))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex C4) B)) (= (@ H2 B4) tptp.one_one_complex))) (= (= (@ _let_2 A2) (@ _let_1 B)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))) (forall ((C4 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.complex)) (H2 (-> tptp.extended_enat tptp.complex))) (let ((_let_1 (@ tptp.groups4622424608036095791omplex H2))) (let ((_let_2 (@ tptp.groups4622424608036095791omplex G))) (=> (@ tptp.finite4001608067531595151d_enat C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B) C4) (=> (forall ((A4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A4) (@ (@ tptp.minus_925952699566721837d_enat C4) A2)) (= (@ G A4) tptp.one_one_complex))) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) (@ (@ tptp.minus_925952699566721837d_enat C4) B)) (= (@ H2 B4) tptp.one_one_complex))) (= (= (@ _let_2 A2) (@ _let_1 B)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))) (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B tptp.set_real) (G (-> tptp.real tptp.real)) (H2 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real H2))) (let ((_let_2 (@ tptp.groups1681761925125756287l_real G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B) C4) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A4) tptp.one_one_real))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real C4) B)) (= (@ H2 B4) tptp.one_one_real))) (= (= (@ _let_2 A2) (@ _let_1 B)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))) (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B tptp.set_real) (G (-> tptp.real tptp.nat)) (H2 (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups4696554848551431203al_nat H2))) (let ((_let_2 (@ tptp.groups4696554848551431203al_nat G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B) C4) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A4) tptp.one_one_nat))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real C4) B)) (= (@ H2 B4) tptp.one_one_nat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B))))))))))) (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B tptp.set_complex) (G (-> tptp.complex tptp.nat)) (H2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat H2))) (let ((_let_2 (@ tptp.groups861055069439313189ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B) C4) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A4) tptp.one_one_nat))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex C4) B)) (= (@ H2 B4) tptp.one_one_nat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B))))))))))) (forall ((C4 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.nat)) (H2 (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2880970938130013265at_nat H2))) (let ((_let_2 (@ tptp.groups2880970938130013265at_nat G))) (=> (@ tptp.finite4001608067531595151d_enat C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B) C4) (=> (forall ((A4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A4) (@ (@ tptp.minus_925952699566721837d_enat C4) A2)) (= (@ G A4) tptp.one_one_nat))) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) (@ (@ tptp.minus_925952699566721837d_enat C4) B)) (= (@ H2 B4) tptp.one_one_nat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B))))))))))) (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B tptp.set_real) (G (-> tptp.real tptp.int)) (H2 (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups4694064378042380927al_int H2))) (let ((_let_2 (@ tptp.groups4694064378042380927al_int G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B) C4) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A4) tptp.one_one_int))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real C4) B)) (= (@ H2 B4) tptp.one_one_int))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B))))))))))) (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B tptp.set_complex) (G (-> tptp.complex tptp.int)) (H2 (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int H2))) (let ((_let_2 (@ tptp.groups858564598930262913ex_int G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B) C4) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A4) tptp.one_one_int))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex C4) B)) (= (@ H2 B4) tptp.one_one_int))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B))))))))))) (forall ((C4 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.int)) (H2 (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2878480467620962989at_int H2))) (let ((_let_2 (@ tptp.groups2878480467620962989at_int G))) (=> (@ tptp.finite4001608067531595151d_enat C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B) C4) (=> (forall ((A4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A4) (@ (@ tptp.minus_925952699566721837d_enat C4) A2)) (= (@ G A4) tptp.one_one_int))) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) (@ (@ tptp.minus_925952699566721837d_enat C4) B)) (= (@ H2 B4) tptp.one_one_int))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B))))))))))) (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B tptp.set_real) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups713298508707869441omplex H2))) (let ((_let_2 (@ tptp.groups713298508707869441omplex G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B) C4) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A4) tptp.one_one_complex))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real C4) B)) (= (@ H2 B4) tptp.one_one_complex))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B))))))))))) (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B tptp.set_complex) (G (-> tptp.complex tptp.complex)) (H2 (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups3708469109370488835omplex H2))) (let ((_let_2 (@ tptp.groups3708469109370488835omplex G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B) C4) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A4) tptp.one_one_complex))) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex C4) B)) (= (@ H2 B4) tptp.one_one_complex))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B))))))))))) (forall ((C4 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (B tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.complex)) (H2 (-> tptp.extended_enat tptp.complex))) (let ((_let_1 (@ tptp.groups4622424608036095791omplex H2))) (let ((_let_2 (@ tptp.groups4622424608036095791omplex G))) (=> (@ tptp.finite4001608067531595151d_enat C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) C4) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B) C4) (=> (forall ((A4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A4) (@ (@ tptp.minus_925952699566721837d_enat C4) A2)) (= (@ G A4) tptp.one_one_complex))) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) (@ (@ tptp.minus_925952699566721837d_enat C4) B)) (= (@ H2 B4) tptp.one_one_complex))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B))))))))))) (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B tptp.set_real) (G (-> tptp.real tptp.real)) (H2 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real H2))) (let ((_let_2 (@ tptp.groups1681761925125756287l_real G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B) C4) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A4) tptp.one_one_real))) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real C4) B)) (= (@ H2 B4) tptp.one_one_real))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B))))))))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X5) tptp.one_one_nat))) (= (@ _let_1 S2) (@ _let_1 T3))))))) (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2880970938130013265at_nat G))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G X5) tptp.one_one_nat))) (= (@ _let_1 S2) (@ _let_1 T3))))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X5) tptp.one_one_int))) (= (@ _let_1 S2) (@ _let_1 T3))))))) (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2878480467620962989at_int G))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G X5) tptp.one_one_int))) (= (@ _let_1 S2) (@ _let_1 T3))))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups3708469109370488835omplex G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X5) tptp.one_one_complex))) (= (@ _let_1 S2) (@ _let_1 T3))))))) (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.complex))) (let ((_let_1 (@ tptp.groups4622424608036095791omplex G))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G X5) tptp.one_one_complex))) (= (@ _let_1 S2) (@ _let_1 T3))))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X5) tptp.one_one_real))) (= (@ _let_1 S2) (@ _let_1 T3))))))) (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups97031904164794029t_real G))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G X5) tptp.one_one_real))) (= (@ _let_1 S2) (@ _let_1 T3))))))) (forall ((T3 tptp.set_nat) (S2 tptp.set_nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups6464643781859351333omplex G))) (=> (@ tptp.finite_finite_nat T3) (=> (@ (@ tptp.ord_less_eq_set_nat S2) T3) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) (@ (@ tptp.minus_minus_set_nat T3) S2)) (= (@ G X5) tptp.one_one_complex))) (= (@ _let_1 S2) (@ _let_1 T3))))))) (forall ((T3 tptp.set_nat) (S2 tptp.set_nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (=> (@ tptp.finite_finite_nat T3) (=> (@ (@ tptp.ord_less_eq_set_nat S2) T3) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) (@ (@ tptp.minus_minus_set_nat T3) S2)) (= (@ G X5) tptp.one_one_real))) (= (@ _let_1 S2) (@ _let_1 T3))))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X5) tptp.one_one_nat))) (= (@ _let_1 T3) (@ _let_1 S2))))))) (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2880970938130013265at_nat G))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G X5) tptp.one_one_nat))) (= (@ _let_1 T3) (@ _let_1 S2))))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X5) tptp.one_one_int))) (= (@ _let_1 T3) (@ _let_1 S2))))))) (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2878480467620962989at_int G))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G X5) tptp.one_one_int))) (= (@ _let_1 T3) (@ _let_1 S2))))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups3708469109370488835omplex G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X5) tptp.one_one_complex))) (= (@ _let_1 T3) (@ _let_1 S2))))))) (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.complex))) (let ((_let_1 (@ tptp.groups4622424608036095791omplex G))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G X5) tptp.one_one_complex))) (= (@ _let_1 T3) (@ _let_1 S2))))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X5) tptp.one_one_real))) (= (@ _let_1 T3) (@ _let_1 S2))))))) (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups97031904164794029t_real G))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G X5) tptp.one_one_real))) (= (@ _let_1 T3) (@ _let_1 S2))))))) (forall ((T3 tptp.set_nat) (S2 tptp.set_nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups6464643781859351333omplex G))) (=> (@ tptp.finite_finite_nat T3) (=> (@ (@ tptp.ord_less_eq_set_nat S2) T3) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) (@ (@ tptp.minus_minus_set_nat T3) S2)) (= (@ G X5) tptp.one_one_complex))) (= (@ _let_1 T3) (@ _let_1 S2))))))) (forall ((T3 tptp.set_nat) (S2 tptp.set_nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (=> (@ tptp.finite_finite_nat T3) (=> (@ (@ tptp.ord_less_eq_set_nat S2) T3) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) (@ (@ tptp.minus_minus_set_nat T3) S2)) (= (@ G X5) tptp.one_one_real))) (= (@ _let_1 T3) (@ _let_1 S2))))))) (forall ((T3 tptp.set_real) (S2 tptp.set_real) (H2 (-> tptp.real tptp.nat)) (G (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S2) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S2)) (= (@ H2 X5) tptp.one_one_nat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups4696554848551431203al_nat G) S2) (@ (@ tptp.groups4696554848551431203al_nat H2) T3))))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (H2 (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ H2 X5) tptp.one_one_nat))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups861055069439313189ex_nat G) S2) (@ (@ tptp.groups861055069439313189ex_nat H2) T3))))))) (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (H2 (-> tptp.extended_enat tptp.nat)) (G (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ H2 X5) tptp.one_one_nat))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups2880970938130013265at_nat G) S2) (@ (@ tptp.groups2880970938130013265at_nat H2) T3))))))) (forall ((T3 tptp.set_real) (S2 tptp.set_real) (H2 (-> tptp.real tptp.int)) (G (-> tptp.real tptp.int))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S2) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S2)) (= (@ H2 X5) tptp.one_one_int))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups4694064378042380927al_int G) S2) (@ (@ tptp.groups4694064378042380927al_int H2) T3))))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (H2 (-> tptp.complex tptp.int)) (G (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ H2 X5) tptp.one_one_int))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups858564598930262913ex_int G) S2) (@ (@ tptp.groups858564598930262913ex_int H2) T3))))))) (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (H2 (-> tptp.extended_enat tptp.int)) (G (-> tptp.extended_enat tptp.int))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ H2 X5) tptp.one_one_int))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups2878480467620962989at_int G) S2) (@ (@ tptp.groups2878480467620962989at_int H2) T3))))))) (forall ((T3 tptp.set_real) (S2 tptp.set_real) (H2 (-> tptp.real tptp.complex)) (G (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S2) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S2)) (= (@ H2 X5) tptp.one_one_complex))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups713298508707869441omplex G) S2) (@ (@ tptp.groups713298508707869441omplex H2) T3))))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (H2 (-> tptp.complex tptp.complex)) (G (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ H2 X5) tptp.one_one_complex))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups3708469109370488835omplex G) S2) (@ (@ tptp.groups3708469109370488835omplex H2) T3))))))) (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (H2 (-> tptp.extended_enat tptp.complex)) (G (-> tptp.extended_enat tptp.complex))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ H2 X5) tptp.one_one_complex))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups4622424608036095791omplex G) S2) (@ (@ tptp.groups4622424608036095791omplex H2) T3))))))) (forall ((T3 tptp.set_real) (S2 tptp.set_real) (H2 (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S2) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S2)) (= (@ H2 X5) tptp.one_one_real))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups1681761925125756287l_real G) S2) (@ (@ tptp.groups1681761925125756287l_real H2) T3))))))) (forall ((T3 tptp.set_real) (S2 tptp.set_real) (G (-> tptp.real tptp.nat)) (H2 (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S2) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S2)) (= (@ G X5) tptp.one_one_nat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups4696554848551431203al_nat G) T3) (@ (@ tptp.groups4696554848551431203al_nat H2) S2))))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (H2 (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X5) tptp.one_one_nat))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups861055069439313189ex_nat G) T3) (@ (@ tptp.groups861055069439313189ex_nat H2) S2))))))) (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.nat)) (H2 (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G X5) tptp.one_one_nat))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups2880970938130013265at_nat G) T3) (@ (@ tptp.groups2880970938130013265at_nat H2) S2))))))) (forall ((T3 tptp.set_real) (S2 tptp.set_real) (G (-> tptp.real tptp.int)) (H2 (-> tptp.real tptp.int))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S2) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S2)) (= (@ G X5) tptp.one_one_int))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups4694064378042380927al_int G) T3) (@ (@ tptp.groups4694064378042380927al_int H2) S2))))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.int)) (H2 (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X5) tptp.one_one_int))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups858564598930262913ex_int G) T3) (@ (@ tptp.groups858564598930262913ex_int H2) S2))))))) (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.int)) (H2 (-> tptp.extended_enat tptp.int))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G X5) tptp.one_one_int))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups2878480467620962989at_int G) T3) (@ (@ tptp.groups2878480467620962989at_int H2) S2))))))) (forall ((T3 tptp.set_real) (S2 tptp.set_real) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S2) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S2)) (= (@ G X5) tptp.one_one_complex))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups713298508707869441omplex G) T3) (@ (@ tptp.groups713298508707869441omplex H2) S2))))))) (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.complex)) (H2 (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X5) tptp.one_one_complex))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups3708469109370488835omplex G) T3) (@ (@ tptp.groups3708469109370488835omplex H2) S2))))))) (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.complex)) (H2 (-> tptp.extended_enat tptp.complex))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G X5) tptp.one_one_complex))) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups4622424608036095791omplex G) T3) (@ (@ tptp.groups4622424608036095791omplex H2) S2))))))) (forall ((T3 tptp.set_real) (S2 tptp.set_real) (G (-> tptp.real tptp.real)) (H2 (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S2) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S2)) (= (@ G X5) tptp.one_one_real))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S2) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups1681761925125756287l_real G) T3) (@ (@ tptp.groups1681761925125756287l_real H2) S2))))))) (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups129246275422532515t_real G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_real (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))) (forall ((G (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups6464643781859351333omplex G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_complex (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))) (forall ((G (-> tptp.nat tptp.extended_enat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups7961826882256487087d_enat G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_7803423173614009249d_enat (@ _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.groups705719431365010083at_int G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_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.groups708209901874060359at_nat G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_nat (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))) (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 ((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 ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N2)) (@ (@ tptp.times_times_real (@ G M2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N2))))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups6464643781859351333omplex G))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N2)) (@ (@ tptp.times_times_complex (@ G M2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N2))))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.extended_enat))) (let ((_let_1 (@ tptp.groups7961826882256487087d_enat G))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N2)) (@ (@ tptp.times_7803423173614009249d_enat (@ G M2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N2))))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups705719431365010083at_int G))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N2)) (@ (@ tptp.times_times_int (@ G M2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N2))))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups708209901874060359at_nat G))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N2)) (@ (@ tptp.times_times_nat (@ G M2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N2))))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.groups129246275422532515t_real G))) (let ((_let_3 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_real (@ G _let_3)) (@ _let_2 (@ _let_1 N2))))))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.groups6464643781859351333omplex G))) (let ((_let_3 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_complex (@ G _let_3)) (@ _let_2 (@ _let_1 N2))))))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.extended_enat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.groups7961826882256487087d_enat G))) (let ((_let_3 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_7803423173614009249d_enat (@ G _let_3)) (@ _let_2 (@ _let_1 N2))))))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.groups705719431365010083at_int G))) (let ((_let_3 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_int (@ G _let_3)) (@ _let_2 (@ _let_1 N2))))))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.groups708209901874060359at_nat G))) (let ((_let_3 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_nat (@ G _let_3)) (@ _let_2 (@ _let_1 N2))))))))) (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N2))))) (forall ((G (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (= (@ (@ tptp.groups6464643781859351333omplex G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_complex (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N2))))) (forall ((G (-> tptp.nat tptp.extended_enat)) (N2 tptp.nat)) (= (@ (@ tptp.groups7961826882256487087d_enat G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.times_7803423173614009249d_enat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups7961826882256487087d_enat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N2))))) (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N2))))) (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N2))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups129246275422532515t_real G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.times_times_real (@ G M2)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ (@ tptp.times_times_complex (@ (@ tptp.groups6464643781859351333omplex G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.times_times_complex (@ G M2)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.extended_enat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ (@ tptp.times_7803423173614009249d_enat (@ (@ tptp.groups7961826882256487087d_enat G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.times_7803423173614009249d_enat (@ G M2)) (@ (@ tptp.groups7961826882256487087d_enat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups705719431365010083at_int G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.times_times_int (@ G M2)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups708209901874060359at_nat G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.times_times_nat (@ G M2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))) (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2)) (@ (@ tptp.groups705719431365010083at_int (lambda ((K2 tptp.nat)) (@ G (@ tptp.suc K2)))) (@ tptp.set_ord_lessThan_nat N2)))) (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((K2 tptp.nat)) (@ G (@ tptp.suc K2)))) (@ tptp.set_ord_lessThan_nat N2)))) (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((I4 tptp.complex)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_complex I4) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G I4)))))) (=> (not (= A2 tptp.bot_bot_set_complex)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups766887009212190081x_real F) A2)) (@ (@ tptp.groups766887009212190081x_real G) A2)))))) (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real)) (G (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (forall ((I4 tptp.extended_enat)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_Extended_enat I4) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G I4)))))) (=> (not (= A2 tptp.bot_bo7653980558646680370d_enat)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups97031904164794029t_real F) A2)) (@ (@ tptp.groups97031904164794029t_real G) A2)))))) (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real A2) (=> (forall ((I4 tptp.real)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_real I4) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G I4)))))) (=> (not (= A2 tptp.bot_bot_set_real)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups1681761925125756287l_real F) A2)) (@ (@ tptp.groups1681761925125756287l_real G) A2)))))) (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat A2) (=> (forall ((I4 tptp.nat)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_nat I4) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G I4)))))) (=> (not (= A2 tptp.bot_bot_set_nat)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups129246275422532515t_real F) A2)) (@ (@ tptp.groups129246275422532515t_real G) A2)))))) (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((I4 tptp.int)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_int I4) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G I4)))))) (=> (not (= A2 tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups2316167850115554303t_real F) A2)) (@ (@ tptp.groups2316167850115554303t_real G) A2)))))) (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((I4 tptp.complex)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_complex I4) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_nat _let_1) (@ G I4)))))) (=> (not (= A2 tptp.bot_bot_set_complex)) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups861055069439313189ex_nat F) A2)) (@ (@ tptp.groups861055069439313189ex_nat G) A2)))))) (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat)) (G (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (forall ((I4 tptp.extended_enat)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_Extended_enat I4) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_nat _let_1) (@ G I4)))))) (=> (not (= A2 tptp.bot_bo7653980558646680370d_enat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups2880970938130013265at_nat F) A2)) (@ (@ tptp.groups2880970938130013265at_nat G) A2)))))) (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat)) (G (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real A2) (=> (forall ((I4 tptp.real)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_real I4) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_nat _let_1) (@ G I4)))))) (=> (not (= A2 tptp.bot_bot_set_real)) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups4696554848551431203al_nat F) A2)) (@ (@ tptp.groups4696554848551431203al_nat G) A2)))))) (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((I4 tptp.int)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_int I4) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_nat _let_1) (@ G I4)))))) (=> (not (= A2 tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups1707563613775114915nt_nat F) A2)) (@ (@ tptp.groups1707563613775114915nt_nat G) A2)))))) (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.int)) (G (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((I4 tptp.complex)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_complex I4) A2) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) _let_1) (@ (@ tptp.ord_less_int _let_1) (@ G I4)))))) (=> (not (= A2 tptp.bot_bot_set_complex)) (@ (@ tptp.ord_less_int (@ (@ tptp.groups858564598930262913ex_int F) A2)) (@ (@ tptp.groups858564598930262913ex_int G) A2)))))) (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups861055069439313189ex_nat F) A2)) (exists ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A2) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ F X4))))))) (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups1707563613775114915nt_nat F) A2)) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A2) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ F X4))))))) (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2880970938130013265at_nat F) A2)) (exists ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) A2) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ F X4))))))) (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups858564598930262913ex_int F) A2)) (exists ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A2) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ F X4))))))) (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.int))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2878480467620962989at_int F) A2)) (exists ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) A2) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ F X4))))))) (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups705719431365010083at_int F) A2)) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A2) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ F X4))))))) (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.int))) (=> (@ tptp.finite_finite_int A2) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups1705073143266064639nt_int F) A2)) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A2) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ F X4))))))) (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups708209901874060359at_nat F) A2)) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A2) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ F X4))))))) (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (X tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X))) (let ((_let_2 (@ tptp.groups861055069439313189ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_nat (@ G X)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_1 tptp.bot_bot_set_complex))))))))) (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.nat)) (X tptp.extended_enat)) (let ((_let_1 (@ tptp.insert_Extended_enat X))) (let ((_let_2 (@ tptp.groups2880970938130013265at_nat G))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_nat (@ G X)) (@ _let_2 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ _let_1 tptp.bot_bo7653980558646680370d_enat))))))))) (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.nat)) (X tptp.real)) (let ((_let_1 (@ tptp.insert_real X))) (let ((_let_2 (@ tptp.groups4696554848551431203al_nat G))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_nat (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_real A2) (@ _let_1 tptp.bot_bot_set_real))))))))) (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.nat)) (X tptp.int)) (let ((_let_1 (@ tptp.insert_int X))) (let ((_let_2 (@ tptp.groups1707563613775114915nt_nat G))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_nat (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_int A2) (@ _let_1 tptp.bot_bot_set_int))))))))) (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.int)) (X tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X))) (let ((_let_2 (@ tptp.groups858564598930262913ex_int G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_int (@ G X)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_1 tptp.bot_bot_set_complex))))))))) (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.int)) (X tptp.extended_enat)) (let ((_let_1 (@ tptp.insert_Extended_enat X))) (let ((_let_2 (@ tptp.groups2878480467620962989at_int G))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_int (@ G X)) (@ _let_2 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ _let_1 tptp.bot_bo7653980558646680370d_enat))))))))) (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.int)) (X tptp.real)) (let ((_let_1 (@ tptp.insert_real X))) (let ((_let_2 (@ tptp.groups4694064378042380927al_int G))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_int (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_real A2) (@ _let_1 tptp.bot_bot_set_real))))))))) (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.real)) (X tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X))) (let ((_let_2 (@ tptp.groups766887009212190081x_real G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_real (@ G X)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_1 tptp.bot_bot_set_complex))))))))) (forall ((A2 tptp.set_Extended_enat) (G (-> tptp.extended_enat tptp.real)) (X tptp.extended_enat)) (let ((_let_1 (@ tptp.insert_Extended_enat X))) (let ((_let_2 (@ tptp.groups97031904164794029t_real G))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_real (@ G X)) (@ _let_2 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ _let_1 tptp.bot_bo7653980558646680370d_enat))))))))) (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.real)) (X tptp.real)) (let ((_let_1 (@ tptp.insert_real X))) (let ((_let_2 (@ tptp.groups1681761925125756287l_real G))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_real (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_real A2) (@ _let_1 tptp.bot_bot_set_real))))))))) (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex X) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_nat (@ G X)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex))))))))) (forall ((A2 tptp.set_Extended_enat) (X tptp.extended_enat) (G (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2880970938130013265at_nat G))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ (@ tptp.member_Extended_enat X) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_nat (@ G X)) (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ (@ tptp.insert_Extended_enat X) tptp.bot_bo7653980558646680370d_enat))))))))) (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups4696554848551431203al_nat G))) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real X) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_nat (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))))))))) (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat G))) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int X) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_nat (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))))))))) (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex X) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_int (@ G X)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex))))))))) (forall ((A2 tptp.set_Extended_enat) (X tptp.extended_enat) (G (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2878480467620962989at_int G))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ (@ tptp.member_Extended_enat X) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_int (@ G X)) (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ (@ tptp.insert_Extended_enat X) tptp.bot_bo7653980558646680370d_enat))))))))) (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups4694064378042380927al_int G))) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real X) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_int (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))))))))) (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex X) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_real (@ G X)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex))))))))) (forall ((A2 tptp.set_Extended_enat) (X tptp.extended_enat) (G (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups97031904164794029t_real G))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ (@ tptp.member_Extended_enat X) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_real (@ G X)) (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ (@ tptp.insert_Extended_enat X) tptp.bot_bo7653980558646680370d_enat))))))))) (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real G))) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real X) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_real (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))))))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.real)) (P5 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (let ((_let_2 (@ _let_1 P5))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups129246275422532515t_real G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_real (@ _let_4 (@ _let_5 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.complex)) (P5 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (let ((_let_2 (@ _let_1 P5))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups6464643781859351333omplex G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_complex (@ _let_4 (@ _let_5 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.extended_enat)) (P5 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (let ((_let_2 (@ _let_1 P5))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups7961826882256487087d_enat G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_7803423173614009249d_enat (@ _let_4 (@ _let_5 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int)) (P5 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (let ((_let_2 (@ _let_1 P5))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups705719431365010083at_int G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_int (@ _let_4 (@ _let_5 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat)) (P5 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (let ((_let_2 (@ _let_1 P5))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups708209901874060359at_nat G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_nat (@ _let_4 (@ _let_5 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))) (forall ((S2 tptp.set_complex) (A tptp.complex) (B2 (-> tptp.complex tptp.nat)) (C (-> tptp.complex tptp.nat))) (let ((_let_1 (@ (@ tptp.groups861055069439313189ex_nat C) (@ (@ tptp.minus_811609699411566653omplex S2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_2 (= (@ (@ tptp.groups861055069439313189ex_nat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) (@ (@ tptp.times_times_nat (@ B2 A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups861055069439313189ex_nat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) _let_1))))))) (forall ((S2 tptp.set_Extended_enat) (A tptp.extended_enat) (B2 (-> tptp.extended_enat tptp.nat)) (C (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ (@ tptp.groups2880970938130013265at_nat C) (@ (@ tptp.minus_925952699566721837d_enat S2) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat))))) (let ((_let_2 (@ (@ tptp.member_Extended_enat A) S2))) (=> (@ tptp.finite4001608067531595151d_enat S2) (and (=> _let_2 (= (@ (@ tptp.groups2880970938130013265at_nat (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) (@ (@ tptp.times_times_nat (@ B2 A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups2880970938130013265at_nat (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) _let_1))))))) (forall ((S2 tptp.set_real) (A tptp.real) (B2 (-> tptp.real tptp.nat)) (C (-> tptp.real tptp.nat))) (let ((_let_1 (@ (@ tptp.groups4696554848551431203al_nat C) (@ (@ tptp.minus_minus_set_real S2) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_2 (@ (@ tptp.member_real A) S2))) (=> (@ tptp.finite_finite_real S2) (and (=> _let_2 (= (@ (@ tptp.groups4696554848551431203al_nat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) (@ (@ tptp.times_times_nat (@ B2 A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups4696554848551431203al_nat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) _let_1))))))) (forall ((S2 tptp.set_int) (A tptp.int) (B2 (-> tptp.int tptp.nat)) (C (-> tptp.int tptp.nat))) (let ((_let_1 (@ (@ tptp.groups1707563613775114915nt_nat C) (@ (@ tptp.minus_minus_set_int S2) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_2 (@ (@ tptp.member_int A) S2))) (=> (@ tptp.finite_finite_int S2) (and (=> _let_2 (= (@ (@ tptp.groups1707563613775114915nt_nat (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) (@ (@ tptp.times_times_nat (@ B2 A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups1707563613775114915nt_nat (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) _let_1))))))) (forall ((S2 tptp.set_complex) (A tptp.complex) (B2 (-> tptp.complex tptp.int)) (C (-> tptp.complex tptp.int))) (let ((_let_1 (@ (@ tptp.groups858564598930262913ex_int C) (@ (@ tptp.minus_811609699411566653omplex S2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_2 (= (@ (@ tptp.groups858564598930262913ex_int (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) (@ (@ tptp.times_times_int (@ B2 A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups858564598930262913ex_int (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) _let_1))))))) (forall ((S2 tptp.set_Extended_enat) (A tptp.extended_enat) (B2 (-> tptp.extended_enat tptp.int)) (C (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ (@ tptp.groups2878480467620962989at_int C) (@ (@ tptp.minus_925952699566721837d_enat S2) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat))))) (let ((_let_2 (@ (@ tptp.member_Extended_enat A) S2))) (=> (@ tptp.finite4001608067531595151d_enat S2) (and (=> _let_2 (= (@ (@ tptp.groups2878480467620962989at_int (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) (@ (@ tptp.times_times_int (@ B2 A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups2878480467620962989at_int (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) _let_1))))))) (forall ((S2 tptp.set_real) (A tptp.real) (B2 (-> tptp.real tptp.int)) (C (-> tptp.real tptp.int))) (let ((_let_1 (@ (@ tptp.groups4694064378042380927al_int C) (@ (@ tptp.minus_minus_set_real S2) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_2 (@ (@ tptp.member_real A) S2))) (=> (@ tptp.finite_finite_real S2) (and (=> _let_2 (= (@ (@ tptp.groups4694064378042380927al_int (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) (@ (@ tptp.times_times_int (@ B2 A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups4694064378042380927al_int (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) _let_1))))))) (forall ((S2 tptp.set_complex) (A tptp.complex) (B2 (-> tptp.complex tptp.real)) (C (-> tptp.complex tptp.real))) (let ((_let_1 (@ (@ tptp.groups766887009212190081x_real C) (@ (@ tptp.minus_811609699411566653omplex S2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_2 (= (@ (@ tptp.groups766887009212190081x_real (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) (@ (@ tptp.times_times_real (@ B2 A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups766887009212190081x_real (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) _let_1))))))) (forall ((S2 tptp.set_Extended_enat) (A tptp.extended_enat) (B2 (-> tptp.extended_enat tptp.real)) (C (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ (@ tptp.groups97031904164794029t_real C) (@ (@ tptp.minus_925952699566721837d_enat S2) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat))))) (let ((_let_2 (@ (@ tptp.member_Extended_enat A) S2))) (=> (@ tptp.finite4001608067531595151d_enat S2) (and (=> _let_2 (= (@ (@ tptp.groups97031904164794029t_real (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) (@ (@ tptp.times_times_real (@ B2 A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups97031904164794029t_real (lambda ((K2 tptp.extended_enat)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) _let_1))))))) (forall ((S2 tptp.set_real) (A tptp.real) (B2 (-> tptp.real tptp.real)) (C (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.groups1681761925125756287l_real C) (@ (@ tptp.minus_minus_set_real S2) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_2 (@ (@ tptp.member_real A) S2))) (=> (@ tptp.finite_finite_real S2) (and (=> _let_2 (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) (@ (@ tptp.times_times_real (@ B2 A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B2 K2)) (@ C K2)))) S2) _let_1))))))) (forall ((X (-> tptp.nat tptp.nat tptp.nat)) (Xa2 tptp.nat) (Xb tptp.nat) (Xc tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.set_fo2584398358068434914at_nat X))) (let ((_let_2 (@ (@ tptp.ord_less_nat Xb) Xa2))) (=> (= (@ (@ (@ _let_1 Xa2) Xb) Xc) Y) (and (=> _let_2 (= Y Xc)) (=> (not _let_2) (= Y (@ (@ (@ _let_1 (@ (@ tptp.plus_plus_nat Xa2) tptp.one_one_nat)) Xb) (@ (@ X Xa2) Xc))))))))) (= tptp.set_fo2584398358068434914at_nat (lambda ((F5 (-> tptp.nat tptp.nat tptp.nat)) (A3 tptp.nat) (B3 tptp.nat) (Acc2 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat B3) A3)) Acc2) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat F5) (@ (@ tptp.plus_plus_nat A3) tptp.one_one_nat)) B3) (@ (@ F5 A3) Acc2))))) (forall ((B tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real F))) (=> (@ tptp.finite_finite_real B) (=> (@ (@ tptp.ord_less_eq_set_real A2) B) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real B) A2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F B4)))) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F A4)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B)))))))) (forall ((B tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real F))) (=> (@ tptp.finite3207457112153483333omplex B) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex B) A2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F B4)))) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F A4)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B)))))))) (forall ((B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups97031904164794029t_real F))) (=> (@ tptp.finite4001608067531595151d_enat B) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) B) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) (@ (@ tptp.minus_925952699566721837d_enat B) A2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F B4)))) (=> (forall ((A4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A4) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F A4)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B)))))))) (forall ((B tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups4694064378042380927al_int F))) (=> (@ tptp.finite_finite_real B) (=> (@ (@ tptp.ord_less_eq_set_real A2) B) (=> (forall ((B4 tptp.real)) (=> (@ (@ tptp.member_real B4) (@ (@ tptp.minus_minus_set_real B) A2)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F B4)))) (=> (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) A2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F A4)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B)))))))) (forall ((B tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int F))) (=> (@ tptp.finite3207457112153483333omplex B) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B) (=> (forall ((B4 tptp.complex)) (=> (@ (@ tptp.member_complex B4) (@ (@ tptp.minus_811609699411566653omplex B) A2)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F B4)))) (=> (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) A2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F A4)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B)))))))) (forall ((B tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2878480467620962989at_int F))) (=> (@ tptp.finite4001608067531595151d_enat B) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) B) (=> (forall ((B4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B4) (@ (@ tptp.minus_925952699566721837d_enat B) A2)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F B4)))) (=> (forall ((A4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A4) A2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F A4)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B)))))))) (forall ((B tptp.set_nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real F))) (=> (@ tptp.finite_finite_nat B) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B) (=> (forall ((B4 tptp.nat)) (=> (@ (@ tptp.member_nat B4) (@ (@ tptp.minus_minus_set_nat B) A2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F B4)))) (=> (forall ((A4 tptp.nat)) (=> (@ (@ tptp.member_nat A4) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F A4)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B)))))))) (forall ((B tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real F))) (=> (@ tptp.finite_finite_int B) (=> (@ (@ tptp.ord_less_eq_set_int A2) B) (=> (forall ((B4 tptp.int)) (=> (@ (@ tptp.member_int B4) (@ (@ tptp.minus_minus_set_int B) A2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F B4)))) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F A4)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B)))))))) (forall ((B tptp.set_nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups705719431365010083at_int F))) (=> (@ tptp.finite_finite_nat B) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B) (=> (forall ((B4 tptp.nat)) (=> (@ (@ tptp.member_nat B4) (@ (@ tptp.minus_minus_set_nat B) A2)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F B4)))) (=> (forall ((A4 tptp.nat)) (=> (@ (@ tptp.member_nat A4) A2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F A4)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B)))))))) (forall ((B tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.groups1705073143266064639nt_int F))) (=> (@ tptp.finite_finite_int B) (=> (@ (@ tptp.ord_less_eq_set_int A2) B) (=> (forall ((B4 tptp.int)) (=> (@ (@ tptp.member_int B4) (@ (@ tptp.minus_minus_set_int B) A2)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F B4)))) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) A2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F A4)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B)))))))) (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.complex)) (A tptp.complex)) (let ((_let_1 (@ tptp.groups3708469109370488835omplex F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_4 (@ (@ tptp.member_complex A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (= _let_5 tptp.zero_zero_complex)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide1717551699836669952omplex _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))) (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.complex)) (A tptp.extended_enat)) (let ((_let_1 (@ tptp.groups4622424608036095791omplex F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat))))) (let ((_let_4 (@ (@ tptp.member_Extended_enat A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (not (= _let_5 tptp.zero_zero_complex)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide1717551699836669952omplex _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))) (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.complex)) (A tptp.real)) (let ((_let_1 (@ tptp.groups713298508707869441omplex F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_4 (@ (@ tptp.member_real A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite_finite_real A2) (=> (not (= _let_5 tptp.zero_zero_complex)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide1717551699836669952omplex _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))) (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.complex)) (A tptp.int)) (let ((_let_1 (@ tptp.groups7440179247065528705omplex F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_4 (@ (@ tptp.member_int A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite_finite_int A2) (=> (not (= _let_5 tptp.zero_zero_complex)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide1717551699836669952omplex _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))) (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.complex)) (A tptp.nat)) (let ((_let_1 (@ tptp.groups6464643781859351333omplex F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))) (let ((_let_4 (@ (@ tptp.member_nat A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite_finite_nat A2) (=> (not (= _let_5 tptp.zero_zero_complex)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide1717551699836669952omplex _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))) (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (A tptp.complex)) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_4 (@ (@ tptp.member_complex A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (= _let_5 tptp.zero_zero_nat)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))) (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat)) (A tptp.extended_enat)) (let ((_let_1 (@ tptp.groups2880970938130013265at_nat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat))))) (let ((_let_4 (@ (@ tptp.member_Extended_enat A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (not (= _let_5 tptp.zero_zero_nat)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))) (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat)) (A tptp.real)) (let ((_let_1 (@ tptp.groups4696554848551431203al_nat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_4 (@ (@ tptp.member_real A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite_finite_real A2) (=> (not (= _let_5 tptp.zero_zero_nat)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))) (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat)) (A tptp.int)) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_4 (@ (@ tptp.member_int A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite_finite_int A2) (=> (not (= _let_5 tptp.zero_zero_nat)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))) (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.int)) (A tptp.complex)) (let ((_let_1 (@ tptp.groups858564598930262913ex_int F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_4 (@ (@ tptp.member_complex A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (= _let_5 tptp.zero_zero_int)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide_divide_int _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))) (forall ((A tptp.extended_enat) (N2 tptp.nat)) (= (@ (@ tptp.comm_s3181272606743183617d_enat A) (@ tptp.suc N2)) (@ (@ tptp.groups7961826882256487087d_enat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_p3455044024723400733d_enat A) (@ tptp.semiri4216267220026989637d_enat I3)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))) (forall ((A tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) (@ tptp.suc N2)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real I3)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))) (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) (@ tptp.suc N2)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ tptp.semiri1314217659103216013at_int I3)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))) (forall ((A tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) (@ tptp.suc N2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ tptp.semiri1316708129612266289at_nat I3)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))) (= tptp.comm_s3181272606743183617d_enat (lambda ((A3 tptp.extended_enat) (N tptp.nat)) (@ (@ tptp.groups7961826882256487087d_enat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_p3455044024723400733d_enat A3) (@ tptp.semiri4216267220026989637d_enat (@ (@ tptp.minus_minus_nat N) I3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N)))) (= tptp.comm_s7457072308508201937r_real (lambda ((A3 tptp.real) (N tptp.nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_real A3) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat N) I3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N)))) (= tptp.comm_s4660882817536571857er_int (lambda ((A3 tptp.int) (N tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_int A3) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat N) I3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N)))) (= tptp.comm_s4663373288045622133er_nat (lambda ((A3 tptp.nat) (N tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_nat A3) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat N) I3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N)))) (forall ((G (-> tptp.nat tptp.real)) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups129246275422532515t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M2)) (@ tptp.suc (@ _let_1 N2)))) (@ (@ tptp.groups129246275422532515t_real (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.times_times_real (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N2))))) (forall ((G (-> tptp.nat tptp.complex)) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups6464643781859351333omplex G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M2)) (@ tptp.suc (@ _let_1 N2)))) (@ (@ tptp.groups6464643781859351333omplex (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.times_times_complex (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N2))))) (forall ((G (-> tptp.nat tptp.extended_enat)) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups7961826882256487087d_enat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M2)) (@ tptp.suc (@ _let_1 N2)))) (@ (@ tptp.groups7961826882256487087d_enat (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.times_7803423173614009249d_enat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N2))))) (forall ((G (-> tptp.nat tptp.int)) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M2)) (@ tptp.suc (@ _let_1 N2)))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.times_times_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N2))))) (forall ((G (-> tptp.nat tptp.nat)) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M2)) (@ tptp.suc (@ _let_1 N2)))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.times_times_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N2))))) (forall ((F (-> tptp.nat tptp.int)) (A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int F) (@ (@ tptp.set_or1269000886237332187st_nat A) B2)) (@ (@ (@ (@ tptp.set_fo2581907887559384638at_int (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.plus_plus_int (@ F A3)) __flatten_var_0))) A) B2) tptp.zero_zero_int))) (forall ((F (-> tptp.nat tptp.complex)) (A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex F) (@ (@ tptp.set_or1269000886237332187st_nat A) B2)) (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.plus_plus_complex (@ F A3)) __flatten_var_0))) A) B2) tptp.zero_zero_complex))) (forall ((F (-> tptp.nat tptp.extended_enat)) (A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.groups7108830773950497114d_enat F) (@ (@ tptp.set_or1269000886237332187st_nat A) B2)) (@ (@ (@ (@ tptp.set_fo2538466533108834004d_enat (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.extended_enat)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ F A3)) __flatten_var_0))) A) B2) tptp.zero_z5237406670263579293d_enat))) (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat F) (@ (@ tptp.set_or1269000886237332187st_nat A) B2)) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F A3)) __flatten_var_0))) A) B2) tptp.zero_zero_nat))) (forall ((F (-> tptp.nat tptp.real)) (A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real F) (@ (@ tptp.set_or1269000886237332187st_nat A) B2)) (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.plus_plus_real (@ F A3)) __flatten_var_0))) A) B2) tptp.zero_zero_real))) (forall ((A tptp.extended_enat) (N2 tptp.nat)) (= (@ (@ tptp.comm_s3181272606743183617d_enat A) (@ tptp.suc N2)) (@ (@ tptp.groups7961826882256487087d_enat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_p3455044024723400733d_enat A) (@ tptp.semiri4216267220026989637d_enat (@ (@ tptp.minus_minus_nat N2) I3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))) (forall ((A tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) (@ tptp.suc N2)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat N2) I3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))) (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) (@ tptp.suc N2)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat N2) I3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))) (forall ((A tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) (@ tptp.suc N2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat N2) I3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))) (@ (@ 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) (@ (@ tptp.sums_nat (lambda ((N tptp.nat)) tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) tptp.zero_zero_real)) tptp.zero_zero_real) (@ (@ tptp.sums_int (lambda ((N tptp.nat)) tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) tptp.zero_zero_complex)) tptp.zero_zero_complex) (forall ((G (-> tptp.nat tptp.real)) (S2 tptp.real) (A2 tptp.set_nat) (S5 tptp.real) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.sums_real G) S2) (=> (@ tptp.finite_finite_nat A2) (=> (= S5 (@ (@ tptp.plus_plus_real S2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N)) (@ G N)))) A2))) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.member_nat N) A2)) (@ F N)) (@ G N)))) S5))))) (forall ((F (-> tptp.nat tptp.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 ((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 ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (= (@ (@ tptp.groups861055069439313189ex_nat F) A2) tptp.one_one_nat) (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A2) (= (@ F X4) tptp.one_one_nat)))))) (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (= (= (@ (@ tptp.groups1707563613775114915nt_nat F) A2) tptp.one_one_nat) (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (= (@ F X4) tptp.one_one_nat)))))) (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (= (@ (@ tptp.groups2880970938130013265at_nat F) A2) tptp.one_one_nat) (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) A2) (= (@ F X4) tptp.one_one_nat)))))) (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (= (= (@ (@ tptp.groups708209901874060359at_nat F) A2) tptp.one_one_nat) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A2) (= (@ F X4) tptp.one_one_nat)))))) (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups861055069439313189ex_nat F) A2)) (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X4))))))) (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups1707563613775114915nt_nat F) A2)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X4))))))) (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups2880970938130013265at_nat F) A2)) (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) A2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X4))))))) (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups708209901874060359at_nat F) A2)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X4))))))) (forall ((F (-> tptp.int tptp.nat)) (A2 tptp.set_int)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups1707563613775114915nt_nat F) A2)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X4 tptp.int)) (@ tptp.semiri1314217659103216013at_int (@ F X4)))) A2))) (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups708209901874060359at_nat F) A2)) (@ (@ tptp.groups705719431365010083at_int (lambda ((X4 tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ F X4)))) A2))) (forall ((I tptp.nat) (J tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat I) J)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X4 tptp.int)) X4)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int I)) (@ tptp.semiri1314217659103216013at_int J))))) (forall ((I6 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real I6) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I4)))) (= (@ tptp.ln_ln_real (@ (@ tptp.groups1681761925125756287l_real F) I6)) (@ (@ tptp.groups8097168146408367636l_real (lambda ((X4 tptp.real)) (@ tptp.ln_ln_real (@ F X4)))) I6))))) (forall ((I6 tptp.set_set_nat) (F (-> tptp.set_nat tptp.real))) (=> (@ tptp.finite1152437895449049373et_nat I6) (=> (forall ((I4 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat I4) I6) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I4)))) (= (@ tptp.ln_ln_real (@ (@ tptp.groups3619160379726066777t_real F) I6)) (@ (@ tptp.groups5107569545109728110t_real (lambda ((X4 tptp.set_nat)) (@ tptp.ln_ln_real (@ F X4)))) I6))))) (forall ((I6 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I4)))) (= (@ tptp.ln_ln_real (@ (@ tptp.groups766887009212190081x_real F) I6)) (@ (@ tptp.groups5808333547571424918x_real (lambda ((X4 tptp.complex)) (@ tptp.ln_ln_real (@ F X4)))) I6))))) (forall ((I6 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int I6) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I4)))) (= (@ tptp.ln_ln_real (@ (@ tptp.groups2316167850115554303t_real F) I6)) (@ (@ tptp.groups8778361861064173332t_real (lambda ((X4 tptp.int)) (@ tptp.ln_ln_real (@ F X4)))) I6))))) (forall ((I6 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat I6) (=> (forall ((I4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I4) I6) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I4)))) (= (@ tptp.ln_ln_real (@ (@ tptp.groups97031904164794029t_real F) I6)) (@ (@ tptp.groups4148127829035722712t_real (lambda ((X4 tptp.extended_enat)) (@ tptp.ln_ln_real (@ F X4)))) I6))))) (forall ((I6 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat I6) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I4)))) (= (@ tptp.ln_ln_real (@ (@ tptp.groups129246275422532515t_real F) I6)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((X4 tptp.nat)) (@ tptp.ln_ln_real (@ F X4)))) I6))))) (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I) J))) (= (@ (@ tptp.groups705719431365010083at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat I) _let_1)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X4 tptp.int)) X4)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int I)) (@ tptp.semiri1314217659103216013at_int _let_1)))))) (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real)) (S tptp.real) (T tptp.real)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ G N3))) (=> (@ (@ tptp.sums_real F) S) (=> (@ (@ tptp.sums_real G) T) (@ (@ tptp.ord_less_eq_real S) T))))) (forall ((F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat)) (S tptp.nat) (T tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N3)) (@ G N3))) (=> (@ (@ tptp.sums_nat F) S) (=> (@ (@ tptp.sums_nat G) T) (@ (@ tptp.ord_less_eq_nat S) T))))) (forall ((F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int)) (S tptp.int) (T tptp.int)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N3)) (@ G N3))) (=> (@ (@ tptp.sums_int F) S) (=> (@ (@ tptp.sums_int G) T) (@ (@ tptp.ord_less_eq_int S) T))))) (forall ((F (-> tptp.nat tptp.nat))) (=> (forall ((N3 tptp.nat)) (= (@ F N3) tptp.zero_zero_nat)) (@ (@ tptp.sums_nat F) tptp.zero_zero_nat))) (forall ((F (-> tptp.nat tptp.real))) (=> (forall ((N3 tptp.nat)) (= (@ F N3) tptp.zero_zero_real)) (@ (@ tptp.sums_real F) tptp.zero_zero_real))) (forall ((F (-> tptp.nat tptp.int))) (=> (forall ((N3 tptp.nat)) (= (@ F N3) tptp.zero_zero_int)) (@ (@ tptp.sums_int F) tptp.zero_zero_int))) (forall ((F (-> tptp.nat tptp.complex))) (=> (forall ((N3 tptp.nat)) (= (@ F N3) tptp.zero_zero_complex)) (@ (@ tptp.sums_complex F) tptp.zero_zero_complex))) (forall ((I tptp.nat) (F (-> tptp.nat tptp.nat))) (@ (@ tptp.sums_nat (lambda ((R4 tptp.nat)) (@ (@ (@ tptp.if_nat (= R4 I)) (@ F R4)) tptp.zero_zero_nat))) (@ F I))) (forall ((I tptp.nat) (F (-> tptp.nat tptp.real))) (@ (@ tptp.sums_real (lambda ((R4 tptp.nat)) (@ (@ (@ tptp.if_real (= R4 I)) (@ F R4)) tptp.zero_zero_real))) (@ F I))) (forall ((I tptp.nat) (F (-> tptp.nat tptp.int))) (@ (@ tptp.sums_int (lambda ((R4 tptp.nat)) (@ (@ (@ tptp.if_int (= R4 I)) (@ F R4)) tptp.zero_zero_int))) (@ F I))) (forall ((I tptp.nat) (F (-> tptp.nat tptp.complex))) (@ (@ tptp.sums_complex (lambda ((R4 tptp.nat)) (@ (@ (@ tptp.if_complex (= R4 I)) (@ F R4)) tptp.zero_zero_complex))) (@ F I))) (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (G (-> tptp.nat tptp.nat)) (B2 tptp.nat)) (=> (@ (@ tptp.sums_nat F) A) (=> (@ (@ tptp.sums_nat G) B2) (@ (@ tptp.sums_nat (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F N)) (@ G N)))) (@ (@ tptp.plus_plus_nat A) B2))))) (forall ((F (-> tptp.nat tptp.int)) (A tptp.int) (G (-> tptp.nat tptp.int)) (B2 tptp.int)) (=> (@ (@ tptp.sums_int F) A) (=> (@ (@ tptp.sums_int G) B2) (@ (@ tptp.sums_int (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_int (@ F N)) (@ G N)))) (@ (@ tptp.plus_plus_int A) B2))))) (forall ((F (-> tptp.nat tptp.real)) (A tptp.real) (G (-> tptp.nat tptp.real)) (B2 tptp.real)) (=> (@ (@ tptp.sums_real F) A) (=> (@ (@ tptp.sums_real G) B2) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_real (@ F N)) (@ G N)))) (@ (@ tptp.plus_plus_real A) B2))))) (forall ((C tptp.real) (F (-> tptp.nat tptp.real)) (D tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N)))) (@ (@ tptp.times_times_real C) D)) (@ (@ tptp.sums_real F) D)))) (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex)) (D tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N)))) (@ (@ tptp.times_times_complex C) D)) (@ (@ tptp.sums_complex F) D)))) (forall ((C tptp.real) (F (-> tptp.nat tptp.real)) (D tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) C))) (@ (@ tptp.times_times_real D) C)) (@ (@ tptp.sums_real F) D)))) (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex)) (D tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) C))) (@ (@ tptp.times_times_complex D) C)) (@ (@ tptp.sums_complex F) D)))) (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 ((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 ((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.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)) (= (@ (@ 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.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 ((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 ((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 ((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 ((N6 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat N6) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N6)) (= (@ F N3) tptp.zero_zero_int))) (@ (@ tptp.sums_int F) (@ (@ tptp.groups3539618377306564664at_int F) N6))))) (forall ((N6 tptp.set_nat) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat N6) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N6)) (= (@ F N3) tptp.zero_zero_complex))) (@ (@ tptp.sums_complex F) (@ (@ tptp.groups2073611262835488442omplex F) N6))))) (forall ((N6 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat N6) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N6)) (= (@ F N3) tptp.zero_zero_nat))) (@ (@ tptp.sums_nat F) (@ (@ tptp.groups3542108847815614940at_nat F) N6))))) (forall ((N6 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat N6) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N6)) (= (@ F N3) tptp.zero_zero_real))) (@ (@ tptp.sums_real F) (@ (@ tptp.groups6591440286371151544t_real F) N6))))) (forall ((P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.collect_nat P))) (=> (@ tptp.finite_finite_nat _let_1) (@ (@ tptp.sums_int (lambda ((R4 tptp.nat)) (@ (@ (@ tptp.if_int (@ P R4)) (@ F R4)) tptp.zero_zero_int))) (@ (@ tptp.groups3539618377306564664at_int F) _let_1))))) (forall ((P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.collect_nat P))) (=> (@ tptp.finite_finite_nat _let_1) (@ (@ tptp.sums_complex (lambda ((R4 tptp.nat)) (@ (@ (@ tptp.if_complex (@ P R4)) (@ F R4)) tptp.zero_zero_complex))) (@ (@ tptp.groups2073611262835488442omplex F) _let_1))))) (forall ((P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.collect_nat P))) (=> (@ tptp.finite_finite_nat _let_1) (@ (@ tptp.sums_nat (lambda ((R4 tptp.nat)) (@ (@ (@ tptp.if_nat (@ P R4)) (@ F R4)) tptp.zero_zero_nat))) (@ (@ tptp.groups3542108847815614940at_nat F) _let_1))))) (forall ((P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.collect_nat P))) (=> (@ tptp.finite_finite_nat _let_1) (@ (@ tptp.sums_real (lambda ((R4 tptp.nat)) (@ (@ (@ tptp.if_real (@ P R4)) (@ F R4)) tptp.zero_zero_real))) (@ (@ tptp.groups6591440286371151544t_real F) _let_1))))) (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat A2) (@ (@ tptp.sums_int (lambda ((R4 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.member_nat R4) A2)) (@ F R4)) tptp.zero_zero_int))) (@ (@ tptp.groups3539618377306564664at_int F) A2)))) (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat A2) (@ (@ tptp.sums_complex (lambda ((R4 tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.member_nat R4) A2)) (@ F R4)) tptp.zero_zero_complex))) (@ (@ tptp.groups2073611262835488442omplex F) A2)))) (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (@ (@ tptp.sums_nat (lambda ((R4 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.member_nat R4) A2)) (@ F R4)) tptp.zero_zero_nat))) (@ (@ tptp.groups3542108847815614940at_nat F) A2)))) (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat A2) (@ (@ tptp.sums_real (lambda ((R4 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.member_nat R4) A2)) (@ F R4)) tptp.zero_zero_real))) (@ (@ tptp.groups6591440286371151544t_real F) A2)))) (forall ((M2 tptp.nat) (Z3 tptp.int)) (@ (@ tptp.sums_int (lambda ((N tptp.nat)) (@ (@ tptp.times_times_int (@ (@ (@ tptp.if_int (= N M2)) tptp.one_one_int) tptp.zero_zero_int)) (@ (@ tptp.power_power_int Z3) N)))) (@ (@ tptp.power_power_int Z3) M2))) (forall ((M2 tptp.nat) (Z3 tptp.real)) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ (@ tptp.if_real (= N M2)) tptp.one_one_real) tptp.zero_zero_real)) (@ (@ tptp.power_power_real Z3) N)))) (@ (@ tptp.power_power_real Z3) M2))) (forall ((M2 tptp.nat) (Z3 tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ (@ tptp.if_complex (= N M2)) tptp.one_one_complex) tptp.zero_zero_complex)) (@ (@ tptp.power_power_complex Z3) N)))) (@ (@ tptp.power_power_complex Z3) M2))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.ln_ln_real X) (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) tptp.one_one_real)) (@ tptp.suc N))))))))) _let_124 _let_123 (forall ((B2 tptp.nat) (K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B2)) (@ tptp.semiri5074537144036343181t_real K))) (@ tptp.semiri1314217659103216013at_int 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 ((R2 tptp.complex) (M2 tptp.nat)) (let ((_let_1 (@ tptp.suc M2))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex R2) K2)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex R2) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ tptp.semiri8010041392384452111omplex K2))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) M2)) (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_complex R2) _let_1))))) (forall ((R2 tptp.real) (M2 tptp.nat)) (let ((_let_1 (@ tptp.suc M2))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real R2) K2)) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real R2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real K2))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) M2)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_real R2) _let_1))))) (forall ((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 ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.binomial _let_1) N2) _let_1))) (= (@ tptp.suminf_nat (lambda ((N tptp.nat)) tptp.zero_zero_nat)) tptp.zero_zero_nat) (= (@ tptp.suminf_real (lambda ((N tptp.nat)) tptp.zero_zero_real)) tptp.zero_zero_real) (= (@ tptp.suminf_int (lambda ((N tptp.nat)) tptp.zero_zero_int)) tptp.zero_zero_int) (= (@ tptp.suminf_complex (lambda ((N tptp.nat)) tptp.zero_zero_complex)) tptp.zero_zero_complex) (forall ((X tptp.real)) (= (= (@ tptp.real_V1803761363581548252l_real X) tptp.zero_zero_real) (= X tptp.zero_zero_real))) (forall ((X tptp.real)) (= (= (@ tptp.real_V4546457046886955230omplex X) tptp.zero_zero_complex) (= X tptp.zero_zero_real))) (= (@ tptp.real_V1803761363581548252l_real tptp.zero_zero_real) tptp.zero_zero_real) (= (@ tptp.real_V4546457046886955230omplex tptp.zero_zero_real) tptp.zero_zero_complex) (= (@ tptp.archim6058952711729229775r_real tptp.zero_zero_real) tptp.zero_zero_int) (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_nat tptp.zero_zero_nat) (@ tptp.suc K)) tptp.zero_zero_nat)) (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_real tptp.zero_zero_real) (@ tptp.suc K)) tptp.zero_zero_real)) (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_int tptp.zero_zero_int) (@ tptp.suc K)) tptp.zero_zero_int)) (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_complex tptp.zero_zero_complex) (@ tptp.suc K)) tptp.zero_zero_complex)) (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) (K tptp.nat)) (= (= (@ (@ tptp.binomial N2) K) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat N2) K))) (forall ((A tptp.nat)) (= (@ (@ tptp.gbinomial_nat A) tptp.zero_zero_nat) tptp.one_one_nat)) (forall ((A tptp.int)) (= (@ (@ tptp.gbinomial_int A) tptp.zero_zero_nat) tptp.one_one_int)) (forall ((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 ((X tptp.real) (Y tptp.real)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real X)) (@ tptp.real_V1803761363581548252l_real Y)))) (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex X)) (@ tptp.real_V4546457046886955230omplex Y)))) (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)) (= (@ (@ tptp.binomial N2) tptp.zero_zero_nat) tptp.one_one_nat)) (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))) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X))) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_real X) tptp.zero_zero_real))) (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real V)) X))) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X))) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_real X) tptp.one_one_real))) (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_real X) (@ tptp.numeral_numeral_real V)))) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X))) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X)) tptp.one_one_int) (@ (@ tptp.ord_less_real X) tptp.one_one_real))) (forall ((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 ((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 ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)) X))) (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)))) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) X))) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) tptp.one_one_int) (@ (@ tptp.ord_less_real X) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) X))) (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_real X) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))))) (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)) X))) (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.archim6058952711729229775r_real Y)))) (forall ((N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K) (= (@ (@ tptp.binomial N2) K) tptp.zero_zero_nat))) (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real X))) X)) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.archim6058952711729229775r_real Y)) (@ (@ tptp.ord_less_real X) Y))) (forall ((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 ((M2 tptp.nat) (R2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M2))) (let ((_let_2 (@ _let_1 R2))) (let ((_let_3 (@ tptp.binomial (@ (@ tptp.plus_plus_nat _let_2) K)))) (let ((_let_4 (@ _let_1 K))) (= (@ (@ tptp.times_times_nat (@ _let_3 _let_4)) (@ (@ tptp.binomial _let_4) K)) (@ (@ tptp.times_times_nat (@ _let_3 K)) (@ (@ tptp.binomial _let_2) M2)))))))) (forall ((R2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat R2) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.binomial N2) R2)) (@ (@ tptp.power_power_nat N2) R2)))) (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 ((Z3 tptp.int) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_int Z3) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z3)) X))) (forall ((X tptp.real) (Z3 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X)) Z3) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real Z3)))) (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ tptp.suc (@ (@ tptp.plus_plus_nat A) B2))))) (let ((_let_2 (@ tptp.suc A))) (= (@ (@ tptp.times_times_nat _let_2) (@ _let_1 _let_2)) (@ (@ tptp.times_times_nat (@ tptp.suc B2)) (@ _let_1 A)))))) (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.archim6058952711729229775r_real Y))) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X) Y)))) (forall ((Z3 tptp.int) (X tptp.real)) (= (@ (@ tptp.plus_plus_int Z3) (@ tptp.archim6058952711729229775r_real X)) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real Z3)) X)))) (forall ((X tptp.real) (Z3 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X)) Z3) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X) (@ tptp.ring_1_of_int_real Z3))))) (forall ((K tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.binomial N2))) (=> (@ (@ tptp.ord_less_eq_nat K) M2) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ (@ tptp.times_times_nat (@ _let_1 M2)) (@ (@ tptp.binomial M2) K)) (@ (@ tptp.times_times_nat (@ _let_1 K)) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N2) K)) (@ (@ tptp.minus_minus_nat M2) 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 ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_complex A))) (= (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex A) tptp.one_one_complex)) _let_1) (@ (@ tptp.plus_plus_complex (@ _let_2 K)) (@ _let_2 _let_1)))))) (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_real A))) (= (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real A) tptp.one_one_real)) _let_1) (@ (@ tptp.plus_plus_real (@ _let_2 K)) (@ _let_2 _let_1)))))) (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real N2)))) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ _let_1 K) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K)))))) (forall ((N6 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat N6) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N6)) (= (@ F N3) tptp.zero_zero_int))) (= (@ tptp.suminf_int F) (@ (@ tptp.groups3539618377306564664at_int F) N6))))) (forall ((N6 tptp.set_nat) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat N6) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N6)) (= (@ F N3) tptp.zero_zero_complex))) (= (@ tptp.suminf_complex F) (@ (@ tptp.groups2073611262835488442omplex F) N6))))) (forall ((N6 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat N6) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N6)) (= (@ F N3) tptp.zero_zero_nat))) (= (@ tptp.suminf_nat F) (@ (@ tptp.groups3542108847815614940at_nat F) N6))))) (forall ((N6 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat N6) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N6)) (= (@ F N3) tptp.zero_zero_real))) (= (@ tptp.suminf_real F) (@ (@ tptp.groups6591440286371151544t_real F) N6))))) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.real_V7735802525324610683m_real X))) (@ (@ tptp.ord_less_real _let_1) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real _let_1)) tptp.one_one_real))))) (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex X))) (@ (@ tptp.ord_less_real _let_1) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex _let_1)) tptp.one_one_complex))))) (forall ((X tptp.real)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X)) tptp.one_one_int) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)))) (forall ((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 ((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 ((K tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real K))) (=> (@ (@ tptp.ord_less_eq_real _let_1) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real A) _let_1)) K)) (@ (@ tptp.gbinomial_real A) K))))) (forall ((A tptp.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 ((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 ((P (-> tptp.int Bool)) (T tptp.real)) (= (@ P (@ tptp.archim6058952711729229775r_real T)) (forall ((I3 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real I3))) (=> (and (@ (@ tptp.ord_less_eq_real _let_1) T) (@ (@ tptp.ord_less_real T) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))) (@ P I3)))))) (forall ((X tptp.real) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real A))) (= (= (@ tptp.archim6058952711729229775r_real X) A) (and (@ (@ tptp.ord_less_eq_real _let_1) X) (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))))) (forall ((Z3 tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real Z3))) (=> (@ (@ tptp.ord_less_eq_real _let_1) X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X) Z3))))) (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 ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int (@ tptp.archim6058952711729229775r_real A)) (@ tptp.archim6058952711729229775r_real B2))) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.times_times_real A) B2))))))) (forall ((Z3 tptp.int) (X tptp.real)) (= (@ (@ tptp.ord_less_int Z3) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real Z3)) tptp.one_one_real)) X))) (forall ((X tptp.real) (Z3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) Z3) (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real Z3)) tptp.one_one_real)))) (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)))))) (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 ((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 ((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)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.binomial N2) K)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.archim6058952711729229775r_real X))) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real _let_1)) X) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))) (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 ((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.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) (M2 tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.gbinomial_complex A))) (=> (@ (@ tptp.ord_less_eq_nat K) M2) (= (@ (@ tptp.times_times_complex (@ _let_1 M2)) (@ (@ tptp.gbinomial_complex (@ tptp.semiri8010041392384452111omplex M2)) K)) (@ (@ tptp.times_times_complex (@ _let_1 K)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex A) (@ tptp.semiri8010041392384452111omplex K))) (@ (@ tptp.minus_minus_nat M2) K))))))) (forall ((K tptp.nat) (M2 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.gbinomial_real A))) (=> (@ (@ tptp.ord_less_eq_nat K) M2) (= (@ (@ tptp.times_times_real (@ _let_1 M2)) (@ (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real M2)) K)) (@ (@ tptp.times_times_real (@ _let_1 K)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.minus_minus_nat M2) K))))))) (forall ((Q3 tptp.real) (P5 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 P5) Q3)))) Q3)) P5))) (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 ((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 ((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 ((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 ((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.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ (@ tptp.plus_plus_complex A) tptp.one_one_complex))) (= (@ (@ tptp.gbinomial_complex _let_2) _let_1) (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex _let_2) (@ tptp.semiri8010041392384452111omplex _let_1))) (@ (@ tptp.gbinomial_complex A) K)))))) (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ (@ tptp.plus_plus_real A) tptp.one_one_real))) (= (@ (@ tptp.gbinomial_real _let_2) _let_1) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real _let_2) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.gbinomial_real A) K)))))) (forall ((Q3 tptp.real) (P5 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q3) (@ (@ tptp.ord_less_real P5) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real P5) Q3)))) tptp.one_one_real)) Q3)))) _let_122 (forall ((A tptp.complex) (K tptp.nat)) (= (@ (@ tptp.gbinomial_complex (@ tptp.uminus1482373934393186551omplex A)) K) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) (@ tptp.semiri8010041392384452111omplex K))) tptp.one_one_complex)) K)))) (forall ((A tptp.real) (K tptp.nat)) (= (@ (@ tptp.gbinomial_real (@ tptp.uminus_uminus_real A)) K) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real K))) tptp.one_one_real)) K)))) (forall ((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) (N2 tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((J2 tptp.nat)) (@ (@ tptp.gbinomial_complex (@ tptp.semiri8010041392384452111omplex J2)) 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.groups6591440286371151544t_real (lambda ((J2 tptp.nat)) (@ (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real J2)) 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 ((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 ((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 ((B2 tptp.nat) (N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (=> (@ (@ 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))) B2) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B2)) (@ tptp.semiri5074537144036343181t_real K))) (@ tptp.semiri1314217659103216013at_int N2))))))) (= (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_30)) (@ tptp.suminf_real (lambda ((K2 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K2)) tptp.one_one_real)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat)))))) (forall ((A tptp.complex) (M2 tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex A) K2)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex A) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ tptp.semiri8010041392384452111omplex K2))))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex M2)) tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_complex A) (@ (@ tptp.plus_plus_nat M2) tptp.one_one_nat))))) (forall ((A tptp.real) (M2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real A) K2)) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real A) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real K2))))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M2)) tptp.one_one_real)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_real A) (@ (@ tptp.plus_plus_nat M2) tptp.one_one_nat))))) (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 ((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))))) (= tptp.archim8280529875227126926d_real (lambda ((X4 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 X4))) (@ tptp.archim7802044766580827645g_real X4)) (@ tptp.archim6058952711729229775r_real X4)))) (forall ((M2 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 M2))) tptp.one_one_complex))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.power_power_complex _let_2) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) M2)))))) (forall ((M2 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 M2))) tptp.one_one_real))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.power_power_real _let_2) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) M2)))))) (forall ((X tptp.nat) (Y tptp.nat)) (= (= (@ tptp.set_ord_atMost_nat X) (@ tptp.set_ord_atMost_nat Y)) (= X Y))) (forall ((X tptp.int) (Y tptp.int)) (= (= (@ tptp.set_ord_atMost_int X) (@ tptp.set_ord_atMost_int Y)) (= X Y))) (forall ((I tptp.extended_enat) (K tptp.extended_enat)) (= (@ (@ tptp.member_Extended_enat I) (@ tptp.set_or8332593352340944941d_enat K)) (@ (@ tptp.ord_le2932123472753598470d_enat I) K))) (forall ((I tptp.real) (K tptp.real)) (= (@ (@ tptp.member_real I) (@ tptp.set_ord_atMost_real K)) (@ (@ tptp.ord_less_eq_real I) K))) (forall ((I tptp.set_nat) (K tptp.set_nat)) (= (@ (@ tptp.member_set_nat I) (@ tptp.set_or4236626031148496127et_nat K)) (@ (@ tptp.ord_less_eq_set_nat I) K))) (forall ((I tptp.set_int) (K tptp.set_int)) (= (@ (@ tptp.member_set_int I) (@ tptp.set_or58775011639299419et_int K)) (@ (@ tptp.ord_less_eq_set_int I) K))) (forall ((I tptp.nat) (K tptp.nat)) (= (@ (@ tptp.member_nat I) (@ tptp.set_ord_atMost_nat K)) (@ (@ tptp.ord_less_eq_nat I) K))) (forall ((I tptp.int) (K tptp.int)) (= (@ (@ tptp.member_int I) (@ tptp.set_ord_atMost_int K)) (@ (@ tptp.ord_less_eq_int I) K))) (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.set_ord_atMost_nat K))) (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_ord_atMost_real X)) (@ tptp.set_ord_atMost_real Y)) (@ (@ tptp.ord_less_eq_real X) Y))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.set_or4236626031148496127et_nat X)) (@ tptp.set_or4236626031148496127et_nat Y)) (@ (@ tptp.ord_less_eq_set_nat X) Y))) (forall ((X tptp.set_int) (Y tptp.set_int)) (= (@ (@ tptp.ord_le4403425263959731960et_int (@ tptp.set_or58775011639299419et_int X)) (@ tptp.set_or58775011639299419et_int Y)) (@ (@ tptp.ord_less_eq_set_int X) Y))) (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_ord_atMost_nat X)) (@ tptp.set_ord_atMost_nat Y)) (@ (@ tptp.ord_less_eq_nat X) Y))) (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_atMost_int X)) (@ tptp.set_ord_atMost_int Y)) (@ (@ tptp.ord_less_eq_int X) Y))) (forall ((Z3 tptp.int)) (= (@ tptp.archim2898591450579166408c_real (@ tptp.ring_1_of_int_real Z3)) tptp.zero_zero_real)) (forall ((L tptp.set_nat) (H2 tptp.set_nat) (H3 tptp.set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.set_or4548717258645045905et_nat L) H2)) (@ tptp.set_or4236626031148496127et_nat H3)) (or (not (@ (@ tptp.ord_less_eq_set_nat L) H2)) (@ (@ tptp.ord_less_eq_set_nat H2) H3)))) (forall ((L tptp.set_int) (H2 tptp.set_int) (H3 tptp.set_int)) (= (@ (@ tptp.ord_le4403425263959731960et_int (@ (@ tptp.set_or370866239135849197et_int L) H2)) (@ tptp.set_or58775011639299419et_int H3)) (or (not (@ (@ tptp.ord_less_eq_set_int L) H2)) (@ (@ tptp.ord_less_eq_set_int H2) H3)))) (forall ((L tptp.nat) (H2 tptp.nat) (H3 tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.set_or1269000886237332187st_nat L) H2)) (@ tptp.set_ord_atMost_nat H3)) (or (not (@ (@ tptp.ord_less_eq_nat L) H2)) (@ (@ tptp.ord_less_eq_nat H2) H3)))) (forall ((L tptp.int) (H2 tptp.int) (H3 tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.set_or1266510415728281911st_int L) H2)) (@ tptp.set_ord_atMost_int H3)) (or (not (@ (@ tptp.ord_less_eq_int L) H2)) (@ (@ tptp.ord_less_eq_int H2) H3)))) (forall ((L tptp.real) (H2 tptp.real) (H3 tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.set_or1222579329274155063t_real L) H2)) (@ tptp.set_ord_atMost_real H3)) (or (not (@ (@ tptp.ord_less_eq_real L) H2)) (@ (@ tptp.ord_less_eq_real H2) H3)))) (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.extended_enat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.groups7108830773950497114d_enat G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ _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 ((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.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.extended_enat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.groups7961826882256487087d_enat G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_7803423173614009249d_enat (@ _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 ((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)))))) (= (@ tptp.set_ord_atMost_nat tptp.zero_zero_nat) (@ _let_66 tptp.bot_bot_set_nat)) (forall ((H2 tptp.extended_enat)) (not (= tptp.bot_bo7653980558646680370d_enat (@ tptp.set_or8332593352340944941d_enat H2)))) (forall ((H2 tptp.real)) (not (= tptp.bot_bot_set_real (@ tptp.set_ord_atMost_real H2)))) (forall ((H2 tptp.nat)) (not (= tptp.bot_bot_set_nat (@ tptp.set_ord_atMost_nat H2)))) (forall ((H2 tptp.int)) (not (= tptp.bot_bot_set_int (@ tptp.set_ord_atMost_int H2)))) (forall ((A tptp.int)) (not (@ tptp.finite_finite_int (@ tptp.set_ord_atMost_int A)))) (forall ((H3 tptp.int) (L tptp.int) (H2 tptp.int)) (not (= (@ tptp.set_ord_atMost_int H3) (@ (@ tptp.set_or1266510415728281911st_int L) H2)))) (forall ((H3 tptp.real) (L tptp.real) (H2 tptp.real)) (not (= (@ tptp.set_ord_atMost_real H3) (@ (@ tptp.set_or1222579329274155063t_real L) H2)))) _let_121 _let_120 _let_119 _let_118 _let_117 (= tptp.set_ord_atMost_nat (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat)) (forall ((K tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K)) (@ tptp.set_ord_atMost_nat K))) (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ tptp.set_ord_atMost_nat _let_1) (@ (@ tptp.insert_nat _let_1) (@ tptp.set_ord_atMost_nat K))))) (forall ((H2 tptp.int) (L3 tptp.int) (H3 tptp.int)) (not (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_atMost_int H2)) (@ (@ tptp.set_or1266510415728281911st_int L3) H3)))) (forall ((H2 tptp.real) (L3 tptp.real) (H3 tptp.real)) (not (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_ord_atMost_real H2)) (@ (@ tptp.set_or1222579329274155063t_real L3) H3)))) (= tptp.finite_finite_nat (lambda ((S6 tptp.set_nat)) (exists ((K2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat S6) (@ tptp.set_ord_atMost_nat K2))))) (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.archim2898591450579166408c_real X))) (forall ((X tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.archim2898591450579166408c_real X)) tptp.one_one_real)) (forall ((X tptp.real)) (= (@ tptp.archim2898591450579166408c_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)) (@ tptp.archim2898591450579166408c_real X))) (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat K))) (= (@ tptp.set_ord_atMost_nat _let_1) (@ (@ tptp.insert_nat _let_1) (@ tptp.set_ord_atMost_nat (@ tptp.pred_numeral K)))))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (= (@ (@ tptp.ord_le7203529160286727270d_enat (@ tptp.set_or8332593352340944941d_enat A)) (@ tptp.set_or8419480210114673929d_enat B2)) (@ (@ tptp.ord_le72135733267957522d_enat A) B2))) (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_ord_atMost_real A)) (@ tptp.set_or5984915006950818249n_real B2)) (@ (@ tptp.ord_less_real A) B2))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_ord_atMost_nat A)) (@ tptp.set_ord_lessThan_nat B2)) (@ (@ tptp.ord_less_nat A) B2))) (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_atMost_int A)) (@ tptp.set_ord_lessThan_int B2)) (@ (@ tptp.ord_less_int A) B2))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.binomial K2) M2))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.binomial (@ tptp.suc N2)) (@ tptp.suc M2)))) (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.extended_enat)) (N2 tptp.nat)) (= (@ (@ tptp.groups7108830773950497114d_enat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N2))) (@ (@ tptp.plus_p3455044024723400733d_enat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups7108830773950497114d_enat (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.int)) (I tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F I3)) (@ F (@ tptp.suc I3))))) (@ tptp.set_ord_atMost_nat I)) (@ (@ tptp.minus_minus_int (@ F tptp.zero_zero_nat)) (@ F (@ tptp.suc I))))) (forall ((F (-> tptp.nat tptp.real)) (I tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F I3)) (@ F (@ tptp.suc I3))))) (@ tptp.set_ord_atMost_nat I)) (@ (@ tptp.minus_minus_real (@ F tptp.zero_zero_nat)) (@ F (@ tptp.suc I))))) (forall ((C (-> tptp.nat tptp.complex)) (N2 tptp.nat) (D (-> tptp.nat tptp.complex))) (= (forall ((X4 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 X4) I3)))) _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ D I3)) (@ (@ tptp.power_power_complex X4) 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 ((X4 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 X4) I3)))) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ D I3)) (@ (@ tptp.power_power_real X4) I3)))) _let_1)))) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) N2) (= (@ C I3) (@ D I3)))))) (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_atMost_nat N2))))) (forall ((G (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (= (@ (@ tptp.groups6464643781859351333omplex G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_complex (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_atMost_nat N2))))) (forall ((G (-> tptp.nat tptp.extended_enat)) (N2 tptp.nat)) (= (@ (@ tptp.groups7961826882256487087d_enat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N2))) (@ (@ tptp.times_7803423173614009249d_enat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups7961826882256487087d_enat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_atMost_nat N2))))) (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_atMost_nat N2))))) (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_atMost_nat N2))))) (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 ((J2 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ A I3) J2))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J2)) 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 ((J2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ A I3) J2))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J2)) N2)))) (@ tptp.set_ord_lessThan_nat N2)))) (forall ((A (-> tptp.nat tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (@ A I3)) (@ tptp.set_ord_lessThan_nat I3)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.groups705719431365010083at_int (lambda ((J2 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ (@ A I3) J2))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J2)) N2)))) (@ tptp.set_ord_lessThan_nat N2)))) (forall ((A (-> tptp.nat tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (@ A I3)) (@ tptp.set_ord_lessThan_nat I3)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ (@ A I3) J2))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J2)) N2)))) (@ tptp.set_ord_lessThan_nat N2)))) (forall ((R2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat R2) K2)) K2))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.binomial (@ tptp.suc (@ (@ tptp.plus_plus_nat R2) N2))) N2))) (forall ((N2 tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat N2) J2)) N2))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat N2) M2)) tptp.one_one_nat)) M2))) (forall ((N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat N2) J2)) N2))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat (@ _let_1 M2)) tptp.one_one_nat)) (@ _let_1 tptp.one_one_nat))))) (forall ((X tptp.real)) (= (= (@ tptp.archim2898591450579166408c_real X) X) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_real X) tptp.one_one_real)))) (forall ((C (-> tptp.nat tptp.complex)) (N2 tptp.nat) (K tptp.nat)) (=> (forall ((W tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex W) 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 ((W tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real W) 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 ((C (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (= (forall ((X4 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex X4) 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 ((X4 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real X4) 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 ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ tptp.archim2898591450579166408c_real X)) (@ tptp.archim2898591450579166408c_real Y)))) (let ((_let_2 (@ tptp.archim2898591450579166408c_real (@ (@ tptp.plus_plus_real X) Y)))) (let ((_let_3 (@ (@ tptp.ord_less_real _let_1) tptp.one_one_real))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)))))))) (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.extended_enat)) (N2 tptp.nat)) (= (@ (@ tptp.groups7108830773950497114d_enat G) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups7108830773950497114d_enat (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.int)) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M2) 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 M2))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) _let_1))))))) (forall ((F (-> tptp.nat tptp.extended_enat)) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M2) N2))) (let ((_let_2 (@ tptp.groups7108830773950497114d_enat F))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ _let_2 (@ tptp.set_ord_atMost_nat M2))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) _let_1))))))) (forall ((F (-> tptp.nat tptp.nat)) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M2) 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 M2))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) _let_1))))))) (forall ((F (-> tptp.nat tptp.real)) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M2) 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 M2))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) _let_1))))))) (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real G) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N2))))) (forall ((G (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (= (@ (@ tptp.groups6464643781859351333omplex G) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_complex (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N2))))) (forall ((G (-> tptp.nat tptp.extended_enat)) (N2 tptp.nat)) (= (@ (@ tptp.groups7961826882256487087d_enat G) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_7803423173614009249d_enat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups7961826882256487087d_enat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N2))))) (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N2))))) (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N2))))) (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 ((A tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex A) (@ tptp.semiri8010041392384452111omplex K2))) K2))) (@ 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.real) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real K2))) K2))) (@ 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 ((G (-> tptp.nat tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups977919841031483927at_nat (@ tptp.produc6842872674320459806at_nat G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I3 tptp.nat) (J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I3) J2)) N2))))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ G I3) (@ (@ tptp.minus_minus_nat K2) I3)))) (@ tptp.set_ord_atMost_nat K2)))) (@ tptp.set_ord_atMost_nat N2)))) (forall ((G (-> tptp.nat tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups4567486121110086003t_real (@ tptp.produc1703576794950452218t_real G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I3 tptp.nat) (J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I3) J2)) N2))))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ G I3) (@ (@ tptp.minus_minus_nat K2) I3)))) (@ tptp.set_ord_atMost_nat K2)))) (@ tptp.set_ord_atMost_nat N2)))) (forall ((G (-> tptp.nat tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups4075276357253098568at_int (@ tptp.produc6840382203811409530at_int G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I3 tptp.nat) (J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I3) J2)) N2))))) (@ (@ tptp.groups705719431365010083at_int (lambda ((K2 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ (@ G I3) (@ (@ tptp.minus_minus_nat K2) I3)))) (@ tptp.set_ord_atMost_nat K2)))) (@ tptp.set_ord_atMost_nat N2)))) (forall ((G (-> tptp.nat tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups4077766827762148844at_nat (@ tptp.produc6842872674320459806at_nat G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I3 tptp.nat) (J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I3) J2)) N2))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ (@ G I3) (@ (@ tptp.minus_minus_nat K2) I3)))) (@ tptp.set_ord_atMost_nat K2)))) (@ tptp.set_ord_atMost_nat N2)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N2) K2)) (@ (@ tptp.minus_minus_nat M2) K2)))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.binomial (@ tptp.suc N2)) M2)))) (forall ((M2 tptp.nat) (N2 tptp.nat) (R2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.binomial M2) K2)) (@ (@ tptp.binomial N2) (@ (@ tptp.minus_minus_nat R2) K2))))) (@ tptp.set_ord_atMost_nat R2)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat M2) N2)) R2))) (forall ((X tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X))) (let ((_let_2 (@ tptp.minus_minus_int tptp.one_one_int))) (= (@ (@ tptp.times_times_int (@ _let_2 X)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.set_ord_atMost_nat N2))) (@ _let_2 (@ _let_1 (@ tptp.suc N2))))))) (forall ((X tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X))) (let ((_let_2 (@ tptp.minus_minus_complex tptp.one_one_complex))) (= (@ (@ tptp.times_times_complex (@ _let_2 X)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_atMost_nat N2))) (@ _let_2 (@ _let_1 (@ tptp.suc N2))))))) (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X))) (let ((_let_2 (@ tptp.minus_minus_real tptp.one_one_real))) (= (@ (@ tptp.times_times_real (@ _let_2 X)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_atMost_nat N2))) (@ _let_2 (@ _let_1 (@ tptp.suc N2))))))) (forall ((C (-> tptp.nat tptp.complex)) (K tptp.nat) (N2 tptp.nat)) (=> (not (= (@ C K) tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z6 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex Z6) I3)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_complex))))))) (forall ((C (-> tptp.nat tptp.real)) (K tptp.nat) (N2 tptp.nat)) (=> (not (= (@ C K) tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((Z6 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real Z6) I3)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_real))))))) (forall ((C (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (= (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex X4) I3)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_complex)))) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I3) N2) (not (= (@ C I3) tptp.zero_zero_complex)))))) (forall ((C (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((X4 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real X4) I3)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_real)))) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I3) N2) (not (= (@ C I3) tptp.zero_zero_real)))))) (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 ((B4 (-> tptp.nat tptp.int))) (not (forall ((Z4 tptp.int)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ C I3)) (@ (@ tptp.power_power_int Z4) I3)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int Z4) A)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ B4 I3)) (@ (@ tptp.power_power_int Z4) 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 ((B4 (-> tptp.nat tptp.complex))) (not (forall ((Z4 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex Z4) I3)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex Z4) A)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ B4 I3)) (@ (@ tptp.power_power_complex Z4) 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 ((B4 (-> tptp.nat tptp.real))) (not (forall ((Z4 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real Z4) I3)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real Z4) A)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ B4 I3)) (@ (@ tptp.power_power_real Z4) I3)))) (@ tptp.set_ord_lessThan_nat N2)))))))))) (forall ((C (-> tptp.nat tptp.int)) (N2 tptp.nat) (A tptp.int)) (exists ((B4 (-> tptp.nat tptp.int))) (forall ((Z4 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 Z4) I3)))) _let_1) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int Z4) A)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ B4 I3)) (@ (@ tptp.power_power_int Z4) 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.complex)) (N2 tptp.nat) (A tptp.complex)) (exists ((B4 (-> tptp.nat tptp.complex))) (forall ((Z4 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 Z4) I3)))) _let_1) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex Z4) A)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ B4 I3)) (@ (@ tptp.power_power_complex Z4) 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.real)) (N2 tptp.nat) (A tptp.real)) (exists ((B4 (-> tptp.nat tptp.real))) (forall ((Z4 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 Z4) I3)))) _let_1) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real Z4) A)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ B4 I3)) (@ (@ tptp.power_power_real Z4) 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 ((M2 tptp.nat) (N2 tptp.nat) (X tptp.int)) (let ((_let_1 (@ tptp.power_power_int X))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M2) N2)) (@ (@ tptp.times_times_int (@ _let_1 M2)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N2) M2))))))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (X tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X))) (let ((_let_2 (@ tptp.groups2073611262835488442omplex _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M2) N2)) (@ (@ tptp.times_times_complex (@ _let_1 M2)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N2) M2))))))))) (forall ((M2 tptp.nat) (N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.power_power_real X))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M2) N2)) (@ (@ tptp.times_times_real (@ _let_1 M2)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N2) M2))))))))) (forall ((G (-> tptp.nat tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups977919841031483927at_nat (@ tptp.produc6842872674320459806at_nat G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I3 tptp.nat) (J2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I3) J2)) N2))))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ G I3) (@ (@ tptp.minus_minus_nat K2) I3)))) (@ tptp.set_ord_atMost_nat K2)))) (@ tptp.set_ord_lessThan_nat N2)))) (forall ((G (-> tptp.nat tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups4567486121110086003t_real (@ tptp.produc1703576794950452218t_real G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I3 tptp.nat) (J2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I3) J2)) N2))))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ G I3) (@ (@ tptp.minus_minus_nat K2) I3)))) (@ tptp.set_ord_atMost_nat K2)))) (@ tptp.set_ord_lessThan_nat N2)))) (forall ((G (-> tptp.nat tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups4075276357253098568at_int (@ tptp.produc6840382203811409530at_int G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I3 tptp.nat) (J2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I3) J2)) N2))))) (@ (@ tptp.groups705719431365010083at_int (lambda ((K2 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ (@ G I3) (@ (@ tptp.minus_minus_nat K2) I3)))) (@ tptp.set_ord_atMost_nat K2)))) (@ tptp.set_ord_lessThan_nat N2)))) (forall ((G (-> tptp.nat tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups4077766827762148844at_nat (@ tptp.produc6842872674320459806at_nat G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I3 tptp.nat) (J2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I3) J2)) N2))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ (@ G I3) (@ (@ tptp.minus_minus_nat K2) I3)))) (@ tptp.set_ord_atMost_nat K2)))) (@ tptp.set_ord_lessThan_nat N2)))) (forall ((A tptp.nat) (B2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat A) B2)) N2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.binomial N2) K2))) (@ (@ tptp.power_power_nat A) K2))) (@ (@ tptp.power_power_nat B2) (@ (@ tptp.minus_minus_nat N2) K2))))) (@ 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.extended_enat)) (N2 tptp.nat)) (= (@ (@ tptp.groups7108830773950497114d_enat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ (@ tptp.groups7108830773950497114d_enat (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.plus_p3455044024723400733d_enat (@ 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 ((M2 tptp.nat) (A (-> tptp.nat tptp.int)) (N2 tptp.nat) (B2 (-> tptp.nat tptp.int)) (X tptp.int)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) I4) (= (@ A I4) tptp.zero_zero_int))) (=> (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) J3) (= (@ B2 J3) 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 X) I3)))) (@ tptp.set_ord_atMost_nat M2))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((J2 tptp.nat)) (@ (@ tptp.times_times_int (@ B2 J2)) (@ (@ tptp.power_power_int X) J2)))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((R4 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_int (@ A K2)) (@ B2 (@ (@ tptp.minus_minus_nat R4) K2))))) (@ tptp.set_ord_atMost_nat R4))) (@ (@ tptp.power_power_int X) R4)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M2) N2))))))) (forall ((M2 tptp.nat) (A (-> tptp.nat tptp.complex)) (N2 tptp.nat) (B2 (-> tptp.nat tptp.complex)) (X tptp.complex)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) I4) (= (@ A I4) tptp.zero_zero_complex))) (=> (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) J3) (= (@ B2 J3) tptp.zero_zero_complex))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I3)) (@ (@ tptp.power_power_complex X) I3)))) (@ tptp.set_ord_atMost_nat M2))) (@ (@ tptp.groups2073611262835488442omplex (lambda ((J2 tptp.nat)) (@ (@ tptp.times_times_complex (@ B2 J2)) (@ (@ tptp.power_power_complex X) J2)))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.groups2073611262835488442omplex (lambda ((R4 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_complex (@ A K2)) (@ B2 (@ (@ tptp.minus_minus_nat R4) K2))))) (@ tptp.set_ord_atMost_nat R4))) (@ (@ tptp.power_power_complex X) R4)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M2) N2))))))) (forall ((M2 tptp.nat) (A (-> tptp.nat tptp.real)) (N2 tptp.nat) (B2 (-> tptp.nat tptp.real)) (X tptp.real)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) I4) (= (@ A I4) tptp.zero_zero_real))) (=> (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) J3) (= (@ B2 J3) 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 X) I3)))) (@ tptp.set_ord_atMost_nat M2))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J2 tptp.nat)) (@ (@ tptp.times_times_real (@ B2 J2)) (@ (@ tptp.power_power_real X) J2)))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((R4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_real (@ A K2)) (@ B2 (@ (@ tptp.minus_minus_nat R4) K2))))) (@ tptp.set_ord_atMost_nat R4))) (@ (@ tptp.power_power_real X) R4)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M2) N2))))))) (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ (@ tptp.groups129246275422532515t_real (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.times_times_real (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N2)))) (forall ((G (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (= (@ (@ tptp.groups6464643781859351333omplex G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ (@ tptp.groups6464643781859351333omplex (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.times_times_complex (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N2)))) (forall ((G (-> tptp.nat tptp.extended_enat)) (N2 tptp.nat)) (= (@ (@ tptp.groups7961826882256487087d_enat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ (@ tptp.groups7961826882256487087d_enat (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.times_7803423173614009249d_enat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N2)))) (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.times_times_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N2)))) (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.times_times_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N2)))) (forall ((C (-> tptp.nat tptp.complex)) (N2 tptp.nat) (K tptp.complex)) (= (forall ((X4 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex X4) I3)))) (@ tptp.set_ord_atMost_nat N2)) K)) (and (= (@ C tptp.zero_zero_nat) K) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2)) (= (@ C X4) tptp.zero_zero_complex)))))) (forall ((C (-> tptp.nat tptp.real)) (N2 tptp.nat) (K tptp.real)) (= (forall ((X4 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real X4) I3)))) (@ tptp.set_ord_atMost_nat N2)) K)) (and (= (@ C tptp.zero_zero_nat) K) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2)) (= (@ C X4) tptp.zero_zero_real)))))) (forall ((A tptp.complex) (B2 tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex A) B2)) N2) (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N2) K2))) (@ (@ tptp.power_power_complex A) K2))) (@ (@ tptp.power_power_complex B2) (@ (@ tptp.minus_minus_nat N2) K2))))) (@ tptp.set_ord_atMost_nat N2)))) (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (N2 tptp.nat)) (= (@ (@ tptp.power_8040749407984259932d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) B2)) N2) (@ (@ tptp.groups7108830773950497114d_enat (lambda ((K2 tptp.nat)) (@ (@ tptp.times_7803423173614009249d_enat (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.semiri4216267220026989637d_enat (@ (@ tptp.binomial N2) K2))) (@ (@ tptp.power_8040749407984259932d_enat A) K2))) (@ (@ tptp.power_8040749407984259932d_enat B2) (@ (@ tptp.minus_minus_nat N2) K2))))) (@ tptp.set_ord_atMost_nat N2)))) (forall ((A tptp.int) (B2 tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int A) B2)) N2) (@ (@ tptp.groups3539618377306564664at_int (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N2) K2))) (@ (@ tptp.power_power_int A) K2))) (@ (@ tptp.power_power_int B2) (@ (@ tptp.minus_minus_nat N2) K2))))) (@ tptp.set_ord_atMost_nat N2)))) (forall ((A tptp.nat) (B2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat A) B2)) N2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.binomial N2) K2))) (@ (@ tptp.power_power_nat A) K2))) (@ (@ tptp.power_power_nat B2) (@ (@ tptp.minus_minus_nat N2) K2))))) (@ tptp.set_ord_atMost_nat N2)))) (forall ((A tptp.real) (B2 tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real A) B2)) N2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N2) K2))) (@ (@ tptp.power_power_real A) K2))) (@ (@ tptp.power_power_real B2) (@ (@ tptp.minus_minus_nat N2) K2))))) (@ tptp.set_ord_atMost_nat N2)))) (forall ((A tptp.complex) (B2 tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex A) B2)) N2) (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N2) K2))) (@ (@ tptp.comm_s2602460028002588243omplex A) K2))) (@ (@ tptp.comm_s2602460028002588243omplex B2) (@ (@ tptp.minus_minus_nat N2) K2))))) (@ tptp.set_ord_atMost_nat N2)))) (forall ((A tptp.int) (B2 tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int A) B2)) N2) (@ (@ tptp.groups3539618377306564664at_int (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N2) K2))) (@ (@ tptp.comm_s4660882817536571857er_int A) K2))) (@ (@ tptp.comm_s4660882817536571857er_int B2) (@ (@ tptp.minus_minus_nat N2) K2))))) (@ tptp.set_ord_atMost_nat N2)))) (forall ((A tptp.real) (B2 tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real A) B2)) N2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N2) K2))) (@ (@ tptp.comm_s7457072308508201937r_real A) K2))) (@ (@ tptp.comm_s7457072308508201937r_real B2) (@ (@ tptp.minus_minus_nat N2) K2))))) (@ tptp.set_ord_atMost_nat N2)))) (forall ((M2 tptp.nat) (A (-> tptp.nat tptp.nat)) (N2 tptp.nat) (B2 (-> tptp.nat tptp.nat)) (X tptp.nat)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) I4) (= (@ A I4) tptp.zero_zero_nat))) (=> (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) J3) (= (@ B2 J3) 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 X) I3)))) (@ tptp.set_ord_atMost_nat M2))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.times_times_nat (@ B2 J2)) (@ (@ tptp.power_power_nat X) J2)))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((R4 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_nat (@ A K2)) (@ B2 (@ (@ tptp.minus_minus_nat R4) K2))))) (@ tptp.set_ord_atMost_nat R4))) (@ (@ tptp.power_power_nat X) R4)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M2) N2))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.archim6058952711729229775r_real Y)))) (let ((_let_2 (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X) Y)))) (let ((_let_3 (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.archim2898591450579166408c_real X)) (@ tptp.archim2898591450579166408c_real Y))) tptp.one_one_real))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))))) (forall ((P5 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.int)) (H2 (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P5) (=> (@ (@ tptp.ord_less_eq_nat K) P5) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((J2 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_nat J2) K)) (@ G J2)) (@ (@ (@ tptp.if_int (= J2 K)) tptp.zero_zero_int) (@ H2 (@ (@ tptp.minus_minus_nat J2) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P5)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((J2 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_nat J2) K)) (@ G J2)) (@ H2 J2)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P5) (@ tptp.suc tptp.zero_zero_nat)))))))) (forall ((P5 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.complex)) (H2 (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P5) (=> (@ (@ tptp.ord_less_eq_nat K) P5) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((J2 tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_nat J2) K)) (@ G J2)) (@ (@ (@ tptp.if_complex (= J2 K)) tptp.zero_zero_complex) (@ H2 (@ (@ tptp.minus_minus_nat J2) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P5)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((J2 tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_nat J2) K)) (@ G J2)) (@ H2 J2)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P5) (@ tptp.suc tptp.zero_zero_nat)))))))) (forall ((P5 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.extended_enat)) (H2 (-> tptp.nat tptp.extended_enat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P5) (=> (@ (@ tptp.ord_less_eq_nat K) P5) (= (@ (@ tptp.groups7108830773950497114d_enat (lambda ((J2 tptp.nat)) (@ (@ (@ tptp.if_Extended_enat (@ (@ tptp.ord_less_nat J2) K)) (@ G J2)) (@ (@ (@ tptp.if_Extended_enat (= J2 K)) tptp.zero_z5237406670263579293d_enat) (@ H2 (@ (@ tptp.minus_minus_nat J2) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P5)) (@ (@ tptp.groups7108830773950497114d_enat (lambda ((J2 tptp.nat)) (@ (@ (@ tptp.if_Extended_enat (@ (@ tptp.ord_less_nat J2) K)) (@ G J2)) (@ H2 J2)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P5) (@ tptp.suc tptp.zero_zero_nat)))))))) (forall ((P5 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.nat)) (H2 (-> tptp.nat tptp.nat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P5) (=> (@ (@ tptp.ord_less_eq_nat K) P5) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J2 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat J2) K)) (@ G J2)) (@ (@ (@ tptp.if_nat (= J2 K)) tptp.zero_zero_nat) (@ H2 (@ (@ tptp.minus_minus_nat J2) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P5)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J2 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat J2) K)) (@ G J2)) (@ H2 J2)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P5) (@ tptp.suc tptp.zero_zero_nat)))))))) (forall ((P5 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.real)) (H2 (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P5) (=> (@ (@ tptp.ord_less_eq_nat K) P5) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((J2 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_nat J2) K)) (@ G J2)) (@ (@ (@ tptp.if_real (= J2 K)) tptp.zero_zero_real) (@ H2 (@ (@ tptp.minus_minus_nat J2) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P5)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J2 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_nat J2) K)) (@ G J2)) (@ H2 J2)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P5) (@ tptp.suc tptp.zero_zero_nat)))))))) (forall ((P5 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.complex)) (H2 (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P5) (=> (@ (@ tptp.ord_less_eq_nat K) P5) (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((J2 tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_nat J2) K)) (@ G J2)) (@ (@ (@ tptp.if_complex (= J2 K)) tptp.one_one_complex) (@ H2 (@ (@ tptp.minus_minus_nat J2) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P5)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((J2 tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_nat J2) K)) (@ G J2)) (@ H2 J2)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P5) (@ tptp.suc tptp.zero_zero_nat)))))))) (forall ((P5 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.real)) (H2 (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P5) (=> (@ (@ tptp.ord_less_eq_nat K) P5) (= (@ (@ tptp.groups129246275422532515t_real (lambda ((J2 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_nat J2) K)) (@ G J2)) (@ (@ (@ tptp.if_real (= J2 K)) tptp.one_one_real) (@ H2 (@ (@ tptp.minus_minus_nat J2) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P5)) (@ (@ tptp.groups129246275422532515t_real (lambda ((J2 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_nat J2) K)) (@ G J2)) (@ H2 J2)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P5) (@ tptp.suc tptp.zero_zero_nat)))))))) (forall ((P5 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.int)) (H2 (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P5) (=> (@ (@ tptp.ord_less_eq_nat K) P5) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((J2 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_nat J2) K)) (@ G J2)) (@ (@ (@ tptp.if_int (= J2 K)) tptp.one_one_int) (@ H2 (@ (@ tptp.minus_minus_nat J2) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P5)) (@ (@ tptp.groups705719431365010083at_int (lambda ((J2 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_nat J2) K)) (@ G J2)) (@ H2 J2)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P5) (@ tptp.suc tptp.zero_zero_nat)))))))) (forall ((P5 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.nat)) (H2 (-> tptp.nat tptp.nat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P5) (=> (@ (@ tptp.ord_less_eq_nat K) P5) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((J2 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat J2) K)) (@ G J2)) (@ (@ (@ tptp.if_nat (= J2 K)) tptp.one_one_nat) (@ H2 (@ (@ tptp.minus_minus_nat J2) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P5)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((J2 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat J2) K)) (@ G J2)) (@ H2 J2)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P5) (@ tptp.suc tptp.zero_zero_nat)))))))) (forall ((M2 tptp.nat) (A tptp.complex) (X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat M2))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex M2)) A)) K2)) (@ (@ tptp.power_power_complex X) K2))) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat M2) K2))))) _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex (@ tptp.uminus1482373934393186551omplex A)) K2)) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X)) K2))) (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex X) Y)) (@ (@ tptp.minus_minus_nat M2) K2))))) _let_1)))) (forall ((M2 tptp.nat) (A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat M2))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M2)) A)) K2)) (@ (@ tptp.power_power_real X) K2))) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat M2) K2))))) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real (@ tptp.uminus_uminus_real A)) K2)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X)) K2))) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.minus_minus_nat M2) K2))))) _let_1)))) (forall ((N2 tptp.nat) (Z3 tptp.complex) (A tptp.complex)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (= (@ (@ tptp.power_power_complex Z3) 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 Z3) I3)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_complex)))) (forall ((N2 tptp.nat) (Z3 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (= (@ (@ tptp.power_power_int Z3) 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 Z3) I3)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_int)))) (forall ((N2 tptp.nat) (Z3 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (= (@ (@ tptp.power_power_real Z3) 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 Z3) I3)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_real)))) (forall ((X tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_2 (@ tptp.power_power_complex X))) (let ((_let_3 (@ (@ tptp.groups2073611262835488442omplex _let_2) (@ tptp.set_ord_atMost_nat N2)))) (let ((_let_4 (= X tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat)))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 (@ _let_2 (@ tptp.suc N2)))) (@ _let_1 X)))))))))) (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (let ((_let_2 (@ tptp.power_power_real X))) (let ((_let_3 (@ (@ tptp.groups6591440286371151544t_real _let_2) (@ tptp.set_ord_atMost_nat N2)))) (let ((_let_4 (= X tptp.one_one_real))) (and (=> _let_4 (= _let_3 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat)))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_real (@ _let_1 (@ _let_2 (@ tptp.suc N2)))) (@ _let_1 X)))))))))) (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.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 ((M2 tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.gbinomial_complex (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.plus_plus_nat M2) K2))) K2)) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) K2)))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) M2))) (forall ((M2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat M2) K2))) K2)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) K2)))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) M2))) (forall ((M2 tptp.nat) (A tptp.complex) (X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat M2))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex M2)) A)) K2)) (@ (@ tptp.power_power_complex X) K2))) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat M2) K2))))) _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex K2)) A)) tptp.one_one_complex)) K2)) (@ (@ tptp.power_power_complex X) K2))) (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex X) Y)) (@ (@ tptp.minus_minus_nat M2) K2))))) _let_1)))) (forall ((M2 tptp.nat) (A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat M2))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M2)) A)) K2)) (@ (@ tptp.power_power_real X) K2))) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat M2) K2))))) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real K2)) A)) tptp.one_one_real)) K2)) (@ (@ tptp.power_power_real X) K2))) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.minus_minus_nat M2) K2))))) _let_1)))) (forall ((N2 tptp.nat) (A (-> tptp.nat tptp.int)) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ A I3)) (@ (@ tptp.power_power_int X) 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 X) Y)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((J2 tptp.nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ A (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat J2) K2)) tptp.one_one_nat))) (@ (@ tptp.power_power_int Y) K2))) (@ (@ tptp.power_power_int X) J2)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N2) J2))))) (@ tptp.set_ord_lessThan_nat N2))))))) (forall ((N2 tptp.nat) (A (-> tptp.nat tptp.complex)) (X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I3)) (@ (@ tptp.power_power_complex X) 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 X) Y)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((J2 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ A (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat J2) K2)) tptp.one_one_nat))) (@ (@ tptp.power_power_complex Y) K2))) (@ (@ tptp.power_power_complex X) J2)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N2) J2))))) (@ tptp.set_ord_lessThan_nat N2))))))) (forall ((N2 tptp.nat) (A (-> tptp.nat tptp.real)) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ A I3)) (@ (@ tptp.power_power_real X) 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 X) Y)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ A (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat J2) K2)) tptp.one_one_nat))) (@ (@ tptp.power_power_real Y) K2))) (@ (@ tptp.power_power_real X) J2)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N2) J2))))) (@ tptp.set_ord_lessThan_nat N2))))))) (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_nat _let_1) M2))) (= (@ (@ tptp.groups3542108847815614940at_nat (@ tptp.binomial (@ (@ tptp.plus_plus_nat _let_2) tptp.one_one_nat))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.power_power_nat _let_1) _let_2))))) (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.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 ((M8 tptp.real)) (forall ((Z4 tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex Z4))) (=> (@ (@ tptp.ord_less_eq_real M8) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex Z4) I3)))) (@ tptp.set_ord_atMost_nat 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 ((M8 tptp.real)) (forall ((Z4 tptp.real)) (let ((_let_1 (@ tptp.real_V7735802525324610683m_real Z4))) (=> (@ (@ tptp.ord_less_eq_real M8) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real Z4) I3)))) (@ tptp.set_ord_atMost_nat N2)))) (@ (@ tptp.times_times_real E2) (@ (@ tptp.power_power_real _let_1) (@ tptp.suc N2)))))))))) (forall ((N2 tptp.nat) (A (-> tptp.nat tptp.int)) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ A I3)) (@ (@ tptp.power_power_int X) 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 X) Y)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((J2 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) J2)) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J2)) N2))) (@ (@ tptp.power_power_int X) J2)))) (@ tptp.set_ord_lessThan_nat N2))))))) (forall ((N2 tptp.nat) (A (-> tptp.nat tptp.complex)) (X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I3)) (@ (@ tptp.power_power_complex X) 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 X) Y)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((J2 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) J2)) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J2)) N2))) (@ (@ tptp.power_power_complex X) J2)))) (@ tptp.set_ord_lessThan_nat N2))))))) (forall ((N2 tptp.nat) (A (-> tptp.nat tptp.real)) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ A I3)) (@ (@ tptp.power_power_real X) 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 X) Y)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J2 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) J2)) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J2)) N2))) (@ (@ tptp.power_power_real X) J2)))) (@ tptp.set_ord_lessThan_nat N2))))))) (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 ((M2 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)) M2))))) (@ tptp.numeral_numeral_real _let_1))) tptp.zero_zero_real))) _let_116 _let_115 (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (=> (@ tptp.summable_real F) (=> (forall ((D5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))) D5))) (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))))) (= tptp.binomial (lambda ((N tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N) K2))) (let ((_let_2 (@ tptp.ord_less_nat N))) (@ (@ (@ tptp.if_nat (@ _let_2 K2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ _let_2 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K2))) (@ (@ tptp.binomial 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 K2)))))))) (forall ((L tptp.int) (K tptp.int) (N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat M2) 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 M2)))) (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) M2)))))) _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))) (= tptp.semiri1316708129612266289at_nat (lambda ((N tptp.nat)) N)) (= (@ tptp.sin_real tptp.zero_zero_real) tptp.zero_zero_real) (= (@ tptp.sin_complex tptp.zero_zero_complex) tptp.zero_zero_complex) _let_114 (= (@ tptp.sgn_sgn_int tptp.zero_zero_int) tptp.zero_zero_int) _let_113 _let_114 _let_113 (= (@ tptp.sgn_sgn_complex tptp.one_one_complex) tptp.one_one_complex) (= (@ tptp.sgn_sgn_int tptp.one_one_int) tptp.one_one_int) (= (@ tptp.sgn_sgn_real tptp.one_one_real) tptp.one_one_real) (forall ((A tptp.real) (B2 tptp.real)) (= (@ tptp.sgn_sgn_real (@ (@ tptp.divide_divide_real A) B2)) (@ (@ tptp.divide_divide_real (@ tptp.sgn_sgn_real A)) (@ tptp.sgn_sgn_real B2)))) (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.real)) (= (@ tptp.sgn_sgn_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real (@ tptp.sgn_sgn_real A)))) (@ tptp.summable_nat (lambda ((N tptp.nat)) tptp.zero_zero_nat)) (@ tptp.summable_real (lambda ((N tptp.nat)) tptp.zero_zero_real)) (@ tptp.summable_int (lambda ((N tptp.nat)) tptp.zero_zero_int)) (@ tptp.summable_complex (lambda ((N tptp.nat)) tptp.zero_zero_complex)) (forall ((I tptp.nat) (F (-> tptp.nat tptp.nat))) (@ tptp.summable_nat (lambda ((R4 tptp.nat)) (@ (@ (@ tptp.if_nat (= R4 I)) (@ F R4)) tptp.zero_zero_nat)))) (forall ((I tptp.nat) (F (-> tptp.nat tptp.real))) (@ tptp.summable_real (lambda ((R4 tptp.nat)) (@ (@ (@ tptp.if_real (= R4 I)) (@ F R4)) tptp.zero_zero_real)))) (forall ((I tptp.nat) (F (-> tptp.nat tptp.int))) (@ tptp.summable_int (lambda ((R4 tptp.nat)) (@ (@ (@ tptp.if_int (= R4 I)) (@ F R4)) tptp.zero_zero_int)))) (forall ((I tptp.nat) (F (-> tptp.nat tptp.complex))) (@ tptp.summable_complex (lambda ((R4 tptp.nat)) (@ (@ (@ tptp.if_complex (= R4 I)) (@ F R4)) tptp.zero_zero_complex)))) (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 ((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.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.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.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ tptp.sgn_sgn_int A)) (@ _let_1 A)))) (= (@ tptp.cos_real tptp.zero_zero_real) tptp.one_one_real) (= (@ tptp.cos_complex tptp.zero_zero_complex) tptp.one_one_complex) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.sgn_sgn_real B2))) (= (@ (@ tptp.divide_divide_real A) _let_1) (@ (@ tptp.times_times_real A) _let_1)))) (= (@ tptp.semiri1406184849735516958ct_int tptp.zero_zero_nat) tptp.one_one_int) (= (@ tptp.semiri5044797733671781792omplex tptp.zero_zero_nat) tptp.one_one_complex) (= (@ tptp.semiri1408675320244567234ct_nat tptp.zero_zero_nat) tptp.one_one_nat) (= (@ tptp.semiri2265585572941072030t_real tptp.zero_zero_nat) tptp.one_one_real) (forall ((C tptp.real) (F (-> tptp.nat tptp.real))) (= (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N)))) (or (= C tptp.zero_zero_real) (@ tptp.summable_real F)))) (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex))) (= (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N)))) (or (= C tptp.zero_zero_complex) (@ tptp.summable_complex F)))) (forall ((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 ((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 ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (@ tptp.summable_nat (lambda ((R4 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.member_nat R4) A2)) (@ F R4)) tptp.zero_zero_nat))))) (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat A2) (@ tptp.summable_real (lambda ((R4 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.member_nat R4) A2)) (@ F R4)) tptp.zero_zero_real))))) (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat A2) (@ tptp.summable_int (lambda ((R4 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.member_nat R4) A2)) (@ F R4)) tptp.zero_zero_int))))) (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat A2) (@ tptp.summable_complex (lambda ((R4 tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.member_nat R4) A2)) (@ F R4)) tptp.zero_zero_complex))))) (forall ((P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat P)) (@ tptp.summable_nat (lambda ((R4 tptp.nat)) (@ (@ (@ tptp.if_nat (@ P R4)) (@ F R4)) tptp.zero_zero_nat))))) (forall ((P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat P)) (@ tptp.summable_real (lambda ((R4 tptp.nat)) (@ (@ (@ tptp.if_real (@ P R4)) (@ F R4)) tptp.zero_zero_real))))) (forall ((P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat P)) (@ tptp.summable_int (lambda ((R4 tptp.nat)) (@ (@ (@ tptp.if_int (@ P R4)) (@ F R4)) tptp.zero_zero_int))))) (forall ((P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat P)) (@ tptp.summable_complex (lambda ((R4 tptp.nat)) (@ (@ (@ tptp.if_complex (@ P R4)) (@ F R4)) tptp.zero_zero_complex))))) (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.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (= (@ tptp.sgn_sgn_int A) tptp.one_one_int))) (= (@ tptp.semiri1406184849735516958ct_int _let_80) tptp.one_one_int) (= (@ tptp.semiri5044797733671781792omplex _let_80) tptp.one_one_complex) (= (@ tptp.semiri1408675320244567234ct_nat _let_80) tptp.one_one_nat) (= (@ tptp.semiri2265585572941072030t_real _let_80) tptp.one_one_real) (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.semiri4449623510593786356d_enat _let_1) (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.semiri4216267220026989637d_enat _let_1)) (@ tptp.semiri4449623510593786356d_enat 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 ((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)))))) (= (@ tptp.sin_real _let_112) tptp.zero_zero_real) (= (@ tptp.sin_complex _let_110) tptp.zero_zero_complex) (forall ((L tptp.int) (K tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int L))) (= (@ _let_1 (@ (@ tptp.times_times_int K) (@ tptp.sgn_sgn_int R2))) (or (@ _let_1 K) (= R2 tptp.zero_zero_int))))) (forall ((L tptp.int) (R2 tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int L))) (= (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int R2)) K)) (or (@ _let_1 K) (= R2 tptp.zero_zero_int))))) (forall ((L tptp.int) (R2 tptp.int) (K tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int L) (@ tptp.sgn_sgn_int R2))) K) (and (@ (@ tptp.dvd_dvd_int L) K) (=> (= R2 tptp.zero_zero_int) (= K tptp.zero_zero_int))))) (forall ((R2 tptp.int) (L tptp.int) (K tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int R2)) L)) K) (and (@ (@ tptp.dvd_dvd_int L) K) (=> (= R2 tptp.zero_zero_int) (= K tptp.zero_zero_int))))) (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.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ tptp.sgn_sgn_real A) (@ tptp.uminus_uminus_real tptp.one_one_real)))) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.sin_real X))) (let ((_let_2 (@ tptp.cos_real X))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real _let_2) _let_2)) (@ (@ tptp.times_times_real _let_1) _let_1)) tptp.one_one_real)))) (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.sin_complex X))) (let ((_let_2 (@ tptp.cos_complex X))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex _let_2) _let_2)) (@ (@ tptp.times_times_complex _let_1) _let_1)) tptp.one_one_complex)))) (forall ((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 ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.cos_real X)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.sin_real X)) _let_1)) tptp.one_one_real))) (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.cos_complex X)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.sin_complex X)) _let_1)) tptp.one_one_complex))) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.sin_real X)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.cos_real X)) _let_1)) tptp.one_one_real))) (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.sin_complex X)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.cos_complex X)) _let_1)) tptp.one_one_complex))) (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real _let_112) _let_111)) tptp.zero_zero_real) (= (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex _let_110) _let_109)) tptp.zero_zero_complex) (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.sin_real Y))))) (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.sin_complex (@ (@ tptp.plus_plus_complex X) Y)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.sin_complex X)) (@ tptp.cos_complex Y))) (@ (@ tptp.times_times_complex (@ tptp.cos_complex X)) (@ tptp.sin_complex Y))))) (forall ((X tptp.real)) (=> (= (@ tptp.cos_real X) tptp.one_one_real) (= (@ tptp.sin_real X) tptp.zero_zero_real))) (forall ((X tptp.complex)) (=> (= (@ tptp.cos_complex X) tptp.one_one_complex) (= (@ tptp.sin_complex X) tptp.zero_zero_complex))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.semiri1408675320244567234ct_nat N2))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat M2)) (@ tptp.semiri1408675320244567234ct_nat N2)))) (forall ((A tptp.real)) (= (= (@ tptp.sgn_sgn_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((A tptp.int)) (= (= (@ tptp.sgn_sgn_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))) (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.int)) (= (= (@ tptp.sgn_sgn_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))) (forall ((X tptp.real)) (= (= (@ tptp.sgn_sgn_real X) tptp.zero_zero_real) (= X tptp.zero_zero_real))) (forall ((X tptp.complex)) (= (= (@ tptp.sgn_sgn_complex X) tptp.zero_zero_complex) (= X tptp.zero_zero_complex))) (forall ((A tptp.int) (B2 tptp.int)) (= (@ tptp.sgn_sgn_int (@ (@ tptp.times_times_int A) B2)) (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int A)) (@ tptp.sgn_sgn_int B2)))) (forall ((A tptp.real) (B2 tptp.real)) (= (@ tptp.sgn_sgn_real (@ (@ tptp.times_times_real A) B2)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real A)) (@ tptp.sgn_sgn_real B2)))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (@ tptp.sgn_sgn_complex (@ (@ tptp.times_times_complex A) B2)) (@ (@ tptp.times_times_complex (@ tptp.sgn_sgn_complex A)) (@ tptp.sgn_sgn_complex B2)))) (forall ((B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.sgn_sgn_int A))) (=> (= (@ tptp.sgn_sgn_int B2) _let_1) (= (@ tptp.sgn_sgn_int (@ (@ tptp.plus_plus_int A) B2)) _let_1)))) (forall ((B2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.sgn_sgn_real A))) (=> (= (@ tptp.sgn_sgn_real B2) _let_1) (= (@ tptp.sgn_sgn_real (@ (@ tptp.plus_plus_real A) B2)) _let_1)))) (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri1406184849735516958ct_int N2) tptp.zero_zero_int))) (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri5044797733671781792omplex N2) tptp.zero_zero_complex))) (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri4449623510593786356d_enat N2) tptp.zero_z5237406670263579293d_enat))) (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri1408675320244567234ct_nat N2) tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri2265585572941072030t_real N2) tptp.zero_zero_real))) (forall ((C tptp.real)) (= (@ tptp.summable_real (lambda ((Uu3 tptp.nat)) C)) (= C tptp.zero_zero_real))) (forall ((C tptp.complex)) (= (@ tptp.summable_complex (lambda ((Uu3 tptp.nat)) C)) (= C tptp.zero_zero_complex))) (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (exists ((N8 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F N3))) (@ G N3))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real F)))) (forall ((F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.real))) (=> (exists ((N8 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N3))) (@ G N3))))) (=> (@ tptp.summable_real G) (@ tptp.summable_complex F)))) (forall ((G (-> tptp.nat tptp.real)) (N6 tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real G) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N6) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F N3))) (@ G N3)))) (@ tptp.summable_real F)))) (forall ((G (-> tptp.nat tptp.real)) (N6 tptp.nat) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_real G) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N6) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N3))) (@ G N3)))) (@ tptp.summable_complex F)))) (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)) (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 ((X tptp.real) (Y tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real X) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.sin_real Y))))) (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.cos_complex (@ (@ tptp.minus_minus_complex X) Y)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.cos_complex X)) (@ tptp.cos_complex Y))) (@ (@ tptp.times_times_complex (@ tptp.sin_complex X)) (@ tptp.sin_complex Y))))) (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.sin_real Y))))) (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex X) Y)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex (@ tptp.cos_complex X)) (@ tptp.cos_complex Y))) (@ (@ tptp.times_times_complex (@ tptp.sin_complex X)) (@ tptp.sin_complex Y))))) (forall ((F (-> tptp.nat tptp.real))) (= (@ tptp.summable_real (lambda ((N tptp.nat)) (@ F (@ tptp.suc N)))) (@ tptp.summable_real F))) (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (=> (@ tptp.summable_real F) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N) K)))))) (forall ((X tptp.real)) (=> (= (@ tptp.sin_real X) tptp.zero_zero_real) (= (@ tptp.real_V7735802525324610683m_real (@ tptp.cos_real X)) tptp.one_one_real))) (forall ((X tptp.complex)) (=> (= (@ tptp.sin_complex X) tptp.zero_zero_complex) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.cos_complex X)) tptp.one_one_real))) (forall ((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 ((N6 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat N6) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N6)) (= (@ F N3) tptp.zero_zero_nat))) (@ tptp.summable_nat F)))) (forall ((N6 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat N6) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N6)) (= (@ F N3) tptp.zero_zero_real))) (@ tptp.summable_real F)))) (forall ((N6 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat N6) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N6)) (= (@ F N3) tptp.zero_zero_int))) (@ tptp.summable_int F)))) (forall ((N6 tptp.set_nat) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat N6) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N6)) (= (@ F N3) tptp.zero_zero_complex))) (@ tptp.summable_complex F)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_nat M2) N2) (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat M2)) (@ tptp.semiri1408675320244567234ct_nat N2))))) (forall ((B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.sgn_sgn_int B2))) (let ((_let_2 (@ tptp.sgn_sgn_int A))) (=> (not (= _let_1 _let_2)) (=> (not (= _let_2 tptp.zero_zero_int)) (=> (not (= _let_1 tptp.zero_zero_int)) (= _let_2 (@ tptp.uminus_uminus_int _let_1)))))))) (forall ((B2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.sgn_sgn_real B2))) (let ((_let_2 (@ tptp.sgn_sgn_real A))) (=> (not (= _let_1 _let_2)) (=> (not (= _let_2 tptp.zero_zero_real)) (=> (not (= _let_1 tptp.zero_zero_real)) (= _let_2 (@ tptp.uminus_uminus_real _let_1)))))))) (= (@ tptp.sgn_sgn_complex _let_108) _let_108) (= (@ tptp.sgn_sgn_int _let_107) _let_107) (= (@ tptp.sgn_sgn_real _let_106) _let_106) (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)) (@ (@ 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)) (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 ((K tptp.int)) (not (forall ((N3 tptp.nat) (L4 tptp.int)) (not (= K (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int L4)) (@ tptp.semiri1314217659103216013at_int N3))))))) (forall ((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 ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1406184849735516958ct_int M2)) (@ tptp.semiri1406184849735516958ct_int N2)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat M2)) (@ tptp.semiri1408675320244567234ct_nat N2)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri2265585572941072030t_real M2)) (@ tptp.semiri2265585572941072030t_real N2)))) (forall ((C tptp.real) (F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N)))) (=> (not (= C tptp.zero_zero_real)) (@ tptp.summable_real F)))) (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N)))) (=> (not (= C tptp.zero_zero_complex)) (@ tptp.summable_complex F)))) (forall ((N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (@ (@ tptp.dvd_dvd_int (@ tptp.semiri1406184849735516958ct_int N2)) (@ tptp.semiri1406184849735516958ct_int M2)))) (forall ((N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (@ (@ tptp.dvd_dvd_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ tptp.semiri1408675320244567234ct_nat M2)))) (forall ((N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (@ (@ tptp.dvd_dvd_real (@ tptp.semiri2265585572941072030t_real N2)) (@ tptp.semiri2265585572941072030t_real M2)))) (@ tptp.summable_real _let_105) (@ tptp.summable_complex _let_104) (@ tptp.summable_int _let_103) (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)) (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.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.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.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.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 ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.semiri1408675320244567234ct_nat N2))) (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.int)) (= (= (@ tptp.sgn_sgn_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) M2) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.dvd_dvd_nat M2) (@ tptp.semiri1408675320244567234ct_nat N2))))) (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.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.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)) (Z3 tptp.real)) (= (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_real Z3) N)))) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z3) N)))))) (forall ((F (-> tptp.nat tptp.complex)) (Z3 tptp.complex)) (= (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_complex Z3) N)))) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z3) N)))))) (forall ((F (-> tptp.nat tptp.real)) (Z3 tptp.real)) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z3) N)))) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_real Z3) N)))))) (forall ((F (-> tptp.nat tptp.complex)) (Z3 tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z3) N)))) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_complex Z3) N)))))) (forall ((F (-> tptp.nat tptp.real)) (M2 tptp.nat) (Z3 tptp.real)) (= (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ (@ tptp.plus_plus_nat N) M2))) (@ (@ tptp.power_power_real Z3) N)))) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z3) N)))))) (forall ((F (-> tptp.nat tptp.complex)) (M2 tptp.nat) (Z3 tptp.complex)) (= (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ (@ tptp.plus_plus_nat N) M2))) (@ (@ tptp.power_power_complex Z3) N)))) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z3) N)))))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_nat M2) N2) (@ (@ tptp.ord_less_int (@ tptp.semiri1406184849735516958ct_int M2)) (@ tptp.semiri1406184849735516958ct_int N2))))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_nat M2) N2) (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat M2)) (@ tptp.semiri1408675320244567234ct_nat N2))))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_nat M2) N2) (@ (@ tptp.ord_less_real (@ tptp.semiri2265585572941072030t_real M2)) (@ tptp.semiri2265585572941072030t_real N2))))) (forall ((W2 tptp.complex) (Z3 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.sin_complex W2)) (@ tptp.sin_complex Z3)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.cos_complex (@ (@ tptp.minus_minus_complex W2) Z3))) (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex W2) Z3)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) (forall ((W2 tptp.real) (Z3 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.sin_real W2)) (@ tptp.sin_real Z3)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.cos_real (@ (@ tptp.minus_minus_real W2) Z3))) (@ tptp.cos_real (@ (@ tptp.plus_plus_real W2) Z3)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (forall ((W2 tptp.complex) (Z3 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.sin_complex W2)) (@ tptp.cos_complex Z3)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.sin_complex (@ (@ tptp.plus_plus_complex W2) Z3))) (@ tptp.sin_complex (@ (@ tptp.minus_minus_complex W2) Z3)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) (forall ((W2 tptp.real) (Z3 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.sin_real W2)) (@ tptp.cos_real Z3)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real W2) Z3))) (@ tptp.sin_real (@ (@ tptp.minus_minus_real W2) Z3)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (forall ((W2 tptp.complex) (Z3 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.cos_complex W2)) (@ tptp.sin_complex Z3)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.sin_complex (@ (@ tptp.plus_plus_complex W2) Z3))) (@ tptp.sin_complex (@ (@ tptp.minus_minus_complex W2) Z3)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) (forall ((W2 tptp.real) (Z3 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.cos_real W2)) (@ tptp.sin_real Z3)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real W2) Z3))) (@ tptp.sin_real (@ (@ tptp.minus_minus_real W2) Z3)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (forall ((W2 tptp.complex) (Z3 tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ tptp.sin_complex W2)) (@ tptp.sin_complex Z3)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_1) (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex W2) Z3)) _let_1)))) (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex W2) Z3)) _let_1)))))) (forall ((W2 tptp.real) (Z3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ tptp.sin_real W2)) (@ tptp.sin_real Z3)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_1) (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real W2) Z3)) _let_1)))) (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real W2) Z3)) _let_1)))))) (forall ((W2 tptp.complex) (Z3 tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_complex (@ tptp.sin_complex W2)) (@ tptp.sin_complex Z3)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_1) (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex W2) Z3)) _let_1)))) (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex W2) Z3)) _let_1)))))) (forall ((W2 tptp.real) (Z3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_real (@ tptp.sin_real W2)) (@ tptp.sin_real Z3)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_1) (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real W2) Z3)) _let_1)))) (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real W2) Z3)) _let_1)))))) (forall ((W2 tptp.complex) (Z3 tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_complex (@ tptp.cos_complex W2)) (@ tptp.cos_complex Z3)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_1) (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex W2) Z3)) _let_1)))) (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex Z3) W2)) _let_1)))))) (forall ((W2 tptp.real) (Z3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_real (@ tptp.cos_real W2)) (@ tptp.cos_real Z3)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_1) (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real W2) Z3)) _let_1)))) (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real Z3) W2)) _let_1)))))) (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 ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1406184849735516958ct_int N2)) (@ tptp.semiri1406184849735516958ct_int M2)) tptp.zero_zero_int))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ tptp.semiri1408675320244567234ct_nat M2)) tptp.zero_zero_nat))) (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 ((F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.real))) (=> (exists ((N8 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N3))) (@ G N3))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F N))))))) (forall ((F (-> tptp.nat tptp.real)) (I tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.summable_real F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N3))) (=> (@ _let_1 (@ F I)) (@ _let_1 (@ tptp.suminf_real F))))))) (forall ((F (-> tptp.nat tptp.nat)) (I tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N3))) (=> (@ _let_1 (@ F I)) (@ _let_1 (@ tptp.suminf_nat F))))))) (forall ((F (-> tptp.nat tptp.int)) (I tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ tptp.summable_int F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N3))) (=> (@ _let_1 (@ F I)) (@ _let_1 (@ tptp.suminf_int F))))))) (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 ((X tptp.real)) (= (@ tptp.uminus_uminus_real (@ tptp.sin_real X)) (@ tptp.cos_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))) (forall ((X tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ tptp.sin_complex X)) (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))) (forall ((F (-> tptp.nat tptp.int)) (X 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))) X)) (@ (@ tptp.ord_less_eq_int (@ tptp.suminf_int F)) X)))) (forall ((F (-> tptp.nat tptp.nat)) (X tptp.nat)) (=> (@ tptp.summable_nat F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat N3))) X)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suminf_nat F)) X)))) (forall ((F (-> tptp.nat tptp.real)) (X tptp.real)) (=> (@ tptp.summable_real F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N3))) X)) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real F)) X)))) (forall ((N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.suc M2))) (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 M2) N2)))))))) (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.real)) (= (= (@ tptp.sgn_sgn_real A) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))) _let_102 _let_101 (= 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 ((R2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat R2) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N2) R2)))) (@ (@ tptp.power_power_nat N2) R2)))) (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 ((F (-> tptp.nat tptp.int)) (X 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))) X)) (@ tptp.summable_int F)))) (forall ((F (-> tptp.nat tptp.nat)) (X 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))) X)) (@ tptp.summable_nat F)))) (forall ((F (-> tptp.nat tptp.real)) (X 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))) X)) (@ tptp.summable_real F)))) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.real_V7735802525324610683m_real (@ tptp.sgn_sgn_real X)))) (let ((_let_2 (= X tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))) (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex (@ tptp.sgn_sgn_complex X)))) (let ((_let_2 (= X tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))) (forall ((A (-> tptp.nat tptp.int)) (B 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))) B)) (@ tptp.summable_int A)))) (forall ((A (-> tptp.nat tptp.nat)) (B 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))) B)) (@ tptp.summable_nat A)))) (forall ((A (-> tptp.nat tptp.real)) (B 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))) B)) (@ tptp.summable_real A)))) (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 ((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 ((N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (= (@ tptp.semiri1408675320244567234ct_nat M2) (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc N2)) M2)))))) (forall ((X tptp.real) (M2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.plus_plus_real X))) (= (@ tptp.sin_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M2))) tptp.pi)) _let_1))) (@ tptp.cos_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M2)) tptp.pi)) _let_1))))))) (forall ((F (-> tptp.nat tptp.int)) (I6 tptp.set_nat)) (=> (@ tptp.summable_int F) (=> (@ tptp.finite_finite_nat I6) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.member_nat N3) (@ tptp.uminus5710092332889474511et_nat I6)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N3)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) I6)) (@ tptp.suminf_int F)))))) (forall ((F (-> tptp.nat tptp.nat)) (I6 tptp.set_nat)) (=> (@ tptp.summable_nat F) (=> (@ tptp.finite_finite_nat I6) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.member_nat N3) (@ tptp.uminus5710092332889474511et_nat I6)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F) I6)) (@ tptp.suminf_nat F)))))) (forall ((F (-> tptp.nat tptp.real)) (I6 tptp.set_nat)) (=> (@ tptp.summable_real F) (=> (@ tptp.finite_finite_nat I6) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.member_nat N3) (@ tptp.uminus5710092332889474511et_nat I6)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N3)))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real F) I6)) (@ tptp.suminf_real F)))))) (forall ((X tptp.real) (M2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.plus_plus_real X))) (= (@ tptp.cos_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M2))) tptp.pi)) _let_1))) (@ tptp.uminus_uminus_real (@ tptp.sin_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M2)) tptp.pi)) _let_1)))))))) (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))))))) (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) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (= (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat M2)) (@ tptp.semiri1408675320244567234ct_nat N2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat)) M2))))) (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat)) (=> (@ tptp.summable_int F) (=> (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M3) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F M3)))) (@ (@ 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 ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M3) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F M3)))) (@ (@ 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 ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M3) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F M3)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N2))) (@ tptp.suminf_real F))))) (forall ((F (-> tptp.nat tptp.real)) (Z3 tptp.real)) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z3) N)))) (= (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z3) 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 Z3) N))))) Z3))))) (forall ((F (-> tptp.nat tptp.complex)) (Z3 tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z3) N)))) (= (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z3) 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 Z3) N))))) Z3))))) (forall ((F (-> tptp.nat tptp.real)) (Z3 tptp.real)) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z3) N)))) (= (@ (@ tptp.times_times_real (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_real Z3) N))))) Z3) (@ (@ tptp.minus_minus_real (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z3) N))))) (@ F tptp.zero_zero_nat))))) (forall ((F (-> tptp.nat tptp.complex)) (Z3 tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z3) N)))) (= (@ (@ tptp.times_times_complex (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_complex Z3) N))))) Z3) (@ (@ tptp.minus_minus_complex (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z3) N))))) (@ F tptp.zero_zero_nat))))) (forall ((F (-> tptp.nat tptp.complex)) (E2 tptp.real)) (=> (@ tptp.summable_complex F) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (not (forall ((N9 tptp.nat)) (not (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N9) M5) (forall ((N7 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex F) (@ (@ tptp.set_or1269000886237332187st_nat M5) N7)))) 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 ((N9 tptp.nat)) (not (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N9) M5) (forall ((N7 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.groups6591440286371151544t_real F) (@ (@ tptp.set_or1269000886237332187st_nat M5) N7)))) E2)))))))))) (forall ((R2 tptp.real) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (=> (@ tptp.summable_real F) (exists ((N9 tptp.nat)) (forall ((N7 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N9) N7) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ tptp.suminf_real (lambda ((I3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I3) N7)))))) R2))))))) (forall ((R2 tptp.real) (F (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (=> (@ tptp.summable_complex F) (exists ((N9 tptp.nat)) (forall ((N7 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N9) N7) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ tptp.suminf_complex (lambda ((I3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I3) N7)))))) R2))))))) (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)))))) (forall ((X tptp.real)) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)) (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1))))) (@ tptp.sin_real X))) (= tptp.semiri5044797733671781792omplex (lambda ((M tptp.nat)) (@ (@ (@ tptp.if_complex (= M tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex M)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)))))) (= tptp.semiri4449623510593786356d_enat (lambda ((M tptp.nat)) (@ (@ (@ tptp.if_Extended_enat (= M tptp.zero_zero_nat)) tptp.one_on7984719198319812577d_enat) (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.semiri4216267220026989637d_enat M)) (@ tptp.semiri4449623510593786356d_enat (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)))))) (= tptp.semiri1406184849735516958ct_int (lambda ((M tptp.nat)) (@ (@ (@ tptp.if_int (= M tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)))))) (= tptp.semiri1408675320244567234ct_nat (lambda ((M tptp.nat)) (@ (@ (@ tptp.if_nat (= M tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)))))) (= tptp.semiri2265585572941072030t_real (lambda ((M tptp.nat)) (@ (@ (@ tptp.if_real (= M tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat M) 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.semiri4449623510593786356d_enat N2) (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.semiri4216267220026989637d_enat N2)) (@ tptp.semiri4449623510593786356d_enat (@ (@ 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 ((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 ((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 ((W2 tptp.complex) (Z3 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.cos_complex W2)) (@ tptp.cos_complex Z3)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.cos_complex (@ (@ tptp.minus_minus_complex W2) Z3))) (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex W2) Z3)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) (forall ((W2 tptp.real) (Z3 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.cos_real W2)) (@ tptp.cos_real Z3)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.cos_real (@ (@ tptp.minus_minus_real W2) Z3))) (@ tptp.cos_real (@ (@ tptp.plus_plus_real W2) Z3)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (forall ((W2 tptp.complex) (Z3 tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ tptp.cos_complex W2)) (@ tptp.cos_complex Z3)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_1) (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex W2) Z3)) _let_1)))) (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex W2) Z3)) _let_1)))))) (forall ((W2 tptp.real) (Z3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ tptp.cos_real W2)) (@ tptp.cos_real Z3)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_1) (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real W2) Z3)) _let_1)))) (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real W2) Z3)) _let_1)))))) (forall ((C tptp.real) (N6 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 N6) 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) (N6 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 N6) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F (@ tptp.suc N3)))) (@ (@ tptp.times_times_real C) (@ tptp.real_V1022390504157884413omplex (@ F N3)))))) (@ tptp.summable_complex F)))) (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat) (I tptp.nat)) (=> (@ tptp.summable_int F) (=> (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M3) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F M3)))) (=> (@ (@ tptp.ord_less_eq_nat N2) I) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F I)) (@ (@ 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) (I tptp.nat)) (=> (@ tptp.summable_nat F) (=> (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M3) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F M3)))) (=> (@ (@ tptp.ord_less_eq_nat N2) I) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I)) (@ (@ 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) (I tptp.nat)) (=> (@ tptp.summable_real F) (=> (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M3) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F M3)))) (=> (@ (@ tptp.ord_less_eq_nat N2) I) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N2))) (@ tptp.suminf_real F))))))) (= tptp.gbinomial_complex (lambda ((A3 tptp.complex) (K2 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex A3) (@ tptp.semiri8010041392384452111omplex K2))) tptp.one_one_complex)) K2)) (@ tptp.semiri5044797733671781792omplex K2)))) (= tptp.gbinomial_real (lambda ((A3 tptp.real) (K2 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A3) (@ tptp.semiri5074537144036343181t_real K2))) tptp.one_one_real)) K2)) (@ tptp.semiri2265585572941072030t_real K2)))) (forall ((X tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.nat tptp.real))) (=> (= X tptp.zero_zero_real) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M) tptp.zero_zero_nat)) (@ tptp.semiri2265585572941072030t_real M))) (@ (@ tptp.power_power_real X) M)))) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_nat))))) (forall ((X tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real))) (=> (= X tptp.zero_zero_real) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M))) (@ (@ tptp.power_power_real X) M)))) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_real))))) (forall ((X tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.int tptp.real))) (=> (= X tptp.zero_zero_real) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M) tptp.zero_zero_int)) (@ tptp.semiri2265585572941072030t_real M))) (@ (@ tptp.power_power_real X) M)))) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_int))))) (forall ((X tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.complex tptp.real))) (=> (= X tptp.zero_zero_real) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M) tptp.zero_zero_complex)) (@ tptp.semiri2265585572941072030t_real M))) (@ (@ tptp.power_power_real X) M)))) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_complex))))) (forall ((X tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.extended_enat tptp.real))) (=> (= X tptp.zero_zero_real) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M) tptp.zero_z5237406670263579293d_enat)) (@ tptp.semiri2265585572941072030t_real M))) (@ (@ tptp.power_power_real X) M)))) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_z5237406670263579293d_enat))))) (forall ((X tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_real T6) X) (= (@ tptp.cos_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M)) (@ (@ tptp.power_power_real X) M)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real T6) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N2))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2))))))))) (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_real X) T6) (@ (@ tptp.ord_less_real T6) tptp.zero_zero_real) (= (@ tptp.cos_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M)) (@ (@ tptp.power_power_real X) M)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real T6) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N2))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2))))))))) (forall ((N2 tptp.nat)) (=> (@ (@ 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 ((A tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_real A) _let_1) (@ (@ tptp.divide_divide_real (@ (@ tptp.groups129246275422532515t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_real A) (@ tptp.semiri5074537144036343181t_real I3)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri2265585572941072030t_real _let_1))))) (forall ((A tptp.int) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_int A) _let_1) (@ (@ tptp.divide_divide_int (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_int A) (@ tptp.semiri1314217659103216013at_int I3)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri1406184849735516958ct_int _let_1))))) (forall ((A tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_nat A) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_nat A) (@ tptp.semiri1316708129612266289at_nat I3)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri1408675320244567234ct_nat _let_1))))) (forall ((L tptp.int) (K tptp.int) (N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.divide_divide_nat M2) 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 M2))) (@ (@ 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) M2)))))))))))))))))) (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_real T6) X) (= (@ tptp.sin_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M)) (@ (@ tptp.power_power_real X) M)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T6) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N2))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2))))))))) _let_100 _let_99 (forall ((X tptp.complex) (Y tptp.complex)) (@ (@ tptp.sums_complex (lambda ((P6 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 P6) (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 P6) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P6) N))))) (@ tptp.semiri2265585572941072030t_real P6)))) (@ (@ tptp.power_power_complex X) N))) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat P6) N)))) tptp.zero_zero_complex))))) (@ tptp.set_ord_atMost_nat P6)))) (@ (@ tptp.times_times_complex (@ tptp.sin_complex X)) (@ tptp.sin_complex Y)))) (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.sums_real (lambda ((P6 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 P6) (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 P6) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P6) N))))) (@ tptp.semiri2265585572941072030t_real P6)))) (@ (@ tptp.power_power_real X) N))) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat P6) N)))) tptp.zero_zero_real))))) (@ tptp.set_ord_atMost_nat P6)))) (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.sin_real Y)))) (forall ((X tptp.complex) (Y tptp.complex)) (@ (@ tptp.sums_complex (lambda ((P6 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) P6)) (@ (@ 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 P6) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P6) N))))) (@ tptp.semiri2265585572941072030t_real P6))) (@ (@ tptp.power_power_complex X) N))) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat P6) N)))) tptp.zero_zero_complex)))) (@ tptp.set_ord_atMost_nat P6)))) (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex X) Y)))) (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.sums_real (lambda ((P6 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) P6)) (@ (@ 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 P6) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P6) N))))) (@ tptp.semiri2265585572941072030t_real P6))) (@ (@ tptp.power_power_real X) N))) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat P6) N)))) tptp.zero_zero_real)))) (@ tptp.set_ord_atMost_nat P6)))) (@ tptp.cos_real (@ (@ tptp.plus_plus_real X) Y)))) (forall ((X tptp.complex) (Y tptp.complex)) (@ (@ tptp.sums_complex (lambda ((P6 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 P6) (@ _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 P6) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P6) N))))) (@ tptp.semiri2265585572941072030t_real P6))) (@ (@ tptp.power_power_complex X) N))) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat P6) N)))) tptp.zero_zero_complex))))) (@ tptp.set_ord_atMost_nat P6)))) (@ (@ tptp.times_times_complex (@ tptp.cos_complex X)) (@ tptp.cos_complex Y)))) (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.sums_real (lambda ((P6 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 P6) (@ _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 P6) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P6) N))))) (@ tptp.semiri2265585572941072030t_real P6))) (@ (@ tptp.power_power_real X) N))) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat P6) N)))) tptp.zero_zero_real))))) (@ tptp.set_ord_atMost_nat P6)))) (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.cos_real Y)))) _let_98 (forall ((A tptp.real) (X tptp.real) (B2 tptp.real)) (= (= (@ (@ tptp.real_V1485227260804924795R_real A) X) (@ (@ tptp.real_V1485227260804924795R_real B2) X)) (or (= A B2) (= X tptp.zero_zero_real)))) (forall ((A tptp.real) (X tptp.complex) (B2 tptp.real)) (= (= (@ (@ tptp.real_V2046097035970521341omplex A) X) (@ (@ tptp.real_V2046097035970521341omplex B2) X)) (or (= A B2) (= X tptp.zero_zero_complex)))) (forall ((A tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real A) tptp.zero_zero_real) tptp.zero_zero_real)) (forall ((A tptp.real)) (= (@ (@ tptp.real_V2046097035970521341omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)) (forall ((A tptp.real) (X tptp.real)) (= (= (@ (@ tptp.real_V1485227260804924795R_real A) X) tptp.zero_zero_real) (or (= A tptp.zero_zero_real) (= X tptp.zero_zero_real)))) (forall ((A tptp.real) (X tptp.complex)) (= (= (@ (@ tptp.real_V2046097035970521341omplex A) X) tptp.zero_zero_complex) (or (= A tptp.zero_zero_real) (= X tptp.zero_zero_complex)))) (forall ((X tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real tptp.zero_zero_real) X) tptp.zero_zero_real)) (forall ((X tptp.complex)) (= (@ (@ tptp.real_V2046097035970521341omplex tptp.zero_zero_real) X) tptp.zero_zero_complex)) (forall ((B2 tptp.real) (U tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real U))) (= (= (@ (@ tptp.plus_plus_real B2) (@ _let_1 A)) (@ (@ tptp.plus_plus_real A) (@ _let_1 B2))) (or (= A B2) (= U tptp.one_one_real))))) (= (@ tptp.sin_coeff tptp.zero_zero_nat) tptp.zero_zero_real) (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 ((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 ((X tptp.real) (A tptp.real) (B2 tptp.real)) (=> (not (= X tptp.zero_zero_real)) (=> (= (@ (@ tptp.real_V1485227260804924795R_real A) X) (@ (@ tptp.real_V1485227260804924795R_real B2) X)) (= A B2)))) (forall ((X tptp.complex) (A tptp.real) (B2 tptp.real)) (=> (not (= X tptp.zero_zero_complex)) (=> (= (@ (@ tptp.real_V2046097035970521341omplex A) X) (@ (@ tptp.real_V2046097035970521341omplex B2) X)) (= A B2)))) (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.plus_plus_real (@ _let_1 X)) (@ _let_1 Y))))) (forall ((X tptp.real) (Y tptp.real) (Xa2 tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.plus_plus_real X) Y)) Xa2) (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real X) Xa2)) (@ (@ tptp.real_V1485227260804924795R_real Y) Xa2)))) (forall ((A tptp.real) (B2 tptp.real) (X tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.plus_plus_real A) B2)) X) (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real A) X)) (@ (@ tptp.real_V1485227260804924795R_real B2) X)))) (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B2) A) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) C)) (@ (@ tptp.real_V1485227260804924795R_real B2) C))))) (forall ((A tptp.real) (B2 tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) X)) (@ (@ tptp.real_V1485227260804924795R_real B2) X))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real C))) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B2)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B2)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B2) A)))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real C))) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_real B2) A))))) (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real C))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_real A) B2))))) (forall ((X tptp.real) (Y tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real A))) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y)))))) (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real C))) (=> (@ (@ tptp.ord_less_eq_real B2) A) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B2)))))) (forall ((X tptp.real) (U tptp.real) (V tptp.real) (A tptp.real)) (let ((_let_1 (= V tptp.zero_zero_real))) (= (= X (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.divide_divide_real U) V)) A)) (and (=> _let_1 (= X tptp.zero_zero_real)) (=> (not _let_1) (= (@ (@ tptp.real_V1485227260804924795R_real V) X) (@ (@ tptp.real_V1485227260804924795R_real U) A))))))) (forall ((X tptp.complex) (U tptp.real) (V tptp.real) (A tptp.complex)) (let ((_let_1 (= V tptp.zero_zero_real))) (= (= X (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.divide_divide_real U) V)) A)) (and (=> _let_1 (= X tptp.zero_zero_complex)) (=> (not _let_1) (= (@ (@ tptp.real_V2046097035970521341omplex V) X) (@ (@ tptp.real_V2046097035970521341omplex U) A))))))) (forall ((U tptp.real) (V tptp.real) (A tptp.real) (X tptp.real)) (let ((_let_1 (= V tptp.zero_zero_real))) (= (= (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.divide_divide_real U) V)) A) X) (and (=> _let_1 (= X tptp.zero_zero_real)) (=> (not _let_1) (= (@ (@ tptp.real_V1485227260804924795R_real U) A) (@ (@ tptp.real_V1485227260804924795R_real V) X))))))) (forall ((U tptp.real) (V tptp.real) (A tptp.complex) (X tptp.complex)) (let ((_let_1 (= V tptp.zero_zero_real))) (= (= (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.divide_divide_real U) V)) A) X) (and (=> _let_1 (= X tptp.zero_zero_complex)) (=> (not _let_1) (= (@ (@ tptp.real_V2046097035970521341omplex U) A) (@ (@ tptp.real_V2046097035970521341omplex V) X))))))) (forall ((A tptp.real) (E2 tptp.real) (C tptp.real) (B2 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 B2) E2)) D)) (@ (@ tptp.ord_less_eq_real C) (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.minus_minus_real B2) A)) E2)) D)))) (forall ((A tptp.real) (E2 tptp.real) (C tptp.real) (B2 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 B2) E2)) D)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.minus_minus_real A) B2)) E2)) C)) D))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.real_V1485227260804924795R_real A) B2)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real)) (= A tptp.zero_zero_real))))) (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) B2)) tptp.zero_zero_real) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B2)) (= A tptp.zero_zero_real)))) (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.real_V1485227260804924795R_real A) B2))))) (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) X)) tptp.zero_zero_real)))) (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) X)) tptp.zero_zero_real)))) (forall ((A tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.real_V1485227260804924795R_real A) X)))))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (@ _let_1 A) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real))) (@ _let_1 (@ (@ tptp.real_V1485227260804924795R_real A) B2))))) (forall ((A tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ _let_1 X))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) X)) tptp.zero_zero_real)))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_eq_real C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) C)) (@ (@ tptp.real_V1485227260804924795R_real B2) D)))))))) (forall ((A tptp.real) (B2 tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ _let_1 B2) (=> (@ _let_1 X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) X)) (@ (@ tptp.real_V1485227260804924795R_real B2) Y)))))))) (forall ((X tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) X)) X)))) (forall ((X tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) X) (@ (@ tptp.plus_plus_real X) X))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.sin_coeff _let_1) (@ (@ tptp.divide_divide_real (@ tptp.cos_coeff N2)) (@ tptp.semiri5074537144036343181t_real _let_1))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.cos_coeff _let_1) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real (@ tptp.sin_coeff N2))) (@ tptp.semiri5074537144036343181t_real _let_1))))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ tptp.summable_real (lambda ((K2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K2)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1)))))))) (forall ((C (-> tptp.nat tptp.complex)) (X tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N)) (@ (@ tptp.power_power_complex X) N)))) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N)) (@ C N))) (@ (@ tptp.power_power_complex X) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N)) (@ (@ tptp.power_power_complex X) N))))))) (forall ((C (-> tptp.nat tptp.real)) (X tptp.real)) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N)) (@ (@ tptp.power_power_real X) N)))) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ C N))) (@ (@ tptp.power_power_real X) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N)) (@ (@ tptp.power_power_real X) N))))))) (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_complex X))) (let ((_let_3 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)))) (let ((_let_4 (@ _let_3 X))) (=> (not (= (@ tptp.cos_complex X) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex _let_4) tptp.zero_zero_complex)) (= (@ tptp.tan_complex _let_4) (@ (@ tptp.divide1717551699836669952omplex (@ _let_3 _let_2)) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex _let_2) (@ tptp.numeral_numeral_nat _let_1)))))))))))) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_real X))) (let ((_let_3 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)))) (let ((_let_4 (@ _let_3 X))) (=> (not (= (@ tptp.cos_real X) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real _let_4) tptp.zero_zero_real)) (= (@ tptp.tan_real _let_4) (@ (@ tptp.divide_divide_real (@ _let_3 _let_2)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real _let_2) (@ tptp.numeral_numeral_nat _let_1)))))))))))) _let_97 _let_96 _let_95 (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.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))) _let_94 _let_93 (= (@ tptp.abs_abs_complex tptp.zero_zero_complex) tptp.zero_zero_complex) _let_94 _let_93 (forall ((A tptp.real)) (= (= (@ tptp.abs_abs_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((A tptp.int)) (= (= (@ tptp.abs_abs_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))) (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ tptp.abs_abs_real A)) (= A tptp.zero_zero_real))) (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ tptp.abs_abs_int A)) (= A tptp.zero_zero_int))) (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int A))) (= (@ (@ tptp.times_times_int _let_1) _let_1) (@ (@ tptp.times_times_int A) A)))) (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real A))) (= (@ (@ tptp.times_times_real _let_1) _let_1) (@ (@ tptp.times_times_real A) A)))) _let_92 (= (@ tptp.abs_abs_complex tptp.one_one_complex) tptp.one_one_complex) _let_91 (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B2)))) (= (@ tptp.abs_abs_int _let_1) _let_1))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B2)))) (= (@ tptp.abs_abs_real _let_1) _let_1))) (forall ((A tptp.real) (B2 tptp.real)) (= (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real A) B2)) (@ (@ tptp.divide_divide_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B2)))) (forall ((A tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))) (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))) (forall ((A tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))) (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))) (forall ((M2 tptp.real) (K tptp.real)) (= (@ (@ tptp.dvd_dvd_real (@ tptp.abs_abs_real M2)) K) (@ (@ tptp.dvd_dvd_real M2) K))) (forall ((M2 tptp.int) (K tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.abs_abs_int M2)) K) (@ (@ tptp.dvd_dvd_int M2) K))) (forall ((M2 tptp.real) (K tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real M2))) (= (@ _let_1 (@ tptp.abs_abs_real K)) (@ _let_1 K)))) (forall ((M2 tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int M2))) (= (@ _let_1 (@ tptp.abs_abs_int K)) (@ _let_1 K)))) (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 ((X tptp.int)) (= (@ tptp.ring_1_of_int_int (@ tptp.abs_abs_int X)) (@ tptp.abs_abs_int (@ tptp.ring_1_of_int_int X)))) (forall ((X tptp.int)) (= (@ tptp.ring_1_of_int_real (@ tptp.abs_abs_int X)) (@ tptp.abs_abs_real (@ tptp.ring_1_of_int_real X)))) (= (@ tptp.tan_real tptp.zero_zero_real) tptp.zero_zero_real) (= (@ tptp.tan_complex tptp.zero_zero_complex) tptp.zero_zero_complex) (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n3304061248610475627l_real P))) (= (@ tptp.abs_abs_real _let_1) _let_1))) (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n2684676970156552555ol_int P))) (= (@ tptp.abs_abs_int _let_1) _let_1))) (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A))) (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))) (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) A) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A))) (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) A) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A))) (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int) (= A tptp.zero_zero_int))) (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.abs_abs_real A)) (not (= A tptp.zero_zero_real)))) (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.abs_abs_int A)) (not (= A tptp.zero_zero_int)))) (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.groups4538972089207619220nt_int F) A2))) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I3 tptp.int)) (@ tptp.abs_abs_int (@ F I3)))) A2))) (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.groups6591440286371151544t_real F) A2))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ tptp.abs_abs_real (@ F I3)))) A2))) (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A) (@ tptp.abs_abs_real B2))) tptp.zero_zero_real) (or (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (= B2 tptp.zero_zero_real)))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real A) (@ tptp.abs_abs_real B2))) (or (@ _let_1 A) (= B2 tptp.zero_zero_real))))) (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.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (= (@ tptp.abs_abs_int A) (@ tptp.uminus_uminus_int A)))) (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.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ tptp.abs_abs_int (@ tptp.sgn_sgn_int A)) tptp.one_one_int))) (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.complex)) (= (@ tptp.abs_abs_complex (@ tptp.sgn_sgn_complex A)) (@ tptp.zero_n1201886186963655149omplex (not (= A tptp.zero_zero_complex))))) (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.real)) (= (@ tptp.sgn_sgn_real (@ tptp.abs_abs_real A)) (@ tptp.zero_n3304061248610475627l_real (not (= A tptp.zero_zero_real))))) (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.int)) (= (@ tptp.sgn_sgn_int (@ tptp.abs_abs_int A)) (@ tptp.zero_n2684676970156552555ol_int (not (= A tptp.zero_zero_int))))) (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I3 tptp.int)) (@ tptp.abs_abs_int (@ F I3)))) A2))) (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ tptp.abs_abs_real (@ F I3)))) A2))) (forall ((A tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N2)) (or (not (= A tptp.zero_zero_real)) (= N2 tptp.zero_zero_nat)))) (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N2)) (or (not (= A tptp.zero_zero_int)) (= N2 tptp.zero_zero_nat)))) (forall ((X tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real X)) tptp.one_one_real)) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)))) (forall ((X tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex X)) tptp.one_one_complex)) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)))) (forall ((X tptp.real) (B2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real B2))) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real X)) _let_1)) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X) _let_1))))) (forall ((X tptp.real) (B2 tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex X)) (@ tptp.numera6690914467698888265omplex B2))) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X) (@ tptp.numeral_numeral_real B2))))) (forall ((A tptp.int) (B2 tptp.int)) (= (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) B2)) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int B2) A)))) (forall ((A tptp.real) (B2 tptp.real)) (= (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) B2)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B2) A)))) (forall ((X tptp.int) (Y tptp.int)) (= (= (@ tptp.abs_abs_int X) (@ tptp.abs_abs_int Y)) (or (= X Y) (= X (@ tptp.uminus_uminus_int Y))))) (forall ((X tptp.real) (Y tptp.real)) (= (= (@ tptp.abs_abs_real X) (@ tptp.abs_abs_real Y)) (or (= X Y) (= X (@ tptp.uminus_uminus_real Y))))) (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))) _let_92 _let_91 (forall ((A tptp.int) (B2 tptp.int)) (= (@ tptp.abs_abs_int (@ (@ tptp.times_times_int A) B2)) (@ (@ tptp.times_times_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B2)))) (forall ((A tptp.real) (B2 tptp.real)) (= (@ tptp.abs_abs_real (@ (@ tptp.times_times_real A) B2)) (@ (@ tptp.times_times_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B2)))) (forall ((A tptp.complex) (B2 tptp.complex)) (= (@ tptp.abs_abs_complex (@ (@ tptp.times_times_complex A) B2)) (@ (@ tptp.times_times_complex (@ tptp.abs_abs_complex A)) (@ tptp.abs_abs_complex B2)))) (forall ((A tptp.real)) (= (= (@ tptp.abs_abs_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((A tptp.int)) (= (= (@ tptp.abs_abs_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))) (forall ((A tptp.complex)) (= (= (@ tptp.abs_abs_complex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))) (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) B2) (@ (@ tptp.ord_less_eq_real A) B2))) (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) B2) (@ (@ tptp.ord_less_eq_int A) B2))) (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real A) (@ tptp.abs_abs_real A))) (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) (@ tptp.abs_abs_int A))) (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.abs_abs_real A))) (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.abs_abs_int A))) (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A))) (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))) (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real A)) tptp.zero_zero_real))) (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int))) (forall ((A tptp.real) (B2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real A) B2))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B2)))) (forall ((A tptp.int) (B2 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.plus_plus_int A) B2))) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B2)))) (forall ((A tptp.real) (C tptp.real) (B2 tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real B2))) (let ((_let_2 (@ tptp.abs_abs_real A))) (=> (@ (@ tptp.ord_less_real _let_2) C) (=> (@ (@ tptp.ord_less_real _let_1) D) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real _let_2) _let_1)) (@ (@ tptp.times_times_real C) D))))))) (forall ((A tptp.int) (C tptp.int) (B2 tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int B2))) (let ((_let_2 (@ tptp.abs_abs_int A))) (=> (@ (@ tptp.ord_less_int _let_2) C) (=> (@ (@ tptp.ord_less_int _let_1) D) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int _let_2) _let_1)) (@ (@ tptp.times_times_int C) D))))))) (forall ((A tptp.real) (B2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B2))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B2) A)))) (forall ((A tptp.int) (B2 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B2))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int B2) A)))) (forall ((A tptp.real) (B2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B2)))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) B2)))) (forall ((A tptp.int) (B2 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B2)))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) B2)))) (forall ((A tptp.real) (B2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B2))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) B2)))) (forall ((A tptp.int) (B2 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B2))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) B2)))) (forall ((B2 tptp.real) (A tptp.real)) (=> (not (= B2 tptp.zero_zero_real)) (= (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real A) B2)) (@ (@ tptp.divide_divide_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B2))))) (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))) (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))) (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) B2) (and (@ (@ tptp.ord_less_eq_real A) B2) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) B2)))) (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) B2) (and (@ (@ tptp.ord_less_eq_int A) B2) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) B2)))) (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) B2) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) B2))) (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) B2) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) B2))) (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) B2) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) B2)))) (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) B2) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) B2)))) (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int A)) B2) (and (@ (@ tptp.ord_less_int A) B2) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) B2)))) (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real A)) B2) (and (@ (@ tptp.ord_less_real A) B2) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) B2)))) _let_90 _let_89 (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.abs_abs_int A)) (@ tptp.sgn_sgn_int A)) A)) (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.abs_abs_real A)) (@ tptp.sgn_sgn_real A)) A)) (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.abs_abs_complex A)) (@ tptp.sgn_sgn_complex A)) A)) (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int A)) (@ tptp.abs_abs_int A)) A)) (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real A)) (@ tptp.abs_abs_real A)) A)) (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.sgn_sgn_complex A)) (@ tptp.abs_abs_complex A)) A)) (forall ((X tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int X)) (@ tptp.abs_abs_int X)) X)) (forall ((X tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real X)) (@ tptp.abs_abs_real X)) X)) (forall ((B2 tptp.int) (A tptp.int)) (=> (= (@ tptp.sgn_sgn_int B2) (@ tptp.sgn_sgn_int A)) (= (@ tptp.abs_abs_int (@ (@ tptp.plus_plus_int A) B2)) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B2))))) (forall ((B2 tptp.real) (A tptp.real)) (=> (= (@ tptp.sgn_sgn_real B2) (@ tptp.sgn_sgn_real A)) (= (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real A) B2)) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B2))))) (forall ((X tptp.real)) (=> (forall ((E tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) E))) (= X tptp.zero_zero_real))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.times_times_real (@ tptp.abs_abs_real Y)) X) (@ tptp.abs_abs_real (@ (@ tptp.times_times_real Y) X))))) (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (= (@ (@ tptp.times_times_int (@ tptp.abs_abs_int Y)) X) (@ tptp.abs_abs_int (@ (@ tptp.times_times_int Y) X))))) (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (and (or (@ _let_1 A) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real)) (or (@ _let_1 B2) (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real))) (= (@ tptp.abs_abs_real (@ (@ tptp.times_times_real A) B2)) (@ (@ tptp.times_times_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B2)))))) (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (and (or (@ _let_1 A) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)) (or (@ _let_1 B2) (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int))) (= (@ tptp.abs_abs_int (@ (@ tptp.times_times_int A) B2)) (@ (@ tptp.times_times_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B2)))))) (forall ((A tptp.real) (B2 tptp.real)) (= (= (@ tptp.abs_abs_real A) B2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B2) (or (= A B2) (= A (@ tptp.uminus_uminus_real B2)))))) (forall ((A tptp.int) (B2 tptp.int)) (= (= (@ tptp.abs_abs_int A) B2) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B2) (or (= A B2) (= A (@ tptp.uminus_uminus_int B2)))))) (forall ((A tptp.real) (B2 tptp.real)) (= (= A (@ tptp.abs_abs_real B2)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (or (= B2 A) (= B2 (@ tptp.uminus_uminus_real A)))))) (forall ((A tptp.int) (B2 tptp.int)) (= (= A (@ tptp.abs_abs_int B2)) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (or (= B2 A) (= B2 (@ tptp.uminus_uminus_int A)))))) (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.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.abs_abs_int A))) tptp.zero_zero_int)) (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (= (@ (@ tptp.divide_divide_real (@ tptp.abs_abs_real X)) Y) (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real X) Y))))) (forall ((A tptp.real) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N2))) (forall ((A tptp.int) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N2))) (= tptp.abs_abs_int (lambda ((A3 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int A3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int A3)) A3))) (= tptp.abs_abs_real (lambda ((A3 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A3) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A3)) A3))) (= tptp.abs_abs_int (lambda ((A3 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int A3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int A3)) A3))) (= tptp.abs_abs_real (lambda ((A3 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A3) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A3)) A3))) (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (= (@ tptp.abs_abs_int A) (@ tptp.uminus_uminus_int A)))) (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ tptp.abs_abs_real A) (@ tptp.uminus_uminus_real A)))) (forall ((X tptp.real) (A tptp.real) (R2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) A))) R2) (and (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) R2)) X) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.plus_plus_real A) R2))))) (forall ((X tptp.int) (A tptp.int) (R2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X) A))) R2) (and (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) R2)) X) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.plus_plus_int A) R2))))) (forall ((A tptp.real) (B2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) B2))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B2)))) (forall ((A tptp.int) (B2 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) B2))) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B2)))) (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B2)) (@ (@ tptp.plus_plus_real C) D)))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) C))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B2) D))))) (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B2)) (@ (@ tptp.plus_plus_int C) D)))) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) C))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int B2) D))))) (forall ((X tptp.real) (A tptp.real) (R2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) A))) R2) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) R2)) X) (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real A) R2))))) (forall ((X tptp.int) (A tptp.int) (R2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X) A))) R2) (and (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) R2)) X) (@ (@ tptp.ord_less_int X) (@ (@ tptp.plus_plus_int A) R2))))) (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.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 ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (exists ((N8 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ F N3))) (@ G N3))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.abs_abs_real (@ F N))))))) (forall ((X tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.abs_abs_real X)))) (forall ((X tptp.int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.abs_abs_int X)))) (forall ((N2 tptp.int) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.ring_1_of_int_real N2))) X) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X)))) (forall ((N2 tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ tptp.ring_1_of_int_int N2))) X) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) X)))) (forall ((N2 tptp.int) (X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ tptp.ring_1_of_int_real N2))) X) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_less_real tptp.one_one_real) X)))) (forall ((N2 tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ tptp.ring_1_of_int_int N2))) X) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) X)))) (forall ((A tptp.real) (N2 tptp.nat) (X tptp.real) (B2 tptp.real)) (=> (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real A)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N2)) X) (=> (= X (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real B2)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real B2)) N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= A B2))))) (forall ((Z3 tptp.real) (M2 tptp.int)) (let ((_let_1 (@ tptp.minus_minus_real Z3))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ _let_1 (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real Z3))))) (@ tptp.abs_abs_real (@ _let_1 (@ tptp.ring_1_of_int_real M2)))))) _let_88 _let_87 _let_86 (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) (@ tptp.abs_abs_real Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X)) (@ tptp.abs_abs_int Y)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))))) (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) Y))))) (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X)) Y))))) (forall ((P (-> tptp.real tptp.real Bool)) (X tptp.real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X5) (@ (@ P X5) (@ (@ tptp.power_power_real X5) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P (@ tptp.abs_abs_real X)) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (forall ((P (-> tptp.int tptp.int Bool)) (X tptp.int)) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X5) (@ (@ P X5) (@ (@ tptp.power_power_int X5) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P (@ tptp.abs_abs_int X)) (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real))) (forall ((X tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X)) tptp.one_one_int))) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real))) (forall ((X tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int X)) tptp.one_one_int))) (forall ((N2 tptp.nat) (A tptp.real) (B2 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 B2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B2) N2))))) (forall ((N2 tptp.nat) (A tptp.int) (B2 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 B2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B2) N2))))) (forall ((I6 tptp.set_Extended_enat) (X (-> tptp.extended_enat tptp.real)) (A (-> tptp.extended_enat tptp.real)) (B2 tptp.real) (Delta tptp.real)) (=> (forall ((I4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I4) I6) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X I4)))) (=> (= (@ (@ tptp.groups4148127829035722712t_real X) I6) tptp.one_one_real) (=> (forall ((I4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I4) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A I4)) B2))) Delta))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups4148127829035722712t_real (lambda ((I3 tptp.extended_enat)) (@ (@ tptp.times_times_real (@ A I3)) (@ X I3)))) I6)) B2))) Delta))))) (forall ((I6 tptp.set_real) (X (-> tptp.real tptp.real)) (A (-> tptp.real tptp.real)) (B2 tptp.real) (Delta tptp.real)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X I4)))) (=> (= (@ (@ tptp.groups8097168146408367636l_real X) I6) tptp.one_one_real) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A I4)) B2))) 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)) (@ X I3)))) I6)) B2))) Delta))))) (forall ((I6 tptp.set_set_nat) (X (-> tptp.set_nat tptp.real)) (A (-> tptp.set_nat tptp.real)) (B2 tptp.real) (Delta tptp.real)) (=> (forall ((I4 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat I4) I6) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X I4)))) (=> (= (@ (@ tptp.groups5107569545109728110t_real X) I6) tptp.one_one_real) (=> (forall ((I4 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat I4) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A I4)) B2))) Delta))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups5107569545109728110t_real (lambda ((I3 tptp.set_nat)) (@ (@ tptp.times_times_real (@ A I3)) (@ X I3)))) I6)) B2))) Delta))))) (forall ((I6 tptp.set_int) (X (-> tptp.int tptp.real)) (A (-> tptp.int tptp.real)) (B2 tptp.real) (Delta tptp.real)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X I4)))) (=> (= (@ (@ tptp.groups8778361861064173332t_real X) I6) tptp.one_one_real) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A I4)) B2))) 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)) (@ X I3)))) I6)) B2))) Delta))))) (forall ((I6 tptp.set_Extended_enat) (X (-> tptp.extended_enat tptp.int)) (A (-> tptp.extended_enat tptp.int)) (B2 tptp.int) (Delta tptp.int)) (=> (forall ((I4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I4) I6) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ X I4)))) (=> (= (@ (@ tptp.groups2025484359314973016at_int X) I6) tptp.one_one_int) (=> (forall ((I4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I4) I6) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ A I4)) B2))) Delta))) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.groups2025484359314973016at_int (lambda ((I3 tptp.extended_enat)) (@ (@ tptp.times_times_int (@ A I3)) (@ X I3)))) I6)) B2))) Delta))))) (forall ((I6 tptp.set_real) (X (-> tptp.real tptp.int)) (A (-> tptp.real tptp.int)) (B2 tptp.int) (Delta tptp.int)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ X I4)))) (=> (= (@ (@ tptp.groups1932886352136224148al_int X) I6) tptp.one_one_int) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ A I4)) B2))) Delta))) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.groups1932886352136224148al_int (lambda ((I3 tptp.real)) (@ (@ tptp.times_times_int (@ A I3)) (@ X I3)))) I6)) B2))) Delta))))) (forall ((I6 tptp.set_set_nat) (X (-> tptp.set_nat tptp.int)) (A (-> tptp.set_nat tptp.int)) (B2 tptp.int) (Delta tptp.int)) (=> (forall ((I4 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat I4) I6) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ X I4)))) (=> (= (@ (@ tptp.groups8292507037921071086at_int X) I6) tptp.one_one_int) (=> (forall ((I4 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat I4) I6) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ A I4)) B2))) Delta))) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.groups8292507037921071086at_int (lambda ((I3 tptp.set_nat)) (@ (@ tptp.times_times_int (@ A I3)) (@ X I3)))) I6)) B2))) Delta))))) (forall ((I6 tptp.set_nat) (X (-> tptp.nat tptp.int)) (A (-> tptp.nat tptp.int)) (B2 tptp.int) (Delta tptp.int)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ X I4)))) (=> (= (@ (@ tptp.groups3539618377306564664at_int X) I6) tptp.one_one_int) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ A I4)) B2))) Delta))) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ A I3)) (@ X I3)))) I6)) B2))) Delta))))) (forall ((I6 tptp.set_int) (X (-> tptp.int tptp.int)) (A (-> tptp.int tptp.int)) (B2 tptp.int) (Delta tptp.int)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ X I4)))) (=> (= (@ (@ tptp.groups4538972089207619220nt_int X) I6) tptp.one_one_int) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ A I4)) B2))) Delta))) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I3 tptp.int)) (@ (@ tptp.times_times_int (@ A I3)) (@ X I3)))) I6)) B2))) Delta))))) (forall ((I6 tptp.set_nat) (X (-> tptp.nat tptp.real)) (A (-> tptp.nat tptp.real)) (B2 tptp.real) (Delta tptp.real)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X I4)))) (=> (= (@ (@ tptp.groups6591440286371151544t_real X) I6) tptp.one_one_real) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A I4)) B2))) Delta))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ A I3)) (@ X I3)))) I6)) B2))) Delta))))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ tptp.topolo6980174941875973593q_real (lambda ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1))))))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (= (@ tptp.arctan X) (@ tptp.suminf_real (lambda ((K2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K2)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1))))))))) _let_85 (forall ((X tptp.real) (N2 tptp.nat)) (=> (not (= X tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (exists ((T6 tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real T6))) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ tptp.abs_abs_real X)) (= (@ tptp.exp_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X) M)) (@ tptp.semiri2265585572941072030t_real M)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.exp_real T6)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) 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 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 ((X tptp.int)) (= (@ (@ tptp.dvd_dvd_int X) tptp.one_one_int) (= (@ tptp.abs_abs_int X) tptp.one_one_int))) (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int Z3)) tptp.one_one_int) (= Z3 tptp.zero_zero_int))) (forall ((X tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 X)))) (forall ((X tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X)))) (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)))) (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B2) (=> (@ (@ tptp.dvd_dvd_int B2) A) (= (@ tptp.abs_abs_int A) (@ tptp.abs_abs_int B2))))) (forall ((M2 tptp.int) (N2 tptp.int)) (=> (= (@ tptp.abs_abs_int (@ (@ tptp.times_times_int M2) N2)) tptp.one_one_int) (= (@ tptp.abs_abs_int M2) tptp.one_one_int))) (forall ((S2 tptp.set_int)) (= (not (@ tptp.finite_finite_int S2)) (forall ((M tptp.int)) (exists ((N tptp.int)) (and (@ (@ tptp.ord_less_eq_int M) (@ tptp.abs_abs_int N)) (@ (@ tptp.member_int N) S2)))))) (forall ((S2 tptp.set_int)) (= (not (@ tptp.finite_finite_int S2)) (forall ((M tptp.int)) (exists ((N tptp.int)) (and (@ (@ tptp.ord_less_int M) (@ tptp.abs_abs_int N)) (@ (@ tptp.member_int N) S2)))))) (= 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 ((I tptp.int) (D tptp.int)) (=> (not (= I tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int D) I) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int D)) (@ tptp.abs_abs_int I))))) (forall ((M2 tptp.int) (N2 tptp.int)) (=> (not (= M2 tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int M2) N2)) M2) (= (@ tptp.abs_abs_int N2) tptp.one_one_int)))) (forall ((M2 tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I4 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat M2) 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 M2) N2) (=> (@ (@ tptp.ord_less_eq_int (@ F M2)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N2)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M2) I4) (@ (@ tptp.ord_less_eq_nat I4) N2) (= (@ F I4) K)))))))) (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))))))) (= tptp.bit_se6528837805403552850or_nat (lambda ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M tptp.zero_zero_nat)) N) (@ (@ (@ tptp.if_nat (= N tptp.zero_zero_nat)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat M) _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 M) _let_1)) (@ (@ tptp.divide_divide_nat N) _let_1))))))))) (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))))))) (= tptp.bit_se6528837805403552850or_nat (lambda ((M 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 M)) (not (@ _let_2 N)))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se6528837805403552850or_nat (@ (@ tptp.divide_divide_nat M) _let_1)) (@ (@ tptp.divide_divide_nat N) _let_1)))))))) (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N2))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X) _let_1))) N2)) (@ tptp.exp_real X)))))) (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N2))) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X) _let_1))) N2)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X))))))) (forall ((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)))))) (= tptp.divide_divide_int (lambda ((K2 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.nat2 (@ tptp.abs_abs_int K2))) (@ tptp.nat2 (@ tptp.abs_abs_int L2))))) (@ (@ (@ tptp.if_int (= L2 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (= (@ tptp.sgn_sgn_int K2) (@ tptp.sgn_sgn_int L2))) (@ tptp.semiri1314217659103216013at_int _let_1)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat _let_1) (@ tptp.zero_n2687167440665602831ol_nat (not (@ (@ tptp.dvd_dvd_int L2) K2))))))))))) (forall ((N2 tptp.nat)) (= (@ tptp.nat2 (@ tptp.semiri1314217659103216013at_int N2)) N2)) (forall ((K tptp.num)) (= (@ tptp.nat2 (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_nat K))) (forall ((P Bool)) (= (@ tptp.nat2 (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2687167440665602831ol_nat P))) (= (@ tptp.nat2 tptp.one_one_int) _let_80) (forall ((Z3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z3) tptp.zero_zero_int) (= (@ tptp.nat2 Z3) tptp.zero_zero_nat))) (forall ((I tptp.int)) (= (= (@ tptp.nat2 I) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_int I) tptp.zero_zero_int))) (forall ((W2 tptp.int) (Z3 tptp.int)) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W2)) (@ tptp.nat2 Z3)) (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z3) (@ (@ tptp.ord_less_int W2) Z3)))) (forall ((K tptp.num)) (= (@ tptp.nat2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.zero_zero_nat)) (forall ((N2 tptp.nat)) (= (@ tptp.nat2 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) tptp.zero_zero_nat)) (forall ((Z3 tptp.int)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 Z3)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z3))) (and (=> _let_2 (= _let_1 Z3)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))) (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.nat2 Z3)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z3))) (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 ((X tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2) (@ tptp.nat2 Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2) Y))) (forall ((Y tptp.int) (X tptp.num) (N2 tptp.nat)) (= (= (@ tptp.nat2 Y) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))) (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.dvd_dvd_nat N2) (@ tptp.nat2 (@ tptp.abs_abs_int K))) (@ (@ tptp.dvd_dvd_int (@ tptp.semiri1314217659103216013at_int N2)) K))) (forall ((K tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.nat2 (@ tptp.abs_abs_int K))) N2) (@ (@ tptp.dvd_dvd_int K) (@ tptp.semiri1314217659103216013at_int N2)))) (forall ((X tptp.real) (A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real X))) A) (@ (@ tptp.ord_less_eq_real X) (@ tptp.semiri5074537144036343181t_real A)))) (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.nat2 Z3)) (@ (@ tptp.ord_less_int tptp.one_one_int) Z3))) (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 ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2)) (@ tptp.nat2 A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)) A))) (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 A)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))) (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 A)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))) (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2)) (@ tptp.nat2 A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)) A))) (= tptp.zero_zero_nat (@ tptp.nat2 tptp.zero_zero_int)) (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y)))) (= (lambda ((P2 (-> tptp.nat Bool))) (exists ((X7 tptp.nat)) (@ P2 X7))) (lambda ((P3 (-> tptp.nat Bool))) (exists ((X4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X4) (@ P3 (@ tptp.nat2 X4)))))) (= (lambda ((P2 (-> tptp.nat Bool))) (forall ((X7 tptp.nat)) (@ P2 X7))) (lambda ((P3 (-> tptp.nat Bool))) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X4) (@ P3 (@ tptp.nat2 X4)))))) (forall ((Z3 tptp.int) (Z8 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z3) (=> (@ _let_1 Z8) (= (= (@ tptp.nat2 Z3) (@ tptp.nat2 Z8)) (= Z3 Z8)))))) (forall ((Z3 tptp.int) (W2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z3) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W2)) (@ tptp.nat2 Z3)) (@ (@ tptp.ord_less_int W2) Z3)))) (forall ((M2 tptp.nat) (Z3 tptp.int)) (= (@ (@ tptp.ord_less_nat M2) (@ tptp.nat2 Z3)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M2)) Z3))) (forall ((X tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 X)) N2) (@ (@ tptp.ord_less_eq_int X) (@ tptp.semiri1314217659103216013at_int N2)))) (forall ((M2 tptp.nat) (Z3 tptp.int)) (= (= (@ tptp.semiri1314217659103216013at_int M2) Z3) (and (= M2 (@ tptp.nat2 Z3)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z3)))) (forall ((Z3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z3) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 Z3)) Z3))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B2))) (@ (@ tptp.plus_plus_nat A) B2))) (forall ((W2 tptp.int) (Z3 tptp.int)) (= (@ tptp.nat2 (@ tptp.abs_abs_int (@ (@ tptp.times_times_int W2) Z3))) (@ (@ tptp.times_times_nat (@ tptp.nat2 (@ tptp.abs_abs_int W2))) (@ tptp.nat2 (@ tptp.abs_abs_int Z3))))) _let_84 (forall ((W2 tptp.int) (Z3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W2) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W2)) (@ tptp.nat2 Z3)) (@ (@ tptp.ord_less_int W2) Z3)))) (forall ((W2 tptp.int) (Z3 tptp.int)) (=> (or (@ (@ tptp.ord_less_int tptp.zero_zero_int) W2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z3)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 W2)) (@ tptp.nat2 Z3)) (@ (@ tptp.ord_less_eq_int W2) Z3)))) (forall ((W2 tptp.int) (M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W2))) (= (= (@ tptp.nat2 W2) M2) (and (=> _let_1 (= W2 (@ tptp.semiri1314217659103216013at_int M2))) (=> (not _let_1) (= M2 tptp.zero_zero_nat)))))) (forall ((M2 tptp.nat) (W2 tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W2))) (= (= M2 (@ tptp.nat2 W2)) (and (=> _let_1 (= W2 (@ tptp.semiri1314217659103216013at_int M2))) (=> (not _let_1) (= M2 tptp.zero_zero_nat)))))) (forall ((P (-> tptp.nat Bool)) (I tptp.int)) (= (@ P (@ tptp.nat2 I)) (and (forall ((N tptp.nat)) (=> (= I (@ tptp.semiri1314217659103216013at_int N)) (@ P N))) (=> (@ (@ tptp.ord_less_int I) 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 ((Z3 tptp.int) (Z8 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z3) (=> (@ _let_1 Z8) (= (@ tptp.nat2 (@ (@ tptp.plus_plus_int Z3) Z8)) (@ (@ tptp.plus_plus_nat (@ tptp.nat2 Z3)) (@ tptp.nat2 Z8))))))) (forall ((Z3 tptp.int) (Z8 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z3) (= (@ tptp.nat2 (@ (@ tptp.times_times_int Z3) Z8)) (@ (@ tptp.times_times_nat (@ tptp.nat2 Z3)) (@ tptp.nat2 Z8))))) _let_83 (forall ((P (-> tptp.real Bool)) (E2 tptp.real)) (=> (forall ((D5 tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_real D5) E) (=> (@ P D5) (@ 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 ((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 ((P (-> tptp.real Bool)) (E2 tptp.real)) (=> (forall ((D5 tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_real D5) E) (=> (@ P D5) (@ 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 ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ tptp.nat2 (@ (@ tptp.minus_minus_int X) Y)) (@ (@ tptp.minus_minus_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y))))))) (forall ((Z8 tptp.int) (Z3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z8) (=> (@ (@ tptp.ord_less_eq_int Z8) Z3) (= (@ tptp.nat2 (@ (@ tptp.minus_minus_int Z3) Z8)) (@ (@ tptp.minus_minus_nat (@ tptp.nat2 Z3)) (@ tptp.nat2 Z8)))))) (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 ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X)) tptp.zero_zero_nat))) (forall ((Z3 tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z3) (= (@ tptp.nat2 (@ (@ tptp.power_power_int Z3) N2)) (@ (@ tptp.power_power_nat (@ tptp.nat2 Z3)) N2)))) (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) X) (=> (@ (@ tptp.ord_less_real X) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2))) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X)) N2)))) (forall ((X tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X)) A) (@ (@ tptp.ord_less_eq_nat X) (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real A))))) (= (@ tptp.nat2 _let_82) _let_81) (forall ((Z3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z3) (= (@ tptp.suc (@ tptp.nat2 Z3)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int tptp.one_one_int) Z3))))) (forall ((W2 tptp.int) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W2) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W2)) M2) (@ (@ tptp.ord_less_int W2) (@ tptp.semiri1314217659103216013at_int M2))))) (forall ((Z3 tptp.int) (Z8 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z3) tptp.zero_zero_int) (= (@ tptp.nat2 (@ (@ tptp.times_times_int Z3) Z8)) (@ (@ tptp.times_times_nat (@ tptp.nat2 (@ tptp.uminus_uminus_int Z3))) (@ tptp.nat2 (@ tptp.uminus_uminus_int Z8)))))) (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.nat2 (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B2)))))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat A) B2))) (and (=> _let_2 (= _let_1 (@ (@ tptp.minus_minus_nat B2) A))) (=> (not _let_2) (= _let_1 (@ (@ tptp.minus_minus_nat A) B2))))))) (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N2)) X) (=> (@ (@ tptp.ord_less_real X) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2))) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X)) N2)))) (forall ((Z8 tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int Z3) Z8))) (let ((_let_2 (@ tptp.nat2 Z3))) (let ((_let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ tptp.nat2 Z8)))) (let ((_let_4 (@ (@ tptp.ord_less_int Z8) 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 ((Z3 tptp.int) (M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z3))) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.nat2 Z3)) M2) (and (=> _let_1 (@ (@ tptp.dvd_dvd_int Z3) (@ tptp.semiri1314217659103216013at_int M2))) (=> (not _let_1) (= M2 tptp.zero_zero_nat)))))) (= tptp.bit_se1412395901928357646or_nat (lambda ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M tptp.zero_zero_nat)) N) (@ (@ (@ tptp.if_nat (= N tptp.zero_zero_nat)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat (@ (@ tptp.modulo_modulo_nat M) _let_1)) (@ (@ tptp.modulo_modulo_nat N) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M) _let_1)) (@ (@ tptp.divide_divide_nat N) _let_1))))))))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or4665077453230672383an_nat M2) 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 M2) (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat)))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (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)))) _let_79 (forall ((L tptp.nat) (U tptp.nat)) (@ tptp.finite_finite_nat (@ (@ tptp.set_or4665077453230672383an_nat L) U))) (forall ((M2 tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat M2) (@ tptp.suc M2)) (@ (@ tptp.insert_nat M2) tptp.bot_bot_set_nat))) (forall ((Y tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) _let_1) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 X)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat _let_1) (@ tptp.suc tptp.zero_zero_nat)) _let_1))) (forall ((X tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X)))) (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y)))) (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M tptp.nat)) (and (@ (@ tptp.ord_less_nat M) N2) (@ P M))) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)) (@ P X4))))) (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ P M))) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)) (@ P X4))))) (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_31) (forall ((M2 tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat M2) tptp.zero_zero_nat) tptp.bot_bot_set_nat)) (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 ((N6 tptp.set_nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N6) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)) (@ tptp.finite_finite_nat N6))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M2))) (let ((_let_2 (@ _let_1 (@ tptp.suc N2)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat M2) 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.groups708209901874060359at_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc tptp.zero_zero_nat)) N2)) (@ tptp.semiri1408675320244567234ct_nat N2))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)) (@ tptp.semiri1408675320244567234ct_nat N2))) (forall ((M2 tptp.nat) (K tptp.num)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M2))) (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 M2) _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 ((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.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.plus_plus_nat N2) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat N2) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.plus_plus_nat N2) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))) (= tptp.bit_se1412395901928357646or_nat (lambda ((M 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 M)) (not (@ _let_2 N))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M) _let_1)) (@ (@ tptp.divide_divide_nat N) _let_1)))))))) (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups3542108847815614940at_nat _let_1) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K)) (@ (@ tptp.minus_minus_nat (@ _let_1 K)) tptp.one_one_nat)))) (forall ((N2 tptp.nat) (A (-> tptp.nat tptp.nat)) (B2 (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2))) (=> (forall ((I4 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I4) J3) (=> (@ (@ tptp.ord_less_nat J3) N2) (@ (@ tptp.ord_less_eq_nat (@ A I4)) (@ A J3))))) (=> (forall ((I4 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I4) J3) (=> (@ (@ tptp.ord_less_nat J3) N2) (@ (@ tptp.ord_less_eq_nat (@ B2 J3)) (@ B2 I4))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat N2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_nat (@ A I3)) (@ B2 I3)))) _let_1))) (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat A) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat B2) _let_1))))))) (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 ((L tptp.int) (U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or4662586982721622107an_int L) U))) (forall ((U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) U))) (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))) (forall ((X21 Bool) (X222 Bool)) (= (@ tptp.vEBT_size_VEBT (@ (@ tptp.vEBT_Leaf X21) X222)) tptp.zero_zero_nat)) (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 ((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 ((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 ((U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) U)) (@ tptp.nat2 U))) (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))) (forall ((M2 tptp.nat) (K tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se545348938243370406it_int M2) K)) N2) (and (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.bit_se1146084159140164899it_int K) (@ (@ tptp.minus_minus_nat N2) M2))))) (forall ((M7 tptp.set_nat) (I tptp.nat)) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) M7)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K2)) M7) (@ (@ tptp.ord_less_nat K2) I))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (and (@ (@ tptp.member_nat K2) M7) (@ (@ tptp.ord_less_nat K2) (@ tptp.suc I))))))))) (forall ((M7 tptp.set_nat) (I tptp.nat)) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) M7) (= (@ tptp.suc (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K2)) M7) (@ (@ tptp.ord_less_nat K2) I)))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (and (@ (@ tptp.member_nat K2) M7) (@ (@ tptp.ord_less_nat K2) (@ tptp.suc I))))))))) (forall ((M7 tptp.set_nat) (I tptp.nat)) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) M7) (not (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (and (@ (@ tptp.member_nat K2) M7) (@ (@ tptp.ord_less_nat K2) (@ tptp.suc I)))))) tptp.zero_zero_nat)))) (forall ((M2 tptp.nat) (Q3 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se547839408752420682it_nat M2) Q3)) N2) (and (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.bit_se1148574629649215175it_nat Q3) (@ (@ tptp.minus_minus_nat N2) M2))))) (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 ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N2) (@ (@ (@ tptp.case_nat_o false) (@ tptp.ord_less_eq_nat M2)) N2))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.ord_max_nat M2) _let_1) (@ (@ (@ tptp.case_nat_nat _let_1) (lambda ((M4 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat M4) N2)))) M2)))) (forall ((N2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.ord_max_nat _let_1) M2) (@ (@ (@ tptp.case_nat_nat _let_1) (lambda ((M4 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat N2) M4)))) M2)))) (forall ((N6 tptp.set_nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N6) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat N6)) N2))) (forall ((S2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.finite_card_nat S2)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) X4)) 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 ((Z6 tptp.complex)) (= (@ (@ tptp.power_power_complex Z6) N2) C)))) N2)))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((Z6 tptp.complex)) (= (@ (@ tptp.power_power_complex Z6) N2) tptp.one_one_complex)))) N2))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M2))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((K2 tptp.nat)) K2)) (@ _let_1 N2))))) _let_78 _let_77 (forall ((X tptp.nat)) (= (@ (@ tptp.bezw X) tptp.zero_zero_nat) (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (= tptp.nat_prod_decode_aux (lambda ((K2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat M) K2)) (@ (@ tptp.product_Pair_nat_nat M) (@ (@ tptp.minus_minus_nat K2) M))) (@ (@ tptp.nat_prod_decode_aux _let_1) (@ (@ tptp.minus_minus_nat M) _let_1)))))) (forall ((X tptp.nat) (Xa2 tptp.nat) (Y tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.suc X))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat Xa2) X))) (=> (= (@ (@ tptp.nat_prod_decode_aux X) Xa2) Y) (and (=> _let_2 (= Y (@ (@ tptp.product_Pair_nat_nat Xa2) (@ (@ tptp.minus_minus_nat X) Xa2)))) (=> (not _let_2) (= Y (@ (@ tptp.nat_prod_decode_aux _let_1) (@ (@ tptp.minus_minus_nat Xa2) _let_1))))))))) (forall ((S2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S2) (exists ((R3 (-> tptp.nat tptp.nat))) (and (@ (@ tptp.strict1292158309912662752at_nat R3) (@ tptp.set_ord_lessThan_nat (@ tptp.finite_card_nat S2))) (forall ((N7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N7) (@ tptp.finite_card_nat S2)) (@ (@ tptp.member_nat (@ R3 N7)) S2))))))) (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.root N2) X) (@ (@ tptp.powr_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real N2))))))) (forall ((X tptp.real)) (= (@ (@ tptp.root (@ tptp.suc tptp.zero_zero_nat)) X) X)) (forall ((X tptp.real)) (= (@ (@ tptp.root tptp.zero_zero_nat) X) tptp.zero_zero_real)) (forall ((N2 tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (= (@ _let_1 X) (@ _let_1 Y)) (= X Y))))) (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.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 ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (= (@ (@ tptp.root N2) X) tptp.zero_zero_real) (= X tptp.zero_zero_real)))) (forall ((N2 tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_real X) Y))))) (forall ((N2 tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_real X) Y))))) (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) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (= (@ (@ tptp.root N2) X) tptp.one_one_real) (= X tptp.one_one_real)))) (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) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_real (@ (@ tptp.root N2) X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) tptp.zero_zero_real)))) (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) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N2) X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real)))) (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) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_real (@ (@ tptp.root N2) X)) tptp.one_one_real) (@ (@ tptp.ord_less_real X) tptp.one_one_real)))) (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) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N2) X)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real)))) (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 ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N2) X)) N2) X)))) (forall ((N2 tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_real (@ _let_1 X)) (@ _let_1 Y)))))) (forall ((N2 tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y)))))) (forall ((N2 tptp.nat) (X tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ _let_1 (@ (@ tptp.power_power_real X) K)) (@ (@ tptp.power_power_real (@ _let_1 X)) K))))) (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ _let_1 (@ tptp.abs_abs_real X)) (@ tptp.abs_abs_real (@ _let_1 X)))))) (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.sgn_sgn_real (@ (@ tptp.root N2) X)) (@ tptp.sgn_sgn_real X)))) (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.root N2) X)))))) (forall ((N2 tptp.nat) (N6 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_nat N2) N6) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ tptp.ord_less_real (@ (@ tptp.root N6) X)) (@ (@ tptp.root N2) X)))))) (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) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.root N2) X))))) (forall ((N2 tptp.nat) (N6 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_nat N2) N6) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.root N2) X)) (@ (@ tptp.root N6) X))))))) (forall ((N2 tptp.nat) (N6 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_nat N2) N6) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N6) X)) (@ (@ tptp.root N2) X)))))) (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N2) X)) N2) X)))) (forall ((N2 tptp.nat) (Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (= (@ (@ tptp.power_power_real Y) N2) X) (= (@ (@ tptp.root N2) X) Y))))) (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.root N2) (@ (@ tptp.power_power_real X) N2)) X)))) (forall ((N2 tptp.nat) (N6 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_nat N2) N6) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N2) X)) (@ (@ tptp.root N6) X))))))) (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) (X tptp.real)) (let ((_let_1 (@ (@ tptp.root N2) X))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real _let_1)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real _let_1)) N2)) X)))) (forall ((N2 tptp.nat) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B2) (= (@ tptp.ln_ln_real (@ (@ tptp.root N2) B2)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real B2)) (@ tptp.semiri5074537144036343181t_real N2)))))) (forall ((N2 tptp.nat) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.log B2))) (=> (@ (@ 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) (B2 tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B2) (= (@ (@ tptp.log (@ (@ tptp.root N2) B2)) X) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.log B2) X)))))) (forall ((P (-> tptp.real Bool)) (N2 tptp.nat) (X tptp.real)) (= (@ P (@ (@ tptp.root N2) X)) (and (=> (= N2 tptp.zero_zero_nat) (@ P tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (forall ((Y5 tptp.real)) (=> (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y5)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y5)) N2)) X) (@ P Y5))))))) (= (@ tptp.complete_Sup_Sup_nat tptp.bot_bot_set_nat) tptp.zero_zero_nat) (forall ((K5 tptp.set_nat)) (=> (not (= K5 tptp.bot_bot_set_nat)) (@ (@ tptp.member_nat (@ tptp.complete_Inf_Inf_nat K5)) K5))) (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 ((N2 tptp.nat)) (= (@ (@ tptp.compow_nat_nat N2) tptp.suc) (@ tptp.plus_plus_nat N2))) (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 ((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))) (@ (@ (@ (@ tptp.semila1623282765462674594er_nat tptp.ord_max_nat) tptp.zero_zero_nat) (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y5) X4))) (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.ord_less_nat Y5) X4))) (forall ((Xa2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.times_times_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X4 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 X4))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U2)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U2))))))) __flatten_var_0))) Xa2) X)))) (forall ((M7 tptp.set_nat)) (=> (@ tptp.finite_finite_nat M7) (= (@ tptp.gcd_Gcd_nat M7) (@ tptp.gcd_Gcd_nat (@ (@ tptp.minus_minus_set_nat M7) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))))) (forall ((P (-> tptp.int Bool)) (X tptp.int)) (=> (forall ((Y3 tptp.product_prod_nat_nat)) (@ P (@ tptp.abs_Integ Y3))) (@ P X))) (forall ((Z3 tptp.int)) (not (forall ((X5 tptp.nat) (Y3 tptp.nat)) (not (= Z3 (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat X5) Y3))))))) (forall ((X tptp.product_prod_nat_nat)) (= (@ tptp.nat2 (@ tptp.abs_Integ X)) (@ (@ tptp.produc6842872674320459806at_nat tptp.minus_minus_nat) X))) (= tptp.zero_zero_int (@ tptp.abs_Integ _let_25)) (= tptp.semiri1314217659103216013at_int (lambda ((N tptp.nat)) (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat N) tptp.zero_zero_nat)))) (forall ((X tptp.product_prod_nat_nat)) (= (@ tptp.uminus_uminus_int (@ tptp.abs_Integ X)) (@ tptp.abs_Integ (@ (@ tptp.produc2626176000494625587at_nat (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y5) X4))) X)))) (= tptp.one_one_int (@ tptp.abs_Integ _let_24)) (forall ((Xa2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((X4 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 X4) V4)) (@ (@ tptp.plus_plus_nat U2) Y5)))) __flatten_var_0))) Xa2) X))) (forall ((Xa2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((X4 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 X4) V4)) (@ (@ tptp.plus_plus_nat U2) Y5)))) __flatten_var_0))) Xa2) X))) (forall ((Xa2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.plus_plus_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X4 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 X4) U2)) (@ (@ tptp.plus_plus_nat Y5) V4)))) __flatten_var_0))) Xa2) X)))) (forall ((Xa2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.minus_minus_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X4 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 X4) V4)) (@ (@ tptp.plus_plus_nat Y5) U2)))) __flatten_var_0))) Xa2) X)))) (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)))))) (= (@ 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 ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 M2) (=> (@ _let_1 N2) (= (@ tptp.num_of_nat (@ (@ tptp.plus_plus_nat M2) N2)) (@ (@ tptp.plus_plus_num (@ tptp.num_of_nat M2)) (@ tptp.num_of_nat N2))))))) (forall ((N2 tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.minus_minus_nat J) (@ tptp.suc I))) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat I) J))) N2) (@ tptp.suc (@ (@ tptp.plus_plus_nat I) N2))))) (= tptp.ord_less_eq_int (lambda ((X4 tptp.int) (Xa3 tptp.int)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((Y5 tptp.nat) (Z6 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) Z6)))) __flatten_var_0))) (@ tptp.rep_Integ X4)) (@ tptp.rep_Integ Xa3)))) (= tptp.ord_less_int (lambda ((X4 tptp.int) (Xa3 tptp.int)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((Y5 tptp.nat) (Z6 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) Z6)))) __flatten_var_0))) (@ tptp.rep_Integ X4)) (@ tptp.rep_Integ Xa3)))) _let_76 (forall ((N2 tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.minus_minus_nat J) I)) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat I) J))) N2) (@ tptp.suc (@ (@ tptp.plus_plus_nat I) N2))))) _let_75 _let_74 (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 ((L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc L)) U) (@ (@ tptp.set_or6659071591806873216st_nat L) U))) (forall ((A tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat A) B2)))) (forall ((B2 tptp.nat) (A tptp.nat)) (@ (@ tptp.ord_less_eq_nat B2) (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat A) B2)))) (forall ((K tptp.nat) (M2 tptp.nat)) (= (@ tptp.nat_prod_encode (@ (@ tptp.nat_prod_decode_aux K) M2)) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle K)) M2))) _let_73 (= tptp.minus_minus_int (@ _let_72 (@ tptp.produc27273713700761075at_nat (lambda ((X4 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 X4) V4)) (@ (@ tptp.plus_plus_nat Y5) U2)))) __flatten_var_0))))) (= tptp.plus_plus_int (@ _let_72 (@ tptp.produc27273713700761075at_nat (lambda ((X4 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 X4) U2)) (@ (@ tptp.plus_plus_nat Y5) V4)))) __flatten_var_0))))) (forall ((C tptp.nat) (Y tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat X) Y))) (let ((_let_2 (@ (@ tptp.ord_less_nat X) Y))) (let ((_let_3 (@ (@ tptp.ord_less_nat C) Y))) (and (=> _let_3 (= (@ (@ tptp.image_nat_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_nat I3) C))) _let_1) (@ (@ tptp.set_or4665077453230672383an_nat (@ (@ tptp.minus_minus_nat X) C)) (@ (@ tptp.minus_minus_nat Y) C)))) (=> (not _let_3) (and (=> _let_2 (= (@ (@ tptp.image_nat_nat (lambda ((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 ((L tptp.int) (U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or6656581121297822940st_int L) U))) (forall ((I tptp.nat) (J tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ (@ tptp.set_or1269000886237332187st_nat I) J)) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc I)) (@ tptp.suc J)))) (forall ((I tptp.nat) (J tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat I) J)) (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc I)) (@ tptp.suc J)))) (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 ((A2 tptp.set_nat)) (not (@ (@ tptp.member_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) A2)))) (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))) (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))))) _let_70 (= tptp.ord_less_int (@ _let_69 (@ tptp.produc8739625826339149834_nat_o (lambda ((X4 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 X4) V4)) (@ (@ tptp.plus_plus_nat U2) Y5)))) __flatten_var_0))))) (= tptp.ord_less_eq_int (@ _let_69 (@ tptp.produc8739625826339149834_nat_o (lambda ((X4 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 X4) V4)) (@ (@ tptp.plus_plus_nat U2) Y5)))) __flatten_var_0))))) _let_68 (= tptp.finite_finite_int (lambda ((S6 tptp.set_int)) (exists ((K2 tptp.int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_int_int tptp.abs_abs_int) S6)) (@ tptp.set_ord_lessThan_int K2))))) (= tptp.nat2 (@ (@ (@ tptp.map_fu2345160673673942751at_nat tptp.rep_Integ) tptp.id_nat) _let_26)) (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.image_nat_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat A) B2)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B2)))) (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.image_nat_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or4665077453230672383an_nat A) B2)) (@ (@ tptp.set_or4662586982721622107an_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B2)))) (forall ((L tptp.int) (U tptp.int)) (= (@ (@ tptp.image_int_int (lambda ((X4 tptp.int)) (@ (@ tptp.plus_plus_int X4) 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)))))) (= (@ tptp.finite410649719033368117t_unit tptp.top_to1996260823553986621t_unit) tptp.one_one_nat) (forall ((A tptp.real)) (let ((_let_1 (@ (@ tptp.image_real_real (@ tptp.times_times_real A)) tptp.top_top_set_real))) (let ((_let_2 (= A tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 (@ (@ tptp.insert_real tptp.zero_zero_real) tptp.bot_bot_set_real))) (=> (not _let_2) (= _let_1 tptp.top_top_set_real)))))) _let_67 _let_67 (not (@ tptp.finite_finite_int tptp.top_top_set_int)) (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat tptp.set_ord_lessThan_nat) tptp.top_top_set_nat)) 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) (forall ((N2 tptp.nat)) (@ (@ tptp.member_int (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.image_int_int tptp.abs_abs_int) tptp.top_top_set_int))) (= tptp.top_top_set_nat (@ _let_66 _let_61)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.image_nat_nat (lambda ((M tptp.nat)) (@ (@ tptp.modulo_modulo_nat M) N2))) tptp.top_top_set_nat) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)))) _let_65 (forall ((N2 tptp.nat) (X tptp.real) (D6 tptp.real)) (let ((_let_1 (@ tptp.root N2))) (let ((_let_2 (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.power_power_real (@ _let_1 X)) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))))))) (let ((_let_3 (= D6 _let_2))) (let ((_let_4 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (not (= X tptp.zero_zero_real)) (=> (=> _let_4 (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) _let_3)) (=> (=> _let_4 (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (= D6 (@ tptp.uminus_uminus_real _let_2)))) (=> (=> (not _let_4) _let_3) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) D6) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))))))))) (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N2))) (@ (@ tptp.power_power_real (@ _let_1 X)) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))))))) (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 ((X4 tptp.real)) (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real X4) (@ 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) (X tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.power_power_real (@ _let_1 X)) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))) (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (X tptp.real) (N2 tptp.nat)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M3 tptp.nat) (X5 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M3)) (@ (@ Diff (@ tptp.suc M3)) X5)) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real))) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T6)) (@ tptp.abs_abs_real X)) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M))) (@ (@ tptp.power_power_real X) M)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T6)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2))))))))) (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (X tptp.real) (N2 tptp.nat)) (=> (and (= (@ Diff tptp.zero_zero_nat) F) (forall ((M3 tptp.nat) (X5 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M3)) (@ (@ Diff (@ tptp.suc M3)) X5)) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)))) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T6)) (@ tptp.abs_abs_real X)) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M))) (@ (@ tptp.power_power_real X) M)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T6)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2)))))))) (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (=> (not (= X tptp.zero_zero_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.power_power_real (@ _let_1 X)) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))) (forall ((H2 tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real H2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M3 tptp.nat) (T6 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M3) N2) (@ (@ tptp.ord_less_eq_real H2) T6) (@ (@ tptp.ord_less_eq_real T6) tptp.zero_zero_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M3)) (@ (@ Diff (@ tptp.suc M3)) T6)) (@ (@ tptp.topolo2177554685111907308n_real T6) tptp.top_top_set_real)))) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_real H2) T6) (@ (@ tptp.ord_less_real T6) tptp.zero_zero_real) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M))) (@ (@ tptp.power_power_real H2) M)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T6)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real H2) N2))))))))))) (forall ((H2 tptp.real) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H2) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M3 tptp.nat) (T6 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M3) N2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_eq_real T6) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M3)) (@ (@ Diff (@ tptp.suc M3)) T6)) (@ (@ tptp.topolo2177554685111907308n_real T6) tptp.top_top_set_real)))) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_eq_real T6) H2) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M))) (@ (@ tptp.power_power_real H2) M)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T6)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real H2) N2)))))))))) (forall ((H2 tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M3 tptp.nat) (T6 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M3) N2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_eq_real T6) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M3)) (@ (@ Diff (@ tptp.suc M3)) T6)) (@ (@ tptp.topolo2177554685111907308n_real T6) tptp.top_top_set_real)))) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_real T6) H2) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M))) (@ (@ tptp.power_power_real H2) M)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T6)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real H2) N2))))))))))) (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N2 tptp.nat) (X tptp.real)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (not (= X tptp.zero_zero_real)) (=> (forall ((M3 tptp.nat) (X5 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M3)) (@ (@ Diff (@ tptp.suc M3)) X5)) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real))) (exists ((T6 tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real T6))) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ tptp.abs_abs_real X)) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M))) (@ (@ tptp.power_power_real X) M)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T6)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2)))))))))))) (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N2 tptp.nat) (X tptp.real)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M3 tptp.nat) (T6 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M3) N2) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T6)) (@ tptp.abs_abs_real X))) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M3)) (@ (@ Diff (@ tptp.suc M3)) T6)) (@ (@ tptp.topolo2177554685111907308n_real T6) tptp.top_top_set_real)))) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T6)) (@ tptp.abs_abs_real X)) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M))) (@ (@ tptp.power_power_real X) M)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T6)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2))))))))) (forall ((N2 tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B2 tptp.real) (C tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M3 tptp.nat) (T6 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M3) N2) (@ (@ tptp.ord_less_eq_real A) T6) (@ (@ tptp.ord_less_eq_real T6) B2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M3)) (@ (@ Diff (@ tptp.suc M3)) T6)) (@ (@ tptp.topolo2177554685111907308n_real T6) tptp.top_top_set_real)))) (=> (@ _let_1 C) (=> (@ (@ tptp.ord_less_eq_real C) B2) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) B2) (=> (not (= X C)) (exists ((T6 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real T6))) (let ((_let_2 (@ tptp.ord_less_real X))) (let ((_let_3 (@ _let_2 C))) (and (=> _let_3 (and (@ _let_2 T6) (@ _let_1 C))) (=> (not _let_3) (and (@ (@ tptp.ord_less_real C) T6) (@ _let_1 X))) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M) C)) (@ tptp.semiri2265585572941072030t_real M))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) C)) M)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T6)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) C)) N2))))))))))))))))))) (forall ((N2 tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M3 tptp.nat) (T6 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M3) N2) (@ (@ tptp.ord_less_eq_real A) T6) (@ (@ tptp.ord_less_eq_real T6) B2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M3)) (@ (@ Diff (@ tptp.suc M3)) T6)) (@ (@ tptp.topolo2177554685111907308n_real T6) tptp.top_top_set_real)))) (=> (@ (@ tptp.ord_less_eq_real A) C) (=> (@ (@ tptp.ord_less_real C) B2) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_real C) T6) (@ (@ tptp.ord_less_real T6) B2) (= (@ F B2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M) C)) (@ tptp.semiri2265585572941072030t_real M))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real B2) C)) M)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T6)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real B2) C)) N2)))))))))))) (forall ((N2 tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M3 tptp.nat) (T6 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M3) N2) (@ (@ tptp.ord_less_eq_real A) T6) (@ (@ tptp.ord_less_eq_real T6) B2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M3)) (@ (@ Diff (@ tptp.suc M3)) T6)) (@ (@ tptp.topolo2177554685111907308n_real T6) tptp.top_top_set_real)))) (=> (@ (@ tptp.ord_less_real A) C) (=> (@ (@ tptp.ord_less_eq_real C) B2) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_real A) T6) (@ (@ tptp.ord_less_real T6) C) (= (@ F A) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M) C)) (@ tptp.semiri2265585572941072030t_real M))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real A) C)) M)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T6)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real A) C)) N2)))))))))))) (forall ((N2 tptp.nat) (H2 tptp.real) (Diff (-> tptp.nat tptp.real tptp.real)) (K tptp.nat) (B tptp.real)) (=> (forall ((M3 tptp.nat) (T6 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M3) N2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_eq_real T6) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M3)) (@ (@ Diff (@ tptp.suc M3)) T6)) (@ (@ tptp.topolo2177554685111907308n_real T6) tptp.top_top_set_real)))) (=> (= N2 (@ tptp.suc K)) (forall ((M5 tptp.nat) (T7 tptp.real)) (let ((_let_1 (@ tptp.suc M5))) (let ((_let_2 (@ (@ tptp.minus_minus_nat N2) _let_1))) (=> (and (@ (@ tptp.ord_less_nat M5) N2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T7) (@ (@ tptp.ord_less_eq_real T7) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((U2 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N2) M5))) (@ (@ tptp.minus_minus_real (@ (@ Diff M5) U2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((P6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff (@ (@ tptp.plus_plus_nat M5) P6)) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real P6))) (@ (@ tptp.power_power_real U2) P6)))) (@ tptp.set_ord_lessThan_nat _let_1))) (@ (@ tptp.times_times_real B) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real U2) _let_1)) (@ tptp.semiri2265585572941072030t_real _let_1)))))))) (@ (@ tptp.minus_minus_real (@ (@ Diff _let_1) T7)) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((P6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff (@ (@ tptp.plus_plus_nat (@ tptp.suc M5)) P6)) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real P6))) (@ (@ tptp.power_power_real T7) P6)))) (@ tptp.set_ord_lessThan_nat _let_2))) (@ (@ tptp.times_times_real B) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real T7) _let_2)) (@ tptp.semiri2265585572941072030t_real _let_2)))))) (@ (@ tptp.topolo2177554685111907308n_real T7) tptp.top_top_set_real))))))))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X9 tptp.real)) (@ tptp.suminf_real (lambda ((K2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K2)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X9) _let_1)))))))) (@ tptp.suminf_real (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K2)) (@ (@ tptp.power_power_real X) (@ (@ tptp.times_times_nat K2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) (forall ((N2 tptp.nat) (X tptp.real) (S tptp.set_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X4 tptp.real)) (@ (@ tptp.power_power_real X4) N2))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.power_power_real X) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))))) (@ (@ tptp.topolo2177554685111907308n_real X) S))) (forall ((M7 tptp.set_nat)) (=> (@ tptp.finite_finite_nat M7) (=> (not (= M7 tptp.bot_bot_set_nat)) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) M7)) (= (@ tptp.gcd_Gcd_nat M7) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.image_nat_set_nat (lambda ((M tptp.nat)) (@ tptp.collect_nat (lambda ((D4 tptp.nat)) (@ (@ tptp.dvd_dvd_nat D4) M))))) M7)))))))) (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((D4 tptp.nat)) (@ (@ tptp.dvd_dvd_nat D4) N2)))) N2))) (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))))) _let_64 _let_63 (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (=> (@ (@ tptp.ord_less_real (@ A tptp.zero_zero_nat)) tptp.zero_zero_real) (forall ((N7 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N7))) (@ (@ tptp.member_real (@ tptp.suminf_real (lambda ((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 ((N7 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N7))) (@ (@ tptp.member_real (@ tptp.suminf_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3))))) (@ (@ tptp.set_or1222579329274155063t_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ tptp.set_ord_lessThan_nat _let_1))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))))))))) (forall ((A (-> tptp.nat tptp.real)) (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 ((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))))) (not (= tptp.at_top_nat tptp.bot_bot_filter_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 (lambda ((X4 tptp.nat)) (@ (@ tptp.times_times_nat X4) C))) tptp.at_top_nat) tptp.at_top_nat))) (forall ((C tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ (@ tptp.filterlim_nat_nat (@ tptp.times_times_nat C)) tptp.at_top_nat) tptp.at_top_nat))) (forall ((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 ((N7 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N7)) L4)) (@ (@ (@ tptp.filterlim_nat_real F) _let_1) tptp.at_top_nat) (forall ((N7 tptp.nat)) (@ (@ tptp.ord_less_eq_real L4) (@ G N7))) (@ (@ (@ tptp.filterlim_nat_real G) _let_1) tptp.at_top_nat))))))))) (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((R3 tptp.real)) (exists ((N8 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N3) (@ (@ tptp.ord_less_real R3) (@ X8 N3)))))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((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.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N))))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (forall ((R2 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_real R2) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N)))))) (@ tptp.topolo2815343760600316023s_real R2)) 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 ((N7 tptp.nat)) (@ (@ tptp.ord_less_eq_real L) (@ (@ tptp.plus_plus_real (@ F N7)) E))))) (@ (@ (@ tptp.filterlim_nat_real F) (@ tptp.topolo2815343760600316023s_real L)) tptp.at_top_nat))))) (forall ((R2 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_real R2) (@ tptp.uminus_uminus_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N))))))) (@ tptp.topolo2815343760600316023s_real R2)) tptp.at_top_nat)) (forall ((R2 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real R2) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N)))))))) (@ tptp.topolo2815343760600316023s_real R2)) tptp.at_top_nat)) (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (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 ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1))))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))) (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 ((N7 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))) N7)))) 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 ((N7 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))) N7)) 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 ((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 ((C tptp.nat) (P (-> tptp.nat Bool))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) X5) (@ P X5))) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))) (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat P) tptp.at_top_nat) (exists ((N5 tptp.nat)) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N5) N) (@ P N)))))) (forall ((F3 tptp.filter_nat)) (= (@ (@ tptp.ord_le2510731241096832064er_nat F3) tptp.at_top_nat) (forall ((N5 tptp.nat)) (@ (@ tptp.eventually_nat (@ tptp.ord_less_eq_nat N5)) F3)))) (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 ((N2 tptp.nat) (F (-> tptp.real tptp.real)) (F3 tptp.filter_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_bot_real) F3) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (@ (@ (@ tptp.filterlim_real_real (lambda ((X4 tptp.real)) (@ (@ tptp.power_power_real (@ F X4)) N2))) tptp.at_top_real) F3))))) (forall ((N2 tptp.nat) (F (-> tptp.real tptp.real)) (F3 tptp.filter_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_bot_real) F3) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ (@ (@ tptp.filterlim_real_real (lambda ((X4 tptp.real)) (@ (@ tptp.power_power_real (@ F X4)) N2))) tptp.at_bot_real) F3))))) (= _let_62 _let_62) (forall ((S2 tptp.set_int)) (= (not (@ tptp.finite_finite_int S2)) (not (@ tptp.finite_finite_nat (@ (@ tptp.image_int_nat (@ (@ tptp.comp_int_nat_int tptp.nat2) tptp.abs_abs_int)) S2))))) (@ 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)))) (= (@ tptp.set_or1210151606488870762an_nat tptp.zero_zero_nat) _let_61) (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 ((K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K) (@ tptp.order_mono_nat_nat (lambda ((M tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat K) M)) M))))) (= (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.image_nat_set_nat tptp.set_or1210151606488870762an_nat) tptp.top_top_set_nat)) tptp.bot_bot_set_nat) _let_60 (forall ((K tptp.nat)) (= (@ tptp.set_ord_atLeast_nat (@ tptp.suc K)) (@ tptp.set_or1210151606488870762an_nat K))) (= (@ 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)))) _let_58 (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))) (@ tptp.fun_is_measure_int (@ (@ tptp.comp_int_nat_int tptp.nat2) tptp.abs_abs_int)) (forall ((N6 tptp.set_nat)) (@ (@ tptp.inj_on_nat_nat tptp.suc) N6)) (forall ((N6 tptp.set_nat) (K tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.member_nat N3) N6) (@ (@ tptp.ord_less_eq_nat K) N3))) (@ (@ tptp.inj_on_nat_nat (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_nat N) K))) N6))) (@ (@ tptp.inj_on_set_nat_nat tptp.nat_set_encode) (@ tptp.collect_set_nat tptp.finite_finite_nat)) _let_56 (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_valid X) Xa2)) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (= Xa2 tptp.one_one_nat)) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) Summary2)) (and (= Deg2 Xa2) (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_VEBT_valid X5) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X6))) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X6))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((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 ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I3)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I3))))) (=> _let_2 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X6)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X4) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X4) (and (@ (@ tptp.ord_less_nat Mi3) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma3)))))))))))))) Mima)))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid X) Xa2) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (not (= Xa2 tptp.one_one_nat))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) Summary2)) (not (and (= Deg2 Xa2) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_VEBT_valid X2) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X6))) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X6))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((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 ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I3)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I3))))) (=> _let_2 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X6)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X4) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X4) (and (@ (@ tptp.ord_less_nat Mi3) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma3)))))))))))))) Mima))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_valid X) Xa2) Y) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (= Y (not (= Xa2 tptp.one_one_nat)))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) Summary2)) (= Y (not (and (= Deg2 Xa2) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_VEBT_valid X4) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X6))) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X6))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((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 ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I3)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I3))))) (=> _let_2 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X6)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X4) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X4) (and (@ (@ tptp.ord_less_nat Mi3) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma3)))))))))))))) Mima)))))))))))) (forall ((Mima2 tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (Deg3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg) (@ (@ tptp.divide_divide_nat Deg) _let_1)))) (= (@ (@ tptp.vEBT_VEBT_valid (@ (@ (@ (@ tptp.vEBT_Node Mima2) Deg) TreeList2) Summary)) Deg3) (and (= Deg Deg3) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_VEBT_valid X4) (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X6))) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X6))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg)) (forall ((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 ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I3))))) (=> _let_2 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X6)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg) _let_1)) TreeList2) Ma3) (forall ((X4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X4) (@ (@ tptp.power_power_nat _let_1) Deg)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg) _let_1)) TreeList2) X4) (and (@ (@ tptp.ord_less_nat Mi3) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma3)))))))))))))) Mima2)))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_valid X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (=> (= Y (= Xa2 tptp.one_one_nat)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) Summary2))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_2)))) (=> (= X _let_1) (=> (= Y (and (= Deg2 Xa2) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_VEBT_valid X4) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_3) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat _let_2) _let_3)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X6))) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X6))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((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 ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I3)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I3))))) (=> _let_2 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X6)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X4) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X4) (and (@ (@ tptp.ord_less_nat Mi3) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma3)))))))))))))) Mima))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid X) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)) (not (= Xa2 tptp.one_one_nat)))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (let ((_let_3 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) Summary2))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (= Deg2 Xa2) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_VEBT_valid X2) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X6))) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X6))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((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 ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I3)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I3))))) (=> _let_2 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X6)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X4) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X4) (and (@ (@ tptp.ord_less_nat Mi3) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma3)))))))))))))) Mima)))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_valid X) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)) (= Xa2 tptp.one_one_nat))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (let ((_let_3 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) Summary2))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (and (= Deg2 Xa2) (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_VEBT_valid X5) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X6))) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X6))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((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 ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I3)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I3))))) (=> _let_2 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X6)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X4) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X4) (and (@ (@ tptp.ord_less_nat Mi3) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma3)))))))))))))) Mima))))))))))))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat J) K))) (let ((_let_2 (@ tptp.set_or4665077453230672383an_nat I))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ _let_2 _let_1) (@ (@ tptp.sup_sup_set_nat (@ _let_2 J)) (@ (@ tptp.set_or4665077453230672383an_nat J) _let_1))))))) _let_55 _let_54 _let_53 (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat M2) N2)) (@ tptp.transi6264000038957366511cl_nat tptp.pred_nat)) (@ (@ tptp.ord_less_nat M2) N2))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat M2) N2)) (@ tptp.transi2905341329935302413cl_nat tptp.pred_nat)) (@ (@ tptp.ord_less_eq_nat M2) N2))) _let_52 (forall ((M2 tptp.num)) (= (@ (@ tptp.bit_take_bit_num tptp.zero_zero_nat) M2) tptp.none_num)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N2)) tptp.one) (@ tptp.some_num tptp.one))) (forall ((N2 tptp.nat) (M2 tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N2)) (@ tptp.bit0 M2)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q5 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q5)))) (@ (@ tptp.bit_take_bit_num N2) M2)))) (forall ((N2 tptp.nat) (M2 tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N2)) (@ tptp.bit1 M2)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num N2) M2))))) _let_51 (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ tptp.suc M2)) (@ tptp.suc N2)) (@ tptp.suc (@ (@ tptp.ord_min_nat M2) N2)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_min_nat tptp.zero_zero_nat) N2) tptp.zero_zero_nat)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_min_nat N2) tptp.zero_zero_nat) tptp.zero_zero_nat)) (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)))) (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 ((M2 tptp.nat) (I tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ (@ tptp.minus_minus_nat M2) I)) (@ (@ tptp.minus_minus_nat N2) I)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.ord_min_nat M2) N2)) I))) (forall ((M2 tptp.nat) (N2 tptp.nat) (Q3 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.ord_min_nat M2) N2)) Q3) (@ (@ tptp.ord_min_nat (@ (@ tptp.times_times_nat M2) Q3)) (@ (@ tptp.times_times_nat N2) Q3)))) (forall ((M2 tptp.nat) (N2 tptp.nat) (Q3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M2))) (= (@ _let_1 (@ (@ tptp.ord_min_nat N2) Q3)) (@ (@ tptp.ord_min_nat (@ _let_1 N2)) (@ _let_1 Q3))))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_min_nat M2) (@ tptp.suc N2)) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((M4 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_min_nat M4) N2)))) M2))) (forall ((N2 tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ tptp.suc N2)) M2) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((M4 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_min_nat N2) M4)))) M2))) _let_50 _let_49 (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ (@ tptp.bij_betw_nat_complex (lambda ((K2 tptp.nat)) (@ tptp.cis (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ tptp.semiri5074537144036343181t_real K2))) (@ tptp.semiri5074537144036343181t_real N2))))) (@ tptp.set_ord_lessThan_nat N2)) (@ tptp.collect_complex (lambda ((Z6 tptp.complex)) (= (@ (@ tptp.power_power_complex Z6) N2) tptp.one_one_complex)))))) (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.suc I))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) J) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat I) J)) (@ (@ tptp.cons_nat _let_1) (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat _let_1) J))))))) (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.suc I))) (=> (@ (@ tptp.ord_less_nat _let_1) J) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat I) J)) (@ (@ tptp.cons_nat _let_1) (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat _let_1) J))))))) (forall ((M7 tptp.set_nat) (N6 tptp.set_nat)) (= (@ (@ (@ tptp.bij_betw_nat_nat tptp.suc) M7) N6) (= (@ (@ tptp.image_nat_nat tptp.suc) M7) N6))) (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 ((Z6 tptp.complex)) (= (@ (@ tptp.power_power_complex Z6) N2) tptp.one_one_complex)))) (@ tptp.collect_complex (lambda ((Z6 tptp.complex)) (= (@ (@ tptp.power_power_complex Z6) N2) 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 ((X tptp.list_nat) (Y tptp.nat)) (=> (= (@ tptp.nat_list_encode X) Y) (=> (=> (= X tptp.nil_nat) (not (= Y tptp.zero_zero_nat))) (not (forall ((X5 tptp.nat) (Xs2 tptp.list_nat)) (=> (= X (@ (@ tptp.cons_nat X5) Xs2)) (not (= Y (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X5) (@ tptp.nat_list_encode Xs2)))))))))))) (= (@ tptp.nat_list_encode tptp.nil_nat) tptp.zero_zero_nat) (forall ((X tptp.nat) (Xs tptp.list_nat)) (= (@ tptp.nat_list_encode (@ (@ tptp.cons_nat X) Xs)) (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X) (@ tptp.nat_list_encode Xs)))))) (= tptp.upto_aux (lambda ((I3 tptp.int) (J2 tptp.int) (Js tptp.list_int)) (@ (@ (@ tptp.if_list_int (@ (@ tptp.ord_less_int J2) I3)) Js) (@ (@ (@ tptp.upto_aux I3) (@ (@ tptp.minus_minus_int J2) tptp.one_one_int)) (@ (@ tptp.cons_int J2) Js))))) (forall ((I tptp.int) (J tptp.int)) (let ((_let_1 (@ (@ tptp.upto I) J))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int I) J))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int I) J)) (and (=> _let_2 (= _let_1 (@ (@ tptp.cons_int I) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I) tptp.one_one_int)) J)))) (=> (not _let_2) (= _let_1 tptp.nil_int))))))) (forall ((X tptp.int) (Xa2 tptp.int) (Y tptp.list_int)) (let ((_let_1 (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int X) Xa2)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int X) Xa2))) (=> (= (@ (@ tptp.upto X) Xa2) Y) (=> _let_1 (not (=> (and (=> _let_2 (= Y (@ (@ tptp.cons_int X) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int X) tptp.one_one_int)) Xa2)))) (=> (not _let_2) (= Y tptp.nil_int))) (not _let_1)))))))) (forall ((I tptp.int) (J tptp.int)) (= (= (@ (@ tptp.upto I) J) tptp.nil_int) (@ (@ tptp.ord_less_int J) I))) (forall ((I tptp.int) (J tptp.int)) (= (= tptp.nil_int (@ (@ tptp.upto I) J)) (@ (@ tptp.ord_less_int J) I))) (forall ((J tptp.int) (I tptp.int)) (=> (@ (@ tptp.ord_less_int J) I) (= (@ (@ tptp.upto I) J) tptp.nil_int))) (forall ((I tptp.int)) (= (@ (@ tptp.upto I) I) (@ (@ tptp.cons_int I) tptp.nil_int))) (forall ((I tptp.int) (K tptp.nat) (J tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int I) (@ tptp.semiri1314217659103216013at_int K)))) (=> (@ (@ tptp.ord_less_eq_int _let_1) J) (= (@ (@ tptp.nth_int (@ (@ tptp.upto I) J)) K) _let_1)))) (forall ((I tptp.int) (J tptp.int)) (= (@ tptp.size_size_list_int (@ (@ tptp.upto I) J)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int J) I)) tptp.one_one_int)))) (forall ((M2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.numeral_numeral_int M2))) (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 ((M2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2)))) (let ((_let_2 (@ tptp.numeral_numeral_int M2))) (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 ((M2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2)))) (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 ((M2 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 M2)))) (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_48 (= tptp.upto_aux (lambda ((I3 tptp.int) (J2 tptp.int) (__flatten_var_0 tptp.list_int)) (@ (@ tptp.append_int (@ (@ tptp.upto I3) J2)) __flatten_var_0))) (forall ((I tptp.int) (J tptp.int)) (@ tptp.distinct_int (@ (@ tptp.upto I) J))) _let_47 (forall ((I tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I))) (=> (@ (@ tptp.ord_less_eq_int I) J) (=> (@ (@ tptp.ord_less_eq_int J) K) (= (@ _let_1 K) (@ (@ tptp.append_int (@ _let_1 J)) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int J) tptp.one_one_int)) K))))))) (forall ((I tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I))) (=> (@ (@ tptp.ord_less_eq_int I) J) (=> (@ (@ tptp.ord_less_eq_int J) K) (= (@ _let_1 K) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J) tptp.one_one_int))) (@ (@ tptp.upto J) K))))))) _let_46 _let_45 (= tptp.upto (lambda ((I3 tptp.int) (J2 tptp.int)) (@ (@ (@ tptp.if_list_int (@ (@ tptp.ord_less_eq_int I3) J2)) (@ (@ tptp.cons_int I3) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I3) tptp.one_one_int)) J2))) tptp.nil_int))) (forall ((X tptp.int) (Xa2 tptp.int) (Y tptp.list_int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int X) Xa2))) (=> (= (@ (@ tptp.upto X) Xa2) Y) (and (=> _let_1 (= Y (@ (@ tptp.cons_int X) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int X) tptp.one_one_int)) Xa2)))) (=> (not _let_1) (= Y tptp.nil_int)))))) (forall ((I tptp.int) (J tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I) J) (= (@ (@ tptp.upto I) J) (@ (@ tptp.cons_int I) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I) tptp.one_one_int)) J))))) (forall ((I tptp.int) (J tptp.int)) (let ((_let_1 (@ tptp.upto I))) (=> (@ (@ tptp.ord_less_eq_int I) J) (= (@ _let_1 J) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J) tptp.one_one_int))) (@ (@ tptp.cons_int J) tptp.nil_int)))))) _let_44 (forall ((I tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I))) (=> (@ (@ tptp.ord_less_eq_int I) J) (=> (@ (@ tptp.ord_less_eq_int J) K) (= (@ _let_1 K) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J) tptp.one_one_int))) (@ (@ tptp.cons_int J) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int J) tptp.one_one_int)) K)))))))) (forall ((X tptp.list_nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.accp_list_nat tptp.nat_list_encode_rel))) (=> (= (@ tptp.nat_list_encode X) Y) (=> (@ _let_1 X) (=> (=> (= X tptp.nil_nat) (=> (= Y tptp.zero_zero_nat) (not (@ _let_1 tptp.nil_nat)))) (not (forall ((X5 tptp.nat) (Xs2 tptp.list_nat)) (let ((_let_1 (@ (@ tptp.cons_nat X5) Xs2))) (=> (= X _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 ((M2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (let ((_let_2 (@ tptp.numeral_numeral_nat M2))) (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 ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.upt M2) N2))) (= (@ tptp.remdups_nat _let_1) _let_1))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ tptp.tl_nat (@ (@ tptp.upt M2) N2)) (@ (@ tptp.upt (@ tptp.suc M2)) N2))) (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (= (@ tptp.hd_nat (@ (@ tptp.upt I) J)) I))) (forall ((M2 tptp.nat) (I tptp.nat) (J tptp.nat)) (= (@ (@ tptp.drop_nat M2) (@ (@ tptp.upt I) J)) (@ (@ tptp.upt (@ (@ tptp.plus_plus_nat I) M2)) J))) (forall ((I tptp.nat) (J tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.upt I) J)) (@ (@ tptp.minus_minus_nat J) I))) (forall ((I tptp.nat) (M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I) M2))) (let ((_let_2 (@ tptp.upt I))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) N2) (= (@ (@ tptp.take_nat M2) (@ _let_2 N2)) (@ _let_2 _let_1)))))) (forall ((J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (@ (@ tptp.upt I) J) tptp.nil_nat))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or4665077453230672383an_nat M2) N2)) (@ (@ tptp.upt M2) N2))) (forall ((I tptp.nat) (J tptp.nat)) (= (= (@ (@ tptp.upt I) J) tptp.nil_nat) (or (= J tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat J) I)))) (forall ((I tptp.nat) (K tptp.nat) (J tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I) K))) (=> (@ (@ tptp.ord_less_nat _let_1) J) (= (@ (@ tptp.nth_nat (@ (@ tptp.upt I) J)) K) _let_1)))) (forall ((I tptp.nat)) (= (@ (@ tptp.upt I) tptp.zero_zero_nat) tptp.nil_nat)) (forall ((M2 tptp.nat) (N2 tptp.nat) (Ns tptp.list_nat) (Q3 tptp.nat)) (let ((_let_1 (@ (@ tptp.cons_nat N2) Ns))) (= (= (@ (@ tptp.cons_nat M2) _let_1) (@ (@ tptp.upt M2) Q3)) (= _let_1 (@ (@ tptp.upt (@ tptp.suc M2)) Q3))))) _let_43 (forall ((I tptp.nat) (J tptp.nat)) (@ tptp.distinct_nat (@ (@ tptp.upt I) J))) _let_42 _let_41 (= tptp.set_ord_lessThan_nat (lambda ((N tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt tptp.zero_zero_nat) N)))) _let_40 (= tptp.set_ord_atMost_nat (lambda ((N tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt tptp.zero_zero_nat) (@ tptp.suc N))))) (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (= (@ (@ tptp.upt I) J) (@ (@ tptp.cons_nat I) (@ (@ tptp.upt (@ tptp.suc I)) J))))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat J) K))) (let ((_let_2 (@ tptp.upt I))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ _let_2 _let_1) (@ (@ tptp.append_nat (@ _let_2 J)) (@ (@ tptp.upt J) _let_1))))))) (forall ((I tptp.nat) (J tptp.nat) (X tptp.nat) (Xs tptp.list_nat)) (= (= (@ (@ tptp.upt I) J) (@ (@ tptp.cons_nat X) Xs)) (and (@ (@ tptp.ord_less_nat I) J) (= I X) (= (@ (@ tptp.upt (@ (@ tptp.plus_plus_nat I) tptp.one_one_nat)) J) Xs)))) (= tptp.upt (lambda ((I3 tptp.nat) (J2 tptp.nat)) (@ (@ (@ tptp.if_list_nat (@ (@ tptp.ord_less_nat I3) J2)) (@ (@ tptp.cons_nat I3) (@ (@ tptp.upt (@ tptp.suc I3)) J2))) tptp.nil_nat))) (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.upt I))) (let ((_let_2 (@ _let_1 (@ tptp.suc J)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat I) J))) (and (=> _let_3 (= _let_2 (@ (@ tptp.append_nat (@ _let_1 J)) (@ (@ tptp.cons_nat J) tptp.nil_nat)))) (=> (not _let_3) (= _let_2 tptp.nil_nat))))))) (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.upt I))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ _let_1 (@ tptp.suc J)) (@ (@ tptp.append_nat (@ _let_1 J)) (@ (@ tptp.cons_nat J) tptp.nil_nat)))))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.map_nat_nat tptp.suc) (@ (@ tptp.upt M2) N2)) (@ (@ tptp.upt (@ tptp.suc M2)) (@ tptp.suc N2)))) (forall ((N2 tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_nat I3) N2))) (@ (@ tptp.upt tptp.zero_zero_nat) M2)) (@ (@ tptp.upt N2) (@ (@ tptp.plus_plus_nat M2) N2)))) (forall ((M2 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 M2)) (@ tptp.suc N2))) (@ (@ tptp.upt M2) N2))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (= (@ tptp.groups4561878855575611511st_nat (@ (@ tptp.upt M2) N2)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or4665077453230672383an_nat M2) N2))))) (forall ((M2 tptp.nat) (N6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) M2) (= (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L2) M2) (= (@ tptp.groups4561878855575611511st_nat L2) N6))))) (@ (@ 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 M2) tptp.one_one_nat)) (= (@ tptp.groups4561878855575611511st_nat L2) N6)))))) (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L2) M2) (= (@ (@ tptp.plus_plus_nat (@ tptp.groups4561878855575611511st_nat L2)) tptp.one_one_nat) N6))))))))) (forall ((M2 tptp.nat) (N6 tptp.nat)) (= (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L2) M2) (= (@ tptp.groups4561878855575611511st_nat L2) N6))))) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N6) M2)) tptp.one_one_nat)) N6))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_nat) (@ (@ tptp.upt M2) N2))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) (@ (@ tptp.upt M2) N2))) (forall ((Ns tptp.list_nat) (I tptp.nat)) (=> (@ (@ tptp.sorted_wrt_nat tptp.ord_less_nat) Ns) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Ns)) (@ (@ tptp.ord_less_eq_nat I) (@ (@ tptp.nth_nat Ns) I))))) (forall ((I tptp.int) (J tptp.int)) (@ (@ tptp.sorted_wrt_int tptp.ord_less_int) (@ (@ tptp.upto I) J))) (forall ((M2 tptp.int) (N2 tptp.int)) (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) (@ (@ tptp.upto M2) N2))) (forall ((M2 tptp.nat)) (= (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I3 tptp.nat) (J2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I3) J2)) M2)))) (@ (@ tptp.produc457027306803732586at_nat (@ tptp.set_ord_atMost_nat M2)) (lambda ((R4 tptp.nat)) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat M2) R4)))))) _let_39 (forall ((N2 tptp.nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat tptp.bNF_Ca8665028551170535155natLeq) (@ (@ tptp.produc457027306803732586at_nat (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.ord_less_nat X4) N2)))) (lambda ((Uu3 tptp.nat)) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.ord_less_nat X4) N2)))))) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_nat X4) N2) (@ (@ tptp.ord_less_nat Y5) N2) (@ (@ tptp.ord_less_eq_nat X4) Y5))))))) _let_38 (forall ((N2 tptp.nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat tptp.bNF_Ca8665028551170535155natLeq) (@ (@ tptp.produc457027306803732586at_nat (@ (@ tptp.order_underS_nat tptp.bNF_Ca8665028551170535155natLeq) N2)) (lambda ((Uu3 tptp.nat)) (@ (@ tptp.order_underS_nat tptp.bNF_Ca8665028551170535155natLeq) N2)))) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_nat X4) N2) (@ (@ tptp.ord_less_nat Y5) N2) (@ (@ tptp.ord_less_eq_nat X4) Y5))))))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.order_underS_nat tptp.bNF_Ca8665028551170535155natLeq) N2) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.ord_less_nat X4) N2))))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.upt M2) N2))) (= (@ (@ tptp.linord738340561235409698at_nat (lambda ((X4 tptp.nat)) X4)) _let_1) _let_1))) (forall ((I tptp.int) (J tptp.int)) (let ((_let_1 (@ (@ tptp.upto I) J))) (= (@ (@ tptp.linord1735203802627413978nt_int (lambda ((X4 tptp.int)) X4)) _let_1) _let_1))) (forall ((N2 tptp.nat)) (= (@ tptp.field_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_nat X4) N2) (@ (@ tptp.ord_less_nat Y5) N2) (@ (@ tptp.ord_less_eq_nat X4) Y5)))))) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.ord_less_nat X4) N2))))) (@ tptp.wf_nat _let_37) (forall ((D tptp.int)) (@ tptp.wf_int (@ tptp.int_ge_less_than2 D))) (forall ((D tptp.int)) (@ tptp.wf_int (@ tptp.int_ge_less_than D))) (forall ((S2 tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat S2)) (exists ((R3 (-> tptp.nat tptp.nat))) (and (@ tptp.order_5726023648592871131at_nat R3) (forall ((N7 tptp.nat)) (@ (@ tptp.member_nat (@ R3 N7)) S2)))))) (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (=> (@ tptp.order_5726023648592871131at_nat F) (@ (@ tptp.ord_less_eq_nat N2) (@ F N2)))) (forall ((S2 tptp.set_nat) (S tptp.nat)) (=> (not (@ tptp.finite_finite_nat S2)) (=> (@ (@ tptp.member_nat S) S2) (exists ((N3 tptp.nat)) (= (@ (@ tptp.infini8530281810654367211te_nat S2) N3) S))))) (forall ((S2 tptp.set_nat) (N2 tptp.nat)) (=> (not (@ tptp.finite_finite_nat S2)) (@ (@ tptp.ord_less_eq_nat N2) (@ (@ tptp.infini8530281810654367211te_nat S2) N2)))) (forall ((S2 tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat S2)) (@ tptp.order_5726023648592871131at_nat (@ tptp.infini8530281810654367211te_nat S2)))) (forall ((S2 tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat S2)) (= (@ (@ tptp.image_nat_nat (@ tptp.infini8530281810654367211te_nat S2)) tptp.top_top_set_nat) S2))) (forall ((S2 tptp.set_nat) (N2 tptp.nat)) (=> (@ tptp.finite_finite_nat S2) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.finite_card_nat S2)) (@ (@ tptp.ord_less_eq_nat N2) (@ (@ tptp.infini8530281810654367211te_nat S2) N2))))) (forall ((S2 tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat S2)) (@ (@ (@ tptp.bij_betw_nat_nat (@ tptp.infini8530281810654367211te_nat S2)) tptp.top_top_set_nat) S2))) (forall ((P (-> tptp.nat Bool))) (=> (@ P tptp.zero_zero_nat) (= (@ tptp.ord_Least_nat P) tptp.zero_zero_nat))) (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat) (Q (-> tptp.nat Bool)) (M2 tptp.nat)) (=> (@ P N2) (=> (@ Q M2) (=> (not (@ P tptp.zero_zero_nat)) (=> (forall ((K3 tptp.nat)) (= (@ P (@ tptp.suc K3)) (@ Q K3))) (= (@ tptp.ord_Least_nat P) (@ tptp.suc (@ tptp.ord_Least_nat Q)))))))) (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P N2) (=> (not (@ P tptp.zero_zero_nat)) (= (@ tptp.ord_Least_nat P) (@ tptp.suc (@ tptp.ord_Least_nat (lambda ((M tptp.nat)) (@ P (@ tptp.suc M))))))))) (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (= (@ tptp.last_nat (@ (@ tptp.upt I) J)) (@ (@ tptp.minus_minus_nat J) tptp.one_one_nat)))) (forall ((A2 tptp.set_nat)) (let ((_let_1 (@ tptp.vimage_nat_nat tptp.suc))) (= (@ _let_1 (@ (@ tptp.insert_nat tptp.zero_zero_nat) A2)) (@ _let_1 A2)))) (forall ((F3 tptp.set_nat)) (= (@ tptp.finite_finite_nat (@ (@ tptp.vimage_nat_nat tptp.suc) F3)) (@ tptp.finite_finite_nat F3))) (forall ((N2 tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.vimage_nat_nat tptp.suc))) (= (@ _let_1 (@ (@ tptp.insert_nat (@ tptp.suc N2)) A2)) (@ (@ tptp.insert_nat N2) (@ _let_1 A2))))) (forall ((X tptp.nat)) (= (@ tptp.nat_set_decode (@ (@ tptp.divide_divide_nat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.vimage_nat_nat tptp.suc) (@ tptp.nat_set_decode X)))) (forall ((A2 tptp.set_nat)) (= (@ tptp.nat_set_encode (@ (@ tptp.vimage_nat_nat tptp.suc) A2)) (@ (@ tptp.divide_divide_nat (@ tptp.nat_set_encode A2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B2 tptp.nat)) (=> (@ P K) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B2))) (@ P (@ tptp.order_Greatest_nat P))))) (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B2 tptp.nat)) (=> (@ P K) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B2))) (@ (@ tptp.ord_less_eq_nat K) (@ tptp.order_Greatest_nat P))))) (forall ((P (-> tptp.nat Bool)) (B2 tptp.nat)) (=> (exists ((X_1 tptp.nat)) (@ P X_1)) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B2))) (@ P (@ tptp.order_Greatest_nat P))))) (forall ((N2 tptp.nat)) (@ tptp.bNF_We3818239936649020644el_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_nat X4) N2) (@ (@ tptp.ord_less_nat Y5) N2) (@ (@ tptp.ord_less_eq_nat X4) Y5))))))) (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 ((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 ((Y tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw Y) (@ (@ tptp.modulo_modulo_nat X) Y)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Y) (= (@ (@ tptp.bezw X) Y) (@ (@ tptp.product_Pair_int_int _let_2) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_1)) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X) Y)))))))))) (forall ((X tptp.nat) (Xa2 tptp.nat) (Y tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.bezw Xa2) (@ (@ tptp.modulo_modulo_nat X) Xa2)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X) Xa2) Y) (and (=> _let_3 (= Y (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_3) (= Y (@ (@ tptp.product_Pair_int_int _let_2) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_1)) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X) Xa2))))))))))))) (= tptp.bezw (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw Y5) (@ (@ tptp.modulo_modulo_nat X4) 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 X4) Y5)))))))))) (forall ((X tptp.nat) (Xa2 tptp.nat) (Y tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.bezw_rel) (@ (@ tptp.product_Pair_nat_nat X) Xa2)))) (let ((_let_2 (@ (@ tptp.bezw Xa2) (@ (@ tptp.modulo_modulo_nat X) Xa2)))) (let ((_let_3 (@ tptp.product_snd_int_int _let_2))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X) Xa2) Y) (=> _let_1 (not (=> (and (=> _let_4 (= Y (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_4) (= Y (@ (@ tptp.product_Pair_int_int _let_3) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_2)) (@ (@ tptp.times_times_int _let_3) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X) Xa2)))))))) (not _let_1)))))))))) (forall ((A tptp.nat) (B2 tptp.nat) (S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ tptp.ord_less_nat S) T) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.product_Pair_nat_nat A) S)) (@ (@ tptp.product_Pair_nat_nat B2) T))) tptp.fun_pair_less)))) (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.product_Pair_nat_nat X))) (= (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ _let_1 Y)) (@ _let_1 Z3))) tptp.fun_pair_less) (@ (@ tptp.ord_less_nat Y) Z3)))) (forall ((A tptp.nat) (B2 tptp.nat) (S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.product_Pair_nat_nat A) S)) (@ (@ tptp.product_Pair_nat_nat B2) T))) tptp.fun_pair_less))) (forall ((X tptp.nat) (Xa2 tptp.nat) (Y tptp.product_prod_nat_nat)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.nat_pr5047031295181774490ux_rel) (@ (@ tptp.product_Pair_nat_nat X) Xa2)))) (let ((_let_2 (@ tptp.suc X))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat Xa2) X))) (=> (= (@ (@ tptp.nat_prod_decode_aux X) Xa2) Y) (=> _let_1 (not (=> (and (=> _let_3 (= Y (@ (@ tptp.product_Pair_nat_nat Xa2) (@ (@ tptp.minus_minus_nat X) Xa2)))) (=> (not _let_3) (= Y (@ (@ tptp.nat_prod_decode_aux _let_2) (@ (@ tptp.minus_minus_nat Xa2) _let_2))))) (not _let_1))))))))) (forall ((A tptp.nat) (B2 tptp.nat) (S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ tptp.ord_less_eq_nat S) T) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.product_Pair_nat_nat A) S)) (@ (@ tptp.product_Pair_nat_nat B2) T))) tptp.fun_pair_leq)))) (forall ((A tptp.nat) (B2 tptp.nat) (S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.product_Pair_nat_nat A) S)) (@ (@ tptp.product_Pair_nat_nat B2) T))) tptp.fun_pair_leq))) (@ (@ (@ tptp.ordering_top_nat tptp.dvd_dvd_nat) (lambda ((M tptp.nat) (N tptp.nat)) (and (@ (@ tptp.dvd_dvd_nat M) N) (not (= M N))))) tptp.zero_zero_nat) (@ (@ (@ tptp.ordering_top_nat (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y5) X4))) (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.ord_less_nat Y5) X4))) tptp.zero_zero_nat) (= tptp.ord_le2932123472753598470d_enat (lambda ((M tptp.extended_enat) (__flatten_var_0 tptp.extended_enat)) (@ (@ (@ tptp.extended_case_enat_o (lambda ((N1 tptp.nat)) (@ (@ (@ tptp.extended_case_enat_o (lambda ((M1 tptp.nat)) (@ (@ tptp.ord_less_eq_nat M1) N1))) false) M))) true) __flatten_var_0))) (= tptp.ord_le72135733267957522d_enat (lambda ((M tptp.extended_enat) (N tptp.extended_enat)) (@ (@ (@ tptp.extended_case_enat_o (lambda ((M1 tptp.nat)) (@ (@ (@ tptp.extended_case_enat_o (@ tptp.ord_less_nat M1)) true) N))) false) M))) (forall ((K tptp.nat) (M2 tptp.nat)) (= (@ tptp.nat_prod_decode (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle K)) M2)) (@ (@ tptp.nat_prod_decode_aux K) M2))) _let_36 (forall ((A0 tptp.nat) (P (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.accp_nat tptp.nat_list_decode_rel))) (=> (@ _let_1 A0) (=> (=> (@ _let_1 tptp.zero_zero_nat) (@ P tptp.zero_zero_nat)) (=> (forall ((N3 tptp.nat)) (let ((_let_1 (@ tptp.suc N3))) (=> (@ (@ tptp.accp_nat tptp.nat_list_decode_rel) _let_1) (=> (forall ((X2 tptp.nat) (Y6 tptp.nat)) (=> (= (@ (@ tptp.product_Pair_nat_nat X2) Y6) (@ tptp.nat_prod_decode N3)) (@ P Y6))) (@ P _let_1))))) (@ P A0)))))) (forall ((X tptp.nat) (Y tptp.list_nat)) (=> (= (@ tptp.nat_list_decode X) Y) (=> (=> (= X tptp.zero_zero_nat) (not (= Y tptp.nil_nat))) (not (forall ((N3 tptp.nat)) (=> (= X (@ tptp.suc N3)) (not (= Y (@ (@ tptp.produc2761476792215241774st_nat (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.cons_nat X4) (@ tptp.nat_list_decode Y5)))) (@ tptp.nat_prod_decode N3)))))))))) (=> (@ (@ tptp.accp_nat tptp.nat_list_decode_rel) tptp.zero_zero_nat) _let_35) _let_35 (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ tptp.accp_nat tptp.nat_list_decode_rel) _let_1) (= (@ tptp.nat_list_decode _let_1) (@ (@ tptp.produc2761476792215241774st_nat (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.cons_nat X4) (@ tptp.nat_list_decode Y5)))) (@ tptp.nat_prod_decode N2)))))) (forall ((N2 tptp.nat)) (= (@ tptp.nat_list_decode (@ tptp.suc N2)) (@ (@ tptp.produc2761476792215241774st_nat (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.cons_nat X4) (@ tptp.nat_list_decode Y5)))) (@ tptp.nat_prod_decode N2)))) (forall ((X tptp.nat) (Y tptp.list_nat)) (let ((_let_1 (@ tptp.accp_nat tptp.nat_list_decode_rel))) (=> (= (@ tptp.nat_list_decode X) Y) (=> (@ _let_1 X) (=> (=> (= X tptp.zero_zero_nat) (=> (= Y tptp.nil_nat) (not (@ _let_1 tptp.zero_zero_nat)))) (not (forall ((N3 tptp.nat)) (let ((_let_1 (@ tptp.suc N3))) (=> (= X _let_1) (=> (= Y (@ (@ tptp.produc2761476792215241774st_nat (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.cons_nat X4) (@ tptp.nat_list_decode Y5)))) (@ tptp.nat_prod_decode N3))) (not (@ (@ tptp.accp_nat tptp.nat_list_decode_rel) _let_1)))))))))))) _let_33 (@ (@ tptp.inj_on_nat_char tptp.unique3096191561947761185of_nat) _let_32) (= (@ (@ tptp.image_char_nat tptp.comm_s629917340098488124ar_nat) tptp.top_top_set_char) _let_32) (@ (@ tptp.pcr_int _let_24) tptp.one_one_int) (@ (@ tptp.pcr_int _let_25) tptp.zero_zero_int) (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))))))))))) (forall ((X tptp.real)) (=> (@ (@ tptp.member_real X) tptp.field_5140801741446780682s_real) (not (forall ((M3 tptp.nat) (N3 tptp.nat)) (=> (not (= N3 tptp.zero_zero_nat)) (=> (= (@ tptp.abs_abs_real X) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real M3)) (@ tptp.semiri5074537144036343181t_real N3))) (not (@ (@ tptp.algebr934650988132801477me_nat M3) N3)))))))) (forall ((N2 tptp.nat)) (@ (@ tptp.algebr934650988132801477me_nat (@ tptp.suc N2)) N2)) (forall ((N2 tptp.nat)) (@ (@ tptp.algebr934650988132801477me_nat N2) (@ tptp.suc N2))) (forall ((N2 tptp.nat)) (@ (@ tptp.algebr934650988132801477me_nat (@ tptp.suc tptp.zero_zero_nat)) N2)) (forall ((N2 tptp.nat)) (@ (@ tptp.algebr934650988132801477me_nat N2) (@ tptp.suc tptp.zero_zero_nat))) (forall ((P (-> tptp.product_prod_nat_nat Bool))) (= (@ (@ tptp.eventu1038000079068216329at_nat P) (@ (@ tptp.prod_filter_nat_nat tptp.at_top_nat) tptp.at_top_nat)) (exists ((N5 tptp.nat)) (forall ((M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N5) M) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N5) N) (@ P (@ (@ tptp.product_Pair_nat_nat N) M))))))))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.algebr934650988132801477me_nat (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) N2))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.algebr934650988132801477me_nat N2) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))) (@ (@ _let_28 (@ tptp.produc27273713700761075at_nat (lambda ((X4 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 X4) V4)) (@ (@ tptp.plus_plus_nat Y5) U2)))) __flatten_var_0)))) tptp.minus_minus_int) (@ (@ _let_28 (@ tptp.produc27273713700761075at_nat (lambda ((X4 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 X4) U2)) (@ (@ tptp.plus_plus_nat Y5) V4)))) __flatten_var_0)))) tptp.plus_plus_int) (@ (@ (@ _let_20 (@ _let_19 (lambda ((Y4 Bool) (Z2 Bool)) (= Y4 Z2)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X4 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 X4) V4)) (@ (@ tptp.plus_plus_nat U2) Y5)))) __flatten_var_0)))) tptp.ord_less_int) (@ (@ (@ _let_20 (@ _let_19 (lambda ((Y4 Bool) (Z2 Bool)) (= Y4 Z2)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X4 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 X4) V4)) (@ (@ tptp.plus_plus_nat U2) Y5)))) __flatten_var_0)))) tptp.ord_less_eq_int) (@ (@ _let_28 (@ tptp.produc27273713700761075at_nat (lambda ((X4 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 X4))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U2)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U2))))))) __flatten_var_0)))) tptp.times_times_int) (@ (@ _let_27 (@ tptp.produc2626176000494625587at_nat (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y5) X4)))) tptp.uminus_uminus_int) (@ (@ (@ (@ tptp.bNF_re4555766996558763186at_nat tptp.pcr_int) (lambda ((Y4 tptp.nat) (Z2 tptp.nat)) (= Y4 Z2))) _let_26) tptp.nat2) (@ (@ (@ (@ tptp.bNF_re6830278522597306478at_int (lambda ((Y4 tptp.nat) (Z2 tptp.nat)) (= Y4 Z2))) tptp.pcr_int) (lambda ((N tptp.nat)) (@ (@ tptp.product_Pair_nat_nat N) tptp.zero_zero_nat))) tptp.semiri1314217659103216013at_int) (@ (@ _let_18 (@ tptp.produc27273713700761075at_nat (lambda ((X4 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 X4))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U2)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U2))))))) __flatten_var_0)))) (@ tptp.produc27273713700761075at_nat (lambda ((X4 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 X4))) (@ (@ 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)))) (forall ((X tptp.nat) (Y tptp.nat) (U tptp.nat) (V tptp.nat)) (= (@ (@ tptp.intrel (@ (@ tptp.product_Pair_nat_nat X) Y)) (@ (@ tptp.product_Pair_nat_nat U) V)) (= (@ (@ tptp.plus_plus_nat X) V) (@ (@ tptp.plus_plus_nat U) Y)))) (@ (@ (@ (@ tptp.bNF_re8246922863344978751at_nat tptp.intrel) (lambda ((Y4 tptp.nat) (Z2 tptp.nat)) (= Y4 Z2))) _let_26) _let_26) (@ (@ _let_17 (@ tptp.produc2626176000494625587at_nat (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y5) X4)))) (@ tptp.produc2626176000494625587at_nat (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y5) X4)))) (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (= (@ tptp.abs_Integ X) (@ tptp.abs_Integ Y)) (@ (@ tptp.intrel X) Y))) (@ (@ tptp.intrel _let_25) _let_25) (@ (@ tptp.intrel _let_24) _let_24) _let_23 (@ (@ (@ _let_22 (@ _let_21 (lambda ((Y4 Bool) (Z2 Bool)) (= Y4 Z2)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X4 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 X4) V4)) (@ (@ tptp.plus_plus_nat U2) Y5)))) __flatten_var_0)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X4 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 X4) V4)) (@ (@ tptp.plus_plus_nat U2) Y5)))) __flatten_var_0)))) (@ (@ (@ _let_22 (@ _let_21 (lambda ((Y4 Bool) (Z2 Bool)) (= Y4 Z2)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X4 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 X4) V4)) (@ (@ tptp.plus_plus_nat U2) Y5)))) __flatten_var_0)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X4 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 X4) V4)) (@ (@ tptp.plus_plus_nat U2) Y5)))) __flatten_var_0)))) (@ (@ (@ _let_20 (@ _let_19 (lambda ((Y4 Bool) (Z2 Bool)) (= Y4 Z2)))) tptp.intrel) (lambda ((Y4 tptp.int) (Z2 tptp.int)) (= Y4 Z2))) (@ (@ _let_18 (@ tptp.produc27273713700761075at_nat (lambda ((X4 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 X4) V4)) (@ (@ tptp.plus_plus_nat Y5) U2)))) __flatten_var_0)))) (@ tptp.produc27273713700761075at_nat (lambda ((X4 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 X4) V4)) (@ (@ tptp.plus_plus_nat Y5) U2)))) __flatten_var_0)))) (@ (@ _let_18 (@ tptp.produc27273713700761075at_nat (lambda ((X4 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 X4) U2)) (@ (@ tptp.plus_plus_nat Y5) V4)))) __flatten_var_0)))) (@ tptp.produc27273713700761075at_nat (lambda ((X4 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 X4) U2)) (@ (@ tptp.plus_plus_nat Y5) V4)))) __flatten_var_0)))) (@ tptp.bi_tot896582865486249351at_int tptp.pcr_int) (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) tptp.less_than) (@ (@ tptp.ord_less_nat X) Y))) (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N2 tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList2) Summary))) (=> (@ (@ tptp.vEBT_invar_vebt _let_1) N2) (= (@ (@ tptp.vEBT_VEBT_elim_dead _let_1) (@ tptp.extended_enat2 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) _let_1)))) (forall ((N2 tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat N2) (@ tptp.extended_enat2 tptp.zero_zero_nat)) N2)) (forall ((N2 tptp.extended_enat)) (let ((_let_1 (@ tptp.extended_enat2 tptp.zero_zero_nat))) (= (@ (@ tptp.minus_3235023915231533773d_enat _let_1) N2) _let_1))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.extended_enat2 M2)) (@ tptp.extended_enat2 N2)) (@ tptp.extended_enat2 (@ (@ tptp.plus_plus_nat M2) N2)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.extended_enat2 M2)) (@ tptp.extended_enat2 N2)) (@ (@ tptp.ord_less_nat M2) N2))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.extended_enat2 M2)) (@ tptp.extended_enat2 N2)) (@ (@ tptp.ord_less_eq_nat M2) N2))) (forall ((M2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat M2)) (@ tptp.extended_enat2 N2)) (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat M2)) N2))) (forall ((M2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat M2)) (@ tptp.extended_enat2 N2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat M2)) N2))) (forall ((M2 tptp.nat) (N2 tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.extended_enat2 (@ tptp.suc M2))) N2) (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.extended_enat2 M2)) N2))) (forall ((A2 tptp.set_Extended_enat) (N2 tptp.nat)) (=> (forall ((Y3 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat Y3) A2) (@ (@ tptp.ord_le2932123472753598470d_enat Y3) (@ tptp.extended_enat2 N2)))) (@ tptp.finite4001608067531595151d_enat A2))) (forall ((X tptp.extended_enat) (Y tptp.extended_enat) (N2 tptp.nat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.plus_p3455044024723400733d_enat X) Y)) (@ tptp.extended_enat2 N2)) (exists ((Y7 tptp.nat) (X9 tptp.nat)) (and (= X (@ tptp.extended_enat2 X9)) (= Y (@ tptp.extended_enat2 Y7)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X9) Y7)) N2))))) (forall ((X tptp.nat)) (= (= tptp.zero_z5237406670263579293d_enat (@ tptp.extended_enat2 X)) (= X tptp.zero_zero_nat))) (forall ((X tptp.nat)) (= (= (@ tptp.extended_enat2 X) tptp.zero_z5237406670263579293d_enat) (= X tptp.zero_zero_nat))) (= tptp.zero_z5237406670263579293d_enat (@ tptp.extended_enat2 tptp.zero_zero_nat)) (forall ((N2 tptp.extended_enat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat N2) (@ tptp.extended_enat2 M2)) (not (forall ((K3 tptp.nat)) (=> (= N2 (@ tptp.extended_enat2 K3)) (not (@ (@ tptp.ord_less_nat K3) M2))))))) (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N2 tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList2) Summary))) (=> (@ (@ tptp.vEBT_invar_vebt _let_1) N2) (= (@ (@ tptp.vEBT_VEBT_elim_dead _let_1) tptp.extend5688581933313929465d_enat) _let_1)))) (forall ((M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.extended_enat2 M2)) tptp.extend5688581933313929465d_enat))) (let ((_let_2 (= M2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.zero_z5237406670263579293d_enat)) (=> (not _let_2) (= _let_1 tptp.extend5688581933313929465d_enat)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_7803423173614009249d_enat tptp.extend5688581933313929465d_enat) (@ tptp.extended_enat2 N2)))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.zero_z5237406670263579293d_enat)) (=> (not _let_2) (= _let_1 tptp.extend5688581933313929465d_enat)))))) _let_16 _let_15 _let_14 _let_13 _let_12 (forall ((A2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (not (= A2 tptp.bot_bo7653980558646680370d_enat)) (= (@ tptp.extended_eSuc (@ tptp.lattic921264341876707157d_enat A2)) (@ tptp.lattic921264341876707157d_enat (@ (@ tptp.image_80655429650038917d_enat tptp.extended_eSuc) A2)))))) _let_11 (forall ((Y tptp.nat) (X tptp.extended_enat)) (= (= (@ tptp.extended_enat2 Y) (@ tptp.extended_eSuc X)) (exists ((N tptp.nat)) (and (= Y (@ tptp.suc N)) (= (@ tptp.extended_enat2 N) X))))) (forall ((X tptp.extended_enat) (Y tptp.nat)) (= (= (@ tptp.extended_eSuc X) (@ tptp.extended_enat2 Y)) (exists ((N tptp.nat)) (and (= Y (@ tptp.suc N)) (= X (@ tptp.extended_enat2 N)))))) (forall ((N2 tptp.nat)) (= (@ tptp.extended_eSuc (@ tptp.extended_enat2 N2)) (@ tptp.extended_enat2 (@ tptp.suc N2)))) (forall ((A2 tptp.set_Extended_enat)) (=> (not (= A2 tptp.bot_bo7653980558646680370d_enat)) (= (@ tptp.extended_eSuc (@ tptp.comple4398354569131411667d_enat A2)) (@ tptp.comple4398354569131411667d_enat (@ (@ tptp.image_80655429650038917d_enat tptp.extended_eSuc) A2))))) (forall ((N2 tptp.nat)) (@ (@ tptp.order_2888998067076097458on_nat (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.ord_less_nat X4) N2)))) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_nat X4) N2) (@ (@ tptp.ord_less_nat Y5) N2) (@ (@ tptp.ord_less_eq_nat X4) Y5))))))) (forall ((N2 tptp.nat)) (@ (@ tptp.order_2888998067076097458on_nat (@ tptp.field_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_nat X4) N2) (@ (@ tptp.ord_less_nat Y5) N2) (@ (@ tptp.ord_less_eq_nat X4) Y5))))))) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_nat X4) N2) (@ (@ tptp.ord_less_nat Y5) N2) (@ (@ tptp.ord_less_eq_nat X4) Y5))))))) (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ (@ tptp.if_int false) X) Y) Y)) (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ (@ tptp.if_int true) X) Y) X)) (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat false) X) Y) Y)) (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat true) X) Y) X)) (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ (@ tptp.if_real false) X) Y) Y)) (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ (@ tptp.if_real true) X) Y) X)) (forall ((X tptp.complex) (Y tptp.complex)) (= (@ (@ (@ tptp.if_complex false) X) Y) Y)) (forall ((X tptp.complex) (Y tptp.complex)) (= (@ (@ (@ tptp.if_complex true) X) Y) X)) (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (= (@ (@ (@ tptp.if_Extended_enat false) X) Y) Y)) (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (= (@ (@ (@ tptp.if_Extended_enat true) X) Y) X)) (forall ((X tptp.set_int) (Y tptp.set_int)) (= (@ (@ (@ tptp.if_set_int false) X) Y) Y)) (forall ((X tptp.set_int) (Y tptp.set_int)) (= (@ (@ (@ tptp.if_set_int true) X) Y) X)) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ (@ tptp.if_set_nat false) X) Y) Y)) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ (@ tptp.if_set_nat true) X) Y) X)) (forall ((X tptp.vEBT_VEBT) (Y tptp.vEBT_VEBT)) (= (@ (@ (@ tptp.if_VEBT_VEBT false) X) Y) Y)) (forall ((X tptp.vEBT_VEBT) (Y tptp.vEBT_VEBT)) (= (@ (@ (@ tptp.if_VEBT_VEBT true) X) Y) X)) (forall ((X tptp.list_int) (Y tptp.list_int)) (= (@ (@ (@ tptp.if_list_int false) X) Y) Y)) (forall ((X tptp.list_int) (Y tptp.list_int)) (= (@ (@ (@ tptp.if_list_int true) X) Y) X)) (forall ((X tptp.list_nat) (Y tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat false) X) Y) Y)) (forall ((X tptp.list_nat) (Y tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat true) X) Y) X)) (forall ((X (-> tptp.int tptp.int)) (Y (-> tptp.int tptp.int))) (= (@ (@ (@ tptp.if_int_int false) X) Y) Y)) (forall ((X (-> tptp.int tptp.int)) (Y (-> tptp.int tptp.int))) (= (@ (@ (@ tptp.if_int_int true) X) Y) X)) (forall ((X tptp.option_num) (Y tptp.option_num)) (= (@ (@ (@ tptp.if_option_num false) X) Y) Y)) (forall ((X tptp.option_num) (Y tptp.option_num)) (= (@ (@ (@ tptp.if_option_num true) X) Y) X)) (forall ((X tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int false) X) Y) Y)) (forall ((X tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int true) X) Y) X)) (forall ((P Bool)) (or (= P true) (= P false))) (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat false) X) Y) Y)) (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat true) X) Y) X)) _let_10 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 99.14/99.41 )
% 99.14/99.41 % SZS output end Proof for ITP234^1
% 99.14/99.41 % cvc5---1.0.5 exiting
% 99.14/99.42 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------